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6/01 cJCIRCantoDuopes-p. 1 5

 

ENVIRONMENTAL EFFECT S ON CRACK HEALING AND STATIC FATIGUE
BEHAVIOR OF GLASS AND POLYCRYSTALLINE CERAMICS

VOLUME I
By

Brett Allen Wilson

A DISSERTATION

Submitted to
Michigan State University
in Partial Fulfillment of the Requirements
for the Degree of

DOCTOR OF PHILOSOPHY

Department of Materials Science and Mechanics

1998

ABSTRACT
ENVIRONMENTAL EFFECTS ON CRACK HEALING AND STATIC FATIGUE
BEHAVIOR OF GLASS AND POLYCRYSTALLINE CERAMICS

By

Brett Allen Wilson

An Environmental Scanning Electron Microscope (ESEM) was used for in-situ studies
of static fatigue growth of Vickers indent cracks in polycrystalline alumina. Cracks
advanced via static fatigue along a tortuous path with grain bridging and crack
deflections on the order of a single grain diameter.

In-situ ESEM studies of healing of Vickers indent cracks in soda-lime silicate
glass found healing to occur at 8 % r.h. and at 400 °C. Increased levels of initial
humidity decreased the temperature at which healing initiated. The crack morphology
included slow crack regression from the crack tip towards the indent impression and
multiple crack pinch-off (above 550 °C). Debris in a crack hindered complete healing.

Conventional heating was used in healing of soda-lime silica glass where
Vickers crack lengths were measured via optical microscopy. Microscopy showed
crack tip blunting, pinch-off, and sub—surface spheroidization. The more complete
healing observed for cracks aged in 45 % r.h. than in 0 % r.h. was attributed to water

vapor entering the glass structure and decreasing the local glass transition temperature

and viscosity along the crack faces.

Crack healing experiments on polycrystalline alumina were performed using
both conventional and microwave heating. No effect of aging environment was found
for conventional healing of alumina. The relative crack healing ([ZCW-Zch/Zcmm)
behavior for 49 and 98 N indent cracks was nearly identical. Crack healing was
modeled by a diffusive transport model originally developed by Dutton and Stevens
showing significantly lower activation energies for conventional compared to
microwave heating. Microwave heating at 10 °C/minute had much greater healing

than at 75 °C/minute.

 

DEDICATION

I would like to dedicate this Dissertation to my family (my mom and Dad, brother and
sister-in-law, grandmas and grandpa, aunts and uncle). Without their love and support,

I would not have had the self-confidence to try a PhD or the fortitude to survive one.

iv

 

ACKNOWLEDGEMENTS

First and foremost I would like to acknowledge and thank Dr. Case for his instruction,
guidance, and support throughout my time working toward a PhD. I would like to
acknowledge the Michigan Research Excellence Funds for the financial support of the
ESEM project and the CMSC including Dr. Drzal, Mike Rich, Steve Rozeveld, and
Richard Schalek for their assistance and for the use of the ESEM and the Surface
Analysis Lab. I would also like to acknowledge Dr. Clarence Suelter, Dr. Merle
Heidemann, Dr. Joyce Parker and the Division of Science Education for their
facilitation of my teaching growth and for awarding me a NASA Research Teaching
Assistantship which partially funded my teaching work for a year and enabled my re-
design of the MSM 250 Lab. 1 would like to thank several people for their help John
Helmuth (for the composite plate), Kurt Niemeyer (for cutting tabs), Kiyong Lee (for
microwaving specimens), Jong Gi Lee (for microwaving a specimen), and Ben Simkin
(for running the Camscan). I would also like to acknowledge Dr. Martin Crimp for
making the field emission SEM available for my use. I would like to acknowledge
Pat Sneary, Ben Simkins, Mark Wilenski, and my father for useful discussions about
my work. I definitely must recognize and thank Julian Ambriz, Pat Sneary, and

Wendy Reffeor for their friendship, support, and help in keeping me going.

TABLE OF CONTENTS

LIST OF TABLES .............................................. xi
LIST OF FIGURES ........................................... xviii
1. INTRODUCTION AND RESEARCH OBJECTIVES .................... l
1.1 Introduction .............................................. 1
1.2 Research Objectives ......................................... 2
2. LITERATURE REVIEW ....................................... 4
2.1 Static Fatigue Behavior of Ceramics ............................. 4
2.1.1 Atomic Bonding in Ceramics ................................ 4
2.1.2 Room Temperature Tensile Behavior .......................... 5
2.1.3 Static Fatigue Investigations ................................. 8
2.1.3.1 Standard Static Fatigue Testing ........................... 9
2.1.3.2 Findings of Standard Static Fatigue Testing .................. 10

2.2 Crack Healing in Ceramics ................................... 11
2.2.1 Role of Environment ..................................... 12
2.2.2 Crack Morphology Changes during Thermal Healing of Cracks ....... 16
2.2.3 Crack Healing Investigations Via Strength Recovery Testing ......... 18
2.2.4 Crack Healing Investigations of Vickers Indent Cracks Lengths ....... 25
2.3 Capabilities of an Environmental Scanning Electron Microscope ......... 27
2.4 Focus of the Current Investigation .............................. 28
3. EXPERIMENTAL PROCEDURE ................................ 32
3.1 Materials ............................................... 32
3.11 Soda-Lime Silica Glass ................................... 32
3.12 Coors Alumina ......................................... 33
3.1.2 Microwave Sintered Alumina ............................... 33
3.2 Basic Sample Preparation .................................... 34
3.2.1 Sample Cutting ......................................... 34
3.2.1.1 Low Speed Diamond Saw .............................. 34
3.2.1.1.1 Cutting ......................................... 34
3.2.1.1.2 Cleaning and Grinding .............................. 35
3.2.1.2 High Speed Diamond Saw .............................. 36
3.2.1.2.1 Mounting a Sample on the High Speed Saw ............... 38

3.2.1.2.2 Locating the sample in the cutting saw’s y-z space ........... 39

vi

3.2.1.2.3 Setting the saw table’s x-limits ........................ 41

3.2.1.2.4 Setting the computer to control cutting ................... 42
3.3.2 Polishing ............................................. 44
3.3.2.1 Polishing Compound .................................. 44
3.2.2.2 Polishing Cloth and Oil ................................ 46
3.2.2.3 Charging the Polishing Cloth ............................ 47
3.2.2.4 Polishing Samples .................................... 47
3.2.2.4.1 Polishing of Ceramic Materials ........................ 48
3.2.2.4.2 Polishing of Alumina Specimens ....................... 48
3.2.3 Indentation ............................................ 49
3.3 Materials Characterization .................................... 50
3.3.1 Density Determination .................................... 50
3.3.1.1 Materials Preparation for Density Measurements ............... 51
3.3.1.2 Density Measurements ................................. 51
3.3.2 Microstructure ......................................... 52
3.4 Indentation Measurement Testing ............................... 53
3.4.1 Multiple Experimenter Measurements ......................... 53
3.4.2 Optical and Environmental Scanning Electron Microscope Measurements
...................................................... 54
3.5 Static Fatigue: ESEM Crack Growth Investigations .................. 54
3.5.1 Ceramic Tensile Specimen Preparation
...................................................... 55
3.5.1.1 Preparation of Rectangular Specimens of Glass and Coors Alumina . 55
3.5.1.2 Preparation of Specimen Tabs ............................ 57
3.5.1.3 Tab Attachment onto Rectangular Ceramic Specimens ........... 57
3.5.2 Vickers Indentation Cracks on Tensile Specimens ................. 58
3.5.3 ESEM Testing ......................................... 59
3.5.3.1 Control of Relative Humidity in the ESEM .................. 60
3.5.3.2 Placement of Specimens in the Tensile Stage ................. 62
3.5.3.3 Static Fatigue Testing .................................. 62
3.6 Crack Healing ............................................ 63
3.6.1 In-Situ Healing Investigations using an ESEM ................... 64
3.6.1.1 Soda-Lime Silica Glass Specimens ........................ 64
3.6.1.2 Setting Relative Humidity before Crack Healing Testing ......... 64
3.6.1.3 In-situ ESEM Testing .................................. 65
3.6.1.3.1 Healing at Temperatures up to 600 °C (Experiments A and B) . . . 67
3.6.1.3.2 Healing as a Function of Temperature (Experiment C) ........ 67
3.6.1.3.3 Healing as a function of Time at 430 °C (Experiment D) ...... 67
3.6.1.3.4 Healing as a function of Relative Humidity (Experiments E-H) . . 7O
3.6.1.3.5 Healing with New Hot Stage Heater (Experiments I-M) ....... 70
3.6.1.4 Temperature Measurement of New Hot Stage Heater ............ 72
3.6.2 Conventional Experiments ................................ 73
3.6.2.1 Conventional Healing Procedure .......................... 73
3.6.2.1.1 Temperature Measurement during Conventional Healing ....... 74
3.6.2.1.2 Conventional Furnaces Used for Healing .................. 74
3.6.2.1.3 Specimen Placement into the Tube Furnaces ............... 75

vii

3.6.2.2 Healing in Soda-Lime Silica Glass ........................ 76

3.6.2.2.1 Soda-Lime Silica Healing Specimen Preparation ............ 76
3.6.2.2.2 Relief of Specimen Residual Stress ...................... 83
3.6.2.2.3 Strength Testing and Sub-Surface Healing (Experiments 1 and 2) 84
3.6.2.2.4 Effects of Stress Relief Cycle (Experiment 3) .............. 86
3.6.2.2.5 Effect of Aging Environment, Time and Temperature (Experiments
4—7) ................................................. 86
3.6.2.2.6 Residual Stress Relief Testing ......................... 86
3.6.2.3 Healing in Alumina ................................... 88
3.6.2.3.1 Alumina Specimen Preparation ........................ 88
3.6.2.3.2 Effects of Aging Humidity and Temperature in Two Aluminas
(Experiment 1) ......................................... 94
3.6.2.3.3 Effects of Aging Humidity, Time, and Temperature in Coors
Alumina (Experiment 2) .................................. 94
3.6.3 Microwave Healing ...................................... 96
3.6.3.1 Specimen Preparation .................................. 96
3.6.3.2 Microwave and Conventional Heating ...................... 96
4. RESULTS AND DISCUSSION ................................. 100
4.1 Materials Characterization ................................... 100
4.1.1 Density Measurements ................................... 100
4.1.2 Microstructure ........................................ 100
4.2 Indentation Measurement Testing .............................. 102
4.2.1 Multiple Experimenter Measurements ........................ 102
4.2.1.1 Crack Length Measurement Variation with Experimenter ......... 102
4.2.2 Optical and ESEM Measurements ........................... 106
4.3 Static Fatigue: ESEM Crack Growth Investigations ................. 107
4.3.1 Soda-Lime Silica Glass .................................. 107
4.3.1.1 Failures from Mounting Specimens in the Tensile Stage ......... 110
4.3.1.2 Failures from Automatic ESEM Stage Control Procedures ....... 110
4.3.1.3 Testing of a Mounted Sample ........................... 111
4.3.2 Coors Alumina ........................................ 112
4.3.2.1 Stainless Steel Tabs .................................. 112
4.3.2.2 Specimen B ....................................... 115
4.3.2.3 Specimen C ....................................... 120
4.3.2.4 Specimen F ........................................ 122
4.3.2.5 Specimen H ....................................... 122
4.3.2.6 Specimen J ........................................ 126
4.3.2.7 Relative Crack Length and Applied Tensile Load ............. 129
4.4 Crack Healing ........................................... 133
4.4.1 In-Situ ESEM Investigations of Healing in Soda-Lime Silica Glass . . . 133
4.4.1.1 In-Situ ESEM Testing ................................ 135
4.4.1.1.] Healing at Temperatures up to 600 °C (Experiments A and B)
................................................... 135
4.4.1.1.2 Healing as a Function of Temperature (Experiment C)
................................................... 145

viii

4.4.1.1.3 Healing as a function of Time at 430 °C (Experiment D) ..... 146
4.4.1.1.4 Healing as a function of Relative Humidity (Experiments E-H)

................................................... 149
4.4.1.1.4.1 Effect of Humidity on the Temperature where Healing Initiates
................................................... 149
4.4.1.1.4.2 Effect of Humidity on Healing with Isothermal Holds at 430 °C
................................................... 152
4.4.1.1.5 Healing with New Hot Stage Heater (Experiments I-M) ...... 159
4.4.1.2 Further Temperature Measurement of New Hot Stage Heater ..... 160
4.4.1.3 Heat Transfer Calculation of Temperature Differences of New Heater
.................................................... 161
4.4.2.1 Soda-Lime Silica Glass ............................... 168
4.4.2.1.1 Crack Healing and Strength Testing (Experiment 1) ......... 168
4.4.2.1.2 Surface and Sub—Surface Crack Healing (Experiment 2) ...... 176
4.4.2.1.3 Effects of Stress Relief Cycle (Experiment 3) ............. 178
4.4.2.1.4 Effects of Aging Environment and Healing Temperature (Experiment
4) ................................................. 184
4.4.2.1.4.1 Aging Environments of O and 45 % r.h. ................ 189
4.4.2.1.4.2 Review of Literature on the Presence of Water in Glass ..... 190
4.4.2.1.4.3 Aging Environment of 100 % r.h. .................... 195
4.4.2.1.5 Effects of Aging Environment and Time at 525 °C (Experiment 5)
................................................... 196
4.4.2.1.6 Effects of Aging Environment and Time at 575 °C (Experiment 6)
................................................... 198
4.4.2.1.7 Effects of Aging Environment and Time at 550 °C (Experiment 7)
................................................... 198
4.4.2.1.8 Residual Stress Relief Cycle Testing .................... 204
4.4.2.1.8.1 Bulk Viscous Flow of Glass During Heating Cycle ........ 206
4.4.2182 Residual Stress Relieved During Heating Cycle ........... 206
4.4.2.1.8.4 Analysis of a 4 Month Age after Heat Treatment Cycle ..... 212
4.4.2.185 Analysis of Stress Relief Cycles A-E of Experiments 3-7 . . . . 213
4.4.2.2 Polycrystalline Alumina ............................... 213
4.4.2.2.] Effects of Aging Humidity and Temperature in Two Aluminas
(Experiment 1) ........................................ 216
4.4.2.2.1.1 Healing in Coors Alumina (Experiment 1) .............. 220
4.4.2.2.1.2 Healing in Microwave Sintered Alumina (Experiment 1) . . . . 223
4.4.2.2.2 Effects of Aging Humidity, Time, and Temperature in Coors Alumina
(Experiment 2) ........................................ 225
4.4.2.2.2.1 Post-Annealing Crack Length Measurements (Experiment 2) . . 225
4.4.2.2.2.2 Healing Time and Aging Environment (Experiment 2) ...... 227
4.4.2.2.2.3 Aging Environment Effect on Healing (Experiment 2) ...... 232
4.4.2.2.2.4 Time and Temperature Effect on Healing (Experiment 2) . . . . 235
4.4.2.2.2 Crack Morphology Changes in Coors Alumina ............ 238
4.4.3 Microwave Healing in Polycrystalline Alumina ................. 245
4.4.3.1 Healing in Conventional and Microwave Annealing ............ 245
4.4.3.2 Differences in Microwave and Conventional Healing ........... 246

   

4.4.3.3 Healing Differences Between Slow and Fast Microwave Heating . . 250
4.4.3.4 Literature Review of Diffusion during Microwave Heating ....... 253
4.4.4 Diffusional Healing Model

..................................................... 257
4.4.4.1 Review of Healing in LiF by Raj et a1. [55] ............... 258
4.4.4.2 Review of Healing in LiF by Wang et a1. [30] .............. 260
4.4.4.3 Re—Examination Raj et a1. [55] and Wang et a1. [30] .......... 262
4.4.4.2 Conventional Healing in Coors and Microwave Sintered Alumina . . 265
4.4.4.3 Conventional and Microwave Healing in Coors Alumina ........ 267
5. SUMMARY AND CONCLUSIONS ............................. 276
5.1 Static Fatigue Crack Growth ................................. 276
5.2 Crack Healing ........................................... 277
5.2.1 In-Situ ESEM Observation of Soda-Lime Silica Glass ............. 277
5.2.2 Conventional Healing ................................... 278
5.2.2.1 Soda-Lime Silica Glass ............................... 278
5.3.2.2 Conventional Healing in Polycrystalline Alumina
.................................................... 280
5.3.3 Microwave Healing ..................................... 280
5.3.4 Crack Healing Model ................................... 281
6. REFERENCES ............................................ 283
APPENDD( A: SATURATION BEHAVIOR IN CY CLIC
AND STATIC FATIGUE IN CERAMICS .......................... 291
A.l Literature Review ........................................ 291
A.l.l Fatigue in Ceramics .................................... 291
A.l.2 Cyclic Fatigue ........................................ 291
A.l.3 Thermal Fatigue ...................................... 295
A2 Results and Discussion .................................... 297
A3 Conclusions ............................................ 299
A.4 References for Appendix A ................................. 302
APPENDD( B: CRACK LENGTH DATA FROM CONVENTIONAL
HEALING EXPERIMENTS, MICROWAVE HEALING EXPERIMENTS,
AND STRESS RELIEF CYCLE TESTING ......................... 307

 

LIST OF TABLES

Table 1 Humidity conditions during five different heating cycles of Holden and
Frechette [35] and resulting effects on crack closure and tested strength in soda-lime
silica glass. ................................................. 13

Table 2 Example of the program data entered in order to cut a single 114.3 X 114.3
X 1.0 mm (4.5 X 4.5 X 0.04 inch) Coors alumina plate into 1 cm2 (0.16 in2)
samples using the computer control of the high speed cutting saw. (Note that <>
indicates keyboard keys that were hit or data that was entered). ............ 43

Table 3 ESEM hot stage heating schedule for the experiment investigating healing up
to 600 °C (Experiment A). ...................................... 68

Table 4 ESEM hot stage heating schedule for the experiment investigating healing up
to 610 °C (Experiment B). ...................................... 68

Table 5 ESEM hot stage heating schedule for experiment investigating healing as a
function of temperature (Experiment C). ............................ 69

Table 6 ESEM hot stage heating schedule for initial experiment investigating healing
as a function of time at a fixed temperature of 430 °C (Experiment D). ....... 69

Table 7 ESEM hot stage heating schedule for experiments investigating healing as a
function of time at a fixed temperature of 430 °C (Experiments E-H). ........ 71

Table 8 Thermal annealing temperature and times for conventional healing in soda-
lime silica glass (Experiments 1 to 7). Specimen, indent, aging and annealing
condition are detailed in Table 9. ................................. 77

Table 9 Details of specimen, indent, aging, and annealing conditions for conventional
healing in soda-lime silica glass (Experiments 1-7) ...................... 78

Table 10 Indentation conditions referred to in Table 9 for soda-lime silica specimens
used in conventional healing (Experiments 1-7). ...................... 79

Table 11 Stress relief cycles referred to in Table 9 for soda-lime silica specimens used
in conventional healing (Experiments 1-7). ........................... 79

xi

Table 12 Thermal annealing temperature and times for conventional healing in alumina
(Experiments 1 and 2). Specimen, indent, aging and annealing condition are detailed
in Table 13. ................................................ 90

Table 13 Details of specimen, indent, aging, and annealing conditions for conventional
healing in alumina (Experiments 1-2). .............................. 91

Table 14 Indentation conditions referred to in Table 13 for alumina specimens used in
conventional healing (Experiments 1-2). ............................ 92

Table 15 Thermal annealing cycle for alumina specimens used in conventional healing
(Experiments 1-2) ............................................. 92

Table 16 Thermal annealing temperature and times for microwave and conventional
healing in alumina (Experiments 1-3). Specimen, indent, aging and annealing
condition are detailed in Table 17. ................................ 97

Table 17 Details of specimen, indent, aging, and annealing conditions for microwave
and conventional healing in alumina (Experiments 1-3) ................... 98

Table 18 Indentation conditions referred to in Table 16 for alumina specimens used in
conventional healing (Experiments 1-2). ............................ 98

Table 19 Density measurements for soda-lime silica, Coors alumina, and microwave
alumina specimens using an Archimedes’ method. .................... 101

Table 20 Average and standard deviation of indent crack lengths in soda-lime silica
glass measured by six different researchers using an optical microscope to determine
the level of operator error typically present in Vickers indentation measurements.

........................................................ 104

Table 21 Average and standard deviation of indent crack lengths in Coors alumina
measured by six different researchers using an optical microscope to determine the
level of operator error typically present in Vickers indentation measurements. . 104

Table 22 Average and standard deviation of indent crack lengths in microwave
Sintered alumina measured by six different researchers using an optical microscope
to determine the level of operator error typically present in Vickers
measurements. ............................................. 105

Table 23 Average and standard deviation of indent crack lengths in silicon nitride

measured by six different researchers using an optical microscope to determine the
level of operator error typically present in Vickers indentation measurements. . 105

xii

Table 24 Summary of ESEM static fatigue testing of Coors alumina tensile specimens.
(S.S. indicates stainless steel and C.R.S.S. indicates cold rolled stainless steel).

Table 25 ESEM static fatigue testing of the 49 N Vickers indent in Coors alumina
tensile Specimen B (Table 24) which was made with composite tabs affixed with
epoxy. ................................................... 1 16

Table 26 ESEM static fatigue testing of the 49 N Vickers indent in Coors alumina
tensile Specimen C (Table 24) which was made with composite tabs affixed with
epoxy. (References to the left or right half cracks were with respect to the
orientation of the crack in the ESEM micrograph). .................... 116

Table 27 ESEM static fatigue testing of the 98 N Vickers indent in Coors alumina
tensile Specimen F (Table 24) which was made with non-cold rolled stainless steel
tabs affixed with high temperature cement. (References to the left or right half
cracks were with respect to the orientation of the crack in the ESEM
micrograph). .............................................. 1 17

Table 28 ESEM static fatigue testing of the 98 N Vickers indent in Coors alumina
tensile Specimen H (Table 24) which was made with cold rolled stainless steel tabs
affixed with high temperature cement. (References to the left or right half cracks
were with respect to the orientation of the crack in the ESEM micrograph). . . 118

Table 29 ESEM static fatigue testing of the 98 N Vickers indent in Coors alumina
tensile Specimen I (Table 24) which was made with composite tabs affixed with
high temperature cement. (References to the left or right half cracks were with
respect to the orientation of the crack in the ESEM micrograph). .......... 119

Table 30 Relative half indent crack lengths after heating to 370, 400 and 430 °C for
soda-lime silica glass samples with initial relative humidities of 8, 16, 32, and 64%
(Experiments E-H). .......................................... 151

Table 31 Fitting parameters, V1, V2, and V3 and correlation coefficients for the least
squares best fit of relative crack length as a function of time to Equation 13 (Figures
66-69) for initial relative humidities of 8, 16, 32, and 64% (Experiments E-H). 158

Table 32 Thermocouple temperature readings for three different testing conditions at
different ESEM new hot stage heater temperatures. .................... 163

Table 33 Property values for different layers of the sample and ESEM hot stage
assembly for the total heat transfer resistance of Equation 18 (material properties
from [77], dimensions from Figure 72). ............................ 166

Table 34 Property values for free surface convection at the ESEM hot stage surface to

determine the convective heat transfer coefficient, hair (material properties from
[76], dimensions from Figure 72). ................................ 167

Table 35 Change in crack lengths {20mm - 20m} for 6 cracks on each of ten soda-
lime silica glass specimens annealed in the large tube furnace for 30 minutes at 600
°C and for 6 cracks on each of two glass specimens held at laboratory temperature.

........................................................ 169

Table 36 Change in crack lengths {2cmm - 20M} for groups of specimens from Table
35 ....................................................... 170

Table 37 Modulus of Rupture (stress at failure) for three-point bend testing of
specimens of glass annealed in the large tube furnace for 30 minutes at 600 °C and
of two glass specimens held at laboratory temperature. ................. 170

Table 38 Change in crack lengths {20mm - 2cm} for heavy and faint portions of
healed indent cracks for glass specimens annealed in the large tube furnace for 30
minutes at 550 °C. (Sample 1 fracture upon indentation with a 98 kg load). . . 177

Table 39 Healed crack length change (29mm - 20M) for glass specimens prepared with
a stress relief cycle of 30 minutes at 550 °C, indented and aged in air for 24 hours,
and annealed for 15 minutes in the small tube furnace (Experiment 3). ...... 181

Table 40 Healed crack length change (2cinitial - Zone“) for glass specimens prepared with
a stress relief cycle of 30 minutes at 550 °C, indented and aged in air for 24 hours,
and annealed in the small tube furnace (Experiment 3). ................. 181

Table 41 Healed crack length change (2cmw - 2cm) for glass specimens prepared with
a stress relief cycle of 60 minutes at 600 °C, indented and aged in air for 24 hours,
and annealed in the small tube furnace (Experiment 3). ................. 182

Table 42 Healed crack length change (2cm,l - 2cm) for glass specimens prepared
without a stress relief cycle, indented and aged in air for 24 hours, and annealed in
the small tube furnace (Experiment 3). ........................... 182

Table 43 Healed crack length change (20mm - 2cm) for glass specimens prepared with
a stress relief cycle of 180 minutes at 587 °C (8 °C/ minute ramp rate), aged for 24
hours, and annealed for 60 minutes in the small tube furnace (Experiment
4). ...................................................... 186

Table 44 Healed crack length change (2cinitial - Zone“) for glass specimens prepared with
a stress relief cycle of 180 minutes at 587 °C (10 °C/ minute ramp rate), aged for 24
hours, and annealed at 525 °C in the small tube furnace (Experiment 5). ..... 197

xiv

Table 45 Healed crack length change (2cm,l - 2cm) for glass specimens prepared with
a stress relief cycle of 180 minutes at 587 °C (10 °C/ minute ramp rate), aged for 24
hours, and annealed at 575 °C in the small tube furnace (Experiment 6). ..... 199

Table 46 Healed crack length change (2cinitial - Zone“) for glass specimens prepared with
a stress relief cycle of 180 minutes at 587 °C (5 °C/ minute ramp rate), aged for 24
hours, and annealed at 550 °C in the large tube furnace (Experiment 7). ..... 200

Table 47 Holding and maximum specimen temperature for glass specimens prepared
with a stress relief cycle of 180 minutes at 587 °C (5 °C/ minute ramp rate), aged for
24 hours, and annealed at 550 °C in the large tube furnace (Experiment 7). . . . 202

Table 48 Pre-heat-treatment (2CR) and post-heat-treaunent (2CA) mean and standard
deviation of 22 indent crack lengths in glass specimens along with calculated
residual stress relieved during small tube furnace heating cycles at different
temperatures and times. ....................................... 205

Table 49 Calculated t* values for glass specimens using Equation 24 with data from
Table 48. Hypothesis decisions for comparison of individual glass heat treatment
cycle specimen means with the overall pre- and post— heat-treatment group means
using on = 0.01, n = 172, and t (1-/2; n) = 2.609. ..................... 211

Table 50 Mean and standard deviation for pre-heat-treatment (2CR) and post-heat-
treatment (2CA) crack lengths in glass specimens. The specimens were heat treated
and then aged for either 4 months or 24 hours before post-heat—treatment
indentation ................................................. 214

Table 51 Calculated t* values for glass specimens aged for either 24 hours or 4
months using Equation 24 and Table 50 data. Hypothesis decisions for comparison
of individual heat treatment cycle means with the overall pre-heat-treatment and
post-heat-treatment group means from Table 48 using or = 0.01, n = 172, and t (l-/2;
n) = 2.609. ................................................ 214

Table 52 Mean and standard deviation for post-Stress-Relief-Cycle (2CA) crack lengths
in glass specimens with Stress Relief Cycles A-E which were tested in Experiments
3-7. .................................................... 215

Table 53 Mean and standard deviation of the healed crack length change (20mm -
2cm“) after 60 minutes at healing temperature for Coors alumina specimens with
indents aged for a single 24 hour period in an environment of 0, 45, or 100 % r.h.
and indents aged for 24 hours in 45 % r.h. before a second 24 hour age in an
environment of 0, 45, or 100 % r.h.. Temperature was measured via an R-Type
thermocouple placed in the furnace next to the specimens. ............... 218

XV

Table 54 Mean and standard deviation of the healed crack length change (20,,“-
2c“) after 60 minutes at healing temperature for microwave Sintered alumina with
indents aged for a single 24 hour period in an environment of 0, 45, or 100 % r. h.
and indents aged for 24 hours in 45 % r.h. before a second 24 hour age in an
environment of 0, 45, or 100 % r.h.. Temperature was measured via an R-Type
thermocouple placed in the furnace next to the specimens. ............... 219

Table 55 Mean and standard deviation of the healed crack length change (2cm -
2cm.) for Coors alumina specimens aged for 24 hours in air, a desiccator, or a water
chamber before annealing in the large tube furnace (Experiment 2). Temperature
was measured via an R-Type thermocouple placed next to the samples in the
furnace. .................................................. 226

Table 56 Mean and standard deviation of the healed crack length change (29mm -
2cm) for Coors alumina specimens aged for 24 hours in 45 % r.h. before a 60
minute anneal by microwave heating. (Maximum temperature was within 2 °C of set
temperature). .............................................. 247

Table 57 Mean and standard deviation of the healed crack length change (2cm -
2c“) for Coors alumina specimens aged for 24 hours in 45 % r.h. before annealing
for 60 minutes by conventional heating. Temperature overshoot above the set
temperature from a 10 °C/minute ramp rate resulted in higher holding and maximum
temperatures. .............................................. 247

Table B.1 Crack lengths (pm) from conventional healing of soda-lime silica glass
(Conventional Healing of Glass Experiment 1, Section 4.4.2.1.1). .......... 308

Table B.2 Crack lengths (pm) from conventional healing of soda-lime silica glass
(Conventional Healing of Glass Experiment 2, Section 4.4.2.1.2). .......... 311

Table B.3 Crack lengths (pm) from conventional healing of soda-lime silica glass
(Conventional Healing of Glass Experiment 3, Section 4.4.2.1.3). .......... 312

Table B.4 Crack lengths (pm) from conventional healing in soda-lime silica glass
(Conventional Healing of Glass Experiment 4, Section 4.4.2.1.4). .......... 322

Table B.5 Crack lengths (pm) from conventional healing in soda-lime silica glass
(Conventional Healing of Glass Experiment 5, Section 4.4.2.1.5). .......... 324

Table B.6 Crack lengths (pm) from conventional healing in soda-lime silica glass
(Conventional Healing of Glass Experiment 6, Section 4.4.2.1.6). .......... 326

Table B.7 Crack lengths (pm) from conventional healing in soda-lime silica glass
(Conventional Healing of Glass Experiment 7, Section 4.4.2.1.7). .......... 327

xvi

 

 

 

 

Table B.8 Crack lengths (pm) from residual stress relief testing in soda-lime silica
glass (Residual Stress Relief Cycle Testing, Section 4.4.2.1.8). ........... 329

Table B.9 Crack lengths (pm) from conventional healing of alumina at a nominal
temperature of 1005 °C (Conventional Healing of Alumina Experiment 1, Section
4.4.2.2.1). (N.A. indicates Not Applicable and NM. indicates Not Measured) . 334

Table B.10 Crack lengths (pm) from conventional healing of alumina at a nominal
temperature of 1237 °C (Conventional Healing of Alumina Experiment 1, Section
4.4.2.2.1). (N.A. indicates Not Applicable and NM. indicates Not Measured) . 336

Table B.ll Crack lengths (pm) from conventional healing of alumina at a nominal
temperature of 1469 °C (Conventional Healing of Alumina Experiment 1, Section
4.4.2.2.1). (N.A. indicates Not Applicable and NM. indicates Not Measured) . 338

Table B.12 Crack lengths (pm) from conventional healing in Coors alumina
(Conventional Healing of Alumina Experiment 2, Section 4.4.2.2.2). ........ 340

Table B.13 Crack lengths (pm) from conventional and microwave healing in Coors
alumina (Microwave Healing of Alumina, Section 4.4.3) ................. 345

xvii

LIST OF FIGURES

Figure 1 Schematic of low speed cutting saw showing the cutting arm, the diamond
wheel and the specimen location. ................................. 37

Figure 2 Schematic of the high speed cutting saw showing the specimen plate, glass
and steel mounting plates, and the magnetic chuck. ..................... 37

Figure 3 Schematic of computer controlled cutting on the high speed saw showing
rough and fine incremental movements of the saw blade, continuous movements of
the sample, and locations of the first two outs, for a sample cut using the data values
shown in Table 2. ........................................... 45

Figure 4 Schematic of samples mounted on polishing plate for automatic polishing.
(From four to twenty one specimens were polished at one time). ........... 45

Figure 5 Schematic of tabbed tensile specimens used in static fatigue testing (note
indent size is exaggerated) ....................................... 56

Figure 6 Plot of ESEM chamber pressure versus temperature showing curves of
constant relative humidity [after 53]. ............................... 61

Figure 7 Schematic of soda-lime silica glass specimens used in ESEM investigations
of crack healing. ............................................. 66

Figure 8 Schematic of the ESEM hot stage showing the t0p of the heater assembly, the
silicon carbide spacer, the crucible and the indented glass specimen. ......... 66

Figure 9 Schematic of the second ESEM hot stage showing the top of the heater
assembly, the crucible and the glass specimen with a K-Type thermocouple
attached .................................................... 7 1

Figure 10 Schematic of indent placement in the rectangular glass specimens used in

conventional healing Experiments 1 and 2 (note that the while the indent locations
are to scale the indent sizes are exaggerated). ......................... 80

xviii

Figure 11 Schematic of indent placement in the square glass specimens used in
conventional healing Experiments 3 - 7 (note that the while the indent locations are
to scale the indent sizes are exaggerated). ........................... 80

Figure 12 Schematic of specimen location on the tube dee for conventional healing in
glass Experiments 1 and 2. ...................................... 81

Figure 13 Schematic of specimen location on the boat for conventional healing in
glass Experiments 3 - 7 ......................................... 81

Figure 14 Schematic of specimen location in the boat for conventional healing in glass
Experiment 7 and conventional healing in alumina Experiment 2. ........... 82

Figure 15 Schematic of the rectangular glass specimens used for the residual stress
measurement experiments showing the ground upper right hand comer (note that
while the indent locations are to scale the indent sizes are exaggerated). ...... 89

Figure 16 Schematic of rectangular glass specimen location in boat for residual stress
measurement experiments. ...................................... 89

Figure 17 Schematic of Coors alumina specimens used in conventional healing
Experiment 1 (note that the while the indent locations are to scale the indent sizes
are exaggerated). ............................................. 93

Figure 18 Schematic of Coors alumina specimens used in conventional healing
Experiment 1 (note that the while the indent locations are to scale the indent sizes
are exaggerated). ............................................. 93

Figure 19 Schematic of Coors alumina specimens used in conventional healing
Experiment 2 (note that the while the indent locations are to scale the indent sizes
are exaggerated). ............................................. 95

Figure 20 Schematic of Coors alumina and microwave Sintered alumina specimen
location in ceramic boat for conventional healing Experiment 1. ............ 95

Figure 21 Schematic of Coors alumina specimens used in microwave and conventional
healing experiments (note that the while the indent locations are to scale the indent
sizes are exaggerated). ......................................... 99

Figure 22 Schematic of Coors alumina specimen location in ceramic boat for
microwave healing experiments. .................................. 99

Figure 23 ESEM micrograph of thermally etched Coors alumina used in grain size
determination showing a small grain size of 2.1 :l: 0.2 pm. ............... 103

xix

Figure 24 ESEM micrograph of thermally etched microwave sintered alumina used in
grain size determination showing a grain size of 20.6 i- 3.6 pm. ........... 103

Figure 25 Measured crack length, 2c1, for glass, Coors alumina, microwave sintered
alumina, and silicon nitride. Each data point was an average of five measurements
by an individual researcher and horizontal lines were group averages of six
researchers ................................................. 108

Figure 26 ESEM micrograph of indentation cracks in a soda-lime silica glass specimen
used in multiple researcher measurement experiments. .................. 108

Figure 27 ESEM micrograph of indentation cracks in a Coors alumina specimen used
in multiple researcher measurement experiments. ..................... 109

Figure 28 ESEM micrograph of indentation cracks in a microwave sintered alumina
specimen used in multiple researcher measurement experiments. ........... 109

Figure 29 ESEM micrograph of the left indent crack of Coors alumina Specimen C
(T ables 24 and 26) showing the growth after 25, 50 and 85 minutes at 92 MPa and
32% r.h. and 25 minutes at 92 MPa and 42% r.h.. .................... 123

Figure 30 ESEM micrograph of the left indent crack of Coors alumina Specimen C
(Tables 24 and 26) showing the growth after 25 and 50 minutes at 100 MPa and
32% r.h ................................................... 123

Figure 31 ESEM micrograph of the left indent crack of Coors alumina Specimen C
(T ables 24 and 26) showing the growth after 25 minutes at 32% r.h. and 105, 111,
and 116 MPa. .............................................. 124

Figure 32 ESEM micrograph of the left indent crack of Coors alumina Specimen H
(Tables 24 and 28) showing the initial left indent crack with an applied stress of 16
MPa from the self tightening grips. ............................... 127

Figure 33 ESEM micrograph of the left indent crack of Coors alumina Specimen H
(T ables 24 and 28) showing the initial left indent crack after increasing the applied
stress to 40 MPa. ........................................... 127

Figure 34 ESEM micrograph of the left indent crack of Coors alumina Specimen H
(T ables 24 and 28) showing the growth after 25 minutes at 40 MPa and 32% r.h..
........................................................ 128

Figure 35 ESEM micrograph of the left indent crack of Coors alumina Specimen H
(Tables 24 and 28) showing the growth after 50 minutes at 40 MPa and 32% r.h.
along with the bridged grain which is located at the end of the 25 minute crack
tip. ..................................................... 128

XX

 

Figure 36 ESEM micrograph of the left indent crack of Coors alumina Specimen J
(Tables 24 and 29) showing the growth after time at 32% r.h. and 60 to 90 MPa
along with the growth which occurred as the load was increased to 80 and 90
MPa. .................................................... 130

Figure 37 ESEM micrograph of the left indent crack of Coors alumina Specimen J
(Tables 24 and 29) revealing two instances of grain bridging from the 80 and 90
MPa static fatigue cycles. ...................................... 130

Figure 38 A higher magnification ESEM micrograph of Figure 37 revealing the
instances of grain bridging from the 90 MPa static fatigue cycle of the left indent
crack of Coors alumina Specimen J (Tables 24 and 29). ................ 131

Figure 39 Plot of static fatigue crack growth for the left indent crack as a function of
constant applied load for Coors alumina Specimen C (Tables 24 and 26) with a 49 N
indent and composite tabs. ..................................... 131

Figure 40 Plot of static fatigue crack growth as a function of constant applied load for
Coors alumina Specimen F (Tables 24 and 27) with a 98 N indent and stainless steel
tabs. .................................................... 132

Figure 41 Plot of static fatigue crack growth as a function of constant applied load for
Coors alumina Specimen H (Tables 24 and 28) with a 98 N indent and cold rolled
stainless steel tabs. .......................................... 132

Figure 42 Plot of static fatigue crack growth as a function of constant applied load for
Coors alumina Specimen J (Tables 24 and 29) with a 98 N indent and composite
tabs. .................................................... 134

Figure 43 Plot of crack growth for static fatigue cycles at constant applied load and
relative humidity for Coors alumina Specimens C, F, H, J (Tables 24 to 29). . . 134

Figure 44 ESEM micrograph of indent cracks of the soda-lime silica glass specimen at
300 °C with an initial relative humidity of 10% (Experiment A). .......... 137

Figure 45 ESEM micrograph of the soda-lime silica glass specimen upon reaching 600
°C exhibiting crack healing. The same indentation crack system prior to healing, is
shown in Figure 44 (Experiment A). .............................. 137

Figure 46 ESEM micrograph of the indent crack (labeled in Figure 45) five minutes
after reaching 600 °C exhibiting a faint outline along the healed portion of the crack

(Experiment A). ............................................ 138

Figure 47 A higher magnification ESEM micrograph of the crack tip of the crack
shown in Figure 46 demonstrating that the faint outline was a closed portion of the
crack with a small depression at the specimen surface (Experiment A). ...... 138

xxi

Figure 48 ESEM micrograph of indent cracks of the soda-lime silica glass specimen
after 2 hours and 20 minutes at 600 °C illustrating the disappearance of the faint
portion of the crack depicted in Figures 46 and 47 (Experiment A). ........ 139

Figure 49 ESEM micrograph of the indent crack (labeled [3 in Figure 48) after an hour
and 22 minutes at 600 °C showing multiple areas of crack pinch-off (arrows)
(Experiment A). ............................................ 139

Figure 50 ESEM micrograph of the indent crack (labeled in Figure 48 and shown in
Figure 49) after two hours and 3 minutes at 600 °C demonstrating further
morphology changes of the pinched-off regions of the crack (Experiment A). . . 141

Figure 51 ESEM micrograph of soda-lime silica glass specimen an hour and 42
minutes after reaching 550 °C exhibiting crack pinch-off (Experiment B). . . . . 141

Figure 52 A higher magnification ESEM micrograph of the same crack shown in
Figure 51 revealing the crack and crack tip shape in the pinched off regions

(Experiment B). ............................................ 142

Figure 53 ESEM micrograph of glass specimen after 28 minutes at 550 0C displaying
pinch-off and showing the location of the debris with an arrow (Experiment B).

Figure 54 Schematic of the half indent crack (Figure 53) depicting the multiple crack
pinch-off, and the location of the debris (Experiment B). ................ 143

Figure 55 ESEM micrograph of the indent crack (Figure 53) at 575 °C showing a
close up of area near the debris (arrow) and crack healing approaching the debris

(Experiment B). ............................................ 143

Figure 56 ESEM micrograph of the indent (Figure 53) at 600 °C showing a close up
of area near debris (arrow) and crack healing passing the debris without complete
healing (Experiment B). ....................................... 144

Figure 57 ESEM micrograph of the indent (Figure 53) at 610 °C showing healing from
the bottom part of the crack approaching the debris (arrow) without complete healing
in the area of the debris (Experiment B). ........................... 144

Figure 58 Schematic of half of a Vickers indentation crack (a) before heat-treatment,
(b) after partial healing showing the typical regression of the crack from the tip
toward the indent impression together with multiple pinch-off, and (c) containing
debris (Experiment B) after partially healing that includes crack regression toward
the debris from the end of the crack near the indent impression. ........... 147

Figure 59 ESEM micrograph of a 105 m long indention crack in a soda-lime silica
glass specimen at 27 °C and 8% initial relative humidity (Experiment C). . . . . 147

xxii

Figure 60 Relative change in crack length (C(T)/C(R.T.)) as a function of temperature
' for a soda-lime silica glass specimen observed in-situ in an ESEM (Experiment
C) ....................................................... 148

Figure 61 ESEM micrograph of the same indention crack shown in Figure 59 after 8
minutes at 430 °C displaying a decrease in the crack length to 46 um (Experiment
C) ....................................................... 148

Figure 62 ESEM micrograph of the indention cracks in a soda-lime silica glass
specimen at 21 °C and 14% initial relative humidity (Experiment D). ....... 150

Figure 63 ESEM micrograph of the same indention crack shown in Figure 62 after
110 minutes at 430 0C (Experiment D). ............................ 150

Figure 64 Relative change in length (C(T)/C(R.T.)) of crack as a function of time at
430 °C for a glass specimen initially at 14 % r.h. observed in-situ in an ESEM
(Experiment D). ............................................ 151

Figure 65 Relative change in crack length (C(T)/C(R.T.)) as a function of temperature
for soda-lime silica glass specimens with different initial humidity levels observed
in-situ in an ESEM (Experiments E-H). ............................ 154

Figure 66 Plot of the general form of Equation 13 with the constants V1 and V2 shown
and constant V3 representing the initial rate of change of the relative crack length.
........................................................ 154

Figure 67 Relative change in crack length (C(T)/C(400°C)) for all 4 indent half cracks
as a function of time at 430 °C for a glass specimen initially held at 8% r.h.
(Experiment B). Data points indicate ESEM measurements. Curve is a least squares
best fit to Equation 13. ....................................... 155

Figure 68 Relative change in crack length (C(T)/C(400°C)) for all 4 indent half cracks
as a function of time at 430 °C for a glass specimen initially held at 16% r.h.
(Experiment F). Data points indicate ESEM measurements. Curve is a least squares
best fit to Equation 13. ....................................... 155

Figure 69 Relative change in crack length (C(T)/C(400°C)) for all 4 indent half cracks
as a function of time at 430 °C for a glass specimen initially held at 32% r.h.
(Experiment G). Data points indicate ESEM measurements. Curve is a least squares
best fit to Equation 13. ....................................... 156

Figure 70 Relative change in crack length (C(T)/C(400°C)) for all 4 indent half cracks
as a function of time at 430 °C for a glass specimen initially held at 64% r.h.
(Experiment H). Data points indicate ESEM measurements. Curve is a least squares
best fit to Equation 13. ....................................... 156

xxiii

Figure 71 Plot of the fitting parameters, V,, V3, and Vl-V2 as a function of the initial
relative humidity for the least squares best fit of the relative crack length as a
function of time to Equation 13 (Figures 67-70) (Experiments E-H). ........ 158

Figure 72 Schematic of the ESEM heating stage for heat transfer determination of the
surface temperature ........................................... 164

Figure 73 Optical micrograph of indent B of glass specimen eleven aged in room
temperature air. Other specimens were annealed at 600 °C (Table 33). The
horizontal crack in the unannealed specimen was approximately 190 pm in length.

........................................................ 172

Figure 74 Higher magnification optical micrograph of the indent in unannealed glass
shown in Figure 73. Unannealed crack widths were less than approximately 1.5

Figure 75 Optical micrograph of indent B of glass specimen eight annealed at 600 °C
for 30 minutes in the large tube furnace. The horizontal crack in the annealed
specimen was approximately 156 pm in length. ...................... 173

Figure 76 Higher magnification optical micrograph of the indent shown in Figure 75.
The crack width increased during annealing to greater than approximately 6 pm. 173

Figure 77 Higher magnification optical micrograph of one of the indent cracks shown
in Figure 76. The crack tip appears blunted after annealing. ............. 174

Figure 78 Optical micrograph of indent B of glass specimen four which was annealed
at 600 °C for 30 minutes in the large tube furnace. The horizontal crack in the
annealed specimen was approximately 184 pm in length. ................ 174

Figure 79 Higher magnification optical micrograph of indent shown in Figure 78. The
crack width increased during annealing to greater than approximately 6 pm. . 175

Figure 80 Higher magnification optical micrograph of one of the indent cracks shown
in Figure 79. Extensive pinch-off at the end of the crack has occurred after
annealing .................................................. 175

Figure 81 Conventional SEM micrograph of sub-surface portion of indent in glass

specimen six, annealed at 550 °C for 30 minutes in the large tube furnace. The
specimen was fractured through the healed indent using Kirchner’s method [64].

Figure 82 Higher magnification conventional SEM micrograph of the specimen in
Figure 81 showing quasi-circular voids from region near the arrow of Figure 81.

xxiv

Figure 83 Higher magnification conventional SEM micrograph of the specimen in
Figure 82 showing quasi-circular voids. ............................ 180

Figure 84 Mean crack length change (2cm,l - 2cm) versus healing time for glass
specimens prepared with a stress relief cycle of 30 minutes at 550 °C, aged in air for
24 hours, and annealed in the small tube furnace (error bars indicate standard
deviations of six cracks) (Experiment 3). 2cm“ values were approximately
221 um. .................................................. 185

Figure 85 Mean crack length change (20mm - 2cm) versus healing time for glass
specimens prepared with a stress relief cycle of 60 minutes at 600 °C, aged in air for
24 hours, and annealed in the small tube furnace (error bars indicate standard
deviations of six cracks) (Experiment 3). 2cinitm values were approximately
219 um. .................................................. 185

Figure 86 Mean crack length change (2cm,l - 2cm) versus healing time for glass
specimens prepared without a prior stress relief cycle, aged in air for 24 hours, and
annealed in the small tube furnace (error bars indicate standard deviations of six
cracks) (Experiment 3). 20m values were approximately 202 pm. ........ 186

Figure 87 Mean crack length change (2cm,l - 2cm) versus healing temperature for
glass specimens prepared with a stress relief cycle of 180 minutes at 587 °C (8 °C/
minute ramp rate), aged for 24 hours in 0 or 45 % r.h., and annealed for 60 minutes
in the small tube furnace (error bars indicate standard deviations of six cracks)
(Experiment 4). ............................................. 187

Figure 88 Mean crack length change (20mm - 2cm) versus healing temperature for
glass specimens prepared with a 180 minute stress relief cycle at 587 °C (8 °C/min.
ramp rate), aged for 24 hours in 100 % r.h., and annealed for 60 minutes in the
small tube furnace (error bars indicate standard deviations of six cracks) (Experiment
4). ...................................................... 188

Figure 89 Circular chart recorder measurements of temperature and humidity during
indent crack aging in air. Measurements were made during a day in the time period
when healing experiments were performed. ......................... 188

Figure 90 Two-dimensional schematic of the structure of glass with water present both
as hydroxyl groups and as molecular water [after 78, 80]. ............... 192

Figure 91 Mean crack length change (2cm - 2cm) versus healing time for glass
specimens prepared with a stress relief cycle of 180 minutes at 587 °C (10 °C/
minute ramp rate), aged for 24 hours, and annealed at 525 °C in the small tube
furnace (error bars indicate standard deviations of six cracks) (Experiment 5). . 197

XXV

Figure 92 Mean crack length change (2cinitial - 2cm) versus healing time for glass
specimens prepared with a stress relief cycle of 180 minutes at 587 °C (10 °C/
minute ramp rate), aged for 24 hours, and annealed at 575 °C in the small tube
furnace (error bars indicate standard deviations of six cracks) (Experiment 6). . 199

Figure 93 Mean crack length change (2cm,l - 2cm“) versus healing time for glass
specimens prepared with a stress relief cycle of 180 minutes at 587 °C (5 °C/ minute
ramp rate), aged for 24 hours, and annealed at 550 °C in the large tube furnace
(error bars indicate standard deviations of six cracks) (Experiment 7). ....... 200

Figure 94 Mean crack length change (2cinitial - 2cm”) versus healing time for glass
specimens prepared with a stress relief cycle of 180 minutes at 587 °C (5 °C/ minute
ramp rate), aged for 24 hours, and annealed at 550 °C in the large tube furnace
(error bars indicate standard deviations of six cracks) (Experiment 7). ....... 202

Figure 95 Temperature profile of two different thermal annealing ramp rates for glass
specimens annealed for 60 minutes in the large tube furnace (Experiment 7). . . 203

Figure 96 Pre- and post-heat-treatment mean of 22 indent crack lengths of glass
specimens heat treated in different cycles as indicated in Table 48 (data points
indicate means, vertical bars indicate standard deviations from mean, and horizontal
lines indicates means for all seven cycles together). ................... 208

Figure 97 Plot of the Coors and microwave alumina samples’ temperature as a
function of time for a ramp rate of 10 °C per minute up to the hold temperature of
1469 °C (Experiment 1). ...................................... 217

Figure 98 Plot of the Coors and microwave alumina samples’ temperature as a
function of time for a ramp rate of 10 °C per minute up to 1175 °C followed by a
ramp rate of 2.5 °C per minute up to the hold temperature of 1469 °C (Experiment
1). ...................................................... 217

Figure 99 Mean crack length change (20initial - 2cm) versus healing temperature for
Coors alumina specimens annealed for 60 minutes in the large tube furnace (error
bars indicate standard deviations of six cracks). Before annealing, indent cracks
underwent a single age of 24 hours in 0, 45, or 100 % r.h. or a double age with an
initial 24 hour age in 45 % r.h. followed by a 24 hour age in O, 45, or 100 % r.h.

(Experiment 1). ............................................. 221

Figure 100 Mean crack length change (2cm,l - 2cm) versus healing temperature for
Coors alumina specimens annealed for 60 minutes in the large tube furnace (error
bars indicate standard deviations of six cracks). Before annealing, indent cracks
underwent a single age of 24 hours in 0 % r.h. or a double age with an initial 24
hour age in air followed by a 24 hour age in 0 % r.h. (Experiment 1). ...... 222

xxvi

Figure 101 Mean crack length change (2cm - 2cm“) versus healing temperature for
Coors alumina specimens with a single age of 24 hours in 0, 45, or 100 % r.h.
before annealing for 60 minutes in the large tube furnace (error bars indicate
standard deviations of six cracks) (Experiment 1). ..................... 222

Figure 102 Mean crack length change (2cm - 2cm) versus temperature for
microwave sintered alumina specimens annealed for 60 minutes in the large tube
furnace (error bars indicate standard deviations of six cracks). Before annealing,
indent cracks underwent a single 24 hours age in 0, 45, or 100 % r.h. or a double
age with an initial 24 hour age in air followed by a 24 hour age in 0, 45, or 100 %
r.h. (Experiment 1). .......................................... 224

Figure 103 Schematic of Vickers indents made in Coors alumina and microwave
sintered alumina. In the Coors alumina specimens, one major crack extends from
each of the four indent impression comers. In microwave sintered alumina, chipping
occurs and multiple cracks extend from the indent impression comers. ...... 228

Figure 104 Schematic of the minimum continuous crack length, 2CMC , as measured
for conventionally healed Coors alumina specimens in Experiment 2. ....... 228

Figure 105 Mean crack length change (2cm - 2cm) versus healing time for Coors
alumina specimens aged for 24 hours in air, a desiccator, or a water chamber before
annealing for up to 120 minutes at 1005 °C in the large tube furnace (error bars
indicate standard deviations of six cracks) (Experiment 2). ............... 229

Figure 106 Mean crack length change (2cm,l - 2cm) versus healing time for Coors
alumina specimens aged for 24 hours in air, a desiccator, or a water chamber before
annealing for up to 1410 minutes at 1005 °C in the large tube furnace (error bars
indicate standard deviations of six cracks) (Experiment 2). ............... 229

Figure 107 Mean crack length change (2cm,l - 2cm.) versus healing time for Coors
alumina specimens aged for 24 hours in air, a desiccator, or a water chamber before
annealing for up to 120 minutes at 1121 °C in the large tube furnace (error bars
indicate standard deviations of six cracks) (Experiment 2). ............... 230

Figure 108 Mean crack length change (2cm - 20“) versus healing time for Coors
alumina specimens aged for 24 hours in air, a desiccator, or a water chamber before
annealing for up to 120 minutes at 1469 °C in the large tube furnace (error bars
indicate standard deviations of six cracks) (Experiment 2). ............... 230

Figure 109 Mean crack length change (29m - 2cm.) versus healing temperature for
Coors alumina specimens aged for 24 hours in a desiccator before annealing for 60,
90, or 120 minutes in the large tube furnace (error bars indicate standard deviations
of six cracks) (Experiment 2). ................................... 231

xxvii

Figure 110 Mean crack length change (20min - 2cm) versus healing temperature for
Coors alumina specimens aged for 24 hours in air, a desiccator, or a water chamber
before annealing for 60 minutes in the large tube furnace (error bars indicate
standard deviations of six cracks) (Experiment 2). ..................... 233

Figure 111 Mean crack length change (20mm - 2cm) versus healing time for Coors
alumina specimens annealed for up to 120 minutes in the large tube furnace (error
bars indicate standard deviations of 3 specimens and 18 cracks) (Experiment 2). 236

Figure 112 Mean crack length change (20mm - 2cm) versus healing time for Coors
alumina specimens annealed for up to 1410 minutes in the large tube furnace (error
bars indicate standard deviations of 3 specimens and 18 cracks) (Experiment 2). The
best fit line is for annealing at 1005 °C for times of 90 to 1410 minutes.

Figure 113 Mean crack length change (20mm - 2cm) versus healing temperature for
Coors alumina specimens annealed for 60 or 120 minutes in the large mbe furnace
(error bars indicate standard deviations of 3 specimens and 18 cracks) (Experiment
2). ...................................................... 237

Figure 114 Conventional Field Emission SEM micrograph of an indent crack in the
Coors alumina specimen annealed at 1353 °C for 120 minutes in a large tube
furnace. The first healed region, the crack tip and the location of pores on and B
(reference points for Figures 115, 116, and 117). ..................... 239

Figure 115 Conventional Field Emission SEM micrograph of the crack in Figure 114
(Coors alumina annealed at 1353 °C for 120 minutes in the large tube furnace). The
healed region located at a greater distance from the indent impression than the crack
tip and pores 0t and B (for reference). ............................. 239

Figure 116 Conventional Field Emission SEM micrograph of the healed portion of the
crack in Figure 115 (Coors alumina annealed at 1353 °C for 120 minutes in the large
tube furnace). Open voids of less than 2 pm in length and pore or (for
reference). ................................................ 240

Figure 117 Conventional Field Emission SEM micrograph of the healed crack (Figure
114) (Coors alumina annealed at 1353 °C for 120 minutes in the large tube furnace).
The surface trace of the healed crack resembles the thermally etched grain
boundaries of the Coors alumina. Pore B is included for reference. ........ 240

Figure 118 Conventional Field Emission SEM micrograph of an indent crack in the
Coors alumina specimen annealed at 1469 °C for 120 minutes in the large tube
furnace. The first healed region, the crack tip. Grain on serves as a reference point
for Figures 119, 120, and 121. .................................. 241

xxviii

Figure 119 Conventional Field Emission SEM micrograph of the crack in Figure 118
(Coors alumina annealed at 1469 °C for 120 minutes in the large tube furnace). The
healed region after the crack tip, a crack void. Grain or for reference ........ 241

Figure 120 Conventional Field Emission SEM micrograph of the healed portion of the
crack (Figure 119) (Coors alumina annealed at 1469 °C for 120 minutes in the large
tube furnace). The circular crack void of less than 0.3 pm in diameter. Grain on is
included for reference. ........................................ 242

Figure 121 Conventional Field Emission SEM micrograph of the healed crack (Figure
118) (Coors alumina annealed at 1469 °C for 120 minutes in the large tube furnace).
The circular crack void, an elliptical crack void. ...................... 242

Figure 122 Conventional Field Emission SEM micrograph of the healed portion of the
crack (Figure 121) (Coors alumina annealed at 1469 °C for 120 minutes in the large
tube furnace). The elliptical crack void has pinched off into an elliptical crack void
approximately 1.3 pm in length and a nearly circular crack void of 0.3 pm in length.

........................................................ 243

Figure 123 Conventional Field Emission SEM micrograph of the healed crack (Figure
121) (Coors alumina annealed at 1469 °C for 120 minutes in the large tube furnace).
The elliptical crack void with a maximum crack opening displacement (COD) of
approximately 0.2 pm. ........................................ 243

Figure 124 Mean crack length change (33me - 2cm.) versus holding temperature for
49 N Vickers indent cracks in Coors alumina which were aged for 24 hours in 45 %
r.h. before annealing for 60 minutes with conventional or microwave heating at slow
or fast rates (10 or 75 °C/min.) (error bars indicate standard deviations of six cracks).

........................................................ 248

Figure 125 Mean crack length change (2cm,l - 2cm) versus holding temperature for
98 N Vickers indent cracks in Coors alumina which were aged for 24 hours in 45 %
r.h. before annealing for 60 minutes with conventional or microwave heating at slow
or fast rates (10 or 75 °C/min.) (error bars indicate standard deviations of six cracks).

........................................................ 248

Figure 126 Relative change in crack length ({2cmm - 2chwll20m) versus holding
temperature for 49 and 98 N Vickers indent cracks in Coors alumina which were
aged for 24 hours in 45 % r.h. before annealing for 60 minutes with conventional or
microwave heating at slow or fast rates (10 or 75 °C/minute) (error bars indicate
standard deviations of six cracks). ................................ 249

xxix

Figure 127 Relative change in crack length ({Zcmma - 20M}/2cinm) versus holding

- healing temperature for 49 and 98 N Vickers indent cracks in Coors alumina which
were aged for 24 hours in 45 % r.h. before annealing for 60 minutes with
conventional or microwave heating at slow or fast rates (10 or 75 °C/minute) (error
bars indicate standard deviations of six cracks). Microwave heating temperatures
were increased 125 °C to simulate an adjustment for possible errors in
measurement. .............................................. 251

Figure 128 Schematic of cracks used by Raj et a1. [55] to study crack healing in LiF
single crystal samples. ........................................ 259

Figure 129 Plot used by Raj et al. to determine the activation energy for healing in
single crystal LiF [55] ......................................... 259

Figure 130 Plot to determine the activation energy for healing using model of Stevens
and Dutton [56] for data of laser induced cracks in LiF by Wang et al. [30]. . . 263

Figure 131 Determination of the activation energy using model by Stevens and Dutton
[56] for healing of data of Raj et a1. [55] for racks in LiF. ............... 263

Figure 132 Healing for cracks in alumina heated conventionally at a slow rate of 10
°C/ minute (data from Conventional Healing in Alumina Experiment 1, Section
4.4.2.2.1). The lines represent a least-squares fit of the data to the model by Stevens
and Dutton [56]. (Error bars indicate standard deviations of six cracks). ..... 268

Figure 133 Healing for cracks heated conventionally at a slow rate of 10 °C/min. (CS)
or heated via microwaves at a slow (MS) or fast (MF) rate of 75 °C/min. (data from
Section 4.4.3). The lines represent a least-squares fit of the data to the model by
Stevens and Dutton [56]. (Error bars indicate standard deviations of six cracks).

Figure 134 Healing of 49 N cracks heated conventionally at a slow rate of 10 °C/min.
(CS) or heated via microwaves at a slow (MS) or fast (MF) rate of 75 °C/min. (data
from Section 4.4.3). The lines represent a least-squares fit of the data to the model
by Stevens and Dutton [56]. (Error bars indicate standard deviations of six
cracks). .................................................. 269

Figure 135 Healing of 98 N indent cracks heated conventionally at a slow rate of 10
°C/min. (CS) or via microwaves at a slow (MS) or fast (MF) rate of 75 °C/min. (data
from Section 4.4.3). The lines represent a least-squares fit of the data to the model
by Stevens and Dutton [56]. (Error bars indicate standard deviations of six cracks).

........................................................ 269

XXX

 

Figure 136 Healing for 49 and 98 N indent cracks heated conventionally at a slow rate
of 10 °C/min. (CS) (data from Section 4.4.3). The lines represent a least-squares fit
of the data to the model by Stevens and Dutton [56]. (Error bars indicate standard
deviations of six cracks). ...................................... 270

Figure 137 Healing for 49 and 98 N indent cracks heated via microwaves at a slow
(MS) rate of 10 °C/min. (data from Section 4.4.3). The lines represent a least-
squares fit of the data to the model by Stevens and Dutton [56]. (Error bars indicate
standard deviations of six cracks). ................................ 270

Figure 138 Healing for 49 and 98 N indent cracks heated conventionally at a slow rate
of 10 °C/min. (CS) or heated via microwaves at a slow (MS) or fast (MF) rate of 75
°C/min. (data from Section 4.4.3). The lines represent a least-squares fit of the data
to the model by Stevens and Dutton [56]. Equal slopes were forced for data with
identical thermal histories. (Error bars indicate standard deviations of six cracks).

........................................................ 272

Figure 139 Healing for 49 and 98 N indent cracks heated conventionally at a slow rate
of 10 °C/ minute (CS) or heated via microwaves at a slow (MS) or fast (MF) rate of
75 °C/ minute (data from Section 4.4.3). The lines represent a least-squares fit of
the data to the model by Stevens and Dutton [56]. Equal slopes were forced for data
with identical thermal histories. The fast and slow microwave data has been forced
to be equal by subtracting 255 and 555 °C, respectively, from the measured
microwave healing temperatures (Error bars indicate standard deviations of six
cracks). .................................................. 273

Figure A.1 Hysteresis loops of 3Y-TZP. Note the change (S,>S2>S3) and the shifts of
loops due to strain accumulation (from [A.28]). ...................... 296

Figure A.2 Cumulative plastic strain as a function of cycles for 3Y-I'ZP in cyclic
mechanical fatigue (from [A.28]). Solid curves are a regression analysis using
Equation A.2. .............................................. 296

Figure A.3 Regression analysis using Equation A.2 (solid curves) for the low cycle
mechanical fatigue of Mg-PSZ [A.34, A.28]. ........................ 298

Figure A.4 Regression analysis using Equation A.2 for the mechanical fatigue of
polycrystalline alumina at R=10 at maximum stress of -268 MPa for a specimen
ultrasonically cleaned after every 5,000 cycles [A.42, A.l8]. ............. 298

Figure A.5 Crack growth rate as a function of stress intensity, K“m (from
[A.IOD. .................................................. 301

Figure A.6 Regression analysis (solid curve) using Equation A.2 for the mechanical
fatigue of Mg—PSZ [A.34, A.lO] .................................. 301

xxxi

1. INTRODUCTION AND RESEARCH OBJECTIVES

1.1 Introduction

Ceramic materials are used in many different areas including electronics, dentistry,
automotive engine components, industrial tooling, and biological prostheses.
Mechanical, electrical, and magnetic properties are important for these applications.
The presence of cracks in a ceramic part will change the mechanical, electrical and
magnetic properties of the material.

Static fatigue (which is also termed stress rupture or environmentally-assisted
slow crack growth) of ceramics and ceramic composites involves crack pr0pagation at
stresses lower than the stress required for instantaneous fracture. A ceramic material
subjected to a static (constant) load thus can exhibit a decreasing mechanical strength
as function of time. Strength degradation is typically linked to the stress corrosion of
pre-existing flaws in the material, where stress corrosion occurs via the interaction of
the ambient environment and highly strained atomic bonds at the crack tip. Water,
even in concentrations of parts per million (ppm) as in the ambient environment, can
lead to very significant stress corrosion and static fatigue in ceramics.

For a number of important application areas for ceramic composites, static
fatigue can be an important concern. For example, ceramic engine components are

stressed in high temperature environments that can include water vapor, since water is

2

produced during the combustion of hydrocarbon fuels.
Crack healing could be used as the last step in ceramic manufacturing to
reduce or eliminate cracks in the final part. Crack healing in ceramics could also

potentially be used to repair ceramic parts which had been damaged in service.

1.2 Research Objectives
The main objective of this research is to investigate the effects of time, temperature
and humidity on crack healing and static fatigue crack growth behavior in ceramics.

Static fatigue crack growth was investigated in-situ using a tensile stage in the
ESEM. The growth of Vickers indentation cracks over time at different levels of load
and humidity was observed.

Crack healing behavior of glass was observed in-situ using a hot stage for the
Environmental Scanning Electron Microscope (ESEM). Additional healing studies for
glass were performed in conventional furnaces at temperatures below that for bulk
viscous flow in the glass to further investigate and attempt to model the effects of
time, temperature and humidity without having sample damage or bulk dimension
changes which would be undesirable for industrial healing processes. Healing of
polycrystalline alumina in conventional furnaces was studied at temperatures of less
than 1500 °C where the specimen surfaces would not be damaged by excessive
thermal etching or other bulk specimen damage or dimension changes could occur
which would be undesirable for industrial healing processes. Healed polycrystalline
alumina specimens where observed in a field emission scanning electron microscope to

reveal the morphology changes in polycrystalline alumina during healing at

3
temperatures below 1500 °C. Microwave heating of polycrystalline alumina was also
performed to compare crack healing behavior in conventional and microwave furnaces.
The activation energy and preexponential factor for diffusion during crack
healing were re-analyzed using the original data for two investigations from the
literature on crack healing in single crystal LiF ceramics. The re-calculated activation
energies and preexponential factors for diffusion were compared to the originally

calculated values and were used to reach different conclusions about the diffusional

healing mechanism(s).

2. LITERATURE REVIEW

2.1 Static Fatigue Behavior of Ceramics

Static fatigue in ceramics refers to a time-dependent weakening of a material under
constant stress due to environmentally-assisted subcritical (slow) crack growth. Static
fatigue is a combination of a mechanical behavior of ceramics under tensile load and
an environmental effect. The mechanical behavior of ceramics is related to the atomic
bonding behavior of ceramic materials. The room temperature tensile behavior of

ceramics is predominantly brittle in nature.

2.1.1 Atomic Bonding in Ceramics

Ceramics are ionically and covalently bonded inorganic materials. Examples of
ceramics with ionic bonding are: NaCl (sodium chloride), MgO (magnesium oxide),
LiF (lithium fluoride), SiO2 (silica), and A1203 (alumina). Ceramic materials such as
SiC (silicon carbide), Si3N4 (silicon nitride), BN (boron nitride), WC (tungsten
carbide), and TiB2 (titania diboride) are examples of covalently bonded ceramic
materials [1-2]. Ionic and covalently bonded ceramics typically have a high bond
strength, which is reflected in the high melting temperatures observed for ceramics
(typically higher than 2000 °C) [3]. Close packing of the atoms in crystalline

materials requires that the atoms be essentially spherical, of identical size and have

5
non-directional bonding between atoms [1]. Ceramic materials which are composed of
two or more types of atoms often have atoms that can be very different in size and so
may not be close packed even if ionically bonded. In fact, most ceramic crystal
structures are very far from being close packed [2].

The open crystal structure of most ceramics coupled with the high bond
strength means that very few ceramic materials have dislocation motion below 1000 to
1200 °C [2]. NaCl, LiF and MgO are examples of ceramic materials which have
dislocation movement at low temperatures, however, these are not commonly used
ceramic materials, at least not by themselves (MgO is commonly added to other
ceramic materials such as SiO2 and A1203). Single crystals of A1203 do not have
dislocation motion until temperatures above 1260 °C [4]. Ceramic materials with
covalent bonding have limited dislocation motion even at high temperatures. Ceramic
glasses will not have dislocation motion either, since they are by definition non-

crystalline solids.

2.1.2 Room Temperature Tensile Behavior

Since most common ceramic materials (SiC, Si3N4, BN, WC, A1203 and glass) do
NOT have dislocation motion at room temperature, ceramics have very limited
plastic deformation and fracture in a BRITTLE manner. The stress-strain behavior
for most monolithic ceramics simply consists of elastic deformation until fiacture. On
an atomic level, elastic strain is actually the result of changes in interatomic spacing
due to the applied stress. The elastic modulus for covalently bonded ceramics is

higher than that observed in metals due to the higher strength of the covalent bonding

6

compared to metallic bonding. For example SiC has an elastic modulus of over 400
GPa [3], while many common steels have elastic moduli around 200 GPa [5].

The theoretical strength to break the atomic bonds during tensile loading of

ceramics can be calculated using the elastic modulus, E, and is typically % to g [3-

4]. However, the actual fracture strengths of polycrystalline ceramics are only about

% to —10£06[3-4]. The failure at actual applied loads well below the theoretical

fracture strength is the result of the presence of pores, flaws, and cracks which cause
local regions of stress concentration.

The fracture toughness, K1,, measures the material’s resistance to crack growth:

K4 =Ya/7_r\/E (1)

where Klc is the fracture toughness (also the critical stress intensity factor), Y is a
geometric factor dependent on specimen and crack geometry, 0 is the stress at failure,
c is the half the crack length (2c). For aluminum alloys KIc values range from 20 to
40 MPa m”, while for steels, Kk values range from 60 to over 100 MPa m°'5 [6]. The
fracture toughness values for ceramics are much lower. For example, the fracture
toughness for soda lime silicate glass ranges from 0.7 to 0.8 MPa rn‘L5 [7].
Polycrystalline ceramics have fracture toughness values which are slightly higher than
that for glass, but that are still much lower than that of metals. A1203 has a Kk value
of 4.0 MPa m”, while Si3N4 has about the highest fracture toughness value for non-

transforrnation toughened ceramics with a K1c value of 5.6 MPa m"5 [6].

 

7

The lack of crack resistance means that very small flaws in ceramic specimens
act as stress concentrators from which cracks form and subsequently grow. The flaws
can be surface flaws resulting from scratches, machining or thermal shock. The flaws
can also be volume flaws from pores (voids left over from sintering), or microcracks
caused by thermal expansion anisotropy, thermal expansion mismatch between phases,
or phase transformations. Control or elimination of flaws in ceramics during
processing is the aim of research in ceramic processing, however, in practical
applications it is virtually impossible. The limited ability to control the flaw size leads
to a variation in the population of flaws for a given specimen.

For specimens with low crack resistance, as the applied tensile stress is
increased, the cracks will continue growing until the largest crack grows to a critical
length. At the critical crack length, the local stress intensity factor exceeds the
fracture toughness of the material and results in fracture. The larger the size of the
flaw in the ceramic specimen, the higher the stress intensity at the flaw, and
consequently the lower the fracture strength of the specimen.

Due to the variation in fracture strengths in tensile loading resulting from stress
concentration at flaws, along with the difficulty of preparing ceramic test specimens
having normal tensile test specimen geometries, different strength testing is used for
ceramics than metals and polymers. Three or four point bend testing is commonly
performed on ceramics and is often referred to by ceramists as modulus of ruptrrre
(MOR) testing or bend strength testing. Since ceramics do not have plastic
deformation, the stress state in bend testing is known from linear fracture mechanics

analysis. The tensile forces are at a maximum on one surface, decrease to zero at the

 

8

midplane of the specimen, and reach a maximum compressive force at the other
surface. Only a fraction of the specimen is under maximum tensile stress during bend
testing, while in normal tensile testing the entire volume of the specimen in the
reduced cross sectional area is under maximum stress. From a statistical standpoint,
the chance of an unusually large flaw being under maximum stress is very small in
bending and very probable in normal tensile testing. Consequently, much less scatter
in fracture strength data is observed in bend testing than in tensile testing requiring

fewer specimens for testing in bend testing than in tensile testing.

2.1.3 Static Fatigue Investigations

In ceramics, "fatigue" is a word that is not just used to describe the behavior of a
material under varying load (as in metals). "Fatigue" is used for many different time-
dependent phenomena observed in ceramics. For ceramics, the term "cyclic
mechanical fatigue" is used to describe the behavior of ceramics under varying
mechanical load and is the equivalent of the term "fatigue" used in metals literature.
Other examples of the use of the term in ceramics include "thermal fatigue" where the
strength decreases from repeated thermal shock and "static fatigue" where the
phenomena of a reduction in strength and/or a growth in cracks under a gm
MM is a result of environmental effects. In static fatigue of ceramics, growth
of flaws occurs at stress levels lower than required for instantaneous failure and is also
referred to as subcritical crack growth [8-9]. Subcritical crack growth can continue

until a critical crack length is reached and catastrophic failure ensues [8-9].

2.1.3.1 Standard Static Fatigue Testing

Testing of static fatigue subcritical crack growth in ceramics is traditionally performed
by direct optical measurement of a macrocrack under constant mechanical load for
double cantilever beam specimens or double-torsion specimens [9-20]. Double
cantilever beam and double-torsion testing measures the crack length as a function of
time under constant load. The crack length and time measurements are converted to
change in crack length per unit time (da/dt or V) values while the load and the crack
length measurements are converted to stress intensity (K) values. The data is reported
as crack velocity (V) versus stress intensity (K,) data.

The cracks in DCB specimens are macrocracks, and it is now recognized that,
at least in part, the difficulty with using DCB data to predict static fatigue lifetimes is
the fact that most in-service failures originate from microcracks [21]. Microcracks,
include microcracks or "natural flaws" that are inherent in the material, such as
microcracks that occur due to handling, processing flaws, etc. For microcracks,
subcritical crack propagation behavior under constant load (static fatigue) can differ
substantially from that behavior observed for macrocracks [21].

In static fatigue "lifetime" testing (where time to failure under a static load is
measured), often the surfaces are abraded to approximate a "natural" flaw population,
that is a flaw population that originates from handling, cutting, grinding, or the initial
processing (sintering) of the ceramic specimen. However, for abraded specimens, it is
impossible to obtain information on the initial flaw length and position, thus one can
not determine the stress state under which the flaws begin to propagate. Furthermore,

details of the crack propagation process itself are unaccessible.

10
2.1.3.2 Findings of Standard Static Fatigue Testing
Glass has been the focus of much of the static fatigue testing of subcritical crack
growth in ceramic s. Wierderhom performed double cantilever static fatigue
experiments on soda-lime-silicate glass in environments with 0.017% to 100% relative
humidity and 25 °C [8]. The experiments revealed an increase in crack velocity with
increasing relative humidity. The importance of water vapor on the static fatigue has
been well established from many other experiments [10-12, 22]. Further studies by
Wierderhom and others have shown the existence of very slow static fatigue crack
growth in vacuum (i.e. without the presence of water vapor) for soda-lime-silicate,
aluminosilicate, borosilicate, and high leaded glasses [23—24]. The rate of the static
fatigue slow crack growth depended strongly on the composition of the glass material
tested. For example, no static fatigue slow crack growth was observed for fused silica
and low-alkali borosilicate glasses tested in vacuum [23-24]. For polycrystalline
ceramics, the static fatigue crack growth has been related to the amount of glassy
phase located at the grain boundaries. The microstructure of the material also plays an
important role in static fatigue crack growth [13, 22].

The process of static fatigue is relatively complicated, in that some researchers
associate static fatigue primary with environmental attack at glassy phases between
grains or at interfaces between matrix and reinforcing phases. For example, Choi and
Horibe [22] relate static fatigue in alumina and silicon nitride to the glassy phase
between grains of the ceramic. Choi and Horibe [22] found that silicon nitride
specimens that contained an appreciable glassy phase are relatively sensitive to static

fatigue, while reaction bonded silicon nitride (RBSN), which contains very little glassy

1 1
phase, is relatively insensitive to static fatigue. However, for higher temperature
applications, static fatigue results from the reaction bonding process which leaves
unreacted silicon in the interior of RBSN. This unreacted silicon can be converted to
silica upon heating in air. The silica evolved within RBSN specimens renders RBSN
useless for high temperature applications. In a study of both static and cyclic fatigue
in silicon nitride, Jacobs and Chen [25] found a stress intensity-crack velocity (K-v)
relation for static fatigue of silicon nitride that is similar to that observed for silicate
glasses. Jacobs and Chen [25] then infer that the similarity of the static fatigue
behavior for silicon nitride and silicate glasses may be due to the Y-Si-Al-O-N glass at
the grain boundaries.

In both glassy silica ($0,) and single-crystal alumina (A1203), water and NH3
(ammonia) chemisorb on the highly strained bonds at the crack tip [26-28]. Michalske
et a1. [29] give a model in which a polar molecule such as water or NH3 undergo a
"concerted reaction" with the Al-O or Si-O bonds that results in the breaking of the
bond and hence the propagation of the crack. Thus static fatigue is NOT always
associated with grain boundaries containing silicate glass. Single-crystal alumina
certainly does not have grain boundaries and so the bonds being broken are Al-O
bonds rather than Si-O bonds. Thus while silicate phases at grain boundaries may be

important, such phases are apparently not required for static fatigue in ceramics.

2.2 Crack Healing in Ceramics
Crack healing has been observed in a variety of different ceramic materials including

single crystals [30-32], polycrystalline ceramics [31, 33—34], inorganic glasses [35-36],

12
and ceramic composites [37]. Three general mechanisms have been reported for crack
healing in ceramics: diffusion-driven thermal healing, adhesion from intermolecular
forces, and reaction products from chemical reactions at the crack tip [33]. The
environment has been found to influence crack healing in ceramics [35-36, 38-39]. In
diffusion driven thermal healing, morphology changes have been treated theoretically
[40—41] and observed experimentally [30-32, 34, 42-44]. Crack healing has been
investigated via strength recovery testing after thermal annealing cycles [22, 31, 34,
45, 47-52]. Healing in alumina has also been investigated via Vickers indent crack

length changes after thermal annealing [37].

2.2.1 Role of Environment

Crack healing studies in inorganic glasses have frequently emphasized the role of
environmental humidity in the crack healing process. Holden and Frechette studied
the environmental effect on thermal annealing of soda-lime—silica glass by varying the
presence of humidity during different portions of the heating cycle [35]. Cracks were
formed in specimens from thermal down-shock by a metal probe which gave crack
depths ranging from 191 to 900 microns [35]. Five different annealing cycles were
used for cracked specimens annealed to 550 °C by applying the humid environment
(water vapor pressure of 30 kPa) during different portions of the heating cycle and
varying the length of the hold at the annealing temperature (see Table l for detailed
conditions) [35]. After annealing, the specimens were fractured using a ring-on-ring
test and the resulting fracture surfaces were observed using differential interference

contrast (see Table 1 for summary of results) [35]. Based on their results, Holden and

13

Table l Humidity conditions during five different heating cycles of Holden and
' Frechette [35] and resulting effects on crack closure and tested strength in soda-lime

 

 

 

 

 

 

 

silica glass.
Heating Humidity Applied During Cycle Holding Crack Qualitative
Cycle Time Closure Strength
Heating Hold Cooling (Minutes) * aka:
Temperature

1 No Yes No 60 No Very Low
2 Yes No No 60 Yes Very Low
3 Yes Yes No 10 Yes Low
4 Yes Yes No 60 Yes Good
5 Yes Yes No 100 Yes Good

 

 

 

 

 

 

 

 

 

* Crack closure was determined by the absence of the crack during visual
examination after the heating cycle.

** The qualitative strength is a characterization of the ring-on-ring failure load for
the group of samples with a particular heating cycle compared to a group of
samples without thermal shock cracks.

 

14
Frechette [35] proposed an optimum healing cycle for crack healing and also a four
step model for the crack healing in soda-lime silica glass [35]. The reported
conditions optimum healing was: (1) presence of humidity at lower temperatures
during the heating cycle, (2) presence of a residual stress before the annealing cycle,
(3) the presence of humidity at the annealing temperature, (4) holding at the annealing
temperature for a period much longer than that required for the relief of stresses [35].
The proposed model for crack healing in soda-lime silica glass was: (1) adsorption of
water at a temperature below the glass transition temperature, (2) formation of a gel
layer, (3) closure of the crack due to stress relief and (4) drying of the gel in the
presence of a controlled atmosphere [35].

Using an optical microscope, Lehman, Hill, and Sigel observed crack closure of
Vickers indentation cracks in heavy-metal fluoride glass [36] under different relative
humidity levels at temperatures of 22, 50, and 80 °C. The crack closure rate was
greater at higher levels of relative humidity, while crack closure lengths appear to
reach similar values at longer times for all levels of humidity [35]. Temperature was
reported by the authors as a significant factor in crack closure, however, the authors’
plot of crack length as a function of temperature for different humidity levels could
easily be fit by a horizontal line of zero slope (i.e. no significant crack length change
with temperature) [36]. Lehman et al. found no evidence of a gel or any other
reaction product which usually would be crystalline in fluoride glass and consequently
readily identifiable [36].

Stravrindis and Holloway [38] investigated crack healing in glass using a

double torsion loading configuration to observe crack closure and repropagation. The

15

closure and repropagation of cracks in soda-lime silica, borosilicate, and silica glasses
was dependent on the environment [38]. For soda-lime silica specimens, the strain
energy release rate for crack repropagation for a crack which was allowed to close in
air, increased with room temperature aging time in air [38]. An optical reflectivity
developed for the cracked specimen within a few minutes of exposure to air, but a
significant increase in the energy required to repropagate the crack took hours of
exposure of the crack to air [38]. Stravrindis et al. [38] state that the change in
reflectivity may be due to the penetration of water to the two faces of the crack and
that the initial adhesion between the faces of the closed crack may be due to the
formation of a hydrogen bonded network. Stravrindis et al. [38] theorize that the
subsequent increase in the energy required to repropagate the crack after a few hours
of exposure of the crack to air may be due to a progressive interaction between the
water layer and the SiO2 network of the glass.

Michalske and Fuller [39] investigated crack closure and repropagation in soda-
lime silica and vitreous silica glass using a double-cleavage drilled-compression
fracture mechanics configuration. The energy during closing of cracks was humidity
dependent at low temperatures, but was independent of glass composition which the
authors state indicates that the closure may be the result of a physical process such as
hydrogen bonding and not complex chemical reactions [39]. Michalske et al. [39]
develop a model for the hydrogen bonding energy across the crack as a function of
humidity. The model shows a drop in the closure energy at humidity levels of less
than 15%. The authors [39] state that linkages of two or three water molecules

between the crack faces may be possible which would mean that crack faces separated

16

by up to 1 nm may be adhered by hydrogen bonding.

2.2.2 Crack Morphology Changes during Thermal Healing of Cracks
Thermal-annealing induced changes in crack morphology have been treated
theoretically by Nichols and Mullins [40-41]. Nichols and Mullins [40-41] showed
that a semi-infinite cylindrical crack would either evolve (by diffusive transport) into a
string of small spherical pores (ovulation) or into a large sphere (spheroidization).
Experimental observations of crack morphology changes [30-32, 34, 42-44] are
consistent with Nichols and Mullins’ theoretical observations [40-41]. For example,
Yen and Coble [32] thermally annealed internal cracks in single crystal sapphire in air
at temperatures ranging from 1650 to 1810 °C and found that the original continuous
internal cracks broke up into channels of tubular voids which subsequently evolved
into rows of spherical pores. Wang and Harmer [30] used an in-situ optical
microscope to observe healing of internal cracks in single crystal LiF during
isothermal annealing in the temperature range of 620 °C to 820 °C and found that
annealing occurred in three stages: pinching off of plane cracks into cylindrical pores,
ovulation of cylindrical pores, and shrinkage of isolated pores [30]. Gupta
investigated healing in MgO [34], sapphire [31], and alumina [31]. Specimens, which
had cracks formed from thermal down-shocking, were thermally annealed at
temperatures in the 1400 °C to 1700 °C range, fractured in four point bend, and
observed in an SEM [31, 34]. Gupta observed that the cracks at grain boundaries
pinched-off (for MgO and alumina), that the cracks evolved into cylindrical voids

which became rows of spherical pores, and that with further annealing the spherical

l7

pores underwent continuous shrinkage [31, 34].

Hrma, Han, and Cooper [42] investigated indentation crack healing in soda-
lime silica glass at 600, 650, and 675 °C using transmission optical microscopy and
multiple beam interference microscopy on cooled samples. Hrma et al. [42] found a
process of crack healing characterized by several stages with distinct morphological
changes. In the first stage of healing, two different phenomena were reported: 1a)
relaxation of the residual stress created during indentation occurred, 1b) subsurface
crack outlines (which were barely detectable before annealing) became visible after a
short time of heat treatment (e.g. less than 45 minutes at 600 °C) as a result of
blunting of the crack tips via capillarity driven viscous flow of the glass [42]. In the
second stage of healing, the indent cracks receded with a inward motion of the crack
boundaries and radial cracks broke up via pinch off into oval cavities [42]. Grooving
of the crack edges at the crack surface and shrinking of the subsurface cracks into
cylinders and oval cavities characterized the third stage of healing [42]. The last
healing stage consisted of spheroidization of the remaining subsurface cracks and
gradual smoothing of the surface in the region of the indent impression [42].

Cassidy and Gjostein investigated the capillarity-induced smoothing of soda-
lime-silica glass surfaces after heating in air to 640-670 °C [43]. The decay in the
amplitude of periodic surface perturbations was measured with an interference
microscope for specimens cooled to room temperature after being held for 30 to 120
minutes at a set healing temperature [43]. The smoothing process was dominated by
viscous flow (from the convex surface to the concave surface) [43]. Kishi et a1. [44]

investigated the surface flattening in soda-lime silica glass in dry nitrogen at 610-670

18

°C and found that viscous flow dominated the smoothing process. The surface
viscosity was higher than the bulk viscosity of the glass [44]. Kishi et al. [44] noted
that residual water in glass will reduce the viscosity and so heating at temperatures

above 600 °C may deplete the surface of water and result in an increased surface

viscosity [44].

2.2.3 Crack Healing Investigations Via Strength Recovery Testing
Crack healing has been investigated via strength recovery testing after thermal
annealing cycles [22, 31, 34, 45-52]. Lange and Gupta [45] investigated the flexural
strength recovery of thermally shocked ZnO specimens after thermal heating to the
sintering temperature (1100 °C) for 10, 20, and 35 hours. No explicit mention of the
environment in which the specimens were heated is made by the authors other than a
comment that the specimens were heated in a closed ZnO boat [45]. The four-point
bend strength of the thermally shocked specimens before healing was 40% of the
strength of the original, as-machined strength. The healed specimen strength increased
from about 70% of the as-machined strength for 10 minutes of healing at 1100 °C to
nearly 100% of the as-machined strength for the specimens heated for 35 hours at
1100 °C [45]. The grain size in the ZnO specimens also increased with increasing
time at 1100 °C [45].

Lange and Radford [46] investigated the flexural strength recovery of thermally
shocked A1203 specimens after thermal heating in air to the 1700 °C for l, 7, 25, and
50 hours. The thermally shocked specimens had 36% of the strength of as-machined

specimens. The strength of the specimens increased for the 1 and 7 hour specimens to

19

76 and 86% of the as—machined strength, respectively. The specimens heated for 25
and 50 hours had a steadily decreasing strength of 80 and 78% of the as-machined
strength, respectively, which was attributed to grain growth in the specimen [46].

Gupta investigated the bend strength recovery in thermally shocked
polycrystalline MgO specimens after heating in air to 1400, 1500, 1600, and 1650 °C
for 1 to 10 hours [34]. The four-point bend strength of the thermally shocked
specimens was about 30% of the as-machined strength. The amount of recovered
strength increased with increasing temperature from a maximum of about 45% of the
as-machined strength at 1400 °C to about 90% of the as-machined strength at 1600 °C
[34]. The amount of strength recovered also increased dramatically with time for
temperatures above 1400 °C, for example, at 1600 0C the strength increased from
about 60 to 90 % of the as-machined strength for 1 minute of healing compared to 2
minutes of healing [34]. The grain size in the MgO specimens also increased with
increasing time and temperature [34].

Gupta also investigated the strength recovery in thermally shocked
polycrystalline A1203 specimens after heating in vacuum to temperatures 1400, 1500,
1600, and 1700 °C for up to 110 minutes [31]. The temperatures tested were below
the sintering temperature so that grain growth was avoided [31]. The amount of
strength recovery increased both as a function of time and temperature for
temperatures below 1700 °C [31]. The four-point bend strength of the thermally
shocked specimens was about 30% of the as-machined strength. The strength after 10
minutes of healing increased from about 35 to 80 % of the as-machined strength for

healing at 1400 and 1700 °C, respectively. The strength for healing at 1600 °C

20

increased from about 60 to 85 % of the as-machined strength for 10 and 90 minutes,
respectively. At 1700 °C, there was an un-explained decrease in strength (of less than
10% of the as-machined strength) as the time at 1700 °C increased to 110 minutes.
Cracks formed along the grain boundaries after thermal shock [31]. Healing occurred
via the gradual disappearance of the void space between neighboring grains [31].
Grain boundary diffusion was thought by Gupta to aid the healing process since the
healing and strength recovery was more rapid for the polycrystalline alumina than for
similar testing of sapphire (single crystal alumina) [31].

Roberts and Wrona [47] investigated the bend strength recovery in thermally
shocked polycrystalline UO2 specimens after heating in a static helium environment to
1600, 1800, and 2000 °C for 1 to 10 hours [34]. The four-point bend strength of the
thermally shocked specimens was about 20% of the as-machined strength. Full
strength recovery occurred after heating for approximately 3 hours at 2000 °C and
approximately 11 hours at 1800 °C [34]. The strength after 4 and 32 hours of healing
at 1600 °C was about 50 and 70 % of the as-machined strength, respectively. The
cracks healed initially via crack pinch-off into a line of pores of irregular cylindrical
or spherical shape [34]. Healing continued via shrinkage of the pores into nearly
spherical shaped pores which remained as grain-boundary porosity [34]. A model by

Nichols and Mullins for the shape change of pores during sintering [41]

_ .35: = (A exp(—Q/RT))C2 = kc2 (2)

was used by Roberts and Wrona [47] to help model the change in strength from

0,2 052 k’t
__ : __ _ 3
.fl l.) + .2 ()

healing where C is the pore diameter, t is the time at temperature, T is the
temperature, A is a pre-exponential constant, Q is the activation energy for healing, R
is the gas constant, k is a constant containing the activation energy in an Arrhenius
relationship, 6, is the as-shocked strength, of is the uncracked fracture strength, 6, is
the strength after healing for a time, t, and k’ is a constant that can be related to
temperature with an Arrhenius relationship. Roberts and Wrona [47] found an
activation energy for healing of 230 kJ/mole, while reporting that for UO2 the
activation energy for volume diffusion is about 419 kJ/mole and for grain boundary
diffusion in sintering it is about 314 kJ/mole. The authors conclude that the healing is
probably dominated by grain boundary diffusion [47].

Bandyopadhyay and Roberts [48] investigated the bend strength recovery in
thermally shocked polycrystalline UO2 specimens after heating in a static helium
environment to temperatures of 1290 to 1740 °C for 1 hour and to 1400 °C for times
up to 8 hours [49]. Healing, in the form of strength recovery, occurred in two stages
[48]. The first stage of healing was characterized by crack pinch-off and some
sintering of the crack-like pores [48]. The second stage of healing was controlled by
continued sintering of crack-er pores by a diffusional process [48].

Bandyopadhyay and Kennedy [49] investigated the bend strength recovery in
thermally shocked polycrystalline UO2 specimens after heating in a static helium

environment to temperatures ranging from 1450 to 1920 °C for 1 to 48 hours [49].

22
The healing behavior of specimens with different levels of thermal shock was studied
[49]. The four-point bend strength of specimens thermally shocked at 130 to 700 °C
decreased from about 35 to 19 % of the as-machined strength, respectively. As the
thermal shock quench increased from 120 to 700 °C, the number crack density per cm
increased from 1 to more than 20 and the maximum crack width increased from about
4 to 12 pm [49]. The authors state that an empirical relationship between crack
density and maximum crack width could be determined so that either parameter could
be used to further study healing at different levels of thermal shock [49]. An
exponential relationship was found between the time required for complete healing and
the crack density [49]. The activation energy for healing was 410 kJ/mole using the

following equation
. = m Texp(%l (4)

where tc is the time required for complete healing, m is a temperature independent
constant, T is the healing temperature, Q is the activation energy for healing, and R is
the gas constant [49]. Volume diffusion was reported as the process for the healing of
the thermal shock cracks in UO2 since the activation energy for healing calculated
using Equation 4 (410 kJ/mole) was near the reported activation energy for volume
diffusion of 419 kJ/mole [49].

Tomozawa, Hirao and Bean [50] investigated the bend strength increase in
soda-lime silica glass after annealing. Cylindrical specimens with a Vickers indent
were thermal shocked to cause the indent crack to extend beyond the range expected

for the residual stress created during indentation [50]. The thermal shocked specimens

23

were annealed at 510 °C for one hour and furnace cooled before four-point bend
testing at liquid nitrogen temperatures [50]. The strength of the annealed specimens
increased by 20 to 30% without a decrease in the crack length during annealing [50].
The increase in strength was attributed to blunting of the crack tip during the thermal
annealing [50].

Hirao and Tomozawa [51] further investigated the bend strength increase after
annealing in Vickers indented cylindrical specimens of soda-lime silica glass. The
specimens were annealed in air and in vacuum at both 510 °C and 570 °C for one hour
[51]. The specimens annealed in vacuum had a strength increase of about 16 and 26
MPa for 20 minutes of healing at 510 and 570 °C, respectively, without a decrease in
the crack lengths [51]. The specimens annealed in air had a strength increase of about
28 and 38 MPa for 20 minutes of healing at 510 and 570 °C, respectively, without a
decrease in the crack lengths [51]. The strength increased faster with respect to time
and reached a higher strength value for the specimens annealed at 570 °C compared to
the specimens annealed at 510 °C [51]. Residual stress was eliminated during the
annealing process in both environments according to measurements via a
polarmicroscope [51]. Crack tip blunting is mentioned as the cause of the strength

increase in the glass after reference to the Inglis equation for stress concentration

u

of = %ath[%2 (5)

where of is the fracture strength, on, is the theoretical strength of the material, p is the

crack tip radius, and C is the crack length. The authors comment that slow crack

24

growth effects of the environment would result in a decrease in strength and not an
increase in strength, that the measured crack length did not change, and consequently
conclude that the only mechanism for a fracture strength increase after annealing
would be an increase in the crack tip radius (i.e. crack tip blunting).

Hirao et al. [51] also investigated the surface flattening of soda-lime silica
glass after annealing in vacuum and environments with water vapor present using
similar techniques originally used by Kishi et al. [44]. Viscous flow was the dominant
mechanism for the smoothing process in vacuum and in the presence of water vapor.
The surface viscosity was lower for specimens annealed in the presence of water vapor
than for specimens annealed in vacuum [51]. The increased viscous flow for
specimens annealed in the presence of water was used as an explanation for the
increased strength recovery for specimens annealed in air compared to specimens
annealed in vacuum [51].

Choi and Tikare investigated the crack healing of an alumina with a residual
glassy phase (Coors ADS96R with 4% silicates added as sintering aids) using four-
point bend testing of specimens with Vickers indents and single-edge-precrack—beam
testing [22]. Specimens with 49 N Vickers indent cracks were annealed for 30
minutes in air at temperatures ranging from 25 to 1400 °C and in argon gas at 1200 °C
[22]. Annealed and as-indented specimens were tested in four-point bend at room
temperature [22]. As-indented bend strength was about 215 MPa [22]. Specimens
annealed at 800 °C had bend strengths of about 256 MPa, while specimens annealed at
1200 °C and higher had strengths equal to the as-machined strength of about 375 MPa

and had the indent impression essentially disappear completely from optical

25

microscopy examination [22]. The crack healing was reported to occur from a
material transport mechanism within the specimen [22]. The specimens annealed at
1200 °C in argon exhibited similar strength increases to specimen annealed in air at
1200 °C [22].

Healing of large macrocracks in single-edge-precrack-beam specimens was also
investigated by Choi and Tikare [22] using SEM observation of fracture surfaces of
as-precracked specimens and healed precracked specimens [22]. The as-precracked
specimens predominantly fractured intergranularly with straight cleavage planes and
some crack branching along other cleavage planes and sharp grain edges [22]. The
healed precracked specimens had rounded crack edges and glassy striations on the
cleavage planes [22]. Healed specimens exhibited degraded fatigue resistance in slow
crack growth testing via dynamic fatigue experiments with a decrease in the fatigue
susceptibility parameter, N, from 107 for the as-indented specimens to 68 for the
specimens healed for 30 minutes at 1200 °C [22]. The authors suggest that since the
healed specimens have degraded fatigue resistance and since glass has poor fatigue (N
values of 20 to 40), then the crack healing mechanism was viscous flow of the glassy

grain boundary driven by capillary forces [22].

2.2.4 Crack Healing Investigations of Vickers Indent Cracks Lengths
Thompson, Chan, Harmer, and Cook investigated the Vickers indent crack lengths
during healing of A1203 and Ale3-SiC nanocomposite [37]. The specimens were
viewed un-coated in an SEM at a 3.1 KeV accelerating voltage after being indented

and after annealing for 2 hours in argon at 1300 °C [37]. The specimen aging time

26

between indenting and thermal annealing was not explicitly stated [37]. The crack
path for a 10 N indent in a composite specimen was predominantly transgranular while
in a monolithic alumina specimen the crack path was predominantly intergranular [37].
In the annealed composite, the crack opening displacement decreased such that the
faces of the crack came into contact. A "surface trace" along the original crack plane
was observed on SEM micrographs which the authors state indicates that the fracture
surface did not bond completely [37]. In the annealed composite, the last 2-3 microns
of the crack at the original crack tip disappeared and was termed by the authors as the
only true healing of the crack [37]. The authors conclude that the healing mechanism
must have been adhesion of the crack faces rather than a diffusive transport healing of
the crack since the crack morphology did not change via pinch-off into isolated pores
or continuous reduction of the spheroidized pores [37].

In the annealed monolithic A1203, crack healing (in the form of a decrease in
the crack length) did not occur, instead, crack length and the crack opening
displacement increased [37]. The crack grew as a result of a more rapid decay of the
microstructural toughening than the residual stress field driving force [37]. (The
microstructural toughening was attributed to frictional traction between adjacent gains
and the decay during annealing was the result of the reduction in the thermal

CXpansion mismatch with increasing temperature [37].) The authors explain that the
entended cracks failed to heal (once the residual stress was relieved) because: 1) the
tortuous fracture path may have made it difficult for the crack faces to match and
come together and 2) the frictional tractions may not have disappeared upon annealing

and may inhibit asperities from sliding past each other thus preventing crack closure

 

27

[37].

2.3 Capabilities of an Environmental Scanning Electron Microscope

Conventional scanning electron microscopes (SEM) use electrons to form an image of
a specirnen’s surface. The Everhart-Thornley detector collects secondary electrons
(SE) and back scattered electrons (BSE) generated from interactions between the
incident electrons and the surface [53]. The specimen chamber in an SEM must
remain under vacuum for an image to be formed by using the Everhart-Thornley
detector [53].

An environmental scanning electron microscope (ESEM) also uses electrons to
form an image of a specirnen’s surface. However, the ESEM uses a gaseous detection
device (GDD) to collect SE and BSE electrons and thus the sample chamber in an
ESEM can have a gaseous environment [54]. The ESEM has a number of pressure
levels along the path of the electron beam. The differing pressure levels are separated
by pressure limiting apertures (PLA) which allow the electron gun to be under high
vacuum while the specimen chamber can be pressurized up to 25 Torr [54]. The GDD
operates with a positive bias of a few hundred volts. A SE emitted from the sample
surface is accelerated toward the detector. Along the way, the emitted SE collides
with a gas molecule which ejects an electron from the gas molecule. This process is
repeated and results in an avalanche process [54] which amplifies the SE signal. The
process of electron ejection from a gas molecule creates positive gas ions which help
neutralize the buildup of a negative charge on the sample surface and allows the use

of nonconducting samples without a conductive coating [53]. Danilatos has shown no

28

loss of resolution using the GDD detector in a gaseous environment compared to using
an Everhart-Thomley detector at high vacuum [54].

The unique capabilities of the ES EM allow in-situ study of the crack healing
and static fatigue crack growth of ceramics. The ability to have pressures up to 25
Torr in the specimen chamber allow the ceramic specimens to be in a humid
environment, at least initially. (As the temperature increases the relative humidity
drops rapidly, such that at temperatures above 100 °C, the relative humidity at
pressures below 10 Torr becomes negligibly small [54]). Also, the ESEM can
examine ceramic specimens without the conductive coating required for a conventional
SEM. The absence of the surface coating allows the surface of the specimen to be
exposed to the environment in the ESEM chamber and make static fatigue testing

possible in the ESEM.

2.4 Focus of the Current Investigation

In the literature, no static fatigue studies reported observations of static fatigue crack
growth in-situ. The present investigation will develop a technique to study crack
growth in ceramics in the presence of water vapor in-situ using an Environmental
Scanning Electron Microscope (ESEM). Tensile specimens of a soda-lime silica and a
polycrystalline alumina will be tested in-situ using this technique. The effect of the
level of relative humidity and the magnitude of the applied stress on the static fatigue
crack growth in polycrystalline alumina will be investigated. The study will also focus
on in-situ observation of the crack path in polycrystalline alumina to determine if the

static fatigue crack growth is intergranular or intragranular and if grain bridging

 

 

 

29

occurs.

In the literature, only a single in-situ crack healing study of crack healing in
ceramics has been reported [30] and no in-situ healing studies of glass specimens or
polycrystalline specimens have been reported in the literature. The present
investigation will study crack healing in soda-lime silica glass in-situ using an
Environmental Scanning Electron Microscope (ESEM). The crack morphology
changes during healing for temperatures up to 600 °C will be studied in the soda-lime
silica glass.

Limited crack healing studies in soda-lime silica glass below 600 °C have been
performed [35-36, 50-51]. At temperatures of 600 °C and above, bulk viscous flow
occurs in soda-lime silica glass and can result in bulk dimensional changes or sample
damage which would be undesirable for an industrial healing process. Of the studies
of healing in soda-lime silica at temperatures below 600 °C, some have observed crack
length reductions upon annealing [35-36], while others have observed no change in
crack length after annealing [50-51]. The present investigation observes the crack
healing behavior of soda-lime silica glass at temperatures below 600 °C both in-situ in
an ESEM and with optical microscopy before and after thermal annealing in a
conventional furnace. The effect of time and temperature on the length of Vickers
indent cracks in soda-lime silica glass will be studied.

Investigations into the effect of humidity on healing in glass have been in the
form of studies of crack closure at temperatures below 100 °C [36, 38-39] or of
studies of high temperature healing using an induced humidity at high temperatures

[35, 50]. Investigations of the effect of the initial humidity (before heating) on the

30

crack healing behavior of glass at temperatures below 600 °C would be useful in
determining the potential usefulness of the process for industrial repair of glass parts
damaged in service. Crack length changes during thermal annealing of soda-lime
silica specimens initially held at different levels of humidity are observed in this study
using both in-situ ESEM measurements and with optical microscopy measurements
before and after thermal annealing in a conventional furnace. The in-situ study will
investigate the effect of initial humidity on the temperature at which crack healing
begins and on crack healing behavior for an isothermal hold. The current investigation
also studied the effect of an initial 24 hour aging cycle with relative humidities of 0,
45, and 100 % on the crack healing behavior of soda-lime silica glass after annealing
in a conventional furnace.

While some crack healing studies of A1203 have used inert atmospheres during
annealing [31, 37] and other studies have used air as the atmosphere during annealing
[22, 46], no study has specifically investigated the effect of humidity on the crack
healing behavior of A1203. Crack healing in A1203 has been predominantly studied via
strength testing [21, 31, 46] where crack healing effects inferred from changes in
strength can be confused by strength changes due to increases in grain size by
diffusion at the annealing temperatures [46], and crack tip blunting [SO-51] during
heating. This study investigates crack length changes in polycrystalline A1203 during
thermal annealing in a conventional furnace for specimens initially held for a 24 hour
aging cycle with relative humidities of 0, 45, and 100 %. The study will also
investigate the healing behavior of two different polycrystalline A1203 materials, a

microwave sintered alumina made at Michigan State University, and a commercially

m Lji-fl r-t‘. ~. .-.u.

31

available alumina made by Coors. The effect of indent crack size on the healing
behavior of A1203 will also be investigated.

Heating in microwave furnaces has been found to increase sintering of alumina
and silicon nitride, increase oxygen diffusion in single crystal alumina, and increase
grain growth in alumina compared to heating to similar temperatures in conventional
furnaces. No studies in the literature have considered the healing behavior of ceramics
annealed in a microwave furnace. The present study includes investigating crack
length changes as a function of microwave and conventional heating. The effect on
the crack length behavior of a slow and fast ramp rate during microwave annealing
will also be investigated.

Few studies in the literature have attempted to determine the activation energies
for diffusion during the healing process [30, 47, 55]. A model by Stevens and Dutton
[56] for high temperature static fatigue crack growth via diffusion will be used in the
current study to determine diffusive activation energies for the healing process in
polycrystalline A1203 from microwave and conventional annealing. A re-analysis of
work by Raj et al. [55] and Wang et al. [30] using the model by Stevens and Dutton

[56] will also be performed in the current work.

3. EXPERIMENTAL PROCEDURE

3.1 Materials

Static fatigue and crack healing experiments on soda-lime silica glass and alumina
were performed. Commercially available glass slides were used to make soda-lime
silica specimens because of the ease of availability, low cost, and dimensional
uniformity. Commercially available electronic substrates made of alumina were used
to make alumina specimens because of their availability and dimensional uniformity.
Microwave sintered alumina disks manufactured at Michigan State University were

also used to make alumina specimens due to their availability and low cost.

3.11 Soda-Lime Silica Glass

The soda-lime silica glass material used in this study was in the form of glass slides
(Plain End Micro Slides, VWR Scientific, Media, Pennsylvania). The glass slides
were received precleaned and fully annealed. The as-received dimensions of the glass
sides were 76.2 mm X 25.4 mm X 1.1 mm (3.0 in X 1.0 in X 0.045 in). The
manufacturer reported composition was 72 wt.% SiOz, 14.3 wt.% NaZO, 6.3 wt.%
CaO, 4.1 wt.% MgO, 1.1 wt.% A1203, and 1.2 wt.% K20, with less than 1 wt.% of
other materials. The manufacturer reported that the density was 2.4024 g/cm”. The

manufacturer reported softening point, annealing point, and strain point were 724, 545,

32

33

and 511 °C, respectively. The annealing temperature of the glass was previously
experimentally detemrined to be around 580 °C [57]. Viscous flow was reported to

occur in the glass slides at temperatures above 600 °C [57].

3.12 Coors Alumina

Specimens (here-after referred to as Coors Alumina) were made from commercially
available alumina (Coors Ceramics, ADS-995 Alumina Substrate). The manufacturer
reported that the material is 99.5% pure alumina. The alumina was manufactured
using a tape casting process and was received in 114.3 mm X 114.3 mm X 1.0 mm
(4.5 in X 4.5 in X 0.04 in) billets. The manufacturer reported that the mean grain size
of the alumina was less than 2.5 microns (using an intercept method) and that the

density was 3.88 g/cm3 (using ASTM specification C373).

3.1.2 Microwave Sintered Alumina

The material referred to here-after as Microwave Sintered Alumina was made at
Michigan State University [58]. The specimens were made using Sumitomo AKP-SO
powder which is 99.9% pure alumina. The AKP-SO powder and no other powders (i.e.
no sintering aids or other additions) was uniaxially dry pressed into disks 15.0 mm
(0.6 inch) in diameter and 1.0 mm (0.04 inch) thick. The microwave sintering was
done using a 2.45 GHz single-mode microwave cavity (W avemat CMPR250
Microwave), equipped with an automated sliding short and launch probe positions

controls [59, 60].

34

3.2 Basic Sample Preparation
Sample preparation for material characterization, static fatigue testing, and crack
healing testing required use of many of the same basic techniques of cutting,

polishing, and indenting.

3.2.1 Sample Cutting
Samples were cut into the desired dimensions for static fatigue and crack healing

testing using either a low speed diamond saw or a high speed diamond saw.

3.2.1.1 Low Speed Diamond Saw
Preparing samples for static fatigue or crack healing using the low speed diamond saw
required actual cutting with the low speed saw as well as cleaning after cutting and

grinding to remove chips made during cutting.

3.2.1.1.1 Cutting

Low speed cutting was performed using a commercial low speed diamond saw
(Buehler Isomet Low Speed Saw) with commercially available diamond wafering
blades (Norton 101.6 mm (4 in.) diameter and 0.3 mm (0.012 in.) thick Diamond
Wheel) and cutting oil (Leco VC—50 Cutting Oil). The saw had a stationary rotating
blade with a movable arm which held the sample above the saw (Figure 1).

Specimens were cut to the desired length by adjusting the micrometer connected to the
saw arm. In the schematic shown in Figure 1, the micrometer moved the cutting arm

and sample into and out of the plane of the paper.

35

Weights were placed on the arm to help increase cutting speed (Figure 1).
However, there was a limit to the weight that could be added since too much weight
on the arm would result in a sizable chip at the edge of the sample before the cut was
complete. The most effective weights found for cutting were 35 g (1.2 oz) washers.
The smaller weight of each individual washer resulted in the ability to get the
optimum combination of high cutting rate and small chip size. The washers were
added or removed during testing when the cutting rate slowed or as the saw cut neared

completion, to reduce the weight and consequently reduce the chip size.

3.2.1.1.2 Cleaning and Grinding

After cutting on the low speed saw and removing the specimens from the cutting oil
reservoir, the samples were cleaned to remove the cutting oil. The samples were first
soaked in water with powdered glassware soap added (Alconox Powder Detergent).
The samples were removed, rinsed with tap water, wiped by hand with more powdered
glassware soap, rinsed again with tap water, and placed on laboratory paper towels
(Forthoward Envision Singlefold Towels) to dry.

To remove the chips made during cutting, the edges of the specimens were
ground using SiC grinding paper (Mager Scientific C Weight Waterproof Paper). The
areas with larger chips were ground first with a 240 grit paper. All specimen edges
were ground to a 400 grit finish with 400 grit paper. The specimens were then rinsed
with tap water, washed by hand with powdered glassware soap, rinsed with tap water,
rinsed with deionized (D.I.) water, and placed on laboratory paper towels.

To remove grinding debris from the samples, the samples were ultrasonicated.

 

36

.A 150 ml beaker of DI. Water was placed in an ultrasonic cleaner (Buehler Ultrasonic
Cleaner) which was half filled with DI. water. The samples were placed in the beaker
with tweezers and left in the ultrasonic bath for 15 minutes. The samples were
removed with tweezers from the beaker with the ultrasonic cleaner still on. The
samples were rinsed with DJ. water and then placed on laboratory paper towels to dry.
From this point on samples were always handled with tweezers to prevent

contamination of the samples with finger grease.

3.2.1.2 High Speed Diamond Saw

High speed cutting was done on a commercial computer controlled machine (K.O. Lee
Slicer/Dicer) with a 1.4 mm (0.055 in.) thick diamond wheel (Norton Diamond Wheel
with a 177.8 mm (7.0 in.) diameter and a inner opening of 31.8 mm (1.25 in). Cutting
fluid (5% concentration of Mobil Oil’s Mobilnet S-122 in tap water) cooled the saw
blade and rinsed away cutting debris. To prevent bacteria from becoming airborne
during cutting an anti-bacterial agent ("00" wafers by Malacron) was added to the
cutting fluid.

The high speed saw had a cutting table which moved back and forth in the x-
direction at a set rate of speed (usually set at 6.3) (Figure 2). The blade itself moved
in both the y- and z-directions (Figure 2). The blade was computer controlled to move
down in the z-direction in programmed increments to make a cut in the sample. Once
a cut of programmed depth was completed via computer control, the blade moved in
the negative z-direction and then in the y-direction a programmed distance to the

location of the next cut.

37

weights

 

Micrometer &
Pivot Point

Figure 1 Schematic of low speed cutting saw showing the cutting arm, the diamond
wheel and the specimen location.

Diamond Wheel

Sample
Plate

  

Figure 2 Schematic of the high speed cutting saw showing the specimen plate, glass
and steel mounting plates, and the magnetic chuck.

38
3.2.1.2.1 Mounting a Sample on the High Speed Saw
The sample was mounted on the table of the high speed saw via a magnetic chuck
(Walker Ceramax Permanent Magnetic Chuck, Figure 2). N on-metallic materials, like
ceramics, were affixed to a magnetic steel plate (Figure 2) and then to the plate with
the specimen in place were mounted on the saw. The steel plate was 127 mm X 127
mm X 9.5 mm (5.0 in. X 5.0 in. X 0.375 in.). To prevent the saw from cutting into
the steel plate and "gumrning" up the diamond blade, a 6.4 mm (0.25 in.) thick glass
plate was placed between the sample to be cut and the steel plate (Figure 2). Several
different glass plates were used. Each glass plate was cut with a hand held glass
cutter to approximate dimensions of 108 mm X 108 mm X 6.4 mm (4.25 in. X 4.25
in. X 0.25 in.).

Therrnoset (Buehler Thermoplastic Cement) was used to affix the glass plate to
the steel plate as well as to bond the cutting sample to top of the glass plate. The
steel plate was first placed on a hot plate (Cole Parmer Model 4658 Stirrer/Hot Plate).
The hot plate was turned on and the temperature was set to 6 27’3 on the hot plate’s
scale, which goes from 0 to 10. When the steel plate was hot enough to melt the
thermoset, the entire top of the steel plate was covered with thermoset. After a few
minutes had passed so that the therrnoset had spread out as evenly as possible, the
glass plate was placed on top of the steel plate. The glass plate was moved in small
circles on the steel plate until almost all of the air bubbles between the two plates
were removed. At least two comers of the glass plate and the steel plate were lined

up so as to make it easier to align the sample on the saw for cutting.

To mount the sample on the glass plate, the glass plate was covered with

39

thermoset in an area slightly larger than the area of the specimen to be cut. Once the
thermoset spread out evenly on the glass surface, the sample was placed on the glass
plate and moved in small circles in order to remove the air bubbles. The sample was
then lined up with the edges of the glass and steel plates to aid in alignment of the
sample before cutting. The hot plate was then turned off and unplugged. Care was
taken to make sure that during cooling the samples did not move relative to one
another.

The specimen was typically allowed to cool for 24 hours, then was mounted on
the saw. The lever on the front, right side of the magnetic chuck activated the
magnet. When the sample was loaded into the saw, the lever was rotated 180° clock-
wise so that the lever rested in the far right position. The sample was placed on the
top surface of the magnetic chuck and aligned with the back, left comer of the chuck.
The magnetic chuck was then activated by rotating the lever 180° counter-clock-wise

so that the lever rested in the far left position.

3.2.1.2.2 Locating the sample in the cutting saw’s y-z space

Before cutting, the computer, which controlled the cutting process, had to be oriented
with respect to the sample top surface (z-direction) and sample back edge (y-direction)
(Figure 2). Errors in locating the sample in the cutting saw’s y-z space resulted in
saw cuts in the wrong places or in the saw cutting through the sample, glass plate, and
steel plate in a fraction of a second. Thus, sample location errors may cause a great
deal of damage to the sample, the saw blade, the cutting saw itself, and/or the saw

operator.

40

The top surface of the sample was the first to be defined. The "log" mode of
the cutting saw computer was entered. The left handwheel controlled the mechanical
movement of the saw in the z—direction. Each division on the handwheels corresponds
to a 0.0025 mm (0.0001 in.) in travel of the saw blade. The saw was lowered using
the z-direction handwheel until the blade was within about 1 mm (0.04 in.) above the
surface of the material to be cut. A small ~6 cm2 (~1 in”) piece of notebook paper
was placed between the saw blade and the sample surface. The paper was used as a
0.05 mm (0.002 in.) spacer between the saw blade and the sample. The "Move Dog"
button on the computer key pad was depressed and held to move the saw table back
and forth in the x-direction. The handwheel was used to lower the saw blade while
the piece of paper was kept between the sample and the saw blade. The lowering of
the saw blade via the handwheel was continued until the piece of paper would catch
between the saw blade and sample and cause the saw blade to rotate. The z-direction
height on the handwheel was noted. The z-height was increased and the saw was
moved across the sample in the y-direction and the process was repeated to find the
highest point on the sample. Many other different y-direction locations were used
across the entire sample so that the maximum z-height for the entire sample surface
could be determined.

Once the maximum z-sample-height was determined, the saw then was moved
in the y-direction so that the saw was not above the sample. The handwheel was used
to lower the saw to the maximum specimen z-height. In the "Jog Z-Direction" mode
screen the saw was jogged down 0.05 mm (0.002 in.) which was the assumed

thickness of the paper. Finally, the computer read out for the z-height was zeroed in

 

41

the "Jog Z-Direction" mode screen.

The y-distance for the back edge of the sample was found in a similar manner
using a small piece of notebook paper between the saw blade and the back edge of the
sample, the y-direction handwheel, and the "Jog Y-Direction" mode screen. When the
minimum y-distance for the back edge was found, the z-height was increased using the
"Jog Z-Direction" mode screen. In the "Jog Y-Direction" mode screen the saw was
jogged forward 0.05 mm (0.002 in.) (the assumed thickness of the paper) and then
jogged forward to the location of the first saw cut. The computer read out for the y-
height was zeroed in the "Jog Y-Direction" mode screen. Finally, the z-height was
increased to a reading of -25.400 mm (-1.0000 in.) using the "Jog Z-Direction" mode

screen and the z-direction read out was re-zeroed.

3.2.1.2.3 Setting the saw table’s x-limits

The mechanical movement of the table back and forth in the x-direction was
controlled by two Dog Stops which indicate the end of travel to the left and right.
The end of movement to the left or to the right was signalled to the computer via a
magnetic sensor and two Sensor Stops.

The Dog Stops had to be adjusted depending on the location of the specimen
on the chuck and on the width of the specimen in the x-direction. Each Stop Dog was
adjusted by loosening a lock nut, sliding the Stop Dog on the rail to a new location,
and re-tightening the lock nut. The location of the left and right stop dogs were
adjusted so that the saw cut all the way across the specimen in the x-direction and

would move passed the specimen approximately an extra 6.4 mm (0.25 in.).

42
The Sensor Stops were also adjusted by loosening a lock nut, sliding the
Sensor Stop on the rail to a new location, and re-tightening the lock nut. The Sensor
Stops were adjusted so that they would just trip the magnetic sensor as the table
started to change directions. The magnetic sensor had a small red light which would

be lit when the sensor was tripped by one of the two Sensor Stops.

3.2.1.2.4 Setting the computer to control cutting
The computer for the high speed saw operated in the English system of units.
Computer controlled cutting of specimens was performed using the "Slot Cut" mode of
the computer. Table 2 is an example of the program data entered in order to cut a
single 114.3 mm X 114.3 mm X 1.0 mm (4.5 in. X 4.5 in. X 0.04 in.) Coors alumina
plate into 1 cm2 (0.16 inz) samples. Figure 3 is a schematic showing slot cutting
process for the first two outs of a sample cut using the data values shown in Table 2.
The program data in Table 2 were set up to make nine initial cuts which made ten 10
mm X 114.3 mm X 1.0 mm (0.4 in. X 4.5 in. X 0.04 in.) strips. The sample plate
mounted on the saw was then rotated 90° and remounted, and the computer controlled
cutting was then resumed to make the 9 additional cuts necessary to make 10 mm X
10 mm X 1.0 mm (0.4 in. X 0.4 in. X 0.04 in.) square samples.

During computer control cutting, the sample was cyclically moved back and
forth to the left and right (Figure 3). When the sample was changing directions, the
saw blade was moved down toward the sample in incremental steps (Figure 3).

Initially, the saw blade was moved down a larger distance referred to as a rough

43

Table 2 Example of the program data entered in order to cut a single 114.3 X 114.3
‘X 1.0 mm (4.5 X 4.5 X 0.04 inch) Coors alumina plate into 1 cm2 (0.16 inz) samples
using the computer control of the high speed cutting saw. (Note that 0 indicates
keyboard keys that were hit or data that was entered).

Main Menu
<F2> Program Selection
<F2> Slot Grind
<Page>
<F1> Routines <01>
<F2> Cycles <0>
<F3> R-Rghinc <00.2>
<F4> L-Rghinc <00.2>
<F5> R-Fininc <00.00005>
<F6> L—Fininc <00.00005>
<F7> Dwell <0.5>
<F8> x-alt-y <Yes>
<Page>
<F1> Spindle <Yes>
<F2> Coolant <Yes>
<F3> erhead <No>
<F4> Aux <No>
<F5> Sprkout <00>
<F6> Z-Ref <0.5>
<F7> Dress <No>
<Page>
<Fl> Z1 Total <01.0450>
<F2> Rapid <0.0>
<F3> RH Dis <00.9999>
<F4> Y1 Index <00.45>
<FS> Repeats <008>
<F6> Y2 Start <0.0>
<Page>

44

increment After moving in rough increments for a preset distance, RH Dis (Table 3),
the sample was moved a smaller distance referred to as a fine increment (Figure 3).
The saw continued to increment down in the z-direction and cutting through the
sample in fine increments until a preset distance of travel was reached which was
referred to as 21 Total (Table 3 and Figure 3). When the cut was completed, the saw
blade raised above the sample and moved in the y-direction to the location of the next

cut (Figure 3) where the process was repeated.

3.3.2 Polishing

Polishing of the ceramic materials was performed on an automatic polisher (Leco VP-
50 12" Wheel Polisher with AP-50 Auto Polishing Attachment). To automatically
polish samples, the samples had to be mounted on a special polishing plate (Figure 4).
The samples were mounted using thermoset in a similar manner to that described in
Section 3.3.1.2.1. The polishing plate was heated on the hot plate and thermoset was
melted on the surface in locations where samples were to be placed. From four to
twenty one specimens were placed in a circular pattern and about 32 mm (1.25 in.)
from the edge of the polishing plate (Figure 4). The samples were also placed such

that they were evenly spaced with respect to distance between each sample.

3.3.2.1 Polishing Compound
Diamond polishing compound (Warren Diamond Synthetic Diamond Paste - Medium
Concentration) was used to polish the specimens with the usual sequence of polishing

compounds being 20, 17, 15, 10, 6, and 1 micron. The time at each grit size varied,

45

Saw blade:
moves in steps as
sample changes left

 

 

  
 

and right directions = 00000
x
x Rough
1' Increments
I: of 0.2"
Y = 0.0" — z = 0.9999
Y = 0.45: .59°°"d.-~ -
C'u't ' ' ' '- Flne
Increments
of 0.00005'
0045'. 2 = 1.0450
Thick

 

X:
Sample moves continuously left and right
Figure 3 Schematic of computer controlled cutting on the high speed saw showing
rough and fine incremental movements of the saw blade, continuous movements of the
sample, and locations of the first two cuts, for a sample cut using the data values
shown in Table 2.

E 1:. [El 5'! 1:. [El

Polishing 18'7
Samples :.l mm

   

  

 

_1L “

Figure 4 Schematic of samples mounted on polishing plate for automatic polishing.
(From four to twenty one specimens were polished at one time).

46

but the normal polishing times were 15, 45, 30, 30, 30, and 30 minutes, respectively,

for the normal sequence of polishing compounds.

3.2.2.2 Polishing Cloth and Oil

The type of polishing cloth and the type of polishing oil used with the diamond
polishing compound was extremely important. Two types of polishing cloths were
used. One of the polishing clothes was used only for the diamond paste sizes of 20
microns and larger (Buehler Ultrapad) and the other was used for all diamond paste
sizes less than 20 microns (Leco Techtronic). Originally silicon oil was used during
polishing, but a commercial polishing oil was found to be more effective (Leco
Microid Diamond Compound Extender). While the silicon oil could be handled
without worry of skin contact, the commercial polishing oil which contained ethylene
glycol was an EXTREME skin irritant. Whenever polishing was performed with the
commercial polishing oil, contact with the oil was avoided and protective gloves were
worn.

The polishing cloths had adhesive backing and were mounted directly onto the
polishing platen (Leco 12" Aluminum or Leco 12" Brass Platen). The polishing cloths
were expensive and the adhesive backing was extremely sticky, so care had to be
taken when mounting the polishing cloths. To mount the cloths, a ring cover was
made from the protective circular cover which was placed over the adhesive of a
polishing a polishing cloth by the manufacturer. The circular cover was removed from
the back of a polishing cloth and had the center cut out so that a ring of only the

outside 75 mm (3 in.) remained. The ring cover also had a single cut across it so that

47

it was no longer continuous. The ring cover was placed on the adhesive back of the
new polishing cloth. The polishing cloth was then aligned on the polishing platen.
The center of the polishing cloth was depressed so that the adhesive stuck and the ring
cover was removed from the adhesive back. The rest of the adhesive back was
depressed starting at the center and working outward so as to try to prevent any air
bubbles to be trapped. Air bubbles in the cloth can result in the tearing of the cloth

during polishing and possible damage to the samples and/or the polisher.

3.2.2.3 Charging the Polishing Cloth

Once a polishing cloth was placed on a platen, the platen was placed on the polisher
and the polishing cloth was charged with diamond paste. About 1-2 ml of polishing
oil was placed on the polishing cloth. The polishing wheel was then started and the
polishing oil was spread evenly across the surface of the polishing cloth. The
polishing wheel was subsequently shut off and diamond paste was placed in several

spots on the polishing cloth and spread evenly across the cloth surface.

3.2.2.4 Polishing Samples
Polishing consisted of a general polishing procedure that could be used for polishing
any ceramic materials and a specific polishing procedure used for polishing the

alumina.

48
3.2.2.4.1 Polishing of Ceramic Materials
To start polishing, the appropriate platen with a polishing cloth for whichever micron
diamond paste was to be used was placed on the polisher and charged as described in
section 3.2.2.3. The sample plate was placed on the polishing wheel and the
automatic polishing unit was moved over onto the sample plate. The polisher was
started at a speed of 125 RPM and the automatic polishing unit was started to move
the sample plate. The polishing was continued for the appropriate amount of time.
The polisher was then turned off and the sample plate was removed. The samples
were washed with a big brush (6 in. long and 3 in. diameter beaker brush) along with
soap (Alconox Detergent) and water to remove the polishing compound and oil. The
samples were not ultrasonically cleaned since an ultrasonic cleaner large enough to
hold the polishing plate was not available. The polishing plate and samples were dried
with paper towels. The process was then repeated for a different size polishing

compound.

3.2.2.4.2 Polishing of Alumina Specimens

The first diamond size used in polishing samples was 20 micron diamond paste. The
purpose of this step was to grind flat and polish each of the mounted samples. For
most samples, 15 minutes of polishing at 20 micron grit size was sufficient to grind
each of the mounted samples so that they were flat and all of their surface area was
ground. Some samples having irregular height or other problems were not ground flat
having portions which were not being polished after 30 minutes of polishing at 20

microns. For these samples longer times at 20 microns were necessary or larger sized

49
diamond paste was used (e.g. 25 or 35 microns).

After each of the mounted samples was ground flat, the samples were polished
for 45 minutes with the 17 micron diamond paste. The criteria for a sufficient polish
with the 17 micron diamond paste was that all of the specimens have a slightly shiny
surface. It was very important that all of the samples were slightly shiny before
moving on to the next diamond compound or very long times at the next size diamond
compound was necessary. Once the samples were sufficiently polished at 17 microns,
the samples were polished for 30 minutes with the 15 micron diamond paste. The
criteria for a sufficient polish with the 15 micron diamond paste was that all of the
specimens have a mirror-like surface. Samples that did not have a mirror surface after
the 15 micron stage never had a polished finish. Samples with a mirror finish were
then polished for 30 minutes at each of the remaining polishing steps (10, 6, and 1

micron diamond paste).

3.2.3 Indentation

Indentation was done using a commercial hardness tester (Buehler Semirnacro
Hardness Tester). The loads available with the hardness tester used were 0.98, 4.9,
9.8, 49, 98, 196 N. Along with indentation load, the loading rate could be set with a
dial in the range of 40 to 300 microns/second and the loading time could be set with a
dial in a range of 5 to 35 seconds. A Vickers indentor tip (Osaka Diamond Vickers
Indentor) was used for all indentations. The sample stage could be moved in the x-
and y-directions using two separate micrometers. The micrometers were delineated in

the SI units of millimeters and had a range of 0 to 25 mm (0 to 0.984 in.).

50

The hardness tester had an optical microscope attached which had a magnifying
factor of 200x. The optical microscope allowed for the measurement of width of the
indent impressions and length of the cracks on specimens. In the optical display there
were two lines that could be moved within the display. The distance between the lines
could be adjusted using a digital micrometer. The digital display of the micrometer
was zeroed by depressing the zeroing button, once the two lines were moved together
until they were just barely touching using the micrometer movement controls. After
being properly zeroed, the digital micrometer display gave the distance between the

lines as displayed on the specimen surface in tenths of micrometers.

3.3 Materials Characterization

The soda-lime silica glass, Coors alumina and microwaved alumina material used for
experimental studies of static fatigue and crack healing were characterized before
testing. The density of the glass and alumina was measured. The grain size of Coors

alumina and microwave alumina was measured from micrographs.

3.3.1 Density Determination
An Archimedes’ method was used to determine the density of soda-lime silica glass,
Coors alumina and microwave sintered alumina. The testing used ASTM specification

C378 as a guideline.

51

3.3.1.1 Materials Preparation for Density Measurements

Specimens of glass and Coors alumina were first cut to a smaller size from the as
received material while the microwave sintered alumina disks were used as-received
for density measurement testing. Glass specimens were cut using a low speed saw to
nominal dimensions of 76 mm X 10 mm X 1.1 mm (3.0 in X 0.4 in X 0.045 in) and
Coors alumina specimens were cut with the high speed saw to nominal dimensions of
55 mm X 10 mm X 1 mm (2.2 in X 0.4 in X 0.04 in). The glass and Coors alumina
samples were cleaned after cutting using acetone to remove the thermoset and the
cutting oil. To remove any residual oil or other possible contamination, all samples
were cleaned with soap and water (Alconox Powder Detergent), rinsed with deionized

(D.I.) water, and allowed to dry at room temperature for at least 24 hours.

3.3.1.2 Density Measurements

Weighing was performed using a balance with a display to 0.0001 g (Sartarous Model
A210P). The dry weight (Wm) of the samples was measured initially. Samples were
then placed in a beaker of DI. water. To completely wet the samples, the beaker and
samples were placed in a vacuum chamber and the vacuum chamber was evacuated
with a rotary vacuum pump for at least 5 minutes. The suspended weight (Wm) of
the samples was measured using the balance with a hook holding the sample in DI.
water. Before the sample suspended weights were taken, the balance was tared with
the hook suspended in the DI. water without a sample. After each specirnen’s
suspended weight was measured, the sample was again placed in DI. water. The wet

weight (Wm) of each sample was measured by removing the sample from the DI

52

water, dabbing it with a KimWipe to remove excess water, and placing the sample on

the balance pan.

The measured density (pmm ), was calculated using

9 :___d., . (6)

For a sintered polycrystalline sample, the maximum, theoretical, sample density is the
atomic density of a single crystal of the compound. For A1203, the theoretical density
(pm) is 3.965 g/cm3 [61]. Samples with a measured density less than the theoretical
density did not completely densify during sintering. The difference between the
measured density and the theoretical density of a sample indicates the degree of

sintering. The percentage of theoretical density was found using

 

% theoretical density = pm * 100% . (7)
pthao

3.3.2 Microstructure

Micrographs of thermally etched surfaces of Coors alumina and microwave alumina
were taken using the ESEM. The surfaces of the two types of alumina were thermally
etched during microwave heating to temperatures above 1500 °C. The grain size for
the polycrystalline alumina samples was calculated from the micrographs using a line
intercept method with a stereographic correction of 1.5. For each alumina material, a

minimum of 37 lines from three separate micrographs was used for the grain size

53

calculation.

3.4 Indentation Measurement Testing

The crack system used to study both crack healing and static fatigue in the current
investigation was the Vickers indent crack system. For a Vickers indent, the surface
lengths of the radial cracks in the x- and y-direction were measured and recorded as
2cl and 2oz, respectively. The crack lengths and especially the change in crack lengths
were used to indicate changes in crack healing or static fatigue phenomena with
changes in different variables such as time, humidity, temperature, and stress level.
Due to the importance of indentation measurements to the crack healing and static
fatigue investigations, experiments were performed to compare optical measurements
between different researchers and to compare optical and ESEM measurements, as

described below.

3.4.1 Multiple Experimenter Measurements

Samples of borosilicate glass, Coors Alumina, Microwave Alumina and Silicon Nitride
were used. The samples were cut with a low speed diamond saw (Section 3.2.1.1) and
the polycrystalline samples were polished to a 1 micron finish (Section 3.2.2). Each
sample had a Vickers indent placed on the polished surface (Section 3.2.3) by a single
experimenter. The x- and y-direction crack lengths (2cl and 2c?) of the indents were
measured five different times by each of six different experimenters using the optical
microscope attached to the indentor (Section 3.2.3). The mean and standard deviation

was determined for each experimenter’s five measurements of a given crack length. A

54
group average for a given crack was determined from the mean crack lengths recorded

for each of the six experimenters.

3.4.2 Optical and Environmental Scanning Electron Microscope Measurements
The x- and y-direction crack lengths (2cl and 2c,) of the indents for the glass, Coors
Alumina and Microwave Alumina were measured using the Environmental Scanning
Electron Microscope (ESEM). The indent lengths were measured: (1) on the ESEM
screen using the ESEM computer and (2) manually from the micrographs taken on the
ESEM. The crack lengths measured on the ESEM screen used the ESEM computer
measurement tool which entailed clicking the computer mouse at both ends of the
crack being measured and recording the computer determined length. The cracks were
measured from 200 X 200 mm (8 X 8 inch) micrographs by measuring the length of
the crack with a ruler, measuring the micron bar length with a ruler, and calculating

the crack length.

3.5 Static Fatigue: ESEM Crack Growth Investigations

In-situ observation of crack growth in ceramics under constant applied load was
performed using the Environmental Scanning Electron Microscope. Tensile specimens
of glass and Coors alumina were prepared for the study. A Vickers indent was placed
on the center of one of the tensile specimen faces, was located, and observed in the

ESEM. The effects of constant applied load, humidity, and time upon crack growth

were investigated

 

55

3.5.1 Ceramic Tensile Specimen Preparation

Tensile specimens for static fatigue testing of soda-lime silica glass and Coors alumina
were made by using a tabbing technique normally used in the tensile testing of
composite materials (ASTM D3039). The tabs were made from either a glass-epoxy
composite or stainless steel. The tabs were mounted onto the specimens using an

epoxy adhesive or a high temperature cement (Figure 5).

3.5.1.1 Preparation of Rectangular Specimens of Glass and Coors Alumina
Rectangular specimens of soda-lime silicate glass were cut using the low speed
diamond saw (Section 3.2.1.1) to dimensions of 10 mm X 50 mm X 1.1 mm (0.4 in.
X 2.0 in. X 0.04 in.). After cutting, the lengthwise edges of the rectangular specimens
were beveled with 240, 320, 400 and 600 grit SiC fixed-abrasive paper. The samples
were ultrasonically cleaned in DI. water to remove grinding debris.

Coors alumina specimens were cut using the high speed diamond saw (Section
3.2.1.2) to dimensions of 10 mm X 55 mm X 1 mm (0.4 in. X 2.17 in. X 0.04 in.).
After cutting, the specimens were polished to a 1 micron finish using an automatic
polisher, as described in Section 3.2.2. Four or five specimens were mounted at a
time for polishing. Once the specimens were removed from the polishing plate, the
edges of static fatigue specimens were beveled with 240, 320, 400 and 600 grit SiC

fixed-abrasive paper. After edge beveling the samples were ultrasonically cleaned in

D.I. water to remove debris from polishing or grinding.

56

TQQ Vigw
1‘ 57mm 4

 

 

 

 

 

 

38mm 9.5mm

Vicke rs
Indent

 

 

   

\ Vickers Indent

Figure 5 Schematic of tabbed tensile specimens used in static fatigue testing (note
indent size is exaggerated).

57

3.5.1.2 Preparation of Specimen Tabs
Tabs for making tensile specimens were fabricated from either a glass-epoxy
composite or stainless steel. The composite tabs were made from a 1.9 mm (0.075
in.) thick composite plate composed of alternating 0°/90° layers of E293 epoxy
reinforced with 7781 glass fibers. The stainless steel tabs were made from a 3.175
mm (0.125 in.) thick, 304 stainless steel strip.

The composite material and stainless steel strips were cut into 10 mm X 10
mm (0.394 in. X 0.394 in.) squares. In some cases, the stainless steel squares were
then cold rolled to a thickness of 2.1 mm (0.09 in.). All composite and cold rolled
stainless steel squares were ground on a 120 grit belt grinder to smooth rough sides

and to place an angle of approximately 45’ on one of the sides.

3.5.1.3 Tab Attachment onto Rectangular Ceramic Specimens
The tabs were mounted on rectangular specimens (Figure 5) of soda-lime silicate glass
and polished Coors alumina using either epoxy (Omega, Omegabond 200) or high
temperature cement (Omega cc High Temperature Cement). The epoxy adhesive was
purchased in packages which had premeasured quantities of resin and catalyst. The
epoxy was mixed in the package before mounting the tabs. The high temperature
cement was mixed using approximately 3 parts powder to 1 part of the liquid. The
liquid was added to the cement mixture until the cement paste reduced in viscosity to
the point that the cement could be spread evenly.

To keep the adhesive from getting on the glass and Coors alumina specimen

surfaces, and to help keep the desired gage length, the rectangular specimens were

58

wrapped in paper out to a width of 27 mm (1.063 in.) or 35 mm (1.378 in.) for glass
and Coors alumina, respectively. After the specimens were wrapped, the epoxy or
cement adhesive was placed on the ends of the specimens using 2.1 mm (0.083 in.)
diameter wooden applicators and 4 tabs were placed on the top and bottom of each
specirnen’s ends (Figure 5). The tabs were moved in a small circular motion to aid in
getting complete wetting of the adhesive to the tab and the specimen. The tabs were
re-aligned by hand once the specimen was set down.

The adhesives used had to cure before the specimens were ready for testing.
The tensile specimens prepared using the epoxy adhesive were cured at 220 °C for 3.5
hours in a furnace (Lindburg 1200 °C Box Muffle Furnace). Tensile specimens
prepared using the high temperature cement were cured for 24 hours at room
temperature. For some of the stainless steel tabbed specimens, after the tabs were
cured, each side of the specimen was ground on 240 grit SiC paper to help reduce
non-parallelness between the tabs at either end of the specimen and thus reduce

torsional forces upon loading.

3.5.2 Vickers Indentation Cracks on Tensile Specimens

A single Vickers indent was placed in the center of the face of the glass and Coors
alumina tensile specimens. For the glass specimens, the Vickers indent was made
using a 9.8 N load, a loading rate of 70 urn/sec, and a load time of 15 seconds. For
the Coors alumina specimens, the Vickers indent was made using a 49 or 98 N load, a
loading rate of 70 rim/sec, and a load time of 15 seconds. The location of the indent

was marked with a black marker (Sanford Sharpie Permanent Marker). The location

59

was indicated by two lines starting next to the indent, with one line going at a +45°
angle and the other going at a -45° angle to the edge of the specimen.

As a Vickers indentor tip is unloaded from the surface of a ceramic, a residual
tensile field is developed from the indentation impression that was formed. The
residual stress provides a driving force for the growth of radial cracks [62]. The
growth of the radial cracks is balance by the fracture toughness of the material [62].
After an indentor is removed from a ceramic surface, the radial cracks may continue
to grow due to environmental subcritical crack growth [63]. The slow crack growth of
the radial cracks will decrease as the crack length increases [63] and will saturate in
time. Consequently, all specimens indented in this work were aged for 24 hours
before testing to allow for the slow crack growth to saturate. For the static fatigue
testing, indented tensile specimens were aged for 24 hours in air so that the crack
length changes measured during testing would be the result of static fatigue crack
growth from the externally applied stress and not the result of slow crack growth from

the residual stress field of the indent impression.

3.5.3 ESEM Testing

All Environmental Scanning Electron Microscopy testing in the current study was
performed using a Philips Electroscan Model 2020 ESEM with water vapor as the fill
gas. All specimens tested in the current study were observed in the ESEM without a
conductive coatingfi A LaB6 filament with a 20 KeV accelerating voltage was used
along with the second largest objective aperture to image the ceramic specimens.

When micrographs were taken, the ESEM chamber pressure was maintained in the

60

range of 1.7 to 2.5 Torr to provide the optimum balance between a pressure large
enough to reduce charging and provide a strong signal for increased resolution and a
pressure low enough to not cause a reduction in the signal from interference from the
increased number of gas molecules between the sample and the electron detector.

For static fatigue testing a tensile stage (No. 18211 Tensile Substage, Ernest F.
Fullam Inc., Latham, NY) was used along with the bullet gaseous electron detector.
The tensile stage had a self tightening grip design with load applied by a screw driven
mechanism. The load measured by the tensile stage load cell was displayed on an
external display in units of pounds. The load was controlled manually through the

ESEM’s Rotation stage control.

3.5.3.1 Control of Relative Humidity in the ESEM
The relative humidity was controlled in the ESEM sample chamber using H20 as the
fill gas. Danilatos [54] details the functional dependance of relative humidity on
temperature and pressure and the control of relative humidity in an ESEM (Figure 6).
The relative humidity in the ESEM specimen chamber was regulated by the
ESEM chamber pressure and the sample temperature. The chamber pressure was
computer controlled to levels set by the operator. The chamber pressure could be
varied between 0 and 10 Torr. For optimum resolution for the ceramic specimens
tested, the ideal chamber pressure was in the range of 1.7 to 2.5 Torr. At lower (less
than about 1.5 Torr) and higher (greater then about 3.0 Torr) pressure the resolution of

the ESEM decreased.

61

 

10

.‘1
or
r

Chgmber Pressure (Torr)
a» r

 

 

 

 

Temperature (°C)

Figure 6 Plot of ESEM chamber pressure versus temperature showing curves of
constant relative humidity [after 53].

62
3.5.3.2 Placement of Specimens in the Tensile Stage
During standard Operating procedures for ESEM operation, the stage controls went
through an automatic calibration sequence. The tensile stage had to be disconnected
and removed from the ESEM before this calibration sequence or the large tensile stage
would damage the ESEM. In order to mount the specimen for testing, the rotation
control switch was used to increase or decrease the tensile stage’s gage length. Once
the proper gage length was reached, the specimen could be mounted in the tensile
stage by tightening the two bolts on each of the two top grip plates. Due to the self-
tightening design of the grips, a small tensile load was applied as the bolts on the grip
plates were tightened.

After the specimen was mounted in the tensile stage, the tensile stage needed to
be removed from the ESEM and the ESEM stage controls needed to be calibrated
again. The re-calibration of the stage controls was performed in order to zero the
rotation stage control. The ESEM automatically zeros the rotation when the ESEM
chamber door is closed. If the rotation was not already at zero, then specimen fracture
occurred as the ESEM returned the rotation to zero which resulted in a large tensile or
compressive load applied to the sample. After re-calibration, the tensile stage was
attached to the ESEM, the ESEM chamber door was closed, and the specimen

chamber was evacuated down to the single digit Torr range.

3.5.3.3 Static Fatigue Testing
Normal ESEM operating procedures were followed with a sample chamber pressure of

about 2.4 Torr, which resulted in a humidity level of about 10%. After the electron

63

beam was aligned and the indent was located, micrographs of the indentation cracks
were taken to determine the initial specirnen’s crack lengths. The load applied to the
sample was increased to the level at which static fatigue testing was to occur.
Micrographs of the indentation cracks were taken at this point to determine whether or
not crack growth had occurred due to the increase in load.

When the desired load for static fatigue testing was reached, the relative
humidity was increased to 21, 32, or 42 % by increasing the water vapor pressure to
5.0, 7.5, or 10.0 Torr in the ESEM sample chamber. The increased humidity level
was held for time intervals of usually 25 minutes or more. After the desired time
interval at the raised humidity level, the ESEM sample chamber pressure was reduced
to 2.5 Torr so that micrographs were taken at maximum resolution. After the
micrographs were taken, the humidity and applied load were adjusted to desired levels

for another static fatigue time interval and the process was repeated.

3.6 Crack Healing

Crack healing investigations were performed with: 1) in-situ heating and in-situ
observation using an Environmental Scanning Electron Microscope (ESEM), 2)
conventional heating and observation using optical microscopy before and after
thermal annealing, and 3) microwave heating and observation using optical microscopy

before and after thermal annealing.

64
3.6.1 In-Situ Healing Investigations using an ESEM
In-situ observation of the healing of Vickers indents in soda-lime-silicate glass was
performed using an Environmental Scanning Electron Microscope. The change in
crack length and crack morphology as a function of time and temperature was studied.
The effect of the initial humidity level on the crack healing behavior was also
investigated in-situ by varying the initial temperature of the sample and ESEM sample

chamber pressure to change the initial humidity conditions of the sample.

3.6.1.1 Soda-Lime Silica Glass Specimens

The glass specimens used for the in-situ ESEM crack healing study were cut using a
low speed diamond saw (described in Section 3.2.1.1). The comers of the cut 4 mm
X 4 mm X 1.1 mm (0.158 in. X 0.158 in. X 0.045 in.) specimens were slightly
rounded by sequentially using 240 and 400 grit SiC fixed-abrasive paper. A Vickers
indent was placed in the center of a 4 mm X 4 nun (0.158 in. X 0158 in.) specimen
face with a 9.8 N load applied using a loading speed of 15 urn/sec and load time of 70
seconds. The location of the indent was marked with a black marker (Sanford Sharpie
Permanent Marker) to aid in locating the indent on the sample surface in the ESEM

(Figure 7). The indented specimens were aged for at least 24 hours before testing.

3.6.1.2 Setting Relative Humidity before Crack Healing Testing
As described in Section 3.5.3.1, the level of relative humidity can be set in an ESEM
by controlling the ESEM sample chamber pressure and the temperature. For optimum

resolution for the glass specimens tested, the chamber pressure used was in the range

 

65
of 1.7 to 2.5 Torr. The initial temperature of the specimen was regulated by the
circulating water system for the hot stage in order to set the relative humidity of the
sample chamber using pressures in the range of 1.7 to 2.5 Torr. The water
temperature was controlled by a chiller (Endocal RTE-100, NESLAB Instruments, Inc.,
Newington, NH) which was capable of both heating and cooling the water. The water
chiller temperature was adjusted by the temperature dial on the chiller and measured

by a mercury in glass thermometer submerged in the cooling water reservoir.

3.6.1.3 In-situ ESEM Testing
The glass specimens were tested in an ESEM (Philips-Electroscan Model 2020 ESEM)

using a special high temperature gaseous electron detector and a hot stage (Philips-
Electroscan ESEM Hot Stage) capable of temperatures up to 1000 °C. A small
ceramic crucible with an inner diameter of 5.7 mm (0.224 in.) and an inner depth of
1.15 mm (0.045 in.) held the sample in the hot stage. The sample was fixed to the
crucible using silver paint. The crucible was placed on top of a small silicon carbide
disk (approximately 0.75 mm (0.03 in.) thick) which rested on the top of the small
heating elements of the hot stage (Figure 8).

Once the specimen was placed in the ESEM hot stage, the chamber was
evacuated and the ESEM electron beam was aligned. The initial relative humidity
was set by the temperature of the sample (which could be reduced from room
temperature via the cooling water) and by the pressure in the ESEM sample chamber

(Section 3.6.1.2). Micrographs of the initial indent cracks were taken before the

specimen was heated.

 

66

Markings to help
locate indent
in ESEM 4

 

Figure 7 Schematic of soda-lime silica glass specimens used in ESEM investigations
of crack healing.

lndented Glass Specimen

 
  
   
 

 

1.1
Atiixed with
mm Silver Paint
1.15 .
mm Crucrble
0.9
mm
0.75
mm SiC Block
Heating
Element

Top of Heating Assembly
Figure 8 Schematic of the ESEM hot stage showing the top of the heater assembly,
the silicon carbide spacer, the crucible and the indented glass specimen.

67

The heating schedule was selected by specifying a list of data for temperature
set point, ramp rate, and dwell time. Once heating began, micrographs of the indent
cracks were taken at selected times and temperatures. When the micro graphs were
taken, the water flow from the chiller was temporarily turned off in order to increase
resolution by reducing vibrations caused by the water flow. When micrographs were
not being taken, the magnification was reduced along with the brightness and contrast.
A complete experiment typically took from 3.5 to 6 hours of ESEM beam time along

with about 2 hours of setup and clean up.

3.6.1.3.1 Healing at Temperatures up to 600 °C (Experiments A and B)

The reduction in crack length and the changes in crack shape for glass specimens were
investigated for healing temperatures up to 600 °C or higher. The heating rates and
dwell times for the two samples heated to temperatures of 600 °C and higher are

shown in Tables 3 and 4.

3.6.1.3.2 Healing as a Function of Temperature (Experiment C)
The healing behavior of the indent crack in glass was investigated as a function of
temperature from room temperature to 490 °C. The heating rates and dwell times for

this experiment are shown in Table 5.

3.6.1.3.3 Healing as a function of Time at 430 ’C (Experiment D)
Healing was investigated as a function of time with temperature fixed at 430 °C. The

heating rates and dwell times for Experiment D are shown in Table 6.

Table 3 ESEM hot stage heating schedule for the experiment investigating healing up

to 600 °C (Experiment A).

68

 

 

 

 

 

 

 

 

 

 

Ramp Set Point Ramp Rate Dwell Time
Cycle (°C) (°C/minute) (min.)

1 300 20 5

2 400 20 10

3 500 10 20

4 550 5 30

5 600 2 135

 

Table 4 ESEM hot stage heating schedule for the experiment investigating healing up

to 610 °C (Experiment B).

 

 

 

 

 

 

 

 

 

 

 

 

Ramp Set Point Ramp Rate Dwell Time
Cycle (°C) (°C/minute) (min.)

1 400 20 1

2 500 10 30

3 550 5 1 10

4 560 1 15

5 575 1 35

6 600 1 30

7 610 1 10

 

 

 

69

Table 5 ESEM hot stage heating schedule for experiment investigating healing as a
function of temperature (Experiment C).

 

 

 

 

 

 

 

Ramp Set Point Ramp Rate Dwell Time
Cycle (°C) (°C/minute) (min.)

1 400 20 10

2 430 5 35

3 450 1 10

4 470 1 10

5 490 l 40

 

 

 

 

 

Table 6 ESEM hot stage heating schedule for initial experiment investigating healing
as a function of time at a fixed temperature of 430 “C (Experiment D).

 

 

 

 

 

 

 

 

Ramp Set Point Ramp Rate Dwell Time
Cycle (°C) (°C/minute) (min.)

1 370 20 15

2 400 5 15

3 430 2 30

4 *25* #201: an:

5 370 20 15

6 430 10 17 5

 

 

 

 

 

* ESEM shut down, so specimen was cooled to room temperature and

was re-booted.

the ESEM

7O

3.6.1.3.4 Healing as a function of Relative Humidity (Experiments E-H)
Healing was investigated as a function of initial relative humidity levels for isothermal
holds at 430 °C. For Experiments E-H, the initial relative humidity levels were set at
8, 16, 32, or 64%, respectively. The heating rates and dwell times used for

Experiments E—H were identical and are shown in Table 7.

3.6.1.3.5 Healing with New Hot Stage Heater (Experiments I-M)
After another operator had damaged the hot stage and a new heater was installed on
the hot stage, healing was investigated as a function of initial relative humidity levels
for isothermal holds at 430 °C. For Experiments I-M, the initial relative humidity
level was set at 48%. The heating rates and dwell times used for Experiments I-M
were the same as Experiments E-H and are shown in Table 7.

In Experiment M, a K-type thermocouple (Omega 0.005 inch diameter K-Type
Wire) was mounted to a glass specimen using high temperature cement (Omega cc
High Temperature Cement) and the specimen was mounted to the crucible with high
temperature cement (Figure 9). The K-type thermocouple was connected to the extra
thermocouple connection in the door of the ESEM. The connection on the outside of
the ESEM door was connected to a K-type Ice Point (Omega K-type Ice Point) which
was connected to a digital voltmeter. The temperature was found using the voltage

reading and standard thermocouple tables.

71

Table 7 ESEM hot stage heating schedule for experiments investigating healing as a
function of time at a fixed temperature of 430 °C (Experiments E-H).

 

 

 

 

 

 

 

 

 

 

Ramp Set Point Ramp Rate Dwell Time
Cycle (°C) (°C/minute) (min.)
1 370 20 15
2 400 10 15
3 430 5 90
C t B d'
We?“ righteofihé'li,
Specimen Sample Surface

K-T e
Thermoygouple
+

  

Cement bonding
Specrmen In
rucr e

Heating
Element

Top of Heating Assembly

Figure 9 Schematic of the second ESEM hot stage showing the top of the heater
assembly, the crucible and the glass specimen with a K-Type thermocouple attached.

72

3.6.1.4 Temperature Measurement of New Hot Stage Heater

The temperature at the sample surface was compared to the ESEM controller
temperature reading for three sets of conditions. The first and second investigations
used a sample cemented in a crucible with a thermocouple bonded to the sample
surface (Figure 9). For the third investigation a thermocouple was bonded directly to
the crucible with silver paint. In the first investigation, the crucible was set on top of
the heater assembly, while in the second and third investigations the crucible was
bonded to the heater assembly with silver paint. In all three investigations the
thermocouple was connected to the extra thermocouple connection in the door of the
sample chamber. The sample temperature was measured using an ice point, digital
voltmeter, and thermocouple tables. The ESEM controller temperature was read
directly from the hot stage controller digital display.

Also studied during the first investigation was the precision of the
thermocouple reading using the ESEM chamber door pass-through port. The precision
of the thermocouple reading using the pass-through port was determined during an
isothermal hold at 430 °C by comparing the temperature reading using the pass-
through to a direct thermocouple reading inside the ESEM chamber. The temperature
inside the sample chamber was determined by connecting the thermocouple to an ice
point and voltmeter inside the sample chamber and reading the voltmeter through a
sample chamber view port. The temperature using the pass-through was determined
by connecting the thermocouple to the pass-through port inside the ESEM chamber,
connecting an ice point and voltmeter to the pass-through port outside the ESEM, and

reading the voltmeter.

73

3.6.2 Conventional Experiments

Conventional crack healing experiments were performed on soda-lime silica glass,
Coors alumina and microwave sintered alumina specimens. In conventional crack
healing experiments, cracks were made in a specimen, aged, characterized, heated in a
furnace, and then re-characterized to note changes in the cracks brought on by the

healing cycle.

3.6.2.1 Conventional Healing Procedure

Specimens of a specific geometry and size were prepared. Selected glass samples then
underwent a heating cycle to remove the residual stresses created by sample
preparation. Vickers indent cracks were made in the sample with a set load, loading
rate, and load time. The specimens with the indent cracks were aged for 24 or 48
hours in laboratory air (about 45 %r.h.), a desiccator (about 0 %r.h.), or a wet
chamber (about 100 %r.h.) before characterization and healing. Characterization was
performed using the optical microscope part of the indentor to measure the crack
lengths (2cl and 2c?) and to sketch the crack shapes. Thermal annealing via
conventional furnace heating consisted of placing the sample in a furnace boat, placing
the boat in a tube furnace, ramping to a predetermined temperature, holding for a
predetermined amount of time, and cooling to room temperature. After the thermal
annealing cycle, the crack lengths (2cl and 2c?) were measured and the crack shapes

were sketched using the optical microscope part of the indentor.

74
3.6.2.1.] Temperature Measurement during Conventional Healing
The temperature was measured during conventional healing using either a J-Type
thermocouple or an R-Type thermocouple. The J-Type thermocouple wire (Omega
0.010 inch Iron—Constantan Thermocouple wire) was used for temperature
measurements of less than 700 °C. The R-Type thermocouple wire (Omega 0.015 inch
Platinum-Platinum/ 13%Rhodium Thermocouple wire) was used for temperature
measurements above 700 °C.

The thermocouples were attached to an Ice-Point of the same type as the
thermocouple wire (Omega J-Type or R-Type Ice Point). The J -Type thermocouple
voltage was read with a digital voltmeter (Fluke Model 77 Multimeter) attached to the
output of the Ice-Point using the 300 mV scale. The R-type thermocouple voltage was
recorded on a chart recorder (Cole Parmer 2 Channel 200 mm Flatbed Chart Recorder)
with 20 mV full scale and a chart speed of 10 cm per hour. The voltage (read from
the digital voltmeter or the chart recording) was converted to temperature using

Thermocouple Reference Tables (Omega Thermocouple Reference Tables).

3.6.2.1.2 Conventional Furnaces Used for Healing

Two furnaces were used for conventional healing: 1) a large tube furnace capable of
temperatures up to 1500 °C and 2) a small tube furnace capable of temperatures up to
1000 °C. The large tube furnace (MRL Thermtec Horizontal 30" Hot Zone Tube
Furnace) had a controller (Omega 812 Four Segment Programmable Controller) which
allowed ramp rate, hold temperature and hold time to be set. The furnace cooled at

the rate set on the controller until the temperature decreased to approximately 450 °C,

75

after which the furnace "free" cooled to room temperature due to the large thermal
mass of the furnace.

The small tube furnace was made at MSU. The tube furnace had a 76 mm (3
inch) irmer diameter and 305 mm (12 inch) long heating element (NR3-4 Insulated
Nicrome Wire Electric Heating Element by CM, Inc., Bloomfield, NJ.) which was
surrounded by insulation and encased in a 305 mm (12 inch) diameter by 380 mm (15
inch) long stainless steel cover. Inserted inside the cylindrical heating element was a
25 mm (1 inch) diameter, 1.5 mm (0.6 inch) thick and 405 mm (16 inch) long, open
ended, glass tube. On the top, outer surface of the glass tube was a K-Type
thermocouple (Omega 0.0005 inch thick "cement on" foil thermocouple) which was
mounted with thermocouple cement (Omega cc high temperature cement). The
thermocouple was connected to a controller (Omega CN5001K2). The controller only
allowed a single temperature to be set and did not allow other parameters such as
heating rate or hold time to be set. Since the hold time was not automatically
controlled, when the sample temperature reached the desired temperature the time was
noted and after the desired amount of time had passed the furnace was unplugged and
allowed to cool to room temperature. The furnace ramp rate was approximately 7

°C/minute.

3.6.2.1.3 Specimen Placement into the Tube Furnaces
The indented and aged specimens were placed in a boat with a 1-2 mm (0.04-0.08 in.)
thick layer of alumina powder (Buehler Micropolish A) in the bottom (to prevent the

sample sticking to the boat). For the small tube furnace, the boat (Coors CB 10

76

65564) was inserted into the furnace tube a distance of 229 mm (9 in.). For the large
tube furnace, a rectangular boat (Coors 03526) with dimensions of 100 mm X 45 mm
X 19 mm (3.94 in. X 1.77 in. X 0.75 in.) or a tube dee with dimensions of 254 mm X
38.1 mm (10 in. X 1.5 in.) was inserted into the furnace tube a distance of 765 m
(30.13 in.). The thermocouple used for temperature measurement was inserted with
the boat such that the thermocouple was at the same position in the furnace tube as the
specimens. Once the sample and thermocouple were in place, a piece of fibrous
insulation (AP Green Inswool HTZ) was used to fill and insulate the opening of the

furnace tube.

3.6.2.2 Healing in Soda-Lime Silica Glass

Seven different experiments with a total of 113 specimens and 654 cracks were used
to investigate healing in soda-lime silica glass (Table 8). The specimens were
prepared (Table 9), heated to remove residual stress (Table 9), indented (Table 9 and
10), aged for 24 hours (Table 9), and annealed (Table 8 and 9). Some specimens
underwent a heating cycle after preparation to relieve the specimen residual stress

(Table 9 and 11).

3.6.2.2.] Soda-Lime Silica Healing Specimen Preparation

For crack healing in soda-lime silica glass, long rectangular specimens and small
square specimens were used (Table 9). The long rectangular specimens were cut with
the high speed saw (Section 3.2.1.2) to nominal dimensions of 76 mm X 11.4 rrrrn X

1.1 mm (3.0 in. X 0.45 in. X 0.045 in.). The small square specimens were cut with

 

 

 

 

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Table 10 Indentation conditions referred to in Table 9 for soda-lime silica specimens
used in conventional healing (Experiments 1-7).

 

 

 

 

Indenting Condition Load Loading Rate Loading Time
(N) (pm/S) (S)
or 9.8 50 10
B 9.8 70 15

 

 

 

 

 

Table 11 Stress relief cycles referred to in Table 9 for soda-lime silica specimens used
in conventional healing (Experiments 1-7).

 

 

 

 

 

 

 

Stress Prior Stress Furnace Hold Hold Ramp Rate
Relief Relief Temperature (°C) Time ("C/Minute)
Cycle Cycle (Minutes)
A None Box Muffle 550 30 Unknown
B None Box Muffle 600 60 Unknown
C None Rapid Temp 587 180 ~ 8
D C Large Tube 587 180 10
E D Large Tube 587 180 5

 

 

 

 

 

 

 

80

0.8 0.8
mm mm

 

Figure 10 Schematic of indent placement in the rectangular glass specimens used in
conventional healing Experiments 1 and 2 (note that the while the indent locations are
to scale the indent sizes are exaggerated).

2.0 mm

2.0 mm

 

L

.I

.14
[ 2.0mm T 2.0mm 7|

Figure 11 Schematic of indent placement in the square glass specimens used in
conventional healing Experiments 3 - 7 (note that the while the indent locations are to
scale the indent sizes are exaggerated).

81

Glass Healing
Specimen Mullite

 

 

 

Alumina
Powder
Bed

Figure 12 Schematic of specimen location on the tube dee for conventional healing in
glass Experiments 1 and 2.

Borosilicate
Glass Specimens

Mullite

5 Boat

    

Figure 13 Schematic of specimen location on the boat for conventional healing in
glass Experiments 3 - 7.

82

AIumina Mullite
Powder Bed S Boat

‘1 Soda-Lime Silica
Specimen

 

Figure 14 Schematic of specimen location in the boat for conventional healing in
glass Experiment 7 and conventional healing in alumina Experiment 2.

83

the low speed saw (Section 3.2.1.1) to nominal dimensions of 7.5 mm X 7.5 mm X
1.1 mm (0.3 in. X 0.3 in. X 0.045 in.).

The rectangular specimens had the long 76 mm X 1.1 mm (3.0 in. X 0.045 in.)
edges of the specimens beveled using 240, 320, 400, and 600 grit SiC grinding paper
(Mager Scientific C Weight Waterproof Paper). The square specimens were ground
using 240, and 400 grit SiC grinding paper to remove chips formed during cutting.
For some of the square samples, one, two, or three comers were ground flat to help
indicate specimen orientation and to help differentiate specimens with different
annealing or aging conditions. All specimens were rinsed after grinding or beveling

with tap water and placed on laboratory paper towels.

3.6.2.2.2 Relief of Specimen Residual Stress

Before indentation, some soda-lime silica healing specimens underwent a heating cycle
to relieve the residual stress created during sample preparation (Tables 9 and 11).
Heating was performed in one of three different furnaces: 1) a box muffle furnace
(Lindburg 1200 °C Box Muffle Furnace: 7.5 in. X 5.25 in. X 14 in.) without an
independent means of sample temperature measurement, 2) a rapid temp furnace (C*M
Rapid Temp Furnace) with a J-Type thermocouple used for sample temperature
measurement, 3) the large tube furnace (Section 3.6.2.1.2) with an R-Type

thermocouple used for sample temperature measurement.

84
3.6.2.2.3 Strength Testing and Sub-Surface Healing (Experiments 1 and 2)
In addition to the 10 healing samples prepared for Experiment 1 (Table 7 and 8), two
additional samples were prepared and were left to continue to age in air without
thermal annealing. After the annealed samples had cooled and all the crack lengths
were measured, all 12 specimens were tested in three-point bend using a displacement
controlled mechanical testing machine (Instron model 4206 Automated Testing
System, Canton, MA). The samples were tested in laboratory air with a crosshead
speed of 0.50 mm/minute (0.02 inch/minute) and an outer span distance of 60 mm (2.4
inch). The initial dimensions of width and thickness, the fracture load and
displacement, and the location of the fracture were recorded for each sample. From
the initial sample dimensions and the fracture load, the fracture stress (Modulus of
Rupture) was calculated.

To investigate the sub-surface crack healing for each of the 6 specimens healed
in Experiment 2 (Table 7 and 8), a method originally developed by Kirchner [64] was
used in an attempt to fracture through the partially healed indents. Kirchner’s [64]
technique was used to avoid subcritical crack extension of the partially healed
indentation crack by avoiding direct loading on the partially healed crack. By
focusing through the transparent glass specimen, a series of four to six 9.8 N indents
was placed on the specimen face opposite the partially healed indentation crack,
aligned with the partially healed indent crack. From four to eight, 49 N indents
(collinear with the 9.8 N indents) led to crack coalescence and catastrophic failure of
the partially healed specimen being indented.

Specimens which were fractured through the partially healed indent using

85

.Kirchner’s method (Experiment 1) or three-point bend testing (Experiment 1) were
analyzed in an SEM (JEOL JSM-6400V). The SEM was operated with a LaB6
filament having a 20 KeV accelerating voltage. The second largest aperture was used
to help increase the resolution. The fractured samples needed to be less than 2 or 3
mm (0.8 or 0.12 inch) in height in order to further increase resolution by having the
smallest working distance possible and to allow the samples to be inserted in the small
sample exchange of the SEM. Since the fractured specimen halves were 38 mm (1.5
inch) long, the fracture specimens were cut 2 or 3 mm (0.8 or 0.12 inch) from the
fractured ends with the low speed diamond saw (Section 3.2.1.1). After cutting, the
samples were washed with powdered glassware soap (Alconox Powder Detergent),
rinsed with tap water, and dried. To ensure removal of the cutting oil from the
samples before placing in the SEM vacuum environment, the samples were also
soaked for 30 minutes in acetone, and dried again.

Both halves of the fractured specimens were placed next to each other on an
SEM stub with one of the two halves rotated 1800 such that the fractured ends were
together when mounted and the top surfaces were parallel. The samples were mounted
on the SEM stub using five minute epoxy (Five Minute Epoxy Gel, Devcon
Corporation, Davers, MA). After the epoxy had dried, conductive carbon paint (SPI
Supplies, West Chester, PA) was applied to the top comers of the samples to the base
of the SEM stub to help in charge removal during SEM analysis of the non-conducting
samples. The carbon paint was allowed to dry for a minimum of 30 minutes. After
the sample the carbon paint was dry, the samples were gold coated to eliminate

charging during SEM analysis.

86
3.6.2.2.4 Effects of Stress Relief Cycle (Experiment 3)

An initial survey of the healing behavior of the soda-lime silica glass was done for a
range of temperatures and times for square specimens (Tables 8 and 9). As a part of
this study the effects of the stress relief cycle (Table 9 and 11) on crack healing was
investigated using samples that had undergone two different stress relief cycles (A and

B from Table 11) and samples that had not ben annealed.

3.6.2.2.5 Effect of Aging Environment, Time and Temperature (Experiments 4-7)
The effects of aging environment, annealing temperature, and annealing time on crack
healing was investigated using samples that had undergone aging in three different
environments (Table 9) and thermally annealing them for different times at different

temperatures (Table 8).

3.6.2.2.6 Residual Stress Relief Testing

Machining such as cutting and grinding can lead to development of residual stresses
on the surfaces of the machined samples. Residual surface stresses created during
machining change the driving force for radial indent crack growth discussed in Section
3.5.2 and result in an increase or decrease in the indent crack length. The driving
forces for the healing process could also be affected by the residual surface stresses
created during specimen preparation and result in a change in observed crack healing.
Radial crack lengths of indents made before and after different heating cycles in
machined soda-lime silica specimens were used to calculate the residual stress relieved

during the thermal cycle and to determine the optimum stress relied heating cycle

87

conditions for the glass specimens.

Rectangular residual stress specimens were cut using the low speed diamond
saw (Section 3.2.1.1) to nominal dimensions of 25.4 X 7.5 X 1.1 mm (1.0 X 0.3 X
0.045 inch, Figure 15) and square specimens were prepared as described in Section
3.6.2.2.1. Testing began by indenting (with conditions or from Table 10) at the
numbered indent locations (Figure 15). After 24 hours, the cracks for each of the
numbered indents was measured and sketched. The samples subsequently underwent a
heating cycle to relieve residual stress created during machining. Testing continued by
indenting in the capitol lettered indent locations (Figure 15). After 24 hours, the
cracks for each of the lettered indents was measured and sketched.

At higher temperatures, there was concern that the glass would begin to flow
viscoelastically. To protect the mullite boat from possible molten glass, a 2 to 3 mm
(0.08 to 0.13 inch) bed of alumina powder (Buehler Micropolish A) was placed in the
bottom of a 87.4 X 17.5 mm (3.44 X 0.69 inch) mullite boat (Coors CB 10 65564)
and an ~50 X ~10 X 1.0 mm (~2.0 X ~0.4 X 0.04 inch) Coors alumina sample was
placed on top of the powder bed as a setter. The residual stress specimen was placed
on top of the alumina setter as shown in Figure 16. In addition to the 25.4 X 7.5 X
1.1 mm (1.0 X 0.3 X 0.045 inch) rectangular residual stress specimen, two 7.5 X 7.5
X 1.1 mm (0.3 X 0.3 X 0.045 inch) square specimens were stacked on top of each
other and placed on the alumina setter as shown in Figure 16. The boat was placed in
the small tube furnace (Section 3.6.2.1.2) and heated with the sample temperature

measured using a J-Type thermocouple (Section 3.6.2.1.1).

88

3.6.2.3 Healing in Alumina

Two different experiments with a total of 72 specimens and 540 cracks were used to
investigate healing in two different kinds of alumina (Table 12). Specimens were

prepared (Table 13), indented (Table 13 and 14), aged (Table 13), and thermally

annealed (Table 15).

3.6.2.3.1 Alumina Specimen Preparation

The Coors alumina samples were cut to nominal dimensions of 10 mm X 10 mm X 1
mm (0.4 in. X 0.4 in. X 0.04 in.) using the high speed cutting saw (Section 3.2.1.2).
The cut Coors alumina squares and the as-received microwave alumina disks were
polished using the automatic polisher (Section 3.2.2). To identify the orientation of
the square Coors alumina samples in Experiment 1 the bottom right comer was ground
flat using 240 grit SiC grinding paper. To identify the orientation of square Coors
alumina samples and distinguish between the three samples aged under different
conditions in Experiment 2, the bottom right corner of the specimens either had one,
two or three 1.5 mm (0.06 inch) round holes sonic milled to a depth of about 0.4 mm
(0.016 inch). The polished microwave sintered alumina disks were cut into quarters
using the low speed diamond saw (Section 3.2.1.1 ). The quartered microwave
sintered alumina specimens were ground to remove chips formed during cutting with
the low speed saw. The Coors alumina squares and the microwave alumina quarters
were washed with powdered glassware soap (Alconox Powder Detergent), rinsed with

tap water, and placed in an ultrasonic bath of De-Ionized (D.I.) water for 10 to 15

minutes to remove any debris from polishing or from grinding.

89

2.0 2.0
mm mm

2.0

 

Figure 15 Schematic of the rectangular glass specimens used for the residual stress
measurement experiments showing the ground upper right hand comer (note that while
the indent locations are to scale the indent sizes are exaggerated).

Borosilicate
Glass Specimens

    

Mullite
Boat

Alumina
Powder

Figure 16 Schematic of rectangular glass specimen location in boat for residual stress
measurement experiments.

90

 

 

 

 

 

 

 

 

 

 

 

 

    

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20mm

1.5 mm

 

15 20

mm mm
Figure 17 Schematic of Coors alumina specimens used in conventional healing
Experiment 1 (note that the while the indent locations are to scale the indent sizes are
exaggerated).

. 20
mm

5
m

a—l

1.5 mm

2.0 mm

2.0 mm

1.5 mm

 

' 2.0 l '5 l
mm mm

Figure 18 Schematic of Coors alumina Specimens used in conventional healing
Experiment 1 (note that the while the indent locations are to scale the indent sizes are
exaggerated).

94
Indents were made in the Coors alumina and Microwave sintered alumina [65]
(Tables 13 and 14). Crack healing cycles were performed in the large tube furnace
with the samples placed in a ceramic boat (Figure 20). The cooling rate and the initial
heating rate were set to 10 °C/minute. To reduce the furnace temperature overshoot,
for some samples the heating rate was reduced to 2.5 °C when the furnace reached 80

or 84% of the final temperature (calculated in Kelvin) (Table 15).

3.6.2.3.2 Effects of Aging Humidity and Temperature in Two Aluminas
(Experiment 1)

Initially, indents l - 3 were made (Figure 17 and 18), measured after about 30
minutes, and then were aged in laboratory air (Table 13). After 24 hours a second set
of indents (A - C in Figures 17 and 18) was made for each sample. The crack lengths
were measured about 30 minutes after indentation. Both specimens then were aged
another 24 hours in either laboratory air, a desiccator, or a wet chamber (Table 13).
After the second 24 hour age the indent crack lengths were again measured. Samples

were thermal annealed (Table 12 and 15) and the indent crack lengths were measured.

3.6.2.3.3 Effects of Aging Humidity, Time, and Temperature in Coors Alumina
(Experiment 2)

Three indented Coors alumina samples were aged under different humid environments
for 24 hours (Table 13). The aged samples were thermally annealed together (Table

12 and 13) in a furnace boat (Figure 13) in the large tube furnace (Section 3.6.2.1.2).

95

3.0 mm

3.0 mm

 

 

I. .l: .l
[ 3.0mm 1 3.0mm 1

Figure 19 Schematic of Coors alumina specimens used in conventional healing
Experiment 2 (note that the while the indent locations are to scale the indent sizes are
exaggerated).

Alumina Mullite
Powder Bed S Boat

Microwave Alumina
Specimen

‘7 Coors Alumina
Specimen

 

Figure 20 Schematic of Coors alumina and microwave sintered alumina specimen
location in ceramic boat for conventional healing Experiment 1.

96
3.6.3 Microwave Healing

Three different experiments with a total of 15 specimens and 180 cracks were used to
investigate microwave and conventional healing in Coors alumina (Table 16).
Specimens were prepared (Table 17), indented (Table 17 and 18), aged (Table 17), and

annealed in a microwave or in a conventional furnace (Table 16).

3.6.3.1 Specimen Preparation

Coors alumina samples were heated in either a conventional furnace or in a microwave
furnace. Specimens heated in the conventional and microwave furnace were prepared
in the same manner. The Coors alumina specimens were prepared in the same manner
as the samples for conventional crack healing in alumina Experiment 2 (Section

3.6.2.3.3).

3.6.3.2 Microwave and Conventional Heating

Microwave heating was performed in the same microwave apparatus described in
Section 3.1.2.. The temperatures were held to within +/- 2 °C of the set temperature
for one hour without an overshoot greater than 2 °C. Conventional heating was
performed in the tube furnace described in Section 3.6.2.1 with samples placed in a

ceramic boat (Figure 22).

Table 16 Thermal annealing temperature and times for microwave and conventional
healing in alumina (Experiments 1-3). Specimen, indent, aging and annealing
condition are detailed in Table 17.

 

Experiment

  

Temperature
(°C)

 

 

 

 

Time

(Minutes)

Heating
Mode

Heating
Rate
(°C/Minute)

   

Total
Number
of Cracks

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

1 1237 60 Microwave 10 12
1295 12

1353 12

1411 12

1469 12

2 1237 60 Microwave 3O 12
1295 12

1353 12

141 l 12

1469 12

3 1237 60 Conventional 10 12
1295 12

1353 12

1411 12

L: 1469 12

 

 

 

 

 

 

 

98

Table 17 Details of specimen, indent, aging, and annealing conditions for microwave
and conventional healing in alumina (Experiments 1-3).

 

Experiment Type of Indent Indenting Indenting Aging Aging

A1203 Geometry Condition Condition Time Humidity

for Indents for (Days) (~%r.h.)
1, 2, 3 Indents

 

 

 

 

 

 

 

 

 

 

 

A, B, C
l Coors Figure 30 a [3 24 45
2 Coors Figure 30 a. B 24 45
3 Coors Figure 30 o: B 24 45

 

Table 18 Indentation conditions referred to in Table 16 for alumina specimens used in
conventional healing (Experiments 1-2).

 

 

Indenting Condition Load Loading Rate Loading Time
(N) (pm/S) (S)
a 49 7O 15

 

[3 98 7o 15

 

 

 

 

 

 

 

 

2.0 mm

1.5 mm

 

1.5 2.0

mm mm
Figure 21 Schematic of Coors alumina specimens used in microwave and
conventional healing experiments (note that the while the indent locations are to scale
the indent sizes are exaggerated).

Alumina Mullite
Powder Bed Boat

"2 Coors Alumina
' Specimen

 

Figure 22 Schematic of Coors alumina specimen location in ceramic boat for
microwave healing experiments.

4. RESULTS AND DISCUSSION

4.1 Materials Characterization

The soda-lime silica glass, Coors alumina and microwave alumina material used for
experimental studies of static fatigue and crack healing were characterized before
testing. The density of the glass and alumina was measured. The grain size of Coors

alumina and microwave sintered alumina was measured from micrographs.

4.1.1 Density Measurements

Specimens of soda-lime silica glass, Coors alumina and microwave sintered alumina
were prepared as described in Section 3.3.1.1. The density was determined using an
Archimedes’ described in Section 3.3.1.2 on four samples of each material. The
average density and standard deviation were determined (Table 19). The percent
theoretical density for the Coors alumina and microwave alumina were 97.3i0.3 and

98.110.2%, respectively, based on a theoretical density of 3.965 g/cm3 [61].

4.1.2 Microstructure
Micrographs of thermally etched surfaces of Coors alumina and microwave alumina
were taken using the ESEM to determine the grain size using a line intercept method.

An example of the thermally etched surface of the Coors alumina and microwave

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102

alumina can be seen in Figures 23 and 24, respectively. The Coors alumina grain size
was 2.1i0.2 microns and the microwave sintered alumina grain size was 20.6i3.6

microns.

4.2 Indentation Measurement Tasting
Indentation measurements experiments were performed to compare optical
measurements between different researchers. Additional indentation measurement

experiments were performed to compare optical and ESEM measurements.

4.2.1 Multiple Experimenter Measurements

Measurements of crack lengths in soda-lime-silicate glass, Coors alumina, microwave
alumina, and silicon nitride were made by multiple experimenters as outlined in
Section 3.4. 1. The average and standard deviation of five different measurements
were reported by each of six different researchers for each material (Table 20-23).
From the data reported by the six researchers the average for the group was calculated

(Table 20-23).

4.2.1.1 Crack Length Measurement Variation with Experimenter

The standard deviations for indent crack length measurements by each researcher for
glass, Coors alumina, microwave alumina, and silicon nitride were less than 3, 5, 6,
and 9 microns, respectively (Tables 20 - 23). The indent crack length measurement
standard deviations by each researcher were less than 1.5%, 2.5%, 2%, and 3% of the

group average crack length measurement for glass, Coors alumina, microwave

 

 

103

 

r.» ,. ‘ 2..., , m .- _ -4 ‘ ‘ l.
Figure 23 ES micrograph of thermally etched Coors alumina used in grain size
determination showing a small grain size of 2.1 i 0.2 pm.

Figure 24 ESEM rnpicrograh of thermally etched icowave sintered alumina used in
grain size determination showing a grain size of 20.6 i 3.6 pm.

104

Table 20 Average and standard deviation of indent crack lengths in soda-lime silica
glass measured by six different researchers using an optical microscope to determine
the level of operator error typically present in Vickers indentation measurements.

 

 

 

 

 

 

 

 

 

 

 

 

 

Researcher 2cl (microns) 2c2 (microns)
Mean and Mean and
Standard Deviation Standard Deviation
1 225.3 i 2.0 221.8 i 2.7
2 215.8 :l: 1.4 215.3 i 1.4
3 210.6 i 2.3 214.9 :l: 1.2
4 209.2 :1: 0.6 210.9 1 0.6
5 214.4 i 0.5 214.8 :1: 0.8
6 210.8 i 0.3 221.3 i 0.3
Group Average 214.4 216.5
ESEM Micrograph 215.0 :1: 2.3 216.3 i 1.2
ESEM Computer Screen 210.0 :1: 1.2 212.0 2!: 0.0

 

 

Table 21 Average and standard deviation of indent crack lengths in Coors alumina
measured by six different researchers using an optical microscope to determine the
level of operator error typically present in Vickers indentation measurements.

 

 

 

 

 

 

 

 

 

 

 

 

 

Researcher 2cl (microns) 2c2 (microns)
Mean and Mean and
Standard Deviation Standard Deviation
1 272.9 i 4.8 253.2 :l: 1.0
2 262.2 :t 4.8 240.0 :l: 0.8
3 267.5 i 1.2 243.1 i 2.5
4 267.1 :l: 1.4 242.6 :l: 3.4
5 248.8 :1: 2.4 229.3 :l: 4.5
6 239.4 :l: 3.3 216.7 :l: 0.5
Group Average 259.7 237.5
ESEM Micrograph 264.1 i 2.2 261.2 1- 1.4
ESEM Computer Screen 266.0 :1: 0.5 264.0 i 2.0

 

 

105

Table 22 Average and standard deviation of indent crack lengths in microwave
sintered alumina measured by six different researchers using an optical microscope to
determine the level of operator error typically present in Vickers measurements.

 

 

 

 

 

 

 

 

 

 

 

 

 

Researcher 2c1 (microns) 2c2 (microns)
Mean and Mean and
Standard Deviation Standard Deviation

1 353.6 i 1.9 355.3 i 1.5

2 388.8 :I: 3.4 368.7 :l: 7.7

3 432.3 i 2.5 393.7 :l: 2.8

4 385.4 :1: 2.8 359.3 :l: 1.4

5 389.4 :l: 1.7 382.8 i 2.7

6 324.7 :t 5.3 331.4 :1: 0.5

Group Average 379.0 365.1

ESEM Micrograph 376.7 i 1.8 356.3 i 1.1
ESEM Computer Screen 377.0 :1: 1.0 353.8 1 0.8

 

 

Table 23 Average and standard deviation of indent crack lengths in silicon nitride
measured by six different researchers using an optical microscope to determine the
level of operator error typically present in Vickers indentation measurements.

 

 

 

 

 

 

 

 

 

 

 

Researcher 2cl (microns) 2c2 (microns)
Mean and Mean and
Standard Deviation Standard Deviation

1 351.5 i 1.3 376.3 :1: 1.8

2 345.6 :1: 3.5 365.7 1 8.8

3 350.6 1 1.3 373.0 i 1.5

4 344.2 :1: 3.0 368.5 i 2.7

5 355.0 i 2.9 370.3 :1: 5.1

6 334.8 :1: 5.4 349.0 1 3.5

Group Average 346.0 :1: 7.2 367.1 :l: 9.6

 

 

106
alumina, and silicon nitride, respectively (Tables 20 - 23, Figure 25).

For glass, Coors alumina, microwave alumina, and silicon nitride, each
researcher’s mean measured indent crack length, 2c,, is shown in Figure 25 as a data
point. The average of all the researcher’s measured means is shown in Figure 25 as a
horizontal line. The data points for glass, Coors alumina, and silicon nitride are
scattered near to the line representing the group average, however, the data points for
microwave alumina show a higher degree of scattering about the average (Figure 25).
The coefficient of variation, CV, is a measure of the relative variability in a data set
and is given by

CV = i. * 100% (8)
X

where s is the standard deviation and 2? is the mean for the data set The low
coefficient of variation for each researcher of less than 2.0% for the glass and Coors
alumina materials, together with the small scatter of the individual researcher’s
measurements around the average measurement for all researchers (Figure 25) showed
that the glass and Coors alumina would make good materials for further crack length

investigations.

4.2.2 Optical and ESEM Measurements
The Vickers indented soda-lime—silicate glass, Coors alumina, and microwave alumina
specimens (Section 4.2.1) were also analyzed via an Environmental Scanning Electron

Microscope (ESEM) by the first researcher (Section 3.4.1). The crack lengths were

107

measured from micrographs of the indent cracks at a magnification of 325x (Figures
26 - 28 and Tables 20 — 23). Indent crack length measurements were also made "on
screen" by the first researcher using the ESEM computer measurement tool (Tables 20
- 23). The ESEM indent crack length measurement differed from the optical
microscope measured group average by 1% to 6.5% for glass and 2% to 9% for Coors
alumina. The difference in optical and ESEM measurements for glass and Coors
alumina was a result of the higher resolution of the electron microscope compared to
the optical microscope as well as the higher magnification used for the ESEM

measurements.

4.3 Static Fatigue: ESEM Crack Growth Investigations

In-situ observation of crack growth in ceramics under constant applied load was
performed using the Environmental Scanning Electron Microscope (ESEM). Tensile
specimens of glass and Coors alumina were prepared for the study. A Vickers indent
was placed on the center of one of the tensile specimen faces and was observed in the
ESEM. The effects of constant applied load, humidity, and time upon crack growth

were investigated

4.3.1 Soda-Lime Silica Glass

Soda-lime silica glass tensile specimens were prepared as described in Section 3.5. 1.
Thirteen glass tensile specimens were prepared using composite tabs affixed with
epoxy. One specimen was prepared with composite tabs affixed with high temperature

cement. A 9.8 N Vickers indent was placed in the face of each of the tensile

108

 

 

 

 

 

 

 

 

 

 

 

500 h
’e‘ 3 '
e400 -- . _ .
(‘u’ : l ; A A
5' - i
g 300 --
3 : . A O O
is ' ° 0
S 200-; ' G v 3 v
0 -
'0 -
2 .
:I _ .
g 100 __ Matenal
2 : 9 Glass A Silicon Nitride
Z 0 Coors Alumina ' Microwave Sintered Alumina
0 l l l l l l
0 1 2 3 4 5 6 7
Flese rcher

Figure 25 Measured crack length, 20,, for glass, oors alumina, microwave sintered
alumina, and silicon nitride. Each data point was an average of five measurements by an
individual researcher and horizontal lines were group averages of six researchers.

   

Figure 26 ESEM micrograp ‘ of indentation cra ks in a soda-lime silica gls specimen
used in multiple researcher measurement experiments.

     

109

 

‘ .

 

‘. «W cm . - - - W. , .. .-...... a 3; ~ .
Figure 27 ESEM micrograph of indentation cracks in a Coors alumina specimen used in
multiple researcher measurement experiments.

Figure 28 ESEM micrograph of indentatio crac in a microwave sintered alumina
specimen used in multiple researcher measurement experiments.

110

specimens and allowed to age for 24 hours as described in Section 3.2.3.

4.3.1.1 Failures from Mounting Specimens in the Tensile Stage
The indented tensile specimens were placed in the tensile stage of the ESEM as
described in Section 3.5.3.2. Eleven of the thirteen composite tab/epoxy adhesive
tensile specimens fractured during mounting into the tensile stage. Of the eleven
specimen failures during mounting, 5 failures occurred at a tab, 5 failures occurred
between the indent and a tab, and one of the failures occurred at the indent

With the edges beveled to reduce the stress concentration, the indent crack of
about 200 microns in length should be the largest flaw in the specimens. Failure at
locations other than through the indent, indicated that other flaws, perhaps loaded by
non-tensile stresses, developed in the specimens. The most likely type of non-tensile
stress would be torsional stress from tabs which were not perfectly parallel. Since five
specimens failed at the tab, torsional stress from tabs which were not perfectly parallel

seemed to be the major problem.

4.3.1.2 Failures from Automatic ESEM Stage Control Procedures

Two of the thirteen composite tab/epoxy adhesive tensile specimens were successfully
mounted into the tensile stage. When the specimen chamber door was closed, the
ESEM automatically zeroed the Rotation stage control, which regulates the tensile
stage displacement Consequently, large compressive or tensile stresses fractured the
glass samples. To prevent the fracture of specimens by the automatic stage control

procedure of the ESEM, additional steps of removing the tensile stage after specimen

 

1 l 1
mounting and then re-calibrating the stage controls were added to the experimental

design (Section 3.5.3.2).

4.3.1.3 Testing of a Mounted Sample

High temperature cement adhesive was used in lieu of epoxy to bond tabs to a
specimen (Section 3.5.1.3). The specimen with composite tabs affixed with cement
was successfully mounted into the tensile stage. The self tightening grips applied a
tensile load of about 3 to 4 MPa after mounting. The chamber door was successfully
closed without fracture of the specimen using the additional procedural steps of
removing the tensile stage, re-calibrating the stage controls, and replacing the tensile
stage before closing the door. Static fatigue testing was started as described in Section
3.5.3.3. Micrographs of the initial indent crack length were taken and then the load
was increased.

The specimen with cement bonded composite tabs fractured during the increase
of load at about 17 MPa at the tab. The fracture of the tabs at 17 MPa indicated that
even though there was an improvement in getting parallel faces for the tabs using the
high temperature cement, there was still too much torsional stress developing in the
tabs. The static fatigue testing of glass was suspended at this point and testing of
Coors alumina was undertaken. The alumina, a polycrystalline material, was expected
to be more resistant to small torsional forces caused by specimen preparation
problems. It was hoped that improvements in the specimen preparation procedures

could be found with the alumina and later be applied to the testing glass.

112

4.3.2 Coors Alumina

Coors alumina tensile specimens were prepared as described in Section 3.5.1.
Alumina tensile specimens were prepared using composite and stainless steel tabs
affixed with epoxy or high temperature cement. A 49 or 98 N Vickers indent was
placed in the face of each of the tensile specimens and allowed to age for 24 hours as
described in Section 3.2.3. The indented tensile specimens were placed in the tensile
stage of the ESEM as described in Section 3.5.3.2.

A summary of the ESEM static fatigue testing of the Coors alumina specimens
is shown in Table 24. Indent cracks which opened or grew during testing were
perpendicular to the direction of the applied stress. References to the left or right half
cracks were with respect to the orientation of the crack in the ESEM micrograph.
Before static fatigue testing began, failure occurred at the tabs for specimens B, D, E,
G, and 1. Whether the tabs for the specimens were made from the glass fiber/ epoxy
matrix composite or from stainless steel did not appear to make a difference with

respect to failure at the tabs.

4.3.2.1 Stainless Steel Tabs

The stainless steel tabs and the cement adhesive are capable of operating at
temperatures approaching 1000 °C. The use of stainless steel tabs and cement
adhesive in the static fatigue testing procedure developed in the current investigation,
will allow the testing procedure to be used by other investigators for high temperature
testing of ceramic specimens.

The lower viscosity of the cement compared to the epoxy yielded an adhesive

Table 24 Summary of ESEM static fatigue testing of Coors alumina tensile specimens.

113

(8.3. indicates stainless steel and C.R.S.S. indicates cold rolled stainless steel).

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Test Indent Tab Tab Grip Test Details
Size Material Adhesive Load Failure Details
(N) (MPa)

A 49 Composite Cement 10 Failure before testing
Indent failure at ~99 MPa

B 49 Composite Epoxy 10 Testing detailed in Table 25
Tab failure at 99 MPa

C 49 Composite Epoxy 10 Testing detailed in Table 26
Indent failure at 132 MPa

D 49 Composite Epoxy 11 Failure before testing
Tab failure at ~43 MPa

E 49 Composite Cement 11 Failure before testing
Tab failure at 11 MPa

F 98 SS. Cement 15 Testing detailed in Table 27
No failure at end of testing

G 98 C.R.S.S. Cement ~10 Failure before testing
Tab failure at 10 MPa

H 98 C.R.S.S. Cement 13 Grips slipping initially

l6 Grips tightened

Testing detailed in Table 28
Indent failure at 70 MPa

I 98 C.R.S.S. Cement 31 Failure before testing
Tab failure at ~60 MPa

J 98 Composite Cement 17 Testing detailed in Table 29
Indent failure at 100 MPa

 

 

114

layer of uniform thickness easier than the epoxy adhesive. The more uniform adhesive
layer thickness and the possibility of future high temperature testing, led to using
cement predominantly in later testing. Stainless steel tabs made high temperature
testing possible.

The stainless steel material was received in 3.175 mm (0.125 inch) thick strips.
The stainless steel thickness was too large to mount in the small tensile stage of the
ESEM. A reduction in thickness of the stainless steel tabs was necessary. First, the
tensile specimens were prepared with the as-received stainless steel thickness and then
the affixed tabs were ground. Unfortunately, specimens were easily fractured during
grinding. Cold rolling the stainless steel (described in Section 3.5.1.2) led to problems
with the slipping of specimens in the tensile grips due to the increased hardness that
resulted from cold rolling.

Specimen H was made with cold rolled stainless steel tabs and was loaded in
the self tightening tensile grips in a similar manner as other specimens with 13 MPa of
tensile force applied. When the displacement in the tensile fixture was increased to
increase the load of the specimen, the grips slipped over the hardened, cold rolled
stainless steel tabs. Consequently, to increase the load on the sample, the tensile stage
had to be removed from the ESEM, the grips had to tightened, and the tensile stage
had to be remounted in the ESEM. On sample I, the grips were initially tightened to
give an tensile load of 31 MPa to prevent slippage which would necessitate tensile
stage removal and grip tightening. Upon increasing the load in Specimen I, the
sample failed at about 60 MPa. The failure was most likely caused by torsional stress

as a result of uneven tightening of the grip bolts while increasing the load applied by

l 15
the self tightening grip to 31 MPa.

Future specimen preparation for testing after the present investigation would
use cold rolled stainless steel and high temperature cement for tabbing. The cold
rolled stainless steel would be annealed before mounting to reduce the hardness which
caused problems with the grips slipping. Future specimen preparation for testing after
the present investigation would also be aided with the design of a fixture which could
aid in alignment of the tabs during the curing of the adhesive to give parallel tab faces

thus reducing problems with torsional stress and failure at the tabs.

4.3.2.2 Specimen B

Tests performed on Specimens B, C, F, H, and I (which did not fail at the tabs before
testing began) are detailed in Tables 25 through 29. The first test was performed on
Specimen B (Table 25) which was made with composite tabs affixed with epoxy. The
49 N indent of Specimen B had no crack growth at 21% r.h. (relative humidity) for
loads of 77, 89, and 94 MPa and time intervals ranging from 5 to 30 minutes (Table
25). Due to the nature of fracture in brittle materials such as alumina, it is difficult to
make assertions from small sample populations, however, the lack of crack growth for
Specimen B at 21% r.h. and loads up to 94 MPa, seems to indicate that static fatigue
crack growth did not occur in the Coors alumina at 21% r.h. for the loads and times
investigated. The lack of crack growth for Specimen B at 21% r.h. also indicates that
the experimental procedure step (Section 3.5.3) of dropping the humidity to 10% to
take micrographs (in order to increase the resolution of the ESEM) should not have

resulted in crack growth while micrographs were taken at the lower humidity.

.Table 25 ESEM static fatigue testing of the 49 N Vickers indent in Coors alumina
tensile Specimen B (Table 24) which was made with composite tabs affixed with

116

 

 

 

 

 

epoxy.
Load Humidity Time Comments
(MPa) (%) Interval
(min)

77 21 5 No Crack Growth
89 21 30 No Crack Growth
94 21 15 No Crack Growth
99 21 3 Failure at tab

 

 

 

 

 

Table 26 ESEM static fatigue testing of the 49 N Vickers indent in Coors alumina
tensile Specimen C (Table 24) which was made with composite tabs affixed with
epoxy. (References to the left or right half cracks were with respect to the orientation

of the crack in the ESEM micrograph).

 

 

 

 

 

 

 

 

 

 

 

Load Humidity Time Comments
(MPa) (%) Interval
(min)
92 10 — No Crack Growth from load increase
32 25 26 micron growth of left crack
32 25 8 micron growth of left crack
32 35 No growth of left crack
42 25 No growth of left crack
100 10 - No Crack Growth from load increase
32 25 7 micron growth of left crack
32 25 No growth of left crack
32 25 No growth of left crack
105 10 - No Crack Growth from load increase
32 25 6 micron growth of left crack
111 10 - No Crack Growth from load increase
32 25 10 micron growth of left crack
116 10 - No Crack Growth from load increase
32 25 1 micron growth of left crack
132 10 2 Failure through indent

 

 

 

117

Table 27 ESEM static fatigue testing of the 98 N Vickers indent in Coors alumina
tensile Specimen F (Table 24) which was made with non-cold rolled stainless steel
tabs affixed with high temperature cement. (References to the left or right half cracks
were with respect to the orientation of the crack in the ESEM micrograph).

 

 

 

 

 

 

 

 

Load Humidity Time Comments
(MPa) (%) Interval
(min)
50 10 - No Crack Growth from load increase
32 25 growth of 9 pm for left and 8 pm for right crack
32 25 no growth for left and 1 pm growth for right crack
60 10 - N 0 Crack Growth from load increase
32 25 no growth for left or right crack
70 10 - No Crack Growth from load increase
32 25 6 pm growth for left and no growth for right crack
80 10 - N 0 Crack Growth from load increase
32 25 10 pm growth for left and no growth for right
85 10 - No Crack Growth from load increase
32 25 no growth for left or right crack
90 10 - N 0 Crack Growth from load increase
32 25 growth of 3 pm for left and 15 pm for right crack
32 25 no growth for left and 1 pm growth for right crack
18 10 2 Reduced load to remove specimen - no failure

 

 

 

 

 

 

118

Table 28 ESEM static fatigue testing of the 98 N Vickers indent in Coors alumina
tensile Specimen H (Table 24) which was made with cold rolled stainless steel tabs
affixed with high temperature cement. (References to the left or right half cracks were
with respect to the orientation of the crack in the ESEM micrograph).

 

 

 

 

 

 

 

 

 

 

 

 

Load Humidity Time Comments =
(MPa) (%) Interval
(min)
13 10 - Load could not be increased - grips were slipping
16 10 - Self-tightened grips tightened
slipping eliminated
growth of 33 pm for left and 35 pm for right
40 10 - No crack growth from load increase
32 25 growth of 28 pm for left and 28 pm for right
32 25 growth of 12 pm for left and 13 pm for right
32 25 no growth for left and 2 pm growth for right crack
32 25 no growth for left and 6 pm growth for right crack
32 25 no growth for left and 8 pm growth for right crack
32 25 6 pm growth for left and no growth for right crack
50 10 - No Crack Growth from load increase
32 25 growth of 12 pm for left and 6 pm for right
32 25 no growth for left and 2 pm growth for right crack
32 25 8 pm growth for left and no growth for right crack
70 10 7 Continuous indent crack growth until failure

 

 

119

Table 29 ESEM static fatigue testing of the 98 N Vickers indent in Coors alumina
tensile Specimen J (Table 24) which was made with composite tabs affixed with high
temperature cement. (References to the left or right half cracks were with respect to
the orientation of the crack in the ESEM micrograph).

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Load Humidity Time Comments
(MPa) (%) Interval
(min)

40 32 25 no growth for left or right crack

32 25 no growth for left or right crack

32 25 no growth for left or right crack

32 75 no growth for left or right crack
17 10 - ESEM computer crashed - load decreased
17 45 ? Tensile stage with sample removed -

ESEM re-booted

lO - No crack growth with sample put back in ESEM
50 10 - No Crack Growth from load increase

32 25 no growth for left or right crack
60 10 - No Crack Growth from load increase

32 25 no growth for left and 4 pm growth for right crack
7 O 10 - No Crack Growth from load increase

32 25 growth of 8 pm for left and 9 pm for right
80 10 - growth of 6 pm for left and 6 pm for right

32 25 growth of 5 pm for left and 7 pm for right

32 25 11 pm growth for left and no growth for right
90 10 - growth of 4 pm for left and 15 pm for right

25 25 growth of 33 pm for left and 16 pm for right
100 10 ? Continuous indent crack growth until failure

 

 

120
4.3.2.3 Specimen C

The second successful experiment was performed on Specimen C which was made
with composite tabs affixed with epoxy (Table 26). The 49 N indent of Specimen C
had the applied load increased to 92 MPa. Micrographs of the left indent crack were
taken at the initial load of 10 MPa and when the load was increased to 92 MPa. No
crack growth was observed from the micrographs as a result of the load increase from
10 to 92 MPa. The lack of crack growth during the load increase from 10 to 92 MPa
appears to show that non-static fatigue crack growth did not occur in the Coors
alumina specimens at the load levels used in the study.

After the first 25-minute cycle at 32% r.h. and 92 MPa, the left indent crack of
Specimen C increased 26 microns in length and after a second 25-minute cycle at 32%
r.h. and 92 MPa the crack increased 8 microns in length (Table 26). Indent crack
growth at 32% r.h. indicates that static fatigue crack growth occurred in the Coors
alumina under the conditions tested. The crack did not increase in length during the
subsequent cycles at 92 MPa even for the cycle for which the humidity was increased
to 42%r.h. (Table 26). Crack arrest after the second static fatigue cycle indicates that
the static fatigue crack growth saturates or dramatically slows after a certain time
under a constant applied stress even with an increase in the humidity level.

Specimen C failed after 2 minutes at 132 MPa and 10% r.h.. The crack length
constantly increased during the two minutes before rapid crack propagation and failure.
The stress intensity factor, K], for Specimen C at an applied stress, 6, of 132 MPa and

with a half crack length, c, of 203 microns was 2.38 MPan from

121

K, = Yofiq/E (9)

where the geometric factor, Y, was taken as 2.24/1t for a semi-circular surface crack in
a bar under tensile stress [7]. The stress intensity from the applied tensile load at the
crack tip was about 64% of the reported fracture toughness, Kr: , for Coors alumina of
3.70 MPan [66]. The stress intensity at the crack tip was most likely increased
slightly from bending and/or torsional forces caused by nus-alignment of the specimen
tabs. However, assuming only a tensile load on the crack tip, the calculated stress
intensity at the crack tip would exceed the fracture toughness of the Coors alumina at
the applied constant load of 132 MPa when the half crack length increased to 492
microns. Continuous crack growth and ultimate failure of Specimen C at 132 MPa
indicates that there is a maximum in constant applied stress or crack length (since both
will increase the stress intensity factor at the crack tip) above which static fatigue
crack growth does not saturate, resulting in catastrophic failure even at the reduced
humidity level of 10%.

After 25 minutes at 32% r.h. and 92 MPa, one of the two indent half cracks
perpendicular to the direction of the applied stress for Specimen C grew 26 microns
from its original length at 10% and 92 MPa (Table 26 and Figure 29). The same
indent crack continued to grow an additional 8 microns in length after an additional
25-minute static fatigue cycle at 32% r.h. and 92 MPa (Table 26 and Figure 29). The
crack path followed during the static fatigue cycles at 32% r.h. and 92 MPa was semi-
tortuous with grains that bridge the crack behind the crack tip (Figure 29) and crack

deflections (Figure 29) similar in size to those reported for Coors alumina (Section

122

4.1.2). The indent crack also grew during static fatigue cycling at 100, 105, 111, and
116 MPa and 32% r.h. and also followed a tortuous path with crack deflections on

the order of the grain size of the material (Table 26, Figure 30 and 31).

4.3.2.4 Specimen F

A 98 N indent crack on Specimen F was tested at 32% r.h. for loads ranging from 50
to 90 MPa (Table 27 ). For Specimen F, the crack length increased from 417 microns
to 470 microns after the second static fatigue cycle at 90 MPa. Specimen F did not
fail during testing. After the second cycle at 90 MPa, the applied load was decreased
to 18 MPa and Specimen F was removed intact from the tensile stage fixture. Two
25-minute static fatigue cycles were performed on Specimen F at 50 and 90 MPa.
The second cycles at these constant applied load levels had either no crack growth or
a crack growth of only 1 micron (Table 27). The low crack growth rate for the
second cycles again indicates the static fatigue crack growth saturates at a constant
applied load (at least below some critical level of constant applied load). For an
applied load of 90 MPa and a crack length of 470 microns the stress intensity factor

was 2.47 MPan (67% of K1,).

4.3.2.5 Specimen H

Specimen H was prepared with cold rolled stainless steel tabs affixed with high
temperature cement (Table 28). The load from the self tightening grips was initially
13 MPa. When the displacement on the tensile stage was increased to increase the

load, the grips slipped across the cold rolled stainless steel tabs of Specimen H. The

123

 

Figure 30 ESEM micrograph of the lefi indent crack of Coors alumina Specimen C
(Tables 24 and 26) showing the growth after 25, 50 and 85 minutes at 92 MPa and 32%
r.h. and 25 minutes at 92 MPa and 42% r.h.

 

Figure 29 ESEM micrograph of the left indent crack of Coors alumina Specimen C
(Tables 24 and 26) showing the growth after 25 and 50 minutes at 100 MPa and 32% r.h..

124

     

r "W’WW’WF‘H‘ *finwtvffi . 41‘

Figure 31 ESEM micrograph of the left indetn crack of Coors alumina Specimen C
(Tables 24 and 26) showing the growth after 25 minutes at 32% r.h. and 105, 111, and
116 MPa.

125
slippage indicated that the increased hardness of the cold rolled stainless steel tabs
necessitated a larger initial grip load. The tensile stage and sample were removed
from the ESEM sample chamber and the self-tightening grips were tightened
increasing the load applied to the sample to 16 MPa. After the tensile stage and
sample were returned to the ESEM sample chamber, micrographs of the indent cracks
were taken. The crack lengths increased by 33 and 35 microns for the left and right
indent cracks, respectively (Table 28). The crack length increase resulted from
torsional load applied as the 4 grip plate bolts were tightened un-evenly. The load on
the sample was increased to 40 MPa (at 10% r.h.) and no further crack growth
occurred.

Specimen H was tested at 32% r.h. for six 25-minute cycles at 40 MPa and
three 25-minute cycles at 50 MPa (Table 28). The crack length increased from an
initial length of 399 microns to 530 microns after the third static fatigue cycle at 50
MPa. Specimen H failed during testing after 7 minutes of continuous crack growth at
70 MPa constant applied load and 10%r.h. (Table 28).

After the first 25-minute cycle at 40 MPa and 32% r.h., the left and right
indent cracks each lengthened by 28 microns (Table 28). During the second 25-
minute cycle at 40 MPa and 32% r.h., the left and right indent cracks lengthened by
less than half the amount of the first 25-minute cycle (Table 28). The third 25-minute
cycle gave crack length increases of 2 microns or less (Table 28). After each of the
next three cycles only one of the two cracks grew (by 8 microns or less) (Table 28).
The decrease in the static fatigue crack growth on the second cycle and the limited

static fatigue crack growth of the third cycle was similar to the static fatigue crack

126

growth of Specimens C and F (Tables 26 and 27). The static fatigue crack growth for
the fourth, fifth and sixth static fatigue cycles at 32% r.h. and 40 MPa did not saturate
after holding at the same level of applied stress, but merely slowed (Table 28).

The first 25-minute cycle of static fatigue Specimen H at 32% r.h. and a fixed
50 MPa applied load resulted in a 12 and 6 micron growth for the left and right indent
half cracks, respectively (Table 28). The second cycle resulted in very small crack
growth, while the third cycle resulted in only one of the two cracks growing by 8
microns or less (Table 28). Thus for static fatigue of Coors alumina at both 40 MPa
and 50 MPa constant applied load, both cracks grew significantly upon the first static
fatigue cycle, both cracks had limited growth for subsequent static fatigue cycle, and
only one of the two cracks grew by 8 microns or less during further static fatigue
cycling.

The indent crack tip of Specimen H did not advance after the load was
increased from 16 MPa to 40 MPa (Figures 32 and 33). After the first 25-minute
static fatigue cycle at 32% r.h. and 40 MPa, the left crack advanced along a tortuous
path with crack deflections on the order of the diameter of a single Coors alumina
grain (Figure 34). For the second static fatigue cycle at 40 MPa and 32% r.h., an
alumina grain bridged the crack from the end of the first cycle and the start of the

second (Figure 35).

4.3.2.6 Specimen J
A 98 N indent crack on Specimen J was tested under humidity conditions of 32% r.h.

for loads ranging from 40 to 90 MPa (Table 29). For Specimen J, the crack length

127

     

Figure 32 ESEM micrograph of the lefi indent crack of Coors alumina Specimen H
(Tables 24 and 28) showing the initial lefi indent crack with an applied stress of 16 MPa
fi'om the self tightening grips.

 
    

   

r . m, g, .
“ ‘ ' as i a: ,- - - _ . J“ «xi .,
Figure 33 ESEM micrograph of the lefi indent crack of Coors alumina Specimen H

(Tables 24 and 28) showing the initial left indent crack alter increasing the applied stress
to 40 MPa.

128

 

Figure 34 ESM micrograph of the left indent crack of Coors alumina Specimen H
(Tables 24 and 28) showing the growth after 25 minutes at 40 MPa and 32% r.h.

t”... . . 3."!— ,_ .-'"*r——:""'="T*." t1 _ ,
Figure 35 ESEM micrograph of the left indent crack of Coors alumina Specimen H
(Tables 24 and 28) showing the growth after 50 minutes at 40 MPa and 32% r.h along
with the bridged grain which is located at the end of the 25 minute crack tip.

129

increased from 360 microns to 484 microns after the static fatigue cycle at 90 MPa.
Specimen J failed via continuous crack growth at 100 MPa and 10% r.h.. No crack
growth occurred after three 25-minute and one 75-minute cycle at 40 MPa and 32%
r.h.. No crack growth occurred after a 25-minute cycle at 50 MPa and 32% r.h.. The
right indent crack increased 4 microns while the left crack did not increase after 25
minutes at 60 MPa and 32% r.h.. The small crack growth after the first cycle at a
fixed constant applied load was contrary to the behavior of Specimens C, F, and H.
The crack path followed during the 32% r.h. static fatigue cycles at 60, 70, 80,
and 90 MPa were semi-tortuous with grains that bridge the crack behind the crack tip
(Figure 36) and crack deflections (Figure 36) similar in size to those reported for
Coors alumina (Section 4.1.2). The indent crack grew after the load was increased to
80 and 90 MPa and while the humidity was at 10 % r.h. (Table 29 and Figure 36)
which was not a behavior observed in other specimens (Tables 26 - 28). Two grains
bridged the crack formed during the second 25 minute cycle at 80 MPa and during the

first cycle at 90 MPa (Figures 37 and 38).

4.3.2.7 Relative Crack Length and Applied Tensile Load

Four ESEM static fatigue crack growth experiments were performed under constant
load and increased humidity conditions using tabbed tensile specimens (Specimens C,
F, H, and J). The relative half crack length (C, / Co) increased with applied tensile
stress for the composite tab Specimen C (Figure 39). Similarly, the relative indent
crack length (2C, / 2C0) increased with the applied tensile stress for Specimens F, H,

and J (Figures 40 - 42). The relative indent crack length (2C, / 2C0) also increased

130

 

       

     

         

‘ g? . 3H: 1..-“-.- ”H“ , <,--:..wr- 3T“;- ,. ,6 '. . \.

Figure 36 ESEM micrograph of the left indent crack of Coors alumina Specimen J
(Tables 24 and 29) showing the growth after time at 32% r.h. and 60 to 90 MPa along
with the growth which occurred as the load was increased to 80 and 90 MPa.

   

   
  
 

‘ _' ~u_7:~ww’wv _ _ (I 7f . 7
Figure 37 ESEM micrograph of the lelt indent crack of Coors alumina Specimen J
(Tables 24 and 29) revealing two instances of grain bridging from the 80 and 90 MPa

static fatigue cycles.

131

 

Figure 38 A higher magnification ESEM micrograph of Figure 37 revealing the
instances of grain bridging from the 90 MPa static fatigue cycle of the left indent crack
of Coors alumina Specimen J (Tables 24 and 29).

 

 

 

 

 

 

 

 

1.45 _
.1.40-{- 9 e
g :
=$1.35 -E- Three overlapping
(é : data points o
1.30-:- \Y\
E 2 °
%125-3' 5
8 1.20 E. Q 25 minutes at 32% r.h. K‘\
g .1: 9 Three
in : * 25 minutes at 42% r.h. overlapping
I 1.15-:- data points
g . Initial Loading
o“1.10—7
'6 :
“ mos—:—
1.00 :. .L=...l....l....I..n.lrr..l.-..l.--.I.rrrlnL.-:....:....

0 10 20 30 40 50 60 70 80 90 100110120
Applied Constant Tensile Stress (MPa)

Figure 39 Plot of static fatigue crack growth for the left indent crack as a function of
constant applied load for Coors alumina Specimen C (Tables 24 and 26) with a 49 N
indent and composite tabs.

132

1.20

 

25 minutes at 32% r.h.

. Initial Loading

.1.

La.

01
I
I

 

 

 

1.10-—

1.05-

Relative Crack Length 2C(t)/20o
I l I I I T I I
0
0

1 T I

 

 

1.00 _WWF%W+AJJ_
0 10 20 30 40 50 60 70 80 90 100110120
Applied Constant Tensile Stress (MPa)

Figure 40 Plot of static fatigue crack growth as a function of constant applied load for
Coors alumina Specimen F (Tables 24 and 27) with a 98 N indent and stainless steel
tabs.

 

 

 

 

 

 

1.35 _
: 0
01.30 "L 8
0 I
g r-
3 1.25 -} 3
N .
5 : g 25 minutes at 32% r.h.
€1.20 _: . . . .
3 -_- lnItIal Loading
x .-
§ 1.15 ‘f 0
0 2
° 1 10 -'~ I
5: ° - Grips slipped-
% Z 32 um growth
0‘: 1.05 ..'_'_ from tightening
1.00 _W

0 1O 20 30 40 50 60 70 80 90 100110120
Applied Constant Tensile Stress (MPa)
Figure 41 Plot of static fatigue crack growth as a function of constant applied load for

Coors alumina Specimen H (Tables 24 and 28) with a 98 N indent and cold rolled
stainless steel tabs.

133

with increasing time at a constant applied tensile stress (Figures 40 - 42). Specimens
C, F, and I show very similar static fatigue behavior (Figure 43) while Specimen H
appears to be offset from the other specimens (Figure 43). The offset of Specimen H
may result from torsional stress which could have developed when the tensile grip was
tightened to stop the grip from slipping. Torsional stress would increase the load on
the crack shifting the specimen data to the right by the amount of the torsional stress

(Figure 43).

4.4 Crack Healing

Crack healing investigations were performed with: l) in-situ heating and in-situ
observation using an Environmental Scanning Electron Microscope (ESEM), 2)
conventional heating and observation using optical microscopy before and after

thermal annealing, and 3) microwave heating and observation using optical microscopy

before and after thermal annealing.

4.4.1 In-Situ ESEM Investigations of Healing in Soda-Lime Silica Glass

In-situ observation of the healing of Vickers indents in soda-lime-silicate glass was
performed using an Environmental Scanning Electron Microscope. The change in
crack length and crack morphology as a function of time and temperature was studied.
The effect of the initial humidity level on the crack healing behavior was also

investigated.

134

 

 

 

 

 

 

 

1.35 r
i 0
0°1-30 “' 25 minutes at 32% r.h.
N .-
531 25 _f_ x 150 minutes at 32% r.h.
0 ' .
or
5 . Initial Loading
€1.20 --
‘D +
.1
x
g 1.15 -~ g
0
.21J0“:
5 r
m
'- 0
“3 1.05 —_-
I c
1 00 _;A+I.I+IJ+JA_H+LLLL*H_IJ+I_LLI+LI+L+HJJ+LI_LL+IJ+L+HJJ+J_LI_L

 

0 10 20 30 40 50 60 70 80 90 100110120
Applied Constant Tensile Stress (MPa)

Figure 42 Plot of static fatigue crack growth as a function of constant applied load for
Coors alumina Specimen J (Tables 24 and 29) with a 98 N indent and composite tabs.

 

 

 

 

 

1.45 _
E Specimen ,
1.40 -;— Failed
0° ’ ° C
g1.35-_- 31! F Failed Failed
6’ :
or 1.30 --
5 E ° H
§125 -;— n J
-' :
§ 1.20 :—
5 :
m 1-15 "'-" NO Failure
.3 E Grips slipped-
3 1.101:- 32 um growth
C? E from tightening
1.05 “r
1.00 -.' '

 

O 10 20 30 40 50 60 70 80 90100110120130
Applied Constant Tensile Stress (MPa)

Figure 43 Plot of crack growth for static fatigue cycles at constant applied load and
relative humidity for Coors alumina Specimens C, F, H, J (Tables 24 to 29).

 

 

135
4.4.1.1 In-Situ ESEM Testing
Specimens of soda-lime silica glass were prepared for in-situ ESEM crack healing
testing as described in Section 3.6.1.1. The initial relative humidity conditions were
set in the ESEM by adjusting the initial sample chamber pressure and the initial
sample temperature via the cooling water temperature as described in Section 3.6.1.2.
The micrographs of the initial crack lengths were taken before the specimens were
heated. The heating schedules used are described in detail in the subsequent

subsections (Sections 4.4.1.1.1 to 4.4.1.1.5).

4.4.1.1.1 Healing at Temperatures up to 600 °C (Experiments A and B)

The reduction in crack length and the changes in crack shape for soda-lime silica glass
specimens were investigated for healing temperatures of 600 °C or higher. The
heating rates and dwell times for the two samples heated at 600 °C and higher are
described in Section 3.6.1.3.1.

In Experiment A, the specimen was initially held in the ESEM chamber at 25
°C and a water vapor pressure of 2.5 Torr, which corresponds to 10% relative
humidity. The initial indentation crack lengths in the specimen were approximately
190 pm. The crack length at 300 °C was identical to the initial crack length (Figure
44). As the crack was heated from 300 °C to 600 °C, the crack length continually
regressed from the tip toward the indent impression and the crack opening
displacement appeared to reduce as well. At temperatures above 500 °C, crack pinch
off also occurred along the length of the radial indent cracks as the crack tip regressed

toward the indent impression. When the specimen reached 600 °C, the average

 

136

indentation crack length had decreased to 96 pm, a decrease of 50 percent from the
initial crack length (Figure 45). Paint outlines along the healed portions of the crack
made the crack length hard to measure since it was difficult to define the end of the
crack (Figure 46). The faint outline along the healed portion of the crack in Figure 46
(at increased magnification in Figure 47) corresponds to closed portions of the crack
which have a small depression at the surface along the trace where the original crack
was located. After longer times at 600 °C the faint portions of the cracks disappear as
the small depressions along the surface trace heal completely (Figure 48).

While the specimen in Experiment A was held at 600 °C, multiple areas of
crack pinch-off were evident along the length of the crack (Figure 49). The pinch-off
exhibited during healing at 600 °C in the soda—lime silica glass was the result of a
change in crack morphology rather than a simple closing of the crack (Figure 49),
which demonstrates that the healing mechanism was not adhesion due to
intermolecular forces [33, 35].

Crack pinch-off behavior observed in the glass during Experiment A (Figure
49) was similar to that seen in other ceramic materials by other investigators [30-31,
34]. The pinched—off portions of the cracks appear to take on semi-elliptical shape
with the ends of each pinched-off segment being quasi-circular (Figure 50). However,
the indent crack pinch-off (Figure 49) does not show the evenly spaced pinch-off
proposed by Nichols and Mullins [40-41] and observed by other investigators [30-31,
34]. The uneven spacing between crack pinch-off locations may be related to the
increase in crack opening displacement along the length of the crack as one proceeds

from the crack tip to the indent impression. As the crack opening displacement along

137

 

    

Figure 45 ESEM micrograph of the soda-lime silica glass specimen upo reaching 600
°C exhibiting crack healing. The same indentation crack system prior to healing, is
shown in Figure 44 (Experiment A).

.L

138

 

,7 ._..__..,,_ 1...“, ‘1. u.

Figure 46 ESEM icpo the indent crack (labeled in Figure 45) five minutes after
reaching 600 °C exhibiting a faint outline along the healed portion of the crack
(Experiment A).

 
    

 

Figure 47 A higher magnification ESEM micrograph of the crack up of the crack shown
in Figure 46 demonstrating that the faint outline was a closed portion of the crack with a
small depression at the specimen surface (Experiment A).

139

 

 

.'|
c

.)

Figure 48 ESEM mhicrograp of medt of thesoda-lime Silica lass specimen
after 2 hours and 20 minutes at 600 °C illustrating the disappearance of the faint portion
of the crack depicted in Figures 46 and 47 (Experiment A).

Figure 49 ESEM micrograph of the indent crack (labeled in Figure 48) after an hour and
22 minutes at 600 °C showing multiple areas of crack pinch-01f (arrows) (Experiment A).

140
the crack increases (from upper left to lower right hand portion of Figure 49), the
distance between crack pinch-off locations also increases (Figure 49). After a total of
123 minutes at 600 °C (Figure 50), the crack opening displacement decreased. For
example, the crack opening displacements after 82 minutes at 600 °C in the pinch off
regions A, B, and C were 0.12, 0.18, and 0.21 pm, respectively (Figure 49), and after
a total of 123 minutes at 600 °C the crack opening displacements in the pinch off
regions A, B, and C decreased to 0.09, 0.12, and 0.18 pm, respectively (Figure 50).
The quasi-circular ends of the pinched-off regions of the crack, after 82 minutes at 600
°C (Figure 49) became much less rounded after the additional 41 minutes at 600 °C
(Figure 50).

In Experiment B, the glass specimen was initially held in the ESEM chamber
at 25 °C and a water vapor pressure of 2.5 Torr (10% relative humidity). Problems
with the hard drive of the storage computer networked to the ESEM resulted in the
loss of all of the micrographs from the initial indent crack, including the micrographs
of the indent crack after 25 minutes of heating at 550 °C. Crack pinch-off occurred in
soda-lime silica glass at healing temperatures of 550 °C (Figure 51). The pinched-off
portions of the crack had a semi-elliptical shape (Figure 52) and the ends of the
pinched-off portions were quasi-circular in shape (Figure 52).

For one of the cracks in Experiment B, a piece of debris was observed in one
of the cracks (Figure 53), in the pinched-off portion of the crack closest to the indent
impression (Figure 54). Figures 55 to 57 depict, respectively, a close up of the region
of the crack with the debris after 30 minutes at 575 °C, the same region after 5

minutes at 600 °C, and the crack morphology immediately after reaching 610 °C for a

141

     
   

Figure 50 ESEM micrograph of the indent crack (labeled in Figure 48 and shown in
Figure 49) after two hours and 3 minutes at 600 °C demonstrating further morphology
changes of the pinched-off regions of the crack (Experiment A).

 

Figure 51 ESEM migracroph of soda-lime silica glass specunen an 1er and 42 minutes
after reaching 550 °C exhibiting crack pinch-off (Experiment B).

     

        

Figure 52 A higher maognificatin ESEM mroicgraph of the seam crack shown in Figure
51 revealing the crack and crack tip shape in the pinched off regions (Experiment B).

.‘ . «n .

 

pinch-off and showing the location of the debris with an arrow (Experiment B).

143

Region of specimen
depicted in Micrograph

Crack

 

Debris

Pinch-off

 

Indent Impression

Figure 54 Schematic of the half indent crack (Figure 53) depicting the multiple crack
pinch-off, and the location of the debris (Experiment B).

 

Figure 55 ESEM micrograph of the indent crack (Figure 53) at 575 °C showing a close
up of area near the debris (arrow) and crack healing approaching the debris (Experiment
B).

       
   

 

Figure 56 ESEM micrograph of indent (Figure 53) at 600 °C showmg a close up of
area near debris (arrow) and crack healing passing the debris without complete healing
(Experiment B).

   

. , - 4‘ 41* 2 MW 147.13%},4.»
Figure 57 ESEM micrograph of the indent (Figure 53) at 610 °C sh
the bottom part of the crack approaching the debris (arrow) without complete healing in
the area of the debris (Experiment B).

r
J

145

similar field of view as Figure 53.

Healing progressed from the crack tip toward the indent impression (Figure 58)
for each of the radial cracks in Experiments A and B, except for the one radial crack
containing the debris (Experiment B, Figures 53-57). For the radial crack that
contained the debris, crack tip pinch-off and crack regression initially occurred from
the crack tip (Figure 55), as was the case for the other cracks without debris (Figure
58). However, as the crack tip regression and pinch-off healing progressed to the
debris site (Figure 56), the crack healing process changed. In the vicinity of the
debris, the crack is wedged open, apparently without healing (Figure 56). The crack
then regressed toward the debris from the end of the crack near the indent impression
(Figure 57). Also, the crack pinched-off between the debris and the nascent crack tip
(Figure 57 and Figure 58). Near the debris, complete healing still had not occurred
(Figure 57). The impediment of crack healing by debris could adversely affect the
healing of mechanically fatigued ceramics, since debris are generated during the

mechanical fatigue of ceramics [67].

4.4.1.1.2 Healing as a Function of Temperature (Experiment C)

In Experiment C, the specimen initially was held in the ESEM chamber at 27 °C and a
water vapor pressure of 2.1 Torr (8% relative humidity). Subsequently, the specimen
was thermally annealed at temperatures up to 490 °C. The crack healing behavior of
one of the four indent cracks was observed exclusively during heating so that the
healing behavior for smaller intervals of temperature change could be examined (than

if time was divided between observing four cracks). The initial length of the half

146

indent crack studied in Experiment C was 105 pm (Figure 59).

Experiment C exhibited crack healing at lower initial relative humidities and
lower temperatures than in the Experiment A. The half crack length at 400 °C had
decreased by only 4 pm from the original crack length (Figure 60) and after 10
minutes at 430 °C the half crack length was reduced by 30% (Figure 60).
Approximately 8 minutes after the specimen reached 490 °C (Figure 61), the crack
length decreased to 46 pm (a 55% reduction in crack length compared to the initial
crack length). Thus, significant crack healing can occur in soda-lime silica glass at

490 °C and some significant healing occurs at temperatures as low as 430 °C.

4.4.1.1.3 Healing as a function of Time at 430 °C (Experiment D)

In Experiment D (an isothermal hold at 430 °C), the specimen initially was held in the
ESEM chamber at 21 °C and a water vapor pressure of 2.4 Torr (14% relative
humidity). Before the sample was heated, the crack (with half cracks labeled or and B
in Figure 62) had a length, 2C” , of 182 pm at room temperature. After heating to
400 °C, the crack length (2Cafi) remained unchanged. Once the specimen temperature
reached 430 °C, the ESEM computer crashed. The sample was cooled at 20 °C per
minute to room temperature and the ESEM computer was re-booted. The ESEM
electron beam was re-aligned, micrographs of the indent cracks were taken.
Comparison of the micrographs taken before and after the ESEM was re-started,
revealed that the crack length, 2Com, had decreased in length to 170 microns as a result
of the heating from 400 to 430 °C before the computer crash. The crack length 2CaB

remained unchanged after re-heating from room temperature to 370 °C. The change in

147

(a)

Initial crack

 

 

Indent Impression
(b)

partially
healed crack

multiple pinch-off (c)
partially
healed crack

I with debris
Debris

Figure 58 Schematic of half of a Vickers indentation crack (a) before heat-treatment, (b)
after partial healing showing the typical regression of the crack from the tip toward the
indent impression together with multiple pinch-cit, and (c) containing debris
(Experiment B) after partially healing that includes crack regression toward the debris
from the end of the crack near the indent impression.

multiple pinch-oft

 

 

 

Figure 59 ESEM micrograph of a 105 pm long indention crack in a soda-lime silica
glass specimen at 27 °C and 8% initial relative humidity (Experiment C).

I48

 

P
m
I
l

P
a:
l
l

p
A
l
I

0.2 --

Relative Half Crack Length C(T)/C,,_,_

 

 

_
o ....I....I...11....I....1....l....l....l....l....

 

I l l l l I l I I
0 50 100 150 200 250 300 350 400 450 500
Healing Temperature (°C)

Figure 60 Relative change in crack length (C(T)/C(R.T.)) as a function of temperature
for a soda-lime silica glass specimen observed in-situ in an ESEM (Experiment C).

 

minutes at 430 °C displaying a decrease in the crack length to 46 pm (Experiment C).

149

length of crack [3 was measured as a function of time at 430 °C. During thermal
annealing at 430 °C, the crack length initially decreased rapidly but the rate of change

of crack length decreased in time (Figures 63-64).

4.4.1.1.4 Healing as a function of Relative Humidity (Experiments E-H)

For an isothermal hold at 430 °C, the effect of relative humidity on the temperature at
which healing begins was investigated in Experiments E-H. The effect of the initial
relative humidity on the rate of healing and on the total amount of healing also was
investigated in Experiments E-H. Samples in Experiments E, F, G, and H were held
at initial relative humidities of 8, 16, 32, and 64 %, respectively, before heating as

described in Section 3.6.1.3.4.

4.4.1.1.4.l Effect of Humidity on the Temperature where Healing Initiates

For the healing specimen initially held at 8% relative humidity (Experiment E), the
relative crack length did not change at 370 and 400 °C, but had a significant 28.5%
drop by 430 °C (Table 30, Figure 65). For the 16% relative humidity sample
(Experiment F), the relative crack length was not changed at 370 °C, but changed by
6.5% at 400 °C. The 32% r.h. sample (Experiment G) changed 0.6% by 370 °C, while
the 64% r.h. sample (Experiment H) exhibited 25% healing by 370 °C (Table 30,
Figure 65). For Experiments E-H, as the initial relative humidity increased, the
initiation temperature for crack healing decreased and the amount of healing at a given

temperature (above the initiation temperature) increased.

  

Figure 62 ESEM micrograph of the mdoentin cracks in a soda- ime silica glass specimen
at 21 °C and 14% initial relative humidity (Experiment D).

     

'11" '

 
 

Figure 63 13$ch of the same ind 7
minutes at 430 °C (Experiment D).

151

 

_.L
I
I

Heating Run
0 First + Second

I

t?)

 

 

.0
00
l

.9
a:
l

II—I—IIIrlTIIrIUT1I

P
A
1

Relative Half Crack Length C(t)/C,,_,.
.0
'i’

 

 

0 llllllllLlLlllllllllllLlLllJlllLlllILLJI
I I I I I l I I

30 40 50 60 70 80
Time at 430 °C (min.)

 

o
.5.
C
N
0

Figure 64 Relative change in length (C(I')/C(R.T.)) of crack [3 as a function of time at
430 °C for a glass specimen initially at 14 % r.h. observed in-situ in an ESEM
(Experiment D).

Table 30 Relative half indent crack lengths after heating to 370, 400 and 430 °C for
soda-lime silica glass samples with initial relative humidities of 8, 16, 32, and 64%

(Experiments E-H).

 

 

 

 

 

 

 

 

 

Relative Crack Length 8 %r.h. l6 %r.h. 32 % r.h. 64 %r.h.
m 1.000 1.000 0.994 0.750
C(R.T.)
2&3 1.000 0.935 0.923 0.698
C(R.T.)
30%;? 0.725 0.696 0.857 *0.630*
___________L_____l________

 

 

* Cracks had indications of pinch-off along regions of the length of crack.

152
4.4.1.1.4.2 Effect of Humidity on Healing with Isothermal Holds at 430 °C

Case and co-workers [68-73] investigated of thermal fatigue of ceramics and ceramic
composites and applied a semi-empirical relationship to describe the initially large
change and eventual saturation of properties (e. g. elastic modulus and fracture

strength) in time
PN = P0 + 19(1 — exp(-8N)) (10)

where PN is the property value after N thermal shock cycles at a fixed temperature
difference, P0 is the property value before thermal shock testing, D is the saturation
constant (Po - P“), P“, is the steady-state property value after many cycles, and 8 is
the rate constant (rate at which saturation is reached). Case and Wilson [74] applied a
general form of the same empirical relationship to describe the similar behavior found
in mechanical fatigue of ceramics. Case et al. [75] derived a form of the empirical

expression which described the saturation in crack length during thermal fatigue

9W) = a... - (a... - age-B” (11)

Equation 11 can be rewritten to provide a candidate equation to describe the relative

change in crack length as a function of time at 430 °C

C(t : [3.141] _ [(csat ’ Co) e-B: (12)
CO CO

CO

 

OI'

___.._C<'> = V1 — V2[e"V3] (13)

where C(t) is the crack length after time, t; at 430 °C, C(400°C) is the crack length at
400 °C, and where V1, V2, and V3 are constants. The constant V1 is related to the
relative crack length at saturation (C(t—>oo)/C(400°C) (Figure 66). The decrease from
the initial relative crack length to the saturated value of relative crack length is related
to the constant V2 and the initial rate of decrease in relative crack length is related to
the constant V3 (Figure 66).

Each of the data points in Figures 67 - 70 indicate a crack length measurement
from an ESEM micrograph and the solid lines indicate a regression fit of the crack
length data to Equation 13 using fitting parameters V1, V2, and V3. When the
specimen tested with an initial humidity level of 8% (Experiment E) reached 430 °C,
the crack length decreased to less than 80% of the length at 400 °C (Figure 67). For
times of 70 minutes or more at the 430 °C isothermal hold, the relative half crack
length of the 8% relative humidity specimen (Experiment E) saturated reaching a
steady state value of less than 40% of the crack length at 400 °C (Figure 67). For
Experiments E - H, the relative half crack length and time were related effectively by
Equation 13 (Table 31 and Figures 67 - 70), with the possible exception of the sample
tested with a 64% initial humidity (Experiment H, Figure 70). The sample initially
held at 64% relative humidity (Experiment H) had pinch—off along the crack length
which indicated that Equation 13 only describes crack healing by crack tip regression

and not healing in cases where pinch-off occurs.

154

 

0.95 -

0.9 H

‘IlrfiTlllI

0.85 -:—
0.8 '1}
0.75 —§-

0.7 “E-

  

 

0.6 i— . . .
5 E Relative Hum1d1ty(%)

0-6-3 +8 +16 *32+64
C
055 rhr=rrr=...irrri...'Lr..:...=.rrir..:...

350 360 370 380 390 400 410 420 430 440 450
Healing Temperature (°C)

Relative Half Crack Length C(T)/C(R.T.)

 

 

 

 

 

 

Figure 65 Relative change in crack length (C(T)/C(R.T.)) as a function of temperature
for soda-lime silica glass specimens with different initial humidity levels observed in-
situ in an ESEM (Experiments EH).

1

 

 

 

 

 

Relative Half Crack Length C(t)/C(400°C)

 

 

 

010 20 30 40 50 60 70 80 90
Time at 430 °C (min.)

Figure 66 Plot of the general form of Equation 13 with the constants V1 and V2
shown and constant V3 representing the initial rate of change of the relative crack
length.

155

 

 

0.2 --

Relative Half Crack Length C(t)/C(400°C)

 

 

 

010 20 3O 40 50 60 70 80 90
Time at 430 °C (min.)

Figure 67 Relative change in crack length (C(T)/C(400°C)) for all 4 indent half cracks
as a function of time at 430 °C for a glass specimen initially held at 8% r.h.
(Experiment B). Data points indicate ESEM measurements. Curve is a least squares
best fit to Equation 13.

 

1

 

0.2 --

Relative Half Crack Length C(t)/C(400 °C)

1111

010 20 30 40 50 60 70 80 90
Time at 430 °C (min.)

 

 

 

Figure 68 Relative change in crack length (Cm/C(400°C)) for all 4 indent half cracks
as a flmction of time at 430 °C for a glass specimen initially held at 16% r.h.
(Experiment F). Data points indicate ESEM measurements. Curve is a least squares
best fit to Equation 13.

156

 

 

 

 

 

 

1

9 I
O l.
o

S.” 0.8-—
Q .
6’ i
g, 0.6-—
c .-
o

J D
fi .-
9 0.4-‘-
0 r
’5', i
I 1-
g 0.2-.-
E .
m

u: r

o Lrhr:rrrr§rrrr:rr11%....:rrirIUhr%J_rrh:rrrr
0 10 20 30 4O 5O 60 70 80 90

Tlme at 430 °C (min.)

Figure 69 Relative change in crack length (CCU/C(400°C)) for all 4 indent half cracks
as a function of time at 430 °C for a glass specimen initially held at 32% r.h.
(Experiment G). Data points indicate ESEM measurements. Curve is a least squares
best fit to Equation 13.

 

1

 

0.2 --

Relative Half Crack Length C(t)/C(400 °C)

 

 

 

Time at 430 °C (min.)

Figure 70 Relative change in crack length (CCU/C(400°C)) for all 4 indent half cracks
as a function of time at 430 °C for a glass specimen initially held at 64% r.h.
(Experiment H). Data points indicate ESEM measurements. Curve is a least squares
best fit to Equation 13.

157

The exponential fitting parameter, V3, appears approximately constant over the
range of humidity levels, indicating that V3 is independent of humidity level for the
crack healing of the soda-lime silicate specimens tested (Figure 71). If the time at
temperature goes to infinity then the exponential term in Equation 13 goes to zero and
C(t=oo)/C(400°C) becomes equal to V,. Thus, V, represents the steady state relative
half crack length or the final degree of crack healing. The steady state relative half
crack length was similar for the 16, 32 and 64% initial r.h. specimens (Experiments F
-H). The steady state relative half crack length was the lowest for the 8% initial r.h.
specimen (Experiment E) indicating that the greatest healing occurred for the 8% r.h.
sample.

For zero time at 430 °C the exponential term in Equation 13 goes to one and
C(t=0)/C(400°C) becomes equal to {V, - V2}. The difference between V, and V2
represents the initial relative half crack length upon reaching 430 °C after heating from
400 °C. The quantity {V, - V2} was smallest for the 8% relative humidity sample
(Experiment E) thus for the lowest initial humidity there was the smallest amount of
healing by the time 430 °C was initially reached (Figure 71). The 32 % r.h. sample
(Experiment G) exhibited the largest amount of healing by the time the specimen
reached 430 °C as shown by the large {V, - V2} values. The large deviation at 32%
r.h. (Experiment G) compared to the 16 and 64% r.h. samples (Experiments F and H)
indicated the need for further testing in the range of 16 to 64% initial relative
humidity to see if there are maxima for the initial healing in the range of 16 to 64%.
Experiments I through M were conducted at 48% initial relative humidity and the

results are detailed in the Section 4.4.1.1.5.

158

Table 31 Fitting parameters, V,, V,, and V3 and correlation coefficients for the least
squares best fit of relative crack length as a function of time to Equation 13 (Figures
66-69) for initial relative humidities of 8, 16, 32, and 64% (Experiments E-H).

 

 

 

 

 

Initial Relative Fitting Fitting Fitting Correlation
Humidity Parameter Parameter Parameter Coefficient
(%) V1 V2 V3 r
8 0.366 -0.389 0.0414 0.983
16 0.499 -0.264 0.0334 0.928
32 0.532 —O.565 0.0478 0.934
64 0.520 -0.350 0.0212 0.562

 

 

 

 

 

 

 

cg@43000)_ _ -tv,
C(T=400°C)— V‘ v,[e I

 

.a
N

'0’V1 *VS +V1-V2

 

 

.0 .o .o
-b O) m -*
I I I I

.0
to
L

T I I I U I I I I I I I I I I I l I I I IiiT

Curve Fit Variable (V1, V3, or V1 -V2)

 

 

 

IAllIllllllllllllJJlllJlllJllllalfilllllll‘lllllllll

I I I I I I I I

I
10 20 30 40 50 60 70 80 90 100
Initial Relative Humidity (%)

 

O
0

Figure 71 Plot of the fitting parameters, V,, V,, and V,-V2 as a function of the initial
relative humidity for the least squares best fit of the relative crack length as a function
of time to Equation 13 (Figures 67-70) (Experiments E-H).

159

4.4.1.1.5 Healing with New Hot Stage Heater (Experiments I-M)

Samples in Experiments I-M were held at an initial relative humidity of 48% before
heating as described in Section 3.6.1.3.4. After another operator damaged the ESEM
hot stage, a new heater complete with internal thermocouple was installed on the hot
stage. For the samples of Experiments I-L heated to 430 °C, using a newly installed
heater, no healing was observed for isothermal holds at 430 °C. The absence of
healing in Experiments I-L was thought to be the result of a malfunction in the new
hot stage heater. It was believed that the temperature which the sample underwent
during testing was much lower than the temperature displayed by the hot stage. To
investigate the actual sample temperature in relation to the temperature displayed by
the hot stage, a sample was tested with an attached thermocouple (Figure 9,
Experiment M).

In Experiment M, a sample with a thermocouple cemented to the surface was
attached to a crucible as described in Section 3.6.1.3.5 (Figure 9). The crucible was
placed in the hot stage and tested in an identical manner to Experiments E-H and LL.
The measured sample temperature was as much as 90 °C lower than the 430 °C
temperature displayed by the hot stage. The large, 90 °C temperature difference
between the sample temperature and the displayed ESEM temperature in Experiment
M indicated a major problem with the new hot stage heater and the need for further
investigation of the sample surface and hot stage temperature.

In Experiment G, a sample with initial humidity of 32% was found to begin
healing at a temperature around 370 °C with less than a 1% change in crack length

(Section 4.3.2.142). While in Experiment H, a sample with 64% initial relative

160
humidity had crack healing of 25% at 370 °C (Section 4.3.2.142). For the sample

tested at 48% initial relative humidity in Experiment M, the only tangible positive
result that can be reached from the combination of the isothermal holds at a hot stage
displayed temperature of 430 °C, was that soda-lime silica glass held initially at 48%
relative humidity does not heal at a temperature of approximately 340 °C for times of

90 minutes or less.

4.4.1.2 Further Temperature Measurement of New Hot Stage Heater
The sample surface temperature compared to the ESEM controller temperature reading
was first investigated using a sample cemented in a crucible with a thermocouple
bonded to the surface of the sample (as in Experiment M). When the ESEM
temperature displayed was 400 °C, the thermocouple temperature was 343 °C (Table
32). When the ESEM display temperature was holding at 430 °C a voltmeter was
placed in the sample chamber to read the thermocouple directly instead of using the
vacuum pass-through ports on the ESEM door (as described in Section 3.6.1.3.5). The
direct thermocouple reading inside the ESEM sample chamber was identical to the
reading using the vacuum pass-through ports on the ESEM door which indicated that
for past and future ESEM hot stage testing, a sample thermocouple temperature could
be read using the vacuum pass through ports on the ESEM door.

With the old hot stage heater, the crucible had been a fixed part of the heater.
To try to make the new hot stage similar to the old hot stage, the crucible was
attached to the hot stage with silver paint. The specimen-mounted thermocouple

temperature with the crucible affixed to the hot stage was 33 °C lower than the 400 °C

161

temperature displayed by the hot stage (Table 32). To help determine the temperature
drop through the glass specimen, a thermocouple was silver painted directly (without a
glass specimen) to a crucible which was affixed to the new hot stage. A temperature
difference of 28 °C was measured between the thermocouple and the 400 °C
temperature displayed by the hot stage (Table 32). The temperature drop through a
glass specimen was only 5 °C, when the ESEM measured temperature was less than

550 °C (Table 32).

4.4.1.3 Heat Transfer Calculation of Temperature Differences of New Heater

To determine if the temperature differences measured in Section 4.4.1.2 were sirnply
the result of heat lost due to heat transfer through the crucible and the glass specimen,
heat transfer analysis was performed. Heat was transferred from the heater through
the crucible and specimen via conduction, while the heat at the top surface was lost
via free convection. The heat transfer problem was assumed to be a 1-D, steady state
heat transfer with no energy generation and constant thermal conductivity within each
different material. For these assumptions, the heat transfer rate is constant in the
direction of the temperature gradient from the heater surface through the glass
specimen surface [76] (Figure 72).

By treating the thermal resistance to conduction in an analogous manner to the
electrical resistance through an electrical circuit, the heat transfer rate can be expressed
as a function of the temperature drop across a given portion of the total resistance
circuit and the resistance from that portion of the circuit [76]. The heat transfer rate,

qz , through the circuit from the heater to the air is equivalent to the heat transfer rate

162

through the circuit from the sample surface to the air (Figure 72), such that

TESE — Tair : TSud'aca — Tair (l4)

Rtotal Rfcr

‘12:

where TESEM is the temperature reading of the ESEM heater, T“, is the air temperature
inside the ESEM sample chamber, Tm,“ is the temperature at the sample surface, Rm,
is the thermal resistance of the total circuit from the heater to air, and R,“ is the
thermal resistance which results from free convection at the surface. The temperature

at the sample surface can be found using Equation 14 can be rewritten as

T — T .
ESE arr (15)

 

TS ace : Tait
"If Rtoral Rfcs'
where T,,r and Tesm are known quantities and the thermal resistances Rum, and R,“ can

be calculated.

Thermal resistance to heat transport via conduction is given by [76]

Rconducn'on a (16)

where L is the thickness of the material in the direction of heat transfer, k is the
thermal conductivity of the material, and A is the area of the material normal to the
direction of heat transfer [76]. Thermal resistance to heat transport via convection is

given by [7 6]

R =_1_

convection h A

(17)

163

Table 32 Thermocouple temperature readings for three different testing conditions at
different ESEM new hot stage heater temperatures.

 

Testing Conditions TERM: Tm: Tam: T
400°C 430°C 500°C 550°C

Thermocouple Cemented to Glass Sample 340°C 366°C 421°C 459°C
Crucible Set into Heater

Thermocouple Cemented to Glass Sample 367°C 392°C 452°C 492°C
Crucible Silver Painted to Heater

Thermocouple Silver Painted to Crucible 372°C 397°C 457°C 500°C
Crucible Silver Painted t0 Heater

 

 

 

 

 

 

 

 

 

 

T8,, = 25° C
T=TSurlace
1.15
mm
0.9
mm

 

L[————|§:3$Tn_—_il J

 

 

[- 7.4 mm 1

Figure 72 Schematic of the ESEM heating stage for heat transfer determination of the
surface temperature.

164

where h is the free convection heat transfer coefficient of the gas [76]. The resistance

of the total heat transfer circuit in Figure 72, Rm“, is

 

 

 

r
_ LCB LCBL -1 Lcsr -1
Rm, — —— __ + __ .
1‘03 ACE kCBL ACBL kcsr Acsr (18)
1
[( L8 )‘1 + Lcsz ~1+ LCF a} + 1
kg Ag kcsz Acsz kCF ACF hair Aair

where the subscript CB indicates the crucible bottom layer, CBL indicates the cement
bonding layer, g indicates the glass layer, CS indicates the crucible sides and CF
indicates the cement filler layer. The values for thickness, L, and area, A, for each of
the layers indicated with subscripts in Equation 18 can be determined from Figure 72
and the values for k can be determined from handbook values [77] (Table 33). The
surface transfer coefficient of air must be calculated for the free convection at the top
surface. For the current case of no forced convection and lamellar air flow at a
horizontal heated surface, the surface transfer coefficient can be determined [76]

k. .L3T-T. 1
h z 054 arr gBarr P( : arr) 4 (19)
LP vegan,

 

where L,. is the area of the surface divided by the perimeter of the surface, g is
gravitational acceleration (m/sz), B is the expansion coefficient, v is the kinematic
viscosity (m/sz), or is the thermal diffusivity (III/82). For an ideal gas, the expansion
coefficient, [3, is equal to the inverse of the temperature of the gas (UK). A
temperature of 485.5 K was used to determine the material properties for free

convection, as calculated from the average of the temperature at the surface and the

165

temperature of the gas. Using Table 34 and Equation 19, the calculated convective
heat transfer coefficient, h,,,, was 25.7 W/K.

Using the calculated value for hm, the data from Table 33, and Equation 18, the
total heat transfer circuit, Rm, is 929.5 W. The temperature at the sruface was 395
°C, using Equation 15. The heat transfer analysis of the temperature loss through the
crucible and glass sample gave a derived temperature at the glass specimen surface of
395 °C while experimentally the temperature at the glass specimen surface was
determined to be only 367 °C. To investigate the validity of the heat transfer model,
the temperature drop through the glass specimen was determined using the model so
that the calculated temperature drop could be compared to the experimentally
determined temperature drop through the glass specimen of 5 °C (see end of Section
4.4.1.2).

To calculate the temperature drop through the glass specimen, the temperature
must be determined at the location along the heat transfer path before the glass which
resulted from the heat transferred from the heater. Recalling that the heat transfer rate,
qz, through each layer was assumed to be equal, the heat transfer can be expressed as

(Figure 72)

TESEM ' 7“ TES ‘ TBG

a1r_

 

 

‘12 = (20)

Rioral RBG

where the subscript BG indicates before glass, which refers to the location after the
cement layer and before the glass layer along the heat transfer path depicted in Figure

72. The thermal resistance before the glass is (Figure 72)

166

Table 33 Property values for different layers of the sample and ESEM hot stage
assembly for the total heat transfer resistance of Equation 18 (material properties from
[77], dimensions from Figure 72).

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Layer Material Layer Thermal Thickness Area
Subscript Composed of or Conductivity, k of layer, L of layer, A
Designation Closest Material (W/m K) at 400 °C (10“ m) (10" m2)
CB Mullite 4.18 9 4.24 H
CBL Mullite 4. 18 3 2.55
g N a-Ca-Si Glass 2.00 l 1 1.44
CSl Mullite 4.18 3 1.69
C82 Mullite 4.18 l 1.5 1.69
CF Mullite 4.18 5.5 1.11 ||

 

Table 34 Property values for free surface convection at the ESEM hot stage surface to
determine the convective heat transfer coefficient, hd, (material properties from [76],

 

 

 

 

 

 

 

 

 

 

dimensions from Figure 72).
A P LP kair Veir aair Bait
(m2) (m) (m) (W/mK (mZ/s) (1112/8) (l/K)
4.24x10'5 2.311(10'2 1.841th'3 39.71th'3 36.9):10'6 53.9x10’° 2.06x10'6

167

1
REG __ LCB + LCBL -1 + Les] 4], . (21)

'kA kA kA

CB CB CBL CBL CS1 CS]

Using the data from Table 33 with Equations 20 and 21, the temperature directly
before the glass was 397 °C. Thus, the temperature drop through the glass specimen
was determined to be 3 °C from heat transfer analysis. The experimentally determined
temperature drop through the glass specimen was 5 °C (see end of Section 4.4.1.2).

The similarity of the results demonstrates the soundness of the heat transfer
analysis and consequently highlights that the difference in the displayed temperature
and the sample temperature were the result of a large error in the ESEM hot stage
temperature display rather than due to heat loss from heat transfer through the crucible
and the glass specimen. A possible cause for the large error in the ESEM temperature
could be that the thermocouple in the heater used by the hot stage controller was
touching one of the heater wires. Regardless of the cause of the problem, the heater
either needs to be replaced and/or each sample tested must have a thermocouple

attached and measured independently from the ESEM hot stage controller.

4.4.2 Conventional Healing Experiments

Conventional crack healing experiments were performed on soda-lime silica glass,
Coors alumina and microwave sintered alumina specimens. In conventional crack
healing experiments, cracks were made in a specimen, aged, characterized, heated in a

furnace. Changes in the cracks brought on by the healing cycle were noted.

168
4.4.2.1 Soda-Lime Silica Glass

Six different experiments with a total of 113 specimens and 654 cracks were used to
investigate healing in soda-lime silica glass. Some specimens were heated after
preparation and prior to indentation to relieve the residual stress in the specimen due

to cutting and grinding.

4.4.2.1.1 Crack Healing and Strength Testing (Experiment 1)
Indented glass specimens were annealed in a large tube furnace to partially heal the
cracks (Section 3.6.2.2.3). The crack lengths were measured optically from crack tip
to crack tip before and after the thermal annealing cycle. The mean crack length after
the 24 hour age in laboratory air for all 12 specimens was 201.3 i 7.4 microns. The
mean change in crack lengths, {2cm - 2cm}, was calculated for all 12 specimens
(Table 35). The mean crack length changes for the thermally annealed samples
(Specimens 1-10 in Table 35) were higher than the crack length changes for specimens
only aged in air (Specimens 11-12 in Table 35) which indicates that significant crack
healing occurred during the heat treatment at 600 °C. Out of the six indent cracks for
each specimen, zero to six of the indent cracks displayed crack pinch-off when
observed optically (Table 35). The change in crack length significantly decreased as
the number of cracks which displayed pinch-off increased (Table 36).

For the thermally annealed specimens, the three-point bend Modulus of Rupture
values ranged from 72.5 to 101.8 MPa (Table 37). For samples aged in air the
Modulus of Rupture ranged from 46.3 to 47.9 MPa (Table 37). The higher Modulus

of Rupture values for the thermally annealed specimens compared to the unannealed

169

Table 35 Change in crack lengths {2c,n,,,,, - 2cm} for 6 cracks on each of ten soda-
‘lime silica glass specimens annealed in the large tube furnace for 30 minutes at 600 °C
and for 6 cracks on each of two glass specimens held at laboratory temperature.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Specimen Temperature of {2cm,,,_, - 2cm“) Number of indent
Number Heat Treatment Mean and Standard cracks with pinch off
Deviation (pm)
1 600 °C 34.6 :l: 15.2 0
2 600 °C 24.5 :I: 10.1 1
3 600 °C 1.4 i 0.9 6
4 600 °C 16.2 :I: 23.0 4
5 600 °C 1.2 i 9.6 4 II
6 600 °c 14.7 :|: 8.7 5 ||
7 600 °C 32.4 :I: 34.7 3
8 600 °C 45.7 :I: 7.7 0
9 600 °C 2.2 :l: 1.9 6
10 600 °C 12.8 i 11.3 6
lf 11 25 °C = 2.3 :l: 3.8 == 0 =

 

 

 

 

 

O

12 25 °C 1.8 i 1.4 II

Table 36 Change in crack lengths {2c,,,,,,,, - 2G,“) for groups of specimens from Table

170

 

 

 

 

 

35.
Specimens Temperature {2cm - 20w} Number of
Included in of Heat Mean and Standard indent cracks
Group Treatment Deviation (pm) with pinch off
per specimen
1 - 10 600 °C 18.5 i 21.4 0 To 6
l - 2, 8 600 °C 34.9 i 14.8 0 To 1
3-6,9-10 600°C 7.9:l:l3.8 4To6
11 - 12 25 °C 2.0 i 2.8 0

 

 

 

 

 

 

Table 37 Modulus of Rupture (stress at failure) for three-point bend testing of
specimens of glass annealed in the large tube furnace for 30 minutes at 600 °C and of
two glass specimens held at laboratory temperature.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

W Temperature of Wind Rupture

Number Heat Treatment (MPa)
1 600 °c 101.81
2 600 °c 76.0
3 600 °c 72.5
4 600 °c 922*
5 600 °c 85.6
6 600 °C 951* ll
7 600 °c 962* |
8 600 °C 888*
9 600 °c 820*
10 600 °C 936* II
11 25 °c 46.3 H
12 25 °C = 47.9 __I

 

 

 

 

 

 

I Indicates specimens which fractured outside of indent area
* Indicates specimens which fi'actured at the sample edge

171

specimens, indicates partial healing of the indent cracks occurred upon thermal
annealing at 600 °C.

Optical micrographs were taken of the middle indents for: a) a specimen aged
in air (Figures 73 and 74), b) a thermally annealed specimen which does not display
pinch-off (Figures 75 and 77), and c) a thermally annealed specimen which displays
pinch-off (Figures 78 and 80). The width of the cracks of the thermally annealed
specimens were greater than 5 pm (Figures 76, 77, 79, and 80), while the width of the
cracks of the unannealed specimens were around 1 pm or less (Figure 74). The indent
cracks of specimens annealed at 600 °C had a larger crack width (Figures 73 - 80) and
a shorter crack length (Table 36 and Figures 73 - 80) than the indent cracks of the
specimen only aged at room temperature. The change in the appearance of the optical
micrographs of indent cracks of the specimen without a thermal anneal (Figures 73 -
74) and of the specimens which were annealed (Figures 75 - 80), indicated that crack
healing occurred upon thermal annealing. The healed cracks in cases where pinch-off
did not occur (Figures 75 - 77) had a shorter distance from crack tip to crack tip than
healed cracks in cases where pinch-off did occur (Figures 78 - 80, Table 36). For
example, the change in crack length was 44.3 pm for the horizontal crack of indent B
in Specimen 8 (Figures 75 - 77) and was 3.1 pm for the horizontal crack of indent B
in Specimen 4 (Figures 78 - 80). However, if the crack length for the crack with
pinch-off (Figures 78 - 80) was measured fi'om the location of first pinch-off to the
location of first pinch-off on the other side of the indent, then the change in crack

length was 44.4 pm.

 

  

Figure 73 Optical mrograhicp of 1ndent imen eleven aged in room
temperature air. Other specimens were annealed at 600 °C (Table 33). The horizontal
crack in the unannealed specimen was approximately 190 pm in length.

  

: a.

Figure 74 Hrgher magnfinicatio optical micgraroph of the indent in unannealed glass
shown in Figure 73. Unannealed crack widths were less than approximately 1.5 pm.

  
     
 

Figure 75 Optical micrograph of indent B of glass specimen eight annealed at 600 "C for
30 minutes in the large tube filmace. The horizontal crack in the annealed specimen was
approximately 156 pm in length.

   
   

m ’11,
‘ ‘3“ .r

‘ 4* .. ' .NMW :. . s
Figure 76 Higher magnification optical microgra gure 75.
The crack width increased during annealing to greater than approximately 6 pm.

   

174

 

Figure 77 Higher magnrfiocatin optical mrcorgraph of one of the mdent cracks shown in
Figure 76. The crack tip appears blunted after annealing

Figure 78 Optical micrograph of indent B of glass specimen four which annealed at
600 °C for 30 minutes in the large tube furnace. The horizontal crack in the annealed
specimen was approximately 184 pm in length.

 

   

Figure 79 Hrgher magnification optical microhgrap f indet shown in Figure 78. The
crack width increased during annealing to greater than approximately 6 pm.

Figure 80 Hrgher magnification optical micrograph of one of indent cracks shown in
Figure 79. Extensive pinch-off at the end of the crack has occurred after annealing.

176

.4.4.2.l.2 Surface and Sub-Surface Crack Healing (Experiment 2)

Indented glass specimens were annealed in the large tube furnace at 550 °C for 30
minutes and the crack lengths were measured optically from crack tip to crack tip
before and after the thermal annealing cycle. In the optical microscope, the annealed
cracks were observed to have a heavy portion and a very faint portion of the crack
(Table 38). The heavy portion of the crack was characterized by a large crack
opening displacement with a rounded crack tip. The faint portion of the crack
extended from the end of the heavy portion of the crack and had negligible crack
opening displacement.

Healing in the specimens was markedly different for the faint and heavy
portions of the crack. The mean change in the crack length was about 17.7 pm for the
faint portion of the crack and about 48.8 pm for the heavy portion of the crack (Table
38). Healing is indicated by the crack tip regression of the total crack by 17.7, as well
as by the appearance of a negligible crack opening displacement in the faint portion of
the crack.

Optical observations of the specimen surface alone cannot determine if the
cracks below the specimen surface break into cylindrical voids and/or break into
spheres as seen in internal cracks by Wang et al. [30], Gupta [31, 34], and Yen and
Cable [32]. To investigate the crack healing below the surface, the thermally annealed
specimens were fractured through the partially healed indent cracks using the Kirchner
method [64]. The fracture surface of the specimens was observed in a conventional
SEM as detailed in Section 3.6.2.2.3. A line of voids, quasi-circular in cross-section,

was observed for a soda-lime silica glass specimen partially healed by a 30 minute

177

Table 38 Change in crack lengths {20initial - 2cm} for heavy and faint portions of
healed indent cracks for glass specimens annealed in the large tube furnace for 30
minutes at 550 °C. (Sample 1 fracture upon indentation with a 98 kg load).

 

 

 

 

 

 

 

 

Specimen Indent Crack Heavy Part of Faint Part of
Number (2cl or 2oz) Healed Crack Healed Crack
{20mm ' 201ml} (Pm) {zcinitial " 201ml} (pm)
2 1 60.4 6.0 '-
2 54.3 6.8
3 1 18.8 2.4
2 41.7 30.3
4 1 31.5 14.0
2 29.6 20.7
5 1 54.8 41.8
2 58.1 43.4
6 1 57.3 5.9
2 71.5 5.2
Mean and
Standard 48.8 :l: 16.4 17.7 :l: 14.9
Deviation

 

 

 

 

 

 

 

 

178

heat-treatment at 550 °C (Specimen 6 Table 38, Figure 81 - 83). While this
phenomenon needs to be investigated further, the voids seem similar to voids formed

by crack healing and pinch-off discussed by previous researchers [30-32, 34].

4.4.2.1.3 Effects of Stress Relief Cycle (Experiment 3)

Crack healing in glass after 15 minutes of annealing at temperatures of 350 to 500 °C
and below was investigated as described in Section 3.6.2.2.4 using the small tube
furnace. Glass samples were prepared with a stress relief cycle of 550 °C for 30
minutes and aged in air for 24 hours after indentation. The mean crack length change
(Acm = 2cm,l - 2cm) ranged from —2.6 to 0.3 microns with standard deviations
which ranged from 0.5 to 1.9 microns (Table 39). ACM values of 21:3 pm or less were
within an individual investigator’s standard error for crack length measurement in
glass (Section 4.2.1). No significant crack healing occurred at temperatures below 500
°C for a 15 minute hold.

A survey of the effect of a stress relief cycle before aging on crack healing in
glass was performed as described in Section 3.6.2.2.4 using the small tube furnace.
Glass specimens prepared 1) with a stress relief cycle of 550 °C for 30 minutes (Cycle
A from Section 6.62.22), 2) with a stress relief cycle of 600 °C for 60 minutes (Cycle
B from Section 6.6.2.2.2), and 3) without a stress relief cycle were thermally annealed
for times of 15, 30, 45, or 120 minutes and at temperatures of 525, 550, or 575 °C
(Tables 40 - 42). When the glass specimen with stress relief cycle A was being
thermally annealed at 575 °C for 15 minutes in the small tube furnace, the furnace

controller thermocouple failed and the furnace reached an unknown maximum

179

 

Figure 81 Conventional SEM micrograph of sub-surface portion of indent in glass
specimen six, annealed at 550 °C for 30 minutes in the large tube furnace. The specimen
was fractured through the healed indent using Kirchner's method [64].

   

i‘v’ t

Figure 82 Higher magnification conventional SEM micrograph of the specimen in
Figure 81 showing quasi-circular voids from region near the arrow of Figure 81.

180

 

Figure 83 Higher magnification conventional SEM micrograph of the specimen in
Figure 82 showing quasi-circular voids.

181

Table 39 Healed crack length change (29mm - 2cm) for glass specimens prepared
with a stress relief cycle of 30 minutes at 550 °C, indented and aged in air for 24
hours, and annealed for 15 minutes in the small tube furnace (Experiment 3).

 

 

 

 

 

 

 

 

 

 

 

Temp. (°C) 350 375 400 425 450 475 500 ll
Mean (pm) 0.0 -1.1 -0.1 .03 -2.6 0.3 0.17
(20mm ’ ZChuI)
Standard 0.9 1.9 1.3 0.9 0.5 1.0 1.8
Deviation (pm)

 

 

Table 40 Healed crack length change (2cmm - 2cm) for glass specimens prepared
with a stress relief cycle of 30 minutes at 550 °C, indented and aged in air for 24
hours, and annealed in the small tube furnace (Experiment 3).

 

 

 

 

 

 

 

 

 

 

 

 

 

L Temperature :- 525 °C 550 °C 575 °C
Anneal Mean Standard Mean Standard Mean Standard
Time (urn) Deviation (pm) Deviation (pm) Deviation
(pm) (11111) (tun)
15 min. 6.7 3.8 5.2 2.7 61.3' 16.0'
30 min. 7.4 3.2 2.1 1.1 15.3 7.7
45 min. 1.7 1.2 10.6 7.6 28.0 3.7
120 min. 13.8 1.9 20.3 5.0 49.3 9.5
L——L———H——————l L——.LI

 

' Indicates sample for which thermocouple failure occurred.

 

 

 

182

Table 41 Healed crack length change (20mm, - 2cm“) for glass specimens prepared

with a stress relief cycle of 60 minutes at 600 °C, indented and aged in air for 24
hours, and annealed in the small tube furnace (Experiment 3).

 

 

 

 

 

 

 

 

 

 

 

Temperature 525 °C 550 °C 575 °C
Anneal Mean Standard Mean Standard Mean Standard
Time (um) Deviation (pm) Deviation (pm) Deviation
(um) (um) (um)
15 min. * * 7.9 1.7 7.2 3.8
30 min. 22.5 3.6 5.2 1.5 17.1 3.9
45 min. 3.8 2.2 3.8 4.4 31.7 1.5
120 min. * * * * 61.5 4.1
* Testing was not perfonna for tns condition.

 

 

 

 

 

 

Table 42 Healed crack length change (20mm - 2cm.) for glass specimens prepared

without a stress relief cycle, indented and aged in air for 24 hours, and annealed in the
small tube furnace (Experiment 3).

-
.1

 

 

 

 

 

 

 

 

 

 

 

Temperature 525 °C 550 °C 575 °C
Anneal Mean Standard Mean Standard Mean Standard
Time (pm) Deviation (pm) Deviation (pm) Deviation
(tun) (pm) (pm)
15 min. * * -1.2 0.83 19.5 14.7
30 min. 6.1 2.3 2.5 1.3 1.9 1.1
45 min. 0.1 0.8 -4.0 4.3 -0.2 1.8
120 min. * * * * J 0.6 0.9
’ 'I'estrng was not per'formEH for tris condition.

 

 

 

 

 

 

183

temperature and so the Ache,ll value for the sample was not used in further analysis
(Table 40).

For the specimens with stress relief cycle A (Table 40 and Figure 84) which
were healed for 45 minutes or more, Ac,“ increased with time for each temperature
and increased with temperature for each time (Figure 84). For times less than 45
minutes, no correlation of time and temperature with Ache,“ values was apparent (Figure
84).

The lack of correlation of [5cml with time and temperature for healing times
less than 45 minutes indicated that either no crack healing was occurring for the
shorter time periods or that crack length regression was not the dominant mechanism
of crack healing. One other possible healing mechanism could have been a change of
the crack tip shape. Hrma, Han, and Cooper [42] investigated indentation crack
healing in glass at 600, 650, and 675 °C using optical microscopy (see Section 2.2.2
for description of Hrma et al.’s investigation). Hrma et al. [42] concluded that
blunting of the crack tips via capillarity driven viscous flow of the glass occurred
before regression of the crack lengths occurred. However, I-Irma et a1. [42] never
directly observed blunting via optical microscopy. To determine if crack tip blunting
occurred in the current study, the crack tips of the annealed samples were observed via
electron microscopy. ESEM observation was unsuccessful in determining if crack tip
blunting was occun'ing in the samples due to insufficient resolution. Observation of
the samples with a field emission microscope (Carnscan 44FE) was equally
unsuccessful due to problems with sample charging even at accelerating voltages as

low as 2 KeV.

184

For stress relief cycle B, testing for thermal annealing times of 45 minutes and
above was performed at 575 °C (Table 41, Figure 85). The Acw values for samples
with stress relief cycles A and B which were healed at 575 °C, were within one
standard deviation of each other (Tables 40 and 41, Figures 84 and 85). The samples
tested without a stress relief cycle had little or no stress relief even for thermal
annealing of 120 minutes at 575 °C as indicated by the indentation crack lengths
(Table 42 and Figure 86). Since the specimens without a stress relief cycle exhibited
a very different behavior from the specimens tested with a stress relief cycle, and
since the specimens with a stress relief cycle displayed a very similar behavior to each
other, further testing was performed using specimens which had a stress relief cycle at
a temperature between 550 and 600 °C. The stress relief cycle temperature was
determined from thermal mechanical analysis (TMA) and other high temperature
experimentation by Chiu [57] for the same soda-lime silica glass used in this study.
Chin [57] reported a large increase in thermal expansion in the 550 - 600 °C range and
chose a stress relief temperature of 580 °C for his work. Samples for Experiments 4 -

7 were prepared with a stress relief cycle at 587 °C (Section 3.6.2.2.2).

4.4.2.1.4 Effects of Aging Environment and Healing Temperature (Experiment 4)
Specimens prepared for testing as described in Section 3.6.2.2.1 were thermally
annealed in sets of three for 60 minutes at 525, 538, 550, 563, and 575 °C (Table 43
and Figures 87 and 88). Each of the three samples in a set was aged in a different
environment: 1) a desiccator with about 0 % r.h., 2) in laboratory air with about 45 %

r.h. (Figure 89), and 3) a water chamber with about 100 % r.h..

185

 

 

 

 

 

 

 

70
A I Healing Temperature (°C)
53, 60 —;— + 525 1a- 550 * 575
0‘ so 4-
2‘. i
.c l.
‘5. 4o ——
C .
O .
J n
a 30 —-
S r-
o
.5 20 --
m .
a, .
C
2 10 —-
0 I
o " .
o

 

Time at Healing Temperature (min.)

Figure 84 Mean crack length change (20m - 2cm) versus healing time for glass
specimens prepared with a stress relief cycle of 30 minutes at 550 °C, aged in air for
24 hours, and annealed in the small tube furnace (error bars indicate standard
deviations of six cracks) (Experiment 3). 2cm“ values were approximately 221 pm.

Healing Temperature (°C)
4* 525 -V- 550 0 575 /+

 

7O

IUYI

0’
O
l
l

 

 

 

01
O
I

h.
C
l

IU'UTF'IrTTIIIIIfiIrTII

0)
O
1

Change in Crack Length (2cm. - 20,)
i

 

d

O

I
III 1

 

 

 

0 - I l I l l l l I l l I I l l l I I—l ‘ l I l I I ‘4
l r r l.

0 20 40 60 80 100 120 140
Time at Healing Temperature (min.)

Figure 85 Mean crack length change (29m - 2cm) versus healing time for glass
specimens prepared with a stress relief cycle of 60 minutes at 600 °C, aged in air for
24 hours, and annealed in the small tube furnace (error bars indicate standard
deviations of six cracks) (Experiment 3). 20mm, values were approximately 219 um.

186

 

 

 

 

 

 

 

 

70
A t Healing Temperature (°C)
8 60 'E' + 525 + 550 * 575
'5 so {-
o‘ t
8" 40 -_~
5 t
8’ 301:
0)
—l E
g 20 -_-
E I
0 1o-;-
.5 .
S, 0-}—?% 1—
c -
g -
O ~10-E
_20P.l.:.iltrn 19% = =
0 20 40 60 80 100 120

Ttrne at Healing Temperature (min.)

Figure 86 Mean crack length change (2cm,l - 2cm) versus healing time for glass
specimens prepared without a prior stress relief cycle, aged in air for 24 hours, and
annealed in the small tube furnace (error bars indicate standard deviations of six
cracks) (Experiment 3). 2cm,l values were approximately 202 pm.

Table 43 Healed crack length change (2cm - 2cm) for glass specimens prepared
with a stress relief cycle of 180 minutes at 587 °C (~8 °C/ minute ramp rate), aged for
24 hours, and annealed for 60 minutes in the small tube furnace (Experiment 4).

 

 

 

 

 

 

 

 

 

 

 

 

 

Aging Humidity ~O% r.h. ~45% ~100% r.h.

Anneal Mean Standard Mean Standard Mean Standard
Temperature (pm) Deviation (urn) Deviation (pm) Deviation

(11m) (11111) (11111)

525 °C 27.1 5.0 32.3 2.0 39.7 5.4

538 °C 18.2 5.8 35.4 3.1 33.9 1.8

550 °C 23.6 3.7 35.0 2.0 31.4 7.9

563 °C 21.5 7.4 32.9 2.6 30.7 2.4

575 °C 15.6 1.8 25.3 3.6 21.0 8.8

 

 

 

187

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188

 

 

 

 

 

 

 

 

50
A [ Aging Environment
02 “ . 100 °/o r.h.
N 40 4-
L; a
9‘, .
5 30 -— [
or
c .
3 r \
“ +
a 20 ~—
0
.5
m
2’ 10 —-
us
.2
O

o . _% g l . l . l . l _L

 

 

l l l
513 525 538 550 563 575 588
Healing Temperature (°C)

Figure 88 Mean crack length change (20W - 20,“) versus healing temperature for
glass specimens prepared with a 180 minute stress relief cycle at 587 °C (~8 °C/min.
ramp rate), aged for 24 hours in 100 % r.h., and annealed for 60 minutes in the small
tube furnace (error bars indicate standard deviations of six cracks) (Experiment 4).

 

 

 

 

 

 

30 _ . 100
. E:_90
25-- 1
'\ l_,.__r—:'80
A *—' 3 Q
920“ ar-70 0;
T; _ +60 a
‘5 - E E
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.910 .l—30 i
5-: E-ZO
. 3‘10
0 biiiliiiiiHHiiiiiiiiliiiiiiiiiiiiiiiiiii: 0
8:00 12:15 1:25 2:55 7 00 8:35 11 :40 7:59
pml am I pm
TimeofDay

Figure 89 Circular chart recorder measurements of temperature and humidity during
indent crack aging in air. Measurements were made during a day in the time period
when healing experiments were performed.

189

4.4.2.1.4.l Aging Environments of 0 and 45 % r.h.

For specimens aged in air in the temperature range of 525 to 563 °C, Acm, was 33.6
pm (upper horizontal line in Figure 87), while for specimens aged in a desiccator Ac,“
was 23 pm (lower horizontal line in Figure 87). The difference in healing of about 10
pm between specimens healed in air and in a desiccator is significant with respect to
the error in crack healing measurement as discussed in Section 4.2.

With a difference in healing for samples aged in environments of 0 and 45 %
r.h, water vapor appears to be a factor in the healing of glass. Section 4.4.2.1.4.2
discusses the physical effect of water on: a) the structure of glass, and b) properties
such as the glass transition temperature and viscosity. The literature shows that water
significantly reduces the viscosity of the glass and lowers the glass transition
temperature (Section 4.4.2.1.4.2).

Aging samples in water vapor bearing environments results in water vapor
adsorption by the freshly created indentation crack surfaces. The adsorbed water
vapor can enter the glass structure via the crack surfaces before and/or during the
annealing cycle as the temperature is increased. A glass surface layer containing
incorporated water has a lower viscosity and glass transition temperature, Tg , than the
bulk glass. Varying the aging conditions will alter the amount of water that enters the
glass structure. Therefore, the magnitude of the decrement in viscosity and TE may be
a function of the ambient humidity. The higher Ac“, for glass specimens aged in air
compared to specimens aged in a desiccator is consistent with crack surface layers
with higher amounts of incorporated water which results in a lower T8 and viscosity.

At 575 °C, Acheal decreased by 25% and 32% for specimens aged in air and in a

190

desiccator, respectively (Figure 87). The mean Ac“, at 575 °C was about 10 pm
greater for the specimen aged in air than for the specimen aged in a desiccator (Table
43) which was similar to the differences in Acm observed for the two aging
treatments for the temperatures between 525 and 563 °C (Figure 87).

The decrease in Ache“ observed at 575 °C may be related to the specimen
temperature being close to the transition temperature. As glass is heated vibrational
amplitude of the ions increase with the increase in thermal energy [78]. As the glass
approaches the glass transition temperature, structural rearrangements occur which
absorb energy and change the specific volume of the glass [7 8]. The absorption of
energy through molecular rearrangements could decrease the energy available for

healing via atomic diffusion to the crack tip.

4.4.2.1.4.2 Review of Literature on the Presence of Water in Glass
The presence of water in glass and its effect on properties have been studied by many
researchers [79-85]. Bartholomew [79] noted that many studies of water in glass
investigated low water concentration introduced in the glass during the normal melting
process. Water contents of more than a few tenths of a weight percent require a
separate hydration processing step after the initial glass melt is made [79]. Processing
using traditional melting techniques leads to water only in the form of hydroxyl groups
only, while processing with a hydration step leaves hydroxyl groups and molecular
water in the glass [79].

Scholze [80] described the presence of water as hydroxyl groups in the

structure of glass. Scholze found that water is present in pure silica as free OH groups

191

which are bonded to only one Si atom (Figure 90) [80]. In alkali glasses, the OH
groups hydrogen bond to the singly bonded nonbridging oxygen anions created by the
alkali ion additions (Figure 90) [80]. The amount of bonded OH groups increases
with increasing alkali content, since increasing the alkali content increases the number
of nonbridging oxygens (NBOs) [80]. The addition of A1203 to alkali glasses with
water present decreases the amount of bonded OH groups, since alumina causes the
removal of NBOs [80]. The network change via the rupture of the Si-O—Si bridge
from the formation of Si-OH group effects both the viscosity and glass transition
temperature [80]. For example, in a 15:10:75 NazO-CaO-SiO2 glass, the glass
transition temperature decreased by 40 °C due to change in water content from 0.004
to 0.11 weight percent [80].

Jewell, Spess and Shelby [81] found that the water content of three different
commercial soda-lime-silica glasses changed by remelting the glasses under flowing
gas of different water vapor contents [81]. The water content of the as-received
glasses ranged from about 0.015 to 0.045 weight percent and the water content of the
reprocessed glasses ranged from 0.005 to 0.055 weight percent [81]. The glass
transformation temperature decreased by approximately 20 °C with increasing water
content for each of the three glasses [81]. The glass viscosity also decreased with
increasing water content for each of the three glasses with the activation energy for
viscous flow decreasing by 60 to 100 kJ/mol as the water content increased from
about 0.008 to 0.048 wt. % [81]. Infrared spectra bands indicated that the water in the
vitreous network was in the hydroxyl form which created NBOs [81]. The hydroxyl

units interact with network via weaker hydrogen bond instead of the O'-R*-O' ionic

192

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193
link between NBOs formed by alkali or alkaline-earth ions, R“ [81]. In the presence

of the hydroxyl units, the network structure was nearly completely broken at the
hydroxyl site and the effect on the flow behavior was increased compared to that from
the presence of alkali or alkaline-earth ions [81].

Tomozawa et al. [82] studied the thermal properties of sodium silicate
(Na20-3Si07) glasses which underwent a high pressure, hydrothermal, hydration cycle
to give water contents up to 8 weight percent [82]. Infrared spectroscopy found that
water in the glass was in both the hydroxyl and molecular water form [82]. At water
contents below 2 weight percent, infrared spectroscopy showed that the OH
concentration increased rapidly with increasing water content and then reached a
saturation concentration at about 6 weight percent water in the glass [82]. Infrared
analysis also indicated that the molecular water concentration increased slowly at first
as the water concentration increased up to about 6 weight percent, and then almost
increased linearly [82]. The Si-OH content drastically lowered the glass transition
temperature, T3 , since its presence was the result of broken Si-O-Si network bonds
[82]. Thermogravimetric analysis (TGA) showed no water loss at temperatures below
the glass transition temperature of 450 °C [82]. Tomozawa et al. comment that from
the results of their work, the glass transition temperature is expected to drop linearly
with low water content for most oxide glasses (where the water content is low and in
the hydroxyl form) and that an 18 °C drop in T8 is expected for a 0.1 wt. % increase
in the water content of the sodium silicate glass [82].

Schnatter et al. used resonant nuclear reaction to investigate hydrogen profiles

of soda-lime silicate glass hydrated in DI. water [83]. Plain soda-lime silica glass

194
(72.2 mol% S102, 21.4% N320, 6.4% CaO) had a hydration depth 0.2 pm after

hydratation for 5 hours at 23 °C [83]. A nearly 50% decrease in the hydrogen
concentration occurred in the plain soda-lime silica glass after a 12 hour age in
vacuum at 25 °C, while there was only about a 20% decrease in hydrogen
concentration after a one week age in air at 25 °C [83]. Commercial soda-lime silica
glass (72 mol% SiOz, 13% Na20, 5% CaO, 4% MgO, 3% A1203, 1% BaO, 1% B203,
and 1% other oxides) had a hydration depth 0.06 pm after hydratation for 16 hours at
80 °C [83]. Approximately a 14% decrease in the hydrogen concentration occurred in
the commercial soda-lime silica glass after a 12 hour age in vacuum at 25 °C, while
there was no decrease in hydrogen concentration after a one week age in air at 25 °C
[83].

Pantano et al. investigated the Auger Electron Spectroscopy (AES)
compositional profiles of mobile ions in the ion-milled surface of soda-lime silica
glass after exposure to air [84]. At the surface there was an increase in the
concentration of Na atoms and a decrease in Si atoms which resulted in a layer below
the surface where there was a depletion of the Na concentration and an enrichment of
the Si concentration [84]. The Na and Si concentrations returned to the bulk
concentrations of the glass at a depth of approximately 50 nm from the surface [84].
The surface reaction was a Na-H ion exchange between H from the adsorbed water
and Na at the surface and from the subsurface [84]. Thus, Na enrichment at the
surface from formation of a hydroxide and the resulting reaction causes a Na depletion
region which tends to retard further reaction [84].

In his text on glass science Doremus [86] comments that the reaction of silicate

195

glasses with the atmosphere is almost always caused by a reaction with water in the
atmosphere. The unsatisfied Si-O— and Si- bonds at the surface of the glass react
rapidly with the atmospheric water to form SiOH groups [86]. The thermal history of
the glass, the humidity, and the surface treatment after heating and cooling influence
the thickness and structural arrangement of the glass’s hydrated surface layer [86].
Rosington in a review of the surface chemistry of glass also comments that the
previous thermal history of a glass surface can greatly affect the adsorption of
hydroxyl groups to the surface [85]. At ambient temperatures, Doremus states that

water vapor ions exchange predominantly with the alkali ions in the glass

H20 + SiOR * = SiOH + ROH

where R is an alkaline-earth ion such as Na“ [86]. Ionic diffusion through the
hydrated layer formed on the glass surface is much higher than in the dry glass which
Doremus suggests may possibly be due to a weakened network through which ions can

more easily diffuse [86].

4.4.2.1.4.3 Aging Environment of 100 % r.h.

For specimens aged in a water chamber, the annealing temperature significantly
affected healing with Acw decreasing over the entire temperature range of 525 to 575
°C (Figure 88). In contrast for specimens aged in 0 or 45 % r.h., Acw was
approximately constant for healing temperatures of 525, 538, 550, and 563 °C (Figure
87). The continuous decrease in Ac“ with increasing temperature for 100 % r.h.

aging is consistent with crack surface layers having a greater amount of incorporated

196

water since this would reduce the Tg causing structural rearrangements to begin to
occur which would absorb energy required for material transport to fill the crack and
would result in reducing crack healing. A similar decrease in crack healing with
increasing temperature was observed for specimens aged in 0 and 45 % r.h. and

thermally annealed at 575 °C (Figure 87).

4.4.2.1.5 Effects of Aging Environment and Time at 525 °C (Experiment 5)
Specimens prepared for testing as described in Section 3.6.2.2.1 were thermally
annealed in sets of three for 60, 90, 120, 150, and 180 minutes at 525 °C (Table 44
and Figure 91). Each of the three samples in a set was aged in a different
environment: 1) a desiccator with about 0 % r.h., 2) in laboratory air with about 45 %
r.h., and 3) a water chamber with about 100 % r.h.. The healing behavior for aged
specimens thermally annealed at 525 °C for 60 minutes was markedly different in
Experiment 5 (Table 44 and Figure 91) than Experiment 4 (Table 43 and Figures 87
and 88). Ac,“ for specimens healed 60 minutes at 525 °C in Experiment 4 were 27.1,
32.3, and 39.7 pm for 0, 45, and 100 % r.h. (Table 43), respectively, while in
Experiment 5 the Ac,“ values were 1.0, 14.7, and -0.2 pm for 0, 45, and 100 % r.h.,
respectively (Table 44). Two possible factors could have led to the different behavior
of the 525 °C/60 minute samples in Experiment 5 and the lack of a clear time
dependence: 1) 525 °C is the temperature at which healing begins which could lead to
a large scatter in results, and/or 2) the stress relief cycle heating and cooling rate of 10
°C/minute is too fast for complete stress relief. To determine if the low thermal

annealing temperature was the problem in Experiment 5, Experiment 6 tested samples

197

Table 44 Healed crack length change (2cm.I - 2cm) for glass specimens prepared
'with a stress relief cycle of 180 minutes at 587 °C (10 °C/ minute ramp rate), aged for
24 hours, and annealed at 525 °C in the small tube furnace (Experiment 5).

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

ll Aging Humidity - ~0% r.h. J] ~45% || ~100% r.h. |
Anneal Mean Standard f Mean Standard Mean Standard
Time (pm) Deviation (um) Deviation (um) Deviation

(pm) (11111) (111“)
60 1.0 1.3 14.7 5.7 0.2 3.1
90 12.1 1.8 16.8 1.9 16.1 7.2
120 2.1 2.0 8.3 2.4 13.8 2.0
150 13.5 3.4 19.2 1.7 9.5 9.0
180 -4.2 0.9 9.3 1.9 6.0 3.8
50
,2 ' Aging Environment
§ 40_; + 45%r.h. * 0%r.h. & 100 %r.h.
0° r
8 30 -r
c .
46’ ..
ac) .-
_| 20 "b
x 1'
8 C
o 10—-
.5 -
Q)
U)
E O
c .
o
-10 ' . 1 1 1 1 1 1 1
o 30 60 90 120 150 180

Time at 525 °C (min.)

Figure 91 Mean crack length change (2cm - 20,“) versus healing time for glass

specimens prepared with a stress relief cycle of 180 minutes at 587 °C (10 °C/ minute
ramp rate), aged for 24 hours, and annealed at 525 °C in the small tube furnace (error
bars indicate Standard deviations of six cracks) (Experiment 5).

198

with the same stress relief cycle as in Experiment 5, but used a thermal annealing

temperature of 575 °C.

4.4.2.1.6 Effects of Aging Environment and Time at 575 °C (Experiment 6)
Specimens prepared for testing as described in Section 3.6.2.2.1 were thermally
annealed in sets of three for 60, 90, 120, and 150 minutes at 575 °C with each of the
three samples in a set aged in a different environment: 1) a desiccator with about 0 %
r.h., 2) in laboratory air with about 45 % r.h., and 3) a water chamber with about 100
% r.h. (Table 45 and Figure 92). While the Ac,“ value for the 100 % r.h. aged
specimen healed for 60 minutes at 575 °C was essentially the same in Experiment 4
(39.7 pm, Table 43) and Experiment 6 (39.1 pm, Table 45), the Ac,“ values for the 0
and 45 % r.h. aged specimens were very different in Experiment 4 (27.1 and 32.3 pm,
respectively, Table 43) and Experiment 5 (8.3 and 14.1 pm, respectively, Table 44).
As in Experiment 5, no clear time dependent behavior for the 575 °C thermally

annealed specimens was demonstrated in Experiment 6 (Figure 92).

4.4.2.1.7 Effects of Aging Environment and Time at 550 °C (Experiment 7)
Specimens prepared for testing with a 5 °C/minute stress relief cycle ramp rate as
described in Section 3.6.2.2.1 were thermally annealed in sets of three for 60, 90, 120,
240, and 480 minutes at 550 °C with each of the three samples in a set aged in a
different environment: 1) a desiccator with about 0 % r.h., 2) in laboratory air with
about 45 % r.h., and 3) a water chamber with about 100 % r.h. (Table 44 and Figures

92 and 93). The healing in aged specimens thermally annealed at 550 °C for 60

199

Table 45 Healed crack length change (2cm - Zone“) for glass specimens prepared
with a stress relief cycle of 180 minutes at 587 °C (10 °C/ minute ramp rate), aged for

24 hours, and annealed at 575 °C in the small tube furnace (Experiment 6).

 

 

 

 

 

  

 

 

  

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

' Aging Humidity || ~0% r.h. ~45% ~100% r.h. I
Anneal Mean Standard Mean Standard Mean Standard
Time (pm) Deviation (pm) Deviation (pm) Deviation

(pm) (11111) (pin)
60 8.3 2.0 14.1 2.0 39.1 9.5
90 8.3 1.2 11.9 1.9 6.5 6.4
120 2.7 2.1 4.0 1.7 6.1 2.6 H
150 2.8 1.0 18.7 2.4 25.7 6.0 ||
70

f: _ Aging Environment

05 607 + 45%r.h. a. O%r.h. 0 100%r.h.

‘1‘ 50 -{

0° .

at 40 -_

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20 40 60 80

l

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100 120 140 160 180 200
Time at 575 °C (min.)

Figure 92 Mean crack length change (2cm,l - 2015.1) versus healing time for glass

specimens prepared with a stress relief cycle of 180 minutes at 587 °C (10 °C/ minute
ramp rate), aged for 24 hours, and annealed at 575 °C in the small tube furnace (error
bars indicate standard deviations of six cracks) (Experiment 6).

200

Table 46 Healed crack length change (201nm - 2cm) for glass specimens prepared
with a stress relief cycle of 180 minutes at 587 °C (5 °C/ minute ramp rate), aged for
24 hours, and annealed at 550 °C in the large tube furnace (Experiment 7).

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Time at 550 °C (min.)

Aging Humidity ~0% r.h. ~45% ~100% r.h.
Anneal Mean Standard Mean Standard Mean Standard
. (um) Deviation (pm) Deviation (urn) Deviation
Tune RamP Rate (11m) (11111) (urn)
(°C / min.)
60 5 35.3 3.8 46.7 2.5 56.2 9.3
60 5 & 2.5 33.0 1.1 43.2 2.9 37.8 4.6
90 5 & 2.5 36.8 1.5 49.1 5.7 55.2 3.7
120 5 & 2.5 34.9 1.9 40.7 3.2 44.6 5.6
240 5 & 2.5 50.3 3.3 69.9 4.3 66.7 6.6
480 5 & 2.5 41.5 2.3 63.5 5.4 52.6 4.0
Q 70 {—
8 60 ~3-
0° 3
S! 50 —— ,,
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5 10-: + 45 % r.h. * o % r.h.
o ' 1 a . 1 1 1 - 1 1 . 1
0 60 120 180 240 300 360 420 480

Figure 93 Mean crack length change (2cm - 2cm“) versus healing time for glass

specimens prepared with a stress relief cycle of 180 minutes at 587 °C (5 °C/ minute
ramp rate), aged for 24 hours, and annealed at 550 °C in the large tube furnace (error
bars indicate standard deviations of six cracks) (Experiment?)

201

minutes was Slightly higher in Experiment 7 (Table 46 and Figures 93 and 94) than
Experiment 4 (Table 43 and Figures 87 and 88). The Acheal values in Experiment 4
were 23.6, 35.0, and 31.4 pm for specimens aged at 0, 45, and 100 % r.h. (Table 43),
respectively, while in Experiment 7 the Ache“ values were 33.0, 43.2, and 37.8 pm for
specimens aged at 0, 45, and 100 % r.h., respectively (Table 46).

The higher values for Aclml in Experiment 7 compared to Experiment 4 were
likely due to the use of different furnaces for thermal annealing in the two
experiments. The large tube furnace of Experiment 7 has a larger temperature
overshoot than the 1 or 2 °C overshoot of the small tube furnace of Experiment 4
which leads to a significantly larger maximum temperature (Table 47). To reduce the
large 17 °C overshoot from the 5 °C/minute heating rate (Table 47) a second ramp rate
of 2.5 °C/minute was used once the temperature reached 70% of the set temperature
(in Kelvin). The lower heating rate reduced the temperature overshoot to only 6 °C
(Table 47 and Figure 95).

For samples aged in air and thermally annealed for 60 minutes in Experiment
7, ACM was about 10 pm greater than Ache“ for specimens aged in a desiccator (Table
46 and Figure 93). Similar behavior was observed in Experiment 4 (Table 43, Figure
87). The difference in Ac],ml between samples aged in air and in a desiccator increased
with thermal annealing time in Experiment 7 from about 10 microns at 60 nrinutes to
about 22 microns after 480 minutes (Table 46 and Figure 93). For samples aged in air
and samples aged in a desiccator, the ACM increased with healing time for times of
60, 90 and 240 minutes and remained constant or decreased slightly at 480 minutes

(Table 46 and Figure 93). The Specimens healed for 120 minutes did not display an

202

 

 

 

 

 

Aging Environment
'9' 45 % r.h. 9 100 % r.h.

 

 

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120

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180 240 300 360 420 48

Time at 550 °C (min.)

Figure 94 Mean crack length change (20mm - 20“) versus healing time for glass
specimens prepared with a Stress relief cycle of 180 minutes at 587 °C (5 °C/ minute
ramp rate), aged for 24 hours, and annealed at 550 °C in the large tube furnace (error
bars indicate standard deviations of six cracks) (Experiment 7).

Table 47 Holding and maximum Specimen temperature for glass specimens prepared
with a stress relief cycle of 180 minutes at 587 °C (5 °C/ minute ramp rate), aged for
24 hours, and annealed at 550 °C in the large tube furnace (Experiment 7).

 

f
I

 

 

 

 

 

 

 

 

 

 

Time at Thold Ramp Rate + Maximum Temperature, Holding Temperature,
(°C / min.) Tm (°C) Tron. (°C)
60 5 570 553
60 5 & 2.5 559 553
90 5 & 2.5 555 549 II
120 5 & 2.5 555 547 ]|
240 5 & 2.5 557 547 1|
“0 5&z5 5m M9 1

 

203

600

 

Tmax=570 00 A OTmux=559 °C

 

0'1

0

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l

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Ramp Rate
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' ’ 2.5 & 5 °C/min.

Temperature (°C)
[0 0)
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O O
l l

 

 

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O
I

IIIIIUUIlITTIITITIIIIIUIIIIT—IITTITTI—IIIITIITUWU111I1111IT

 

 

 

l I l l
1 OO 1 50 200 250 300
Time (min.)

0
01
0

Figure 95 Temperature profile of two different thermal annealing ramp rates for glass
specimens annealed for 60 minutes in the large tube furnace (Experiment 7).

204

increase Ache,“ compared to Ache,“ for the 90 minute specimen (Table 46 and Figure
93). Additional testing would be required to determine if a different behavior occurs
for samples thermally annealed for times between 90 and 240 minutes or if the 120
minute sample run was an anomaly.

The specimens aged in a water chamber displayed thermal healing behavior
similar to specimens aged in air with Acml values which were within a standard
deviation of each other for healing times between 60 and 480 minutes (Table 46 and
Figure 94). In Experiment 4, the Acheal values for the specimens aged in air and in a
water chamber and thermally annealed at 550 °C for 60 minutes were also within a

standard deviation of each other (Table 43).

4.4.2.1.8 Residual Stress Relief Cycle Testing

Since the residual surface stresses created during machining can change the crack
healing observed, the crack lengths of the indents made before and after different
heating cycles were used to evaluate the residual surface stress in machined glass
samples and the optimum heating conditions required to relieve the stress as described
in Section 3.6.2.2.6. Eleven aged indents were measured before the samples
underwent time-temperature heating cycles (Table 48). Within 23.5 to 24.5 hours after
the specimens underwent a heating cycle, eleven new indents were made in the

specimens, aged, and measured (Table 48).

205

Table 48 Pre-heat-treatment (2CR) and post-heat-treatment (2CA) mean and standard
deviation of 22 indent crack lengths in glass specimens along with calculated residual
stress relieved during small tube furnace heating cycles at different temperatures and
times.

 

Pre-heat-treatment

Heat Treatment Cycle:

 

Post-heat-treatment

 

 

 

 

 

 

 

 

 

Mean and Mean and
Standard Deviation Number Time at Standard Deviation
ZCR (pm) Temperature ZCA (pm)

(Minutes @ °C)
202.5 :1: 6.3 1 45 @ 550 214.9 :1: 5.1
199.9 i 6.6 2 Ti 60 @ 600 214.3 :1: 4.3
3 ~60’ @ ~ 450'
202.8 d: 6.9 60 @ 625 219.1 i 3.4
200.6 i 7.2 4 Ti 60 @ 625 214.5 :1: 4.6
205.5 i 5.9 5 Ti 60 @ 650 208.3 :1: 4.3
203.8 i 5.8 6 T 185 @ 587 216.1 :1: 6.6
7 60 @ 425
204.1 :1: 7.1 180 @ 587 212.3 i 2.8
202.7 :1: 6.8 ALL ALL 214.3 :1: 5.6

 

 

 

 

* Furnace was inadvertently unplugged on heating; after about an hour the furnace

was turned back on and heating was continued to 625 °C.

1 Two samples which had been stacked on top of each other before the heat

treatment cycle were not bonded together after the heating cycle.

it Two samples which had been stacked on top of each other before the heat

treatment cycle were bonded together after the heating cycle.

 

 

206

4.4.2.181 Bulk Viscous Flow of Glass During Heating Cycle

For heat treatment cycles 2, 4, 5, and 6 (Table 48), two 75 mm X 75 mm X 1 mm
(0.3 in. X 0.3 in. X 0.045 in.) glass squares were Stacked upon each other and placed
in the furnace next to the glass Specimen being heat treated to relieve stress. Whether
the two squares bonded together or not during the heat treatment cycle is indicated in
Table 48. Bonding was not observed at 587 °C, but was observed at 600, 625, and
650 °C, indicating that viscous flow begins to occur at temperatures between 587 and
600 °C. Since viscous flow during heat treatment could lead to distorted surfaces,
stress relief cycle temperatures of 587 °C and below were used to avoid surface
irregularities.

The study of crack healing in glass by mechanisms other than viscous flow was
one aim of Section 4.4.2.1. and thus annealing temperatures of 587 °C and below were
used to investigate the healing behavior of glass. Since bonding was not observed
below 587 °C (Table 48), bulk viscous flow should not have occurred during healing
at temperatures of 575 °C or less (Sections 4.4.2.1). Although bulk viscous flow
should not have occurred in the samples, viscous flow along the crack surfaces due to

water absorption during aging may have occurred.

4.4.2.1.8.2 Residual Stress Relieved During Heating Cycle

The change in residual stress in each sample in Table 48 was calculated from the pre-
heat-treatment mean crack lengths and the post-heat—treatment mean crack lengths
(Table 48). Marshall and Lawn [87] describe a method for detemrining the residual

stress relieved during heat treatment using indentation crack lengths made before and

207

after heat treatment. For two sets of indent cracks created at the same indentor load,

the change in stress, AGR, due to thermal heat treatment is described by [87]

 

AUR =

 

(3)11] (22)

 

 

where Kc is the fracture toughness, CR is the pre-heat-treatment half indent crack
length, and CA is the post-heat-treatment half indent crack length. For soda-lime-silica
glass, the fracture toughness is about 0.75 MN/mLs [88] and substituting this value into

Equation 22 resulted in the following equation

1

_ MN 7
AUR - 0.6653 CR CR

 

(31);- 1]. (23)

 

 

Equation 23 was used to calculate the change in residual Stress in each sample using
the pre-heat-treatment mean crack lengths and the post-heat-treatment mean crack
lengths (Table 48). According to the A0,, values calculated from Equation 23, residual
stress ranging from 1.35 to 8.10 MPa was relieved during heat treatment (Table 48).
To get a qualitative view of the effect of heat treatments on the residual stress
relief, the pre- and post- heat-treatment mean crack lengths (Table 48) were plotted as
a function of the heat treatment cycle number (Table 48) in Figure 96, where each
data point represented the mean of 22 indent cracks and the vertical bars represent the
standard deviations from the mean. Horizontal lines represent the mean pre- and post-
heat-treated crack lengths for all seven heat treatment cycles (Figure 96). The pre-

heat-treated crack lengths for each specimen was within one standard deviation of the

208

250

 

I

225 -

lIlj—[I

...._L
fiat-4-

 

-<>— 4-
—+
@-

7’]

200 -

Crack Length (pm)
:1
01
l

 

9 Pre-heat-treatment ' Post-heat-treatment

 

 

 

IIIIIIIII'IIIIIIIfiIIII

 

 

 

100 l i i i i i 4.
0 1 2 3 4 5 6 7 8
Heat Treatment Cycle Number

Figure 96 Pre- and post-heat-treatment mean of 22 indent crack lengths of glass
specimens heat treated in different cycles as indicated in Table 48 (data points indicate
means, vertical bars indicate standard deviations from mean, and horizontal lines
indicates means for all seven cycles together).

209

group mean for all the samples tested. For the post-heat-treated crack lengths of the
specimens, the specimens thermally heated in cycle 3 and 5 appear to be greater than

one Standard deviation from the group mean for all samples tested.

4.4.2.183 Statistical Analysis of Heat Treatment Cycles

The pre- and post- heat-treatment group means were compared statistically using a
two-tailed t—test. To test if the two random and independent population means, 11, and
11;, were equal (or if 11.2 - 111 = 0), the population was assumed to be normal or
approximately normal and the population Sizes, III and n2, were large (111 = r12 = 152).
The decision alternatives were

Ha=11a=ur (O’H’F‘1=O)
1113112731111 (with—11.1950) .

The test statistic, t', followed the t distribution with nl + 112 - 2 degrees of freedom and

was determined by the following equation [89]

t‘ = ”'2 ‘ I"'1 (24)
.9012 ' “1)
where
:2 :2 25
30112—81): iJ’i ()

and where S2 and s1 were the standard deviations of population 2 and 1, respectively.

210

The value for the t distribution was determined from a table [89] by the degrees of
freedom, n, and the a risk. The a risk was the risk of incorrectly concluding that the
hypothesis H() was true. The on risk used was 0.01. The decision rules were:

If |t‘| S t(1 - a/Z; n), conclude H0: #2 = 11.1
If |t“| > t(1 — a/Z; n), conclude H1: p2 at #1

The test statistic for the pre- and post- heat-treatment group means was
calculated using Equation 24 and the data in Table 49 to be 1* = 16.24. With 11 = 152
+ 152 - 2 = 302, the value for t (1 - (ll/2; n) was 2.592. Since 2* > t (1 - (#2; n), the
conclusion reached was that the pre- and post- heat-treated group means were not
equivalent. The statistically significant increase in mean crack length for specimens
indented after heat treatment indicates significant residual stress was relieved during
heat treatment.

Heat treatment cycles 3 and 5 had a post-heat—treatment specimen mean which
were statistically different from the post-heat-treatment group mean (Table 49), while
all of the pre-heat-treatment specimen means were statistically the same as the pre-
heat-treatment group mean, indicating that these heat treatment cycles were no better
or worse at removing residual stress than the other cycles. The post-heat-treatment
mean for heat treatment cycle 5 was statistically lower than the other heat treatment
cycles indicating that heat treatment at 650 °C would not be desirable to remove
residual stress.

The significantly higher sample post-heat-treatment mean for heat treatment

cycle 3 was unexpected because the furnace was inadvertently unplugged on heating

211

Table 49 Calculated f" values for glass specimens using Equation 24 with data from
Table 48. Hypothesis decisions for comparison of individual glass heat treatment
cycle specimen means with the overall pre- and post— heat-treatment group means
using on = 0.01, n = 172, and t (l-a/2; n) = 2.609.

 

 

 

 

 

 

 

 

 

 

Pre-heat-treatment Heat Post-heat-treatment
Treatment
Test Statistic Same mean as CYCIC . Test Statistic Same mean as
t* group mean for Number. t* group mean for
on risk = 0.05 a risk = 0.05
-O.138 Yes 1 0.509 Yes
—1.853 Yes 2 0.000 Yes
0.064 Yes 3 5.61 1 No
-l.287 Yes 4 1.110 Yes
2.039 Yes 5 -5.864 No
0.812 Yes 6 1.217 Yes
0.869 Yes 7 -2.586 Yes

 

 

 

 

 

 

 

212

and after about an hour the furnace was turned back on to continue heating to 625 °C.
Two additional heat treatment cycles were investigated to determine whether the
increased post-heat-treatment crack lengths resulted from the hold at 425 °C or from
heat treatment at 625 °C. For heat treatment cycle 4 (625 °C for 60 minutes), a
significant increase in specimen mean was not observed. To determine if holding at a
temperature around 425 or 450 °C resulted in the increased specimen mean, the
temperature for heat treatment cycle 7 was temporarily held at 425 °C for 60 minutes
before the temperature was increased and held at 625 °C, as in heat treatment cycle 6.
Heat treatment cycle 7 did not have a statistically higher specimen mean (Table 49)
indicating that the 425 °C hold was not responsible for the statistically higher mean in
heat treatment cycle 3.

The heat treatment cycles which were most effective in relieving residual stress
in glass specimens (as represented by the largest mean crack length) had maximum
heat treatment temperatures below 650 °C and were heated continuously up to the
maximum heat treatment temperature (Table 49). Consequently, glass specimens
which were heat treated for other experiments as a part of the current investigation
were heat treated at a maximum holding temperature of less than 600 °C and were

continuously heated to the maximum hold temperature.

4.4.2.1.8.4 Analysis of a 4 Month Age after Heat Treatment Cycle
For specimens aged in laboratory air for 4 months before post-heat-treaunent
indentation testing was performed (Table 50), the post-heat-treatment mean crack

lengths were significantly larger than the group post-heat-treatment mean crack lengths

 

213

of Table 48 indicating that a significantly larger amount of residual stress was relieved
compared to the heat-treatment cycles in Table 48 (Table 51). To check if the four
month age was responsible for the increased stress relief or if it was the heat treatment
at 525 °C, another specimen with identical heat treatment was tested after a 24 hour
age. The specimen aged for 24 hours after heat treatment at 525 °C for 60 minutes
had post-heat-treatment mean crack lengths which were significantly larger than the
group post-heat—treatment mean crack length of Table 48 (Table 51). The data from
Tables 50 and 51 indicate that for future glass sample preparation, the best heat
treatment for residual stress relief would be at 525 °C for 60 minutes or at 425 °C for

180 minutes.

4.4.2.1.8.5 Analysis of Stress Relief Cycles A-E of Experiments 3-7

The post-Stress-Relief-Cycle mean and standard deviation crack lengths were
calculated for the Stress Relief Cycles A-E used in Experiments 3-7 (T able 52). The
residual stress relieved in Cycles A and B is much larger than the residual stress
relieved in Cycles C, D, and B (Table 52). However, comparison of the mean crack
lengths for Stress Relief Cycles C, D, and E to the specimens which did not have a
stress relief cycle demonstrates that Cycles C, D, and E did relieve some residual

Stl'CSS.

4.4.2.2 Polycrystalline Alumina
Two different experiments with a total of 72 specimens and 540 cracks were used to

investigate healing in polycrystalline alumina. Healing in two different types of

214

Table 50 Mean and standard deviation for pre-heat-treatment (2C3) and post-heat-
treatment (2CA) crack lengths in glass specimens. The specimens were heat treated
and then aged for either 4 months or 24 hours before post-heat-treatment indentation.

 

 

 

 

 

Pre-heat— Heat Treatment Cycle: Time After Heat Post-heat-
treatrnent Treatment Cycle treatment
Mean and and Before Mean and
Standard Number Time at Indenting for Standard
Deviation Temperature Post-heat-treatment Deviation
2CR (pm) (Minutes @ °C) Testing 2CA (pm)
197.1 i 6.9 8 180 @ 425 4 Months 222.0 i 2.2
197.6 :l: 9.0 9 60 @ 525 4 Months 221.1 :l: 6.7
206.8 :l: 8.1 10 60 @ 525 24 Hours 223.1 :1: 8.2

 

 

 

 

 

 

 

Table 51 Calculated 1* values for glass specimens aged for either 24 hours or 4
months using Equation 24 and Table 50 data. Hypothesis decisions for comparison of
individual heat treatment cycle means with the overall pre-heat-treatment and post-
heat-treatment group means from Table 48 using a = 0.01, n = 172, and t (141/2; n) =
2.609.

 

 

 

 

 

 

Pre—heat-treatment Heat Post-heat-treatment
Treatment
Test Statistic Same mean as Cycle Test Statistic Same mean as
t* Table 48 group Number: 1* Table 48 group
mean for mean for

a risk = 0.05 on risk = 0.05
-3.564 No 8 l 1.79 No
-2.554 N 0 9 4.54 No
2.262 N O 10 4.87 NO

 

 

 

 

 

 

 

215

Table 52 Mean and standard deviation for post-Stress-Relief-Cycle (2CA) crack
lengths in glass specimens with Stress Relief Cycles A-E which were tested in

Experiments 3—7.

 

 

 

 

 

 

 

 

 

 

 

 

 

Stress Relief Cycle Number Post-Stress-Relief-Cycle
(Described in of Cracks Mean and Standard Deviation 2CA (pm)
Section 3'6'22'2) Measured 45 % r.h. age 0 % r.h. age 100 % r.h. age
A 72 221.3 i 5.5 * *
B 54 219.2 :l: 5.2 * *
C 30 208.1 :l: 5.2 186.8 i 5.8 230.3 :l: 9.0
D 54 210.2 :l: 5.5 187.1 :l: 6.0 232.1 :l: 8.4
E 36 210.0 :l: 7.1 185.9 1 5.3 228.6 :l: 12.1
None 54 201.8 :l: 7.4 * *

 

rSpecimens not tested in this aging envfironment.

 

216

alumina was investigated as a function of time, temperature, and crack aging

environment.

4.4.2.2.1 Effects of Aging Humidity and Temperature in Two Aluminas
(Experiment 1)

Coors and microwave sintered alumina specimens were prepared as described in
Section 3.6.2.3.2 with three indents aged for an initial 24 hour cycle in 45 % r.h.
followed by a second 24 hour cycle in 0, 45, or 100 % r.h., and three other indents on
the same specimen were aged for only a single 24 hour cycle in 0, 45, or 100 % r.h..
The crack lengths were measured optically from crack tip to crack tip before and after
the thermal annealing cycle. Samples were annealed for 60 minutes at 1005, 1237, or
1469 °C with a single heating rate (Figure 97) or with two heating rates (Figure 98).
Healing temperatures were measured via an R-Type thermocouple placed next to the
specimens in the furnace. The mean and standard deviation of the change in crack
lengths, Acw , (where Ache,ll = 20m: - 2cm) was calculated for all specimens (Table
53 and 54).

The first three sets of alumina samples tested were thermally annealed with a
single heating rate of 10 °C/minute (Table 53 and 54) and had a large temperature
overshoot of up to 46 °C (Figure 97). Consequently, the remaining six sets of samples
(Table 53 and 54) were annealed with an initial ramp rate of 10 °C/minute followed by
a reduced ramp rate of 2.5 °C/minute after the sample had increased to 84% of the set
temperature (in units of K). The dual ramp rate significantly reduced the temperature

overshoot by 20 to 30 °C (Figure 98, Tables 53 and 54).

217

 

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0 llllllll11111111415111llllllllJJlllllJlllllllJlllllll
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0 25 50 75 100 125 150 175 200 225 250 275

Figure 97 Plot of the Coors and microwave alumina samples’ temperature as a
function of time for a ramp rate of 10 °C per minute up to the hold temperature of
1469 °C (Experiment 1).

 

11500— 1500 00 ”60'2““ "9‘11 3: .: ‘14900C

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1.000—

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rIIIIIITITIIIIIIIIllIlllj—rfIlI
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Figure 98 Plot of the Coors and microwave alumina sarnples’ temperature as a
function of time for a ramp rate of 10 °C per minute up to 1175 °C followed by a
ramp rate of 2.5 °C per minute up to the hold temperature of 1469 °C (Experiment 1).

218

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4.4.2.2.1.l Healing in Coors Alumina (Experiment 1)
For Coors alumina, the crack length change after annealing (Acw) increased linearly
with increasing healing temperature (Figure 99), and was characterized by a single best
fit line with positive slope regardless of the indent crack aging conditions (Figure 99).
For Coors alumina, Acheal was about 17 pm at 1000 °C and about 130 pm at 1500 °C
(Figure 99).

Aging for a single cycle at 0% r.h. or for two cycles (with the first cycle at
45% r.h. and the second at 0% r.h.) did not appear to change the healing behavior
(Figure 100) indicates that the humidity during aging does not affect crack healing, or
that the effect of humidity during aging is small enough to be within the experimental
error of crack length measurement. The specimens which underwent a single aging
cycle in either 0, 45, or 100 % r.h. behaved identically at the lowest annealing
temperature of 1005 °C (Figure 101). At 1469 °C the specimen healed at 45 % r.h.
had a significantly larger Acw (Figure 101) than the specimens aged at 0 or 100 %
r.h. which had similar Acw values. Thus at 1005 °C, aging does not affect healing,
while Ache“ is affected for anneals at 1469 °C (Figure 101). The differing results for
the environmental consequences on Ac,ml may be related to the experimental protocol
of measuring the crack length after 30 minutes of aging, which may expose the newly
formed cracks to air for the (approximately) 20 minutes needed to measure the cracks.
The exposure could lead to adsorption of water vapor from the air which is not
desorbed during the subsequent 23.5 hours of aging in 0% r.h.. To aid in determining
the effect of the aging environment, the experimental procedure in Experiment 2 was

adjusted as follows: 1) the specimens were immediately placed in their respective

221

 

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Crack Aging Conditions
'.' Single - O % r.h.
"’ Double - O % r.h.

 

 

150-

 

100-4

50—

 

Crack Length Change (ZOO-20,.) (um)

 

 

Lfi I I T I I I I I l I l I I I I I r T

l l l 1 l l l l J l_l L J l l A l l 1 1 l l I

0 I I l I l l
900 1,000 1,100 1,200 1,300 1,400 1,500 1,600

Annealing Holding Temperature (°C)

Figure 100 Mean crack length change (2cm - 2°00) versus healing temperature for
Coors alumina specimens annealed for 60 minutes in the large tube furnace (error bars
indicate standard deviations of six cracks). Before annealing, indent cracks underwent
a single age of 24 hours in O % r.h. or a double age with an initial 24 hour age in air
followed by a 24 hour age in 0 % r.h. (Experiment 1).

 

 

 

 

 

 

 

 

200
Crack Aging Conditions
3 : + Single - o % r.h.
’2 50 * 'B’Single - 100 % r.h.
o 1 ~—
91 _ t Single - 45 % r.h.
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I I I l I I
900 1.000 1.100 1.200 1,300 1,400 1,500 1,600

Annealing Holding Temperature
Figure 101 Mean crack length change (2000.: - 2cm) versus healing temperature for
Coors alumina specimens with a single age of 24 hours in 0, 45, or 100 % r.h. before
annealing for 60 minutes in the large tube furnace (error bars indicate standard
deviations of six cracks) (Experiment 1).

223
aging environments after the indent cracks were made, 2) no crack length
measurements were made until after 24 hours of aging and directly before the
specimens were to be thermally annealed, and 3) only 3 indents were made (instead of

6) in each specimen to help reduce the time required to measure the crack lengths.

4.4.2.2.1.2 Healing in Microwave Sintered Alumina (Experiment 1)

For microwave sintered alumina, Acm, only increased slightly with increasing healing
temperature (Figure 102) as compared to the healing observed in Coors alumina
(Figure 99). For the microwave sintered alumina, Ac“, was about 23 pm at 1000 °C
and 55 pm at 1500 °C (Figure 102). Ac,“ at 1000 °C in the microwave sintered
alumina was similar to the Ache“ in Coors alumina (23 pm from Figure 102 compared
to 17 pm from Figure 99), while at 1500 °C Ac,“ for Coors was much greater than in
the microwave sintered alumina (126 pm from Figure 99 compared to 55 pm from
Figure 102).

For Ache... the overall standard deviation was about 23 pm for all microwave
sintered alumina specimens (Table 54) and about 15.5 pm for all the Coors alumina
specimens (Table 53). The difference in overall standard deviations of about 7.5 pm
cannot be simply a function of the grain size, since microwave sintered alumina grain
size was 21 um compared to the Coors alumina grain size of 2.1 pm (Section 4.1.2).
The larger standard deviations for crack healing in microwave sintered alumina was
likely due to the chipping associated with indentation cracks in microwave sintered
alumina compared to the indentation cracks in the Coors alumina (Figure 103). A

single major crack extends from the corners of each of the four indent impressions for

 

224

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.Coors alumina specimens, while for the microwave sintered alumina specimens,
multiple cracks of significant length extend from each indent impression comer
(Figure 103). To avoid the larger standard deviations of Ac,“ and the lack of
uniformity of the indents, Coors alumina was tested exclusively in the remaining

experiments on the healing in polycrystalline alumina.

4.4.2.2.2 Effects of Aging Humidity, Time, and Temperature in Coors Alumina
(Experiment 2)

Fifty four specimens with a total of 324 cracks were tested as described in Section
3.6.2.3.3 and aged for 24 hours in O, 45, or 100 % r.h.. Three specimens were aged
for 235 hours in O, 45, or 100 % r.h.. The initial crack lengths were essentially
identical regardless of the aging environment with mean and standard deviation lengths
of 279.8 :I: 12.2, 279.3 :I: 12.0, and 280.6 :1: 13.0 pm for 108 cracks aged for 24 hours
in O, 45, or 100 % r.h., respectively. After aging, the specimens were thermally
annealed in sets of three for 60, 90, 120, 180, or 1410 minutes at 1005, 1121, 1237,

1353, or 1469 °C (Table 55).

4.4.2.2.2.l Post-Annealing Crack Length Measurements (Experiment 2)

After annealing, the crack length was NOT measured from crack tip to crack tip as in
previous experiments. Locating the crack tip during optical measurement was difficult
in cases where the crack opening displacement decreased slowly and continuously
along the crack length. Also, crack tip to crack tip measurements were not sufficient

to characterize the crack healing behavior where pinch-off or other discontinuous

226

Table 55 Mean and standard deviation of the healed crack length change (2cmm -

2cm) for Coors alumina specimens aged for 24 hours in air, a desiccator, or a water
chamber before annealing in the large tube furnace (Experiment 2). Temperature was
measured via an R-Type thermocouple placed next to the samples in the furnace.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Annealing Healed Crack Length Change (urn)
Holding Maximum Time Aging in Aging in Aging in
Temperature Temperature (min.) ~ 0% r.h. ~ 45% r.h. ~ 100% r.h.
(°C) (°C)
1007 1015 60 54.4192 49.01106 69.41169
1007 1019 90 104.7119.3 91.91162 847.917.]
1000 1011 120 87.2197 79017.4 105.2112.2
1037 1075 1410 109.5113.4 10781109 11451142
1137 1143 60 77 .718.7 69.2117 .6 71.71113
1129 1 133 90 99.41127 104.9121.4 110.9168
1126 1129 120 104.7111.5 111.3112.2 90.0121.9
1234 1243 60 83.4180 70.11168 104.4111.6
1234 1247 90 128.6186 14l.2130.2 125.4145
1234 1242 120 118.9122.8 123.2122.1 113.5116.7
1237 * 1237 * 180 84.41137 88.5112.7 103.0118.9
1237 * T 1237 * 1 180 ‘I’ 845112.61 993119.01” 12011831
1351 1359 60 1015125.] 12641210 100.3115.2
1362 1369 90 150.5118.1 146.0111.0 159.7127.9
1355 1364 120 14221161 14331159 120.7143.0
1479 1486 60 153.9120.9 l44.4117.2 14671199
1469 * 1469 * 90 14051220 l75.8117.4 17851228
1472 1478 120 1756114.? 17161150 16981196

 

 

Holding and maximum temperature not recorded.
1' Specimens aged in environment for 235 hours instead of 24 hours.

 

227

decreases in the crack opening displacement occurred along the crack length. To
overcome the problems associated with crack tip to crack tip measurements, the
minimum continuous crack length, 2CMC , was used to characterize the crack healing
behavior (Figure 104). 2CMC was measured from the location closest to the indent
impression where the crack appeared to be pinched-off to the location closest to the
indent impression where the crack appeared to be pinched-off (Figure 104). Examples
of the region of first pinch-off are given on labeled micrographs in Section 4.4.2.2.3,

which discusses the crack healing morphology changes in Coors alumina.

4.4.2.2.2.2 Healing Time and Aging Environment (Experiment 2)

AC1)“, increased for 1005 °C samples annealed for 90 minutes compared to samples
annealed for 60 minutes (Figure 105). The increase in A900: for 90 minutes of
annealing at 1005 °C occurred for each aging environments (0, 45, 100 % r.h., Figure
106). For specimens annealed for 120 minutes at 1005 °C, the increase in Ac,“ was
very small or non-existent compared to specimens annealed for 90 minutes (Figure
106). Trends for Ac,“ for 60, 90, and 120 minutes at 1121 and 1469 °C (Figure 107
and 108) were similar to those for annealing for the same times at 1005 °C (Figure
105).

Ac“, increases linearly with temperature when time and aging humidity are
held constant (Figure 109). The correlation coefficients for the linear best fit lines for
the 60 and 120 minute healing times in Figure 109 were 0.971 and 0.942, respectively.
The slopes of the linear best fit of Ache“ and temperature for healing times of 60 and

120 minutes in Figure 109 were 0.185 and 0.192 tun/K, respectively (Figure 109).

 

 

W

Minimum Continuous
Crack Length, 20,“,

fl

228

 

chip

WWW

Figure 103 Schematic of Vickers indents made in Coors alumina and microwave
sintered alumina. In the Coors alumina specimens, one major crack extends from
each of the four indent impression comers. In microwave sintered alumina, chipping
occurs and multiple cracks extend from the indent impression corners.

 

__I

Pinch-off
Regions

 

I

 

W

Indent impression

 

Pinch-off
Regions

Figure 104 Schematic of the minimum continuous crack length, 2CMC , as measured
for conventionally healed Coors alumina specimens in Experiment 2.

 

 

229

 

200
Aging Environment

+ 0%r.h. 1* 45%r.h. . 100%r.h.

.3

\I

01
l

 

 

 

-l _L
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l I

0
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i

 

Change in Crack Length (200 - 20,...)(pm)
8 8
IIII:ITTIIIIIIIIIll{'IIIIIIjIlllllllllll

 

 

11111

lllll

I I L I

 

O
0:
O
O)
O
CO
O
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N
O
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C

Time at 1005 °C (min.)

Figure 105 Mean crack length change (2cm - 200.1) versus healing time for Coors
alumina specimens aged for 24 hours in air, a desiccator, or a water chamber before
annealing for up to 120 minutes at 1005 °C in the large tube furnace (error bars
indicate standard deviations of six cracks) (Experiment 2).

 

Aging Environment
+ 0 °/. r.h. * 45 % r.h. O 100 % r.h.

 

 

 

 

.0 —I .5 _L N
8 8 0" 0 8
I I L l

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Change in Crack Length (2C, - 20,...)(pm)
N
01
I

 

 

oats

L44 1 L I I l I I I l I I I l I A I l J A4

I I I I I
I I I I I I

200 400 600 800 1.000 1,200 1,400 1,600
Time at 1005 °C (min.)

 

0

Figure 106 Mean crack length change (20W - 2cm“) versus healing time for Coors
alumina specimens aged for 24 hours in air, a desiccator, or a water chamber before
annealing for up to 1410 minutes at 1005 °C in the large tube furnace (error bars
indicate standard deviations of six cracks) (Experiment 2).

230

 

N
8

III‘III IIII III I'T III III III III IlII III rT1’r

Aging Environment
+ 0 °/. r.h. *- 45 % r.h. 0 100 °/. r.h.

.L

\I

01
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I l

8 0
1 1

Change in Crack Length (20. - 2C,,,,)(um)
8 8
l l

 

 

 

O
p
.-
p
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0)
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O)
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(D
O
.5
N
O
.5
01
0

Time at 1121 °C (min.)

Figure 107 Mean crack length change (2cm - 2cm) versus healing time for Coors
alumina specimens aged for 24 hours in air, a desiccator, or a water chamber before
annealing for up to 120 minutes at 1121 °C in the large tube furnace (error bars
indicate standard deviations of six cracks) (Experiment 2).

250

 

0

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'9' 0 % r.h. * 45 % r.h. . 100 % r.h.

Change in Crack Len

.0
0 1°» 8 0 8
l l J l

 

 

 

 

 

 

' I
90 120 150
Time at 1469 °C (min.)

0
0)
O
O)
0

Figure 108 Mean crack length change (20100.1 - 2cm“) versus healing time for Coors
alumina specimens aged for 24 hours in air, a desiccator, or a water chamber before
annealing for up to 120 minutes at 1469 °C in the large tube furnace (error bars
indicate standard deviations of six cracks) (Experiment 2).

 

 

231

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232

With nearly identical slopes for healing at 60 and 120 minutes in Figure 109, only the

intercepts change with the healing times.

4.4.2.2.2.3 Aging Environment Effect on Healing (Experiment 2)

The Ache“ values for specimens: 1) aged in 0, 45, or 100 % r.h., 2) annealed for
identical times, and 3) identical temperatures were within a standard deviation of each
other for annealing at 1005, 1121 1469 °C (Figures 105 - 108). Healing at 1005,
1121, and 1469 °C was either not significantly affected by the aging. The samples
aged for 235 hours in O, 45, and 100 % r.h. environments and annealed at 1237 °C for
180 minutes also did not show a significant effect of aging humidity (Table 55).

With no measurable effect of aging environment, all samples annealed for the
same time and temperature (regardless of aging conditions) could be grouped together
in data analysis to determine the effect of annealing time and temperature on Ache“.
The linear best of Acm, and temperature for all fifteen samples and 90 cracks annealed
for 60 minutes was 0.188 ple with a correlation coefficient of 0.932 (Figure 110).

If there is an effect of aging environment, aging for a longer time could
increase the effect, but no significant change in Acw occurred after 235 hours of
aging (Table 55), which is further evidence that aging environment had no effect on
healing in Coors alumina. The current data cannot show conclusively that aging
environment has NO effect on healing (since indenting and aging in the identical
environment would be needed). However, one of the goals of this study was to see if
aging in a different environment before thermal annealing could be used in an

industrial setting to help increase crack healing; to that end, the Table 55 and Figures

233

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234

105 - 110 show that aging in different environments does NOT alter thermal healing
to a large enough extent to warrant consideration for use in an industrial setting.

Aging indented samples in environments with water vapor present results in
water vapor adsorption by the freshly created indentation crack surfaces. In glass
specimens, the adsorbed water vapor can enter the glass structure via the crack
surfaces before and/or during the annealing cycle and can reduce the viscosity and
consequently affect the healing behavior (Section 4.4.2.1.4.1). However, in Coors
alumina effects of aging environment on healing are assumed to be dominated by the
interaction (or lack thereof) of water vapor with the A1203 structure. The lack of an
aging environment effect on healing in the Coors alumina indicates that the interaction
between water vapor and the A1203 crystal structure is small to non-existent.

Many alumina ceramics are processed with sintering aids which result in an
decrease the volume fraction of porosity and the introduction of a glassy phase at the
grain boundaries [8]. For indented alumina specimens with a glassy phase, the
adsorbed water vapor might enter the glassy grain boundary phase and effect healing
via a decrease in the viscosity of the grain boundary phase. The Coors alumina used
in the present study is reported to be 99.9% A1203 (chemically) and so should have
relatively little glassy phase at the grain boundaries. To investigate if the water vapor
would interact with a glassy grain boundary phase in alumina and result in an increase
in healing, future conventional healing experiments with alumina could use Coors AD-

90 since Coors AD-90 is 10% glass.

235

4.4.2.2.2.4 Time and Temperature Effect on Healing (Experiment 2)

The measurements for all three samples and all 18 cracks for each time/temperature
annealing condition were taken as a single set to obtain one mean and standard
deviation for each time/temperature annealing condition (Figure 111), since the best fit
line described the data in Figure 110 well and since there was no noticeable difference
or trend with the aging environment. ACM increased for all annealing temperatures as
the annealing time increased from 60 minutes to 90 minutes (Figure 111). The
differences in Ache“ for annealing times of 90 and 120 minutes are within the standard
deviations for the Ache“ values (Figure 111). For long annealing times such as 1410
minutes, the Acheal at 1005 °C increases slightly with time (Figure 112). More
annealing times between 120 and 1410 minutes and above 1410 minutes would be
required to detennine conclusively the degree of increase in Ac,“ll with healing time at
1005 °C and other temperatures.

Ache“ increases for annealing times of 60 and 120 minutes as the annealing
temperature increases from 1005 to 1469 °C (Figure 113). For annealing at 120
minutes, Acw was approximately 25 to 30 microns larger than the A600 at 60 minutes
over the temperature range of 1005 to 1469 °C (Figure 113). A large increase in Ac,“
at 1469 °C compared to the increases between the other temperatures, may indicate
that Acw does not increase linearly with temperature (Figure 113). Ache“ for 90
minutes of annealing was nearly identical in value and behavior to the 120 minute

healing and consequently was not shown in Figure 113 to avoid obscuring data points.

236

 

200

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Temperature (°C)
'9‘ 1469

0.1353
I>1237
4r1121
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01
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0'"
l

 

 

 

 

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Change in Crack Length (20, - 2G,...)(um)
8
0
III! II III'ITIITIrIFjjII lilj

 

 

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0 30 60 90 120 150
Time at Temperature (min.)

 

Figure 111 Mean crack length change (2cm - 2cm) versus healing time for Coors
alumina specimens annealed for up to 120 minutes in the large tube furnace (error bars
indicate standard deviations of 3 specimens and 18 cracks) (Experiment 2).

 

N
8

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.+_.

75-

 

f

 

Temperature (°C)
01469 A1353 01237 41121 V1005 +1005

Change in Crack Length (20, - 20,...)(um)
ER 23
l l

 

 

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I I I I I I I

0 200 400 600 800 1,000 1,200 1,400 1,600
Time at Temperature (min.)

 

 

 

C

Figure 112 Mean crack length change (2000.: - 2cm) versus healing time for Coors
alumina specimens annealed for up to 1410 minutes in the large tube furnace (error
bars indicate standard deviations of 3 specimens and 18 cracks) (Experiment 2). The
best fit line is for annealing at 1005 °C for times of 90 to 1410 minutes.

 

 

 

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238
‘4.4.2.2.2 Crack Morphology Changes in Coors Alumina
The crack morphology of healed indent cracks in two Coors alumina specimens
annealed in Experiment 2 for 120 minutes was investigated (Figures 114 - 117 and
117 - 123) using a field emission SEM (Camscan 44FE). The specimens were
observed without a conductive coating. The accelerating voltage used to image the
specimens was 4 KeV. Micrographs were taken along the path of the original as-
indented crack. In the micrographs specific pores and grains were identified and
labeled to act as reference points indicating the relative location from one micrograph
to the next.

For the uncoated specimen aged in O % r.h. and annealed at 1353 °C for 120
minutes, the first pinch-off region of healing between the indent and the crack tip is
indicated (Figure 114). The region (where pinch-off first occurs) appears to be a grain
partially bridging the crack before annealing and after annealing is completely healed
across the open crack (Figure 114). For the region of the indent crack from the indent
impression to the crack tip (indicated in Figure 114), the crack opening displacement
(COD) is non-zero except for the first pinch-off region. At a greater distance from the
indent impression than the indicated crack tip (Figure 115), a trace similar in
appearance to thermally etched grain boundaries occurs along parts of what was likely
the pre-annealed path of the crack (Figure 115). Open voids are present along the
crack trace (Figure 116). At further distances away from the crack tip (approximately
40 -45 pm), the trace of the crack becomes less pronounced and Open voids are not
evident (Figure 117).

The trace of the crack is visible in optical microscopy. However, it is very

 

 

239

   

‘K‘

Figure 1 14 Conventional Field Emission SEM micrograph of an indent crack in the
Coors alumina specimen annealed at 1353 °C for 120 minutes in a large tube furnace.

The first healed region, the crack tip and the location of pores a and [3 (reference points
for Figures 115, 116, and 117).

   

Figure 115 Conventional Field Emission SEM micrograph of the crack in Figure 114
(Coors alumina annealed at 1353 °C for 120 minutes in the large tube furnace). The
healed region located at a greater distance from the indent impression than the crack tip
and pores a and B (for reference).

240

 

Figure 116 Conventional Field EmissionSEM micrograph of the healed portion of the
crack in Figure 115 (Coors alumina annealed at 1353 °C for 120 minutes in the large tube
furnace). Open voids of less than 2 pm in length and pore a (for reference).

1 .0 ;. :5

    
 

vn

‘ 275* I74 .

(315010 ,.
.1 I

Figure l 17 Conventional Field Emission SEM micrograph of the healed crack (Figure
114) (Coors alumina annealed at 1353 °C for 120 minutes in the large tube furnace). The
surface trace of the healed crack resembles the thermally etched grain boundaries of the
Coors alumina. Pore B is included for reference.

 

 

0.30 ‘ .
0. .2

 

Figure 118 Conventional Field Emission SEM micrograph of an indent crack inth
Coors alumina specimen annealed at 1469 °C for 120 minutes in the large tube furnace.
The first healed region, the crack tip. Grain a serves as a reference point for Figures 119,
120, and 121.

 

Figure 119 Conventional Field Emission SEM micrograph of the crack in Figure 1 18
(Coors alumina annealed at 1469 °C for 120 minutes in the large tube fumace). The
healed region afier the crack tip, a crack void Grain a for reference.

 

‘0

 

- ' , ‘ . 2:. . ‘- ’
Figure 120 Conventional Field Emission SEM micrograph of the h ed portion of the
crack (Figure 119) (Coors alumina annealed at 1469 °C for 120 minutes in the large tube
furnace). The circular crack void of less than 0.3 pm in diameter. Grain a is included
for reference.

 

118) (Coors alumina annealed at 1469 °C for 120 minutes in the large tube furnace). The
circular crack void, an elliptical crack void.

243

      

Figure 122 Conventional Field Emission SEM micrograph of the healed portion of the
crack (Figure 121) (Coors alumina annealed at 1469 °C for 120 minutes in the large tube
furnace). The elliptical crack void has pinched off into an elliptical crack void
approximately 1.3 pm in length and a nearly circular crack void of 0.3 pm in length.

   
 

Figure 123 Conventional Field Emission SEM micrograph of the healed crack (Figure
121) (Coors alumina annealed at 1469 °C for 120 minutes in the large tube fumaee). The
elliptical crack void with a maximum crack opening displacement (COD) of
approximately 0.2 pm.

   

244

difficult in optical crack length measurements to discern the location of the end of the
open crack. The difficulty in distinguishing the crack tip from the crack trace results
from the slow and continuous decrease in crack opening displacement and the lower
resolution of the optical microscope compared to a field emission SEM. Also, due to
the presence of regions of crack healing at smaller distances from the indent
impression than the crack tip (Figure 117), measurements of the distance to the crack
tip do not describe healing behavior well.

The distance from the midpoint of the indent impression to the first healed
region in the micrograph (Figure 114) was 63 um and the same distance measured
optically was 66 pm. Consequently, to overcome the problems associated with crack
tip measurements, the minimum continuous crack length, 2CM0 was measured
optically for the annealed cracks in Coors alumina for Experiment 2 (Section 4.4.4.2).

For the uncoated specimen aged in air and annealed at 1469 °C for 120
minutes, the thermal etching at grain boundaries is more pronounced (Figure 118 -
123) than for the specimen annealed at 1353 °C (Figures 114 - 117). For the crack
annealed at 1469, a first pinch-off region is evident between the indent and crack tip
(Figure 118). The distance from the midpoint of the indent impression to the first
healed region in the micrograph (Figure 118) was 54 um and the same distance
measured optically was 52 pm.

At a greater distance from the indent impression than the indicated crack tip
(Figure 119), a faint trace of the crack can be observed which follows an intergranular
and transgranular path (Figure 119). Open voids along the length of the crack trace

are almost exclusively found in grains as opposed to along grain boundaries (Figure

 

245

119). The voids were approximately circular (Figure 120) or elliptical in cross section
(Figure 121). The elliptical void which was approximately 1.3 pm long and 0.3 pm
across (Figure 122) and the circular void which was approximately 0.2 pm in diameter

(Figure 123) may have pinched-off from a longer elliptical crack (Figure 122).

4.4.3 Microwave Healing in Polycrystalline Alumina

A total of 15 specimens and 180 cracks were used to investigate microwave healing of
49 and 98 N Vickers indent cracks in Coors alumina. Annealing was performed with
microwave heating with ramp rates of 10 or 75 °C/rninute and (for comparison) with
conventional heating with a ramp rate of 10 °C/rninute (Section 3.6.3.2).

Specimens were prepared as described in Section 3.6.3.1 and aged for 24 hours
in 45 % r.h. to allow the indent crack growth to saturate. After aging, the mean and
standard deviation crack lengths were 287.6 i 14.8 and 454.1 :I: 24.6 pm for the ninety
49 and the ninety 98 N indent cracks, respectively. After annealing crack lengths

were measured from crack tip to crack tip (Table 56 and 57).

4.4.3.1 Healing in Conventional and Microwave Annealing

Acw at 1237 °C was greater than 45 pm for all specimens regardless of heating type
or heating rate (Table 56 - 57 and Figures 124 and 125). A small increase in Ac,“ for
all specimens occurred upon increasing the annealing temperature to 1295 °C (Figure
124 -— 125). At temperatures above 1353 °C, healing increased dramatically for all
specimens.

Ache“ at 1469 °C for the 98 N indent cracks was from 50 to 100 um larger than

 

246

the Acheal for the 49 N indent cracks (Table 57 and Figures 124425). The larger Ache“
for 98 N indent cracks is not necessarily unexpected since the initial crack lengths
were 50% longer for the 98 N indents than for the 49 N indents. The relative crack
healing values mom/20mm“), were almost identical for the 49 and 98 N indent cracks
in samples heated via microwaves and those heated conventionally, regardless of the
heating rate (Figure 126). The only significantly different Acm/Zcm values for the
49 and 98 N indent cracks were at 1353 °C for microwave heating with a slow ramp

rate of 10 °C/minute (Figure 126), the cause of which is not apparent

4.4.3.2 Differences in Microwave and Conventional Healing
At temperatures of 1295 °C and above, A010: microwave heating was greater than from
conventional heating for both 49 and 98 N indent cracks (Figure 124 and 125). The
difference in A0101 for conventional and microwave heating increased dramatically at
temperatures of 1353 °C and above for all heating types and rates (Figure 126). The
difference in Ache“ between microwave and conventional heating at 1411 °C was
greater than 70 and 100 pm for the 49 and 98 N indent cracks, respectively (Figures
124 and 125). The difference in relative crack healing between conventional and
microwave heating at 1411 °C was greater than 20% (Figure 126).

The large increase in healing at temperatures above 1295 °C for microwave
heated cracks compared to conventionally heated cracks could be the result of: 1)
enhanced diffusion via microwave heating (compared to diffusion in conventional
heating at the same temperatures), 2) a different healing mechanism in microwave

healing than for conventional healing, or 3) the temperatures for microwave heating

 

 

Table 56 Mean and standard deviation of the healed crack length change (2cm,l -

247

2cm“) for Coors alumina specimens aged for 24 hours in 45 % r.h. before a 60 minute
anneal by microwave heating. (Maximum temperature was within i2 °C of set

 

 

 

 

 

 

 

 

temperature).
Heating Set and Holding Healed Crack Length Change (urn)
Ramp Rate Temperature
(°C/min.) (°C) 49 N Indent 98 N Indent
10 1237 46.9 :1: 17.7 72.1 :1: 23.4
1295 84.1 :1: 14.4 114.3 i 9.0
1353 151.5 :1: 17.7 175.6 :l: 21.8
1411 199.1 :1: 10.1 338.0 :1: 9.2
1469 199.1 :1: 9.2 337.9 :l: 8.8
75 1237 84.8 i 13.5 99.7 :1: 21.3
1295 68.3 i 18.3 96.4 i 33.5
1353 91.0 i 17.7 155.3 :1: 20.1
1411 136.9 :l: 27.8 216.0 :1: 16.4
1469 157.1 :1: 53.2 273.0 :1: 30.6

 

 

 

 

 

 

 

 

 

 

Table 57 Mean and standard deviation of the healed crack length change (2900.: -

2cm.) for Coors alumina specimens aged for 24 hours in 45 % r.h. before annealing

for 60 minutes by conventional heating. Temperature overshoot above the set

temperature from a 10 °C/minute ramp rate resulted in higher holding and maximum

 

 

 

 

 

 

 

temperatures.
Set Holding Maximum Healed Crack Length Change (urn) ll
Temperature Temperature Temperature
(°C) (°C) (°C) 49 N Indent 98 N Indent I
1237 1245 1291 50.0 :I: 19.7 76.0 :|: 21.0
1295 1309 1344 59.9 :1: 16.1 77.0 :1: 18.1
1353 1354 1394 53.3 i 9.5 60.1 :l: 18.3
1411 1426 1464 66.0 i 17.5 113.5 :1: 21.8
1469 1469 1515 99.0 i 17.9 146.8 :1: 31.7

 

 

 

 

 

 

 

 

248

 

 

 

 

 

 

 

 

250
E . Crack completely
1 - Heating Type - Rate healed to indent
7% ’ impression
: i 9 Conventional-Slow
0‘ 200 -- L
(:1 Z 29: MicrowaveoSlow
0° : Microwave«Fast
8 150 —~
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0 L4 PA % 1 1 J 1 % L 14 1 # n 1 a 4 : 1 1 n L : A l
1 .200 1 .250 1.300 1,350 1 .400 1 .450 1,500

Holding Temperature (°C)

Figure 124 Mean crack length change (2cm... - 2cm.) versus holding temperature for
49 N Vickers indent cracks in Coors alumina which were aged for 24 hours in 45 %
r.h. before annealing for 60 minutes with conventional or microwave heating at slow
or fast rates (10 or 75 °C/min.) (error bars indicate standard deviations of six cracks).

 

 

 

 

 

 

 

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1 .200 1 .250 1.300 1 .350 1 .400 1 .450 1 .500

Holding Temperature (°C)

Figure 125 Mean crack length change (2cm - 2cm.) versus holding temperature for
98 N Vickers indent cracks in Coors alumina which were aged for 24 hours in 45 %
r.h. before annealing for 60 minutes with conventional or microwave heating at slow
or fast rates (10 or 75 °C/min.) (error bars indicate standard deviations of six cracks).

 

 

249

 

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250

actually being larger than measured. The microwave heating literature has many
examples of enhanced behavior observed in microwave heating compared to
conventional heating (Section 4.4.3.4). While some authors suggest that the apparent
increase from microwave heating results from underestimates of the actual specimen
temperature by 100 - 400 °C, other authors have shown that the temperature
measurement in microwave heating is within :l:20 °C (Section 4.4.3.4). In the current
crack healing study, the microwave heating curves would have to be shifted in the
positive x-direction by 125 °C to account for the difference in microwave and
conventional healing (Figure 127). However, microwave heated specimens, with a
slow ramp rate and shifted 125 °C in the positive x-direction (Figure 127) to simulate
an adjustment for temperature measurement errors. would still have larger Ac...“ values
compared to conventional healing (Figure 127). Section 4.4.4 discusses work to
determine the healing diffusion activation energies for the conventional and microwave

heating in the current crack healing study.

4.4.3.3 Healing Differences Between Slow and Fast Microwave Heating

At temperatures of 1295 °C and below, Acm/Zcm for slow and fast microwave
healing are not significantly different, while at temperatures of 1353 °C and higher
Ac...,./2c.,.....l for slow microwave heating becomes much larger than for fast microwave
heating (Figure 126). A specimen with a slower heating rate would be at temperatures
high enough for healing to take place for longer times than a specimen with a faster
heating rate and consequently heal more. Conventional healing of Coors alumina in

Section 4.4.2.2 revealed healing after 60 minute annealing cycles for temperatures as

 

 

251

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252

‘low as 1005 °C. A sample heated with a slow ramp rate (10 °C/minute) to 1295 °C,
would be at temperatures above 1005 °C for about 50 minutes more than a sample
heated with a fast ramp rate (75 °C/minute) which would spend only a total of 8
minutes above 1005 °C. However, healing was essentially the same for slow and fast
microwave heating at 1295 °C (Table 56 and Figure 127) indicating that the amount of
time a specimen spent between 1005 and 1295 °C did not significantly effect
microwave healing behavior.

At 1411 °C, the relative crack healing for slow microwave heating is
approximately 28% higher than for fast microwave heating (Figure 127) and the Ache...
values for 49 and 98 N indent cracks were 62 and 122 pm higher, respectively (Table
56). A specimen heated with a slow ramp rate to 1411 °C, would spend 20 more
minutes at temperatures above 1295 °C than a specimen heated with a fast ramp rate
which would spend a total of only 3 minutes at temperatures above 1295 °C. Thus,
while time above 1005 °C did not effect microwave healing, time above 1295 °C
DOES effect microwave healing. The small difference between the slow and fast
microwave heating rates until temperatures above 1295 °C is similar to the microwave
heating behavior observed in sintering of alumina. Significant sintering rates in
alumina were not observed by Janney and Kinney until temperatures of about 1250 °C
and above [90]. The similarity of conventional and microwave healing at temperatures
of 1295 °C and below, along with the increase in healing for slow microwave heating
at temperatures above 1295 °C indicates that the microwave enhancement occurs at
temperatures above 1300 °C and is increased by the time at temperatures above 1300

°C and not just the time at the maximum holding temperature.

 

253

4.4.3.4 Literature Review of Diffusion during Microwave Heating

Janney and Kimrey studied diffusion in alumina during microwave heating [90-92].
Janney and Kimrey investigated oxygen diffusion in single crystal alumina under
microwave and conventional heating with 18O tracer diffusion experiments [91]. For

temperatures of 1500 - 1800 °C, the diffusion of the oxygen was greatly increased by

 

microwave heating as compared to conventional heating [91]. The activation energy

of 18O diffusion was 390 and 650 kJ/mol (4.04 and 6.74 eV) under microwave and

conventional heating, respectively [91]. ‘
Janney and Kimrey also studied sintering of alumina and found the apparent

activation energy for conventional and microwave sintering of a high purity alumina

(Sumitomo AKP-SO) to be 575 and 160 kJ/mol (5.96 and 1.66 eV), respectively [92].

While pores in alumina are eliminated in the early stages of conventional sintering, in

microwave sintering pores in alumina were eliminated in the later sintering stages

which resulted in a reduction in the grain size of microwave sintered alumina

 

specimens compared to the grain size of samples sintered conventionally to similar
final densities [92]. Janney and Kimrey hypothesize that the reduction of grain size
from microwave sintering indicates that there is an increase of bulk or grain boundary
diffusion under microwave heating more than an increase of surface diffusion [92].
The authors comment that structural and kinetic differences occur during microwave
and conventional sintering which make comparison of the calculated activations
energies actually a comparison of two different processes [92].

Smith, Janney and Mayotte investigated grain growth in dense. hot pressed

alumina after microwave and conventional annealing cycles [92]. The grain growth in

254
microwave heating was accelerated compared to grain growth in conventional heating
[92]. The activation energies for grain growth were 480 and 590 kJ/mol (4.98 and
6.12 eV) for microwave and conventional heating, respectively [92]. Janney et al.
comment that the difference in grain boundary growth activation energy was smaller
than the difference in sintering activation energy because grain boundary growth was
the same process structurally in both microwave and conventional heating while the
sintering activation energy represents both diffusional and structural differences in
microwave and conventional heating [92].

Nightingale et al. studied the sintering and grain growth of 3 mol% yttria
zirconia under microwave and conventional heating [93]. The densities of samples
sintered with microwave heating were higher at lower temperatures compared to
samples heated conventionally [93]. For samples less than 96 % theoretically dense,
the grain size of microwave heated specimens was smaller than that for specimens of
similar density which were heated conventionally [93]. The grain size/density effect in
microwave heating was attributed to a greater increase in lattice diffusion during
microwave heating than surface or grain-boundary diffusion [93]. For 3 mol% yttria
zirconia samples which were greater than 96 % theoretically dense. grain growth was
found to be accelerated in microwave heating and resulted in exaggerated grain growth
[93].

Cheng et al. [94] studied the densification of alumina during microwave and
conventional sintering by measurement of density, shrinkage and grain size [94]. The
sintering rates for microwave heating were found to be much higher than for

conventional heating [94]. The sintering shrinkage and the grain size data were fit to

 

255

densification rate and grain growth rate models [94]. Data fit to the model indicated
that the grain growth during microwave heating was lattice diffusion controlled [94].
The model for densification rate show that the diffusion coefficient for microwave
sintering at 1200 °C was 3 times that for conventional sintering [94].

Wroe and Rowley [95] studied the sintering of 3 mol% yttria zirconia using a
hybrid furnace which allowed the simultaneous application of microwave and radiant
heat [95]. Radiant heating elements in the hybrid furnace could increase the sample
temperature while microwave power could be applied continuously, switched on or
off, or pulsed [95]. Compared to sintering by conventional heating only, microwave-
assisted sintering was found to be enhanced with final densities higher for all samples
sintered in a microwave field [95]. To achieve the same value of linear shrinkage the
microwave-assisted sinterin g temperature was about 80 - 100 °C lower than
conventional sintering [95].

In Wroe and Rowley’s hybrid furnace investigation [95], when the electric field
was switched off during densification, the shrinkage nearly stopped before resuming
along the shrinkage versus temperature curve for conventional heating [95].
Conversely, when the electric field was switched on during conventional heating the
shrinkage increased rapidly and eventually followed the shrinkage versus temperature
curve for microwave heating [95]. The shrinkage behavior after switching the
microwave field on or off indicates that the microwave enhancement is non-thermal in
nature and is consistent with being dependent on the microwave generated electric
field, E [95]. Enhancement of either volume or grain boundary diffusion by the

microwave field is implied since there was evidence of microwave enhancement only

256

in the densification stage of sintering and not during the initial sintering stage [95].

Temperature measurement problems have been cited as a possible explanation
for the diffusion increase in sintering via microwave heating. If the temperature
during microwave sintering was actually higher than measured then that could account
for the reported microwave enhancement of diffusion. However, temperature would
have to be underestimated by 100 to 400 °C if there was no microwave enhancement
[90. 92, 95]. Janney et al. [91] have simultaneously measured the temperature in the
microwave furnace with a thermocouple. 2—color IR pyrometer, and a fiber optic light
pipe [91]. Temperature agreement of i20 °C was found among the different methods
for samples of silicon carbide, silicon/silicon nitride, alumina and zirconia at
temperatures of 500 - 1500 °C [91]. Janney et al. [91] further verified microwave
heating temperature measurements, when, below the 1410 °C melting point, they found
no melting of a silicon sample while at temperatures above the melting temperature
large pools of silicon were observed [91].

Some have suggested that there is an error in temperature measurement for
microwave heated samples which resulted from the grain boundaries being at a higher
temperature than the grains [96]. The higher temperature is suggested to be the result
of grain boundaries which couple more with the microwaves than the bulk, absorbing
more microwave energy [96]. The enhanced sintering of ceramics would then be the
result of accelerated grain boundary diffusion caused by grain boundaries which are at
a significantly higher temperature than the bulk temperature (which is the measured
and reported temperature) [96]. Johnson [96] investigated this possibility using heat

flow calculations for a model system of alumina grains with diameters of 10 pm and

 

 

257

of grain boundaries which readily absorb microwave energy [96]. The heat flow
calculations indicated that for the small dimensions of grain boundary thicknesses and
grain sizes involved, the temperature difference between the grain boundaries and
grains will be a small fraction of a degree [96].

Wroe and Rowley discuss the possibility that an error in microwave heating
temperature measurement results from specimen surface temperatures being lower than
the bulk [95]. Samples heated in a conventional furnace absorb heat at the sample
surface into the bulk, while samples heated in a microwave furnace generate heat
throughout the entire specimen volume and loose heat at the surface [95]. If the
sample temperature was lower than the surface temperature then a difference in
properties would be expected at the surface compared to the bulk. However, a
detailed study of grain size in microwave sintered samples showed a uniform
microstructure indicating a uniform temperature existed during microwave heating

[95].

4.4.4 Diffusional Healing Model

In this dissertation, Stevens and Dutton’s model for high-temperature static-fatigue
crack growth [56] is applied to the description of the temperature dependence of crack
healing for indentation cracks in Coors alumina specimens subjected to both
conventional and microwave heating. As a background for this study, crack healing

studies by Raj et al. [55] and by Wang et a1. [30] are re-analyzed.

 

 

258
4.4.4.1 Review of Healing in LiF by Raj et al. [55]

Partial (100) cleavage cracks were made in lithium fluoride single crystals of
dimensions with 5 mm X 5 mm X 10 mm (Figure 127) [55]. The initial crack front
was observed optically in the [100] direction by focusing into the crystal [55].

The specimens were thermal annealed in air at temperatures of 636 to 760 °C.
A mean crack length was calculated from optical measurements at six positions along
crack front (Figure 128) [55]. After a 40 hour-long transient phase, the crack healing
rate reached a steady state [55]. During the transient phase the crack morphology may
be undergoing a change to an equilibrium crack shape which then remains relatively
constant with an equilibrium value of crack tip radius during the steady state healing
phase. The portion of Raj’s data which is re-analyzed in this dissertation, is the
steady-state healing data.

The crack tip profile was similar at all temperatures, with the crack healing
process leading to crack tip blunting [55]. Raj et al. fit their crack healing data to an
Arrenhius function (Figure 129) [55], which yielded an activation energy of 0.868 eV
(83.7 kJ/mol) for temperatures below 700 °C (Figure 129). The same Arrenhius plot
shows an activation energy of 2.00 eV (192.9 kJ/mol) for temperatures above 700 °C
(Figure 129). Raj et al. conclude that for T > 700 °C healing in LiF was dominated
by volumrnetric diffusion since the experimentally-determined activation energy of 2.0
eV is similar to value of 2.20 eV (212.3 kJ/mol) found for the volumetric activation
energy for fluorine diffusion [reference 8 in [55]]. For T < 700 °C. Raj et al. assumed
crack healing to be dominated by surface diffusion, and the argument presented by Raj

et al. was the "surface diffusion activation energy is expected to be about half that for

 

 

lniil r kzi Viw

 

lniilrkT'zT Viw HI rk'fizT Viw

 

 

c——> 4—0
~05mm ~05mm

Figure 128 Schematic of cracks used by Raj et al. [55] to study crack healing in LiF
single crystal samples.

1 0-3

 

8

IIIII

—

    
  

IIIIII

da/dt (pm/sec.)
m

A
l

I

 

Q=0.868 6V

[0
I

 

 

 

10-5 4 1 1 1 l 1 1 1 1 : r 1
9.5 10 10.5 11

1/Temperature (104/K)

Figure 129 Plot used by Raj et al. to determine the activation energy for healing in
single crystal LiF [55].

-L

 

260
volume diffusion" or approximately 1.10 eV (106.2 kJ/mol) [55].

4.4.4.2 Review of Healing in LiF by Wang et al. [30]
Wang and Harmer [30] used in-situ optical microscopy to observe healing of internal

cracks in 10 mm X 5 mm X 3 mm single crystals of LiF. A laser pulse created three

 

mutually orthogonal penny-shaped internal cracks approximately 1 mm long on the
{100} planes in the specimens [30].

During isothermal annealing in the temperature range of 620 °C to 820 °C, the
cracks healed in stages marked by distinct morphological changes: 1) pinching-off of
plane cracks into cylindrical pores aligned in the radial direction away fi'om the crack
center, 2) ovulation of cylindrical <110> pores into square-shaped pores, 3) regression
of cylindrical <100> pores, 4) development and regression of large plate-shaped pores
or subcracks, and 5) shrinkage of isolated pores [30].

At a particular annealing temperature, Wang cooled the LiF specimens to room
temperature (at a rate of 20 °C/minute) and then removed the specimen from the

furnace for optical microscopy of the pore morphology and subcrack dimensions [30].

 

The subcrack shrinkage rate was strongly effected by the subcrack’s maximum COD,
but not by the initial subcrack length or by annealing time [30]. Consequently, the
shrinkage rates were measured at a given subcrack thickness of approximately 0.2 pm
by choosing similar parent-cracks and subcracks [30]. The mean and standard
deviations of the crack shrinkage rates were determined by measurements on three to
ten subcracks [30].

The activation energy associated with subcrack healing was inferred [30] from

261

the Stevens and Dutton model [56]. Stevens and Dutton initially derived their model
for static fatigue crack growth, but Wang et al [30] demonstrate that the model can
successfully describe crack healing. For the case of no externally applied stress the

Stevens and Dutton model [56] becomes

 

6a _ 7rD _ fl
5 _ R1116?) I1 mi ‘2"

where a is the crack length, t is time, D is the diffusivity, R is the radius of curvature
of the crack edge, L0 is the distance from the crack edge to the external bulk surface, 7
is the surface free energy, 0 is the atomic volume, k is the Boltzmann’s constant, and

T is the temperature [30]. Wang et a1. [30] re-write Equation 26 as
an _ C _ Q
'5; ‘ 7 “PI “I ‘27)

where Q is the activation energy for diffusion that dominates the crack healing

process.

ero‘yQ

C = __
kR2 114%) (28)

Do is the preexponential diffusion factor. Wang et al. [30] find an activation energy

for subcrack healing of 2.0 eV (192.7 kJ/mol) (Figure 130).

 

 

262
4.4.4.3 Re-Examination Raj et al. [55] and Wang et al. [30]

Wang et a1. [30] state that the activation energy calculated using the Stevens and
Dutton model and their data for the healing of internal cracks in LiF agree with Raj’s
activation energy for volume diffusion mechanism that Raj et al. [55] infer from their
data for healing surface cracks in LiF. Wang et a1. [30] add that although Raj et al.
report surface-diffusion dominated healing at low temperatures, surface diffusion
should not be significant in their (Wang’s [30]) study since no direct surface path
existed from the internal cracks to external surface for the laser-induced cracks.
However. unlike the Wang study, Raj et a1. [55] used only an Arrenhius form to
analyze their data [Figure 6 in reference [30]]. Raj et al. reference the Stevens and
Dutton paper [56], but they failed to apply the Stevens and Dutton model to their data.

When the Dutton and Stevens model [56] was used to plot Raj’s [55] crack
healing data, the re-plotted Raj [55] data gives a single activation energy for diffusion
of 1.48 eV (142.8 kJ/mol). No evidence for two activation energies is seen in the re-
plotted data (Figure 131). A single activation energy implies a single diffusion
process, but Raj’s Arrenhius plot (apparently with two differing slopes) had been
interpreted by both Raj [55] and subsequently by Wang [30] as indicative of two
distinct diffusion processes which dominate at differing temperature regimes.

A value of C = 1.4x109 pm*K/s was obtained from the intercept of the authors’
re-plot of Wang’s healing data, least-squares fit to the Stevens and Dutton model,
Equation 27 (Figure 130). The authors extrapolated intercept value for C was similar
to the 2.2x109 pm*K/s value reported by Wang et al. [30], also extrapolated from the

intercept of their data. In addition to determining C via the intercept, Wang et al. [30]

263

 

In (T da/dt) (|n[K pm/sl)

 

IIIIIITIYIIIUIIIITIIIIIIIIIII

 

 

j l l l I l
I

i . . .
10.2 10.7 11.2
1/Temperature (10‘lK)

 

-6 ~10
9.7

5°
to

Figure 130 Plot to determine the activation energy for healing using model of Stevens
and Dutton [56] for data of laser induced cracks in LiF by Wang et al. [30].

 

    

 

 

 

0
.. .:
: O
. Q=1.48 eV
s-z -—
R I
'U
l: C
s -3 ~-
I-
-4 —n—
_5 l 1 1 . 1 Ir . . . . l
9.5 10 10.5 11

1/Temperature (10‘lK)

Figure 131 Determination of the activation energy using model by Stevens and Dutton
[56] for healing of data of Raj et al. [55] for racks in LiF.

 

 

264

found C = 8.7x109 pm*K/s using Equation 28 and the data: D0 = to 6.3 cm2/s (for
single vacancy migration in fluorine, reference 29 cited by Wang [30]), y = 0.34 J/mz,
Q = 1.6x10'23 cm3, k = 1.38x'23 J/atom/K, R = 0.1 pm, and L0 = 1 m (where each
parameter is defined in Equations 27 and 28). However, when the present authors
recalculated C based on Equation 28 and the data listed here, a C value of 8.7x10ll
pm*K/s, which (to two significant figures) is precisely two orders of magnitude larger
than the C value reported by Wang et al. [30].

The two-orders-of-magnitude shift in the value of C significantly affects
Wang’s Do value, which is 1.64x10'2 cm2/s as calculated from Equation 28 using their
value for C which is two orders of magnitude smaller than the literature value Wang
et al. [30] quote for diffusion (from reference 29 as cited by Wang et a1. [30], D0 =
6.3 cm2/s). No value for Do was determined by Raj et al. [55] for the healing in LiF,
but Do can be calculated from the Stevens and Dutton model [56]. From Figure 131,
the intercept of the best fit line was 15.03 which results in a C value of 3.37x10‘
pm*K/s (Equation 27). The average crack tip width in the Raj et al. study [55] was
0.32 pm, implying a crack tip radius, R, of 0.16 pm. Lo, the distance from the crack
tip to the specimen surface was 0.37 cm. D. was 7x10’5 cm2/s using Equation 28 with
'y = 0.34 J/mz, Q = 1.6x10'7'3 cm3 [30], R = 0.16 pm, and L0 = 0.37 cm. D0 found
from Wang’s healing data [30] was three orders of magnitude higher than Do
calculated value from Raj’s data using Equation 28 [55].

The difference of the single activation energy for diffusion of 1.5 eV for the
crack healing study by Raj et al. [55] with the Q of 2.0 eV for healing of internal

cracks Wang et al. coupled with the several orders of magnitude difference in

265

magnitude of D0 between the two healing studies, indicates that different diffusional
healing processes were occurring in the two studies. The difference in Q and D0
values could also be the result of the dramatic difference in crack systems together
with the inability of the model by Stevens and Dutton [56] to account for these
differences with the geometric terms R and L0. The possibility of the differences in
crack systems leading to different Q and D0 values demonstrates the importance of

having identical crack systems in order to compare diffusive crack healing.

4.4.4.2 Conventional Healing in Coors and Microwave Sintered Alumina
The Coors alumina healing data from Section 4.4.2.2.1 shows a linear relationship
when plotted to Equation 27, with a correlation coefficient of 0.981 (Figure 132). A
large scatter in crack lengths for microwave sintered alumina results in a large data
scatter when plotted to Equation 27 (Figure 132). The slopes for the Coors alumina
and microwave sintered alumina were -10245 and -4414 (K), respectively (Figure
132), corresponding to activation energies of 0.883 and 0.380 eV for Coors alumina
and microwave sintered alumina, respectively. The activation energy for Coors
alumina is more than twice that of microwave sintered alumina, however, the large
uncertainty in the microwave sintered alumina activation energy makes any final
conclusions about the similarities or differences between the two aluminas difficult.
Gupta [97] gathered surface diffusion activation energies in polycrystalline and
single crystal alumina from the literature. The activation energies for surface diffusion
in healing-like processes such as thermal grooving, scratch smoothing, and void

breakup ranged from 3.26 to 5.77 eV while the activation energies for surface

 

266

diffusion in the initial stage of sintering ranged from 2.43 to 2.77 eV. Kingery et al.
[24] show self-diffusion coefficients for oxygen in alumina with many of the data sets
for diffusion at temperatures above 1500 °C. One typical data set shows an activation
energy for oxygen ion diffusion in polycrystalline alumina of 4.72 eV and a
preexponential diffusion factor of 1.48 cm2/s [24]. However, the only data points for
temperatures between 1200 and 1422 °C have a different activation energy for oxygen
self diffusion in alumina of 1.76 eV and a preexponential diffusion factor of 2.5x10'9
cm2/s [24]. In grain boundary grooving experiments, Tsoga et al. [98] values for
surface diffusion activation energies and preexponential factors at temperatures below
1450 °C were lower than other experimenters found for temperatures above 1450 °C.
In regard to the creep of polycrystalline alumina, Richerson [8] comments that for
grain sizes of 5 to 60 pm, lattice diffusion of Al3+ ions controls the creep process,
while for finer grain-sized alumina and for temperatures below 1400 °C, creep is
controlled by Al3+ diffusion along the grain boundaries. For the present study, at 1005
- 1469 °C the activation energies in Coors and microwave sintered alumina of 0.883
and 0.380 eV were much lower than the values of 2.43 to 2.77 eV reported in the
literature for surface diffusion at temperatures above 1500 °C. However, surface
diffusion activation energies at temperatures less than 1500 °C for diffusion studies
[24], grain boundary grooving experiments [97], and creep [8] are in the range of 1.76
to 2.66 eV. which are comparable to the values found for the healing of Coors and

microwave sintered alumina.

 

 

267

4.4.4.3 Conventional and Microwave Healing in Coors Alumina

Section 4.4.3 discussed healing in Coors alumina from conventional and microwave
healing. Applying the data recorded in Section 4.4.3 to the model by Stevens and
Dutton [56] allows a direct comparison of the activation energies for healing in
conventional and microwave heating (Figure 133). The slope is directly proportional
to the activation energy (Equation 27), thus the activation energy for conventional
healing was smaller than that of either microwave heating rates while the slow
microwave heating had a larger activation energy than the fast microwave heated
sample (Figure 133 - 135).

Isolation of only one type of heating on a single plot, reveals that the activation
energies appeared to be equivalent for the 49 and 98 N indent cracks with the same
type and rate of heating (Figure 136 - 137). The 49 and 98 N indent cracks on a
given sample, had identical thermal histories. The identical activation energies imply
that an similar diffusion process likely occurred for the 49 and 98 N indent crack for
the same thermal history. The reason for differing intercept values for 49 and 98 N
indent cracks (Figure 136 - 137) will be analyzed later in this section. The intercept is
related to the preexponential diffusion factor, Do , the crack tip radius, r, and the length
from the crack tip to the bulk surface, L (Equation 28).

The 49 and 98 N indent cracks were used together for determining the best fit
line and thus the activation energy for a given heating type and rate. To accomplish
this, the mean difference. Ay, between the In (T dc/dt) values for the 49 and 98 N
indent cracks at each of the 5 temperatures was determined for each heating type and

rate. The mean difference, Ay, was 0.34, 0.41, 0.39 for conventional heating at a slow

 

 

268

 

13.5 -E— Material
' '9' Coors + Microwave Sintered

 

 

 

9.5 -:

 

g)
01
I

In [T dc/dt] (In [K pm/secl)
.‘1
(II
I

 

 

F”
or
1

Y'jl’j’l'll II

 

 

 

9'
0|
5"
m I
I.

1 1 1 l 1 1 1 1 l 1 1 1 1 l 1 1 1 1 l 1 1 1 1 1 1
l l l l

5.75 6 6.25 6.5 6.75 7 7.25

1/Holding Temp. (1 O‘IK)

Figure 132 Healing for cracks in alumina heated conventionally at a slow rate of 10
°C/ minute (data fi'om Conventional Healing in Alumina Experiment 1, Section
4.4.2.21). The lines represent a least-squares fit of the data to the model by Stevens
and Dutton [56]. (Error bars indicate standard deviations of six cracks).

 

 

 

7
" Indent Size/Heating (Type 81 Rate)
. +49 N/CS +49 NIMF +49 N/MS

@6 T ""98 W08 °'V-98N/MF +98 N/MS

U) ' ‘ o

E

:3.

PE.

5

"i?"

0

'0

t.

s

 

 

 

 

5.5 5.75 6 6.25 6.5 6.75
1/Holding Temp. (1 O‘IK)

Figure 133 Healing for cracks heated conventionally at a slow rate of 10 °C/min. (CS)
or heated via microwaves at a slow (MS) or fast (MF) rate of 75 °C/rnin. (data from
Section 4.4.3). The lines represent a least-squares fit of the data to the model by
Stevens and Dutton [56]. (Error bars indicate standard deviations of six cracks).

 

269

 

«h 01 O)
l l l
I I I I r I I I I

In [T dC/dt] (In [K pm/secl)

03
1

Heating (Type 81 Rate)
'9' CS * MF 9 MS

 

 

 

 

 

 

l l I
5.75 6 6.25 6.5

1/Holding Temp. (1 O‘IK)

6.75

 

Figure 134 Healing of 49 N cracks heated conventionally at a slow rate of 10 °C/min.
(CS) or heated via microwaves at a slow (MS) or fast (MF) rate of 75 °C/min. (data
from Section 4.4.3). The lines represent a least-squares fit of the data to the model by
Stevens and Dutton [56]. (Error bars indicate standard deviations of six cracks).

 

7

-b 0'1 0)
l l l
l I I’TTTTT

(D
J
I

 

~~~
~

In [T dC/dt] (In [K urn/secl)

 

Heating (Type 81 Rate)
+ CS "F MF 4* MS

 

 

 

‘~
‘~
s

l l l l l l l 1 l j l l

 

 

1 l l l l I. 1
I I I I

5.75 6 6.25 6.5
1/Holding Temp. (1 O‘IK)

6.75

Figure 135 Healing of 98 N indent cracks heated conventionally at a slow rate of 10
°C/min. (CS) or via microwaves at a slow (MS) or fast (MF) rate of 75 °C/min. (data
from Section 4.4.3). The lines represent a least-squares fit of the data to the model by
Stevens and Dutton [56]. (Error bars indicate standard deviations of six cracks).

 

 

270

 

 

 

 

 

 

 

 

7
lndentSize
+49N'I'98N

56“

0 t

m l-

E

1

>55"

.5

S4-

0

'U

I:

53—
2-...................-.-
5.5 5.75 6 6.25 6.5 6.75

1/Holding Temp. (1 O‘IK)

Figure 136 Healing for 49 and 98 N indent cracks heated conventionally at a slow
rate of 10 °C/min. (CS) (data from Section 4.4.3). The lines represent a least-squares
fit of the data to the model by Stevens and Dutton [56]. (Error bars indicate standard
deviations of six cracks).

 

 

 

 

 

 

 

 

7
” lndentSize
049N *98N
:6"
O
8
E
a.
235‘
5
s4-
0
'0
l:.
.53-
2111L:1111%1111%1111:1_11
5.5 5.75 6 6.25 6.5 6.75

1/Holding Temp. (1 O‘IK)

Figure 137 Healing for 49 and 98 N indent cracks heated via microwaves at a slow
(MS) rate of 10 °C/min. (data from Section 4.4.3). The lines represent a least-squares
fit of the data to the model by Stevens and Dutton [56]. (Error bars indicate standard
deviations of six cracks).

 

 

271

ramp rate, microwave heating at a fast ramp rate, and microwave heating at a slow
ramp rate, respectively. The ln(T dc/dt) data of the 49 N indents and the {ln (T dc/dt)
- Ay} data of the 98 N indents were combined and a best fit line of the combined data
was determined (Figure 138).

The activation energies determined from the combined data were 0.77, 1.06,
and 1.70 eV for slow conventional, fast microwave, and slow microwave heating,
respectively. The activation energy for diffusional healing in Coors alumina was
higher for microwave heating than in conventional healing and the highest activation
energy for diffusional healing for the microwave heating was at the slower rate.

As discussed in Section 4.4.3.4, some investigators attribute reported
differences between microwave and conventional diffusion to an under-measurement
of the actual specimen temperature during microwave heating. To test whether
temperature measurement errors could account for the difference observed in activation
energies for healing in microwave and conventional healing in the present study, the
temperatures for the microwave specimens were adjusted to force the activation
energies to be identical to the activation energy for healing of Coors alumina with
conventional heating (Figure 139). The result is that the temperatures for fast and
slow microwave heating would have to be DECREASED by 255 and 555 °C,
respectively, to obtain the same activation energy found for conventional heating.
Since it is highly unlikely that the temperatures were over-estimated by 255 or 555 °C
during microwave heating, the experimental data in conjunction with the Stevens and
Dutton model demonstrate that the diffusion differences in microwave and

conventional heating cannot be entirely the result of temperature measurement errors.

 

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274

The preexponential diffusion factor, D0 , can be determined from the intercept
of the plots to Stevens and Dutton’s model [56] (Figure 132 - 138) and the material
property data for alumina, 7 equals 1x103 ergs/cm2 [56], Q equals 1.4x10'23 cm3 [56], k
equals 1.38x10'16 ergs/atom*K, L equals the grain size of Coors alumina which was
2.1 pm, and r equals the crack tip radius which can be taken as the atomic radius of
6x104 um [56] since cracks in ceramics have traditional been treated as being
atomically sharp. The preexponential factors for the 49 N indents in Figure 136 were
1.29x10"°, 1.67x10'9, and 1.93x10'7 cm2/s for slow conventional, fast microwave, and
slow microwave heating, respectively. If the geometric factors, L and r, are identical
for the 49 and 98 N indent cracks then the values for the preexponential factor are
different. Using the same L and r values for the 98 N indents, results in
preexponential factors from Figure 136 of 1.8lx10"°, 2.52x10‘9, and 2.58x10'7 cm2/s
for slow conventional, fast microwave, and slow microwave heating, respectively.

Since the 49 and 98 N indents were on the same sample, one might expect
Do(49N) to be equal to D°(98N). If the D(, values for both indent sizes were nominally
identical, then values for L and I cannot both be the same for 49 and 98 N indents. If
it is assumed that L is still equal to the grain size (as was described by Dutton and
Stevens [56] in their model), then L would be the same for both indent sizes. The
crack tip radius, r, would need to be different for the different indents if the Do values
are to be approximately identical. As a first approximation for r, the crack tip radius
for a crack of length, 2c, could be considered to differ for the 49 and 98 N as {6x10‘
4pml“! (1000/c) }, then the preexponential factors for the 49 N indents from Figure 136

become 8.05x10"°, 1.04x10'8, and 1.20x10‘ cm2/s for slow conventional, fast

 

 

275

microwave, and slow microwave heating, respectively, and for the 98 N indents
become 7.25x10'10, 1.01x10'8, and 1.14x10’6 cm2/s for slow conventional, fast

microwave, and slow microWave heating, respectively.

 

5. SUMMARY AND CONCLUSIONS

5.] Static Fatigue Crack Growth

Specimen preparation techniques need to be improved to eliminate the torsional
stresses that develop as a result of non-parallelness of the bonded tabs (Section 4.3.1.3,
and 4.3.2). For the indented polycrystalline alumina specimens, no crack growth was
observed at 10% r.h. level (at least for the load levels and times used for the
polycrystalline alumina specimens studied) (Section 4.3.2). The static fatigue process
for the alumina specimens observed to date takes place with a mean crack velocity
such that the crack growth can be observed, at least for increments on the scale of the
grain dimension (Section 4.3.2). The in-situ observation of the environmental-assisted
growth of the indent cracks revealed that during static fatigue of alumina, grain
bridging occurs (Section 4.3.2).

The crack paths followed during static fatigue in Coors alumina were semi-
tortuous with bridging grains behind the crack tip and crack tip deflection on the order
of the diameter of a single grain (Figures 29-31, 35-38 in Sections 4.3.2.3, 4.3.2.5, and
4.3.2.6). During static fatigue of Coors alumina, significant growth of both cracks
upon the first static fatigue cycle, followed by limited small crack growth for the
subsequent static fatigue cycle (Section 4.3.2). The static fatigue in several alumina

specimens with different applied stress-time paths appeared to show very similar static

276

 

 

277
fatigue behavior for a plot of relative change in crack length as a function of constant

applied tensile stress (Section 4.3.2.7).

5.2 Crack Healing

5.2.1 In-Situ ESEM Observation of Soda-Lime Silica Glass

In-situ electron microscopy was used to observe healing of semi-macro indent cracks
in soda-lime silica glass in a humid environment using an Environmental Scanning
Electron Microsc0pe (ESEM). Crack healing occurred at initial humidities as low as
8% and at temperatures as low as about 400 °C (Section 4.3.2.1.2). In the absence of
debris wedged within the crack, healing began at the crack tip and moved toward the
indent impression (Figure 58 in Section 4.3.2.1.1).

Multiple crack pinch-off was observed as a mechanism of crack healing at
temperatures above 500 °C (Figures 50 - 53 in Section 4.3.2.1.1). Changing crack
morphology rather than a simple crack closing indicated that the healing mechanism
was not adhesion due to intermolecular forces [33, 35] (Figures 48 - 53 in Section
4.3.2.1.1). Crack pinch-off behavior observed in the soda-lime silica glass (Figure 50
in Section 4.3.2.1.1) was similar to that seen in other ceramic materials by other
investigators [30-31, 34].

Debris in a crack hindered complete crack healing (Figures 54 - 58 in Section
4.3.2.1.1). The interaction between crack surface debris and the crack healing process
implies that mechanically fatigued ceramic materials could have healing impeded by
the debris formed during cycling.

As the initial humidity for glass samples was increased, the temperature at

 

278

which crack healing initiated decreased (Section 4.3.2.141). Healing for an initial
humidity of 8 % r.h. did not begin until a heating to a temperatures above 400 °C,
while for initial humidity of 64 % changes large in crack length occurred by 370 °C
(Section 4.3.2.141). The crack length change for an isothermal hold at 430 °C was
found to be described by an empirical equation (Equation 4 in Section 4.3.2.142) and
the constants of the empirical equation appeared to be functions of the initial relative

humidity (Section 4.3.2.142).

5.2.2 Conventional Healing
5.2.2.1 Soda-Lime Silica Glass
Healing in soda-lime silica glass was investigated in six different experiments on 113
specimens and 654 cracks by measuring Vickers indent crack lengths before and after
thermal annealing in a conventional furnace (Section 4.4.2.1). Annealing of Vickers
indented glass specimens for 30 minutes at 600 °C, resulted in a measurable decrease
in crack length and an two-fold increase in the three-point bend strength (Section
4.4.2.1.1). Conventional microscopy of the partially healed indent cracks healed at
temperatures 600 °C, show crack tip blunting (Figure 77) and pinch-off (Figure 80).
SEM microscopy of a fracture surface of a glass specimen healed at 550 °C, revealed
subsurface crack morphology changes (Figure 83) similar in appearance to crack
morphology changes reported in the literature [30-32, 34].

Glass specimens without a stress relief cycle before indentation exhibited a
very different behavior from specimens with a stress relief cycle consisting of heating

to 550 - 500 °C with very slow cooling (Section 4.4.2.1.3). Change in crack length

 

279
from healing, Ache“ , was constant with temperature from 525 to 563 °C for specimens
aged in 0 and 45 % r.h. (Section 442.141) while Ache“ for specimens aged in 100 %
r.h. decreased constantly with temperature (Section 4.4.2.1.4.3). Specimens aged for
24 hours in 45 % r.h. had about 10 um greater A000 heal than specimens aged in O %
r.h. (Section 4.4.2.1.4.1). The difference in healing for specimens aged in different
levels of relative humidity was attributed to water vapor entering into the glass
structure during aging and/or during annealing, which subsequently resulted in a local
decrease in the glass transition temperature and viscosity along the crack surfaces
(Section 4.4.2.1.4.1).

Bulk viscous flow was not found in the soda-lime silica specimens at
temperatures of 587 °C or less, but was observed to occur at temperatures of 600 °C
and above (Section 442.181). The difference between the mean of 22 measured
indent crack lengths for 11 Vickers indents made in "as-machined" specimens and in
the same specimens after undergoing a heating cycle was used to analyze the stress
relieved during the heating cycle (Section 44218.2). Heating cycles at temperatures
of 550 °C and higher in the small tube furnace and large tube furnace all resulted in
specimens with similar mean crack lengths after annealing of 210-215 um (Tables 35
and 38 in Section 442.182), while the specimens heated in the Lindburg box furnace
and specimens heated in the small tube furnace to temperatures of 525 °C and below
had the largest mean crack lengths after heating of 220 um (Tables 37 and 39 in

Section 44218.2).

 

280

5.3.2.2 Conventional Healing in Polycrystalline Alumina

Healing in polycrystalline alumina was investigated for two different alumina materials
in two different experiments on 72 specimens and 540 cracks by measuring Vickers
indent crack lengths before and after thermal annealing in a conventional furnace
(Section 4.4.2.2). No effect of humidity of the aging environment was found in
healing of Coors alumina or microwave sintered alumina (Section 4.4.2.2.1). Ache“
increased dramatically between 1237 and 1469 °C in Coors alumina, but was relatively
insensitive to temperature change in microwave sintered alumina (Section 4.4.2.2.1).
The increase in Acw from annealing times of 60 to 90 minutes was on the order of 30
pm for temperatures from 1005 to 1469 °C, while the change in Achm from 90 to 120
minutes was within the experimental error of the crack length measurements (Section
4.4.2.2.2). Ache“ was 25 to 50 um greater for 98 N indent cracks compared to indent
cracks made with a 49 N load (Section 4.4.3). However, the relative crack healing
(MM/2cm) was found to nearly identical for the 49 and 98 N indent cracks (Section

4.4.3).

5.3.3 Microwave Healing

Healing in polycrystalline Coors alumina was investigated for 15 specimens and 180
cracks by measuring Vickers indent crack lengths before and after thermal annealing
in a microwave or conventional furnace (Section 4.4.2.2). Ac,“ due to microwave
healing was approximately the same as conventional healing for temperatures of 1237
and 1295 °C (Section 4.4.3). At temperatures of 1353 °C and higher, the percent

relative change in crack length (Mm/2cm“) was 15 to 50 % higher from microwave

281

healing than conventional healing (Section 4.4.3). Microwave heating at a slow ramp
rate of 10 °C/minute resulted in a greater amount of healing than microwave heating at

a fast ramp rate of 75 °C/minute (Section 4.4.3).

5.3.4 Crack Healing Model

A re-analysis of work by Wang et al. [30] and Raj et al. [55] were made (Section
4.4.4.1.3). The diffusive crack healing in single crystal LiF by Raj et al. [55] was
controlled by only a single activation energy (using the model Stevens and Dutton
[56]) and not two different activation energies reported by Raj et al. [55] (Section
4.4.4.1.3). Re-analysis of the diffusive healing of internal cracks in LiF by Wang et
al. [30] showed that the preexponential diffusion factor (D0 = 1.64x10'2 cm2/s) was two
orders of magnitude lower than reported by Wang et al. [30] (Section 4.4.4.1.3). Also,
a preexponential diffusion factor (D0 = 7x10’5 cm2/s) was determined for the healing
work of Raj et al. [55] since one was not determined by the authors (Section
4.4.4.1.3). The preexponential factors for healing in LiF experiments by Wang et al.
[30] and Raj et al. [55] were orders of magnitude lower than diffusion literature values
for self-diffusion in LiF (D0 = 6.3 cm2/s [30]).

The Stevens and Dutton model [56] was used to analyze the activation energy
for the diffusive healing in alumina of the present work (Section 4.4.4.2). For Coors
alumina and microwave sintered alumina conventionally heated to temperatures
between 1005 and 1469 °C, the activation energies were 0.883 and 0.380 eV,
respectively (Section 4.4.4.2). The activation energy for Coors alumina is more than

twice that of microwave sintered alumina, however, the large uncertainty in the

 

 

282

microwave sintered alumina activation energy due to the large variation in crack
lengths makes any final conclusions about the activation energies for the two aluminas
diffith (Section 4.4.4.2). The diffusion activation energies and preexponential factors
are lower than reported in the literature [24, 97], but some evidence exists in the
literature for lower values at temperatures below 1500 °C [8, 24, 98] (Section 4.4.4.2).
The activation energies determined for slow conventional, fast microwave, and
slow microwave heating were 0.77, 1.06, and 1.70 eV, respectively (Section 4.4.4.3).
The activation energy for diffusional healing in Coors alumina was higher for
microwave heating than in conventional healing and the highest activation energy for
diffusional healing under microwave heating was at the slower rate (Section 4.4.4.3).
The fast and slow microwave heating temperatures would have to be DECREASED by
255 and 555 °C, respectively, to obtain the same activation energy with the Stevens
and Dutton model [56] found for conventional heating, indicating that the effect of

microwave heating cannot be entirely due to temperature under-measurement.

 

 

10.

11.

12.

6. REFERENCES

R.C. Buchanan, Class notes for Ceramic Engineering 201: University of Illinois
(Fall 1986).

ED. Case, Class notes for MSM 250: Michigan State University (Spring 1994).

D.W.Richerson, m.” -r.. ' En' g ° in; .- ’ 0‘ 3' ° .. ._ e
in Design, Marcel Dekker, New York (1982).

W.D. Kingery, H.K. Bowen, D.R. Uhlmann, Intrflugg’gn to Cerm’gs, 2“"
Edition, John Wiley and Sons, New York (1976).

W.D. Callistcr. Jr., W John
Wiley and Sons, New York (1985).

NE. Dowling, Mechgigfl Behavior of Materifls; Engingring Methfls for

Deformation, Fracture, and Fatigue, Prentice Hall, Englewood Cliffs, New
Jersey (1993).

R.W. Hertzberg: f ' Fr M h ° f E ' '
WM John Wiley and Sons, New York (1976).

 

D. W. Richerson, Marcek Dekker, New York (1982). ‘

W. E. Dbrre. H. Hiibncr.
Springer-Verlag. New York (1984).

T.A. Michalske, B.C. Bunker, S.W. Freirnan, "Stress corrosion of ionic and
mixed ionic/covalent solids," J. Am. Ceram. Soc., 69 [10], 721-24 (1986).

S.W. Freirnan, G.S. White, E.R. Fuller Jr., "Environmentally enhanced crack
growth in soda-lime glass," J. Am. Ceram. Soc., 68 [3], 108-112 (1985).

T.A. Michalske, S.W. Frieman, "A molecular Mechanism for stress corrosion in
vitreous silica," J. Am. Ceram. Soc., 66 [4], 284-288 (1983).

283

 

 

13.

14.

15.

16.

17.

18.

19.

20.

21.

22.

23.

24.

25.

284

G. Himsolt, H. Knoch, H. Huebner, F.W. Kleinlein, "Mechanical properties of
hot-pressed silicon nitride with different grain structures," J. Am. Ceram. Soc.,
62 [1-2], 29—32 (1979).

S. Baskaran, S.B. Bhuduri, D.P.H. Hasselman, "Effect of crystallites on
subcritical crack growth and strain-rate sensitivity of cordierite glass-ceramics,"
J. Am. Ceram. Soc., 68 [3], 112-119 (1985).

RF. Becher, "Slow crack growth behavior in transformation-toughened A1203-
Zr02(Y203) Ceramics," J. Am. Ceram. Soc., 66 [7], 485-488 (1983).

B]. Pletka, S.M. Wiederhom, "A comparison of failure predictions by strength
and fracture mechanics techniques," J. Mat. Sci., 17, 1247-68 (1982).

SM. Wiederhom, S.W. Freiman, E.R. Fuller Jr., C]. Simmons, "Effects of
water and other dielectrics on crack growth," J. Mat. Sci., 17, 3460-3478
(1982).

A.G. Evans, "A method for determining the time-dependent failure
characteristics of brittle materials - and its application to polycrystalline
alumina," J. Mat. Sci., 7, 1137-1146 (1972).

SM. Wiederhom, L.H. Bolz, "Stress corrosion and static fatigue of glass," J.
Am. Ceram. Soc., 53 [10] 543-548 (1970).

SM. Wiederhom, "Influence of water vapor on crack propagation in soda-lime
glass," J. Am. Ceram. Soc., 50 [8] 407-414 (1967).

T. Fett and D. Munz, "Lifetime prediction for ceramic materials under constant

and cyclic loads: " pp 161-74 In W

W American Society for Testing and
Materials, Philadelphia (1994).

G. Choi, S. Horibe, "Static fatigue in ceramic materials: influences of an
inertgranular glassy phase and fracture toughness," J. Mat. Sci., 28, 5931-5936
(1993).

SM. Wiederhom, H. Johnson, A.M. Diness, A.H. Heuer, "Fracture of glass in
vacuum," J. Am. Ceram. Soc., 57 [8] 336-41 (1974).

W.D. Kingery, H.K. Bowen, D.R. Uhlmann, WW
Edition, Wiley-Interscience, New York (1976).

D. S. Jacobs and I. W. Chen, "Mechanical and environmental factors in the
cyclic and static fatigue of silicon nitride," J. Am Ceram. Soc., 77[5], 1153-61,
(1994).

 

26.

27.

28.

29.

30.

31.

32.

33.

34.

35.

36.

37.

38.

285

T. A. Michalske and S. W. Freiman, "A molecular mechanism for stress
corrosion in vitreous silica," J. Am. Ceram. Soc., 66[4], 284-88, (1983).

T. A. Michalske and B. C. Bunker, "Slow fracture model based on strained
silicate structure," J. Appl. Phys., 56[l0], 2686-93, (1984).

W. Wong-Ng, G. S. White, and S. W. Freiman, "Application of molecular
orbital calculations to fracture mechanics: effect of strain on charge distribution
in silica," J. Am. Ceram. Soc, 75[ll], 3097-102 (1992).

T. A. Michalske, "The stress corrosion limit: its measurement and
implications;" pp. 277 - 289 in Fracm Mechanics of germ}; Volume 5,
edited by R. C. Bradt, A. G. Evans, D. P. H. Hasselman, and F. F. Lange,
Plenum Press, New York (1983).

Z. Wang, Y.Z. Li, M.P. Harmer, Y.T. Chou, "Thermal healing of laser-induced
internal cracks in lithium fluoride crystals," J. Am. Ceram. Soc., 75 [6], 1596-
1602 (1992).

T.K. Gupta, "Crack healing and strengthening of thermally shocked alumina,"
J. Am. Ceram. Soc., 59 [5-6], 259-62 (1976).

CF. Yen, R.L. Coble "Spheroidization of tubular voids in alumina crystals at
high temperatures," J. Am. Ceram. Soc., 55 [10], 507-09 (1972).

E. D. Case, J. R Smyth, 0. Hunter Jr, "Microcrack healing during the
temperature cycling of single phase ceramics; " pp. 507- 530 in Engage

WW0; Plenum Press N Y (1983)

T.K. Gupta, "Crack healing in thermally shocked MgO," J. Am. Ceram. Soc.,
58 [3—4], 143 (1975).

M.K.C. Holden, V.D. Frechette, "Healing of glass in humid environments," J.
Am. Ceram. Soc., 72 [11], 2189-93 (1989).

R.L. Lehman, R.B. Hill Jr., G.H. Sigel Jr., "Low-temperature crack closure in
fluoride glass," J. Am. Ceram. Soc., 72 [3], 474-77 (1989).

A.M. Thompson, H.M. Chan, M.P. Harmer, R.F. Cook, "Crack healing and
stress relaxation in A1203-SiC ’nanocomposites’," J. Am. Ceram. Soc., 78 [3],
567-71 (1995).

B. Stavrinidis, D.G. Holloway, "Crack healing in glass," Phys. Chem. Glass, 24
[1] 19-25 (1983).

 

39.

40.

41.

42.

43.

45.

46.

47.

48.

49.

50.

51.

52.

286

T.A. Michalske, E.R. Fuller Jr., "Closure and repropogation of healed cracks in
silicate glass," J. Am. Cer. Soc., 68 [11], 586-90 (1985).

FA. Nichols, "0n the spheroidization of rod-shaped particles of finite length"
J. Mat. Sci., 11, 1077-82 (1976).

RA. Nichols, W.W. Mullins, "Surface- (interface-) and volume-diffusion
contributions to morphological changes driven by capillarity" Trans. Met. Soc.
AIME, 233 [10], 1840-48 (1965).

P. Hrma, W.T. Han, A.R. Cooper, "Thermal healing of cracks in glass," J.
Non-Cryst. Solids, 102, 88-94 (1988).

DC. Cassidy, N.A. Gjostein, "Capillarity-induced smoothing of glass surfaces
by viscous flow," J. Am. Cer. Soc., 53 [3], 161-68 (1970).

A. Kishi, K. Fueki, K. Kitzawa, "Surface viscous flattening kinetics of soda-
lime silicate glass by sinusoidal profile decay method," J. Non-Cyst. Sol., 33,
95-102 (1979).

RF. Lange, T.K. Gupta, "Crack healing by heat treatment," J. Am. Ceram.
Soc., 53 [1], 54-55 (1970).

RF. Lange, K.C. Radford, "Healing of surface cracks in polycrystalline A1203,"
J. Am. Ceram. Soc., 53 [7], 420-21 (1970).

J.T.A. Roberts, B.J. Wrona, "Crack healing in U02," J. Am. Ceram. Soc., 56
[6], 297-99 (1973).

G. Bandyopadhyay, J .T.A. Roberts, "Crack healing and strength recovery in
U02," J. Am. Ceram. Soc., 59 [9-10], 415-19 (1976).

G. Bandyopadhyay, C.R. Kennedy, "Isothermal crack healing and strength
recovery in U02 subjected to varying degrees of thermal shock," J. Am. Ceram.
Soc., 60 [1-2], 48-50 (1977).

M. Tomozawa, K. Hirao, P.E. Bean, "Origin of strength increase of abraded or
indented glass upon annealing," J. Am. Ceram. Soc., 69 [8] C186-88 (1986).

K. Hirao, M. Tomozawa, "Kinetics of crack tip blunting of glasses," J. Am.
Ceram. Soc., 70 [1], 43-48 (1987).

T.K. Gupta, "Kinetics of Strengthening of Thermally Shocked MgO and
A1203," J. Am. Ceram. Soc., 59 [9-10], 448-49 (1976).

 

 

53.

54.
55.
56.
57.

58.

59.
60.
61.
62.

63.

65.

66.

287

SF. Flegler, J .W. Heckman Jr., K.L. Klomparens, WW
Elec n Mi 0 ' An In 'on, W.H. Freeman and Company, NY.
(1993).

GD. Danilatos, "Introduction to the ESEM Instrument," Microscopy Research
and Technique 25, 354-361 (1993).

R. Raj, W. Pavinich, C.N. Ahlquist, "On the sintering rate of cleavage cracks,"
Acta Metall., 23, 399-403 (1975).

R.N. Stevens, R. Dutton, "The propagation of Griffith cracks at high
temperatures by mass transport processes," Mater. Sci. Eng., 8, 220-34 (1971).

CC. Chiu, "Thermal quench of brittle materials," PhD Dissertation at Michigan
State University (1991).

KY. Lee, L.C.G. Cropsey, B.R. Tyszka, E.D. Case, "Grain size, density, and
mechanical properties of alumina batch-processed in a single-mode microwave
cavity," Materials Research Bulletin, 32 [3], 287-295 (1997).

K..Y Lee, E.D. Case, J. Asmussen, Jr., and M. Siegel; pp. 473 rn m
W2, American Ceramic Society, Columbus, OH (1995).

KY. Lee, E.D. Case, J. Asmussen, Jr., and M. Siegel; pp. 491 in ms
of the 11m ESQ Adyanced ngpgsiteg Conference, Ann Arbor, MI (1993).

’ -. NH. 0 1‘ an 1-10. Ph i '1 1-!‘1'1LI0 ,Ed.byR.C.
Weast, CRC Press Inc., Boca Ralton, Florida (1988).

BR Lawn. Won. Cambridge University
Press, New York, NY (1993).

G. R. Anstis, P. Chantikul, B.R. Lawn, D.B. Marshall, "A critical evaluation of
indentation techniques for measuring fracture toughness: 1, direct crack
measurements," I. Am. Ceram. Soc., 64 [9], 533-38 (1981).

HP. Kirchner, "Damage penetration at elongated machining grooved in hot-
pressed Si3N4," J. Am. Ceram. Soc., 67 [2] 127-32 (1984).

Lt. Luke Cropsey, "Statistical analysis of hardness and fiacture values from

single-mode microwave sintered alumina," Independent study project report for
Dr. E.D. Case at Michigan State University, July 2, 1996.

R.,Morrell nu.” of-io f hn ' wrmis:

MW HMSO Becks
London (1987).

 

67.

68.

69.

70.

71.

72.

73.

74.

75.

76.

77.

78.

288

L. Ewart, S. Suresh "Crack propagation in ceramics under cyclic loads" J. Mat.
Sci., 22, 1173-92 (1987).

W.J. Lee, E.D. Case, "Cyclic Thermal Shock in SiC-Whisker-Reinforced
Alumina Composite, " Mat. Sci. Eng., A119, 113-26 (1989).

W.J. Lee, E.D. Case, "Thermal Fatigue in Polycrystalline Alumina, " J. Mat.
Sci., 25, 5043-54 (1990).

Y. Kim, W.J. Lee, ED. Case, "Thermal Fatigue Behavior of Ceramic Matrix
Composites: A Comparison Among Fiber Reinforced Whisker Reinforced,
Particulate Reinforced, and Monolithic Ceramics, "; pp. 871-81 in firms

WWW Technomic Publishing. Lancaster.
PA (1990).

Y. Kim, W ..J Lee, E. D. Case, "Thermal Fatigue 1n SiC Fiber Reinforced
Aluminosilicate Glass Ceramic Composite; " pp. 479 in W
JWWM Eds RB
Bhagat, A. H. Clever, P. Kuman, A. M. Ritter, The Minerals, Metals, and
Materials Society, Warrendale, PA (1990).

W.J. Lee, E.D. Case, "Comparison of Saturation Behavior of Thermal Shock
Damage in a Variety of Brittle Materials, " Mater. Sci. Eng., A154, 1-9 (1992).

ED. Case, Y. Kim, W.J. Lee, "Thermal Fatigue of Ceramics and Ceramic
Composites;" pp. Tll23-T1136 in 24th International SAMPE Technical
ounfrn ‘ o-lum 2 Av an. M -r1. 5' Meetin - on mic ._ en
Eds. T.S. Reinhart, M. Rosenov, RA. Cox, E. Strickholt, Society for the
Advancement of Material and Processing Engineering, Covina, CA (1992).

BA. Wilson, E.D. Case, "Comparison of Mechanical Fatigue with Thermal
Fatigue in Cerarrrics," Scripta Met. Mat, 28, 1571-76 (1993).

ED. Case, Y. Kim, W.J. Lee, "Cyclic thermal shock in SiC whisker reinforced
alumina and in other ceramic systems;" pp. 393-406 in W

Th F ' B vi f v ' , Ed. by GA. Schneider, G.
Petzow, Kluwer Academic Publishers, Netherlands (1993).

FR Increpera. D.P. DeWitt. WM
Edition, John Wiley and Sons, New York, NY (1990).

rm hi ° f ' r 1i ril,Ed.byY.S.
Touloukian, Macmillan Company, New York, NY (1967).

D.G. Holloway, flhe Physical Prgpefl'es of Glass, Wykeharn Publications Ltd.,
London (1973).

 

79.

80.

81.

82.

83.

84.

85.

86.

87.

88.

89.

90.

91.

92.

289

RR Bartholomew, "High-water containing glasses," J. Non-Cryst. Solids, 56
[1-3], 33142 (1983).

H. Scholze, "Gases and Water in Glass: Part Two," Glass Industry, 47 [11],
622-28 (1966).

J .M Jewell, M.S. Spess, J.E. Shelby, "Effect of water concentration on the
properties of commercial soda-lime-silica glass," J. Am. Ceram. Soc., 73 [1],
132-35 (1990).

M. Tomozawa, M. Takata, J. Acocella, E.B. Watson, T. Takamori, "Thermal
properties of sodium silicate (Na20-3Si02) glasses with high water content," J.
Non-Cryst. Solids, 56[1-3], 343-48 (1983).

K.H. Schnatter, R.H. Doremus, W.A. Lanford, "Hydrogen analysis of soda-lime
silicate glass," J. Non-Cryst. Solids, 102, 11-18 (1988).

CG. Pantano Jr., D.B. Dove, G.Y. Onoda Jr., "AES compositional profiles of
mobile ions in the surface of glass," J. Vac. Sci. Technol, 13 [1], 414—18
(1976).

DR. Rosington, "Surface chemistry of glass;" pp. 513-43 in Mtg
glam, Eds. L.D. Pye, H.J. Stevens, W.C. LaCourse, Plenum Press,
NY. (1972).

R.H. Doremus, ngsc Science, John Wiley and Sons, NY. (1973).

DB. Marshall, B.R. Lawn, "Strength degradation of thermally tempered glass
plates," J. Am. Ceram. Soc., 61 [1-2], 21-27 (1978).

1.]. McColm, W5; Plenum Press, New York, NY (1990).

J. Neter, W. Wasserman, G.A. Whitmore, A 1i ' ' 4 E i' , Allyn
and Bacon, Boston, MA (1993).

M. A. Janney, H. D. Kimrey, "Microstructure evolution 1n microwave sintered

alumina" PP 382- 90 In W
American Ceramic Society, Westerville, OH (1990).

M.A. Janney, H.D. Kimrey, W.R. Allen, J.O. Kiggans, "Enhanced diffusion in
sapphire during microwave heating," J. Mater. Sci., 32 [5], 1347-55 (1997).

M.A. Janney, H.D. Kimrey, "Diffusion-controlled processes in microwave-fired
oxide ceramics," MRS Symp. Proc., 289, 215-27 (1989).

 

 

93.

94.

95.

96.

97.

98.

290

S.A. Nightengale, D.P. Dunne, H.K. Worner, "Sintering and grain growth of 3
mol% yttria zirconia in a microwave field," J. Mater. Sci., 31, 5039-43 (1996).

J. Cheng, J. Qiu, J. Zhou, N. Ye, "Densification kinetics of alumina during
microwave sintering," MRS Symp. Soc., 269, 323-28 (1992).

R. Wroe, A.T. Rowley, "Evidence of a non-thermal microwave effect in the
sintering of partially stabilized zirconia," J. Mater. Sci., 31, 2019-26 (1996).

D.L. Johnson, "Microwave heating of grain boundaries in ceramics," J. Am.
Ceram. Soc., 74 [4], 849-50 (1991).

T.K. Gupta, "Instability of Cylindrical Voids in Alumina," J. Am. Ceram. Soc.,
61 [5-6], 191-95 (1978).

A. Tsoga, P. Nikolopoulos, "Groove angles and surface mass transport in
polycrystalline alumina," J. Am. Ceram. Soc., 77[4], 954-60 (1994).

 

APPENDIX A: SATURATION BEHAVIOR IN CYCLIC
AND STATIC FATIGUE IN CERAMICS

A.l Literature Review

A.l.l Fatigue in Ceramics

To begin to understand fatigue in ceramics it is necessary to understand that in
ceramics "fatigue" is a word that is not just used to describe the behavior of a material
under varying load (as in metals), but is used for many different phenomena observed
in ceramics [A. 1]. Examples include the phenomenon of: "static fatigue" where
strength reductions under a constant applied load result from environmental effects
(corrosion at the crack tip), and "thermal fatigue" where the strength decreases from
repeated thermal shock. For ceramics, the term "cyclic mechanical fatigue" is used to
describe behavior of ceramics under varying mechanical load. This, then, is the

equivalent of the term "fatigue" used in metals literature.

A.l.2 Cyclic Fatigue

Historically, cyclic mechanical fatigue in literature has not been investigated in detail
until the last decade (beginning in the mid-1980’s). The reason for this was that since
most common ceramics do not have dislocation motion and so would not have crack
tip plasticity and consequently would not be subject to cyclic fatigue [A.2]. Early

experimental investigators compared cyclic mechanical fatigue with static fatigue and

291

 

292

attributed strength decreases merely to stress corrosion at the crack tip [A3]. A
standard text ceramic materials states that while failure from mechanical fatigue occurs
in metals it is rare in ceramics, adding that static fatigue from stress corrosion is
common in ceramics [A.4].

Gui [A.5] tested alumina samples in both static and cyclic fatigue [A5]. The
specimens were tested in tension/compression to determine the number of cycles or the
time to failure for different stress levels. The cyclic fatigue life was significantly
shorter than the static fatigue lifetime for the same maximum applied stress level.
However, Gui’s [A.5] results were questioned as possibly being the result of batch
variability of the samples [AG] and subsequent static and cyclic fatigue testing by
other investigators (for a different material) found no appreciable difference in failure
lifetimes with the authors adding that stress corrosion of cracks was the likely
mechanism causing failure [A.7]. Later several groups of authors used compact
tension specimens in both static and cyclic fatigue to measure the crack length as a
function of time for an applied stress intensity (or stress intensity range in the case of
cyclic fatigue) [A8, A9]. Dauskardt et al. [A8] and Reece et al. [A.9] showed that
for two different materials the crack length did not increase with time in static loading,
while the crack length increased significantly in cych loading, giving some of the
fust conclusive and accepted evidence that cyclic fatigue occurred in ceramics.

The bulk of the research which has followed has used three different types of
experimental testing. The most common experimental techniques include fatigue crack
growth of long cracks in compact tension specimens [A.lO - A.l3] or flexure

specimens [A. 14 - A.l6], crack growth of notched cyclic compression specimens

 

293

[A.l7 - A22], and fatigue life for different levels of applied stress in flexure or
standard tensile specimens [A.23 - A.27]. Newer, less common, experimental
techniques include measuring the strain as a function of stress at each cycle for
standard tension specimens cyclically loaded with different levels of maximum applied
stress and reporting the plastic strain as a function of stress for each cycle [A.28,
A.29] or reporting the calculated elastic modulus as a function of cycles [A.30, A31].

The experimental technique of fatigue crack growth measurements in ceramics
is the same as in metals. The crack length is measured at preselected numbers of
cycles and the stress intensity and crack growth rates are calculated in the same way
as in metal specimens (for details on calculations see standard fatigue texts [A.32,
A.33]). The data are graphed as crack growth rate (%) versus stress intensity range
(AK). The data, when plotted in log-log, follow Paris Law as do metals

.3“; = c (AK)”‘ (M)
where C is a constant and m is the slope of the linear region [A.32]. For metals the
exponent, m, in Equation A.1 has a value of 2 to 4. For ceramics the exponent is
much higher ranging from 21-42 for different materials [A.9, A.lO, A.lZ].

Fatigue life experimental testing of ceramics in cyclic fatigue is also very
similar to that in metals except that in ceramics stress-life curves are used and not
strain-life as with metals. Stress-life instead of strain-life is used for most ceramics
due to the lack of appreciable plastic strain and absence of dislocation movement in
ceramics.

In an investigation which used a newer experimental technique for investigation

of cyclic fatigue in ceramics, Liu and Chen [A.28] tested the fatigue behavior of 3-

 

 

 

294
mol%-yttria-stabilized tetragonal zirconia polycrystals (3Y-TZP) using uniaxial
tension-compression. Liu and Chen’s investigation revealed a hysteresis effect in the
stress versus plastic strain curve (Figure A.l). The total strain was measured in the
experiment and the plastic strain was found by using the elastic modulus to obtain the
elastic strain contribution. The plastic strain was found by subtracting out the elastic
strain contribution to the total strain. The plastic strain in ceramics is the strain
resulting from the aggregate crack opening displacements by all the microcracks which
open in cyclic loading. The plastic strain is used instead of the total strain because the
strain is dominated by the elastic strain contribution in ceramics. The plastic
contribution to strain from microcracking is extremely small compared to plastic strain
from dislocations in metals (Figure A.l).

Upon initial loading, the beginning of the stress-plastic strain loop has an
infinite slope since initially there is only elastic strain and no plastic strain. As the
loading continues, the slope changes to a finite positive slope which the authors
attribute to a decrease in the elastic modulus caused by microcracking. Upon
unloading, the curve has a constant slope until low loading levels are reached and then
the slope becomes infinite again or nearly infinite. Slope changes indicate a smaller
decrease in plastic strain which the authors attribute to closure of microcracks.

Upon reloading of the specimen for another loading cycle, the initial curve of
the reloading cycle does not follow the unloading curve of the previous curve, but
rather is vertical which the authors attribute to the elastic modulus being undegraded
from the beginning of the previous cycle. The undegraded elastic modulus is

attributed to friction resulting from the contact sliding of microcrack surfaces which

 

 

295
oppose the reversal of plastic deformation.

Another characteristic of the stress-plastic strain curves is that when the test
specimens are unloaded to zero stress after several cycles, the hysteresis loops are still
at a finite residual strain. This residual strain is an accumulation of damage. The
amount of damage accumulated increases with each cycle, but decreases with
successive cycles. Liu and Chen [A.28] note that damage levels are affected more by
increases in mean stress than for increases in stress amplitude, which is shown by
plots of cumulative plastic strain versus cycles for varying maximum stress and mean
stress (Figure A.2). The stress-plastic strain curves (Figure A.1) showed a decrease in
the initial slope of unloading as the number of cycles was increased which was
attributed to a decrease in elastic modulus as damage was accumulated. Failure in the
majority of specimens was traced to internal flaws (usually near the surface) which
were formed during or before sinterin g. Fatigue lifetime was controlled by crack

propagation, most likely [A.28].

A.l.3 Thermal Fatigue
Case et al. [A.35 - A39] noted that thermal fatigue damage in ceramics first
accumulates rapidly then saturates at a sufficiently high number of loading cycles. At
least for low cycle fatigue damage, Case et al. [A.35 - A.39] found that the damage
saturation behavior may be described by the equation

P(N) =P0 + D(1 - exp(—8N)). (Al)
The parameter P is a measurable material property (e. g. elastic modulus) that changes

as a function of the fatigue-induced damage. P(N) is the value of P following N

 

 

 

-’ A.M.-fin ' A

296

500

 

Stress (MPa)
0)
O
O
l

 

 

 

l 1 L4 1 1 I l

75 100 125 150
Plastic Strain (1 E-6)

Figure A.l Hysteresis loops of 3Y-TZP. Note the change (S,>SZ>S3) and the shifts of
loops due to strain accumulation (from [A.28]).

 

 

N
O

O)
0

0|
0

A
O

 

O)
O

N
O

 

Stress Ratio (Um I am)
_ A R=0 . R=0.8

0 . r . l : 1 l 1 . : . l L 1 l I . . .
0 500 1 .000 1 .500 2,000
CYCLES

Figure A.2 Cumulative plastic strain as a function of cycles for 3Y-TZP in cyclic
mechanical fatigue (from [A.28]). Solid curves are a regression analysis using
Equation A.2.

CUMMULATIVE PLASTIC STRAIN (1 E-6)
3
1
r

 

 

 

 

 

 

 

297

fatigue cycles at a fixed stress level. P0 is the microcrack-free value of the property P
and D is the saturation constant. (For large N, P(N) approaches Po + D.) For thermal
fatigue, Case et al. [A.35 - A.39] noted that the parameters P employed to monitor
damage evolution have included elastic modulus, internal friction, strength, and

hardness.

A.2 Results and Discussion

Figure A.3 shows the fit of the mechanical fatigue data from Liu and Chen [A.29] to
Equation A.2. The data points in Figure A.3 indicate the data originally collected by
Liu and Chen [A.28] . The lines through the data points indicate the linear best-fit
regression analysis of Liu and Chen’s [A.28] data, performed by Wilson and Case
using Equation A.2 [A34]. The accumulation of plastic strain with cyclic fatigue is
described quite well by Equation A.2 with regression correlation coefficients, r,
ranging from 0.944 to 0.999 (Figure A.3).

Wilson and Case [A.41] performed similar analysis on data collected by Ewart
and Suresh [A.18]. Ewart and Suresh measured crack growth as a function of the
number of fatigue cycles for compact tension specimens of alumina (A1203). The
authors [A.18] were trying to better understand the mechanisms causing fatigue
damage in ceramics. For one single edge notched cyclic compression test, the sample
was removed and ultrasonically cleaned every 5,000 cycles and in the other test the
sample was not ultrasonically cleaned. Figure A.4 shows the data collected by Ewart
and Ewart and Suresh deduce that this reduction is caused by the accumulation of

debris along the Suresh with the curve in the figure being generated by Wilson and

 

298

 

r A 325 MPa + 350 MPa 3* 375 MPa

 

 

 

 

 

 

   

 

 

 

333 * - 4OOMPa x 425 MPa 0 450 MPa
2’:
E
Z
<
r:
I‘—
a)
$2
'—
‘5’
o.
o 4 : : - : J :
O 20 40 60 80 100

CYCLES (N)

Figure A.3 Regression analysis using Equation A.2 (solid curves) for the low cycle
mechanical fatigue of Mg-PSZ [A.34, A.28].

 

   
 
 
 

 

 

 

 

 

 

 

1.5
3'; DATA
t
:- 0 SideA - Side B
(251.0»
m
.J
x
s
0
2150.5"
g REGRESSION CURVE
LU
<>t — SideA ""SideB
0.0. 1411, -:Jr..:1...:,‘.l

o 5 1'0 15 20 25 30
CYCLES (1 E+4)

Figure A.4 Regression analysis using Equation A.2 for the mechanical fatigue of
polycrystalline alumina at R=10 at maximum stress of -268 MPa for a specimen
ultrasonically cleaned after every 5,000 cycles [A.42, A.l8].

299

Case with a linear least squares regression of the ultrasonically cleaned data to
Equation A.2. Equation A.2 describes the accumulation of fatigue damage in ceramics
quite well with a correlation coefficient of 0.984 [A.4l] (Figure A.4). As can be seen
in Figure A.4, for the specimen that was not ultrasonically cleaned the crack growth
was reduced. crack faces (from damaged grains and grain boundaries) which reduces
the effective driving force for future crack advance [A.l8].

Wilson and Case [A.34] also applied the equation describing damage
accumulation in fatigue of ceramics (Equation A.2) to mechanical fatigue data of
Steffen, Dauskardt and Ritchie [A.lO]. Steffen et al. [A.lO] collected data to produce
crack growth as a function stress intensity data (Figure A.5). Wilson and Case [A.34]
used the actual crack length data originally collected by Steffen et al. [A.lO] to
perform a linear regression to Equation A.2 to analyze the damage accumulation in the

material. The resulting best-fit curve to the data (Figm’e A.6) has a correlation

 

coefficient of 0.984 [A.34].

A.3 Conclusions

In summary, ceramics do have cyclic mechanical fatigue, not just an environmental
effect of stress corrosion at the crack tip. Common cyclic mechanical fatigue testing
of ceramics uses methods similar or identical to fatigue experimentation in metals.
Specifically, crack growth measurements with subsequent fitting to Paris’ Law and
stress-life testing are commonly investigated. More recent experimental work has
found a hysteresis effect in the stress versus plastic strain curves. Wilson and Case

[A.34, A41, A42] use an equation describing the damage saturation behavior of

300
ceramics in thermal fatigue developed by Case et al. [A.35 - A40] to describe cyclic

mechanical fatigue data of many investigators.

 

 

301

 

1E+01

1 E +00 _‘ ll- Long Crack @330 MPa. Ira-1 O 375 MPa, nxo I 330 MPa, Fla-1
1E 01 X435 MPa. n=o 81440 MPa. Ra-‘I A435 MPa. n=o A435 MPa. nao

da +440 MPa. n=.1 X 330 MPa. a=-1
dN 1 E'02 _"

1 E-03 ——
1 E-04 -—
1 E-05 -—
( cygies 1 E-OG T—
1 E-O7 ——
1 E-08 ——
1 E-09 J—
1 E-1O ——
1 E-11 ——
1 E-12 -—
1 E-13

 

 

 

 

 

 

 

1
Kflllx (MPa-mos)

Figure A.5 Crack growth rate as a function of stress intensity, Km (from [A.10]).

 

 

 

MAX. STRESS

AVERAGE CRACK LENGTH (pm)

' A(BSOMPa
0M1 I I I ”1....
0 1 2 3 4 5 6

CYCLES (1E+5)

 

 

 

 

 

Figure A.6 Regression analysis (solid curve) using Equation A.2 for the mechanical
fatigue of Mg-PSZ [A.34, A.lO].

 

A.1

A.2

A.3

A.4

A.5

A.6

A.7

A8

A9

A.4 References for Appendix A

L.S. Williams, "Fatigue and Ceramics;" pp. 245-302 in mm
cf Enginccring charfl'cs, W.W. Kriegel, H. Palrnour III Eds., Interscience
Publishers, NY. (1960).

SM. Wiederhom, B.J. Hockey, D.W. Roberts, Philisophical Magazine, 28, 783
(1973).

DA Krohn, D.P.H. Hasselman, "Static and Cyclic Fatigue Behavior of a
Polycrystalline Alumina," Journal of the American Ceramic Society, 55 [4],
208-11 (1972).

W.D. Kingery, H.K. Bowen, D.R. Uhlmann, W
m John Wiley and Sons, NY. (1976).

F. Guiu, "Cyclic Fatigue of Polycrystalline Alumina in Direct Push-Pull," J.
Mater. Sci., 13 [6] 1357-61 (1978).

A.G. Evans, "Fatigue in Ceramics," International J. of Fracture, 16 [6] 485-98
(1980).

T. Kawakubo, K. Komeya, "Static and Cyclic Fatigue Behavior of a Sintered
Silicon Nitride at Room Temperature," J. Am. Ceram. Soc., 70 [6] 400-05
(1987).

RB. Dauskardt, W. Yu, R.O. Ritchie, "Fatigue Crack Propogation in
Transformation-Toughened Zirconia Ceramic," J. Am. Ceram. Soc., 70 [10]
C248-C252 (1987).

M.J. Reece, F. Guiu, M.F.R. Sammur, "Cyclic Fatigue Crack Propogation in

Alumina under Direct Tension-Compression Loading," J. Am. Ceram. Soc., 72
[2] 348-52 (1989).

302

 

 

 

A.lO

A.ll

A.12

A.13

A. 14

A.15

A.16

A.17

A.18

A.19

A20

303

AA. Steffen, R.H. Dauskardt, R.O. Ritchie, "Cyclic Fatigue-Crack Pr0pogation
in Ceramics: Long and Small Crack Behavior;" pp. 745-52 in M
Prggeedicgc cf mc 4"I Intcmag'onal anfcrcncc cg Fag'guc and Fag'gcc
Threshclds, Vol. 2, H. Kitagawa, T. Tanaka Eds., Materials Component
Engineering Publications Ltd., Edgbaston, UK. (1990).

R.H. Dauskardt, M.R. James, J .R. Porter, R.O. Ritchie, "Cyclic Fatigue-Crack
Growth in a SiC-Whisker-Reinforced Alumina Ceramic Composite: Long- and
Small-Crack Behavior," J. Am. Cer. Soc., 75 [4] 759-71 (1992).

H. Kishimoto, A. Ueno, H. Kawamoto, "Crack Propogation of Sintered Silicon
Nitride under Cyclic Loads (Influence of Difference in Material) J SME Int J
Ser 1 34 [3] 361-6 (1991).

A. Ueno, H. Kishimoto, H. Kawamoto, M. Asakura, "Crack Propogation
Behavior of Sintered Silicon Nitride Under (3'ch Load of High Stress Ratio

and High Frequency," pp- 733-38 in W
In ' nf r F ' F ' Materials and

Component Engineering Publications, Burrrringham, UK (1990).

Y. Mutoh, M. Takahashi, T. Oikawa, H. Okamoto, "Fatigue Crack Growth of
Long and Short Cracks in Silicon Nitride," pp. 211-25 in W
Materials, R.O. Ritchie, R.H. Dauskardt, B.N. Cox Eds., Mat. Comp. Eng.
Publ., Edgbaston, UK. (1991).

DC. Cardonia, C.J. Beevers, Formation and Growth of Short Fatigue Cracks in
a Zirconia-Ceria Alloy," Scripta Met 23 [6] 945-50 (1989).

D. C. Cardona, C. J. Beevers, "Fatigue Behavior of Zirconia-Ceria Alloys," pp.

1023- 29 in Fatigue 90: ProceQings of the 4m Irrtcmag’cnal Confcrenccn cn

W, Materials and Component Engineering
Publications, Burmingham, UK (1990).

L. Ewalt, S. Suresh, "Dynamic Fatigue Crack Growth in Polycrystaline
Alumina under Cyclic Compression," J. Mater. Sci. Lett., 5, 774—8 (1986).

L. Ewalt, S.Suresh, "Crack Propogation in Ceramics under Cyclic Loads," J.
Mater. Sci., 22, 1173-92 (1987).

AA. Morrone, S.R. Nutt, S. Suresh, "Fracture Toughness and Fatigue Crack
Growth Behavior of an A1203-SiC Composite, " J. Mater. Sci., 23, 3206-13
(1988).

S. Suresh, L.A. Sylva, "Room Temperature Fatigue Crack Growth in Cemented
Carbides, " Mat. Sci. Eng., 83, L7-10 (1986).

 

 

A.2]

A.22

A.23

A.24

A.25

A.26

A.27

A.28

A.29

A.3O

A.31

304

S. Suresh, L.X. Han, "Fracture of Silicon Nitride-Silicon Carbide Whisker
Composites under Cyclic Loads," J. Am. Ceranr. Soc., 71 [3], C158-C161
(1988).

LA. Sylva, S. Suresh, "Crack Growth in Transforming Ceramics under Cyclic
Tensile Loads," J. Mater. Sci., 24, 1729-38 (1989).

H. Kamiya, M. Takatsu, K. Ohya, M. Ando, A. Hattori, "Effect of
Microstructure on Cyclic Fatigue Pr0perties of A1203 Composites," J. Ceram.
Soc. Jpn., Int. Ed., 98 [5], 469-476 (1990).

M. Masuda, T. Soma, M. Matsui, I. Oda, "Fatigue of Ceramics (Part 1)-

Fatigue Behavior of Sintered Si3N4 under Tension-Compression Cyclic Stress,"
J. Ceram. Jpn. Inter. Ed., 96, 275-80 (1988).

M. Masuda, N. Yamada, T. Soma, M. Matsui, I. Oda, "Fatigue of Ceramics
(Part 2)- Cyclic Fatigue Properties of Sintered Si3N4 at Room Temperature," J.
Ceram. Jpn. Inter. Ed., 97, 509-14 (1989).

M. Masuda, T. Soma, M. Matsui, I. Oda, "Fatigue of Ceramics (Part 3)- Cyclic
Fatigue Behavior of Sintered Si3N4 at High Temperature," J. Ceranr. Jpn. Inter.
Ed., 97, 601-07 (1989).

M. Masuda, M. Matsui, "Fatigue in Ceramics (Part 1)- Static Fatigue Behavior
of Sintered Si3N4 under Tensile Stress," J. Ceram. Jpn. Inter. Ed., 98, 86-95
(1990).

S-Y Liu, I-W Chen, "Fatigue of Yittria-Stabilized Zirconia: 1, Fatigue Damage,
Fracture Origins, and Lifetime Predictions," J. Am. Ceram. Soc., 74 [6], 1197-
1205 (1991).

S-Y Liu, I-W Chen, "Fatigue Deformation Mechanisms of Zirconia Ceramics,"
J. Am. Ceram. Soc., 75 [5], 1191-204 (1992).

L.M. Butkus, L.P Zawada, G.A. Hartman, "Fatigue Test Methodology and
Results for Ceramic Matrix Composites at Room and Elevated Temperatures,"
pp. 52-68 in W
Advancgfl Matcrials, Eds. M.R. Mitchell, 0. Buck, American Society for
Testing and Materials, Philadelphia (1992).

S. Mall, G. D. Tracy, "Fatigue Behavior of a Quasi-Isotropic Ceramic
Composite under Tensile Fatigue Loading," pp. 628- 37 m Princccm ngs frc

Qcm mpcsr tcs, 61h jl‘s‘chn ical anfcrcncc, Technomic Publishing, Lancaster, PA
(1991).

 

A.32

A33

A34

A.35

A.36

A.37

A.38

A.39

A.40

A.41

305

NE. Dowling, M Beh M ' n M f r
W Prentice Hall Englewood Cliffs New
Jersey (1993).

ST. Rolfe. J.M. Barsom. WWW

Applicag'cns cf Fcacmcc Mmhamcs, Prentice Hall, Englewood Cliffs, New
Jersey (1987).

BA. Wilson, E.D. Case, "Comparison of Mechanical Fatigue with Thermal
Fatigue in Ceramics," Script Met. Matal., 28, 1571-76 (1993).

W.J. Lee, E.D. Case, "Cyclic Thermal Shock in SiC-Whisker-Reinforced
Alumina Composite," Mat. Sci. Eng., A119, 113-26 (1989).

W.J. Lee, E.D. Case, "Thermal Fatigue in Polycrystalline Alumina," J. Mat.
Sci., 25, 5043-54 (1990).

Y. Kim, W.J. Lee, E.D. Case, "Thermal Fatigue in SiC Fiber Reinforced
Aluminosilicate Glass Ceramic Composite;" p. 479 in W
Matrix Qcmpcsites; Prgcscing, Mficling Ed Mcchanjcal Bchavicr, Eds. R.B.
Bhagat, A.H. Clever, P. Kuman, A.M. Ritter, The Minerals, Metals, and
Materials Society, Warrendale, PA (1990).

Y. Kim, W.J. Lee, E.D. Case, "Thermal Fatigue Behavior of Ceramic Matrix
Composites: A Comparison Among Fiber Reinforced Whisker Reinforced,
Particulate Reinforced, and Monolithic Ceramics;" pp. 871- 81 in _ccccg'_gLQ_f

thc Ammcg Smi 1c]: fcr Qcmpositcc, 51h chhcical anfcrcncc, Technomic
Publishing, Lancaster, PA (1990).

W.J. Lee, E.D. Case, "Comparison of Saturation Behavior of Thermal Shock
Damage in a Variety of Brittle Materials," Mat. Sci. Eng., A154, 1-9 (1990).

E. D. Case, Y. Kim, W. J. Lee, "Thermal Fatigue of Ceramics and Ceramic
Composites;" pp. T1123 m2 24 In m tion AMPE T hnic nf r n
Vclcmc 2 Advacccd Mamals; Mg‘cmg me Economic Qhallcn ngc, Eds. T. S.
Reinhart, M. Rosenov, R. A. Cov, E. Strickholt, Society for the Advancement of
Material and Process Engineering, Covina, CA (1992).

BA. Wilson, E.D. Case, "Low Cycle Mechanical and Thermal Fatigue of
Ceramics and Ceramic Composites, with Consideration of Debris Accumulation

Effects," pp. 931-40 in Prccccflings cf mc Amcricac Society fcr Qcmpcsitcs,
Technomic Publishing Co., Lancaster, PA (1993).

 

 

306

A.42 B.A. Wilson, E.D. Case, "Further Study of an Equation Describing Damage
Saturation Behavior in Fatigue of Ceramics and Ceramic Composites," pp. 518-
31 in Advanced Composites Technologies, ESD (The Engineering Society),
Ann Arbor, NH (1993).

 

 

APPENDIX B: CRACK LENGTH DATA FROM CONVENTIONAL
HEALING EXPERIMENTS, MICROWAVE HEALING EXPERIMENTS,
AND STRESS RELIEF CYCLE TESTING

The crack length measurement raw data is recorded for the conventional healing of
glass experiments (Tables 3.1 - B.7), the stress relief cycle testing in glass (Table
B.8), the conventional healing of alumina experiments (Tables B.9 - B.10), and the
microwave healing of alumina experiments (Table B.11).

307

 

 

308

Table B.l Crack lengths (pm) from conventional healing of soda-lime silica glass
(Conventional Healing of Glass Experiment 1, Section 4.4.2.1.1).

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Specimen Temperature 2C 2C
Number (°C) At 24 hr. After Anneal
l 600 209.8 155.9

197.9 140.9
202.3 176.8
196.2 171.8
206.3 189.2
180.1 150.5
2 600 202.1 169
197.4 183.7
212.7 188.6
210.3 170
202.7 191.5
202 177.6
3 600 214.9 213.1
204.6 203.2
205.4 204
186.3 186.8
21 1.3 209.1
203.3 201.5
4 600 194.5 197.3
183.6 198.5
186.9 183.8
199.4 177.3
203.8 160.4
201.2 155

 

 

 

Table 8.1 (cont’d).

309

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Specimen Temperature 2C 2C _—
Number (°C) At 24 hr. After Anneal
5 600 207.7 197.6 L—j-
197.5 206.2
198.9 208.3
198.6 203.1
206 189.9
199.4 196
6 600 206 = 196.4
203.4 205.1
208 190.2
200.5 183.5
200.1 174
199.6 180.5
7 600 209.6 193.2
201.9 199.4
207.6 132.3
196.9 1 10.3
197 .9 192.2
185.4 177.4
8 600 204.6 165
197.2 143.8
209.2 164.9
195.9 145.4
208.2 154.4
203.8 171.2

 

 

 

310
Table 8.1 (cont’d).

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Spgcimcn M AC E
N m r CE) A; 24 hi. Aftcr Anncal
9 600 208.2 208.2

202.5 201.8
195.7 195.5
207.8 204.6
210.5 206.3
206.4 201.8
10 600 204.4 167.5
207.2 192.8
206.7 197.4
198.9 194.2
211.1 206.6
200.9 193.8
1 1 25 202.5 195.3
193.5 193.9
196.8 190.7
206 209.3
202.7 202.7
194.4 190.5
12 25 206.6 202.9
201.2 199.5
208.1 207
191 191.3
203.1 199.7
_ 180.3 178.9

 

 

311

Table B.2 Crack lengths (pm) from conventional healing of soda-lime silica glass
(Conventional Healing of Glass Experiment 2, Section 4.4.2.1.2).

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Specimen Temperature 2C 2C
Number (°C) At 24 hr. After Anneal
1 550 NM. NM.
NM. NM.
2 550 197.5 191.5
185.9 179.1
3 550 205.3 202.9
200.8 170.5
4 550 200.7 186.7
191.5 170.8
5 550 197.7 155.9
191.3 147.9
6 550 206.8 200.9
194.6 _ 189.4

 

 

 

 

 

312

Table B.3 Crack lengths (pm) from conventional healing of soda-lime silica glass
(Conventional Healing of Glass Experiment 3, Section 4.4.2.1.3).

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Temperature Time Stress Relief Cycle 30 24 hr. After i
(°C) (min) min. Anneal
350 15 A 203.3 2207 221.7
206.1 224.3 225.1
207.3 227.3 226.4
202.7 221.1 219.5
204.1 222.4 222.6
204.7 223.2 223.7
375 15 A 197.8 215.2 217.1 a
190.3 206.4 205
197.6 215.7 217.1
200.7 219.6 223.3
197.4 215.1 217.5
186.4 209.7 208.5
400 15 A 176.3 208 207 .6 =1
190.2 218.6 221.2
191.1 220.7 221.2
191.5 221.8 221.4
194.2 225 225.2
194.8 225.1 223.4
425 15 A 199.5 219.3 220 :-
199.8 219.4 220.4
198 218.8 218.6
200.9 221.7 220.2
200.5 219.8 220.9
_ 200.7 219.3 220.2 ,

 

 

 

 

Table B.3 (cont’d).

313

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Temperature Time Stress Relief Cycle 30 24 hr. After]
(°C) (min) min. Anneal
450 15 A 201.5 212 213.8
198.4 210 213

201.2 212 215.3

205.5 219.2 221.2

203.9 216.4 219.1

195.7 209.7 212.7

475 15 A 208.8 227.8 227.2 fl
194.5 212.1 212.1

208 224.3 224.4

203.6 219.3 220.7

198 217.1 215.7

203.8 222.4 221.1J

500 15 A 202.8 220.6 220.7I
197.4 220.8 217.1

202.7 221.4 222.9

197.8 213.7 215.5

198.2 217.9 217.4

201.1 218.7 2191

525 15 A 199.1 220.8 218.1”
198.5 221.4 217.3

200.8 222.2 215.6

203.1 223.8 210.2

203.7 223.2 213.9

= 201.1 222.5 L21—8fl‘

 

 

 

 

Table B.3 (cont’d).

314

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Temperature Time Stress Relief Cycle 30 24 hr. After M
(°C) (min) nrin. Anneal
550 15 A 198 214.8 210.8
180 200.8 190

199.6 216.3 212.9“

199.1 218.6 215.6

197 216.6 210%

202.5 218 213.7]

550 15 B 186.1 203.8 193.4]
189.5 205.9 198.9“

195.2 211.3 203.8"

197.3 213.3 208.2"

197 212.8 203.8

196.3 212.6 204.3

550 15 None 183 190.2 191.9
190 196.1 198.9

189.3 195.2 196.2

189.7 198.7 199

189.7 198.9 199.8

185.2 193.7 194.3%

575 15 A 205.7 223.3 154“
206 231.1 139.8

208 229 180.5

205.2 227.9 176.8

204.1 224.6 180.8

_ 206.5 225.1 161.6

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

315
Table B.3 (cont’d).
Temperature Time Stress Relief Cycle 30 24 hr. Aft;l
(°C) (min) min. Anneal
575 15 B 204 222.7 207.2
207.5 224.2 219.6
197.9 213.8 208.5
203.3 218.7 212.1
202.9 220.6 216
202.3 218 211.5
575 15 None 179.3 194.9 180
186.1 201 195.7
189 205.1 188.9
193.2 207.7 191.3
180.3 195.5 144.2
181.8 195.2 182.3
525 30 A 205.9 227.5 219.6 1
204.2 226.5 213.5
196.5 224.1 220
209.1 230.3 221.4
202.6 220.6 213.6
201.6 220.4 217.1 '
525 30 B 202 219.1 201.2 I
207.1 225.1 204.3
204.6 222.6 203.6
208.5 226.7 199.3
205.7 223.8 200.7
207.9 226.8 200

 

 

 

 

 

 

 

 

 

 

 

 

Table B.3 (cont’d).

316

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Temperature Time Stress Relief Cycle 30 24 hr. WI
(°C) (min) min. Anneal
525 30 None 189.4 200.8 197.2
178.9 195 192.2

195 210.1 203

197.1 209.9 202.9

197.1 210.8 201.4

199.4 210.9 204

550 30 A 204.7 225.1 221.9!
204.2 224.8 221.2

202.9 221.8 221.4

206.9 223.9 222.7

200.1 218 216

r 207.2_ 225.4 223.5

550 30 B - 197 * 220.9 777
205.8 227.1 225.1

202.2 220.7 214.2

204 225.7 218.7

202.4 222.3 218.8"

202.3 222.2 2178'

550 30 None 184.5 212.5 209?
207.2 227.5 221.2

201.4 217.9 215.2

175 220.4 217.6

196.6 212.7 211.4

198.8 211.2 209.1

 

 

 

 

Table B.3 (cont’d).

317

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Temperature Time Stress Relief Cycle 30 24 hr. After 'I
(° C) (min) min. Anneal
575 30 A 209.9 229.7 223.4
209 228.3 202.1

202.2 221.5 215.5

205.2 223.9 211.9

204.7 225.6 206.3

207 226.2 221.3]

575 30 B 207.9 226.9 707—2]
206 227.2 206.7 ll

206.4 223 210.1"

204.4 219.7 199.6"

207.1 223.5 212.9"

205.5 222.7 204 l

575 30 None 161.7 178.8 176.7
189.5 200.7 198.8

190.3 203 199.6

191 203.1 203.3

191.8 204.5 202.5

196.4 207.9 205.5

525 45 A 205.8 224 221.;
207.4 224.1 223.8

202.2 216.8 214.9

204.7 220 216.5

191.4 210.5 210.4

__ 194.8 210.9 _20_8._8_

 

 

 

 

Table B.3 (cont’d).

318

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Temperature Time Stress Relief Cycle 30 24 hr. After Jl
(°C) (min) min. Anneal
525 45 B 203.6 220.1 216.1
204.7 220.6 214.7

200.1 220.1 215.9

184.9 212.7 206.1

204.6 220.9 219.3

203 220.2 219.8

525 45 None 193.7 208.2 208.4 :-
183.3 195.1 196.5

183.3 195.6 195.4

192.3 203 202.7

179.9 198 197

l9__lr .5 208 207.3 M

550 45 A 202.1 218.9 200.1
207.2 225.9 225

204.4 223.5 220.3

205 223.6 217

200.4 220.2 199.2

__ 202.8 222.3 209
$50—— 45 B 201.7 218.6 215.4'
191.7 210 206.1

204.9 219.8 224.8

201.6 218.3 213.9

207.2 224 216.5

_ __ 206.3 _ 221 212.3 1.

 

 

 

 

Table B.3 (cont’d).

319

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Temperature Time Stress Relief Cycle 30 24 hr. After “
(°C) (min) min. Anneal
550 45 None 174.4 195.5 199.4
179 191.1 192.4
195.9 206.6 206.8
200.5 211.2 215.4
171.1 183.9 196.9
186.3 198.8 200.3
575 45 A i 204.9 220.——2_ 189.3
196.8 216 185.4
206.3 223.4 190.6
196.4 208.3 184.3
199.7 213.8 190.8
210.5 225.1 198.3
575 45 B 200.7 214.2 183.3
202.6 215.3 183.7
205.5 219.4 185.5
205.1 220.5 191.3
206.1 218.9 186.9
209.6 224.2 191.64
575 45 None 193.8 206.9 2033
197.4 210.7 212.3
195.4 207 208.5
187.8 194.1 195.2
191.3 201.3 202.5
186.6 200.9 200.2

 

 

 

 

Table B.3 (cont’d).

320

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Temperature Time Stress Relief Cycle 30 24 hr After
(°C) (min) min. Anneal
525 120 A 207.8 : 224.8 210.2
202.1 211.8 201.5

193.9 211.5 197.51

203.5 213.6 199.7

203.5 218.8 205.7

205 225.1 208.5

550 120 A 201.1 223.5 200.2
201.3 225.5 205.2

202.3 225.2 206.3

195.7 219.9 191.3

207.9 228.2 216

202.6 225.7 207.5

575 120 A 206 220.6 166.8
205.7 220.1 158.2

205.1 218.4 165.2

205.4 219.7 166"

207.7 213.7 lfll

202.6 219.8 184.5"

 

Table B.3 (cont’d).

321

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Temperature Time Stress Relief Cycle 30 24 hr. After
(°C) (min) min. Anneal
575 120 B 204? 219.6 155.9
199.9 215.5 160.5
201.8 214.9 150.3
203.1 216.4 159.6
206.6 221.9 155.7
205 219.3 156.9 1
575 120 None 194.1 205.8 205
193.9 203.2 203.9
191.6 203 203.6
195 206.1 204.3
190.4 203.3 202.1
186.4 195.9 195

 

 

 

 

322

Table B.4 Crack lengths (pm) from conventional healing in soda-lime silica glass
(Conventional Healing of Glass Experiment 4, Section 4.4.2.1.4).

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Annealing Cycle: Aged in 0 %r.h. Aged in 45 %r.h. Aged in 100 7651.—
Temperature Time 2C 2C 2C 2C 2C 2C
(°C) (min.) Before After Before After Before After
525 60 193.1 166.5 203 171.1 246.7 206.7
192.7 160.5 209 178.4 248.1 205
186.6 158.5 198.7 168.6 231 201.3
185.2 156.2 208.2 174.3 245.5 203.6
190.6 174 205.7 174.5 242.2 205.2
192.8 162.9 205.5 169.6 241 194.3%
538 60L 184.9 162.1 204.6 170.8 226 192.9 A
183.9 160.5 213.5 175.3 224.5 189.1
181.6 157.4 207.8 167.3 231.5 198.8
175 165.2 210.2 176.6 213.4 182
174.9 163.3 209 173.8 230.8 196.7
180.5 163.4 210.2 179.1 235.9 199
550 60 188.9 161.6 215.5 179.3 231.4 192.7
187.5 168.3 214.2 178.1 213.3 172.1
185.5 163.4 210.5 175.8 238.3 210.1
190 160.5 203.6 165.6 233.8 203.8
189.4 168.9 213.5 181.4 232.8 199.4
187.5 164.5 206.7 173.9 225.8 208.8

 

 

 

 

 

Table B.4 (cont’d).

323

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Annealing Cycle Aged in 0 %r.h. Aged in 45 %r.h. Aged in 100 %r.h.
Temperature Time 2C 2C 2C 2C 2C 2C
(°C) (min.) Before After Before After Before After

563 60 191.6 164 216.2 185.2 228.8 196

188.6 153.9 209.1 174.7 223.2 195.1

183.8 167 194.1 158.5 231.5 199.1

174.2 161.8 200.1 163.8 226.1 192.2

181.9 164.1 211.6 182.1 216.7 187.8

179.6 159.8 215.7 185.2 216.5 188.3

575 60 190.3 176 202.2 180.6 235.8 208.5

193.2 178 212.7 187.9 235.4 221

195.2 175.7 208.1 182.2 225.7 215

192.9 176.9 203.3 182.9 225.1 211.2

188.7 174.6 209.5 179.6 230.8 195.1

193.7 179 211.2 181.8 222.1 197.9

 

 

 

324

Table B.5 Crack lengths (pm) from conventional healing in soda-lime silica glass

(Conventional Healing of Glass Experiment 5, Section 4.4.2.1.5).

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Annealing Cycle Aged in 0 %r.h. Aged in 45 %r.h. Aged in 100 %r.h.
Temperature Time 2C 2C 2C 2C 2C 2C
(°C) (min.) Before After Before After Before After
525 60 187.8 186.7 216.5 198.9 238.6 238
186.1 185 217.4 204.8 235.8 236.6
183.5 181.3 209.5 197.6 221.4 215.6
184.5 185 213.4 187.9 230.8 231.1
181.7 178.8 207.5 200.2 228.9 233.2
174.2 175.1 210.2 196.7 231.6 234_
525 90 194.3 179.4 197.9 180.5 241.9 230.3 P
191.4 182.7 207.6 189.4 236.9 233.8
191.1 178.8 214.4 198.3 243.6 219.5
195.4 183.3 213.9 200.2 241.4 218.5
192.3 180.5 201.2 185.5 234.9 219
191.5 178.7 206.4 186.9 227.7 208.7
525 120 184.2 181.5 212.5 208 239.5 225.5
182.2 180.8 214.5 207.5 239 225.7
191 186.4 204.4 195.9 239.7 227.7
190 185.6 215.6 207.8 241.7 225
185.7 185.9 217.1 207.5 240.8 225.1
183.9 184.4 212.4 200.2 240.6 229.6

 

 

%-

 

 

Table B.5 (cont’d).

325

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Annealing Cycle Aged in 0 %r.h. Aged in 45 %r.h. Aged in 100 %r.h.
Temperature Time 2C 2C 2C 2C 2C 2C
(°C) (min.) Before After Before After Before After
525 150 198.6 184.9 213 194.9 244 242.5
187 172.1 209.3 187.6 244.4 243.1
197.8 179.2 196.9 175.4 228.7 223.9
183.9 169 208.2 190.2 244.4 238.5 '1
192.1 181.2 215.3 197.9 213.6 188.8
_ 193 185.2 219.1 200.5 228.2 209.5 1
525 180- 185.7 189.6 204.5 195-:2- 219.6 219.5 J
185 189.5 197.3 190.8 230.5 222.8
184.2 187.7 213.5 202.1 227.8 219
184.4 187.8 196.9 185.7 227.8 224.3
181.8 185.7 210.9 203.9 225.6 221.3
183 189.1 212.3 202.1 231.5 220

 

 

 

 

326

Table B.6 Crack lengths (pm) from conventional healing in soda-lime silica glass

(Conventional Healing of Glass Experiment 6, Section 4.4.2.1.6).

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Annealing Cycle Aged in 0 %r.h. Aged in 45 %r.h. Aged in 100 %r.h.
Temperature Time 2C 2C 2C 2C 2C 2C
(°C) (min.) Before After Before After Before After

575 60 188.7 179.7 213.4 198.6 235.4 185.8
195.9 185.6 213.8 202 240.4 211.2

187.2 177.7 215.8 200.5 236.9 211.2

193.7 188.8 212.3 200.8 236.1 201.1

193.8 187.5 208.2 194 243.1 196.1

193.2 183.6 213.9 196.7 245.3 197.3
575 90 190.2 182.6 217 207.2 221.8 214.4 I
181.4 172.6 216.9 206.1 220.7 210.4

180.9 174 216.7 201.5 217.8 200.5

190.6 183 211.7 198.5 220.8 214.9

198.8 188.3 208.4 196.3 217.2 218.6

197.6 189.2 208.6 198.4 231.7 232.2

575 120 186.9 183.2 201 165.4 218.7 212.8
188.5 184.1 205.4 171.8 224.5 221.8

182.7 181.9 206.5 174.7 220.6 216.2

177.3 177.1 207 173.1 221.7 213.7

185.2 179.3 204.8 174.2 230.6 220

180 179.1 205.4 174.7 230.2 225.4

575 150 189.3 185.7 214.3 197.6 232.2 212.4
188.8 184.5 213 195.7 232.8 209

182.7 180.7 212.5 196.6 230.8 194

170.1 168.7 212.1 193 224.4 198.5

184.3 180.9 211.5 188.9 238.4 219.3

179.3 177.2 211.3 190.6 237.7 209.3

 

 

 

 

327

Table B.7 Crack lengths (pm) from conventional healing in soda-lime silica glass
(Conventional Healing of Glass Experiment 7, Section 4.4.2.1.7).

 

Annealing Cycle Aged in 0 %r.h. Aged in 45 %r.h. Aged in 100 %r.h.

 

 

Time Ramp Rate 2C 2C 2C 2C 2C 2C
(min) (°C/min) Before After Before After Before After 1
60 5 178 140.7 199.3 152 229.2 162.7

 

190.2 151.7 203.2 155.6 237.1 184.8
179.8 147.5 217.5 170.5 229.7 160.2

178 149.3 212.8 164.1 239 181.7
186.6 146.7 212.4 164.1 238.8 192.3
188.9 153.6 214.5 173.3 231.5 186.6
60 5 and 2.5 187.8 154.5 213.5 171.5 234.6 187.5
186.5 151.9 221.1 181.9 234.3 194.8
185.4 154 212.1 170.7 203.9 170.6
189.3 155.4 215.1 169.8 219.8 184.2
186.3 153.6 212.4 169.3 230.3 193
193.5 161.3 216.9 168.5 228.3 194.3
90 5 and 2.5 189.1 154 211.2 172.7 239.1 186.3
190.6 154.6 198.8 141.7 228.2 175.3
186.4 148.2 215.4 168.1 243.4 191.7
185.2 149.9 213.9 165.9 243.7 190.3
189.9 153.2 216 163.6 240.8 178.9
193.9 154.6 219.3 168.1 236.3 178.1};

 

 

 

 

 

Fl

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Table B.7 (cont’d).

328

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Annealing Cycle Aged in 0 %r.h. Aged in 45 %r.h. Aged in 100 %r.h.
Time Ramp Rate 2C 2C 2C 2C 2C 2C
(min) (°C/min) Before After Before After Before After

120 5 and 2.5 187.3 152.8 217.6 179.4 229.9 188.9

175.9 143 208.4 171.4 231.8 190.9
189.2 151.6 214.5 176.2 215.1 172.6
185.1 148 213.2 167.2 228.8 187
189 155 216 174.5 233.7 177
188.6 155.6 200.2 157.1 219.5 174.7 .
240 5 and 2.5-L 172.1 128.9 188.2 117.2 — 224.4 165.7 J
185.6 133.4 199.4 136.1 232.7 169
176.4 123.3 204.1 138.9 243.7 167
180.1 129.7 207.6 135.6 242.8 167.9
186.5 134.1 204.8 132.8 228.6 165.1
186.7 136.1 203.8 127.8 228.7 165.8
480 5 and 2.5 184.8 144.2 215.9 147.3 202.3 157.5
186.2 140.4 213.1 142.6 196.6 144.4
189.3 149.4 209.8 149.4 206.1 152.3
184.5 143 201.9 144.9 209.2 157.7
182.6 139.8 210.4 152.7 235 178.7
186.4 147.8 205.6 138.6 231.7 175

 

 

 

 

329

Table B.8 Crack lengths (pm) from residual stress relief testing in soda-lime silica

glass (Residual Stress Relief Cycle Testing, Section 4.4.2.1.8).

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Heating Cycle Before After J Heating Cycle Before After I]
Number Cycle Cycle Number Cycle Cycle

1 182.4 219.6" 2 189.8 220.5

203.6 220.4 193.1 222.5

198.8 214.1 199.3 212.3

203.7 204.6 204.8 210.9

206.8 204.1 197.1 214

207.1 220.5 205.6 219.2

191.8 216 200.4 213.6

207 222.1 201.7 210.9

206.5 219.4 205.5 208.2

210.3 210.9 205.9 215.7

209.1 216.4 196.5 212.5

203.8 213.4 191.8 213.8

187 205.9 194.8 214.8

191.3 215.4 198.3 214.9

201.6 218.2 208.9 215.9

206.7 216.2 206.6 220

201.6 218.3 208.6 217.8

206.6 217.7 205.5 214.7

204.5 209.8 197 .6 204.5

195.2 219.5 205.8 217.9

203.9 215 197.4 209.9

206.9 21 1 182.5 209.5

 

 

 

 

 

Table B.8 (cont’d).

330

 

 

f

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Heating Cycle Before After I
Number Cycle Cycle

3 208.3 221.5
200.5 216.4

193.6 217.3

204.7 220.4

193.6 223.9

187.6 219.3

186.3 212.3

212.8 221.7

206.1 216

206.9 216.7

203.4 223.8

206.3 224

209.7 217.6

211.1 215.6

203.4 213.3

203.7 221.9

210.3 222.7

200.6 220.7

205.8 219.8

205.2 222.4

198.8 215.2
202.5 216.1

 

 

 

Heating Cycle
Number

4

'7

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Before After
Cycle Cycle
196.7 219.8
191.5 224.4
207 209.4
205.2 217.5“
204.3 208.9
200 205.11
185 211.3"
195 221.6 “
203.2 209.6
204.6 210.9
211.9 214.6
209.1 212.7
189.4 216.7
204 212.1
202.7 214.6
191.4 215.9
202.3 215.7
189.1 216.8
205.7 215.6
207.1 217.1
205.2 209.7
203.6

219.9

 

 

 

 

 

 

—l

 

Table B.8 (cont’d).

331

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Heating Cycle Before After Heating Cycle Before After ”I
Number Cycle Cycle Number Cycle Cycle
5 208.8 208.5 6 206.3 219.8
211.3 213.1 211.7 219.5
204.6 200.7 207 .6 205.9
203.9 208.3 206.6 220.5 11
209.4 202.2 208.4 218.6‘I
208 208.1 201.4 220.3
203.2 205.9 204.4 215.9
195 202.7 209.1 216.3
209.1 210.8 197 .7 213.9
212.5 215.2 201.3 211.3
198.2 209.7 193 218.1 I
203.5 208.5 196.3 224.3
188 207.9 209.6 221.6
208.7 209.3 210.9 221.2
207.1 210.5 199.4 217 .7
213.9 215.2 192 215.6
199.5 209.6 197 .7 223
205.7 21 1.5 204 221.3
208.9 212.1 210.5 194.1
206.7 207.5 209.9 215.3
209.1 208.8 202.3 213.6
206.5 197 .3 202.6 207 .4

 

 

 

“L

 

 

 

332
Table B.8 (cont’d).

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

I Heating Cycle Before After Heating Cycle Before After

Number Cycle Cycle Number Cycle Cycle

4 7 185.8 213.9 .. 8 199.4 224

193 213.1 198.8 224.1

207.9 207 .7 205.1 221.9
207 .5 215 200.8 224.4
208.8 211.9 203.9 220.6
201.4 214.6 203 224
209.2 206.4 190.1 222.3
207.5 213.1 200.9 223
208.1 209.8 197 .4 2201'
209.5 208 198.1 216.7"
207.4 0 200.3 221.1
209.1 0 205.2 222
203.9 211.7 191.5 226.2
207 .9 208.7 196.9 222.6
203.5 213.6 188.3 224.7
205.4 216.2 198.3 220.7
207 .3 212.5 198.7 220.4
206.1 216.3 177 .3 221
185.6 211.6 189.2 219.3
196.7 215.7 192.2 223.4
210.2 212.2 200.3 222.8
208.4 214.2 204.2 218

 

 

 

 

 

 

333

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Table B.8 (cont’d).
tleatin g Cycle Before After—J Heating Cycle Before After -I
Number Cycle Cycle Number Cycle Cycle
4 9 203.6 4207.1" 10 == 215.3 217.1
203.3 209.5 208.2 223.8
199 222.5 207.3 194.9
209 225.7 191.8 223.61l
205.5 222.6 213.7 225.5"
198.3 222.7 213.9 223.2“
199.2 230.5 211.6 230.7“
196.4 231.4 214.1 230.1
197.6 227.2 209.8 206.9
204.9 228.9 208.6 227.3
201.8 222.7 202.9 227.1
194.8 213.2 192.4 226.5
196.1 214.9 196.9 225.6
207.4 222.4 206 232.1
196.2 216.5 201.4 222.1
197.7 208.8 190.5 231.9
180 226.6 216.3 225.9
196.9 222.2 212.5 222.1
203.6 223.7 216.8 222.4
207.7 218.3 211.4 217.9
170.2 221 205.2 222.4
190 225 212.3 228.2

 

 

 

334

Table B.9 Crack lengths (pm) from conventional healing of alumina at a nominal
temperature of 1005 °C (Conventional Healing of Alumina Experiment 1, Section

4.4.2.2.1). (N.A. indicates Not Applicable and NM. indicates Not Measured)

 

1

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

283.5
_J

 

 

 

 

 

 

Second Coors Alumina Microwave Sintered Alumina
24 hr.
Aging 30 24 hr. 48 hr. After 30 24 hr. 48 hr. After
(‘70 rJ1.) min. Anneal min. Anneal
P 0 279.4 276.6 267.8 253.6 363.1 389.3 391.4 362.6“
264.1 277.6 265.6 255 387 399.6 398.2 361.8
277.3 292.1 293.5 270.2 373.7 376.7 378.3 369.9
270.8 270.6 267.3 236.6 398.2 402.6 403.3 358.4
268.7 286 276.3 260.8 408.2 443.7 442.1 403.3
270.8 287.4 272 265.8 433 432.8 430.7 363.2
275.6 272.1 N.A. 255.7 362.2 356.2 N.A. 343.8
267.5 274.2 N.A. 246.2 364.3 375.1 N.A. 355.1
264.5 275.5 N.A. 247.7 390 409.5 N.A. 387.2
246.3 243.1 N.A. 218.9 352.7 353.9 N.A. 352.4
277.7 267.5 N.A. 250.9 383.8 395.1 N.A. 376.7
285.5 N.A. 260.5 384.3 379.6 N.A. 361.8

 

 

 

 

 

Table B.9 (cont’d)

335

fi

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Second 24 CoorsJAlumina 1' Microwave Sintered Alumina
hr. Aging
(% r.h.) 3O 24 hr. 48 hr. After 30 24 hr. 48 hr. After

min. Anneal min. Anneal

45 292.2 289.5 286.6 268.2 348.3 358.2 351.3 353
298.4 274.8 277.5 263 402.4 403 399.9 399.1

293.6 294.1 282.2 250.3 408.3 412.5 412.1 403.3

276.4 281.9 276 243.2 379.8 41 1 409.9 403.4

314.3 307.6 291.8 269 283.1 310.4 302.9 305.1

289.2 286.4 286.3 267.2 350.2 343.2 341.2 321.3

281.7 280.5 N.A. 269.9 345.9 349.2 N.A. 352.9

262.5 281.8 N.A. 268 422.6 416.6 N.A. 372.4

277.3 292.6 N.A. 248.3 430.3 453.3 N.A. 417.6

280.1 287.1 N.A. 258.3 397.8 407.7 N.A. 425.8

297.7 307.4 N.A. 296.5 440 440.5 N.A. 399.2

276.5 279.1 N.A. 270.7 397.9 402.2 N.A. 339

100 291.8 292.9 296.6 263.4 309.5 319.5 331.2 335.3
288.9 297.2 309.6 247.6 252.1 250.8 257.9 253.1

265.5 270.3 274.4 239.8 389.9 394.7 399.4 353.8

293.6 302 288 279.4 397.9 390.8 398.6 330.2

275.9 298.9 292.7 253.4 380.8 386.6 394.5 371

289.9 296.7 298.9 256.1 406.2 412.5 412.1 398.5

302.2 295.5 N.A. 212 379.6 403.2 N.A. 346

274.8 303.4 N.A. 274.6 404.7 400.7 N.A. 371

285.5 298.7 N.A. 221 383.7 382.3 N.A. 369

281.3 286.7 N.A. 266.2 362.6 393.7 N.A. 379

288.8 292.6 N.A. 240.3 389.3 403.9 N.A. 374.7

265.6 285.6 N.A. 239.9 336.7 376.9 N.A. 292.3

 

 

 

 

336

Table B.l0 Crack lengths (pm) from conventional healing of alumina at a nominal
temperature of 1237 °C (Conventional Healing of Alumina Experiment 1, Section

4.4.2.2.1). (N.A. indicates Not Applicable and NM. indicates Not Measured)

 

1

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Second Coors Alumina Microwave Sintered Alumina
24 hr.

Aging 30 24 hr. 48 hr. After 30 24 hr. 48 hr. After

(‘70 m) min. Anneal min. Anneal

0 280.4 307.3 309.5 207.4 428.3 438.2 430.9 270.5

283.6 286.1 286.3 186.8 380.3 290.6 389.5 277.1

291.7 298.6 303.9 190.3 361 361.3 361.3 296.8

278 285.5 284.5 186.3 366.5 384 384 275.6

288.9 294.8 287.6 168.4 401.5 400.9 400.9 269.5

284 284.9 286.9 172.4 407.5 406.3 406.3 248.7

273.7 286 N.A. 201.8 413.5 420.9 N.A. 268.7

281.9 284.9 N.A. 231.2 401.1 417.7 N.A. 347.6

280 287.9 N.A. 194.2 442.5 361.4 N.A. 256.5

260.3 299.7 N.A. 155 391.3 387 N.A. 319.7

289.9 303.8 N.A. 186 380 398.8 N.A. 300.6

276.7 293.3 N.A. 227.9 428.7 447.9 N.A. 325.7

 

 

 

 

 

 

 

 

 

 

 

Table B.10 (cont’d)

 

337

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Second 24 Coors Alumina Microwave Sintered Aluminfl
hr. Aging

(% r.h.) 30 24 hr. 48 hr. After 30 24 hr. 48 hr. After

min. Anneal min. Anneal

45 250.5 0 309.7 239.6 :1 NM 223.6 262.1 230.5

248.8 0 296.4 209.8 NM 220 224.4 192.6]

260.7 277.8 293.9 237.1 N.M 252.5 249.8 247.3

246.6 290.5 291.4 216.8 NM 245.5 242 220.7

NM. NM. NM. NM. NM 274.8 287 220.3

NM. NM. NM. NM. NM 223.7 225.5 185.3

NM 290.3 N.A. 250.4 NM 254.2 N.A. 194.4

NM 266.3 N.A. 217.4 NM 275.5 N.A. 219.8

NM 294.6 N.A. 243.4 NM 249.9 N.A. 238

NM 294 N.A. 231.7 NM 202.9 N.A. 207.2

NM. NM. NM. NM. NM. NM. NM. NM.

NM. NM. NM. NM. NM. NM. NM. NM. II

100 305.5 307.3 299.2 266.3 411.9 414.1 415.4 387.3

284.6 294.9 280.9 242 430.2 430.9 425.4 373

300.8 315.3 295.5 251.7 359.7 356.5 354.3 357.6

293.3 305.6 296.9 256.2 367.3 375.6 366.2 362.3

293.5 300.4 288.4 284.6 393.9 412 415.2 401.1

301.3 301.6 293.6 263.8 424.2 448.6 450.4 376.5

295.3 278.6 N.A. 263.5 399.7 403.2 N.A. 347.3

311.2 299.2 N.A. 259.3 413.4 421.7 N.A. 424.5

290.7 283.5 N.A. 283.8 453 454.6 N.A. 426.6

290.9 287.7 N.A. 265.1 403.9 427 N.A. 413.91

281.7 289.2 N.A. 270.7 380 391 N.A. 271.1

318.4 L3_07£_N£_=258.6 387.5 375.9 N.A. 32;:

 

 

338

Table 8.11 Crack lengths (pm) from conventional healing of alumina at a nominal
temperature of 1469 °C (Conventional Healing of Alumina Experiment 1, Section
4.4.2.2.1). (N.A. indicates Not Applicable and NM. indicates Not Measured)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Second Coors Alumina Microwave Sintered Alumina
24 hr.
Aging 30 24 hr. 48 hr. After 30 24 hr. 48 hr. After
(% the) min. Anneal min. Anneal
0 293.4 293.4 305.2 164 377.9 378.6 377.2 365.1
284.2 291.5 293.3 166 365.5 365 365.3 365
297.9 298.2 301.1 157.1 424.9 424.4 420.9 384.5"
301.6 301.4 300.2 173.9 420.6 420 418.7 348.8"
288.5 282.3 283.2 213.7 355 378.1 346 309.7
307.7 302.8 305.7 151.9 349.3 366.3 373.5 315.8
278.1 278.4 N.A. 183.1 374.5 378 N.A. 346.6
280.9 296.7 N.A. 168.6 395.7 417.9 N.A. 392.5
289 289.9 N.A. 165.2 394 400.4 N.A. 352.2
289.4 304 N.A. 179.2 380 384.4 N.A. 351.8
288.7 313.8 N.A. 163.2 374.2 380.4 N.A. 357.8
296 305 N.A. 169.8 330.6 342.3 N.A. 288.5

 

 

 

 

 

 

 

 

 

 

Table B.11 (cont’d)

339

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Second 24 Coors Alumina Microwave Sintered Alumina
hr. Aging

(% r.h.) 30 24 hr. 48 hr. After 30 24 hr. 48 hr. After

min. Anneal min. Anneal

45 NM NM 298.8 190.7 NM NM 249.4 214.4

NM NM 296.3 126.7 NM NM 236.3 229.5

NM NM 270.6 155.6 NM NM 261.4 313

NM NM 285.2 135 NM NM 262.8 258.1

NM NM 281.6 163.4 NM NM 249.6 220.5

NM NM 287.6 167.7 NM NM 212.3 201.5

NM 302.3 N.A. 91.2 NM 409.8 N.A. 309.5

NM 279.3 N.A. 99.4 NM 377.8 N.A. 303.1

NM 307.4 N.A. 128.5 N.M 394.9 N.A. 309.2

NM 293.7 N.A. 137.6 N.M 284.3 N.A. 215.1

NM 291.1 N.A. 154.2 NM 376.3 N.A. 266.7

NM 270 N.A. 114.8fi‘ N.M 347.5 N.A. 319.3

100 NM. 299.9 288.4 178. NM. 395.8 405.2 262

NM. 289.4 293.3 170.6 N.M. 405.6 405.2 268.9

NM. 306.8 310 187.8 NM. 382 395.8 337.9

NM. 31 1.6 304.7 182.5 NM. 431 442.2 305.3

NM. 272.4 285.2 206.2 NM. 362.5 388.2 305.3

N.M. 297.9 300.7 177.5 N.M. 392.1 388 320.9

294 311.5 N .A. 188.2 392.4 417 .7 N.A. 358.7

270 275.4 N.A. 174.7 382.3 399.8 N.A. 336.8

292.8 302 N.A. 177.1 409 437.4 N.A. 404.3

287.8 290.8 N.A. 174.6 429.4 445.3 N.A. 375.7

293 301.2 N.A. 202.2 377.7 399.2 N.A. 321.2

268.9 287.8 N.A. 165.7 425.2 408.6 N.A. 351.3

 

 

 

. 5‘

 

Table B.12 Crack lengths (pm) from conventional healing in Coors alumina

340

(Conventional Healing of Alumina Experiment 2, Section 4.4.2.2.2).

 

 

 

 

 

‘A

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Annealing Cycle Aged in 0 %r.h. Aged in 45 %r.h. Aged in 100 %r.h.
Temperature Time 2C 2C 2C 2C 2C 2C

(°C) (min.) Before After Before After Before After

1005 60 258.4 208.8 253.3 216.1 282 187.7

279.1 215 284.2 245.4 269.9 183

285.4 226.6 258.6 191.1 259.6 193.1

288 229.4 296.7 239.3 270.4 221.4

256.1 219.9 263.7 217.7 254.4 185.6

283.8 224.6 278.4 231.4 269.2 218.6

1005 90 262.3 178.5 278.4 170.1 283.3 204

272 179.6 272.7 189.1 273.5 197.7

269.1 169.2 294.6 178.6 289.5 191.6

306.2 167.6 291.9 197.5 282.5 194.3

267.4 176.1 278.8 208.7 292.2 209.4

298.2 176.1 299.4 220.4 290.2 204.7

1005 120 283.3 190.2 281.1 187.9 289.1 179.7

264.9 185 264.8 186.5 307.2 178

270.2 177.8 273.7 199.7 268.9 179

279.5 190.9 273.5 203.5 289 190.2

270.1 200.2 263.3 187 270 166.1

264.9 165.4 262.5 180.1 291.1 191

1037 1410 268.8 171.7 286.6 187.3 272.9 163.6

258.2 132.1 268.9 176.7 276.4 176.8

262.1 168.7 273.5 166.9 272.6 177.6

272.1 168.1 287.1 160.5 247.2 113.9

265.1 136.9 296.1 181.5 279.4 156.8

264.7 156.7 270.6 163.2 282.5 155.4

 

 

 

 

Table B.12 (cont’d).

341

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Annealing Cycle Aged in 0 %r.h. Aged in 45 mged in 100 %r.h.1
Temperature Time 2C 2C 2C 2C 2C 2C

(°C) (min.) Before After Before After Before After i
1121 60 275.9 207.7 279.1 221.3 283.7 207.3
274.3 201.3 298.6 203 282.4 214.2

295.1 199.2 307.5 233.6 272.8 199.2

277.7 199.6 291.8 208.8 286.9 197.2

284.5 207.7 268.3 204.4 258.9 188.4

290.8 216.8 255.2 214.3 265.8 214

1121 90 271.8 159.5 282.9 190.4 291.6 177.6
287.4 166.7 264.8 194.1 283 175.4

276.5 186.4 300 175.7 272.8 161.2

274.8 188.8 294.4 158.3 291.2 182.2

260.3 169.2 287.9 179.5 290 167.2

275.3 179.1 273.1 175.9 271.4 171 _
1121 120 276.3 175.9 298.5 182.2 259.4 202.7-1
297 171.4 290.8 164.1 259.3 153

284.9 179.3 282.1 188.6 295.4 185.4

290.2 190.5 282.9 183.5 298.7 228.7

292.8 205.2 271.9 164.3 283.6 168.1

301 191.8 291.5 167.4 279.1 195.6
1237 =60 289.3 199.9 274.2 fin 287.5 180.5 .
287.1 208.3 255.7 194.7 303.7 217.3

271.2 198.8 272 201.3 296 199.6

290.4 195.2 289.9 191.8 279 178.9

301.4 213.5 255.4 209.9 297.1 181.1

275 198.5 274.8 192.2 297.7 177.1

 

 

 

X

 

Table B.12 (cont’d).

342

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Annealing Cycle Aged in 0 %r.h. Aged in 45 %r.h. Aged in 100 %r.h.
Temperature Time A 2C 2C 2C 2C 2C 2C

(°C) (min.) Before After Before After Before After

1237 90 279.4 154.1 293.4 169.8 302.5 167.3

290.5 168.8 274.3 181.3 279 155.7

299.8 169.6 290.5 124.9 297.4 172.9

296.8 165.9 292.7 164.3 296 172.8

276.9 158.5 306.9 121 297.2 172.6

291.5 146.4 312 161.1 296.1 174.8

1237 120 289.7 169.5 293 154.2 273.8 160.6

264.9 181.8 268.6 170.2 296 164.2

261.9 156.6 283.3 155.4 273.8 148.3

289.8 136.9 259.5 157 289.2 164.7

292 151.8 285.9 124.5 259.3 155.7

272.8 160.9 279.9 169.8 266.7 184.4

1237 180 a 250.6 195.4 264.3 189.7 270.4 164.3

263.2 174.7 276.4 193.3 268.6 160.3

264.4 180.6 275.6 174.3 279.7 195

250.6 162.8 258 170.3 255.8 178.1

268.7 172.1 267.2 191.7 267.9 163.4

265.1 170.8 285.1 176.3 270.8 134.1

1237 180 b 275 209.3 281 166.2 271.4 151.2

270 196.9 279 166.3 295.7 163.4

267 184.9 274.3 182.9 299.3 184.9

281.7 181.2 280.3 157.4 274.8 168.9

251.4 164.8 278.8 193.2 272.4 147.4

263.6 164.8 264.5 195.9 288.8 166.3

 

 

 

 

Table B.12 (cont’d).

343

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Annealing Cycle Aged in 0 %r.h. Aged in 45 %r.h. Aged in 100 %r.h.
Temperature Time 2C 2C 2C 2C 2C 2C
(°C) (min.) Before After Before After Before After
1353 60 261.8 189 294.3 162.9 289.4 189.7
259 194.4 292.6 172.3 269.1 181.4
286.1 149 279.2 188.6 279.8 195.7
278.6 162.2 278.8 163.6 271.8 180.2
277.2 168.5 293.3 145.5 286.8 158.3
272.1 . 163 297.8 144.8 277.5 167.6_
1353 90 286.7 135.8 295.2 136.3 299.3 177.5.
271.4 1 16.2 283.7 146.4 296.4 115
291.7 158.8 289.3 155.4 269.2 125.1
280.5 1 16.9 281.2 125.4 295.4 135.4
275.9 152.7 282.2 148.1 292.2 148.8
300.9 123.5 292 136.3 320.5 1 13.2
1353 120 269.3 118.7 269.6 132.7 264.5 134.7
279.1 117.3 288 163.8 273.1 138.8
283.4 148.9 280.7 143.9 175 149.3
291.5 133.2 290.6 142 293.5 141.9
263.6 147.4 276.4 138.3 287.5 144.6
287.4 155.7 276.4 101.3 281.2 141.2
1469 60 281.4 161.2 286.1 133.3 265.7 97.8
274.7 106 282.7 150.1 263.4 144.7
268 133 272.7 121.7 261.7 132.5
270.9 120.9 27 5.5 130.1 270.9 116.4
286 106.7 264.5 149.9 259.6 122.7
265.7 95.8 274.1 104.4 280.1 107.2

 

 

 

 

Table B.12 (cont’d).

344

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Annealing Cycle Aged in 0 %r.h. Aged in 45 %r.h. Aged in 100 %r.h.
Temperature Time 2C 2C 2C 2C 2C 2C
(°C) _ (min.) Before After Before Afl Before After
1469- 90 270.9 139.4 269 85.6 304.5 119.6
293 139.4 288.7 108.6 268.3 129.4
277.4 162.9 276.1 99 281.8 89.2
255.7 139.2 266.8 98.1 280.8 76.3
266.4 1 16.4 282.6 138.9 273.8 1 16.4
278.1 101.3 300.6 99.1 286.2 93.8
1469 120 280.4 95.5 278.2 86.4 268.7 106.7 |
253.3 86.7 27 1.6 1 11.9 275.6 106.2
287 124.5 271.7 87.1 282.9 134
268.5 96.6 262.3 91.6 288.9 90.3
288.2 124.3 278.8 103 280.2 132.4
281.9 78 256.3 109.6 283.1 91.3 H

 

 

 

345

Table 8.13 Crack lengths (pm) from conventional and microwave healing in Coors
alumina (Microwave Healing of Alumina, Section 4.4.3).

Annealing Cycle 49 N Indent 98 N Indent
Temperature Heating Type Heating Rate 2C 2C 2C 2C

(°C) (°C/min.) Before After Before After

' 1237 Conventional 10 278.4 253.5 469.8

291.3 231.6 431.4
286.7 266.3 447.8

 

 

 

  
    

 

 

 

 

299 236.9 456
287.3 224.5 465.4 414.9
294.4 224.1 466 365.5

 

 

 

Microwave

 

 

 

 

 

Microwave

 

 

 

 

296.8 198.1 449.2 366.8

282.6 214.7 451.8 329.7
305.2 237.1 435.9 349.5

295.1 197.6 480.4 387.14"

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Table 3.13 (cont’d).

346

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Annealing Cycle 49 N Indent 98 N Indent
Temperature Heating Type Heating Rate 2C 2C 2C 2C
(°C) (°C/min.) Before After Before After
1295 Conventional 10 306.9 273.8 454.6 359.4
306.66 245.7 457 381.4
305.9 253.3 441.5 397.6
289.8 204.7 464 365.5 ||
297.6 241.3 466.6 397.4"
269.8 198.5 450.7 371.2
Microwave 10 291.3 189.8 394.1 270
308.5 231.7 430.8 315.7 ll
296.7 224.4 418.8 307.9
284.5 207.9 448.5 334
282.3 211.4 458.8 361.6
299.4 192.7 466.4 342.7 I
Microwave 75 301.1 204.1 476 370.2
297.5 213.9 450.4 354.7
290.8 219.3 488.2 414.2
273.1 209.8 469.4 312
296.6 245.8 447.2 348.9
291.1 247.4 409.4 362

Table B.13 (cont’d).

 

347

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Annealing Cycle 49 N Indent 98 N Indent
Temperature Heating Type Heating Rate 2C 2C 2C 2C
(°C) (°C/min.) Before After Before After
1353 Conventional 10 306.8 243.8 493.6 452.8 1'
293.8 240.7 498.2 414.6
291.2 235.3 490.7 441
276.4 238.4 479.8 442.1
284 219.1 489.4 420.7
287.3 242.7 465.5 385.2
Microwave 10 274.3 152.2 448.8 318.2 I
306.3 138.2 457.7 278.8
279.6 128.6 450.3 260.7
285.7 113.4 467.8 279.2
294.5 158.3 442.9 247.1
305.6 146.1 448.7 278.6
= _r
Microwave 75 268.7 177 486 330.2
278.7 170.3 463.6 296.5
299.8 231.7 454.9 326
273.8 172.9 458.5 271.3
292.3 225.7 457.7 325.4
_ 276.5 166.3 437.8 277.1

 

 

 

Table B.13 (cont’d).

348

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Annealing Cycle 49 N Indent 98 N Indent ]]
Temperature Heating Type Heating Rate 2C 2C 2C 2C
(°C) _ (°C/min.) Before After Before After
141 1 Conventional 10 284.4 190.2 420.1 322.2
279 224 484.5 350.5
256 208.7 453.3 354.2
291.6 216 442.7 326.9
283.4 236.3 434.5 348.5
_ 282.4 205.7 $ 483.2 334.9
Microwave L 10 28:1 75T 446.6 107'
265.2 75 431.1 107
285.6 75 448.5 107
264 75 445.9 107
281.4 75 437.5 107
263.1 75 460.6 107
Microwave 75 281.8 191.4 464.5 239.6 ll
284.4 157.6 462 263
272.6 130.4 482.9 250.9
304.5 135.5 468.1 263
296.5 173.8 469.7 233.8
293.8 123.5 461.2 249.1

 

 

 

 

Table B.13 (cont’d).

349

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Annealing Cycle 49 N Indent 98 N Indent
Temperature Heating Type Heating Rate 2C 2C 2C 2C
(°C) (°C/min.) Before After Before After
1469 Conventional 10 274.4 176.9 462.9 347.2 “
315.8 180.5 455.9 255.8
291.3 210.1 443.5 301.5
289.7 199.8 439.3 286.5
276.2 190.5 442.4 338.1
= I 294.7 190.5 445.4 279.74
Microwave 10 285.1 76.7 446.6 1 10.9
265.2 71.9 431.1 102.2
285.6 79.5 448.5 108.3
264 77.1 445.9 107.7
281.4 71.8 437.5 108.5
x 263.1 73.1 460.6 105.5 .
Microwave 75 265.2 127 469.8 180.6
264.6 66.2 445.8 128
282.8 87.4 443 211.3
268.1 81.7 428.1 189.7
265 218.2 448.5 155.1
279.8 102.6 437.6 169.9