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thesis entitled

The Characterization of Thermal Fatigue Effects

by the Observation of Growth of Indentation

Cracks in Unreinforced Polycrystalline A1203

presented by

Won-Sik Kim

has been accepted towards fulfillment
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THE CHARACTERIZATION OF THERMAL FATIGUE EFFECTS
BY THE OBSERVATION OF GROWTH OF INDENTATION
CRACKS IN UNREINFORCED POLYCRYSTALLINE Al203

By

Won-Sik Kim

A THESIS

Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of

MASTER OF SCIENCE

Department of Materials Science and Mechanics

August 1995

ABSTRACT
THE CHARACTERIZATION OF THERMAL FATIGUE EFFECTS BY THE
OBSERVATION OF GROWTH OF INDENTATION CRACKS IN
UNREINFORCED POLYCRYSTALLINE A1203
By

Won-Sik Kim

In this study, we characterized the thermal fatigue damage for unreinforced
polycrystalline alumina specimens by measuring the cyclic thermal shock induced growth
of Vickers indentation cracks placed in the specimens prior to thermal shock. The

severity of thermal shock damage increased with increasing quench temperature

difference.

A minor amount of crack growth occurred after the introduction of the Vickers
indentation cracks prior to commencing the thermal fatigue testing. The crack initially
grew an average of 4.3 percent but crack growth saturated within 30 minutes.

Grain bridging during thermal fatigue was investigated using a scanning electron
microscope (SEM). Although grain bridging is an often-cited mechanism for energy
dissipation for cracks growing in unreinforced alumina, grain bridging was infrequent in
the specimens included in this study. Thus grain bridging may not account for the

saturation in the thermal fatigue crack length observation in this study.

iii

Acknowledgment

I would like to thank my adviser, Dr. Eldon case for his advice and editing this thesis
throughout my study. I also thank my fellow researchers Brett Wilson, Kiyong Lee, and
Changlin Liu for their help during the my research.

I would also thank my parents for their support during my study. I would like express

my special thanks to my wife, Jeongioo Moon for her help and patience.

Table of Contents

Page
List of Tables viii
List of Figures xii
Section 1 Introduction 1
1.1. Thermal shock resistance parameter 2
1.1.1. Thermal shock resistance without crack initiation 2
1.1.2. Thermal shock resistance related to surface flaws 4
1.2. Comparing the strength degradation behavior as temperature
difference increases: Hasselman plot and statistical method 10
1.2.1. Strength degradation behavior: the Hasselman plot 10
1.2.2. Strength degradation behavior as temperature difference
increases: statistical method 14
1.3. Cyclic thermal shock effects A 18
Section 2 Experimental Procedure 27
2.1. Materials 27
2.2. Polishing 27
2.3. Indentation 30
2.4. The observation of slow crack growth after initial indentation but
before commencing thermal shock 32

2.5. The observation of slow crack growth behavior in room temperature
deionized water and in 80 0C deionized water in absence of thermal
shock 32

2.6. Thermal shock testing 33

2.7. Comparison of transverse and longitudinal crack length for a set of
Vickers cracks subjected to thermal fatigue

2.8. The observation of grain bridging in for specimens thermally
shocked during this study

Section 3 Results and Discussions

3.1. Slow crack growth after initial indentation but before commencing
thermal shock

3.2. Crack growth behavior in room temperature and 80 °C deionized
water in the absence of thermal shock

3.3. Thermal fatigue behavior for unreinforced alumina
3.3.1. Thermal shock testing for a total number of ten thermal cycles
3.3.2. Thermal shock testing for a total number of twenty thermal cycles

3.3.3. The comparison of rate constant with Lee’s data [12] and Ash’s
data [32]

3.3.4. The severity of thermal fatigue damage as a function of
the quench temperature difference

3.3.5. Comparison of crack lengths for a given Vickers crack subject to
thermal fatigue

3.4. Grain bridging in the brittle materials

3.4.1. An overview of grain bridging

3.4.2. Grain bridging model

3.4.3.1. The effect and observation of grain bridging by
Lathabai et a1. [34]

3.4.3.2. The effect and observation of grain bridging by Hay e! a]. [35]
3.4.3.3. The effect and observation of grain bridging by Kagawa [33]

3.4.3.4. The effect and observation of grain bridging by
Swanson et a1. [36]

39

41

42

42

51

54

54

69

78

81

83

85

85

86

86

89

93

96

vi

3.4.3.5. The effect and observation of grain bridging by
Kishimoto et a1. [37]

3.4.3.6. The effect and observation of grain bridging by
Dauskardt [38,39]

3.4.3.7. The effect and observation of grain bridging by
Vekinnis et al. [44]

3.4.3.8. The effect and observation of grain bridging by
Braun et a1. [45]

3.4.3.9. The effect and observation of grain bridging by
Steinbrech et al. [43]

3.4.3.10. The effect and observation of grain bridging by
Rodel et al. [46]

3.4.3.11. The effect and observation of grain bridging by
Reichl et al. [47]

3.4.5. Crack propagation behavior and grain bridging of the
unreinforced polycrystalline alumina included in this study

3.4.6. Grain bridging related to thermal shock for unreinforced
alumina

Section 4 Summary and Conclusions

4.1. Slow crack growth after initial indentation before commencing
thermal shock

4.2. Crack growth behavior in room temperature and 80 °C water in
the absence of thermal shock

4.3. Thermal fatigue behavior unreinforced polycrystalline alumina
4.4. Grain bridging in the brittle materials

Section 5 Appendices
Appendix A. The dimension and label of all specimens

Appendix B. The result of slow crack growth testing after initial
indentation but before commencing thermal shock

97

100

102

104

105

108

109

113

119

125

125

125

125

127

128

128

129

vii

Appendix C. Crack length versus time for Vickers indented specimens
immersed in the room temperature deionized water and
in 80 0C deionized water 133
Appendix D. The thermal shock data 135

Section 6 References 149

viii

List of Tables

page

Table 2.2.1. Heating history for demounting polycrystalline alumina
specimen from aluminum plate and alumina plate. 30

Table 3.1.1. Slow crack growth (in air) after initial indentation for unreinforced
polycrystalline alumina specimens. 43

Table 3.3.1. The results of the least-squares fitting to equation 3.3.1 for the data
of a total of 10 thermal cycles. (where co = initial crack length,
c; = final crack length, N = data points). 67

Table 3.3.2. The least-squares fitting of equation 3.3.1 for 20 quench
specimens (where an = initial crack length, a; = final crack
length, N = data points). 76

Table 3.3.3. The comparison of rate constants for data of Young’s modulus
(Lee’s Work [12]) and data of crack length (this study and Ash’s
work [32]) for unreinforced alumina specimen. 78

Table 3.3.4. The results of linear regression of normalized saturation crack
length for unreinforced polycrystalline alumina specimen using
PLOT-IT program. 81

Table 3.4.1. Lifetime under cyclic loading of alumina for 1 Hz and 100 Hz.
A Vickers indentation crack was inserted with 30 N load [34]. 88

Table 3.4.2. Scanning electron microscope in situ observation of crack for
alumina specimen under cyclic load [34]. 89

Table 3.4.3. The stress behavior versus displacement of polycrystalline
alumina specimen by postfracture test [35]. 91

Table 3.4.4. The effect of grain size and Young’s modulus on crack closure
stress for ceramic materials using an FEM program [33]. 96

Table 3.4.5. The energy release rate behavior for alumina specimens with
different grain size using double torsion testing [44]. 103

Table 3.4.6. The strength behavior for cracks produced by different
indentation loads to observe flaw resistance for Al203-Al2Ti05
composite [45]. 105

Table 3.4.7. The enery release rate as a function of normalized
crack length (crack length/width of specimen) in SENB alumina
specimen which had 16 pm average grain size where the width of
specimen was 7 mm [43]. 108

Table A The dimensions and labels for all polycrystalline alumina specimens
as measured by vemier caliper. 128

Table B-1. The crack lengths and elapsed time to examine the slow crack
growth after introducing Vickers indentation crack for aulmina
specimen (specimen A1-11). 129

Table B-2. The crack lengths and elapsed time to examine the slow crack
growth after introducing Vickers indentation crack for alumina
specimen (specimen A1-13). 130

Table B-3. The crack lengths and elapsed time to examine the slow crack
growth after introducing Vickers indentation crack for alumina
specimen (specimen A1-14). 130

Table B4. The crack lengths and elapsed time to examine the slow crack
growth after introducing Vickers indentation crack for alumina
specimen (specimen A2-8e), where “e” means the edge of
specimen. 131

Table B—5. The crack lengths and elapsed time to examine the slow crack
growth after introducing Vickers indentation crack for alumina
specimen (specimen A2-8m), where “m” means the middle of
specimen. 131

Table B-6. The crack lengths and elapsed time to examine the slow crack
growth after introducing Vickers indentation crack for alumina
specimen (specimen A2-9e), where “e” means the edge of
specimen. 132

Table B-7. The crack lengths and elapsed time to examine the slow crack
growth after introducing Vickers indentation crack for alumina
specimen (specimen A2-9m), where “m” means the middle of
specimen. 132

Table C-l. Crack length versus time for Vickers indentation immersed
in room temperature deionized water (specimen B1-3).

Table C-2. Crack length versus elapsed time for alumina specimen
in hot water (~ 80 °C). The specimen held in 80 °C for 2 hours at
each times (see section 2.5, specimen Bl-4).

Table D-l. Crack length after cyclic thermal shock test which
maximum cycling number is 10 (specimen A4-13 AT = 250 °C).

Table D-2. Crack length after cyclic thermal shock test which
maximum cycling number is 10 (specimen A4—14 AT = 270 °C).

Table D-3. Crack length after cyclic thermal shock test which
maximum cycling number is 10 (specimen A4-15 AT = 290 °C).

Table D-4. Crack length after cyclic thermal shock test which
maximum cycling number is 10 (specimen A6—2 AT = 295 °C).

Table D-5. Crack length after cyclic thermal shock test which
maximum cycling number is 10 (specimen A5-3 AT = 300 0C).

Table 0-6. Crack length after cyclic thermal shock test which
maximum cycling number is 10 (specimen A5-12 AT = 305 °C).

Table 0-7. Crack length after cyclic thermal shock test which
maximum cycling number is 10 (specimen A5-4 AT = 310 0C).

Table D-8. Crack length after cyclic thermal shock test which
maximum cycling number is 10 (specimen A5-11 AT = 315 0C).

Table D-9. Crack length after cyclic thermal shock test which
maximum cycling number is 10 (specimen A5-5 AT = 320 °C).

Table D-10. Crack length after cyclic thermal shock test which
maximum cycling number is 10 (specimen A5-8 AT = 325 °C).

Table 0-1 1. Crack length after cyclic thermal shock test which
maximum cycling number is 3 (specimen A5-7 AT = 330 °C).

Table 0-12. Crack length after cyclic thermal shock test which
maximum cycling number is 20 (specimen A6-3 AT = 250 °C).

Table D-13. Crack length after cyclic thermal shock test which
maximum cycling number is 20 (specimen A6-4 AT = 270 °C).

133

134

135

135

136

136

137

137

138

138

139

139

140

141

142

xi

Table D-14. Crack length after cyclic thermal shock test which
maximum cycling number is 20 (specimen B1-5 AT = 290 °C).

Table 0-15. Crack length after cyclic thermal shock test which

maximum cycling number is 20 (specimen A5-10 AT = 295 0C).

Table 0-16. Crack length after cyclic thermal shock test which

maximum cycling number is 20 (specimen A5-14 AT = 300 °C).

Table D-17. Crack length after cych thermal shock test which
maximum cycling number is 20 (specimen A6-1 AT = 305 °C).

Table D-18. The crack length of bar-shape specimen under the thermal
shock, L1.

Table 0-19. The crack length of bar-shape specimen under the thermal
shock, L2.

Table 0-20. The crack length of bar-shape specimen under the thermal
shock, L3.

143

144

145

146

147

147

148

xii

List of Figures
Figure number page

Figure 1.1.1. Temperature and stress distribution for a plate cooled from the
surface when specimen is heated and quenched [17,18]. 3

Figure 1.2.1. The Hassleman plot which is a schematic of temperature difference
behavior for a ceramic materials [7,21]. 11

Figure 1.2.2. A plot of the mean retained strength versus quench temperature
difference for aluminosilicate after thermal shock [8]. 13

Figure 1.2.3. The average retained strength after thermal shock for cylindrical
polycrystalline 86 % alumina specimen. The quenching medium is
room temperature water [22]. 16

Figure 1.2.4. The average retained strength after thermal shock for borosilicate
glass specimens. The quenching medium is liquid nitrogen [23]. 17

Figure 1.3.1. The crack number density (number of cracks/inch) as a function of
cumulative thermal cycles for graphite epoxy specimens [10,25].
The solid line was obtained by least-squares fit to equation
1.3.1 [10] 19

Figure 1.3.2. Thermal shock damage in terms of modulus of rupture versus the
cumulative number of thermal fatigue cycles for MgO, Al203, and
MgO-Cr203 refractories [10,27]. The solid line was obtained by
least-squares fit to equation 1.3.1 [10]. 21

Figure 1.3.3. The Young’s modulus versus cumulative thermal shock cycles
observed for 60 % alumina refractory [10,28]. The solid line
was obtained by least-squares fit to equation 1.3.1 [10]. 22

Figure 1.3.4. Young modulus versus the cumulative number of thermal fatigue
cycles for unreinforced polycrystalline alumina quenched in a
room temperature deionized water bath. The solid curves represents
least-squares fit of the data to equation 1.3.1 [12]. 25

Figure 1.3.5. Schematic diagram of damage saturation behavior subject to
thermal fatigue damage for ceramic materials [10-11, 29-30]. 26

Figure 2.2.1. a. Position of specimens on the aluminum plate for polishing.
specimens were superglued onto the plate. 28

xiii

Figure 2.2.1. b Alumina plate used to place specimens on when burning off
superglue residue.

Figure 2.2.2. The heating history to demount alumina specimens from alumina

plate by burning super glue using an electrical resistance furnace.

Figure 2.3.1. The position of indentations on the polycrystalline alumina
specimen’s surface for observation of indentation crack growth
behavior.

Figure 2.6.1. Schematic of the electrical resistance heated furnace used in
the thermal fatigue experiments. The average heating rate was
about 2 °C/min.

Figure 2.6.2. Schematic diagram of thermal shock testing specimen holder
which has three parts of steel wire, tongs, and wire screen.

Figure 2.6.3.a. The photograph of (a) entire specimen holder which has three
parts: steel wire, tongs, and wire net for thermal shock testing

Figure 2.6.3. b. The photograph of (b) body of steel wire which was twisted
3 times.

Figure 2.7.1. The dimension of bar-shaped polycrystalline alumina specimen
and the position of indentation cracks. This part of the study
investigated possible asymmetry in the group in the x and y
directions during thermal fatigue.

Figure 3.1.1. Indentation crack length as a function of elapsed time following
indention for unreinforced polycrystalline alumina specimen
(specimen Al-l 1).

Figure 3.1.2. Indentation crack length as a function of elapsed time following
indention for unreinforced polycrystalline alumina specimen
(specimen A1-13).

Figure 3.1.3. Indentation crack length as a function of elapsed time following
indention for unreinforced polycrystalline alumina specimen
(specimen A1-14).

Figure 3.1.4. Indentation crack length as a function of elapsed time following
indentation for unreinforced polycrystalline alumina specimen
(specimen A2—8e where “e” means the indentation was placed
near the edge of the specimen).

28

29

31

34

36

37

37

45

47

xiv

Figure 3.1.5. Indentation crack length as a function of elapsed time following
indentation for unreinforced polycrystalline alumina specimen
(specimen A2-8m where “m” means the indentation was placed
near the middle of the specimen).

Figure 3.1.6. Indentation crack length as a function of elapsed time following
indentation for unreinforced polycrystalline alumina specimen
(specimen A2-9e where “e” means the indentation was placed

near the edge of the specimen).

Figure 3.1.7. Indentation crack length as a function of elapsed time following
indentation for unreinforced polycrystalline alumina specimen
(specimen A2-9m where “m” means the indentation was placed
near the middle of the specimen).

Figure 3.2.1. Crack growth behavior versus elapsed time in room temperature
deionized water for unreinforced alumina specimen
(specimen B1-3).

Figure 3.2.2. The crack growth behavior in deionized water at 80 °C held for 2
hours (specimen B1-4). Crack length measurements were
made after the specimen had been at 80 °C (see section 2.5)

Figure 3.3.1. The crack growth behavior versus the cumulative number of
shock cycles for a total of 10 thermal shock cycles,
AT = 250 "C (specimen A4-13). The solid line represents the
least-squares fit to equation 3.3.1.

Figure 3.3.2. The crack growth behavior versus the cumulative number of
thermal shock cycles for a total of 10 thermal shock cycles,
AT = 270 “C (specimen A4-14). The solid line represents the
least-squares fit to equation 3.3.1.

Figure 3.3.3. The crack growth behavior versus the cumulative number of
thermal shock cycles for a total of 10 thermal shock cycles,
AT = 290 °C (specimen A4-15). The solid line represents the
least-squares fit to equation 3.3.1.

Figure 3.3.4. The crack growth behavior versus the cumulative number of
thermal shock cycles for a total of 10 thermal shock cycles,
AT = 295 °C (specimen A6-2). The solid line represents the
least-squares fit to equation 3.3.1.

49

50

52

53

57

58

59

XV

Figure 3.3.5. The crack growth behavior versus the cumulative number of
thermal shock cycles for a total of 10 thermal shock cycles,
AT = 300 °C (specimen A5-3). The solid line represents the
least-squares fit to equation 3.3.1.

Figure 3.3.6. The crack growth behavior versus the cumulative number of
thermal shock cycles for a total of 10 thermal shock cycles,
AT = 305 0C (specimen A5-12). The solid line represents the
least-squares fit to equation 3.3.1.

Figure 3.3.7. The crack growth behavior versus the cumulative number of
thermal shock cycles for a total of 10 thermal shock cycles,
AT = 310 °C (specimen A54). The solid line represents the
least-squares fit to equation 3.3.1.

Figure 3.3.8. The crack growth behavior versus the cumulative number of
thermal shock cycles for a total of 10 thermal shock cycles,
AT = 315 °C (specimen A5-11). The solid line represents the
least-squares fit to equation 3.3.1.

Figure 3.3.9. The crack growth behavior versus the cumulative number of
thermal shock cycles for a total of 10 thermal shock cycles,
AT = 320 °C (specimen A5-5). The solid line represents the
least-squares fit to equation 3.3.1.

Figure 3.3.10. The crack growth behavior versus the cumulative number of
thermal shock cycles for a total of 10 thermal shock cycles,
AT = 325 0C (specimen A5-8). The solid line represents the
least-squares fit to equation 3.3.1.

Figure 3.3.11 The crack growth behavior versus the cumulative number of
thermal shock cycles for a total of 3 thermal shock cycles,
AT = 330 °C (specimen A5-7). The solid line represents the
least-squares fit to equation 3.3.1.

Figure 3.3.12. a. The results of crack propagation behavior due to the
temperature difference range of 250 - 300 °C for a total of
10 thermal shock cycles. The solid line represents the least-
squares fit to equation 3.3.1.

Figure 3.3.12.b. The results of crack propagation behavior due to the
temperature difference range of 305-330 °C for a total of
10 thermal shock cycles. The solid line represents the least-
squares fit to equation 3.3.1.

60

61

62

63

65

68

68

xvi

Figure 3.3.13. The crack propagation behavior versus the cumulative
number for a total of thermal shock cycles, AT = 250 °C
(specimen A6-3). The solid line represents the least-
squares fit to equation 3.3.1.

Figure 3.3.14. The crack propagation behavior versus the cumulative
number for a total of thermal shock cycles, AT = 270 °C
(specimen A64). The solid line represents the least-
squares fit to equation 3.3.1.

Figure 3.3.15. The crack propagation behavior versus the cumulative
number for a total of thermal shock cycles, AT = 290 °C
(specimen Bl-S). The solid line represents the least-
squares fit to equation 3.3.1.

Figure 3.3.16. The crack propagation behavior versus the cumulative
number for a total of thermal shock cycles, AT = 295 °C
(specimen A5-10). The solid line represents the least-
squares fit to equation 3.3.1.

Figure 3.3.17.a. The crack propagation behavior versus the cumulative
number for a total of thermal shock cycles, AT = 300 0C
(specimen A5-10). The solid line represents the least-
squares fit to equation 3.3.1.

Figure 3.3.17.b. The crack propagation behavior versus the cumulative
number for a total of thermal shock cycles, AT = 300 °C
(specimen A5-10) without abrupt in crack length at 10th
thermal quenching. The solid line represents the least-
squares fit to equation 3.3.1.

Figure 3.3.18. The crack propagation behavior versus the cumulative
number for a total of thermal shock cycles, AT = 305 °C
(specimen A6-1) without abrupt increase in crack length
at 11 thermal quenching. The solid line represents the least-
squares fit to equation 3.3.1.

Figure 3.3.19. The crack propagation behavior versus the cumulative
number for a total of thermal shock cycles with quench
temperature difference range of 250 °C to 305 °C. The solid
line represents a least-squares fit to equation 3.3.1.

70

71

72

73

74

74

75

77

xvii

Figure 3.3.20. Comparison of rate constants as a function of quench
temperature difference for three thermal fatigue studies: this
study and Ash’s work [32] and Young’s modulus data (Lee’s
work [12]). Each of these three studies involved the thermal
fatigue of unreinforced polycrystalline alumina into room
temperature deionized water. The solid line was obtained
from linear regression of data for this study, dotted line
represents linear regression for Lee’s data and double dotted
line is a linear regression of Ash’s data using PLOT IT program. 79

Figure 3.4.21 Rate constants (3b) behavior for 20 quenches as AT increases for
unreinforced alumina specimen. The quenching medium is
deionized water. 80

Figure 3.3.22 Normalized saturation crack length behavior versus quench
temperature difference for polycrystalline alumina specimens
The solid line (10 quenches), dotted line (20 quenches), and double
dotted line (5 quenches [32]) represent a linear regression of the
data using PLOT IT program. 82

Figure 3.3.23. The crack propagation behavior of bar-shaped specimen of
alumina under cyclic thermal shock testing. L1, L2, and L3
represent the position of indentation crack (see section 2.7). 84

Figure 3.4.1. a. Schematic diagram of a possible evolution of bridging crack
(a) deflection for a SiC platelet composite specimen [41]. 87

Figure 3.4.1. b. Schematic diagram of a possible evolution of bridging
(b) crack bridging for a SiC platelet composite specimen
[411- 87

Figure 3.4.2. Schematic diagram of modified four point bend test specimen
of polycrystalline alumina for postfracture tensile test [35]. 90

Figure 3.4.3. The crack closure stress behavior with increasing normalized
distance where normalized distance is the ratio of the crack
separation to half of grain size. The closure stress versus
normalized distance curve shown here was generated by an
FEM program [33]. The definition of the crack deflection angle
w is shown the above. 94

Figure 3.4.4. The change of bridging area for alumina specimen with
increasing crack length as calculated by a finite element
method by Kishimoto et a1. [37]. 99

xviii

Figure 3.4.5. Experimental technique for observing crack length and stress
intensity factor where K..." = maximum stress intensity factor,
K. = crack closure stress intensity factor, and Kn“. = minimum
intensity factor [48]. The specimens were alumina with grain
sizes of 8 and 13 pm [38,39]. 101

Figure 3.4.6. Hysteresis curve of applied load and crack opening displacement
as suggested by Dauskardt [38,39]. 102

Figure 3.4.7. Energy release rate as crack extension increases for alumina
s-DCB alumina specimen [43]. Crack growth was quasi-static
from initial notch to fracture. 106

Figure 3.4.8. Load-displacement behavior and the modified double cantilever
specimen used by Reichl to study grain bridging in alumina
specimen [47]. 111

Figure 3.4.9. The assumption of geometry near the crack tip to calculate the
average bridging stress by Reichl et a1. [47]. 112

Figure 3.4.10. a. The position of SEM observation for unreinforced polycrystalline
alumina specimen after ten thermal quenching (a) AT = 320 0C
behind the crack tip. 115

Figure 3.4.10. b. The position of SEM observation for unreinforced polycrystalline
alumina specimen after ten thermal quenching tip (b) AT = 320 “C
at the middle of the radial crack. 115

Figure 3.4.10. c. The position of SEM observation for unreinforced polycrystalline
alumina specimen after ten thermal quenching (c) AT = 270 °C
around the crack tip. 115

Figure 3.4.10. d. The position of SEM observation for unreinforced polycrystalline
alumina specimen after ten thermal quenching (d) AT = 300 °C
behind the crack tip. 1 15

Figure 3.4.11. a. Crack propagation shape for polycrystalline alumina
specimen after 10 quenched thermal shock at (a) AT =270 116

Figure 3.4.11. b. Crack propagation shape for polycrystalline alumina
specimen after 10 quenched thermal shock at (b) AT = 320. 116

xix

Figure 3.4.12. a. The crack path for polycrystalline alumina specimen
after 10 quenched thermal shock at AT = 320 °C
(a) behind the crack tip. 117

Figure 3.4.12. b. The crack path for polycrystalline alumina specimen after 10
quenched thermal shock at AT = 320 “C (b) at the middle of
the radial crack. 117

Figure 3.4.13. a. The bridging site for polycrystalline alumina specimens
after 10 quenched thermal shock. (a) AT = 270 °C around
the crack tip. 1 18

Figure 3.4.13. b. The bridging site for polycrystalline alumina specimens
after 10 quenched thermal shock. (b) AT = 300 °C
behind the crack tip. 118

Figure 3.4.14. The schematic diagram of the comparison of stress-time
behavior for the mechanical loading and thermal loading [30] 121

Figure 3.4.15. The profile of stress distribution for thermal loading and

bend test. The slope (do/dy) is much stiffer in thermal loading
than in bend test. 123

1. Introduction

When brittle materials are heated or cooled rapidly, they are subjected to thermal
shock which can lead to microcracking or catastrophic failure [1-6]. In addition, many
engineering applications should be considered thermal shock effect if they are under the
condition that the ambient temperature differences are large. Thermal shock tests as be
classified as either single quench thermal shock tests [7-9] or cyclic thermal shock tests
[1 0-1 3]. The single quench thermal shock tests involve heating the specimen and
quenching the specimen into water [5,6], oil [14], or air [3,15]. The retained strength is

measured typically by a 3 or 4 point bend test. The other is cyclic thermal shock test.

Single quench tests are unsatisfactory for applications such as ceramic turbine,
computer main frame memory [16], or solar system collector where the materials are

periodically heated and cooled.

Thermal shock damages can be monitored in variety of methods. Retained strength
measurements are often used [6-7], but the retained strengths fluctuate depending on the
geometry of specimen. Non—destructive measurements, such as elastic modulus and
internal friction, can be used to monitor the evolution of thermal shock damage in a given

specimen [IO-l 3].

In this study, Vickers indentation cracks were induced in unreinforced polycrystalline
alumina specimens. The crack length was measured during thermal fatigue (cyclic

thermal shock).

1.1. Thermal shock resistance parameter

Thermal shock resistance parameters indicate properties critical to thermal shock
damage. These parameters are approximately quantitative measurements of thermal shock

resistance.

1.1.1. Thermal shock resistance without crack initiation

When ceramic materials are heated or cooled rapidly, a temperature gradient appears
through the specimen thickness (Figure 1.1.1)

In general, the thermal stress, on. caused by the difference of the ambient temperature

is given as follows for an infinite slab [17,18].

0'”, = ill—AT (1.1.1)
l—v
where on. = thermal stress

v = Poisson’s ratio
a = thermal expansion coefficient
AT = temperature difference between furnace and water bath.

When fracture occurs, AT = ATm-t and am = can such that [17,18]

0' . (1 — v)
AT = C"!
en! Ea

(1.1.2)
where ATcm = critical temperature difference
6cm = fracture strength.

From Equation 1.1.1, thermal shock resistance parameter, R, is defined as [17,18]

Compression Tension

<——>

m1“

high T

 

\

Surface of slab, low T

Figure 1.1.1. Temperature and stress distribution for a plate cooled from the surface
when specimen is heated and quenched [18,19].

am, (1 — v) kam, (1 — V)
—— r R' - ———-—

R = _
Ea 0 Ea

(1.1.3)

where k = thermal conductivity.
High R and R’ values favor avoidance of crack initiation. Therefore, for high R and
R’ values, the strength and thermal conductivity of materials should be high while

thermal expansion coefficient, Poisson’s ratio and Young’s modulus should be low.

1.1.2. Thermal shock resistance related to surface flaws

Compressibility, B, is the fractional volume change per unit of pressure and is defined

as
31—2v
= —(—E——2 . (1.2.1)
where v = Poisson’s ratio
E = Young’s modulus
The volume changes can be expressed in terms of compressibility [19]
d(V0 — VP) = flVodp (1.2.2)
where V0 = volume of body
Vp = volume of porosity
p = external pressure.
Equation 1.2.2 can be rearranged to yield
= w (1.2.3)

V0 dp

and

1 dV, 1 dV,

Vodp— +Edp.

 

(1 .2.4)

If the lefi side of equation 1.2.4 is the actual compressibility, [3, for a porous elastic
material, then equation 1.2.4 is

pd VP

flu = fi+ °
VoPdP

(1.2.5)

Walsh gave the strain energy for N small penny shaped cracks with half length, c [19] as

dW= 'BZW pdp . (1.2.6)

 

pde = dw= ,6 9(I_ 2V) pdp (1.2.7)

where N = number of crack.
If equation 1.2.1 and 1.2.7 are inserted into equation 1.2.5, we can obtain equation 1.2.8
since pde is work related to crack formation which is identical to an increase in the

strain energy [19].

 

 

1+16(1—v2)Nc3}= 3(1- 2v){1+16(1— v2)Nc3

fl“ =m 9(1—2v)V0 E0 9(1—2v)V0

} (1.2.8).

where E0 is Young’s modulus of the crack-free material and B, is as defined for equation

1
1.2.4. The total energy per unit volume is the sum of elastic energy? E (aAT)2 , and the

fracture energy of the cracks, 2N1tc2I‘ (the factor of 2 indicates two fracture surface)

where I“ is defined surface energy if the crack shapes are circular [l9]

3(aAT)2 E, [1+ 16(1— v2)Nc3

]" +27ch’r (1.2.9)
2(1- 2v) 90— 2V)

 

W, = %E(aAT)2 +27rNc21“ =
. . M
where F rs fracture surface energy and N 18 the number of cracks. If we set I = 0, then

using equation 1.2.9 we can obtain

_ 3(aAT) E, [1 + 16(1— v2)Nc3]_2[16(1-—v2)Nc2

20- 2V) 90- 2V) 3(1 - 2v)

 

 

]+47rNcF=0

3(aAT)2E, 16(1-v2)Nc3 _, 16(1—v2)Nc2

2(1—2v) [1+ 9(1—2v) H 3(1—2v)

 

 

]=47rNcF. (1.2.10)

Rearranging equation 1.2.10 gives

 

2(1—2v)[1+16(1—v2)Nc3]2[16(1— 112)ch

(“An = ”NJ 3E, 9(1 - 2v) 3(1— 2v)

1". (1.2.11)

 

Equation 1.2.11 can be expressed by AT as following

nr1—2 2 111- 2N3 _1
2E,c(zz(1_Vi/)2]2[l+ «901/2106 10 2' (1'2'12)

 

AT=[

 

d W
Equation 1.2.12 suggests a critical temperature when -d—c' = 0, thus critical temperature

above which crack instability occurs is [7]

7:1"(1—2v)2 ‘ 16(1—v2)Nc3 -1

ATC=[2EOa2(1__V)2]2[1+ 9(1_2V) ]c2. (l.2.l3.a)

 

 

The excess energy from the difference between the elastic energy release and surface
the fracture energy is transferred into kinetic energy of crack growth such that the
released energy equals to the surface fracture then the crack propagation terminated when
energy is balanced;

release of elastic energy = increase in surface fiacture energy

thus

initial elastic energy - final elastic energy = final surface energy - initial surface
energy.
From equation 1.2.9, we can obtain the following equation 1.2. 14 [7] for final (critical)

crack length

3mm2 E, 16(1— v2)Nc,3

2(1- v) “1+ 9(1—2v)

16(1- v’)Nc,3
9(1—2v)

 

 

)" —{1+ }"']=27£NI‘(cf2 —c,’) (1.2.14)

where co = initial crack length
Cf: final crack length or critical crack length.

If the initial crack length(co) is much smaller than final crack length(cf), then the terms

16(1—v2)Nc,3 d1 160—1?)ch3
9(1—2v) a" H 9(1-2v)

3

 

 

}"(since Cf is very large) in equation 1.2.14 are

very small, thus equation 1.2.14 can be simplified such that

3(aA7)’ E,

= 2. .2.1
2(1-v) 27er c, (1 5)

16(1— v’)Nc3
9(1- 2 v)

 

If crack length is short in equation 1.2.13, second term of [ 1+ ] can be

ignored, then AT becomes

7rl"(1—2v)2
2E,a2(1- v2)

 

T =[ 15m? (1.2.13.b)

If AT from equation 1.2.13.b is inserted into equation 1.2.15, the critical crack length Cf

becomes [7]

3(1—2v)2
87r(1— v’)c,N

 

c, ={ )5. (1.2.16)

Equation 1.2.16 suggests that the critical crack length is a function of initial crack
length and a weak function of Poisson’s ratio. Other material properties rarely affect
critical crack length. Sack [20] assumed that circular cracks were introduced into a crack-
free material and calculated the change of free energy. When a uniform stress is applied
normal to a brittle material containing circular cracks and if the cracks are much smaller
than the whole body of brittle materials, Sack [20] gave elastic energy of the brittle body

as

G =_§fl:filazcs.

. 3E (1.2.17)

In addition, the crack surface energy is 21tc2F thus the total energy change induced by the

crack is given as

81— 2
— -—-—-—-( V )02c3.

= 2
G 27wF 3E

(1.2.18)

From equation 1.2.18, 3 critical (maximum) crack length can be obtained when dG/dc = O

81-2
_( Vlazz

47ml" E c =0. (1.2.19)

Equation 1.2.19 can be expressed in terms of crack length, c

 

 

IIEF
= . 1.2.20.
0 202 (1 - v2) ( a)
If 0 = of, where Cf is fracture stress, then equation 1.2.20 becomes
IrEF
= . 1.2.20.b
c 20,2 (1 — v2) ( )
Equation 1.2.20 can be expressed in terms of fracture stress,
1
0', ={ FE }2. (1.2.21.a)

2c(1— V2)

If we apply equation 1.2.21 to the initial flaw population, then E = E0 and c = co, of [7,20]
is given by

FE,
0/ = {—3—
2c,(1—v )

NI—

} . (1.2.21.b)

When equation 1.2.16 is divided by equation 1.2.21.b, the initial crack length, co can
be removed, then the relationship between critical crack length and fracture strength is [7]

3(1— 100,2}; (1 2 22)
c = -—-—-—- . . .
f 47tNF E,
If the cracks are circular as was assumed by equation 1.2.22, then the crack growth
resistance, R’”’ is expressed as equation 1.2.21 [7,16] since crack length is proportional to

0,2(1— v)

th ' f
e 1nverse o F E

FE

R”” = --———-.
012(1— v)

(1.2.21)

To avoid catastrophic crack propagation, R”” should be large. Thus the surface energy

and the Young’s modulus should be high and the fracture strength should be low.

10

1.2 Comparing the strength degradation behavior as temperature difference
increases: Hassleman plot and statistical method

1.2.1. Strength degradation behavior: the Hasselman plot

Many researchers have evaluated thermal shock damage in terms of retained strength
as a function of quenching temperature difference. The typical retained strength analysis
is represented by the Hasselman plot which is a schematic diagram of retained strength
and temperature difference that shows there are 3 temperature regions (Figure 1.2.1).

At low quenching temperature differences, there is no change in retained strength. No
crack propagation occurs since the thermal stress is not high enough for cracks to grow.
To initiate cracks a specific quenching temperature difference is required. The second
region is related to the initiation of crack propagation. If cracks propagate, there are two
kinds of behavior : (a) a catastrophic decrease in retained strength and (b) a steady
decrease of retained strength. Hassleman explained the catastrophic decrease in retained
strength in terms of kinetic crack propagation [7]. The steady decrease of retained
strength is caused by quasi-static propagation [7]. The catastrophic decrease of retained
strength tends to occur in high strength ceramic materials which have the high elastic
strain energy and the low resistance to crack growth.

Gupta [21] investigated strength degradation through thermal quenching. Water was
used as a quenching medium. Gupta [21] observed kinetic crack propagation behavior
for both single crystal alumina and polycrystalline alumina specimens with mean grain

size of 10, 34, and 40 um while a gradual decrease in strength also was observed for the

11

 

No thermal shock damage

 

 

 

 

 

 

Strength 1
\
\ \ gradual decrease
‘ e in strength
I constant
I strength
I
l
AT,

Temperature difference

Figure 1.2.1. The Hassleman plot which is a schematic of temperature difference
behavior for a ceramic materials [7,21].

12

larger grain sized (84 um) alumina specimen. In catastrophic decrease of strength (for 10,
34, and 40 um grain sized specimens), the critical temperature differences (ATc) were
about 190 °C. No change in strength was observed at the interval from AT = 190 °C to
AT = 280 °C, then a gradual decrease in strength was followed. Hasselman found that the
strength decreased gradually as the quench temperature differences increased (without a
sudden drop of strength) for low strength materials such as insulating firebrick [7].

The third region corresponds to quasi-static crack propagation. The retained strength
decreases monotonically as temperature difference increases. Bradt et al. [9] contended
that an increase of strength following quenching or thermal tempering follows the second
region. Bradt et al. observed an increase of strength following an interval of quench
temperature difference in which strength is constant. For example, a commercial
aluminosilicate quenched into silicone oil [8] showed an interval of constant strength
followed by a drop of in strength (Figure 1.2.2). However, for quench temperature
differences between 1100 °C and 1400 °C, the residual strength of the aluminosilicate

increased (Figure 1.2.2).

200

l l r l l 1

as

Q

2 150-

5’

or

5

g; 10

m 0?

'c

a)

.E

3 50F

(11

c:

0 r l r 1 r J r l r 1 l r
0 200 400 600 800 1000 1200

13

 

 

 

 

 

 

 

1400

Quench temperature difference, degree C

Figure 1.2.2. A plot of the mean retained strength versus quench temperature
difference for aluminosilicate after thermal shock [8].

14

1.2.2. Strength degradation behavior as temperature difference increases :
statistical method

The statistical approach to thermal shock damage investigates the retained strength of
an entire population of thermally shocked specimens. As an example, Bradt et al. studied
a set of 50 alumina specimens [22], a set of 25 aluminosilicate specimens [8] and a set of
50 borosilicates glass specimens [22,23]. All specimen strengths before and after thermal
shock were measured and the strength distribution was investigated.

Ashizuka et al. [23] measured the strength of borosilicate glass after a thermal shock
into room temperature water or into 77 K liquid nitrogen. The strengths ranged from 3 to
115 MPa at a temperature difference of 500 °C, 10 to 112 MPa at a temperature
difference of 400 °C, and 15 to 110 MPa at a temperature difference of 300 °C in the
water bath while the average strength before thermal shock was about 115 MPa. Strength
distribution indicated that initially low strength specimens tend to fracture at low stresses.
A rapid decrease in strength after thermal shock did not occur at a specific quench
temperature difference. In addition, high strength specimens were not damaged while
low strength specimen were severely affected by thermal shock. The average strengths
are indicative of a quasi-static crack propagation or steady decrease in retained strength
rather than a kinetic crack propagation which can result in a rapid dramatic decrease in
retained strength (Figure 1.2.3-4).

Brat et al. [9] suggest that a specific quench temperature difference may occur for
small specimens size. The specimens’ strength distribution indicated that a specific
thermal stress initiated thermal shock damage for each specimen. Bradt et al. [9,23]

explained there are two types of flaws after thermal shocking for each specimen. One

15

flaw type is the pre-existent flaw population which existed prior to thermal shock. The
other flaw type is induced by the thermal quenching. Thermal shock damage changes the

flaw population and the crack arrest behavior occurs.

16

 

 

200*-

1001-

 

Average strength, MPa

 

 

o r I 1 l 4
0 1 00 200 300

Quench temperature difference, degree C

 

Figure 1.2.3. The average retained strength after thermal shock for cylindrical

polycrystalline 86% alumina specimen. The quenching medium is room
temperature water [22].

17

200 . l 1 I

 

 

‘ ”F

 

 

 

<0
0.
2
£2”
0')
c
g 100 - A
a)
(D
or
‘8
<1)
>
<1:
0 r 4 1 1 r l r 1 1
0 100 200 300 400 500

Quenching temperature difference, degree C

Figure 1.2.4. The average retained strength after thermal shock for borosilicate
glass specimen. The quenching medium is liquid nitrogen [23].

18

1.3. Cyclic thermal shock effects

Most experiments involving thermal-stress-induced damage utilize single quench-
thermal shock testing [21-25]. However, many ceramic applications are actually involved
in repeated cycling in the ambient temperature difference (thermal fatigue) as is the case
for mainframe computer memories and solar cells. Thermal fatigue damage is caused by
the accumulation of repeated temperature difference (thermal loading). Thus one should

consider thermal fatigue damage in designing ceramics for a variety of applications.

Cyclic thermal shock tests have been performed with various materials with differing
properties. Herakovich [26] observed the cyclic thermal shock damage in the air for
graphite epoxy by measuring crack number density (number of cracks/length).
Herakovich [26] thermally fatigued the graphite epoxy specimens using a temperature
difference about 278 °C in an environmental chamber. Figure 1.3.1 shows. crack density
increases as the thermal cycling increases indicating thermal shock damage (crack

number density) is a function of cumulative number of thermal cycles.

Ainsworth et al. [27] performed cyclic thermal shock testing on MgO, A1203, and
MgO-Cr203 refractories with air as the quenching medium. Specimens were placed in a
1204 °C preheated furnace for 10 minutes and then the specimens were cooled in air.
Ainsworth et al. [27] evaluated the thermal shock damage by measuring modulus of
rupture. The strengths decreased as quenching temperature increased (Figure 1.3.2).

Thermal shock damage saturation behavior also is observed in Figure 1.3.2 that is, the

l9

 

Crack density, cracks/ inch

 

 

 

1 l r

0 1o 20
Thermal shock cycles

Figure 1.3.1. The crack number density as the function of cumulative thermal
fatigue cycles for graphite epoxy specimens]10,25]. The solid line was obtained by
least-squares fit to equation 1.3.1 [10].

20

property (strength in Figure 1.3.2) reaches a steady state value, which indicates a

saturation of rnicrocrack damage.

. Semler et al. [28] observed thermal fatigue in high alumina refractories by measuring
strength (modulus of rupture) and Young’s modulus. Specimens were heated in air to
1000 °C (as measured by a thermocouple) by burner flame and then the specimens were
cooled in air to 150-200 °C. Afier 5 thermal shock cycles, a strength decrease of 30-35
percent of strength decrease was observed. Semler et al. also evaluated degradation of
Young’s modulus for high alumina refractory, in which thermal shock damage increased
as the cumulative number of thermal cycles increased (Figure 1.3.3). A saturation of

modulus also was observed for the refractories [28].

21

 

 

 

 

 

 

 

 

r T
O Mgo
I Aluminosilicate

5 A Magnesia-chrome ‘
C» 1b
C .
(D

.1: _
(I)
“U

Q)

.L“.

— —l
(U

E

L.

0
Z -(

11
0 O r 1 r 1 r
0 1 0 20 30

Thermal shock cycles

Figure 1.3.2. Thermal shock damage in terms of modulus of rupture versus the
cumulative number of thermal fatigue cycles for MgO, A1203, and MgO-Cr203
refractory [10,27] at temperature difference 1180 °C in the air. The solid line was
obtained by least-squares fit to equation 1.3.1 [10].

22

 

 

 

 

 

 

'O

m 100 , ,

.E

.9

92

.5.

o 80 _
h

(D

O.

a)“

.2

1?

o 60

E .
yr

0) O

c .

8 40 r 1 r l r l r l r

>- o 2 4 6 8 10

Thermal shock cycles

Figure 1.3.3. The Young’s modulus observed for 60% alumina refractory by
quenched in air [10,28]. The solid line was obtained by least-squares fit to equation

1.3.1 [10].

23

Case et al. [IO-12, 29-3'1] investigated thermal fatigue effects for ceramics and
ceramic composites. Thermal shock damage was evaluated nondestructively by
measuring elastic modulus and internal friction. In Case et al. ’5 study of thermal fatigue,
water [11-12, 29-30], silicon oil [13,30] and liquid nitrogen [13,30] were used as
quenching media. In this thesis, we shall compare the crack length measurements done
for a water quenching medium (this study) to elastic modulus and internal friction
measurements done by Case et al. [10-12, 29-30]. Case et al. also observed that as the
quenching temperature difference increases, the severity of the thermal shock damage
also increases (Figure 1.3.4). In addition, thermal shock damage tended to saturate afier a
few cumulative cycles [IO-12, 29-30]. Figure 1.3.4 shows the Young modulus saturation
during thermal fatigue testing as the thermal shock cycles increases. Case et al. obtained

empirical equation 1.3.1 [10-12, 29-30] from the thermal fatigue data.

E: E0 -a{1-exp(-bN)} (1.3.1)
where E= Young’s modulus

E0 = Young’s modulus of undamaged specimen

a = the thermal shock damage constant

0"
ll

rate constant

N = the number of thermal shock cycles

24

The solid curves in Figure 1.3.4 represent a least-squares fit of the thermal fatigue data
to equation 1.3.1 for unreinforced polycrystalline alumina specimens quenched into a

room temperature deionized water bath [12].

The typical schematic diagram of thermal shock damage saturation (Figure 1.3.5) may

be described in terms of a generalized form of equation 1.3.1, namely

(2:0, — A{1—exp(—aN)} . (1.3.2)

where Q = a material property of specimen

()0 = a material property of specimen of undamaged specimen

A = the thermal shock damage constant

or = rate constant

N = the number of thermal shock cycles.

25

 

 

 

 

 

 

 

 

350 . r r n ' a fl
0 or=2so

(U I or=250
95 340“- A or =270 -
w. A or: 310
2 .
3 m e e e
g 330 - . 'f 4
_co
or t
g k
>9 320 a a a e 7

310 r J L r l l r

 

 

o 20 4o 60 so 100
Thermal shock cycles

Figure 1.3.4. Young’s modulus versus the cumulative number of thermal fatigue
cycles for unreinforced polycrystalline quenched into a room temperature deionized

water bath. The solid curves represent a least-squares fit of the data to equation
1.3.1. [12].

26

 

r T V l r l t l ‘ I r I

Undamaged property

 

Material property

Saturation damage level

 

 

 

 

Number of thremal cycles

Figure 1.3.5. Schematic diagram of damage saturation behavior subject to thermal
fatigue damage for ceramic materials [10-11, 29-30].

2. Experimental Procedure
2.1. Materials

Commercial polycrystalline alumina (Coors ADS 995) was cut into 10 mm x 10 mm x
1 mm specimens from 45 mm x 45 mm x 1 mm billets using K.O. Lee cutting machine.
The alumina plates were sawed at a depth of 1.27 um per pass (one forward or backward
recursion) and the saw speed (left/right) was less than 0.25 cm/minute. The nominal
average grain size was 4.0 pm. All specimen dimensions were measured using vemier

caliper (Mitutoyo) (Appendix A).

2.2. Polishing

Before polishing, sets of 8-12 specimens were mounted on an aluminum plate (Figure
2.2.1) with super glue (Super Glue Corp.). Specimens were polished through 3 steps
using a VARI/POL VP- 50 (Leco Co) polishing system. During polishing, the wheel
speed was 125 rpm and the applied normal load was about 5-7 lbs. The specimens were
polished with 15 um diamond paste (Part No. 810- 914 Leco Corp.) for about 4 hours.
Then using 6 pm diamond paste (Part No. 810-873 Leco Corp.), the specimens were
polished for about 4 hours. Finally, the specimens were polished with 0.3 pm alumina
powder (Buehler micropolish No. 40-6305-080) for about four hours until the specimen
surfaces were mirror-like in appearance. To demount the specimens from the aluminum
plate, the super glue was burned off in an electrical resistance furnace (Lindberg type
51442) for 60 21:5 minutes at 350 °C. The time-temperature history of the furnace for

specimen demounting is given in Figure 2.2.2. and Table 2.2.1

27

28

Alumina specimen

 

Hole for securing aluminum plate
during polishing

Thickness 20 mm

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

192 m

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Alumina plate

Aluminum plate

(a) (b)

Figure 2.2.1. (a) Position of specimens on the aluminum plate for polishing
specimens. were superglued onto the plate. (b) Alumina plate used to place
specimens on when burning off the superglue residue.

29

600 ‘F Illllil' U rrrrrr

""—- Aluminum plate

 

I' Y Wfirfirhtm T fTV‘I'UI

— Alumina plan

Temperature, degree C

 

 

 

0 r 1 1111111 1 s LLMLLL . . .rurd 1 1 1.....1
10'1 10° 19‘ . 1o2 103
Elapsed Time, minutes

 

Figure 2.2.2. The heating history to demount alumina specimens from alumina plate
by burning super glue using an electrical resistance furnace.

30

Table 2.2.1. Heating history for demounting polycrystalline alumina specimen from
aluminum plate and alumina plate.

from aluminum ' residue
T . °C min. T °C min.
0 25 0 25

27 350 49 550

60 350 60 550
873 25 1351 25
1440 25 1440 25

 

After demounting, there was a super glue residue on alumina specimens. Therefore,
the specimens were placed on an alumina plate (Figure 2.2.1) and the plate plus the
specimens were then inserted into furnace and heated for 60 :1: 5 minutes at 550 °C to
remove super glue completely (Figure 2.2.2 and Table 2.2.1). To prevent the alumina
specimens from “sticking” onto the alumina plate, the specimens were placed on a 1 mm
thick coating of alumina powder (Buehler 0.3 micron alpha alumina) which covered the
alumina plate. The thickness of the alumina powder bed was measured by a ruler with a
1 mm scale. The alumina plate contains a glassy phase that could cause sticking, but such
sticking normally does not occur for temperature below 1200 °C, thus the alumina

powder bed is a precaution.

2.3. Indentation

A Vickers semirnacroindenter (Digital Semirnacrohardness Tester, Buehler Ltd.) was
used to introduce cracks in the specimens. A 49 N load was used with loading time of 17
seconds and loading speed of 80 urn/s. Indentation cracks were introduced at the center

or edge of the 1 cm x 1 cm specimen surface (Figure 2.3.1). An optical microscope

31

 

 

 

 

 

 

 

 

A
y-direction
>-
x-direction
10mm
4*. >
25mm? ‘
e
10mm
5 mm e
V
—>-
25mm

Figure 2.3.1. The position of indentations on the polycrystalline alumina specimen’s
surface for observation of indentation crack growth behavior.

32

(x200) mounted on the indenter was utilized to measure crack lengths. A digital readout
gave crack lengths to the nearest 0.1 micron. The procedure for determining crack length
was as follows: The marker of the optical microscope is positioned at two crack tips. The
crack lengths were then measured in the longitudinal direction (x-direction) and

transverse direction (y-direction).

2.4. The observation of slow crack growth after initial indentation but before
commencing thermal shock

After introducing the indentation crack (see section 2.3) crack lengths were measured
using an optical microscope for specimens Al-12 to 14 and A2-8 to 9. Crack growth
behavior following the indentation but before commencing thermal shock was measured

as a function of elapsed time (see Appendix B).

2.5. The observation of slow crack growth behavior in room temperature deionized
water and in 80 0C deionized water in absence of thermal shock

To observe slow crack growth in water, the specimen (Bl-3) was inserted into room
temperature deionized water. The alumina specimens were positioned on the bottom of a
glass beaker (400 mm Kimax) with a water depth of about 7 cm as measured by a ruler (1
mm scale). Crack lengths were measured afier the specimens were removed from the
water. The crack length versus elapsed time are given in Appendix B.

Crack length behavior in 80 °C also was investigated. Specimen (Bl-4) was inserted

into 7 cm deep deionized water in a glass beaker (400 ml Kimax). An alumina specimen

33

was positioned 5 cm from the bottom of beaker using the steel wire screen (0.7 x 0.7 mm
grid with individual wires 0.03 mm in diameter). The alumina specimen was heated to
about 80 °C on Model 4658 stirrer/hot hot plate (Cole-Partner Instrument Co.). The
average heating rate was 3.5 °C/minute. The temperature was measured by mercury in
glass thermometer (V WR SCIENTIFIC INC 61016-208) with 1 °C scale. The specimen
was kept at 80 °C for about 2 hours then cooled at an average rate of 0.35 °C/minute by
turning off the hot plate. Within about 2 and 1/2 hours the water reached room
temperature (23 °C). Specimen (Bl-4) was removed fi'om the water and the crack lengths
were measured using an optical microscope. The 2.5 hour immersion in 80 °C water was

repeated 9 times. The resulting crack lengths and temperatures are given in Appendix C.

2.6. Thermal shock testing

After the indentation cracks had aged for at least 24 hours, the specimens were placed
in the fumace for thermal shock testing. The furnace, which was constructed for thermal
shock testing, was heated by electrical resistance (Figure 2.6.1) at a rate of about 2.0 °C
per minute to temperatures ranging from 272 °C to 352 °C. The temperature was
measured by a digital readout attached to power controller (CN 5001 K, Omega
Engineering Inc.) using a K-type thermocouple. The thermocouple was located about 10
cm from the lid of fumace. The temperature of deionized water bath was typically 22 °C
as measured by mercury in glass thermometer (V WR SCIENTIFIC m C. 61016-208)

which had a 1 °C scale. Quench bath temperature measurements were made before

34

 

 

 

 

 

(a) Top view

. Specimen Holder

 
  
  

Thermocouple

wire Brick Lid

 

Control] -
Specimen

 

 

 

ln-Tb-———

 

 

 

 

 

Water bath

Deionized

water

(b) side view

Figure 2.6.1. Schematic of the electrical resistance heated furnace used in the
thermal fatigue experiments. The average heating rate was about 2 °C/min.

35

specimen was placed in an electrical furnace. The thermometer was located
approximately 3.5 cm from the bottom of water bath and 9.5 cm from the specimen.

The specimen was introduced into the furnace using a specimen holder (Figure 2.6.2)
which was made for this study. The specimen holder consisted of tongs, stainless steel
wire screen, and a steel wire (Figures 2.6.2 and 2.6.3). The tongs were used to hold the
specimen in a fixed position within the furnace. If the tongs were removed then the
alumina specimen plunged into the deionized water bath. Using the tongs, the specimen
was placed approximately 25 cm from the top of the furnace (as measured by a 1 mm
scale ruler). A wire screen which has 0.7 x 0.7 mm grid made up of wires 0.03 mm
diameter held the specimen. The wire screen was made into a bowl shape approximately
1.8 cm x 1.7 cm and 1.2 cm diameter, as measured by ruler with 1 mm scale. The
deionized water flowed through the wire screen during quench thus steel wire screen
likely did not significantly perturb the thermal shock test.

A steel wire with about 64 cm in length was made from 0.85 mm diameter wire (as
measured by ruler with 1 mm scale) and formed the “backbone” of the specimen holder.
The steel wire (0.85 mm in diameter) was flexible thus three strands of wire were twisted
together (Figure 2.6.3).

The specimen remained in the furnace for about 10 to 15 minutes supported by the
specimen holder. The specimen then was quenched into the water bath by removing the
tongs to move the specimen from the furnace to the water bath. The specimen was

located approximately 2.5 cm above (measured by ruler with 1 mm scale) the water bath.

36

 

 

 

 

T 0 Steel wire
64 cm
‘0 Tongs +
28 cm

 

Wire screen to hold the
specimen

Figure 2.6.2. Schematic diagram of the thermal shock testing specimen holder which
has three parts: steel wire, tongs, and wire screen.

 

(b)

Figure 2.6.3. The photograph of (a) entire specimen holder which has three parts of
steel wire, tongs, and wire net for thermal shock testing (b) body of steel wire which
was twisted 3 times.

38

The time elapsed from the initial specimen movement until the specimen reached the
water bath was about 1 second.

The water bath consisted of a 27.5 cm x 14.5 cm x 20.5 cm plastic container
containing a volume of approximately 5 liters of deionized water. The depth of deionized
water was about 14 cm (measured by ruler with 1 mm scale) for all of the thermal shock
experiments. After 1 minute, the specimen was removed from the water bath. Water
remaining on the specimen was removed with paper towels (Kimwipes 34155 Kimberly-
Clark).

The specimen was then placed on movable stage of semimacroindenter. Crack lengths
were measured using an optical microscope with a digital readout which is attached to
semimacroindenter. The elapsed time between removing specimen from the water bath
and measuring crack length was about 5 minutes.

The thermal shock testing was done in two groups. In the first group the specimens
were individually thermally fatigued for total of ten thermal cycles. In the second group,
the specimens were individually fatigued for a total of twenty shock cycles. Specimens
thermally shocked for 10 cycles were at the following quench temperature differences:
250 (A4-13), 270 (A4-14), 290 (A4-15), 295 (A6-2), 300 (AS-3), 305 (AS-12), 310 (A5-
4), 315 (AS-11), 320 (AS-5), 325 (AS-8), and 330 °C (AS-7). For the specimens
quenched 20 times, the quench temperature differences were 250 (A6-3), 270 (A64), 295

(A6-5), 300 (AS-10), 305 (AS-14), and 310 °c (A6-1).

39

2.7. Comparison of transverse and longitudinal crack length for a set of Vickers
cracks subjected to thermal fatigue

Vickers indentation cracks were introduced on the surface of 56.1 mm x 9.4 mm x
0.93 mm bar specimen (Figure 2.7.1). The dimension , the orientation of the x-y axes of
the bar and the position of indentations L1, L2, and L3 are given in Figure 2.7.1 . After 24
hours in air, the specimen was placed in the quench furnace at 282 °C for 10 to 15
minutes (see section 2.6.). The specimen was quenched into a 22 °C deionized water
which was about 14 cm deep. The temperature of water bath was measured by a mercury
in glass thermometer (V WR SCIENTIFIC INC. 61016-208) at nearly the same position as
that used to measure the water bath temperature for the square alumina specimens (see
section 2.6). The same water container as that used for thermal fatigue testing (see
section 2.6) was used. The specimen holder screen (see Figure 2.6.2) was 4.5 cm long to
prevent the bar-shaped specimen from falling from the specimen holder. The specimen
was located about 20 cm from the top of electrical resistance furnace. The bar-shaped
specimen was plunged into a deionized water bath within less than 1 second. The
specimen in the water bath was held at 2.5 cm from the bottom of the water bath. After 1
minute, the specimen was removed from the water bath. Water remaining on the
specimen was removed with paper towels (Kimwipes 34155 Kimberly-Clark). After the
residual water was blotted of the specimen, the specimen placed on the
semimacroindenter stage for crack length measurements. Crack lengths were measured

by optical microscope of semimacroindenter which has digital readout (see section 2.6).

40

28.6 mm

 

10 mm 10 mm

 

4.6 mm:
,L

I ¢ ' >
I/ 56.3 mm

I

0.96 mm thick

9.1 mm

 

 

 

 

 

Figure 2.7.1. The dimension of bar-shaped polycrystalline alumina specimen and the
position of indentation cracks. This part of the study investigated possible
asymmetry in the group in the x and y directions during thermal fatigue.

41

2.8 The observation of grain bridging in for specimens thermally shocked during
this study

Three thermally shocked specimens (A4-l4 at 270 °C, A5-3 at 300 °C, and A5-5 at
320 °C) were gold coated in sputter coater (Model SC 500, EMSCOPE) for 3 minutes.
Specimens were mounted on JEOL 9.5 x 9.5 mm aluminum specimen mounts (TED
PELLA, Inc.) After gold coating for 3 minutes, the thickness of gold coating was
approximately 21 nm, for a deposition rate of 7 nm/min [32]. Specimens were inserted
into a scanning electron microscope (SEM, JEOL, J SM 6400V) chamber using specimen
holder. The accelerating voltage was 20 kV. Micrographs of the crack shapes were taken
at a magnification of 150 and bridging area micrographs were taken at a magnification of

2500.

3. Results and Discussions

3.1. Slow crack growth after initial indentation but before commencing thermal
shock

To evaluate the initial slow crack growth for the indentation cracks prior to thermal
shock testing, the initial indentation crack lengths were measured using an optical
microscope. The crack lengths and time were given by tables in Appendix B.

Plots of crack length versus time are shown in Figures 3.1.1-3.1.7. Following each of
the Vickers indentations, the cracks grew slowly after introducing the indentation crack.
The crack length typically saturated within about 30 minutes following the indentation. In
Figures 3.1.1 to 3.1.7, the open circles represent crack length of transverse direction,
while the open squares indicate the longitudinal direction. Closed circles represent the
crack length for the average of the transverse direction and the longitudinal direction.

For the 7 specimens included in the slow crack growth study, the relative change in the

where Co = mean of initial crack lengths for the two radial cracks that make up the
Vickers crack system.
Cmax = mean of the saturated crack lengths for a given Vickers crack system.
In this study, AC varied fiom 1.024 to 1.130. The AC’s and the time at which last

measurement was done are given in Table 3.1.1.

42

43

Table 3.1.1. Slow crack growth (in air) after initial indentation for unreinforced
polycrystalline alumina specimens.

 

 

 

 

 

 

 

 

 

Specimen label AC Tm,“ (minutes)
Al-ll 1.024 1474
Al-13 1.077 1386
A1-14 1.130 1495

A2-8eM 1.031 1424
A2-8m*** 1.034 1482
A2-9e" 1.056 1436
A2-9m*** 1.035 1435

 

 

 

* Tmax is the time at which last measurement was done.
** e means the edge of specimen.
*** 111 means the middle of specimen.

 

 

 

 

 

 

 

 

 

_ ‘1?)
e 244 ' ‘
e h .4 meancraeklength
.9 . M x-direradrlengtn
g 240 _ 121/T: y-dircrack length -
5 - N
U)
c b
2 236 - _
x .-
O 4
g . .
[i ["1
232 " W N1 .1
.. U .4
l l llllll l L llllll I l l lllllj L l l lllll
10° 101 102 1o3 10‘

Elapsed time after indentaion, (minutes)

Figure 3.1.1. Indentation crack lengths (x- and y-direction, see Figure 2.3.1) as a

function of elapsed time following indentation for polycrystalline alumina (specimen
Al-l 1).

45

 

 

 

 

 

 

 

250 I I I 11111] I r I IIITVI r r r I rrrrl
E 240 T5.) ‘
O
L-
.2
E 230 -
v r as.
.c“
-o- _
O) 220
c ._. -~..
2 ____—Aa—(-:b
x 210 _
0
Lu .4 meancraeklength
0 200. Q/Q x-dir crack length "
(‘ Vb y-direracklength
190 g 1 l l llLll 1 l l 1_LLlll l l l I llel L l l l

 

10° 101 1o2 103 10‘
Elapsed time after indentation, (minutes)

Figure 3.1.2. Indentation crack lengths (x- and y-direction, see Figure 2.3.1) as a
function of elapsed time following indentation for polycrystalline alumina (specimen
A1-13).

46

 

 

 

 

 

 

 

230 . .....n] T ......., . .....nT r .
1:
A 6 2H
g 220— “ a _
h
.2 C- ,
E
v_ 210— -. g
:3) . O 1
j, 200- ' _
x _ Hmeancraeklength
o .
CU Mx—dlra'acklength
h _ —.
O 190 ,- 3’11 y-dircraek length
U
180Lo ‘ ' ‘44“‘11 1111112 A 1 1 1111113 1 1 1 1““ 4
1o 10 10 10 10

Elapsed time after indentation, (minutes)

Figure 3.1.3. Indentation crack lengths (x- and y-direction, see Figure 2.3.1) as a
function of elapsed time following indentation for polycrystalline alumina (specimen
A1-14).

47

 

 

 

 

 

244 - -
E _ 4
9 240 - -
.2 ' ‘
E i
5‘ 236-" -
O)
5 . 1
; 232 L -
o .
E l
0 _ Mmeancraeklength ,
228r Mx—dircmdrlength 4
’ . . ....... .D’. ..D...'.*"'°'?°"l°"?‘t‘...f
10° 101 102 103 10‘

Elapsed time after indentation

Figure 3.1.4. Indentation crack lengths (x- and y-direction, see Figure 2.3.1) as a
function of elapsed time following indentation for polycrystalline alumina (specimen
A2-8e where “e” means the indentation was placed near the edge of the specimen).

48

 

 

  
 

 

 

 

 

240 I ' 'I'Illl r T rrrrrrl r r Irrrrrl u . Irrrrr
A b _ .
8 W1
(:3 2305- _
E
V
S.
*5) 220
C
(D l-
; Hmeancracklength
O 210 _ M x-dircrack length
8 Va y-dircracklength
200 r r 11_rrrrl r r_errrrL 1 Ll‘lll‘l r r rrrxr
10° 10‘ 102 103 10‘

Elapsed time after indentation

Figure 3.1.5. Indentation crack lengths (x- and y-direction, see Figure 2.3.1) as a
function of elapsed time following indentation for polycrystalline alumina (specimen
A2-8m where “m” means the indentation was placed near the middle of the

specimen).

49

 

I YYYIIUI I l I TTW'YUI I T I I'VTII Y I ‘r'tl'

 

260 -

 

 

l
L

240

220 r ”ER—WT ‘ ’ T’LT ..
_ H mean crack length ‘

Q/‘Q x-dir crack length

i 1 1 M y-dircracklength '
200 m 1 114111 1 mint“. 1 1 11.“.
10° 101 102 103 10‘

Elapsed time after indentation

Crack length, (micron)

 

 

l ALIJJII 1

 

Figure 3.1.6. Indentation crack lengths (x- and y-direction, see Figure 2.3.1) as a
function of elapsed time following indentation for polycrystalline alumina (specimen
A2-9e where “e” means the indentation was placed near the edge of the specimen).

50

 

 

 

220 . . .f @rfinr 5:; try-4.11.9.3 .
c. _

 

 

 

 

E

210 - -
2
.9 - .
E
\f 200 - -
.C t
q—r - ..
8’
_q;_ 190 r a _ g 4,3 flag? ‘
x _ H .4 mean crack length
8 . Q/O x-dir crack length
5 180: D4 y-dir crack length ‘

 

 

170 1 1 1141111 1 1 1111111 1 11111111 1 141111.
10° 101 102 103 104
Elapsed time after indentation

 

Figure 3.1.7. Indentation crack lengths (x- and y-direction, see Figure 2.3.1) as a
function of elapsed time following indentation for polycrystalline alumina (specimen
A2-9m where “m” means the indentation was placed near the middle of the

specimen).

51

3.2. Crack growth behavior in room temperature and 80 °C deionized water in the
absence of thermal shock

Water can cause crack extension via an environmentally-assisted slow crack growth
process. Water may affect crack growth during thermal shock testing when the
specimens were in the water bath. Therefore, the effect of water on crack extension was
investigated.

A specimen (B 1 -3) was inserted into deionized water at room temperature after being
indented and aged for 24 hours in air. The crack lengths were measured as a function of
time (Figure 3.2.1). The circles represent mean crack length, the diamonds indicate the
transverse direction crack length and squares indicate the crack length in the longitudinal
direction. The indentation crack length did not change significantly (less than 1 percent,
see Appendix C) during up to 92 hours of immersion in the deionized water. The crack

length data as a flmction of immersion time in the deionized water are given in Appendix

C.

To observe the effect of hot water (~ 80 °C) on a Vickers indentation crack system, a
specimen (Bl-4) was first immersed in room temperature deionized water after being
indented and aged for 24 hours in air. Then the water and specimen were slowly heated
together to about 80 0C in deionized water. The specimen and water were cooled to room
temperature (about 23 °C) in the air. The crack length change ( Figure 3.2.2) was less
than 1 percent (see Appendix C). Thus the hot water (~ 80 °C) apparently does not cause
the cracks to extend. The crack lengths for each measurement during the test are given in

Appendix C.

52

 

 

 

 

 

l ' l ' 1 fi 1 '
T meanlength ‘
1.4 ' x-dlrcraeklength .1
%) L f y-dircracklength J
C
Q . .
x
8
b 1 2 - -
a) r .
.2
q—s
E
G) .1
O:
1.0% ea} 5? e a; e e ‘
- l
1 4 L 1 1 1 1 1 1
0 20 40 60 80 100

Elapsed time (hour)

Figure 3.2.1. Crack growth behavior versus elapsed time in room temperature
deionized water for unreinforced alumina specimen (specimen B1-3).

53

 

 

 

 

 

' I I I I fly I I l I I I T I
O meancracklenglh

1.4”. D x-dircraeklength _.
5 + y-dlrcracklength
U)
C
2 l-
x
8
h 12 - -
O
0
.2
4.:
E
G)
[I

1.0M a ‘31 E 53 @ m E W

L l I I. I I I A I I I l I I I I l
O 4 8 12 16

Total elapsed time in water, hour

Figure 3.2.2. The crack growth behavior in deionized water at 80 °C held for 2
hours for specimen B1-4. Crack length measurements were made after the specimen
had been at 80 °C (see section 2.5)

54

3. 3. Thermal fatigue behavior for unreinforced alumina

3. 3. 1. Thermal cycling to a maximum of ten thermal shock cycles
Thermal shock tests were done for quench temperature differences ranging from 250
to 330 °C (Figure 3.3.1-3.3.11). The crack length data for specimens that underwent a
total of ten thermal shock cycles are given in appendix D.
From equation 1.3.2 (section 1.3), the crack length as a function of cumulative number
of thermal shock cycles can be expressed as
C(N) = cl -(cl —co)exp(—c2N) (3.3.1)
where c = the crack length which is a function of the cumulative number of thermal
shock cycles
co = the initial crack length from data
cl = a free parameter which corresponds to saturated crack length

C2 = free parameter corresponds to rate constant.

The relative crack increments, m at temperature differences ranging from 250

co
°C to 330 °C are plotted in Figures 3.3.1-3.3.11. The solid curves in figures were
obtained by least-squares fit to equation 3.3.1. For quench temperature differences
ranging from 250 °C to 325 °C, the saturated crack length ranged 273.54 pm to 638.52
um (Table 3.3.1). The correlation coefficients of least-squares fit were higher than 0.94
except for quench temperature differences of 300, and 310 °C (Table 3.3.1). The cracks

increased with an increasing number of thermal shock cycles. Eventually, the thermal

55

fatigue damage saturated. Figure 3.3.12 gives the results of crack propagation behavior
due to the temperature difference at (a) 250-300 °C and at (b) 305-330 °C.

At a quench temperature difference 330 °C, the crack growth behavior is different from
the crack growth behavior for lower temperature differences. Afier the fourth quench at
330 °C, the crack grew abruptly to the edge of the specimen. Thus the crack length was
not measured because it was out of range of the scale on microscope. Figure 3.3.11 shows

the crack growth behavior at the quench temperature difference of 330 °C.

56

1.12 a . . . .,

 

.J
..
.—

   
 
 

.3

C

on
1

Relative crack length
'2

 

 

 

1.0 l 1 L 1 I 1 l 1
o 2 4 6 3 10
Number of quenches

Figure 3.3.1. The crack growth behavior versus the cumulative number of thermal
shock cycles a total of 10 thermal shock cycles, AT = 250 °C (specimen A4-13). The
solid line represents the least-squares fit to equation 3.3.1.

57

 

Relative crack length

 

 

 

 

Number of quenches

Figure 3.3.2. The crack growth behavior versus the cumulative number of thermal
shock cycles a total of 10 thermal shock cycles, AT = 270 °C (specimen A4-l4). The
solid line represents the least-squares fit to equation 3.3.1.

58

 

  
 

 

 

 

‘ r ‘ l T r ' l r
1.12— 1i
5 i *
U) l-
C
Q
1‘, 1.03-
9 r
0
q) r
.2
‘5
T) 1.04
a:
.l
1.0 1 l L l i l 1
o 2 4 6 8 10
Number of quenches

Figure 3.3.3. The crack growth behavior versus the cumulative number of thermal
shock cycles a total of 10 thermal shock cycles, AT = 290 °C (specimen A4-15). The
solid line represents the least-squares fit to equation 3.3.1.

59

 

—l~ N
O) 0

Relative crack length
is

 

 

 

1 1 l l l 1 l 4
o 2 4 6 8 10
Number of quenches

—

0.8

 

Figure 3.3.4. The crack growth behavior versus the cumulative number of thermal
shock cycles a total of' 10 thermal shock cycles, AT = 295 0C (specimen A6-2). The
solid line represents the least-squares fit to equation 3.3.].

60

 

 

 

 

 

 

1.3 7 l 7 l I r I I T
. O . $
4
. .
5
8’
_q_) 1.2 4
x
O
9 .
0
o
.2
E 1.1 -
o
a:
1.0 1 L 1 l 1 l 1 4L 1
o 2 4 6 8 10
Number of quenches

Figure 3.3.5. The crack growth behavior versus the cumulative number of thermal
shock cycles a total of 10 thermal shock cycles, AT = 300 °C (specimen A5-3). The
solid line represents the least-squares fit to equation 3.3.1.

61

 

 

 

 

 

2-4 ' T I I I I ' I
5
g 2.0
2
x
0
E .
O
o 1.6
.2
E
0
tr

1.2

1 L 1 l 1 l 1 l 1
o 2 4 6 8 10
Number of quenches

Figure 3.3.6. The crack growth behavior versus the cumulative number of thermal
shock cycles a total of 10 thermal shock cycles, AT = 305 °C (specimen A5-12). The
solid line represents the least-squares fit to equation 3.3.1.

62

 

 

 

 

 

 

16 l L l l L 1
o o o O 4
. -I
5 .
8’
2 1.4 e
x
O
9 .
0
o 1
.2
E 1.2 -
(D .
a:
1.0 V I I I T I 1 I l
o 2 4 6 8 10
Number of quenches

Figure 3.3.7. The crack growth behavior versus the cumulative number of thermal
shock cycles a total of 10 thermal shock cycles, AT = 310 °C (specimen A5-4). The
solid line represents the least-squares fit to equation 3.3.1.

63

 

 

 

 

 

2.4 . , . , 2 I . 1
5
g 2.0
2
x
O
S
0
a, 1.6
.2
E
4:
CK
1.2
1 l 1 l 1 l 1 J 1
o 2 4 6 8 10
Number of quenches

Figure 3.3.8. The crack growth behavior versus the cumulative number of thermal
shock cycles a total of 10 thermal shock cycles, AT = 315 °C (specimen AS-ll). The
solid line represents the least-squares fit to equation 3.3.1.

 

 

 

 

 

2.4 I | I I ' l ‘ l
5 I-
g 2.0
.0.)
x
O
E
0
m 1.6
.2
E
a)
m .

1.2

1 l 1 I 1 l 1 J 1
0 2 4 6 8 10

Number of quenches

Figure 3.3.9. The crack growth behavior versus the cumulative number of thermal
shock cycles a total of 10 thermal shock cycles, AT = 320 °C (specimen AS-S). The
solid line represents the least-squares fit to equation 3.3.1.

65

 

 

 

 

 

2-4 I I I I w I I I
5
g 2.0
2
x
0
9
0
a) 1.6
.2
E
c)
II

1.2

1 l 1 l 1 l 1 l 1
o 2 4 6 8 10
Number of quenches

Figure 3.3.10. The crack growth behavior versus the cumulative number of thermal
shock cycles a total of 10 thermal shock cycles, AT = 325 0C (specimen A5-8). The
solid line represents the least-squares fit to equation 3.3.1.

66

2-4 I I I I I T I I

 

N
0

Relative crack length
a»

_L
N

 

 

l 1 l 1 l

4 6 8 10
Number of quenches

 

Figure 3.3.11 The crack growth behavior versus the cumulative number of thermal
shock cycles a total of 3 thermal shock cycles, AT = 330 °C (specimen A5-7). The
solid line represents the least-squares fit to equation 3.3.1.

67

Table 3.3.1. The results of the least-squares fitting to equation 3.3.1 for the data of a
total of 10 thermal cycles. (where co = initial crack length, Cf = final crack length, N

 

 

 

 

 

 

 

 

 

 

 

 

= data points).

Specimen AT(° C) Co (Inn) or (Ian) mum!) 020ml 1* N
A4-13 250 244.3 272.3 273.54 0.413 0.978 1 1
A4-l4 270 256.6 293.1 316.12 0.101 0.946 1 l
A4-15 290 254.3 284.6 306.80 0.080 0.954 11

A6-2 295 251.4 513.7 542.54 0.260 0.973 1 1
A5-3 300 255.4 327.4 323.21 1.199 0.616 11
A5-12 305 242.3 537.1 638.52 0.157 0.954 11
A5-4 310 251.7 387.0 389.09 1.141 0.852 11
A5-11 315 244.3 538.3 538.69 0.566 0.989 11
A5-5 320 261.1 587.6 585.26 0.274 0.943 11
A5-8 325 247.3 561.2 607.73 0.188 0.979 11
A5-7 330 235.1 526.1 613.25 0.530 0.974 4

 

 

 

 

 

 

 

 

 

* r = correlation coefficient

 

68

 

 

Relative crack length

 

 

l

0 2 4 6 8 10

 

 

 

   

 

    

 

 

Number of quenches
(a)
3 I fl l r l l
O m-31o I or-azo
O (Jr-31o «3 tar-325
g C] or-315 A DT-330
o: .
c
2
’8
e 2 -
d)
.2
E
o
rt
1 1 41 1 1 1 l 1 g
o 2 4 6 8 10
Number of quenches
(b)

Figure 3.3.12 The crack growth behavior versus the cumulative number of thermal
shock cycles for a total of 10 thermal shock cycles, The solid line represents the
least-squares fit to equation 3.3.1. (a) 250 - 300 °C (b) 305-330 0C.

69

3. 3. 2. Thermal cycling to a maximum of twenty thermal shock cycles

To observe the crack growth and damage saturation behavior in more detail, the
number of thermal shock cycles was increased to 20. Temperature differences were 250,
270 290, 295, 300, and 305 °C. The crack length data are given appendix D. The data of
crack length also were least-squares fit to equation 3.3. 1. The results are given in Table
3.3.2. Figures 3.3.13 - 3.3.18 show the results of the crack propagation behavior for each
temperature difference. The solid lines in figures were obtained from the least-squares
fit.

The crack growth behavior also showed crack length saturation. For specimens
thermally shocked for 20 cycles, the saturated crack length ranged 264.35 pm to 546.7
pm. The correlation coefficient ranged from 0.804 up to 0.988. All specimens except
A5-14 (AT =300) had a correlation coefficient greater than 0.931. Specimen A5-l4 was
different from the other specimens in that abrupt crack grth occurred on the 10th

quench for this specimen.

70

 

 

 

 

 

 

1.16 . . .
. . A
1- .a d
S .
*5, 1.12 8 ..
C .
2
x
0 ~ .
g 1.08— ~
0 . .
.2
E .
m 4
o: 1.04 4
1O 1 l 1
0 1o 20
Number of quenches

Figure 3.3.13. The crack propagation behavior versus the cumulative number for a
total of thermal shock cycles, AT = 250 0C (specimen A6-3). The solid line represents
the least-squares fit to equation 3.3.1.

71

 

   
 
 
 

 

 

 

 

1.4 . ,
.1:
*5, 1.3- 4
c
9 l-
x
0
g 124 _
G)
.2
E
0 -
m 1.1

1. 1 l 1

0 10 20

Number of quenches

Figure 3.3.14. The crack propagation behavior versus the cumulative number for a
total of thermal shock cycles, AT = 270 0C (specimen A6-4). The solid line represents
the least-squares fit to equation 3.3.1.

72

2.0

 

.s .1
O) on

Relative crack length
I:

 

.11
N

 

 

 

1.0. . I .
0 1o 20

Number of quenches

Figure 3.3.15. The crack propagation behavior versus the cumulative number for a
total of thermal shock cycles, AT = 290 °C (specimen Bl-S). The solid line represents
the least-squares fit to equation 3.3.1.

73

 

 

 

 

 

2.0 I I
5 1.8""
a)
C
2
x 1.6— ' .1
o
E
o
g 1.4- -
E .
(D
95 1.2- -
1. . ' .
0 10 20

Number of quench

Figure 3.3.16. The crack propagation behavior versus the cumulative number for a
total of thermal shock cycles, AT = 295 °C (specimen A5-10). The solid line
represents the least-squares fit to equation 3.3.1. '

74

 

 

   
 

 

 

 

 

 

 

2.4 fl |
5 1- o o o o o o o o o o O
‘5 .
8
— 2.0- -'
x . O O C O
8 I-
3 E
0
E 1.6- -
2
d)
a:
1.2 -
l
0 10 20
Number of quenches
(a)
T
.1:
._. _
a:
c
2
x II
o
9 4
o
0 _
.2
fl
2
d)
o:
l

 

 

 

0 1o 20
Number of quenches

(b)

Figure 3.3.17. The crack propagation behavior versus the cumulative number for a
total of thermal shock cycles, (a) AT = 300 °C (specimen A5-10) (b) without abrupt
increase in crack length at 10th thermal quenching. The solid line represents the
least-squares fit to equation 3.3.1.

75

 

2.4

 

 

 

 

5 .-
g 2.0
.9
x
0
(U
h
0
a, 1.6
.2
E
d)
n: .

1.2

1 l 1
o 10 20
Number of quenches

Figure 3.3.18. The crack propagation behavior versus the cumulative number for a
total of thermal shock cycles, AT = 305 °C (specimen A6-l). The solid line
represents the least-squares fit to equation 3.3.1.

76

Table 3.3.2. The least-squares fitting of equation 3.3.1 for 20 quench specimens
(where ao = initial crack length, a; = final crack length, N = data points).

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Specimen ATfC) 80 (pm) a; (rim) C1 C2 r N
A6-3 250 230.7 265.15 264.35 1.03 0.952 21
A6—4 270 249.7 331.3 330.56 1.17 0.988 1 l
B l -5 290 227.6 442.4 442.45 1.07 0.976 21

A5-10 295 230.8 418.4 419.42 0.57 0.984 21
A5-l4 300 244.1 538.4 523.76 0.56 0.804 21
A6-1 305 237.3 546.7 543.06 0.73 0.931 21

 

r* correlation coefficient

 

N is the number of data points for the least-squares fit. N includes the measurement of
the crack length 24 hours after indentation and the crack lengths measured following each
of N-l thermal cycles.

The crack propagation behavior for the thermal fatigue is given as a function of
quench temperature difference in Figure 3.4.19. The crack lengths increase as the number

of quenches, eventually the crack lengths saturate.

77

 

 

 

 

 

 

 

 

3.2 1 .
O DT-250 .4
. DTII270
5 2'8" E1 or=2so '-
1.1.0
0) I- . DT=295
C
a) 24_ 11» or-aoo _
x ‘ orsaos 1
8 A A A A A A A A A A A A A
h
A
m U LJ L—J I—I LJ r—I 1f ._, u U U 1.1 fij :1 I.
.2 ~ A
10.:
19.
m 1.6- ' -
a:
1.2 n n A ’\ r\ A A A /\ A A [‘1 A A A L A 1
A V v U v V \J \J \J U U V U U u U V V x)
l l l
0 10 20

Number of quenches

Figure 3.3.19. The crack propagation behavior versus the cumulative number for a
total of thermal shock cycles with quenching temperature difference range of 250 °C

to 305 °C. The solid line represents a least-squares fit to equation 3.3.1.

78

3.3.3. The comparison of rate constant with Lee’s data [12] and Ash’s data [32]

The rate constant (b for this study and Ash’s work [32], and or for Lee’s work [12]) in
equation 3.3.1 is related to quenching temperature difference. The data were obtained by
measuring crack lengths in this study and in Ash’s work [32], while Young’s modulus
was measured for Lee’s work [12]. The calculated values of rate constant from least-
squares fit to equation 3.3.1 were plotted (Figure 3.3.20).

The rate constant increased as the quenching temperature difference increased.
However, rate constants for 20 quenched specimens were very scattered (Figure 3.4.21).
The solid curves in Figure 3.3.20 were obtained from linear regression using a PLOT-IT
program (Scientific Programming Enterprise). The correlation coefficient for Young’s
modulus data was 0.975 but the Ash’s and our coefficients were poor (Table 3.4.1). The
difference in the scatter could stem from the fact that the Young’s modulus measurements
represent the effect of an ensemble average for an entire microcrack population in a
thermally shocked (not indented) specimen. In contrast to the Young’s modulus
measurements by Lee [12], this study relied on a single Vickers indentation crack system
to assess the state of thermal shock damage.

Table 3.3.3. The comparison of rate constants for data of Young’s modulus (Lee’s

Work [12]) and data of crack length (this study and Ash’s work [32]) for
unreinforced alumina specimen.

 

 

 

 

 

slope intercept correlation data points
coefficient
3b for this study (10 0.017 -4.52 0.637 11
quenches)
a for Lee’s data 0.012 -2.90 0.975 5
3b for Ash’s data 0.015 -2.78 0.578 6

 

 

 

 

 

 

79

 

3 r l ' l ' I I, l ' T
U 36 for this study
'3 a. for Lee's data ’41

     

31) for Ash's data

Rate constant

 

 

 

-1 1 L 1 I L I 1 I 1 I 1

220 240 260 280 300 320 340
Temperature difference

Figure 3.3.20. Comparison of rate constants as a function of quench temperature
difference for three thermal fatigue studies: this study and Ash’s work [32] and
Young’s modulus data (Lee’s work [12]). Each of these three studies involved the
thermal fatigue of unreinforced polycrystalline alumina into room temperature
deionized water. The solid line was obtained from linear regression of data for this
study, dotted line represents linear regression for Lee’s data and double dotted line
is a linear regression of Ash’s data using PLOT IT program.

80

 

 

 

 

3-6 I I ; I 1 I I

3.2: 0 -I
g; C .
7,; 2.8 - -
c - .
o . l
0 .
.9 2.4 - -
w . 1
n: _ . .

2.0 - -

. O
1 6 1 l 1 l 1 L 1 l 1 T

'250 260 270 280 290 300 310
Temperature difference, degree C

Figure 3.4.21 Rate constants (3b) behavior for 20 quenches as AT increases for
unreinforced alumina specimen. The quenching medium is deionized water.

81

3.3.4. The severity of thermal fatigue damage as a function of the quench
temperature difference

The severity of thermal shock damage due to an increase in the quench temperature
difference was estimated by calculating a normalized saturation crack length for each
quench temperature difference. The normalized saturation crack length was defined as
saturation crack length/initial crack length.

The saturation crack length increased as the quench temperature difference increased
(Figure 3.5.1). The solid lines in Figure 3.5.1 were obtained by linear regression using
the PLOT-IT program (Scientific Programming Enterprise) and the results are given
Table 3.5.1. The slopes of normalized saturation crack length versus quench temperature
difference showed good agreement with all specimens. The correlation coefficients for
the specimens quenched 20 times were very good. The scatter in the data may be related
to the geometry of specimen, the initial flaw distribution, and the size of the flaws.
Therefore, the thermal fatigue damage is more severe as the quench temperature
difference increases.

Table 3.3.4. The results of linear regression of normalized saturation crack length
for unreinforced polycrystalline alumina specimen using PLOT-IT program.

 

 

 

 

 

Intercept Slope Correlation coefficient Data points
for 10 quench -4.92 0.019 0.76 11
for 20 quench -5.03 0.020 0.96 5
for 5 quench“ -3.28 0.017 0.66 6

 

 

 

 

 

 

* Ash’s data [32]

82

 

O 10 quench

 

«\I
[

ID

 

 

Normalized crack saturation length

I 1 I 1 I 1 I 1 1

220 240 260 280 300 320 340
Temperature difference

I
—L

 

Figure 3.3.22 Normalized saturation crack length behavior versus quench
temperature difference for polycrystalline alumina specimens. The solid line (10
quenches), dotted line (20 quenches), and double dotted line (5 quenches [32])
represent a linear regression of the data using PLOT IT program.

83

3.3.5. Comparison of crack lengths for a given Vickers crack subject to thermal
fatigue

Using a 49 N load, three Vickers indentation crack systems were introduced into the
long transverse face of a unreinforced alumina specimen (9.1 mm x 56.3 mm x 0.96 mm).
The quench temperature difference was 260 °C (see section 2 for details of the
experimental procedure). The longitudinal (x-direction) crack length and vertical (y-
direction) crack length show a slight directional difference in crack growth (Figure 3.3.20

and Appendix D) during thermal shock testing.

The crack grew more in the y-direction than in the x-direction thus the crack
propagation was affected by the crack orientation. The ratio of the crack lengths in the x-
direction and y-direction increased to 1.22 as the thermal shock cycles increased. After

about 3 to 4 thermal shock cycles, the crack length seemed to saturate.

 

 

 

 

 

 

1-4 ‘ 1 fl l ‘ F ' F ' l fl 1
_ we Average
A Q/Q L1 _ n D
g 1 3 - m 12 D ' -
v 4”; 13
>2
'8
to 1.2 - '
X D A A A f.
“5 , . we fi421\ .
O --"" 1' rem—154.5
3: /
g 1.1 r -
1'0 1 I 1 I 1 I 1 I 1 I 1 I 1
0 1 2 3 4 5 6 7
Number of quenches

Figure 3.3.23. The crack propagation behavior of bar-shaped specimen of alumina
under cyclic thermal shock testing. L1, L2, and L3 represent the position of
indentation crack (see section 2.7).

85
3.4. Grain bridging in the brittle materials
3.4.1. An overview of grain bridging

Studies of toughening mechanisms in monophase ceramic materials such as alumina
have shown that a major toughening mechanism is grain bridging [33-47] including crack
deflection [33,41] and crack bowing [3 5]. Grain bridging is observed behind crack tips

[33-38].

Grain bridging is affected by the grain size and crack opening displacement. More
bridging sites exist in coarse grained specimens than in fine grain sized specimens
[34,3 8]. In grain bridging, there is a critical crack opening displacement related to grain
size. Steinbech et al. [43] observed bridging for crack opening displacements less than
1/4 of mean grain size and Hay er al. [35] observed bridging for crack opening
displacements 1/3 of mean grain size. The crack closure stress tends to be a function of
crack opening displacement rather than a function of crack length in a bridging toughened
material [3 8-40]. In addition, the frictional coefficient affects the grain bridging

toughening; the crack closure forces increase as the frictional coefficient increases [33].

Scanning electron microscope observations provide evidence of grain bridging behind
crack tip [34,36,37,41]. Stress-induced microcracking in the wake zone also can impede
crack propagation. Typically, for polycrystalline alumina specimens there is no evidence
of dispersed microcracking near the crack tip by scanning electron microscope
observation. Thus it has been conjectured that stress- induced microcracking near the tip

of a macrocrack is not available in monophase polycrystalline alumina [36,41].

3.4.2. Grain bridging model

Chou et al. [41] suggested a model for the evolution of grain bridging as toughening
mechanism in a SiC platelet alumina composite. Crack deflection occurs and crack
bridging or sliding pullout follows. Chou er al. [41] observed the crack deflection and

grain bridging with a scanning electron microscope (SEM).

Figure 3.4.1 is a schematic diagram of the toughening mechanism in SiC platelet
reinforced alumina. Kawasawa [33] suggested a similar grain bridging model (crack
deflection and crack bridging) as a toughening mechanism for polycrystalline alumina.
Crack bridging as the toughening mechanism of monophase ceramic material is
composed of crack deflection and grain bridging. Bridging sites in turn can be degraded

by cyclic loading [34,3 7].

3.4.3.1. The effect and observation of grain bridging by Lathabai et a1. [34]

Lathabai et al. [34] investigated the effect of grain bridging using commercial alumina
specimens with an average grain size of 23 to 35 um. Disc shaped specimens 22 mm in
diameter and 2 mm thickness used for tension-tension cyclic testing. Plate specimens 100
mm x100 mm x 6 mm were used for a long crack test. Vickers indentation cracks were

introduced with a 30 N load (short crack test) and a 50 N load (long crack test).

In the short crack test, specimens were loaded sinusoidally with a maximum tensile

stress of 100 to 130 MPa keeping the minimum tensile stress at 20 MPa with fi'equency of

le

87

   

(a)

 
   
  

'2-IIV'2‘XMWZI’.

  

.‘é. ...'.. 4...,)(<.\ .1.
::>::$:::1:;i‘tl:£fiddzo‘stb-iklzf‘d

.4 --.\;-:.5»<~3 M

(b)

Figure 3.4.]. Schematic diagrams of a possible evolution of bridging (a) crack
. deflection (b) crack bridging for a SiC platelet composite specimen [41].

and 100 Hz using electro-servo—hydraulic machine. Lathabai et al. measured lifetime

(time to failure) under cyclic tensile loading. Table 3.4.] shows the maximum stress and

lifetime.

Table 3.4.1. Lifetime under cych loading of alumina for 1 Hz and 100 Hz. A

Vickers indentation crack was inserted with 30 N load [34].

 

 

 

 

Frequency, Largest of lowest of Largest lowest N
Hz maximum maximum lifetime, lifetime, (specimens)
cyclic stress, cyclic stress, seconds seconds
MPa MPa
1 130 110 * 10 16
100 130 100 105 2 28

 

 

 

 

 

 

* Fracture did not occur within 24 to 40 hours.

Long crack testing was done using electro-servo-hydraulic machine with stress ratio

0.1 with fi'equency 10 Hz for two alumina compact tension specimens. Toughness

increased as crack propagated. The fiacture toughness was 4.0 MPam"2 at a crack

extension of 0.9 mm. The fracture toughness was 5.3 MPam"2 at a crack extension 7

mm. Toughness saturated at 5.3 MPamm. Grain bridging sites were observed in-situ

using a scanning electron microscope (SEM) during cyclic loading test. Scanning

electron microscopy (SEM) indicated an evolution of grain bridging behind the crack tip

during cyclic loading. Table 3.4.2 summaries the scanning electron microscope

observation. The evidence of the degradation of the grain bridging was the “cumulation

of wear debris” under cyclic loading conditions. Thus frictional traction at sliding grain

bridging facets gradually was reduced by the contacting grains repeatedly sliding back

and forth, resulting in a degradation of specimen toughness.

 

89

Table 3.4.2. Scanning electron microscope in situ observation of crack for alumina
specimen under cyclic load [34].

 

 

 

 

 

 

 

Magnification Position of Observation
observation
x 1000 behind crack tip gain bridging
x 6500 near dislodgnent of gain bridging
gain

x 5000 "‘ crack paths
x 7500 * crack paths
x 5000 * crack paths

 

 

 

 

* not available

3.4.3.2 The effect and observation of grain bridging by Hay et a1. [35]

Hay et al. [35] used 99.7% alumina (fabricated by Johnson Matthey, Alpha Alumina
A123) which were cut into 8.90 mm x 60 mm x 4 mm specimens to observe gain
bridging effects in monophase ceramic materials. The mean gain size of alumina was

about 16 pm.

Post fracture tensile (PSF) testing was performed on a modified four point bend test in
which a second notch is inserted at rear of specimen (Figure 3.4.2). Post fracture tensile
testing identified the critical stress and stress distribution in the wake region of the
alumina specimen since there is no crack-resisting material in front of the crack tip when
crack tip enters second notch at rear of specimen. The results of post fracture test, stress-

displacement behavior, showed that the strength increased from 2.7 MP8 to 5.6 MPa as

90

Load Load

Wedge

 

 

 

Wid

 

 

 

 

otch

Load Load

Figure 3.4.2. Schematic diagram of modified four point bend test specimen of
polycrystalline alumina for postfracture tensile test [35].

91

the crack opening displacement increased from 5 pm to about 7.6 pm (Table 3.4.3).
Strength monotonically decreased with increasing crack opening displacement up to
about 50 pm. At geater CODs, there was a loss of grain bridging associated drop in

strength (Table 3.4.3).

Table 3.4.3. The stress behavior versus displacement of polycrystalline alumina
specimen by postfracture test [35].

 

 

 

 

 

 

 

 

First measurement of Maximum stress and Last measurement of .
stress and displacement stress and displacement
displacement

l 3.2 MPa at3 um 8.4 MPa at5 um 0.1 MPa at 47m

2 3.7 MPa at 3.5 pm 7.6 MPa at 6 um 0.1 MPa at 28 pm

3 3.1 MPaatSum 5.8 MPaat7um 0.1MPaat37um

4 2.3 MPaat6um 4MPaat9um 0.1MPaat48um

5 1.3 MPaat7.6um 2.1 MPaatll um 0.1MPaat35um

Average 2.7 MPa at 5 um 5.6 MPa at 7.6 pm 0.1 MPa at 39 um

 

 

 

 

The gain bridging stress is a function of crack opening displacement and is expressed

 

as follow [35]
a = (1 +L)". (3.4.1)
"I um
where om = critical stress for bridge rupture

um = critical crack opening displacement for bridge rupture

n = constant

 

92

In Hay er al. ’s experiments, bridging in alumina became insignificant at crack opening
displacement of 1/3 of the grain size. Steinbresh er al. [43] observed significant gain
bridging at COD of less than 1/4 of the gain size. The monotonic decrease in strength

during the post fracture test is caused by the loss of bridging area.

Hay et al. [35] compared the COD criterion of polycrystalline alumina (COD’s of
about 1/3 of gain size) with monolithic MgA1203 spinel. Three specimens of monolithic
MgA1203 spinel were used for postfracture testing. For the spinel, the average gain size
for small grain size specimen was 35 um, 75 pm for intermediate gain size specimen,
and 180 um for large gain size specimen. For spinel specimens, gain bridging effects
were sigrificant at COD of less than 1/9 of the gain size. Hay et al. suggested that
“Application of the COD-gain size criteria fitted to the alumina, was found to yield poor
ageement with PFT result (for spinel)...[3 5].” Further, Hay et al. stated that “...Changing
the COD-gain size ratio from 1/3 to 1/9 implies that the load transfer mechanism are less
effective in the spinel than in the alumina and that the geometric aspects of the
microstructure, namely the size, size distribution, and spatial arrangement of gains, do
not uniquely control the wake load character. Rather, there may exist a universal
geometry factor which describes the effects from these geometric components but is
independent of the material properties. The geometric description may require further
modification to account for the various material-specific contributions, such as thermal
expansion anisotropy. The much larger limiting COD (a critical COD for bridge rupture)

at the wake extreme characteristic of alumina probably results primarily from the residual

93

thermoelastic stresses, which promote a more effective load transfer for an equivalent

gain interlocking distance. [3 5]”

3.4.3.3 The effect and observation of grain bridging by Kagawa [33]

Kagawa [33] modeled gain bridging in a material for which the crack first deflects
along a grain boundary. Grain bridging follows when the deflection angle (angle between
the path of crack and crack deflection) is between arctangent of the inverse of the half
gain size and 90°. The Kagawa model assumes the crack bridging does not occur if the
angle is less than arctangent of the inverse of half grain size. To examine the gain
bridging process, a finite element method was used. The Kagawa model [33] assumes a
gain size between 50-100 pm, a Poisson’s ratio of 0.15 and gains that are either square
or hexagonal. The MENTAT—MARC computer progam solved for gain bridging under
mode I loading condition (opening mode). The applied load used was less than
maximum load required for crack propagation. Figure 3.4.3 shows the effect of the crack
deflection angles upon the crack closure stress. At a crack deflection angle of 70°, crack
closure stress gadually increased as crack separation increased since relative sliding
occurred between contacting gains as the applied loading increased. Normalized

distance (Figure 3.4.3) is the ratio of crack separation and half the grain size.

94

 

 

 

Region I Region II Region III
+——->-I‘ —~ *
~ 80° ~
Closure \
stress ’ \ ‘
O
__ 90 700

 

 

 

Normalized distance

   

\l’ = Crack deflection angle

  

3”

Figure 3.4.3. The crack closure stress behavior with increasing normalized distance
where normalized distance is the ratio of the crack separation to half of grain size.
The closure stress versus normalized distance curve shown here was generated by
an FEM program [33]. The definition of the crack deflection angle W is shown the

above.

The crack closure stress for gain bridging behavior as a function of crack separation is
divided into three regions. In the first region, the stress increases as separation increases
to normalized crack ratio of about 0.1 (crack separation/half of gain size) due to
interlocking of the gain faces. The second region shows a gadual decrease of crack
closure stress with increasing crack separation by virtue of rupture of the interlocked
gains. The third region involves a smooth increase of crack closure stress due to relative
sliding at contacted gains. Kagawa suggested that crack closure stress versus normalized
crack displacement curve indicates that the first region (involving interlocking gains) is a

major process in toughening ceramic materials via gain bridging.

Kagawa [33] also calculated that the crack closure stress is a function of gain size
using an FEM progam. The stress increased as gain size decreased. Larger elastic
deformation near gain bridging sites was observed for specimens with lower Young’s
moduli (190 and 380 GPa) compared to specimens with higher Young’s moduli (570
GPa). However, the maximum crack closure stress is not affected by Young’s modulus
(Table 3.4.4). The friction coefficient affects third region where the crack closure stress
increases with increasing crack separation, however, the coefficient of fiiction is

neglected in the first and second region.

Table 3.4.4. The effect of grain size and Young’s modulus on crack closure stress for
ceramic materials using an FEM program [33].

 

 

 

 

 

 

w=80,E=570GPa w=80,Grainsize=60um

Grain size, Maximum E, (GPa) Maximum Normalized

(um) closure stress, closure stress, crack
(MPa) (MPa) separation at
Max. Closure

stress

60 17 190 15.7 0.006

80 14.6 380 15.7 0.009

100 12.5 570 15.7 0.019

 

 

 

 

 

*w = crack deflection angle, E = Young’s modulus. The data were not obtained from
experiment but were calculated via a FEM progam [33].

In summary, Kagawa [33] suggested that gain bridging toughing is affected by gain

size, Young’s modulus, and the fiictional coefficient.

3.4.3.4. The effect and observation of grain bridging by Swanson er al. [36]

Swanson er a1. [36] investigated crack interface gain bridging as a toughening

mechanism using alumina having an average gain size of 20 pm. The crack evolution

was monitored with in-situ optical microscopy observation of mechanically loaded

tapered double cantilever beam (12 mm edge length and 2 mm thickness) specimens. In-

situ optical microscopy also followed crack evolution in disks under axial loading. The

“active sites” in back of the crack tip were examined to observe the evolution (formation

and fissure) of gain bridging. A series of six low magnification (x 100) microgaphs

showed crack bridging during crack propagation. The crack interface bridging and an

 

97

increasing number of gain bridging sites were observed. In the double cantilever

experiment, discontinuous crack gowth was observed.

To examine strength behavior using a controlled flaw test, Vickers indentation cracks
were introduced at the center of a disk specimen (25 mm diameter and 2 mm thickness).
Swanson et al. observed crack propagation from the initial loading until fracture. The
crack gowth was distinguished by a stabilized gowth without catastrophic gowth. The
fracture proceeded mainly by an interganular mode and showed also discontinuous
evolution (crack deflection and grain bridging) behind crack tip as the case for the

cantilever beam specimens.

Microcracking can be a source of resistance of crack gowth near crack tip since the
crack can be arrested by microcracks in the fi'ontal zone of cracks. However, there is no
evidence of extended frontal microcracking in front of crack tip, therefore, it was unlikely
that microcracking affected the frontal zone of the crack. The crack evolution observed
by optical microscopy, in both of the above experiments, gave evidences of gain bridging
behind the crack tip which provided a mechanism to impede fracture. Observation of the
crack evolution showed the crack gew stably and fi'actured without catastrophic crack

gowth.

3.4.3.5. The effect and observation of grain bridging by Kishimoto et al. [37]

Kishimoto et al. [37] observed crack gowth behavior for polycrystalline alumina

specimens (6 specimens for static loading test and 6 specimens for cyclic loading test)

98

having a mean gain size ranging from 1.0 pm to 19 pm in order to examine gain size

effects on gain bridging.

Compact tension specimens (50 mm x 40 mm x16 mm) were loaded in an electro-
servo-hydraulic testing machine. Crack lengths were measured by an optical microscope.
The static load ranged from 63 N to 630 N. Sinusoidal stress (stress ratio is 0.1) was used

for cyclic loading, with a loading rate 2.0 N/s.

The stress intensity factor for crack gowth was much higher in coarse gain sized
specimen (3.5 MPamm) than in fine gain sized specimen (2.3 MPamm). The stress
intensity factor showed a slight decrease just after cyclic loading because the bridging
areas were, Kishimoto et al. explained, degaded by cyclic loading. The slope of the
load-strain curve was slightly larger in coarse gain sized specimens than in fine gain
sized specimens though Young’s modulus for both specimens were the same. The
difference in load-strain slope and in the stress intensity factor can be explained by gain
bridging behind of crack tip. The gain bridging is more effective (as calculated by a
finite element method [37]) in coarse gain sized specimens than fine gain size
specimens. For a large gain size, the bridging site area through metallurgical microscope
increased to about 175 mm2 as crack length increased to 10 mm (Figure 3.4.4) while the
bridging area rarely increased as the crack length increased. The gain size effect found

by Kishimoto [37] agees with the Kagawa’s result [35].

I I I I I I # I I I I I l I I I I I

H coarse grain sized specimen

+ fine grain sized specimen

200- *-

 

100- -

Bridging area, square milimeter

 

 

 

 

o—%r.s.s.e.s.e.s.ts.
2 4 6 10
Crack length, milimeter

Figure 3.4.4. The change of bridging area for alumina specimen with increasing
crack length as calculated by a finite element method by Kishimoto et al. [37].

100

3.4.3.6. The effect and observation of grain bridging by Dauskardt [38,39]

Dauskardt [3 8,39] examined gain bridging degadation under cyclic fatigue with two
coarse gain sized alumina specimens (mean gain sizes of 8 pm and 13 um). Using a 3
mm thick compact tension specimen, testing was done by ASTM standard fatigue crack
gowth procedure (ASTM, 1989) modified for ceramics (Figure 3.4.5 [46]). The load
ratio (minimum/maximum load) was 0.1 with a frequency of 25 Hz. The crack

propagation profile and gain bridging were examined by a scanning electron microscope.

In cyclic and monotonic loading, the gain bridging appeared behind the crack tip (as
observed in SEM microgaphs). The relation of crack opening displacement to bridging
was investigated by measuring crack opening displacement under cyclic loading. The
displacement for loading and unloading displayed a hysteresis curve, a schematic of

which is shown in Figure 3.4.6.

Elastic gain bridging occurred initially during loading. Frictional bridging was
followed after the gain pullout. The fiictional sliding resistance decreased thus the
stiffness decreased. For unloading, frictional bridging appears following the elastic gain
bridging. However, the maximum crack opening displacement measured during the
loading-unloading test was about 1.4 pm which is less than about 1/4 of gain size. The
degadation of gain bridging under cyclic loading can be explained by repetitive sliding

during frictional gain bridging.

101

 

 

 

 

 

0.1 pm thick
metallic Im

 

__{ DC Potential :

 

Crack
length

 

 

Time

 

Back face strain

 

Applied K

 

 

 

.____Km;,,___-

 

    

 

Time

Compression strain

Figure 3.4.5. Experimental technique for observing crack length and stress intensity
factor where K...“ = maximum stress intensity factor, K,. = crack closure stress
intensity factor, and Km". = minimum intensity factor [48]. The specimens were

alumina with grain sizes of 8 and 13 um [38,39].

102

 

  
 
    
 
 

Elastic

bridging
Applied Load

rictional

Elastic bridging

bridging

 

 

 

Crack opening displacement

Figure 3.4.6. Hysteresis curve of applied load and crack opening displacement as
suggested by Dauskardt [38,39].

103

3.4.3.7. The effect and observation of grain bridging by Vekinnis et al. [44]

Vekinnis er al. [42] tested in double torsion 96% alumina specimens which had a
MgO-CaO-A1203 glass matrix (Coors ADS96R). The specimens were cut into 25 x 55 x
0.64 mm fiorn plates. Seven specimens with an average gain size of 7 11m were loaded

in a double-torsion jig mounted in scanning electron microscope (SEM).

The energy release rate increased from 41.7 to 77.1 J/m2 with increasing crack length.
The energy release rate saturated after cracks gew to about 8.8 mm and the saturation
value increased with increasing gain size such that the saturation value of energy release
rate was 67.5 .l/m2 for a 4.1 um gain sized specimen and 110 J/m2 for a 9.3 pm gain

sized specimen (Table 3.4.5).

Table 3.4.5. The energy release rate behavior for alumina specimens with different
grain size using double torsion testing [44].

 

 

 

 

 

 

 

 

 

Grain size, htitial energy release Saturated energy release, Crack length at
um rate, J/m2 rate J /m2 saturation, mm
4.1 34 67.5 11.2
5.6 33.5 77 10.4
6.24 32 80 10
6.6 33 81.5 8
8.43 40 98.5 8.5
9.32 57 105 7.3
9.75 53 110 7.3

 

 

 

 

The gain bridging zone length, which may be defined as the crack extension required

for the energy release rate to obtain steady state, decreased as gain size increased. For

 

104

example, a crack extension of 11.2 mm was required for 4.1 um gain sized specimen
while 7.3 mm was needed for 9.3 pm gain sized specimen. SEM observations
(magrification x 2.0 k to 4.0 k) also showed evidence of gain behind crack tip which can

exert a crack closure force.

3.4.3.8. The effect and observation of grain bridging by Braun et al. [45]

For A1203-A12Ti05 (20 volume % of AlzTiOS) composite disk specimens 30 mm in
diameter and 4 mm thick, Braun et al. [45] introduced an indentation crack at the center
of specimens (5 specimens) using a load range of 20-300 N. Fracture toughness was
investigated by observing crack gowth. The crack lengths were measured by an optical
microscope during the applied loading. Toughness increased with increasing crack length
from 1.8 MPam"2 at a crack length of 100 pm to 4.8 MPamm at a crack length of 2000
um. Scanning electron microscope (SEM) observations showed evidence of gain

interlocking bridging at crack interface during crack extension.

To observe flaw resistance for A1203-A12Ti05 specimen, Vickers indentation cracks
were introduced on a disk specimen (20 mm diameter and 3 mm thickness) and strength
was measured using a three ball point support test. Strength decreased slightly as
indentation load increased from 260 MPa (at an indentation loading 2 N ) to 200 MPa (at
an indentation loading 300 N) (Table 3.4.6). However, the toughness was insensitive to
indentation load; the fracture toughness was 2.9 MPam”2 for a 300 N indentation load

and 2.7 MPamm for 20 N indentation load.

105

Table 3.4.6. The strength behavior for cracks produced by different indentation
loads to observe flaw resistance for A1203-Al2Ti05 composite [45].

 

BdentationloadN 3 5 10 12 100 200 300 I

 

 

 

 

 

 

 

 

[Strength MP8 260 265 265 235 220 200 218 I

 

The observation of crack length as a function of applied load showed an increasing
crack resistance by gain interlocking bridging for the A1203-A12Ti05 composite. SEM
microgaphs revealed the evidence of gain bridging. In addition, indentation load-

strength behavior indicated A1203-A12Ti05 composite is a highly flaw resistant material.

3.4.3.9. The effect and observation of grain bridging by Steinbrech er al. [43]

Steinbrech er al. [43] cold isostatically pressed and then sintered alumina power (CT
8000, Alcoa, Frankfrut am Main, FRG) in air at 1700 °C. The mean gain sizes of the
alumina were 4 pm to 17 pm. Specimens were machined into single edge notched beam
specimens (SENB) of dimension 7 mm x 60 mm x 5 mm and short double cantilever
beam specimens (s-DCB) of dimension 24 mm x 12.5 mm x2 mm. For the s-DCB, the
energy release rate increased to about 103 J/m2 as the cracks extended under load (Figure
3.4.7). The initial energy release rate was less than 20 J/m2 (Figure 3.4.7). The energy
saturates when the crack opening displacement reaches about 1/4 of the gain size. If
crack opening displacement was geater than 1/4 of gain size, no further gain bridging

occurred and the energy release rate saturated.

106

120 . I r I I I

 

 

Energy releasr rate, (Joules/square meter)

 

 

o 1 I L I 1 I 1

0 1 2 3 4
Crack extension, mm

 

Figure 3.4.7. Energy release rate as crack extension increases for alumina s-DCB
alumina specimen [43]. Crack gowth was quasi-static from initial notch to
fracture.

107

For SENB specimens, Steinbrech et al. observed the crack resistance behavior as a
function of crack length (normalized crack length, crack length/width of specimen) at
different notch depths (Table 3.4.7). Initial energy release rates were independent of
initial notch depth. The slope of energy release rate versus normalized crack length
increased as the initial notch depth increased. For the smallest initial notch depth (1.54
mm), the energy release rate saturated but the other SENB specimens did not show a

saturation behavior.

Table 3.4.7 implies that energy saturation behavior is related to crack opening
displacement. The crack length, when crack opening displacements reached 1/4 of the
grain size, increased as initial notch depth increased (T able 3.4.7). Thus the energy
release rate saturated for smallest initial crack depth because crack opening displacement
reached 1/4 of gain size at about 70 percent of final fracture crack length as explained by
the above for s-DCB specimen. However, COD for rest of the SENB specimens reached
1/4 of the gain size at about 88 -100 percent of final crack length thus saturation

behavior may not occur.

Thus, Steinbrech et a1. [43] investigated gain bridging effects in alumina specimens
by measuring the energy release rates. The gain bridging effect displayed a critical crack

opening displacement at which no further gain bridging occurred.

108

Table 3.4.7. The energy release rate as a function of normalized crack length (crack
length/width of specimen) in SENB alumina specimen which had 16 um average
grain size where width of specimen was 7 mm [43].

 

 

 

 

 

 

Notch depth, Initial Initial Final F inal energy Normalized
mm normalized energy normalized release rate, crack length
crack length release rate, crack length J/m2 at COD = 4

J/m2 um

1.5 0.22 20 0.87 105 0.65

2.8 0.4 20 0.9 105 0.79

4.2 0.6 20 0.9 120 8.7

5.3 0.76 20 0.93 105 9.3

 

 

 

 

 

 

3.4.3.10. The effect and observation of grain bridging by Rodel et al. [46]

Rodel et al. [46] observed bridged crack interfaces using a scanning electron
microscope. Alumina disk-shaped specimens (100 mm in diameter and 4 mm thick disk)
were made by hot pressing fine alumina powder (Sumitomo AKP-HP gade) at 1650 °C
for 35 hours under 35 MPa. The density was geater than 99.9 % of theoretical density
and the mean gain size was 11 pm. Disk specimens were machined to form 1 mm thick

compact tension specimens.

Grain bridgings was observed along the crack trace for applied loads of 5 N to 300 N.
The measured crack opening displacement (COD) increased with crack extension fi'om
200 nm at a crack extension 190 pm to 1200 nm at crack extension 1700 um, where crack
extension defined as the change of crack length from the initial crack length. The energy

release rate indicated the existence of a bridging effect since the crack resistance

 

109

increased as the crack extension increased. The energy release rates were from 10 J/m2 at

0 crack extension and increased to 50 J/m2 for a 1700 um crack extension.

3.4.3.11. The effect and observation of grain bridging by Reichl et al. [47]

Reichl et al. [47] determined crack bridging force using polycrystalline alumina whose
mean gain size was 16 um. To measure the crack bridging force, double cantilever beam
specimens (30 mm x 25 mm x 2 mm) were modified by adding a second notch at the rear
of specimen (Figure 3.4.8). The loading-crack opening displacement (COD) curve
(Figure 3.4.8) shows that at a COD of 65 pm, the load abruptly decreases when the crack
tip meets the second rear notch. The load (Po) corresponding to an abrupt load decrease
represents the “load bearing capacity” of wake zone since no obstruction exists at the
crack tip. The maximum COD (8",) of interlocking zone and the wake zone itself are

depicted in Figure 3.4.9. The bridged zone load, P1,, is calculated from
P, = 2&6 l6," (3.4.2)
where 8 = crack opening displacement in the direction of applied load
8m = maximum crack opening displacement for the interlocking zone.
From Figure 3.4.9, bridging stress is

s, = — (3.4.3)

Sb = bridging stress

1 10
z = length of bridging zone
w = width of specimen

Length of bridging zone, 2, is related to COD (Figure 3.4.9) such that
— = —— (3.4.4)

where a = distance between the direction of applied load and the second notch tip.

If equation 3.4.3 is inserted into equation 3.4.2, we can obtain

5
S, = Hug-)2 /wa . (3.4.4)

For 12 polycrystalline alumina specimens, Reichl et al. calculated the bridging stress as

29i3 MPa.

111

 

Load, N

 

 

 

Displacement, pm

1

O

wedge

 

 

 

 

 

‘ ’ rear notch

Figure 3.4.8. Load-displacement behavior and the modified double cantilever
specimen used by Reichl to study grain bridging in alumina specimens [47].

112

 

 

Crack tip of
rear notch

 

End of bridged zone

Figure 3.4.9. The assumption of geometry near the crack tip to calculate the average
bridging stress by Reichl er al. [47].

113

3.4.5. Crack propagation behavior and grain bridging of the unreinforced
polycrystalline alumina included in this study

Using a scanning electron microscope (J EOL, J SM 6400V), crack shape and gain
bridging were observed for three polycrystalline alumina specimens that had been
quenched into deionized water as a part of this study. Each of the three specimens
viewed in the SEM underwent a total of ten thermal shock cycles at a fixed value of AT

prior to the SEM measurements.

In order to determine whether the nature of the gain bridging changes as the severity
of the thermal shock damage changes, the three specimens selected to represent relatively
low, moderate, and high values of thermal fatigue damage. For the low thermal fatigue
specimen, specimen A4-14 was selected which underwent 10 thermal shocks at a quench
-temperature difference of 270 °C. The moderate and highly damaged states were
represented by specimens A5-3 and specimen A5-5, respectively. Specimen A5-3 was
shocked for ten cycles at AT = 300 °C while specimen A5-5 was shocked for 10 cycles at
AT =320 °C. The crack length versus cumulative number of thermal shock data for A4-

14, A5-3, and A5-5 are included in section 3.3 of this thesis.

The relative positions of the SEM crack observation crack is given schematically in
Figure 3.4.10. The crack shape after thermal fatigue is shown in Figure 3.4.1] for (a)
specimen A4-14 with a quench temperature difference of 270 0C (b) specimen A5-5 with

a quench temperature difference of 320 °C. The severity of thermal fatigue damage larger

114

at AT = 320 °C than at AT = 270 °C (Figure 3.4.11) which corresponds to the crack length

measurement .

The crack propagation paths for specimen A5-5 (quench temperature difference 320
0C) were observed at a magrification of x 2500 and an accelerating voltage of 20 kV at
positions (a) behind crack tip and (b) near the center of the radial crack (Figure 3.4.12).
Both crack propagation paths show that cracks gew in a transganular mode and there is
no evidence of gain bridging sites along the surface trace of the crack. Grain bridging
does appear behind the crack tip for the specimen quenched at (a) AT = 270 °C and near

the crack tip for the specimen quenched at (b) AT = 300 °C (Figure 3.4.13).

Grain bridging can be a source of crack gowth resistance. However, the gain
bridging sites were not observed in other areas of these two specimens. Thus, it appears
that the gain bridging rarely affects crack propagation under cyclic thermal shock testing

for the alumina specimens included in this study.

115

 

 

(b)

1
T

 

 

(d)

(C)

Figure 3.4.10. The position of SEM observation for unreinforced polycrystalline
alumina specimen after ten ”thermal quenching (a) AT = 320 °C behind the crack tip
(b) AT = 320 °C at the middle of the radial crack (c) AT = 270 °C around the crack
tip ((1) AT = 300 °C behind the crack tip.

“6

c

, ,
1 1 4s
. 199Pm, F2 L81
JEOL UZBKU X1§@,33mm

(b)

 

Figure 3.4.11. Crack propagation shape for polycrystalline alumina specimen after
10 quenched thermal shock at (a) AT =270 (b) AT = 320.

117

._| E l:l L .3 E1 11 'J '.>=I 3 - - . 3 E: In in

JEDL EBKU

 

Figure 3.4.12. The micrograph of crack path for polycrystalline alumina specimen
after 10 quenched thermal shock at AT = 320 °C (a) behind the crack tip (b) at
middle of the radial crack.

118

 

Figure 3.4.13. The micrograph of bridging site for polycrystalline alumina
specimens after 10 quenched thermal shock. (a) AT = 270 °C around the crack tip
(b) AT = 300 °C behind the crack tip.

119

3.4.6. Grain bridging related to thermal shock for unreinforced alumina

For mechanical loading of ceramics, gain bridging contributes to crack propagation
resistance. Vekinnis et al. [44] measured the energy release rate for 96 % alumina
specimens and showed that the energy release rate increased to about 200 % of the initial
energy release rate. The increase in toughness for unreinforced alumina with increasing
crack length was explained by gain bridging [44].

To evaluate the gain bridging process, a finite element method was used by Kagawa
[33]. The calculated crack closure stress reached 17 MPa for ceramic materials using a
FEM progam. Grain bridging sites also were observed behind the crack tip in
unreinforced alumina specimen via scanning electron microscopy under mechanical
loading by Lathabai [34] and Hay er al. [35].

Grain bridging can be degaded by repeated loading and unloading. Interfacial friction
during cyclic loading degades the toughness of polycrystalline alumina by fracturing the
bridging sites. Kishimoto [37] observed a decrease in fracture toughness, 0.4 MPam"2
immediately after cyclic loading indicating that gain bridging effect decreases under
cyclic loading.

Therefore, the gain bridging is an mechanism for energy dissipation during crack
gowth in unreinforced alumina under mechanical loading.

However, the gain bridging was relatively limited under thermal loading for
unreinforced alumina specimen included in this study. Thus the gain bridging may not

account for the saturation in the thermal fatigue crack length observation in this study.

120

One difference between thermal loading performed in this study and mechanical
loading done by other researchers is the duration time of loading. Lee [30] calculated
time dependent thermal stress. The thermal surface stress increases rapidly to a
maximum stress then decreases slowly while the stress-time behavior is symmetrical in
mechanical loading (Figure 3.4.14). The time required for maximum stress was
calculated as 11 milliseconds for a water quench of alumina [30]. The maximum
mechanical loading time is usually much larger than 10 milliseconds; for example 1000
milliseconds [34,37]. However, the loading time for mechanical loading with a frequency
of 100 Hz [37] is similar (10 milliseconds) to thermal loading. The other difference
related to loading time is that the slope of stress-time curve (do/dt) is much larger in

thermal loading than mechanical loading (Figure 3.4.14).

121

 

Stress

 

Thermal loading

 

Stress

 

 

 

 

Time

Figure 3.4.14. The schematic diagram of the comparison of stress-time behavior for
the mechanical loading and thermal loading [30]

122

Under thermal shock testing, the thermal fatigue damage of material properties (for
example, crack length [32], strength [27], crack number density [25] and elastic modulus
[IO-12]) saturated as the number of thermal cycles increases. The release of elastic
energy is a driving force and the surface fracture energy exerts the retarding force during
crack propagation. When the energy is balanced, the crack gowth is stopped. At a
specific quench temperature difference, the crack gows to a specific value and then crack
length saturates; for example a saturated normalized crack length was 1.14 at AT = 250
°C and a saturated normalized crack length was 2.25 at AT = 320 °C in this study. After
damage saturation occurs, the fracture surface energy may be a barrier for crack gowth.

The spatial distribution through the thickness of the specimen for thermal stress is
given in Figure 3.4.15. The stress distribution results from the temperature gadient
through the specimen thickness. The surface of specimen is in tension and the stress
decreases rapidly from the surface toward the center of specimen (Figure 3.4.15). On the
other hand, the stress distribution in mechanical bend loading is linear through the
specimen thickness (Figure 3.4.15). The slope (do/dy) is much steeper for thermal
loading than for mechanical loading thus the severity of damage on the surface of the

specimen is geater in thermal loading than in mechanical loading.

123

Tension )1 Compression

 

 

 

 

 

 

 

 

 

Surface
\
—>
0 x
/
Surface
(a) Thermal loading
Tension )1 Compression
Surface
+
o x
Surface
(b) Bend test

Figure 3.4.15. The profile of stress distribution for thermal loading and bend test.
The slope (do/dy) is much stiffer in thermal loading than in bend test.

124

The scatter of rate constant in measuring Vickers indentation cracks, b, is larger than
in measuring Young’s modulus, or (Table 3.3.3) which can be explained by following
relationship [1 1]

E = E0[1—fs] (3.3.6)
where E = Young’s modulus
E0 = Young’s modulus of crack free material
a = crack damage parameter
f = a relative weak function of the material’s Poisson’s ratio.
The crack damage parameter for a circular crack is defined as [49]
a = N < c3 > (3.3.7)
where N = number of cracks
<c> = average crack length.
Therefore, Young modulus is proportional to <c3> and represents an average over the
range of crack sizes. Vickers indentation crack measurements represents a single pair of
cracks, not an entire distribution of cracks. Thus, using Vickers indentation crack
measurements to determine the rate constants, b, for crack gowth will result in more
scatter than that observed for the rate constant, a, for the Young’s modulus measurement

data (Table 3.3.3).

4. Summary and Conclusion

4.1. Slow crack growth after initial indentation before commencing thermal shock
A minor amount of slow crack gowth was observed for polycrystalline alumina after

initial indentation before thermal shock. The relative change in the mean crack length

(emu/co, see section 3.1) was 1.024 to 1.130. Within 30 minutes, the crack gowth

saturated.

4.2. Crack gowth behavior in room temperature and 80 °C water in the absence of
thermal shock

Water can potentially cause crack extension via an environmentally-assistanted slow
crack gowth process. Slow crack gowth behavior was observed in room temperature
deionized water and in 80 °C deionized water. For the two polycrystalline alumina
specimens tested, however, the crack extensions in the water were not sigtificant since
the change of crack length was less than 1 percent in each case. Thus, in this study, the

deionized water likely did not sigrificantly affect crack gowth during thermal shock test.

4.3. Thermal fatigue behavior unreinforced polycrystalline alumina

Thermal shock damage for unreinforced alumina specimens was investigated by
measuring the crack length change. Two goups of polycrystalline alumina specimens
were used for thermal fatigue testing. For one set, thermal fatigue tests were done for 10
cumulative quenching cycles with a quench temperature difference range of 250 to 330

°C. For the other set, 20 cumulative thermal shocks were done for polycrystalline

125

126

alumina specimens with a quench temperature difference ranging from 250 °C to 305 °C.
The cracks gew to 115 percent to 227 percent of initial crack length for the specimens
quenched a total of 10 cycles and 115 percent to 230 percent of the initial crack for the
specimens quenched a total of 20 cycles.

The crack lengths were fitted via a least-squares procedure(see section 3.3.1 and
3.3.2). The rate constants obtained fiom the least-squares fit of thermal shock data to
equation 3.3.1, were a function of quench temperature difference. The rate constant
increased as the quench temperature increased. Lee et al.’s [12] and Ash’s [32] rate
constants behavior showed similar trends. However, the correlation coefficients of this
study and Ash’s [32] were very poor but the correlation coefficients for Lee et al.’s data
were much better. The difference in the relative scatter of the data may be related to the
fact that for Lee et al.’s study, the thermal shock damage assessed by measuring Young’s
modulus which is sensitive to the ensemble average of crack length. In contrast, for this
study and Ash’s work, the thermal fatigue damage was assessed in terms of a single
system of Vickers indentation cracks.

The severity of thermal fatigue damage is a function of quench temperature difference,
as measured by the saturation crack length. The normalized saturation crack lengths
(crack length/initial crack length) were linear regessed using a PLOT IT progam. The
slope was 0.019/°C for 10 quenched specimen and 0.020/°C for 20 quenched specimen.
Ash’s data [32] showed a good ageement ( 0.017/°C) with the slopes obtained in this

study.

127

4.4. Grain bridging in the brittle materials

The major toughening mechanism in monophase ceramic material such as alumina is
gain bridging [31-45]. Grain bridging is observed behind of crack tip [31-3 5].
Interlocking of separating interface at the bridging is a source of a crack resistance force.
Grain bridging is more effective for coarse gained material than for fine gained
materials [33,37]. Crack opening displacement also is related to gain bridging showed
that gain bridging may occur when the crack opening displacement is less than 1/3 [3 5]
or 1/4 [43] of gain size of specimen. Evidence of gain bridging is examined through
scanning electron microscope observations behind the crack tip [34, 36,37, 41].

In this study, SEM observations of crack gowth and gain bridging for three
unreinforced polycrystalline alumina specimens which had been subjected to a total of 10
f thermal shock cycles for quench temperature differences of 270, 300, and 320 °C. Grain
bridging appeared at 1 or 2 sites for specimens quenched at 270 °C and 300 °C. However,
gain bridging was not observed in other areas of specimens. Thus, the gain bridging

may not account for the crack saturation of crack length under thermal fatigue testing.

5. Appendices
Appendix A. The dimension and label of all specimens

The following tables list the dimension and label of all specimens used in this study.
The positions of the Vickers indentations (see Figure 2.3.1) are given under the column
labeled “Position.” For thermal shock testing, the temperature difference, AT, and
maximum number of quenching cycles, Amax are included. All dimensions were
measured by vernier caliper (Mitutoyo).

Table A The dimensions and label for all polycrystalline alumina specimens as
measured byvernier caliper.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Label AT, °C Position Nmax Width, mm Length, mm Thickness, mm
Al-ll * m * 10.15 9.94 1.02
A1-1 3 * m * 14.06 9.93 0.99
A1-14 * m * 10.09 9.96 1.01
A2-8e * e * 10.04 9.95 1.0
A2-8m * m "‘ 10.04 9.95 1.0
A2-9e * e * 10.30 9.96 1.04
A2-9m * m * 10.30 9.96 1.04
Bl-3 * m * 9.91 9.89 0.94
B1-4 * m * 10.36 9.98 0.96
A4-1 3 250 m 10 10.34 10.02 1.03
A4-14 270 m 10 10.06 10.38 1.01
A4-15 . 290 m 10 9.99 9.93 1.01
A6-2 295 m 10 9.87 9.95 1.00 .
A5-3 300 m 10 9.95 9.99 1.01
A5-12 305 m 10 10.07 10.07 0.98
A5-4 310 m 10 10.0 10.45 1.02
A5-ll 315 m 10 10.05 10.25 0.99
A5-5 320 m 10 10.05 9.95 0.96
A5-8 325 m 10 10.14 9.97 1.01
A5-7 330 m 10 9.94 10.11 1.03
A6-3 250 m 20 9.95 10.40 1.04
A6-4 270 m 20 13.95 9.95 1.01
Bl-5 290 m 20 10.33 9.91 1.01
A5-10 295 m 20 9.95 10.05 0.90
A5-14 300 m 20 9.94 10.0 0.94
A6-1 305 m 20 9.95 9.90 0.92

 

 

 

 

 

 

 

128

 

129

Appendix B. The result of slow crack gowth testing after initial indentation but
before commencing thermal shock

Following tables are the crack lengths as time elapsed after initial indention crack. The
mean crack lengths were calculated by the average of x-directional and y-directional
crack lengths. The relative crack lengths are also given by dividing initial crack length.
Table B shows the crack length saturated in 30 minutes.

A

Table B-1. The crack lengths and elapsed time to examine the slow crack growth
after introduc'gg Vickers indentation crack for alumina specimen(specimen Al-l 1).

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Time x-dir. crack y- dir. crack A/ 234.2 B/231.3 mean crack C/232.8
minutes length (um), length (urn), length(um),
A B C
2 234.2 231.3 1 1 232.8 1
7 243.7 231.6 1.041 1.001 237.7 1.021
10 244.6 232.6 1.044 1.006 238.6 1.025
13 244.8 232.5 1.045 1.005 238.7 1.025
37 244.1 231.9 1.042 1.003 238.0 1.023
64 244.3 232.1 1.043 1.003 238.2 1.023
96 244.8 232.4 1.045 1.005 238.6 1.025
1320 244.3 231.7 1.043 1.002 238.0 1.023
1357 244.5 231.2 1.044 1.000 237.9 1.022
1474 244.5 232.0 1.044 1.003 238.3 1.024

 

 

130

Table B-2. The crack lengths and elapsed time to examine the slow crack growth

after introducingVickers indentation crack for alumina (specimen Al-l3).

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Time x-dir. crack y- dir. crack A/ B/225. mean crack C/211.0
minutes length (um), length (um), 197.0 0 lengthmm).
A B C
1 197.0 225.0 1 1 211.0 1
3 203.3 228.5 1.032 1.016 215.9 1.023
5 211.5 229.2 1.074 1.019 220.3 1.044
14 209.7 239.2 1.064 1.063 224.5 1.064
21 209.0 241.3 1.061 1.072 225.2 1.067
26 211.5 241.6 1.074 1.074 226.6 1.074
38 213.5 240.7 1.084 1.070 227.1 1.076
68 212.3 241.2 1.078 1.072 226.8 1.075
837 214.0 239.8 1.086 1.066 226.9 1.075
1 178 213.7 240.2 1.085 1.068 227.0 1.076
1386 213.5 240.9 1.084 1.071 227.2 1.077

 

Table B-3. The crack lengths and elapsed time to examine the slow crack growth
after introducing Vickers indentation crack for alumina specimen (specimen Al-l4).

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Time x-dir. crack y- dir. crack A/ 180.1 B/216.1 mean crack C/198.1
minutes length (um), length (um), length(um),
A B C
1 180.1 216.1 1 1 198.1 1

4 184.4 222.8 1.024 1.031 203.6 1.028
8 186.8 221.6 1.037 1.025 204.2 1.031
13 202.6 221.8 1.125 1.026 212.2 1.071
20 207.2 220.3 1.150 1.019 213.8 1.079
28 208.7 225.6 1.159 1.044 217.2 1.096
35 222.2 224.3 1.234 1.038 223.3 1.127
50 223.1 225.1 1.238 1.042 224.1 1.131
537 223.3 224.7 1.240 1.040 224.0 1.131
660 223.6 224.5 1.242 1.039 224.1 1.131
1294 222.7 225.1 1.237 1.042 223.9 1 . 130
1495 223.0 224.8 1.238 1.040 223.9 1.130

 

 

 

 

 

 

 

 

 

131

Table B4. The crack lengths and elapsed time to examine the slow crack growth
after introducing Vickers indentation crack for alumina specimen (specimen A2-8e),'
where “e” means the edge of specimen.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Time x-dir. crack y- dir. crack A/ 232.3 B/227.9 mean crack C/230.1
minutes length (um), length (um), lengthmm),
A B C
2 232.3 227.9 1 1 230.1 1
12 235.3 229.9 1.013 1.009 232.6 1.011
22 240.0 231.6 1.033 1.016 235.8 1.025
29 239.9 230.9 1.033 1.013 235.4 1.023
37 242.4 231.2 1.043 1.014 236.8 1.029
84 241.5 231.5 1.040 1.016 236.5 1.028
143 243.2 231.6 1.047 1.016 237.4 1.032
201 243.6 231.4 1.049 1.015 237.5 1.032
359 243.1 230.9 1.046 1.013 237.0 1.030
514 243.3 231.2 1.047 1.015 237.3 1.031
1220 242.7 231.6 1.045 1.016 237.2 1.031
1424 243.4 230.9 1.048 1.013 237.2 1.031

 

 

 

Table B-5. The crack lengths and elapsed time to examine the slow crack growth
after introducing Vickers indentation crack for alumina specimen (specimen A2-
8m), where “m” means the middle of specimen.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Tlme x-dir. crack y- dir. crack A/ 206.3 B/228.9 mean crack C/217.6
minutes length (um), length (um), 1ength(p.m),
A B C
1 206.3 228.9 1 1 217.6 1
1 1 206.5 230.9 1.001 1.009 218.7 1.005
22 207.7 232.1 1.007 1.014 219.9 1.011
27 208.6 232.8 1.011 1.017 220.7 1.014
34 212.2 233.0 1.029 1.018 222.6 1.023
82 217.9 232.7 1.056 1.017 225.3 1.035
141 218.7 232.2 1.060 1.014 225.5 1.036
199 218.6 232.8 1.060 1.017 225.7 1.037
358 218.4 232.4 1.059 1.015 225.4 1.036
513 218.2 232.7 1.058 1.017 225.5 1.036
1328 218.5 232.2 1.060 1.014 225.4 1.036
1482 218.1 232.1 1.057 1.014 225.1 1.034

 

 

 

 

 

 

 

132

Table M. The crack lengths and elapsed time to examine the slow crack growth
after introducing Vickers indentation crack for alumina specimen (specimen A2-9e),
where “e” means the ed e of specimen.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Time x-dir. crack y- dir. crack A/ 245.7 B/210.1 mean crack C/227.9
minutes length (m). length (urn). length(m).
A B C
2 245.7 210.1 1 1 227.9 1
9 250.0 218.8 1.018 1.041 234.4 1.029
13 251.2 220.2 1.022 1.048 235.7 1.034
18 259.0 221.2 1.054 1.053 240.1 1.054
23 259.9 220.6 1.058 1.050 240.3 1.054
27 260.5 220.5 1.060 1.050 240.5 1.055
31 259.4 220.2 1.056 1.048 239.8 1.052
43 258.7 221.3 1.053 1.053 240.0 1.053
202 259.6 221.5 1.057 1.054 240.6 1.056
357 260.1 221.7 1.058 1.055 240.9 1.057
1053 259.2 220.9 1.055 1.051 240.1 1.053
1264 259.7 221.2 1.057 1.053 240.5 1.055
1436 259.6 221.5 1.057 1.054 240.6 1.056

 

Table B-7. The crack lengths and elapsed time to examine the slow crack growth
after introducing Vickers indentation crack for alumina specimen (specimen A2-
9m), where “m” means the middle of specimen.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Tune x-dir. crack y- dir. crack A/ 214.9 B/179.7 mean crack C/ 197.3
minutes length (um), length (um), length(um),
A B C

1 214.9 179.7 1 1 197.3 1.000
8 215.0 180.6 1.000 1.005 197.8 1.003
12 217.4 181.2 1.012 1.008 199.3 1.010
18 219.2 181.5 1.020 1.010 200.4 1.016
22 219.0 184.5 1.019 1.027 201.8 1.023
26 219.4 189.5 1.021 1.055 204.5 1.037
42 218.7 188.2 1.018 1.047 203.5 1.031
202 218.9 189.0 1.019 1.052 204.0 1.034
356 219.2 189.1 1.020 1.052 204.2 1.034
1052 219.5 188.7 1.021 1.050 204.1 1.035
1263 219.1 189.0 1.020 1.052 204.1 1.034
1435 218.8 189.6 1.018 1.055 204.2 1.035

 

 

 

 

 

 

 

 

 

133

Appendix C. Crack length versus time for Vickers indented specimens immersed in
the room temperature deionized water and in 80 “C deionized water. The specimens
were not subjected to thermal shock.

Following tables give crack length versus time for an indented and aged specimen

immersed in deionized water. Table 01 shows the crack length with elapsed time in

room temperature deionized water. Table C-l is the crack length with water temperature

at each testing. The mean values are the average of the crack lengths in the x-direction

length and in the y-direction.

Table C-l. Crack length versus time for Vickers indentation immersed in room

temperature deionized water (specimen Bl-3).

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Time x-dir. y-dil'. mean A/235.4 B/242.2 C/238.9
(hours) (pm), A M). B WLC

0 235.4 242.4 238.9 1 1 1

1 233.6 238.4 236.0 0.992 0.983 0.988
2 234.7 239.6 237.2 0.997 0.988 0.993
3 233.9 238.5 236.2 0.994 0.984 0.989
4 234.2 241.1 236.0 0.995 0.995 0.995
6 233.6 238.4 237.2 0.992 0.983 0.988
17 234.6 240.7 236.7 0.997 0.993 0.995
20 234.2 240.2 236.6 0.995 0.991 0.993
33 233.7 239.6 237.7 0.993 0.988 0.991
45 234.1 241.2 237.7 0.994 0.995 0.995
49 234.2 239.0 23 7.7 0.995 0.986 0.990
75 233.8 240.9 237.4 0.993 0.994 0.994
92 234.0 240.1 237.1 0.994 0.991 0.992

 

 

134

Table C-2 is the crack length in 80 0C deionized water at each testing. The mean

values are the average of the crack lengths in the x-direction and in the y-direction length.

Table C-2. The crack length versus elapsed time in the hot water (~ 80 °C). The
specimen held in 80 °C for 2 hours at each times (see section 2.5, specimen Bl-4).

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Times Temp. X-dll’. y-dir. mean A/234.1 B/237.3 C/235.7
(° C) (1M). A (tun). 3 (Wu), C

0 234.1 237.3 235.7 1 1 1

1 81 231.0 235.5 233.3 0.987 0.992 0.990
2 76 233.4 236.6 235.0 0.997 0.997 0.997
3 84 233.2 235.9 234.6 0.996 0.994 0.995
4 81 233.0 236.4 234.7 0.995 0.996 0.996
5 82 233.5 237.1 235.3 0.997 0.999 0.998
6 79 232.9 236.6 234.8 0.995 0.997 0.996
7 82 233.1 237 235.1 0.996 0.999 0.997
8 83 233 236.7 234.9 0.995 0.997 0.996
9 81 233.4 236.5 235.0 0.997 0.997 0.997

 

 

135

Appendix D. The thermal shock data
Following tables are all data of thermal shock test for a total of 10 thermal cycles and a
total of 20 quenched specimen using an optical microscope (see section 2.6.)

Table D-l. The crack length after cyclic thermal shock test which maximum cycling
number is 10 (specimen A4-13 AT = 250 °C).

 

 

 

 

 

 

 

 

 

 

 

 

 

# of x-direction y-direction A/233.3 A/255.3 (A+B)/2 C/244.3

Quench Mm) Bum!) (00.x) (96y) Mum!) (COM)
0 233.3 255.3 1 1 244.3 1

1 238.7 260.6 1.023 1.020 249.6 1.021

2 235.4 277.3 1.009 1.086 256.3 1.049

3 241.9 287.7 1.036 1.126 264.8 1.083

4 244.7 289.6 1.048 1.134 267.1 1.093

5 244.1 292.0 1.046 1.143 268.0 1.097

6 246.1 292.6 1.054 1.146 269.3 1.102

7 246.6 291.9 1.057 1.143 269.2 1.102

8 248.8 293.9 1.066 1.151 271.3 1.110

9 247.8 295.5 1.062 1.157 271.6 1.112

10 247.8 296.9 1.062 1.162 272.3 1.114

 

 

 

 

 

 

 

Table D-2. The crack length after cyclic thermal shock test which maximum cycling
number is 10 (specimen A4-14 AT = 270 0C)

 

 

 

 

 

 

 

 

 

 

 

 

 

# of x- y-direction A/252.6 A/260.4 (A+B)/2 C/256.5
Quench direction Bourn) (90.x) (Cay) M(1Lm) (em)
A011“)
0 252.6 260.4 1 1 256.5 1
1 263.7 262.1 1.043 1.006 262.9 1.024
2 260.1 261.4 1.029 1.003 260.7 1.016
3 275.1 275.6 1.089 1.058 275.3 1.073
4 273.1 277.6 1.081 1.066 275.3 1.073
5 273.7 288.6 1.083 1.108 281.1 1.096
6 275.9 293.9 1.092 1.128 284.9 1.110
7 278.3 299.8 1.101 1.151 289.0 1.126
8 279.3 299.9 1.105 1.151 289.6 1.129
9 280.4 304.1 1.110 1.167 292.2 1.139
10 279.8 306.4 1.107 1.176 293.1 1.142

 

 

 

 

 

 

 

 

 

136

Table D-3. The crack length after cyclic thermal shock test which maximum cycling
number is 10 (specimen A4-15 AT = 290 0C).

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

# of x- y—direction A/255.1 A/253.5 (A+B)/2 C/254.3
Quench direction B(um) (00.x) (90y) MGM) (Cm)
A0111!)

0 255.1 253.5 1 1 254.3 1
1 257.5 268.8 1.009 1.060 263.1 1.034
2 258.2 266.9 1.012 1.052 262.5 1.032
3 260.5 268.7 1.021 1.059 264.6 1.040
4 264.5 269.4 1.036 1.062 266.9 1.049
5 268.9 273.9 1.054 1.080 271.4 1.067
6 269.3 273.0 1.055 1.076 271.1 1.066
7 278.5 283.0 1.091 1.116 280.7 1.104
8 278.3 283.4 1.090 1.117 280.8 1.104
9 279.9 284.0 1.097 1.120 281.9 1.108
10 282.4 286.9 1.107 1.131 284.6 1.119

 

Table D4. The crack length after cyclic thermal shock test which maximum cycling
number is 10 (specimen A6-2 AT = 295 °C).

 

 

 

 

 

 

 

 

 

 

 

 

 

# of x- y-direction A/250.3 A/252.5 (A+B)/2 C/251.4
Quench direction B(11m) (co,x) (coy) M(11m) (COM)
AW)

0 250.3 252.5 1 1 251.4 1
1 363.1 331.3 1.450 1.312 347.2 1.381
2 400.3 342.0 1.599 1.354 371.1 1.476
3 433.9 360.6 1.733 1.428 397.2 1.580
4 437.1 394.0 1.746 1.560 415.5 1.652
5 438.1 477.2 1.750 1.889 457.6 1.820
6 498.7 488.5 1.992 1.934 493.6 1.963
7 516.7 502.2 2.064 1.988 509.4 2.026
8 516.3 505.7 2.062 2.002 511.0 2.032
9 520.4 500.7 2.079 1.982 510.5 2.030
10 524.4 503.1 2.095 1.992 513.7 2.043

 

 

 

 

 

 

 

 

 

137

Table D-S. The crack length after cyclic thermal shock test which maximum cycling
number is 10 (specimen A5-3 AT = 300 °C).

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

# of x- y—direction A/267.1 A/243.7 (A+B)/2 C/255.4
Quench direction Bum) (00.x) (00y) Mom) (00M)
AW)

0 267.1 243.7 1 1 255.4 1
1 294.3 326.2 1.101 1.338 310.2 1.214
2 298.4 327.9 1.117 1.345 313.1 1.226
3 295.0 332.7 1.104 1.365 313.8 1.228
4 300.5 330.2 1.125 1.354 315.3 1.234
5 305.3 332.0 1.143 1.362 318.6 1.247
6 309.4 339.8 1.158 1.394 324.6 1.270
7 308.5 344.6 1.154 1.414 326.5 1.278
8 309.5 344.9 1.158 1.415 327.2 1.281
9 308.1 348.4 1.153 1.429 328.2 1.285
10 308.3 346.6 1 . 154 1.422 327.4 1.282

 

Table M. The crack length after cyclic thermal shock test which maximum cycling
number is 10 (specimen A5-12 AT = 305 °C).

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

# of x- y-direction A/249.6 A/235 (A+B)/2 C/242.3
Quench direction Bmm) (00.x) (Cay) Mom) (co...)
Auun)
0 249.6 235.0 1 1 242.3 1
1 264.0 263.0 1.057 1.119 263.5 1.087
2 296.2 288.9 1.186 1.229 292.5 1.207
3 389.2 355.0 1.559 1.510 372.1 1.535
4 502.0 432.1 2.01 1 1.838 467.0 1.927
5 544.3 436.6 2.180 1.857 490.4 2.024
6 566.9 449.2 2.271 1.91 1 508.0 2.096
7 571.1 447.9 2.288 1.905 509.5 2.102
8 584.6 457.2 2.342 1.945 520.9 2.149
9 591.2 481.5 2.368 2.048 536.3 2.213
10 589.1 485.2 2.360 2.064 537.1 2.216

 

 

 

138

Table D7. The crack length after cyclic thermal shock test which maximum cycling
number is 10 (specimen A5-4 AT = 310 °C).

 

 

 

 

 

 

 

 

 

 

 

 

 

# of x- y-direction A/242.7 A7260.8 (A+B)/2 C/251.7
Quench direction B(um) (00.x) (Cay) M(um) (60M)
AGED)
0 242.7 260.8 1 1 251.7 1
1 349.6 343.2 1.440 1.315 346.4 1.375
2 364.1 361.0 1.500 1.384 362.5 1.439
3 367.6 363.6 1.514 1.394 365.6 1.451
4 370.0 364.4 1.524 1.397 367.2 1.458
5 374.4 379.1 1.542 1.453 376.7 1.496
6 378.2 389.0 1.558 1.491 383.6 1.523
7 379.6 387.8 1.564 1.486 383.7 1.523
8 377.2 390.9 1.554 1.498 384.0 1.525
9 379.0 391.4 1.561 1.500 385.2 1.529
10 379.0 395.1 1.561 1.514 387.0 1.537

 

 

 

 

 

 

 

Table D-8. The crack length after cyclic thermal shock test which maximum cycling
number is 10 (specimen A5-ll AT = 315 °C).

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

# of x- y-direction A/246.9. A/241.7 (A+B)/2 C/244.3
Quench direction Bum) (co.x) (co.y) Mm!!!) (coM)
A(11m)

0 246.9 241.7 1 1 244.3 1
1 389.8 315.5 1.578 1.305 352.6 1.443
2 519.8 394.4 2.105 1.631 457.1 1.871
3 527.2 457.3 2.135 1.892 492.2 2.014
4 553.0 458.0 2.239 1.894 505.5 2.069
5 581.8 469.5 2.356 1.942 525.6 2.151
6 590.2 464.6 2.390 1.922 527.4 2.158
7 595.6 470.0 2.412 1.944 532.8 2.180
8 597.9 472.0 2.421 1.952 534.9 2.189
9 600.7 471.3 2.432 1.949 536 2.194
10 607.7 469.0 2.461 1.940 538.3 2.203

 

 

 

139

Table D-9. The crack length after cyclic thermal shock test which maximum cycling
number is 10 (specimen AS-S AT = 320 °C).

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

# of x- y—direction A/261.9 A/260.3 (A+B)/2 C/261.1
Quench direction B(p.m) (co,x) (coy) M(um) (0011)
AOL!!!)

0 261.9 260.3 1 1 261.1 1
1 341.4 309.7 1.303 1.189 325.0 1.246
2 373.9 354.4 1.427 1.361 364.1 1.394
3 475.9 479.8 1.817 1.843 477.8 1.830
4 511.1 520.9 1.951 2.001 516.0 1.976
5 513.1 538.0 1.959 2.066 525.5 2.012
6 525.2 554.3 2.005 2.129 539.7 2.067
7 564.9 580.4 2.156 2.229 572.6 2.193
8 575.1 589.1 2.195 2.263 582.1 2.229
9 580.3 597.8 2.215 2.296 589.0 2.256
10 578.9 596.3 2.210 2.290 587.6 2.250

 

Table D-10. The crack length after cyclic thermal shock test which maximum

cycling number is 10 (specimen A5-8 AT = 325 °C).

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

# of x- y-direction A/249.3 A/245.4 (A+B)/2 C/247.3
Quench direction B(um) (coy) (co,y) M(p.m) (00M)
Amt“)
0 249.3 245.4 1 1 247.3 1
1 313.7 359.1 1.258 1.463 336.4 1.359
2 342.3 367.5 1.373 1.497 354.9 1.434
3 355.1 395.1 1.424 1.610 375.1 1.516
4 440.1 461.8 1.765 1.881 450.9 1.822
5 481.3 499.8 1.930 2.036 490.5 1.982
6 487.5 496.7 1.955 2.024 492.1 1.989
7 504.4 504.1 2.023 2.054 504.2 2.038
8 514.5 530.2 2.063 2.160 522.3 2.111
9 517.4 569.8 2.075 2.321 543.6 2.197
10 541.9 580.6 2.173 2.365 561.2 2.268

 

 

 

140

Table D-ll. The crack length after cyclic thermal shock test which maximum

cycling number is 3 (specimen A5-7 AT = 330 °C).

 

 

 

 

 

 

 

# of x- y—direction A/235.9 A/234.4 (A+B)/2 C/235.1
Quench direction B(um) (cog) (coy) M(um) (00M)
Alum}

0 235.9 234.4 1 1 235.1 1
1 424.3 326.7 1.798 1.393 375.5 1.597
2 598.2 409.6 2.535 1.747 503.9 2.143
3 609.8 442.6 2.584 1.888 526.2 2.238
4 i #

 

 

 

 

 

 

 

* After fourth thermal shock, the crack grew to the edge of specimen. Thus further crack
length measurements would not have been meaningful.

 

141

Table D-12. The crack length after cyclic thermal shock test which maximum
cycling number is 20 (specimen A6-3 AT = 250 0C).

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

# of x- y-direction A/235.0 A/226.4 (A+B)/2 C/230.7
Quench direction BUM) (00.x) (my) Mom) (00M)
AOL!!!)

0 235.0 226.4 1 1 230.7 1
1 248.6 256.9 1.058 1.136 252.7 1.095
2 255.2 261.7 1.086 1.156 258.4 1.120
3 262.9 266.1 1.118 1.175 264.5 1.146
4 261.4 268.1 1.112 1.184 264.7 1.147
5 260.9 265.2 1.110 1.171 263.0 1.140
6 263.5 267.4 1.121 1.181 265.4 1.150
7 262.4 265.5 1.116 1.172 263.9 1.144
8 260.6 267.5 1.108 1.181 264.0 1.144
9 262.6 264.7 1.117 1.169 263.6 1.142
10 264.1 264.9 1.123 1.170 264.5 1.146
11 260.8 267.7 1.109 1.182 264.2 1.145
12 261.5 264.6 1.112 1.168 263.0 1.140
13 261.0 268.1 1.110 1.184 264.5 1.146
14 262.9 267.5 1.118 1.181 265.2 1.149
15 260.1 267.6 1.106 1.181 263.8 1.143
16 262.3 264.3 1.116 1.167 263.3 1.141
17 260.8 267.9 1.109 1.183 264.3 1.145
18 262.9 267.7 1.118 1.182 265.3 1.149
19 261.2 267.2 1.111 1.180 264.2 1.145
20 262.4 267.9 1.116 1.183 265.1 1.149

 

 

 

 

 

 

 

 

142

Table D-l3. The crack length after cyclic thermal shock test which maximum
cycling number is 10 (specimen A6-4 AT = 270 °C).

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

# of x- y-direction A/248.1 A/251.4 (A+B)/2 C/249.7
Quench direction B(p.m) (co,x) (00”!) M(um) (06.14)
AM)

0 248.1 251.4 1 1 249.7 1
1 282.8 331.8 1.139 1.319 307.3 1.230
2 297.1 347.8 1.197 1.383 322.4 1.291
3 301.9 350.5 1.216 1.394 326.2 1.306
4 301.3 357.6 1.214 1.422 329.4 1.319
5 299.2 359.4 1.205 1.429 329.3 1.318
6 303.2 358.2 1.222 1.424 330.7 1.324
7 302.7 360.2 1.220 1.432 331.4 1.327
8 301.9 362.2 1.216 1.440 332.0 1.329
9 299.4 362.1 1.206 1.440 330.7 1.324
10 302.5 360.2 1.219 1.432 331.3 1.326

 

After quench 11, the specimen fell into the bottom of water bath then the crack length of

y-direction grew to edge of specimen.

 

143

Table D-l4. The crack length after cyclic thermal shock test which maximum
cycling number is 20 (specimen Bl-S AT = 290 °C).

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

# of x- y-direction A/234.1 A/221.1 (A+B)/2 C/227.6
Quench direction B(11m) (00,.) (coy) M(um) (06M)
AW)

0 234.1 221.1 1 1 227.6 1
1 408.3 345.9 1.744 1.564 377.1 1.656
2 431.2 386.4 1.841 1.747 408.8 1.796
3 455.4 393.7 1.945 1.780 424.5 1.865
4 482.2 400.4 2.059 1.810 441.3 1.938
5 481.0 402.6 2.054 1.820 441.8 1.941
6 483.4 402.2 2.064 1.819 442.8 1.945
7 482.6 401.3 2.061 1.815 441.9 1.941
8 482.0 403.5 2.058 1.824 442.7 1.945
9 482.5 404.5 2.061 1.829 443.5 1.948
10 481.8 402.0 2.058 1.818 441.9 1.941
1 1 483.5 403.0 2.065 1.822 443.2 1.947
12 482.6 402.2 2.061 1.819 442.4 1.943
13 484.8 404.2 2.070 1.828 444.5 1.952
14 483.1 404.5 2.063 1.829 443.8 1.949
15 482.5 401.5 2.061 1.815 442.0 1.942
16 482.7 404.7 2.061 1.830 443.7 1.949
17 482.5 403.4 2.061 1.824 442.9 1.946
18 481.9 404.0 2.058 1.827 442.9 1.946
19 483.3 403.7 2.064 1.825 443.5 1.948
20 481.3 403.5 2.055 1.824 442.4 1.943

 

 

144

Table D-15. The crack length after cyclic thermal shock test which maximum

cycling number is 20 (specimen A5-10 AT = 295 0C).

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

# of x- y-direction A/232.6 A/229.1 (A+B)/2 C/230.8
Quench direction B(1,1m) (co ,x) (coy) M(um) (60M)
A0611)

0 232.6 229.1 1 1 230.8 1
1 319.5 317.9 1.373 1.387 318.7 1.380
2 364.9 342.0 1.568 1.492 353.4 1.531
3 400.7 344.4 1.722 1.503 372.5 1.613
4 423 .6 389.9 1.821 1.701 406.7 1.762
5 435.6 401.7 1.872 1.753 418.6 1.813
6 433.7 403.0 1.864 1.759 418.3 1.812
7 433.2 403.8 1.862 1.762 418.5 1.812
8 433.5 403.7 1.863 1.762 418.6 1.813
9 433.7 402.8 1.864 1.758 418.2 1.811
10 433.2 403.5 1.862 1.761 418.3 1.812
11 433.3 403.3 1.862 1.760 418.3 1.812
12 433.7 403.2 1.864 1.759 418.4 1.812
13 433.0 403.2 1.861 1.759 418.1 1.811
14 433.6 403.4 1.864 1.760 418.5 1.812
15 430.0 402.6 1.848 1.757 416.3 1.803
16 433.5 403.5 1.863 1.761 418.5 1.812
17 432.7 403.7 1.860 1.762 418.2 1.811
18 433.8 402.8 1.865 1.758 418.3 1.812
19 433.2 403.2 1.862 1.759 418.2 1.811
20 433.6 403.3 1.864 1.760 418.4 1.812

 

 

 

 

 

 

 

 

145

Table D-l6. The crack length after cyclic thermal shock test which maximum
cycling number is 20 (specimen A5-14 AT = 300 0C).

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

# of x- y—direction A/241 A/247.3 (A+B)/2 C/244.1
Quench direction B(um) (co,x) (coy) M(p.m) (06M)
AOL!!!)

0 241.0 247.3 1 1 244.1 1
1 489.9 332.6 2.032 1.344 41 1.2 1.684
2 533.0 359.7 2.211 1.454 446.3 1.828
3 556.7 371.0 2.309 1.500 463.8 1.900
4 560.9 376.5 2.327 1.522 468.7 1.920
5 580.6 382.6 2.409 1.547 481.6 1.972
6 590.3 380.6 2.449 1.539 485.4 1.988
7 588.6 382.5 2.442 1.546 485.5 1.989
8 590.6 381.7 2.450 1.543 486.1 1.991
9 590.2 382.9 2.448 1.548 486.5 1.993
10 592.0 481.7 2.456 1.947 536.8 2.199
11 592.8 479.5 2.459 1.938 536.1 2.196
12 592.7 479.2 2.459 1.937 535.9 2.195
13 592.3 480.8 2.457 1.944 536.5 2.198
14 593.1 482.0 2.461 1.949 537.5 2.202
15 593.1 482.8 2.461 1.952 537.9 2.203
16 591.6 481.5 2.454 1.947 536.5 2.198
17 592.4 481.4 2.458 1.946 536.9 2.199
18 593.7 481.9 2.463 1.948 537.8 2.203
19 592.6 482.0 2.458 1.949 537.3 2.201
20 593.2 483.6 2.461 1.955 538.4 2.205

 

 

146

Table D-17. The crack length after cyclic thermal shock test which maximum

cycling number is 20 (specimen A6-l AT = 305 °C).

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

# of x- y-direction A/238.4 N236.3 (A+B)/2 C/237.3
Quench direction B(pm) (coy) (Co’y) M01111) (0014)
AG“)

0 238.4 236.3 1 1 237.3 1
1 490.4 375.6 2.057 1.589 433.0 1.824
2 497.5 424.9 2.086 1.798 461.2 1.943
3 524.9 446.8 2.201 1.890 485.8 2.046
4 554.5 481.5 2.325 2.037 518.0 2.182
5 556.6 485.7 2.334 2.055 521.1 2.195
6 558.2 492.2 2.341 2.082 525.2 2.212
7 581.3 503.3 2.438 2.129 542.3 2.284
8 580.1 508.0 2.433 2.149 544.0 2.292
9 584.5 514.2 2.451 2.176 549.3 2.314
10 580.8 512.4 2.436 2.168 546.6 2.302
1 1 579.8 509.8 2.432 2.157 544.8 2.295
12 579.4 512.8 2.430 2.170 546.1 2.300
13 582.4 509.3 2.442 2.155 545.8 2.299
14 582.7 511.8 2.444 2.165 547.2 2.305
15 580.2 511.7 2.433 2.165 545.9 2.300
16 582.4 509.4 2.442 2.155 545.9 2.299
17 583.6 511.3 2.447 2.163 547.4 2.306
18 581.2 511.5 2.437 2.164 546.3 2.301
19 583.6 511.4 2.447 2.164 547.5 2.306
20 582.2 511.3 2.442 2.163 546.7 2.303

 

The following tables give the thermal fatigue behavior for an unreinforced alumina

rectangular bar shaped specimen (9.1 mm x 56.3 mm x 0.96 mm ). The crack lengths

were measured using an optical microscope through cyclic thermal testing. The relative

Vickers indentation cracks are indicated by L1, L2, and L3 (see section 2.7). The crack

lengths were measured by L1, L2, L3 order after taking the specimen out of the water.

 

Table D-18. The crack length of bar-shape specimen under the thermal shock, L1.

147

 

 

 

 

 

 

 

 

 

 

number of quench x-dir. crack length, y—dir. crack length, Lly / le
le (tun) Lly (m)
0 218 232.8 1.07
1 225.3 257.4 1.14
2 236.4 270.7 1.15
3 239.5 276.5 1.15
4 240.2 277.8 1.16
5 240.1 277 .6 1.17
6 244.5 278.5 1.14
7 243.6 277.4 1.14

 

 

 

 

Table D-l9. The crack length of bar-shape specimen under the thermal shock, L2.

 

 

 

 

 

 

 

 

 

 

number of quench x-dir. crack length, y-dir. crack length, L2y / L2x
L2x (Wit) L2y (m)
0 234.3 242.7 1.03
1 253.8 298.3 1.18
2 261.3 299.2 1.15
3 261.1 342.2 1.31
4 261.9 343.6 1.31
5 261.8 344.4 1.32
6 259.8 344.3 1.33
7 259.2 343 .9 1.33

 

 

 

 

 

 

Table D-20. The crack length of bar-shape specimen under the thermal shock, L3.

148

 

 

 

 

 

 

 

 

 

 

number of quench x-dir. crack length, y—dir. crack length, L3y / L3x
L3x (Hm) L3y (wt!)
0 220.1 252.8 1.15
1 238.5 272.7 1.14
2 248 280.4 1.13
3 246.3 288.5 1.17
4 247.5 289.9 1.17
5 246 288.2 1.17
6 246.9 289.6 1.17
7 245.3 288.5 1.18

 

 

 

 

 

6. References

1. W.P. Roger and A.F. Emeny, “Contact Thermal Shock Test Ceramics,” J. of Mat.
Sci. 27, 146-152 (1992).

2. EH. Lutz and M.V. Swain, “Interaction between Flaw Resistance, R-curve behavior,
and Thermal Shock degradation in Ceramics,” J. Am. Ceram. Soc. 74 [11]
2859- 68 (1991).

3. K. T. Faber, M.D. Huang, and .A.G. Evans, “Quantitative of Thermal Shock in
Ceramics on a Novel Test Technique,” J. Amer. Ceram. Soc. 64, 296-301 (1981).

4. T.K. Gupta, “Crack Healing in Thermally shocked MgO,” J. Am. Ceram. Soc. 58
[43] (1975).

5. RF. Lange and T.K. Gupta, “Crack Healing by Heat Treatment,” J. Am. Ceram. Soc.
Discussion and Notes, 53, 54-55 (1976).

6. T.K. Gupta, “Crack Healing and Strengthening of Thermally Shocked Alumina,” J.
Am. Ceram. Soc., 259-61(1976).

7. D.P.H. Hasslemann, “Unified Theory of Thermal Shock Fracture Initiation and Crack
Propagation in Brittle Ceramics,” J. Am. Ceram. Soc., 52, 600-04 (1969).

8. H. Ohira and R.C. Bradt, “Strength Distribution of a Quench-strengthen
Aluminasilicate,” J. Am. Ceram. Soc., 71 [1], 35-41 (1988).

9. R.C. Bradt, M. Asnizuka, T.E. Easler and H. Ohira, “Statistical Aspects of the
Thermal Shock Damage and the Quench Strengthening of Ceramics,” Thermal Shock

and Thermal Fatigue Beh_avior of Advanced Ceramics. G. A. Schneider and G. Petzow
447-58, Kluwer Academic Publishers, the Nederlands (1993).

10. W.J. Lee and ED. Case, “Comparison of Saturation Behavior of Thermal Shock
Damage in Variety of Brittle Materials,” Mat. Sci. and Eng., A154 1-9 (1992).

11. ED. Case, Y. Kim, W.J. Lee, “Thermal Shock and Thermal Fatigue Behavior of
Advanced Ceramics,” Thermg Shock and Thermal Fatigue Behavior of Adianced
Ceramics, G. A. Schneider and G. Petzow 393-406, Kluwer Academic Publishers, the
Nederlands (1993).

12. W.J. Lee and ED. Case, “Thermal Fatigue in Polycrystalline Alumina,” J. of Mat.
Sci., 25, 5053-5054 (1990).

149

150

13. Y. Kim, “Cyclic Thermal Shock in Ceramics and Ceramic Composites,” Ph D.
Dissertation, Michigan State Univ., MI (1991).

14. E.H. Lutz, M.V. Swain, and N. Claussen, “Thermal Shock Behavior of Duplex
Ceramics,” J. Am. Ceram. Soc. 74[1], 19-24 ( 1991).

15. J .R. Brockenbrough, L.E. F orsythe and R.L. Rolf, “Reliability of Brittle Materials in
Thermal Shock,” J. Am. Ceram. Soc., 64, 634-37(1986).

16. J .C. Coppla and R.C. Bradt, “Thermal Shock Damage in SiC,” J. Am. Ceram. Soc.,
56, 214-218 (1973).

17. W.D. Kingery, H.K.Bowen, and DR Uhlmann, “Introduction to Ceramics,” 2nd ed.
816-830, John Wiley and Sons, Inc., New York (1976).

18. W.D. Kingery, “Factors Affecting Thermal Stress Resistance of Ceramics Materials,”
J. Am. Ceram. Soc., 38, 3-15 (1955).

19. J .B. Walsh, “Effect of Cracks in the Compressibility of Rock,” J. Geophy. Res., 70
[2], 381-389 (1965).

20. RA. Sack, “Extension of Griffith’s Theory of Rupture to Three Dimensions,” Proc.
Phys. Sci. 58 a, 729-36 (1946).

21. T. K. Gupta, “Strength degradation and crack propagation in thermally shocked
A1203,” J. Am. Ceram. Soc. 55 [5], 249-253(1972).

22. W. P. Rogers, A. F. Emery, R. C. Bradt, and A. L. Kobayashi, “Statistical Study of
Fracture of Ceramic materials in the Water Quench Test,” J. Am. Ceram. Soc 70[6],
406-12 (1987).

23. M. Ashizuka, T. E. Easler, and R. C. Bradt, “Statistical Study of Thermal shock
damage of Borosilicate Glass,” J. Am. Ceram. Soc. 66 [8], 542-550 (1983).

24. S. Schon, H. Prielipp, R Janssen, J. Rodel, and N. Claussen, “Effect of Microstructual
Scale on Thermal Shock Resistance of Aluminum-Reinforced Alumina,” J. Am.
Ceram. Soc. 77 [3], 701-704 (1994).

25. J. H. Ainsworth and R. E. Moore, “Fracture Behavior of Thermally Shocked
Aluminum Oxide,” J. Am. Ceram. Soc. 52 [11], 628-29 (1969).

26. L.T. Herkkovich and M.V. Hyer, “Damage -induced Property Changes in Composite
Subjected to Cyclic Loading,” Eng. Fract. Mech. 25, 779-791 (1986).

27.

28.

29.

30.

31.

32.

33.

34.

35.

36.

37.

38.

39.

151

J. H. Ainsworth and R. H. Herron, “Thermal Shock Damage Resistance of
Refractories,” J. Am. Ceram. Soc. Bulletin 53 [7] 628-29 (1974).

C. E. Semler and TH. Hawisher, “Evaluation of the Thermal Shock Resistance of
Refractories Using the Ribbon Test Method,” J. Am. Ceram. Soc. Bulletin 59 [7],
732-38 (1980).

Y. Kim, W. J. Lee, and E. D. Case, “Thermal Fatigue Behavior of Ceramic Matrix
composite: A Comparison among Fiber Reinforced Whisker Reinforced, Particulate
Reinforced, and Monolithic Ceramics”, in Proceedings of the American Society for
Composites, 5th Technical Conference, Technomic Publications, Lancaster 871-881
(1990).

W. J. Lee, “Thermal Fatigue in Ceramics and Ceramic Matrix Composites”, Ph.D.
Dissertation, Michigan State University, East Lansing, MI (1991).

K. Lee, Personal Communication NSC 820 Class Notes, 1995, Graduate Student,
Materials Science and Mechanics, Michigan State University.

C. E. Ash, “Cyclic Thermal Shock-Crack Growth in Alumina,” Senior Research
Project, Michigan State University. (1994).

Y. Kagawa, “Quantitative Analysis of Closure Stress-Crack Separation Curve in
Grain Bridge Toughening of Polycrystalline Ceramics, Mat. Sci. and Eng., A176 379-
383 (1994).

S. Lathabai, J. Rodel, and B. R. Lawn, “Cyclic Fatigue from Degradation at Bridging
Grains in Alumina,” J. Am. Ceram. Soc., 74 [6] 1340-48 (1991).

J. C. Hay and K. W. White, “Grain-Bridging Mechanism in Monolithic Alumina and
Spinel,” J. Am. Ceram. Soc., 76 [7], 1849 -54 (1993).

P. L. Swanson, C. J. Fairbanks, B. R. Lawn, Y. W. Mai, and B. J. Hockey, “Crack
Interface Grain Boundary in Ceramics: 1, Experimental Study on Alumina,” J. Am.
Ceram. Soc., 70 [4], 279-89 (1987).

H. Kishmoto, A. Ueno, and S. Okawara, “Crack Behavior of Polycrystalline Alumina
under Static and Cyclic Load,” J. Am. Ceram. Soc., 77 [5] 1324-28 (1994).

R. H. Dauskardt, “Cyclic Fatigue-Crack Growth in Grain Growth in Grain bridging
Ceramics,” J. of Eng. Mat. and Tech. 115, 244-251 (1993).

R. H. Dauskardt, “A Frictional-Wear Mechanism for Crack Fatigue-Crack growth in
Grain bridging Ceramics,” Acta Metall. Mater. 41, 2765-2781 (1993).

152

40. Y. W. Mai and B. R. Lawn, “Crack Interface Grain Boundary as a Fracture Resistance
Mechanism in Ceramics: H, Theoretical Fracture Mechanics,” J. Am. Ceram. Soc., 70
[4], 289-94 (1987).

41 .Y. S. Chou and D. J. Green, “Silicon Carbide platelet/Alumina Composite: 1H,
Toughening Mechanism,” J. Am. Ceram. Soc., 76 [8], 1985-92 ( 1993).

42. B. R. Lawn, “Microstructure, R-curve, and Strength of Monophase Ceramics,”
Ceram. Eng. Sci. Proc. 11, 591-593 (1990).

43. R. W. Steinbrech, A. Reichl, and W. Achaarwachter, “R-curve Behavior of Long
Cracks in Alumina,” J Am. Ceram. Soc., 73 [7], 2009-15 (1990).

44. G. Vekinnis, M. F. Ashby, and P. W. R. Beaumont, “R-curve Behavior of A1203
Ceramics,” Acta Metall. Mater. 38 [6], 1151-1 162 (1990).

45. L. M. Braun, S. J. Bennison, and B. R. Lawn, “Short Crack T-curves and Damage
Tolerance in Alumina-Based Composites,” Ceram. Eng. Sci. Proc., 13, 156-163
(1992)

46. J. Rodel, J. F. Kelly, and B. R. Lawn, “In Situ Measurements of Bridged Crack
Interaction in the Scanning Electron Microscope,” J. Am. Ceram. Soc., 73 [11] 3313-
18 (1990).

47. A. Reichl and R. W. Steinbrech, “Determination of Crack-Bridging Forced in
Alumina,” J. Am. Ceram. Soc., 71 [6] C299-01 (1988).

48. R. H. Dauskrdt, D. B. Marshall, and R. O. Rktchie, “Cyclic Fatigue Crack
Propagation in Magnesia-Partially-Sterilized Zirconia Ceramics,” J. Am. Ceram. Soc.,
73 [4] 893-93 (1990).

49. Personal Communication MSM 960 Class Notes, 1994,
Materials Science and Mechanics, Michigan State University.

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