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This is to certify that the
dissertation entitled

MULTl-FUNCTIONAL MATERIALS BY POWDER
PROCESSING FOR A THERMAL PROTECTION SYSTEM
WITH SELF—COOLING CAPABILITY: PERSPIRABLE SKIN

presented by

Ll SUN

has been accepted towards fulfillment
of the requirements for the

Doctoral degree in Mechanical Engineean

 

 

@95‘

Major Professor’s Signature
08/08/2009

Date

MSU is an Afllrmative Action/Equal Opportunity Employer

 

___VIl-lu;l_-.l-I-LL‘Lu-C-.l-l-n‘.~.— W4

 

PLACE IN RETURN Box to remove this checkout from your record.
To AVOID FINES return on or before date due.
MAY BE RECALLED with earlier due date if requested.

 

DATE DUE DATE DUE DATE DUE

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

5/08 KzlPrqlAcc&PreuClRC/Dateom.indd

MULTl-FUNCTIONAL MATERIALS BY POWDER
PROCESSING FOR A THERMAL PROTECTION SYSTEM
WITH SELF-COOLING CAPABILITY: PERSPIRABLE SKIN

By

LI SUN

A DISSERTATION

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

DOCTOR OF PHILOSOPHY

Mechanical Engineering

2009

the

surfs

inhib

ABSTRACT

MULTI-FUNCTIONAL MATERIALS BY POWDER
PROCESSING FOR A THERMAL PROTECTION SYSTEM
WITH SELF-COOLING CAPABILITY: PERSPIRABLE SKIN

By
Ll SUN

Aerodynamic heating generated by the friction between the atmosphere and
the space vehicle’s surface at reentry can enhance the temperature on the
surface as high as 170000. A Thermal Protection System (TPS) is needed to
inhibit the heat entering into the vehicle. Presently, the completely passive
thermal protection is used for TPS. The thermal ablation/erosion and oxidization
reaction of the current TPS is the major threat to the safety of the space vehicle.
Therefore, a new design for TPS with actively self-cooling capability was
proposed by bio-mimicking the perspiration of the human body, henceforth called
Perspirable skin. The design of Perspirable Skin consists of core material
shrink-fitted into a skin panel such as Reinforced Carbon-Carbon (RCC)
Composite. The core material contains a very small Coefficient of Thermal
Expansion (CTE) compared to the panel material. As temperature increases, the
gap between the core and the skin are produced due to the CTE difference.

Compressed gas on board the space vehicle will blow out from the gap once the

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surface temperature reaches a critical value. The cold gas flows over the surface
and mixes with the atmospheric air to compensate for the frictional heat. With
Perspirable Skin, the highest temperature on the surface is expected to decrease,

and we assumed it to be around half of the present temperature.

This dissertation focuses on the selection of the core materials and their
manufacturing by powder processing. Based on a series of experiments, several
results were obtained: 1) the effect of powder mixing on the compaction capability
and sintering capability was determined; 2) a flat 3-layered Al203/Zr02
Functionally Graded Material (FGM) without cracks was fabricated; 3) the factors
contributing to the cracks in the multi-layered materials were investigated; 4) an
isotropic negative thermal expansion material, ZrW203, as well as its composites
with ZrOz were processed by in-situ reaction of W03 and ZrOz; 5) several CTE
prediction models on composites containing ZrW208 were studied and proposed
as a better scheme for applying the contiguity of phase; 6) a novel processing
technique to produce ZrW203- Zr02 continuous FGMs was developed; and 7) the
thermal and mechanical properties of the various materials were measured.
Finally, using finite element analysis (FEA), the complete design of Perspirable

Skin has been accomplished.

To LiangCai, Jing, and our parents

iv

ACKNOWLEDGEMENTS

The first and foremost person I would like to thank is my advisor, Professor
Patrick Kwon. I deeply appreciate the freedom Dr. Kwon gave me, and I also am
grateful that he allowed me to work in the Perspirable Skin project and pursue the
topics I am interested in last four years. I am especially thankful for the broad
training I received from Dr. Kwon. Without his support, encouragement, and

guidance, I would never have had a productive doctoral research.

I would like to thank Professor Dahsin Liu, Professor Alfred Loos, and
Professor XiaoBo Tan for serving on my committee, and for all good suggestions

on my research.

I would like to thank Professor Ctirad Uher and Dr. Xun Shi in the Department
of Physics at University of Michigan, Professor Dave Kim and Yongha Kim in
Mechanical Engineering Division at Washington State University, Vancouver for

an exciting collaboration and stimulating discussions.

I greatly appreciate the immense help I received from the members in the
Kwon group. I owe special thanks to Adam Sneller and Basak Oguz, who worked
with me in the Perspirable Skin. Other labmates, such as Sam Baldauf, Agatha
Bone, Kyunghee Park, Jacob Kloss, and Dr. Hongjoo Rhee, offered me much

help on both my research and study.

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Funding for my research came from AFOSR. I am also grateful for the
support from the following fellowships and awards —DeV|ieg Graduate
Fellowship, Research Enhancement Award, and travel grants from Graduate

School of MSU.

Last, but most importantly, I need to thank the support from my family,
especially LiangCai, who has been the first audience of all my important
presentations, who gives me whole-heart support for my doctoral study, and with

whom our life and work in USA are meaningful.

CHAP'
1. N

1M;

TABLE OF CONTENTS

 

CHAPTER
1. INTRODUCTION ................................................................................... 1
1.1. BACKGROUND AND MOTIVATION .................................................... 1
1.2. MODERN CERAMICS ........................................................................ 5
1.2.1. Monolithic Polycrystalline Ceramics ...................................... 5
1.2.1.1. Alumina ....................................................................... 5
1.2.1.2. Zirconia ....................................................................... 6
1.2.1.3. Silicon Nitride .............................................................. 7
1.2.1.4. Negative Thermal Expansion Ceramics ...................... 7
1.2.2. Ceramic Matrix Composites .................................................. 11
1.2.2.1. Particle-Reinforced Ceramic Matrix Composites ......... 11
1.2.2.2. Fiber-Reinforced Ceramic Matrix Composites ............. 12
1.2.2.3. Micromechanics Prediction Models For Particulate Composites
_ ......................... 12
1.2.3. Ceramic Functionally Graded Materials ................................ 16
1.3. POWDER METALLURGY ................................................................... 19
1.3.1. Introduction ........................................................................... 19
1.3.2. Compaction .......................................................................... 20
1.3.2.1. Procedure ................................................................... 20
1.3.2.2. Powder Mixing Effect on Compaction .......................... 21
1.3.2.3. Dimensional and Density Variation by Compaction ..... 22
1.3.2.4. Constitutive Models for Powder Compaction ............... 23
1.3.3. Sintering ............................................................................... 26
1.3.3.1. Sintering Kinetics ........................................................ 26
1.3.3.2. Sintering Curves and Models ...................................... 29
1.4. DISSERTATION OVERVIEW .............................................................. 31
2. MATERIALS AND FACILITIES ............................................................ 33
2.1. MATERIALS ........................................................................................ 33
2.2. EXPERIMENTAL FACILITIES ............................................................. 36
2.2.1. Introduction of SETARAM SETSYS Evoluation 95 ................ 38

vii

3. THE PHYSICS OF POWDER METALLURGY: COMPACTION ........... 41
3.1 . POWDER MIXING EFFECT ON THE COMPACTION CAPABILITIES OF

CERAMIC POWDERS ......................................................................... 41

3.1.1. Materials and Experimental Procedure ................................. 41

3.1.2. Relative Density-Stress Relationship for Various Powder Mixtures 44

3.1.3. Relative Density-Strain Relationship for Various Powder Mixtures 48

3.1.4. Prediction of Initial Relative Density Versus Powder Proportion Curve

 

Shape from the Characteristics of Powders ................................. 51

3.1.5. Discussion about the Limiting Boundaries of Initial Relative Density
- Powder Proportion Curves - - - - 53

3.1.6. Discussion about the Maximum Packing/Compaction Relative

Density ................................................................................ 57
3.1.7. Conclusions .......................................................................... 59
3.2. DIMENSIONAL VARIATION BY COMPACTION .................................. 60
3.3. DENSITY DISTRIBUTION BY COMPACTION .................................... 65
3.3.1. Experimental Design ............................................................. 65
3.3.2. Measurement Results and Discussion .................................. 67
4. THE PHYSICS OF POWDER METALLURGY: SINTERING ................ 71
4.1. EXPERIMENTS AND DATA CALCULATION ....................................... 71
4.2. POWDER MIXING EFFECT ON PARTICLES AND SINTERED SAMPLES 74
4.2.1. Powder Mixing Effect on Particle Size Distribution Profile ..... 74

4.2.2. Powder Mixing Effect on Microstructures of Sintered Samples 76
4.2.3. Powder Mixing Effect on Dimensions of Sintered Samples... 79

 

4.3. DENSIFICATION RATE-RELATIVE DENSITY CURVES ..................... 81
4.3.1. Alumina Powder System ....................................................... 81
4.3.2. Zirconia Powder System ....................................................... 86
4.4. PHENOMENOLOGICAL CONSTITUTIVE MODELS FOR ALUMINAAND
ZIRCONIA SINTERING CURVES ............................... 87
4.4.1. Model Equation and Calculation Procedure .......................... 87
4.4.2. Models for Alumina Powder Mixtures .................................... 81
4.4.3. Models for Zirconia Powder Mixtures .................................... 93
4.5. CONCLUSIONS .................................................................................. 94

viii

6.1

5. ZrOz-AI203 STEPWISE FGM: MANUFACTURING

AND CRACKS PREVENTION .............................................................. 96
5.1 . EXPERIMENTAL PROCEDURES ....................................................... 97
5.2. POWDERS SLECTION BASED ON SINTERING KINETICS .............. 98
5.3. THE INFLUENCE OF COMPACTION LOAD ...................................... 101
5.4. THE INFLUENCE OF INTERFACE PROFILE ..................................... 103
5.5. THE INFLUENCE OF RAMP/SOAK PROFILE .................................... 105
5.6. SHRINKAGE RATE-SINTEIRNG TEMPERATURE CURVES OF CHOSEN

POWDERS UNDER OPTIMIZED CONDITIONS ....................................... 107
5.7. PHENOMENOLOGICAL CONSTITUTIVE MODELS .......................... 110
5.8. CONCLUSIONS .................................................................................. 113

6. M20; and erzoa-Zroz COMPOSITES: IN-SITU REACTION AND

PHYSICAL PROPERTIES ..................................................................... 1 16
6.1. EXPERIMENTAL PROCESSING ........................................................ 116
6.2. SYNTHESIS OF ZrW203 SUBSTRATE .............................................. 118
6.3. ZrVVzOg/ZrOz COMPOSITES ............................................................. 122

6.3.1. Manufacturing and CTEs ...................................................... 122
6.3.2. Young’s Modulus .................................................................. 127
6.4. ZERO CTE COMPOSITES CONTAINING ZrW203 ............................ 131
6.4.1. Method l: ln-Situ Reaction of Zr02+W03 ............................. 131
6.4.2. Method ll: Cosintering of ZrOz and ZrWzOg ......................... 132
6.4.3. Method III: ln-Situ Reaction of Zr02+W03+AI203 ................ 133
6.4.4. Method IV: ln-Situ Reaction of Zr02+W03z
Another Ramp/Soak Path .................................................... 135
6.4.5. Optimal Fabrication Method and Density Improvement ......... 136
6.5. CRACKS PROPAGATION? ................................................................ 138
6.6. CONCLUSIONS .................................................................................. 140

7. ZrWzOg-Zroz CONTINUOUS FGMs: FABRICATION AND

THERMAL EXPANSION GRADIENT CONTROL ................................. 143
7.1 . EXPERIMENTAL PROCEDURES ....................................................... 143
7.2. CONTINUOUS GRADIENT ................................................................. 146

REFE

7.3. EFFECT OF SOAKING DURATION ON MICROSTRUCTURES ......... 151

7.4. POWDER COMPONENT EFFECT ..................................................... 154
7.5. DISTROTION CONTROL ................................................................... 155
7.6. DENSITY IMPROVEMENT ................................................................. 157
7.7. AXIAL CTEs ........................................................................................ 158
7.8. CONCLUSIONS .................................................................................. 160
8. SUMMARY ............................................................................................ 164
8.1 . CONTRIBUTIONS .............................................................................. 164
8.2. SUGGESTIONS FOR NEXT STEP RESEARCH ................................ 170
REFERENCES ............................................................................................ 171

 

TAE

5.:

LIST OF TABLES

TABLE Page
1.1 Typical properties of N203, ZrOz, and Si3N4. ........................................ 7
1.2 Isotopic negative thermal expansion materials ........................................ 8
2.1 Characteristics of the ceramic powders used in this study. ..................... 33

3.1 The coefficient k in Equation (3.7) for representative TMDAR+CR-15 powder

mixture ..................................................................................................... 49
3.2 The maximum relative packing density calculated by Brouwers’ equation and

from the experiments. .............................................................................. 58
3.3 Material properties for several alumina compacts. ................................... 64
3.4 The lowest and highest density in various samples .................................. 70
4.1 The linear equations calculated for pure TMDAR powder. ....................... 90

5.1 The damage characteristics of FGM samples experienced different compaction
load ......................................................................................................... 102

5.2 Summary of optimized experimental conditions for a 3-layered AI203/ZrOz FGM
............................................................................................................... 108

5.3 The coefficients used to construct the phenomenological constitutive models for
the chosen powder mixtures .................................................................... 111

6.1 The WOg/ZrOz mass ratios of various green samples and the corresponding
resultant ZrWzoaeroz volume ratios in the sintered samples ................. 122

6.2 The continuity values obtained by the microstructure observation for ZrWzog-
ZrOz composite samples with different ZrW208 volume frictions ............. 130

7.1 The mass ratio for each green sample and theoretical thickness/volume ratio
and er208 volume fraction in the sintered samples .............................. 144

7.2 The room temperature axial CTE of each samples under different soaking
durations and of the CTE of the ZrW203/Zr02 composites with the theoretical
volume fraction of ZrVVgOg calculated by the mass ratio of Zr02 and W03 in

Table 7.1 .................................................................................................. 153

xii

FIGUF

1.1

12

1.4

1.5

1.6

2.1

2.2

2.3

3.1

32

3.3

LIST OF FIGURES

FIGURE Page
1 .1 Schematics of Perspirable Skin TPS ....................................................... 3
1.2 Dependence of relative expansion on temperature of NCTE materials 9

1.3

1.4

1.5

1.6

2.1

2.2

2.3

3.1

3.2

3.3

Schematic of thermal contraction mused by thermal motion (filled circles are
cations, and open circles are oxygen atoms. The solid line shows low
temperature bonds position, dash line shows bonds at high temperature and
arrows show the vibration direction of oxygen atoms) .............................. 9

The process of die set compaction .......................................................... 21

Illustration of modified Drucker-Prager/cap elasto-plasticity model. (d is the

material cohesion, and B is the internal angle of friction) .......................... 24
Illustration of the relationship among chapters ......................................... 32
Particle size distribution profiles of various alumina powders ................... 34

The raw powder SEM micrograph of a) TMDAR, b) CR-15, c) CR—6, d) GE-1, e)
TZ3YS, f) CERAC-2003. g) W-Fluka, and h) ZW-OR ............................... 35

The front view of the SETARAM SETSYS Evoluation 95 (1-head cover,
2-fumace side watch, 3-mode changing switch, 4—open/close head switch, 5-side
cover, 6-proctective gas inlet and outlet tube) .......................................... 38

The relative density-stress curves by the compaction for a) CR-15+TMDAR and
b) CR-6+GE-1 ......................................................................................... 46

The initial relative density - coarse powder proportion for all six powder mixture
groups after 0.5MPa pre-Ioad compaction ............................................... 47

The relative density-strain curves by the compaction for a) CR-15+TMDAR and
b) CR-6-I-GE-1 ......................................................................................... 49

xiii

3.5

3.6

3.7

3.8

3.9

3.1

3.1

3.1

3.1

4.1

4.2

4.3

4.4

4.5

4.6

3.4 The dependence of the reciprocal of relative density on the proportion of coarse
powder and its triangle boundary by Westman et al. [69] ......................... 54

3.5 Dependence of the initial density on the vibration time for each powder .. 55

3.6 Triangle boundaries for the initial relative density-powder proportion curve of
CR—15+GE-1 powder group ..................................................................... 56

3.7 Triangle boundaries for the initial relative density-coarse powder proportion

curves of TMDAR+CR-6, CR-6+GE-1 powder groups ............................. 56
3.8 The schematics of external shape measurement ..................................... 61
3.9 The diameter variation along the thickness direction of GE-1 samples 61

3.10 Dependence of largest and smallest diameter difference on the powder
proportion ................................................................................................ 62

3.11 Stress-strain curve of TMDAR ................................................................. 63

3.12 The photo of the middle section of a TMDAR sample. The bottom side in the
picture is also the side contact to the bottom punch in the compaction 68

3.13 The density distribution of TMDAR green sample, zero position is the radial

symmetric axel in Fig.3.12 ....................................................................... 69
4.1 Particle size distributions of the four powders used in this Chapter .......... 72
4.2 Particle size distribution profiles of AI203 powder mixtures ...................... 74

4.3 The area fraction of the second peak in the particle size distribution curves for
varying alumina powder mixtures ............................................................. 76

4.4 SEM micrographs of fully-sintered a) TMDAR, and b) CR-15 (Acceleration
voltage: 15kV, Working distance: 15mm ) ................................................ 77

4.5 Average grain size of fully-sintered alumina samples ............................... 77

4.6 The micrograph of a fully-sintered 40/60 CERAC-2003+TZ3YS sample
(Acceleration voltage: 15kV, Working distance: 15mm) ............................ 78

xiv

4.7 The relationship between the final diameters and the percentage of a) CR-15 in
alumina system and b) CERAC-2003 in Zirconia system under varying
compaction load ...................................................................................... 79

4.8 Densification rate as a function of relative density for TMDAR+CR-15 alumina
powder mixtures ...................................................................................... 81

4.9 Densification rate as a function of relative density for representative
TZ3YS+CERAC-2003 Zirconia system .................................................... 86

4.10 The part-isothennal ramp/soak sintering cycle used in this study to calculate the
phenomenological constitutive models .................................................... 88

4.11 The densification rate — relative density relationship of the 100% TMDAR powder
under the part-isothermal sintering path described in Fig. 4.10 ................ 89

4.12 Comparison of the experimental and calculated results for 100% TMDAR under
a) non-isothennal and b) part-isothennal heating circle ........................... 92

4.13 Comparison of the experimental and calculated results for 100% TZ3YS under a
non-isothermal heating circle ................................................................... 93

5.1 Flow chart detailing the manufacturing process used in this chapter ........ 98

5.2 The densification rate-relative density curves of the three chosen powder
mixtures (ramp rate: 10°C/min). .............................................................. 100

5.3 The punch featuring a jagged surface for making the occlusive interface. 104

5.4 BSE Micrographs of the two interfaces used in this study, a) the occlusive
interface between layer A and layer M and b) the smooth interface between layer
Z and layer M (Acceleration voltage: 25kV, Working distance: 39mm). 105

5.5 Shrinkage ratio changing profile of Powders A and 2 under an isothermal
sintering experiment at 1250°C (dh(t) is the height changing ratio and h(t) is the
height of sample at time t) ....................................................................... 106

5.6 Optimal ramp/soak sintering profile for this study ..................................... 107

XV

5.]

5.1

5.9

6.1

62

6.3

6.4

6.5

6.6

6.7

5.8

5.9

6.10

5.7

5.8

5.9

6.1

6.2

6.3

6.4

6.5

6.7

Shrinkage ratio-temperature curves for chosen three powder-mixtures under
optimized experimental condition (hT is the height of sample at temperature T
and ho is the height of the corresponding green sample) ......................... 108

A representative Backscattered Electron image (BSEI) of the three-layered
AI203/AI203+Zr02/ZrO2 FGM (Acceleration voltage: 22kV, Working distance:
15mm) ..................................................................................................... 109

The comparison of experimental and calculated densification rate vs. relative
density curves (RE gives the experimental result and R0 represents the

calculated result) ..................................................................................... 112

The ramp/soak path used for producing ZrW203 ..................................... 118

a) The XRD pattem of the reaction product and b) the standard powder
diffraction file of ZrW203 (JCPDS 13-557) ............................................... 119

The microstructure of the ZrW208 substrate ........................................... 119

The temperature dependence of CTEs of ZrW203 and CERAC-2003 sintered by
ramp/soak path in Fig. 6.1 ....................................................................... 120

The temperature dependence of thermal conductivity of ZrW203 ............ 121

The temperature dependent CTEs of the various ZrW203/Zr02 composite
samples ................................................................................................... 123

The CTEs of the ZrW203/Zr02 composite samples and corresponding
calculated values from several prediction models at a) room temperature and b)

500°C ...................................................................................................... 124

The microstructure of a ZrW203/Zr02 composite (Sample 3) .................. 126

Young's modulus - temperature curves for composites as well as for ZrW203
and ZrOz sintered by ramp/soak path in Fig.6.1 ....................................... 127

6.10 The calculated Young’s modulus of ZrW203/Zr02 composites by Mori-Tanaka

model and the experimental measurement of composites at a) room temperature,
b) 500°C .................................................................................................. 128

xvi

7.2

7.3

7.4

6.11 CTE-temperature curves for nearly zero CTE composites fabricated by various
processing methods; each data point represents an average of test results for
three samples .......................................................................................... 132

6.12 Micrographs of near-zero CTE composites made by Method a) l b) II, C) III and d)
IV. The larger grains are ZrW203 and the smaller grains are ZrOzlAl203
(Working distance: 15mm, acceleration voltage: 15KV) ........................... 133

6.13 The ramp/soak path used in Method IV ................................................... 136

6.14 The micrograph of near-zero CTE composite made by optimal method (With
0.07 wt% alumina, Working distance: 15mm, acceleration voltage: 15KV)

............................................................................................................... 137
6.15 Thermal cycles used to investigate the crack propagation ....................... 139
6.16 Young’s modulus evolution with the thermal cycles .................................. 139
6.17 Designed geometry for the ZrW203 core [131] ........................................ 142

7.1 Micrographs of several cross-sections for sintered Sample 2 with height of
6.2mm from the position of a) the outer surface, b) 2.6mm away neutral plane, c)
1.8mm away neutral plane, d) 1.2 mm away neutral plane, e) 0.6mm away
neutral plane and f) the neutral plane. The larger grains are ZrW203, which are
surrounded by ZrOz (Working distance 15mm, acceleration voltage: 15KV.)

............................................................................................................... 147

7.2 The radial thermal expansion-position relationship for sintering FGMs at room
temperature. The 0 position is defined as the mid-plane for Sample 1-3 and the
initial W03+Zr02 surface for Sample 4 (Soaking duration: 6 hours) ........ 148

7.3 The radial thermal expansion and the corresponding cross-sectional CTEs for
Sample 4 at room temperature. The sample height is 6.21mm. The 0 position is
defined as the initial WO3+ Zr02 surface and the soaking duration was 6 hours

............................................................................................................... 150
7.4 The CTE-position relationship of Sample 2 for various soaking durations 154

7.5 The CTE-position relationship of Sample 5 .............................................. 155

xvii

 

7.I

7.7

7.8

7.9

7.6

7.7

7.8

7.9

The relationship between the diameters of Zirconia samples sintered by the
ramp/soak path of Fig.6.1 and the percentage of Cerac-2003 in Zirconia powder
mixtures (the diameter of green bodies was 7.94mm) .............................. 156

The axial CTE vs. temperature curve for pure ZrW203 and samples 1-4 (with
0.07 wt% TMDAR powder by mass and 6 hours soaking duration) .......... 158

Designed core shape of Perspirable Skin with ZrW203-Zr02 FGM ......... 161

The FEA results for the best FGM core design a) gap distance at working
condition b) Von Mises stress at working condition c) first stress at room
temperature ............................................................................................. 162

xviii

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CHAPTER 1

INTRODUCTION
1.1 BACKGROUND AND MOTIVATION

Space vehicles that enter a planetary atmosphere like the Space Shuttle
Orbiter (i.e. earth) require the use of a Thermal Protection System (T PS) to
protect them from aerodynamic heating, which is generated at the surface of a
space vehicle due to the combination of compression and surface friction of the
atmosphere [1]. A TPS mainly is used to inhibit the heat entering into the vehicle
[1, 2]. Due to the wide variation of temperatures, the TPS selected for a space
shuttle is composed of many different materials. Each material's temperature
capability, durability, and weight determine the extent of its application on the
vehicle [2]. The orbiters nose cone, including the chin panel, and the leading edge
of the wings are the hottest areas during re-entry [3]. During the reentry back into
the atmosphere, the maximum heating occurs about 20 minutes before
touchdown, the maximum temperature on these surfaces can reach as high as
1700°C [2, 3]. Reinforced Carbon-Carbon composite (RCC), a light gray
composite, along with lnconel foil insulators and quartz blankets, protect these

areas from the highest temperatures and aerodynamic forces [3,4].

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Considering the oxidizing environments, the RCC must have oxidation
protection coating [4]. The common coating materials include SIC, Si3N4 and
SiOz [4]. However, when temperature is as high as 1700°C, the thermal
ablation/erosion speed is considerably high. If the coating layer erodes, the whole
TPS will be damaged, therefore jeopardizing the safety of a space vehicle. To

increase the safety of a space vehicle, new designs of TPS are needed.

Biomimetics, the application of methods and systems, found in nature, to
engineering and technology, has spawned a number of innovations far superior to
what the human mind alone could have devised. Today, the gecko’s powerful
ability to cling to vertical surfaces is inspiring new types of adhesion. Exploring
photosynthesis in leaves has led to the creation of transparent photocells that can
absorb solar rays passing through a window. And Japanese Express Train picked
up speed and reduced energy consumption after modifying the shape of its nose

from the tip of a bullet to that of a kingfisher’s beak [5].

In humans, Perspiration/sweating is primarily means of thennoregulation.
Evaporation of sweat from the skin surface has a cooling effect. In hot weather, or
when the individual's muscles heat up due to exertion, hypothalamus, the
temperature-regulating area of the brain, sends nerve impulses to the sweat
glands stimulating them to increase the size and release sweat. Until the skin

receptors detect that the skin's temperature is back to normal. The brain then

sends
regal:
name
Unive
Shuttl
damag
areas

that is,

sends messages to stop the release of sweat and the sweat glands will shrink to
regular size [6]. Mimicking the process of perspiration, a new designed TPS,
named Perspirable Skin, was proposed by Patrick Kwon group at Michigan State
University in 2005, which is mainly aimed to be used at the hottest areas of Space
Shuttles to reduce their surface temperature at reentry and reduce the TPS
damage chance. By applying Perspirable Skin, the temperature of those hottest
areas is expected to decrease to the half of the present temperature (1700°C),

that is, around 800°C.

 

Figure 1.1 Schematics of Perspirable Skin TPS

lashit
cores
small
tempt
CTE

comp

comp
keepil
lands

whole

For the design of Perspirable Skin, TPS is arranged in a ‘Peg and Hole’
fashion, as shown in Fig. 1.1. The skin panels are with numerous holes, in which
cores (pegs) made of another material are assembled. The core material has
smaller Coefficient of Thermal Expansion (CTE) than that of the skin. As
temperature increases, a gap is produced between the skin and cores due the
CTE difference. Once the temperature reaches the working temperature, a
compressed gas contained in tank inside the space vehicle blow out from the gap.
The cold gas flows over the surface and mixes with the atmospheric air to
compensate the frictional heat between the vehicle and the atmospheric air,
keeping the surface temperature at relatively low temperature. After the vehicles
lands and its surface temperature decreases, the gaps close again. Therefore, the

whole design is an autonomous, reusable cooling system.

From the design idea to the application of Perspirable Skin on the space
vehicles, a series of studies are needed to be performed: 1) core material
selection, 2) materials fabrication, 3) materials properties test, which will be used
as the input parameter of Finite Element Analysis (FEA), 4) structure design by
FEA (including gap and stress analysis), 5) core pieces and RCC panel assembly,

and 6) test at simulated reentry environment.

By three and half years efforts, now Steps 1-4 are almost achieved. This

dissertation presents all research results of Steps 1-3 as well as part results of

Step

1.2 I

resist

lowC

envirr

cerarr

12.1

Step 4.

1.2 MODERN CERAMICS

Ceramics have demonstrated to be the most important materials used in a
wide variety of high temperature applications despite of their inherent brittleness.
Ceramics also are used in those application areas where high hardness, wear
resistance, corrosion resistance and temperature stability, low specific weight, and
low CTE are needed [7,8]. Therefore, considering the high temperature working
environment and the low CTE requirement of core materials of Perspirable Skin,

ceramics are ideal candidates.

1.2.1 Monolithic Polycrystalline Ceramics

New and improved ceramics are now available that have much higher strength
and toughness than prior ceramics. Modern engineering ceramics such as
alumina (AI203). Zirconia (Zr02). silicon carbide (Si3N4). are making more usages

in aerospace, automotive and electronics industry [8].
1.2.1.1 Alumina

Alumina, or aluminum oxide (AI203), is the most mature high-technology
ceramic in terms of quantity produced and variety of industrial uses.

Approximately five million metric tons were produced in 1999 for wear, chemical,

electrical, medical and other applications [9]. Al203 is used in these applications

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because of its excellent combination of properties, including high hardness and
wear resistance, chemical resistance, smooth surface, reasonable strength and

moderate thermal conductivity.

1.2.1.2 Zirconia

Zirconia, or zirconium oxide (ZrOz), is another important high-strength, high
toughness ceramic that has been developed during the last 30 years [10, 11].
Partially stabilized Zirconia (PSZ) has fracture toughness values ranging from
6-15 MPa-m1’2, compared to conventional ceramics with fracture toughness of
about 2-3 MPa-m"2 [11]. The mechanism of toughening in PSZ involves a

volume increase due to a polymorphic transformation that is triggered when an

applied stress causes a crack to form in the ZrOz.

Transformation toughening was a breakthrough in achieving high-strength,
high-toughness ceramic materials. For the first time in history a ceramic material
was now available with an internal mechanism for actually inhibiting crack
propagation. A crack in a normal ceramic travels all the way through the ceramic
with little inhibition, resulting an immediate fracture. PSZ has fracture toughness
three to six times higher than most other ceramics. Zr02 often can provide
sufficient increased life to justify its use on a life cycle cost basis. Therefore, it is
now wildly used as dies for hot extrusion of metals, wire-drawing capstans, golf

cleats, and so on [10, 11].

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Silicon Nitride (Si3N4) has a favorable combination of properties that includes

high strength over a broad temperature range, high hardness, low coefficient of
thermal expansion, moderately high elastic modulus, and unusually high fracture
toughness for a ceramic [12, 13]. This combination of properties leads to excellent
thermal shock resistance, ability to withstand high structural loads at high

temperatures, and superior wear resistance. Si3N4 ceramics have reached

large-scale production for cutting tools, bearings, turbocharger totors, diesel

pre-chambers and variety of custom wear parts [14, 15].

All AIZO3, ZrOz, and Si3N4 are for structural applications. Table 1.1 lists typical

mechanical and thermal properties for the three ceramics.

Table 1.1 Typical properties of Al203, ZrOz, and Si3N4 [8, 10]

 

Material

 

 

 

 

 

 

 

 

 

 

Properties AI203 2702 SI3N4
Density (glcm3) 3.975 6.04 3.48
Young’s Modulus (GPa) 300 200 310
Fracture toughness (MPa-m1/2) 4-5 11-13 6
Flexural strength (MP3) 358 200-360 700
CTE (10-6-00-1) 8.2 8.2-10 3.1
Thermal Conductivity (W/mK) 24.7 27 26

 

1.2.1.4 Negative Thermal Expansion Ceramics

Most materials exhibit positive thermal expansion with increasing temperature.

 

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However, there exist some materials, almost all are ceramics, with anomalous
Negative Themial Expansion (NTE), meaning they shrink when heated. The
thermal contraction of most NTE ceramics is anisotropic. That is, those materials
show positive thermal expansion in one or two dimensions that is coupled with
negative thermal expansion in the other two or one dimensions. For example,
both cordierite (MngIZSi508) and B—eucryptite (LiAlSiO4) show thermal
expansion in two dimensions coupled with thermal contraction in one dimension;
but NZP (NaZr2(PO4)3) shows thermal expansion in one dimension coupled with
thermal contraction in the other two dimensions [16-19]. When these materials are
heated, some bonds expand (For B—eucryptite, Li-O bonds) driving one or
two-dimensional expansion. However, the rigidity of the other bonds (For
B—eucryptite, Al-O and Si-O bonds) forcing the contraction in the other two or one

dimension(s) [16].

Isotropic negative thermal expansion is very rare. Table 1.2 summarizes five

ceramic materials with isotropic negative thermal expansion.

Table 1.2 Isotopic negative thermal expansion materials [16, 18-23]

 

 

 

 

 

 

 

 

 

Material CTE range (10-5-K-1) Temperature range of NTE (K)
TthO7 -9.3 to 4.3 573-480

UPzO'] -7.1 to 3.1 773-1773

ZerO7 -11.1 to 15.4 380-875

ZrWzOs -13.2 to -6.5 3-1050

HszOa -12.9 to -6.4 3-1050

 

 

Fgun

As
expar
Tame

fiae.

IMens

 

05-: r \ —erzoe/Hrw2oa
04: | \ - - ZrV207
0.3- \

a ‘ o o . .\

  
  

ansion (%)
O
't’

0.0{ \' .T~\
3.0.1. \ ~. \

>
% .04: - - - THP205
‘5 .o_5.‘ -~-UP205

 

 

 

o '260'460'660'860'1600'12130'1400'1600
Temperature (K)

Figure 1.2 Dependence of relative expansion on temperature of NCTE materials

As Fig. 1.2 shown, ThP207, UP207, and ZrV207 shows positive thermal

expansion when temperatures are lower than the corresponding range listed in
Table 1.2. Only ZrW203 and HfW203 feature negative CTE over the whole solid

state. However, Hf is a much rare element than Zr. So ZrW203 has been the most

intense study subject of isotropic negative thermal expansion material.

 

Figure 1.3 Schematic of thermal contraction caused by thermal motion (filled

arms
temper

arrows

The
the oer
Ille Irv
hano
trrotolt
intimat
be ver
OI the
linkag,
Vibrate
”Aah

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Z’Wzr

ha ve

ea-

vna\

circles are cations, and open circles are oxygen atoms. The solid line shows low
temperature bonds position, dash line shows bonds at high temperature and

anows show the vibration direction of oxygen atoms) [16].

The M-O-M linkage is the basis for the isotropic negative thermal expansion of
the ceramics in Table 1.2. For ZrW203, the MOM linkage is Zr-O-Zr or WOW.
The five materials share several structural characteristics: 1) the crystal structure
is an open, low-density framework structure; 2) the coordination of oxygen is only
twofold; and 3) the M-0 bond is very strong. These characteristics have two
intimately related consequences: 1) The thermal expansion of the M-0 bond will
be very low, and the thermal vibration of oxygen will be very low in the directions
of the M atoms; and 2) thermal vibration of oxygen perpendicular to the MOM
linkage must be very high. With these unique thermal motions, as oxygen atoms
vibrate, M cations are pulled together as shown in Fig. 1.3, resulting in the

negative thermal expansion of the materials [16, 18, 20].

Several studies on the synthesis of ZrW203 substrates have been performed
[24, 25]. One possible application of ZrW203 is to combine it with positive thermal
expansion materials to produce composites with controllable thermal expansion.
ZrW203/Cu [26], ZrW203/Al [27], ZrW203/Cement [28], and ZrW203IZr02 [29-31]
have been studied. However, the large disparity in the thermal expansion

behavior between different components may present major problems in practical

10

applical
A Zr

substral

mlcroelr

applications for some of the aforementioned composites [26, 27].

A ZrW203-containing composite with a CTE of zero can be used as ceramic
substrate of optical fiber Bragg gratings as well as components of
microelectronics. One advantage of using this kind of composite is the reduction
of both decomposition and deterioration due to the temperature change of the

material system.

1.2.2 Ceramic Matrix Composites

Two primary methods are being used to increase the capability of ceramics for
thermal, mechanical, corrosion and structural applications. One method is to
refine the monolithic polycrystalline ceramics. Si3N4, for example, had a reported
tensile strength around 80 ksi in the 1980s, whereas now it is over 110 ksi [7, 32].
The other method is to combine two or more ceramic components, producing
composites that integrate the properties of the constituent materials. There are
two categories of ceramic matrix composites: particle-reinforced ceramic matrix

composites and continuous fiber-reinforced ceramic matrix composites.
1.2.2.1 guide-Reinforced Cera_mic Matrix Commsites

Adding particles of a second ceramic into a ceramic matrix during the
fabrication process produces a particle-reinforced ceramic matrix composite

(PRCMC). Most second phase ceramic powders are between 0.5 and 40 pm in

diameter. An important PRCMC is titanium carbide (TIC) reinforced AI203, which

11

was developed as a cutting tool insert. TiC- Al203 has higher hardness and lightly
higher toughness than pure Al203 and could cut a wider range of alloys including
hardened steel and chilled cast-iron [33]. Al203 with 15-20% addition of PS2
particles has been reported to have toughness between 6.5 and 15 MPa-m"2
(two to three times that of Al203) and flexure strength between 480 and 1200
MPa (higher than both Al203 and ZrOz) [34]. This material is more resistant to

some forms of wear than both Al203 and ZrOz.
1.2.2.2 Fiber-Reinforced Ceram_ic Matrix Compgsites

In the search for improved toughness for ceramics, material scientists
conceived the idea of reinforcing ceramics with continuous strands of
high-temperature fiber. Embedded continuous ceramic fibers reinforce the
ceramic matrix by deflecting and bridging fractures. Fiber-reinforced ceramic
matrix composites (FRCMC) are composed of a ceramic fiber, a fiber-matrix
interface coating and a ceramic matrix. The fiber is converted to useful form by
using conventional textile-forming techniques. Common fiber materials include
‘SiC, Al203, SiOC, and SiNC. FRCMCs can be used to manufacture heater tubes,

hot-gas filters, heat exchangers, and radiant burner, and so on [35].

1.2.2.3 Micromechanics Prediction Models For Particulate Commsites

Many micromechanics models have been presented to predict the effective or

bulk physical properties of composite materials [36-42]. For particulate

12

composites, the Mori-Tanaka method [36] is widely used to determine the

effective elastic stiffness tensor [41, 42]. The effective stiffness tensor is given by
Cc=Cm+Vp(Cp-Cm)AP (1.1)

where the subscripts c, p, and m represent the composite, inclusion materials,

and matrix material, respectively, C represents stiffness tensor, V is volume

fraction and A,, is the inclusion strain concentrator tensor which relates the

average strain in the inclusion to the applied homogeneous boundary strain. The

Mori-Tanaka method defines AD to be
_ —l
A p — T[le + VpT] (1.2)
where l is the fourth rank identity tensor and T is Wu’s Tensor [43] defined as

T = [I +ESm (C p —Cm )1‘1 (1.3)
where E is Eshelby’s tensor determined by the shape of the inclusion [44] and S

represents compliance tensor.

When applying the Mori-Tanaka scheme to a two-phase composite, one needs
to assume one phase as the matrix and the other as the second, or reinforcement,
phase. In metal matrix composites, the metal phase typically constitutes the
matrix and the hard ceramics phase becomes the reinforcement. In case of
ceramic-ceramic composites, the distinction between reinforcement and matrix
phases may not be so clear. As the volume ratio of the second phase increases,

the second phase becomes more and more continuous and the distinction

13

behree
reache.
threshc
phase

theory,
maten'a
degree
Kwon e

that line

between matrix and second phases become ambiguous. When the volume ratio
reaches a certain threshold, the role of each phase completely reverses. This
threshold value depends on the volume ratio, the shape and morphology of each
phase and the consolidation characteristic of each phase [45]. In percolation
theory, this threshold value is called percolation threshold [46]. In real systems of
materials, both phases can be continuous and thus one needs to define the
degree of contiguity. By incorporating the continuity r] as a weighting function,
Kwon et al. [42] revised the Mori-Tanaka method, producing the following model

that linearly interprets the two extreme cases as

Cc = C+ +q(c— -C+) (1.4)
where C+ is the stiffness tensor calculated from Eqation (1.1) by assuming one
phase to be the matrix phase and C- is the one by assuming that the same phase

to be the second phase. The continuity, n, ranging from 0 to 1, has been defined

by Nishimatsu and Gurland [47].

For the effective CTE prediction of a composite, the rule of mixture (ROM) is
the simplest method based on the CTE and volume fraction of each of its

components. The equation for the ROM is
where o is CTE.

The ROM calculates the effective CTE by assuming a linear relationship

14

betwee
one pl
magnit
therma
Therefr
elastic
Kemer

[40]. TI".

The

between the CTE and volume ratio of each phase. However, the thermal strain in
one phase within a composite is constrained by the other phase and the
magnitude of such strain depends on the shear transfer at the interface. Thus, the
thermal strain features strong dependence on the elastic constants [37-40].
Therefore, several other models were presented, which take into account the
elastic constants for the CTE estimation, including the Turner model [37], the
Kemer model [38], the Rosen-Hashin Bounds model [39] and the Levin model

[40]. The calculation formula for each of the models is shown below:

The Turner Model states

ameVm + aprVp

 

a = 1.

C 1(me +Kpr ( 6)
The Kemer model states
ac = orme + apr

 

+ VmVP (“P _ 0"") 1(me + 1(pr + 3Kpr /4G,,,

And the Rosen-Hashin bounds model states

 

 

4VVG (K —K )(a —a)
“C 3Kpr+4Gp(Km+Kp)/2 +<ame+aPVP>
4
4VVG (K —K )(a -a)
I: m p m m p m p
“C 3Kpr+4Gm(Km+Kp)/2 +(“me+“PVP)

 

 

(1.8)

15

where the K is the bulk modulus, G is the shear modulus, the superscript u

represents upper bound and I signifies lower bound.

Equations (1 .5-1 .8) are only suitable for the isotropic two-phase composites. A
more general equation was presented by Levin [40].
_ -1 ‘
ac—am+(ap—am)(Sp—Sm) (Sc‘Sm) (19)
where the effective compliance tensor, Sc, can be calculated by the Mori-Tanaka

approach [36].

These micromechanics models have been used widely to predict the
mechanical/thermal properties of composites. The predictions from the models
have successfully applied in some cases. However, the main drawback has been
that the applicability of these models is usually limited to the composite with the
volume fraction below 0.6 of reinforce phase. Beyond 0.6 value, one need to use

contiguity concept to reverse the role of each phase in the calculation [42, 47].

1.2.3 Ceramic Functionally Graded Materials

The term Functionally Graded Materials (FGMs) describes a class of
engineering materials exhibiting gradually changed properties with position [48,
49]. The property gradient in FGMs, which can be continuous or stepwise, is
caused by a position-dependent chemical composition or microstructure [49, 50].
FGMs, especially Ceramic Functionally graded materials (CFGMs), were

originally conceived as TPS materials for space structures and fusion reactors

16

[48]. CFMGs can be designed to withstand severe temperature gradients of a
TPS whilst retaining mechanical toughness and oxidation resistance. Several
thermal-barrier coating FGMs for TPS have been investigated, including
ZrOz-Y203 FGM and ZrOz-Alzog FGM [51]. Another important application of
FGMs is to join dissimilar materials with different thermal expansion properties.
Thermal residual stresses developed if directly join two materials with different
CTE, which may result in premature joint failure. Due to the components variation
at different position, the CTE of a FGM can change along one direction. By
matching one end CTE of the FGM to one material and the other end to the
second material, the thermal stress caused by CTE difference or thermal gradient

loading can be reduced [52].

A large variety of production methods have been developed for the processing
of FGMs, such as powder metallurgy (PIM), sheet lamination, laser cladding, and
Chemical Vapor Deposition (CVD), to name a few. Among these methods, PIM is

widely used to fabricate metallic as well as ceramic FGMs [53-55].

A Zirconia/alumina (ZrOzlAl203) FGM has been of great interest for its
potential application as thermal-barrier coating and high-temperature heat
exchanger [51, 56]. By incorporation of ZrOz phase, the tensile strength and
fracture toughness of Al203 increases [56, 57]. Cai et al. [58] produced as many

as 23 successive layers of ZrOzlAl203 laminate. Mott and Evans [59] used an ink

17

jet printing method to produce Zr02/A|203 FGMs. Chang et al. [60] and Moon et

al. [61] produced multi-layered ZrOzlAl203 composites by sequential centrifugal

consolidation.

A critical problem in the manufacturing of FGMs by PIM is the formation of
cracks and/or distortion in the samples [58, 62]. These defects are due to the
residual stress caused by mismatches in thermal expansion and sintering among
the constituent components [58, 63, 64]. Since ZrOz and Al203 feature distinct
sintering behavior and disparate CTE, cracks and/or camber were present in
many ZrOzlAl203 FGM samples as evidenced in the aforementioned research
work [58, 60-62]. Hillman et al. [62] found that differences in sintering kinetics
result in cracks with a large opening displacement (>30um), while thermal
expansion mismatch produces cracks with a small opening displacement (<2pm).
Cai et al. [58] summarized three different crack modes: channeling in tensile
layers, debonding and edge-effect cracks. Some reports [58, 62] show that the
number of cracks can be reduced by controlling heating and cooling rates and
layer composition. Torrecillas et al. [65] studied an FGM system featuring zircon
and molybdenum, concluding that a nearly similar transient shrinkage state for

each layer can lead to the final fully-sintered specimen being free of cracks.

18

 

1.3P0

1.3.1 I

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POWdr

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are b.
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and p
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me

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(n

 

1.3 POWDER METALLURGY

1 .3.1 Introduction

Powder Metallurgy (PIM) is the study of the processing of powders. It is the
most common fabrication method for most ceramic and some metal engineering
components [66]. Compared to most other processing methods, PIM is cheaper.
Therefore, PM was considered to be the best candidate method to fabricate core

materials for Perspirable Skin.

The three main steps of PIM to convert powders into useful objects are 1)
powder processing, 2) forming operations, and 3) sintering [66]. The powder
processing may involve 1) milling, which is the mechanical agitation used to break
particles or agglomerates into smaller particles and 2) mixing, which is the
process of thorough incorporating of two or more powders [67]. Many methods
are being used in forming operations of powders such as injection molding, sluny
techniques and compaction [66]. Conventional uniaxial powder compaction, which
is performed with the pressure applied along one axis using hard tooling of die
and punches, is the most widely used method to compact powders. Samples after
compaction are called “greens”. In pharmacology, green samples can be used
immediately as pharmaceutical tablets. In the case of ceramics or metals, green
samples are the precursor for attaining a dense body by sintering. Sintering

describes the formation of bonds between particles close to their melting point. It

19

can occur
phenome
[66,68]. l

mew:

The ti
subseque
size [69-'
specific 5
the 00m;
friction [7
Ciierent 1

132 Cor

can occur at temperatures below the melting point by solid-state atomic transport
phenomenon. However, some instances involve the formation of a liquid phase
[66, 68]. On a microstructural scale, the bonding occurs as cohesive necks grow

at the particle contacts [66-68].

The three steps of PIM are closely related to each other. Each step affects the
subsequent step(s). The initial powder characteristics, such as average particle
size [69-72], particle shape [73], particle size distribution [70-72, 74, 75] and
specific surface area [70] achieved during powder milling and mixing, influence
the compaction and sintering capability. The pressure [71, 76] and the die wall
friction [77] of the compaction step can affect the shape of green body due to

different density distribution [77-80].

1.3.2 Compaction

1.3.2.1 Procedure

Fig. 1.4 shows the detailed compaction process of a uniaxial die set. The loose,
free flowing powder is introduced into the die cavity in the filling step. The Upper
surface of the powder was flattened. Then the top punch is forced into the die to
compact the powder. After compaction (~80MPa), the relative density of compact
is around 50% for most ceramic powders. In the ejection step, the forces acting
upon the punches are removed and the top punch is used to eject the sample

from the confines of the die [54, 66].

20

Bott

—~
(A,
N
M

I:

SEI
effect c

fine sar

            

I
:1 .
I.
o
o . I -'I

Flattenlng Entry of Compaction Ejection
top punch

 

Figure 1.4 The process of die set compaction.

1.3.2.2 Powder Mixing Effect on Compaction

Several studies have already been preformed investigating the powder mixing
effect on the compaction/packing of particles [69, 73, 81]. By adding single-sized
fine sand/metal balls into single-sized coarse sand/metal balls, Westman et al. [69]
and McGeary [81] determined that the mixtures have reduced porosity, thus
showing better compaction capabilities. For ceramic powders, however, this
conclusion may not always be accurate since ceramic powders are quite different.
Firstly, the particle size of a ceramic powder is usually much smaller than that of
the sand or metal balls. The average particle size of a ceramic powder usually is
on the order of submicronlmicron, while the size of sand or metal balls is on the
order of millimeter to centimeter. Secondly, by chemical/physical treatment, some
ceramic powders can have much better compaction capability than other ceramic
powders even if their material compounds are nearly identical. Thirdly and most
importantly, most ceramic powders have a continuous distribution of particles.

Finally, due to the small particle size and large surface energy, agglomerations

21

prevail in ceramic powders. Compared to the sand or metal balls, these unique
characteristics may result in a unique relationship between the compaction

capability and powder mixing for ceramic powders.
1.3.2.3 Dimensional and Density Variation by Compaction

Due to the series of operation steps of compaction, the green samples contain
a degree of stmctural inhomogeneity of two kinds, namely, density distributions as
the variation of the internal form and the dimensional variability as manifest in the
external shape of the compact [78-80, 82-84]. The former is the
non-homogeneous density distribution within the compact. Some regions have
higher densities than others. The latter is the geometry of the external surface of
the ceramic green body that is invariably not exactly the same as, or a simple
linear scale transformation of the shape of the terminal geometry of die cavity

after the green ejection.

The densities of a green sample are not even everywhere. Aydin et al [78, 79]
designed an experiment, in which they used lead balls as tracers to detect the
densification. Their results are similar to others’ report [82-84]. The high-density
regions exist at the near the bottom central region and on the central axis. And the
low-density regions are at the bottom edges and near the top center. However, the
density distribution range varies as different powders. The limitation of Aydin’s

method is only putting the tracers in several positions, not in a continuous way.

22

Byl
sample
mmpa
sector
the higl

geens.

_._A
(A)
[\3
43

[3

Her
trail-ant
finite e
compac
green p
model
mechar

IIIOCIeIS1

By finite element analysis, Aydin et al [80] found after compaction, the green
samples inside the die have large residual radial stress at about the middle of the
compact, and small redial residual stress on the top and bottom surface. After the
ejection of the green sample, the compact is free in the radial direction. Therefore,
the high stress regions relax radically, resulting larger diameter regions in the final

greens. So finally the lateral shape of a green sample is similar to a barrel.

1.3.2.4 Constitutive Models for Powder Compaction

Historically, ceramic component manufacturers have relied heavily on
trail-and-error to minimize density gradients in powder compacts. More recently,
finite element method (FEM) modeling has been used to predict powder
compaction response and to provide insight into the causes of density gradients in
green powder compacts [76, 78, 79, 85]. A critical component of any predictive
model for powder compaction is the constitutive model that describes the
mechanical behavior of the granulated powder. A series of continuum plasticity
models, originally developed in soil mechanics, have been applied to ceramic
powder compaction [86-89]. In those models, modified Drucker-Prager/cap
elasto-plasticity model (modified D-P model) has been identified for successful
modeling the compaction of granulated Al203 powder during uniaxial die pressing
[78-80, 90]. This model has already been included in the internal library of

commercial FEM code ABAQUS [91] for the simulation of powder compaction.

23

Modif
and the s

01. 02. 3'

Um:

Jo:

As sh
linear shr
stress, a
mean str

Which is

Figure I.

We me

Modified D-P model is expressed in a stress space of the mean stress (Om)
and the second invariant of the deviatoric stress J’21/2. By the principal stresses

01, 0‘2, and 03, Om and J’21/2 are expressed as:

am=%(0‘1+0'2+0'3) (1.10)

12 =%|:(O'l ~02)2 +(a2 — a3)2 + (0'1 -a3)2] (1.11)

As shown in Fig. 1.5, modified D-P model consists principally of two parts: 1) a
linear shear failure surface showing increasing shear stress with increasing mean
stress, and 2) a curved cap that intersects both the shear failure surface and the
mean stress axis. There is also a transition region between the two segments,

which is introduced to provide a smooth surface [78, 87, 89].

 

Moving Cap

Elastic
regime

 

 

Om (Mpa)
Figure 1.5. Illustration of modified Drucker-Prager/cap elasto-plasticity model. (d

is the material cohesion, and B is the internal angle of friction).

24

The shear failure surface function F3 is written as:
FS=JJ'2—(tan,6)mn—d=0 (1.12)

where d is the material cohesion, and ,6 is the internal angle of friction.
Intersection of the load path with the shear failure surface defines the onset of
permanent, plastic deformation by shearing. Intersection of the load path with the
cap marks the onset of permanent, plastic deformation by a combination of shear
and volumetric strain. Loading along the mean stress axis is in hydrostatic
compression, and intersection with the cap produces permanent volumetric strain
along. Loading within the wedge-shaped region defined by the shearing failure
surface, the cap, and the coordinate axis is elastic. Plastic hardening occurs with
the application of increasing mean stress. As the material hardens, the cap curve
expands gradually from the dotted curves to the solid curve in Fig. 1.5. The shape
of the cap (Fe) is controlled by a shape factor R (0<R<1) and a transition
parameter a (typically 0.01<a<0.05 [78]). a is used to provide a smooth transition

surface between the shear failure surface and cap.

 

 

 

 

 

 

- -2
2 R J'2
Fe: [am-pa] + a “R(d+Patanfl)=0 (1.13)
v 1+a-
t. cosfl_

where Pa is an evolution parameter that represents the volumetric plastic stain

driven hardening effects, which relates to the hydrostatic compaction yield stress

25

Pb in the following equation [91]:

== ‘pb-Ihi
p“ (1+Rtanfl)

 

(1.14)

The transition surface between the shear failure surface and the cap is

described as

 

 

Ft = [am-p“]2+I‘/J—'2"I“ afl](d+p.tan/3)]2

cos (1.15)

—a(d+pa tanfl)=0

Totally, the modified D-P model requires seven material parameters as input,
including: bulk modulus (K), shear modulus (G), Young’s modulus (E), Poisson's
ratio (v), angle of internal friction (B), cohension (d), cap shape paramenter (R),
and transition surface parameter (a). One important point is that ceramic powders
are pressure sensitive. So those materials depend on the ambient mean stress.
Aydin et al [78-80] applied modified D-P model to model the compaction of an
alumina powder. They indirectly measured most of the seven input parameters.
And the remaining parameters were estimated from data published in the open
literature. Zeuch et a! [89] designed a series of experiments and measured all

seven parameters directly for an alumina powder.

1.3.3 Sintering

1.3.3.1 Sintering Kinetics

26

lire
associat
(ooarsen'
grain bo
atomic m
looarsen
depender

and 5)Vr

Coble
sintering

1. T;

2.T

SII‘IIE

The macroscopic driving force of sintering is the reduction of excess energy
associated with surfaces by a) the increase in the average size of particles
(coarsening), and b) the elimination of solid/vapor interfaces and the creation of
grain boundary areas, followed by grain growth (densification). The five basic
atomic mass transport mechanisms in sintering are: 1) Evaporation-condensation
(coarsening); 2) Surface diffusion (coarsening); 3) Volume diffusion (densification,
dependent on location of the source); 4) Grain boundary diffusion (densification);

and 5) Viscous or creep flow (densiflcation) [92].

Coble.[93] proposed three stages in sintering. During each stage, different

sintering kinetics takes place.

1. The initial stage: The inter-particle contact area increases by neck growth.

The relative density increases to 65%.

2. The intermediate stage: Continuous pore channels are seen at the triple
points (three-grain junctions) and relative density increases from 65 to

90%.

3. The final stage: Pore phase is eventually pinched off. Continuous pore
channels disappear. Individual pores are either lenticular on grain
boundaries, or rounded within a grain. Pore and grain boundary mobility

increases dramatically at this stage.

Sintering kinetics is dependent on many variables [92], listed as follows,

27

. Temperature: Increasing temperature enhances sintering kinetics as the

potential for diffusion mechanism increases [66, 92].

. Green density: The higher the green density, the less pore volume that has

to be eliminated, the densification rate decreases [66, 70].

. Uniformity of green microstructure: Non-uniformity caused by agglomerate
can lead to abnormal grain growth. Non-unifon'nity after cold die

compaction will lead to shape distortion [70, 80, 84, 93].

. Atmosphere: In some cases, the atmosphere can enhance or reduce

diffusivity [66, 92].

. Impurities: Impurities can be introduced into powders in the powder
process or during compaction step. Some impurities can form a liquid
phase or low-temperature eutectics with main powder during sintering and
then enhance sintering kinetics of main powder. Some compounds, on the
other hand, can lower surface diffusion and grain boundary mobility, finally

decrease the sintering kinetics of main powder [95].

. Particle size: Finer particles have more surface area than coarser particles,
and thus in principal the use of finer particles favors sintering. In practice,
however, very fine particles may lead to agglomeration. The agglomerates
tend to sinter together into larger particles, which not only dissipate the

driving force for densification but also produce large pores among the

28

partially sintered agglomerates.
7. Phase transition: Densification rate changes due to phase transition [96].

8. Size distribution and porosity: Narrow size distribution will reduce abnormal
grain growth. However, wide size distribution enables a denser initial
particle packing [97], reducing sintering kinetics due to less porosity {98].
The effect of size distribution is also investigated by 'I'Ing et al. [74, 75] and
Darcovich et al. [99, 100]. TIng et al. [74, 75] concluded that prior to the
occurrence of grain growth, the densification rate increases as the particle
size distribution width increases. After growth occurs, the rate decreases

as the particle size distribution width of the staring powder increases.

1.3.3.2 Sintering Curves and Models

Two types of curves are commonly used to describe the sintering kinetics: the
shrinkage rate—sintering temperature curve and the densification rate-relative
density curve. For the latter one, the relative density D is the ratio of the mass
density of the sample to the theoretical density of the corresponding powder

mixture. And the densification rate is defined as:

_ 5p _D(T)
pat D(T) (“6)

 

éS(T)

In the last decades, a lot of research has been devoted to predict the

densification kinetics of powder compaction [101-105]. Some of this research

29

attempted to obtain a description from the modeling of physical mechanisms
responsible for sintering. Most of them derived the densification kinetics of a
powder aggregate from the sintering of two contacting spheres by viscous flow
diffusion phenomena. For example, Su et al [104] proposed a master sintering

curve model, and they described the densification rate as:

és (T) = 7QF(D)D:
kT(G(D))

 

cam-£95) (1.17)

where g is the surface eneI‘QY, fl is the atomic volume, I' (D) relates the driving
force and mean diffusion distance, k is the Boltzmann constant, G is the mean

grain diameter, Q is the apparent activation energy, Do is the diffusion coefficients

and R is the gas constant.

Two inherent problems limit the wild application of the physical models for the
densification (sintering) process. One problem is the difficulty to exactly measure
the physical parameters such as the surface energy 9 and the apparent activation
energy Q in Su’s model [104]. Such parameters require a set of very complex
experiments, some of which need to be in an extreme environment, such as high
vacuum and precise temperature. The other problem is that parameter
adjustments are necessary to apply the models from one material to other
materials depending on the diffusion mechanism involved [106]. As a result, other
researchers used an alternative approach, phenomenological model. The

phenomenological model consists of fitting analytical expressions directly from the

30

mwhr
desoribir
emmm

Ane.

where I
and ifw
I0 grair

analyze

1.4 DIS

results of sintering experiments. Thus, it provides a constitutive equation
describing as precisely as possible the real behavior of the material without

regarding the physical meaning of its parameters.

An example of the phenomenological models is presented by Hsueh [107]:

as = Q(T)[Doo(T) —D]" (1.18)
where 080(7) is the theoretically possible full-sintered density at temperature T.
and if we compare formulas (1.18) and (1.17), we can know that 00') is related
to grain size and activation energy. Gillia et al [108] used H'sueh’s model to

analyze the densification kinetics of WC-Co mixture.
1.4 DISSERTATION OVERVIEW

There are seven more chapters in this dissertation. Chapter 2 summarizes
experimental materials and facilities used in the study; Chapter 3 and 4 discuss
compaction and sintering of Powder Metallurgy, respectively, which are the
physical foundations of this research. From Chapter 5 to 7, each chapter presents
the process and properties of one advanced material, including ZrOz-Al203
stepwise FGM, ZrW203 and ZrW203-Zr02 composites, and ZrWzOg-Zroz
continuous FGMs. Finally, Chapter 8 states conclusions and provides suggestion

for future works. Fig. 1.6 illustrates the relationship among the chapters.

31

 

Chap. 8 Summary

   

   

‘

 

 

 

Chap.5. ZrOz-A1203 stepwise FGM:
Manufacturing and cracks prevention

Chap.3. The physics
of powder metallurgy:

Compaction
Chap. 6. ZrW203 and ZrWzOg-ZrOZ composites:

. In-situ reaction and physical properties
Chap.4. The physrcs of

powder metallurgy:
Sintering

Chap.7. ZrWzOg-ZrOz continuous FGMs:
Fabrication and thermal expansion gradient control

 

 

 

 

 

 

 

I Chap. 1. Introduction Chap. 2. Materials and facilities

Figure 1.6. Illustration of the relationship among chapters

32

CHAPTER 2
MATERIALS AND FACILITIES
2.1 MATERIALS

Eight ceramic powders used are listed in Table 2.1, which included four
alumina (Al203) powders, two Zirconia (ZrOz) powders, one tungsten (VI) oxide

(W03) powder and one zirconium tungstate (ZrW203) powder.

Table 2.1 Characteristics of the ceramic powders used in this study

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

. Chemical analysis (ppm)

Powder Material Na K Fe Ca Si Mg a-phase
TMDAR 4 2 5 3 3 100%
CR-lS Al 13 22 2 3 13 90%

203
CR-6 13 22 2 3 l4 <1 100%
615-1 12 15 5 2 42 <1 100%
TZ3YS ZrOz Stabilized by 5.2 wt% Y203
CERAC-2003
W-Fluka wo3 ..--
ZW-OR ZrW208 ---
Powder Mean particle size (um) Mean pore size (pm) Bulk density
TMDAR 0.17 0.09 0.9 g/m2_
CR-lS 0.42 0.18 0.45 g/m2
CR-6 0.60 0.27 0.6 g/m2
GE-l 9.76 0.24 0.45 g/m2
TZ3YS 0.54 0.23 0.75 g/m2
CERAC-2003 1.23 0.27 0.71 g/m2
W-Fluka 8.22 0.29 0.85 g/rn2
ZW-OR 12.33 0.26 0.66 g/m2

 

 

33

 

The four alumina powders are TMDAR (Taimei Chemical CO., LTD., Japan),
CR—15, CR-6, and GE-1 (Baikowski Ind. Corp., USA.) The two Zirconia powders
include TZ3YS (Tosoh 00., Japan) and CERAC-2003 (CERAC Inc., USA.) The
tungsten (VI) oxide powder is W—Fluka (Sigma-Aldrich, U.S.A.). And the zirconium
tungstate powder is ZW-OR, (Teledyne Wah Chang, USA.) All the powders
feature submicron particle sizes. The particle size distribution profile for each
alumina powder is presented in Fig. 2.1. Except the TMDAR and ZW-OR, other

powders are with lognonnal particle size distribution.

 

100 /.// v
E 804 /

3 4

g 60 A

g . ./

g 40. /

'g ‘ +TMDAR

E —o—-CR-15 I

E 20- +CR-8

5

 

 

 

+GE-1 [I

 

n
0.0 0.3 0.6 0.9 1.2 1.5 5 10 15 20 25
Particle size (pm)

Figure 2.1. Particle size distribution profiles of various alumina powders.

The micrographs of the eight raw powders are shown in Fig. 2.2. The TMDAR
and CERAC—2003 are almost agglomerate-free while all other powders feature
many agglomerates. The agglomerates of GE-1, W-Fluka, and ZW-OR are in
flake shape and those of CR-15, CR-6, and TZ3YS are in near-spherical shape.

The single particle shape of all the powders is in near-spherical shape.

34

9.1-. .r. v.

 

h
Figure 2.2 The raw powder SEM micrograph of a) TMDAR, b) CR-15, c) CR—6, d)

GE-1, e) TZ3YS, f) CERAC-2003, g) W-Fluka, and h) ZW-OR.

35

2.2 EXPERIMENTAL FACILITIES

As discussed in Section 1.3, typical techniques of PIM method include powder
mixing, powder characteristics testing, compaction, sintering, mass and volume
measurement, and microstructure observation. To perform these steps, various

facilities were used.

1. The particle size distribution for each grade was measured by a Malvem
MicroPlus particle size analyzer (Malvem Instruments Ltd, UK). The

measurement range of the instrument is 0.1-1000 pm.

2. Powder mixing was processed in a jar mill (U.S. Stoneware 764AVM,
USA.) using 12mm diameter alumina and/or Zirconia mixing media for 48
hours at a 75 rev/min speed, or by a Speed Mixer DAC 150 (FlackTek, Inc.,
USA) for 3 minutes (1 minute for each cycle and totally 3 cycles) at the

angular velocity of 1700 rad/s.

3. Mass was measured by an electronic balance (Adventures AR2140,

OHAUS Corp. USA). The resolution is 0.1 mg.

4. Powder compaction was performed in a single-action die made by 1144
Stress Proof steel. The load to compact powder stacks was in the range of
60 to 210MPa, which was applied by either MTS Insight 300 (MTS
Systems Corp. USA) or CARVER 3912 (CARVER INC., USA). Depending

on the die dimension, the green samples were of 22.02mm, 19.04mm, or

36

7.95mm diameter. The compaction speed of MT S Insight 300 was

10mm/min and the stress resolution is 0.013MPa.

. Green compacts were sintered in air (Carbolite-HTF1700, UK). Several
different ramp/soak sintering cycles were used based on material
properties, which would be discussed in following chapters. The
temperature control resolution of the furnace is 1°C, and the ramp rate can

set up to 15°Clmin.

. The length of samples was measured by a MARATHON electronic digital

caliper. The resolution is 0.01 mm.

. The volumes of the fully-sintered pieces were measured in water by

Archimedes’ principle. The resolution is 0.050m3.

. To attain clear micrographs, the fully-sintered samples were polished using
polisher (Abramin, Denmark) and thermal-etched in a box fumace
(Carbolite-HTF1700, UK). The therrnaI-etch temperature varied with the

materials, which will be discussed in the following chapters.

. Microstructure was observed by Scanning Electron Microscopy (JEOL

6400V, Japan).

10. Real time sintering testing was performed using a Thennomechanical

Analysor (TMA), SETARAM SETSYS Evoluation 95, with argon gas

providing a protective environment.

37

2.2.1 Introduction of SETARAM SETSYS Evaluation 95

SETARAM SETSYS Evoluation 95 is the most important facility used in my
research. It is designed by SETARAM instrumentation, France
(http://www.setaram.com/). This machine measures the deformation of a sample
under non—oscillating stress against time or temperature with prescribed
ramp/soak path. The testing temperature range of SETSYS Evolution 95 is from
room temperature to 1750°C [108]. Figure 2.3 shows the front view of this

analyzer.

 

Figure 2.3. The front view of the SETARAM SETSYS Evoluation 95 (1-head cover,
2-fumace side watch, 3-mode changing switch, 4-open/close head switch, 5-side

cover, 6-proctective gas inlet and outlet tube).

38

When the head cover open, the sample can be put in the sample chamber,
which is an alumina tube. A probe connected to a displacement transducer is
placed in the sample chamber. The position of the probe can be adjusted so its tip
can touch the top surface of the sample. In general, a 5-gram load is applied to
the probe to ensure its contact to a sample throughout the entire experiment. It
has been verified that this small force does not influence the testing results [109].
The displacement transducer equipped in the SETSYS Evolution 95 is
characterized by its robustness and high accuracy; it can detect dimension
changes as small as 0.01 micron. The transducer uses an electromagnetic
system for automatic control of the force applied to the sample, between 0.01 and
1.5 N. The force can be increased by adding weights (up to 200 grams) on a top
plate. Transducer calibration and force control are managed automatically by

computer [108].

The SETSYS Evoluation 95 has a cylindrical furnace. The heating element is
made up of graphite rube and fitted in the centerline of the furnace. The
thermocouple is composed of Pt/Pt-Rh and can withstand temperatures as high

as 1 750°C [1 08].

With its software, the SETSYS Evolution 95 can be used as a dilatometer to
test many material properties, such as the thermal expansion coefficients (CTE),

the softening temperature, the glass transition point, and so on. The SETSYS

39

Evolution 95 is also particularly suitable for measuring controlled-rate sintering.
By measuring the displacement of one dimension and performing calculations,
this TMA can give the shrinkage rate—sintering temperature curve or densification
rate—relative density curve, which will be introduced in Chapter 4. By a set of
specially designed probe and support, the SETSYS Evolution 95 also can perform
3-point flexure measurements, which would give the temperature dependence of

Young’s modulus data of a sample.

40

CHAPTER 3

THE PHYSICS OF POWDER METALLURGY:
COMPACTION

3.1 POWDER MIXING EFFECT ON THE COMPACTION CAPABILITIES OF

CERAMIC POWDERS

As discussed in Section 1.3.2.2, the relationship between the compaction
capability and powder mixing for ceramic powders may not as simple as the
conclusion made by Westman et al. [69] and McGeary [81] for sand or metal balls.
Therefore, the main focus of this section is to study the compaction of ceramic

powders in relation to the powder characteristic and other mixing details.

3.1.1. Materials and Experimental Procedure

In the series of experiments, the four alumina (Al203) powders, TMDAR,
CR-15, CR-6, and GE-1 were investigated. The detailed characteristics for the
powders have been summarized in Section 2.1. In the selection of the four
powders, the study considered CR-15, CR-6, and GE-1, which are all from the
same manufacturer, feature near identical chemical components. The size
distributions of all CR-15, CR-6 and GE-1 are nearly lognorrnal. However, due to

the difference in particle size distributions and mean particle sizes, the

41

compaction capabilities of these three powders are quite different. TMDAR, on the
other hand, was chosen because it is specially treated, both chemically and
physically. Its particle size distribution has a very nanow non-Iognonnal range and
it yields a sintered product with very low porosity. These two characteristics yield
the well-known high compaction/sintering capability of TMDAR powder. Also,
TMDAR is almost agglomerate-free while the other three powders contain

agglomerates (Fig. 2.2).

All possible two-powder combinations with the four powders were mixed in
various mass ratios, and in total six powder mixture systems were produced. The
mixture systems include TMDAR+CR-15, TMDAR+CR-6, TMDAR+GE-1,
CR—15+CR-6, CR-15+GE-1, and CR-6+GE-1. In addition to four unmixed
powders, each system contains nine powder mixtures, in which the proportions of
one powder in the mixtures range between 10% and 90% in 10% intervals. In total,
fifty-four powder mixtures were studied. The powders were mixed with Speed
Mixer DAC 150 (FlackTek, Inc., USA) for 3 minutes (1 minute for each cycle and
totally 3 cycles) at the angular velocity of 1700 rad/s. Six grams of each powder
mixture was measured by Adventurer AR 2140 (Ohaus Corp. USA) with a
0.00019 resolution; and then poured into a single-action die made of 1144 Stress
Proof steel. The inner diameter of the die, Din, is 22.19mm. Before pouring the

powders into the die, the die wall was lubricated with graphite powder (Panef

42

Corp., USA).

The top surface of the powder was flattened and then the top punch was
inserted into the die until it touched the powder. The compaction load was applied
on the top punch by MTS Insight 300 (MTS Systems Corp., USA). The speed was
10mm/min and the stress resolution is 0.013MPa. During the compaction, only the
top punch moved. The compressive forces applied on the top (Ft) and bottom
punches (Fb) as well as the displacement of the top punch (2:) were recorded
continuously as a function of time by the load sensors. At first, the pre-load of
0.5MPa was applied to set an initial state. The preload is necessary to measure
the compact characteristics accurately before starting the main compacting
process. After pre-loadlng, the initial height of each sample, h), was measured.
This was done by measuring the total height of the two punches and the
pre-Ioaded compact inside the die, then subtracting the height of the two punches.
The measurement was achieved by Marathon electronic digital caliper with a
0.02mm resolution and a 150mm measurement range. Considering the diameter
of each compact to be the same as the inner diameter of the die, Din, the initial

relative density, Ri, can be calculated by the following equation:

_pi_m/Vi_ m

Ri - —
pf pf —3‘:75 Dinzhi

 

 

 

(3.1)

where m, V, and p represent mass, volume, and density, respectively, and the

43

subscripts i and f represent initial and theoretically fully value. The theoretical

fully-density of alumina was taken as 3.9759/cm3.

After obtaining the initial relative density, the die set with pre-loaded compact
was put back into the load frame, and then the load of 80MPa was applied to
compact samples. The final green samples produced a diameter of 22.19mm and
their heights ranged from 7.05mm to 9.1mm. Thus, the height/diameter ratios of
compacts were between 0.3 and 0.4. By keeping a low height/diameter ratio, the
transmit force applied on the bottom punch and the applied force on the top punch
were almost identical in the compaction. The discrepancy between the two
recorded forces was less than 0.2%. The masses of the green samples were
measured again after compaction. There was always an expected mass change
due to the attachment of powders to the die wall and the punches as well as the
powder loss during the transport. However, this change was very small, less than
0.4%, and was neglected. Several green samples were coated with nail polish
and then their volumes were measured in water by Archimedes’ principle. Those
values were then compared to the corresponding volumes calculated by the final
sample heights, hf; and diameter, Din, The discrepancies between the two groups
of values were minimal, less than 1.1%. Therefore, only the calculated volumes

are reported in this investigation.

3.1.2 Relative Density-Stress Relationship for Various Powder Mixtures

By the recorded top punch displacement, Z), and the initial compact height, h),

or final compact height, hf, the sample height at time t, ht, can be calculate,

h: =hi-Zt (3.2a)
h, = hf + Zt (3.2b)

The ht calculated by Equation (3.2a) or (3.2b) for any compact was the same.
Therefore, two separate measurements, h,- and hf, for each compact were for

self-consistency.

From the calculated ht, similar to calculating the initial relative density, the

relative density at time t, defined as Rt, can be found as,

pt _m/Vt_ m

Rt = — —
pf pf —3°i75 IrDinzht

 

 

(3.3)

In Equation (3.3), the sample diameter was assumed to be matching the inner

diameter of the die, Din.

The corresponding stress, at, at time t can be obtained by the punch

diameter, Din, and the recorded load, Ft.

Ft _ Ft

St —l-7rDin2
4

at (3.4)

where S; is the cross-sectional area of the top punch.

The relative density-stress curves for each powder mixture group were then

drawn. Fig. 3.1.a and Fig. 3.1.b show the representative curves for the

45

TMDAR+CR-15 and CR-6+GE-1 powder mixture groups, respectively. For clarity,

only six curves were included in each figure.

 

 

 

 

   

 

 

 

 

so

55- ,

50‘ 45‘
§ § ‘
v 45 V a
a 340 ..
a .3 ‘ .
5 4° F
”O 8 35- ,I‘ v
g 35 o OI I. I —CR'6
3 .i I g 30 f , ° - -' ‘MCR-B
a? 30 —TMDAR - - -80% TMDAR g ’1' ' 6095085

- - ~- 60%TMDAR ----40% TMDAR , ""8096 06-6
25 -----20% TMDAR ----- CR-15 25 ° “”654
0 ' ' ' 4'0 ' ' 80 0 ’ 4'0 80
Stress(MPa) Stress (MPa)
a b

Figure 3.1 The relative density-stress curves by the compaction for a)

CR-15+TMDAR and b) CR-6+GE-1.

Under a constant compaction load or stress, the difference of the relative
densities represents the change in the compaction capability in different mixtures.
A higher relative density represents improved compaction capability. Even the
absolute relative density values continuously increase with the compaction load,
the relationship between the relative density and powder proportions remains
similar for each powder mixture group as Observed in Fig. 3.1. Therefore, one can
conclude that the starting powder combination determines the compaction
capability of each powder mixture. In addition, the initial relative densities dictated
by the starting powder combination can be used to quantify and compare the

compaction capability of each powder mixture.

46

The relationships between the initial relative density and the powder
proportion are shown in Fig. 3.2 for all six powder mixture groups. For each curve,
the left end is the 100% of the fine powder and the right end is the 100% of the
coarse powder. The ‘fine” or “coarse” powder is defined by the average particle
size 5 of the powder. From Table 2.1, we know

136E —1 > Den —6 > ECR —15 > 511140.112 (3.5)

 

—l— TM DAR+CR1 5 —O— TMDAR+CR6
+ CR15+GE1 -1'— CR15+CR6
+ CR6+GE1 +TMDAR+GE1

 

 

Initial relative density (%)
l8 8 83 B 8 8 .‘rt 83 8 s t.

 

Figure 3.2 The initial relative density — coarse powder proportion for all six powder

mixture groups after 0.5MPa pre-load compaction.
Fig. 3.2 shows two kinds of relationships between the initial relative density
and the proportion of the coarse powder.

1) Linear relationship: TMDAR+CR-15 and CR-15+CR-6 powder mixture
groups show this characteristic. The maximum relative density

corresponds to 100% of one of the powders.

47

2) Nearly parabolic relationship: The maximum relative density of some
powder groups with this relationship occurs with certain powder mixtures,
such as TMDAR+CR-6, CR-15+GE-1, and CR-6+GE-1. This is similar to
the conclusion of Westman [69] and McGeary [81]. However, the
proportions of coarse powder in the powder mixture that attained the
maximum relative density are between 40% and 60%. These values
differ from the reported 30% by Westman [69] and McGeary [81] for sand
and metal balls. Another powder systems, TMDAR+GE-1, has the

maximum relative density at 100% TMDAR.

3.1.3 Relative Density-Strain Relationship for Various Powder Mixtures

In the study of ceramic powders’ compaction, Aydin et al. [78-80] defined axial

true strain E t as the following,

5t:

 

ht
111(;)| (35)

Fig. 3.3(a) and Fig. 3.3(b) show the representative relative density-strain
curves for the TMDAR+CR-15 and CR-6+GE-1 powder mixture groups,
respectively. Comparing Fig. 3.3 and Fig. 3.1, the powder mixture with better
compaction capability/density in Fig. 3.1 is also with a higher relative density

under any strain values in Fig. 3.3.

48

6C 50

 

 

      
    
 

 

 

 

 

 

 

i—TMDAR ,
55----80%TMDAR ,
‘----60%TMDAR 45‘ - ,
”‘50- " A s 0'
i 1 .' . 12, ’
gas. l/ . €40 .- .
co , . ,I . ' ‘
c . ,' ,o r: '
84° ..z" .- " 8 35 , ."—CR—6
3 35 r .- -"’.r' x' ,,,, ,2 5; v .- - - -80%CR-6
s , ’1' ’3’ ''''' g 30 ' ., - 60%CR-6
a? 30"., x.- .... --- 40%TMDAR m ‘ ..z ----40%CR-6
. ..... ’ ''''' --°--20%TMDAR ' ."" ----'20%CR-6
25 r ------------ CR-15 25 .......... era-1
0.0 ' 0:1 ' 0'2 ' 0:3 ' 0:4 ' 0:5 ' 0:6 0.0 ' 0:1 ‘ 0T2 ' 0T3 ' 0:4 ' (is - 076—
Strain Strain
a b

Figure 3.3 The relative density-strain curves by the compaction for a)

CR-15+TMDAR and b) CR-6+GE-1.

The Mircocal Origin and Wolfram Mathematica software were employed to
calculate the trend functions of the relative density-strain curves. The relationship

exactly fits into the following equation for each powder mixture,
Rt = K‘C‘gt (3.7)

where k has the same unit as density, glcm3. Table 3.1 displays the k value for the

TMDAR+CR-15 powder mixture group.

Table 3.1. The coefficient k in Equation (3.7) for representative TMDAR+CR-15

powder mixture

 

CR-15 0% 10% 30% 50% 70% 90% 100%
k 1.4228 1.3843 1.29 1.1887 1.0688 0.9622 0.908

Equation (3.7) shows that a powder mixture with a higher density/compaction

49

capability has a larger k value. Compared the k values in Table 3.1 to the
corresponding initial relative density value in Fig. 3.2, they are the same. This
indicates the physical meaning of k in Eq. (3.7) is the “initial relative density".
From the relative density and strain definitions in Eq. (3.3) and (3.6) as well as Eq.

(3.1), the conclusion can be verified as below.

 

 

 

 

 

Ri- m i i
T 3.975 . 2 . 1 . 2
—4 IrDm hz +=>Rt—ZflDm ht_ht
-‘ 1 . .‘_- —
Rt: m R1 —-7rDm2hr ht ):>Rt=Riegt (3.8)
3.975 . 2 '
——7rDm ht
4 1
_ ht
t= 1n —
8 (hi) ]

 

 

 

Therefore, the method to compare compaction capability of various powder
mixtures from their relative density-strain curves only needs to consider the initial
relative density value. In other words, from either the relative density-stress or the
relative density-strain curves, one can use Fig. 3.2 to find the difference in the

compaction capabilities of powder mixtures.

It is important to emphasize that the initial relative density is dependent on the
pre-load. For example, when the pre-load reduced to 0.3MPa, the initial relative
density for pure TMDAR was changed to 30.46%. If the stress/strain goes to zero,
the initial density goes to the bulk density listed in Table 2.1. However, even the

absolute value of the initial density varies, the relationship between the relative

50

69056)

oompa

3.1.4 n

3

Sin
eleme.
the di‘
studiel
among
comp?
ohang
‘non-c
Daniel
'IIOIH

rlitluir

 

Daniel
Fora

Vahje

Ifr

the in

density and strain remains equivalent to Equation (3.7) and the order of

compaction capability/relative density remains unchanged.

3.1.4 Prediction of Initial Relative Density Versus Powder Proportion Curve

Shape from the Characteristics of Powders

Since the four powders used are the same material with nearly identical
elements, the linear and parabolic types of curves in Fig. 3.2 may be a result from
the difference in the particle size distributions and mean particle sizes. Numerous
studies [69, 71, 81] mentioned that if fine particles can fill into the interstices
among coarse particles, then the powder mixture should produce a better
compaction capability. In this condition, the total volume does not necessary
change with the addition of fine powder(s). This will be stated as a
“non-disturbance” condition. For a bimodal discrete sphere size system, the
particle size of coarse powder is at least 2.4 times of that of fine powder to make a
“non-disturbance” powder mixture. More strictly, the conditionfic/Df >6.5, is
required for the non-disturbance mixing [110], where 5 represents the average
particle size and the subscript, c or f, represent coarse or fine powder, respectively.
For a continuous size distribution system, the limitation average particle size ratio

value is approximately 3.6 [111, 112].

If the average particle size ratio is less than 3.6, the fine powder cannot fill into

the interstices of the coarse powders. The mixing of the two powders only results

51

in stacking them together mechanically. Therefore, the relative density-powder
proportion curve would be linear. Among the powder mixture systems we
employed, TMDAR+CR-15 and CR—15+CR-6 show this trend. The corresponding
linear curves in Fig. 3.2 verify this assumption. However, the agglomerates in
some powders (Fig. 2.2) may influence the pore/particle size and result in partial
filling of fine particles into coarse particles. The agglomerates may be the reason

why some parts in those two curves are not perfectly linear.

If the average particle size ratio is larger than 3.6, would the mixtures always
have better compaction capability than each powder since the fine powder can fill
into the interstice of the coarse powders? Based on Table 2.1 and Fig. 3.2, that
will not be true. For example, the Dc/Df of TMDAR+GE-1 powder mixture
group equals 57.4. However, its highest density happens with pure TMDAR. This
is due to the large difference in the compaction capabilities of the two powders.
The initial relative density difference between TMDAR and GE-1 is as large as
12.1%. This shows that even the TMDAR does fill into the intersticesof GE-1; the
increase in the compaction capability due to the interstitial filling is negligible
compared to the excellent compaction capability of TMDAR. Therefore, the
excellent compaction capability of TMDAR dominates the compaction of the

mixture, resulting in the highest density with pure TMDAR.

For the remaining three mixture groups with parabolic curves shown in Fig. 3.2,

52

 

the dirt
0.87 at
small e

thus p

 

powde
propo.
When
proper
capahr
exceer
Capab»,
TMDA
dihere
TI‘rerel

018th

3.1.5 I

Th

inIiial

 

the difference in the initial relative density between two powders ranges between
0.87 and 5.9%. In the three curves, the difference in the relative densities are
small enough to be compensated by filling fine powder into the coarse powder,
thus producing mixture(s) that have better compaction capability than the two
powders. The Maximum Compaction Capability (MCC) occurs at 40-60%
proportion of coarse powder, close to the powder with better compaction capability.
When the difference in compaction capability between the powders increases, the
proportion of powders at MCC shifts closer to the powder with better compaction
capability. Once the compaction capability difference between the powders
exceeds a threshold, the peak converts to the powder side with better compaction
capability, as shown in TMDAR+CR-6, CR-15+GE-1, CR-6-I-GE-1, and
TMDAR+GE-1 powder mixture groups. In these four powder mixture groups, the
difference in the initial relative density between two powders ranges 7.1-12.9%.
Therefore, we considered the threshold should be around may be in the 7.1-10%

relative density difference

3.1.5 Discussion about the Limiting Boundaries of Initial Relative Density -

Powder Proportion Curves

The discussion above allows us to conclude that the straight line passing
through both powders’ initial relative densities sets the lower boundary for an

initial relative density - powder proportion curve. Can the upper boundary also be

53

defined?

In Westman and Hugill’s study [69], the reciprocal of relative density Of the
compact was used to quantify the compaction capability of various sand mixtures.
By assuming the fine powder is infinitesimal, one lower boundary was proposed
for the curve, as the CO line in Fig. 3.4. By assuming a larger ball immersed in the
infinitesimal balls/water, the other lower boundary FN was obtained. The study
concluded that the reciprocal of relative density - powder proportion curve should

lie in the triangle CFK.

1.8
1.6:
1.4:
1.23
1.0:
0.8:
— 0.81

 

 

of Relative density

 

 

0-0 3. ' 1 ' l r I . I f
0 20 40 60 80 100

Proportionofcoarsesand(%)

 

Figure 3.4 The dependence of the reciprocal of relative density on the proportion

of coarse powder and its triangle boundary by Westman et al. [69].

Corresponding to Westman and Hugill’s idea, the O and N points in Fig. 3.4
should convert to the maximum initial relative density of the powders in the initial

density versus powder proportion curves. To obtain these maximum initial density

54

values, each powder was put into the die set and then the die set was put on a
plane sieves vibrator (Thomas Scientific, USA). The frequency of the vibration
was set to 60Hz and the amplitude was set to 4mm. During the vibration, the
particles rearranged to an optimal anangement. The die set was then moved to
the MTS machine and the powders were compacted to the 0.5MPa pre-Ioad. Fig.
3.5 shows the dependence of the initial relative densities of the four powders in
relation to the vibration time. Clearly, as a result of the particle rearrangement
caused by the vibration, the initial relative density increases for each powder. The
density increases with vibration duration, and converges to a final value. Each

final value is considered to be the maximum initial relative density value for the

 

 

corresponding powder.
40 _.-.
g
e 35
C
0)
‘O
E 30
g —I—TMDAR
.73 +CR-15
E 25 +01%
+GE-1

 

 

0 '22? 4'0 ' e’o 'abiiao'iéo'iio'
Vibrationduation(min)

Figure 3.5 Dependence of the initial density on the vibration time for each powder.

The lines, FM: and CMf, in Fig. 3.6, are Obtained by connecting the relative

density of the fine powder to the maximum relative density of the coarse powder

55

and the relative density of the coarse powder to the maximum relative density of
the fine powder, respectively. These two lines will build the upper boundaries for
the initial relative density-coarse powder proportion curve of CR-15+GE-1 powder

mixture group. And the triangle FCK creates the enclosed boundary.

 

 

 

 

 

40- Mf Mc'
.é‘ K
«II
8
'o 30-
O
n> I
E
g; 25-

F ~ C
20 ' l f t ' l ' r '
0 20 40 60 80 100
Proportion ofGE-1 powder(%)

Figure 3.6 Triangle boundaries for the initial relative density-powder proportion

curve of CR-15+GE-1 powder group.

 

+ CR-6+GE-1

 

Relatlve densrty (%)
R 83 B 8 8 it 8 83 8 8

 

 

0'2'0'4'0T80780'100
Proportion of coarse powder (%)

Figure 3.7 Triangle boundaries for the initial relative density-coarse powder

proportion curves of TMDAR+CR-6, CR-6+GE-1 powder groups.

56

Fig. 3.7 shows the triangle boundaries for TMDAR+CR-6 and CR-6+GE-1
powder mixture groups. Clearly, as CR-15+GE-1, each initial relative density
versus coarse powder proportion curve in Fig. 3.7 also lies within the

corresponding triangle.
3.1.6 Discussion about the Maximum Packing/Compaction Relative Density

Brouwers [110] proposed an analytical expression to calculate the void
fraction/packing density of continuous particle distribution powders of the

Iognorrnal type. The equation is

0' max)—(1—¢1)fl/(1+a2)

:1—
¢ ¢(dmin

(3.9)

where (I) is the void fraction of the powder with continuous particle size distribution,

dmax and dmin represent the maximum and minimum particle sizes, respectively.
()1 is the void fraction of assumed uniformly sized particles with the average
particle size, a is the distribution modulus, and B is the scaled gradient of the void
fraction. Commonly, both ()1 and B can be set as constant, and in Brouwers’ study
()1 =0.5 and [3 = 0.35 for fairiy angular quartz. The distribution modulus a is
typically between 0 and 0.37 and when a equals 0, the maximum packing fraction
is obtained. Following the Brouwers’ parameter setting of 4’1 and [3, the range of

maximum relative packing densities of each powder was calculated, as presented

in Table 3.2.

57

 

raue
equah

To
powde
conrn
exper
CRti

vaueI

DOW0

Ihecn

IS the

theu

Oh
TMD/

BqUa.

 

 

Table 3.2. The maximum relative packing density calculated by Brouwers’

equation and from the experiments

 

TMDAR CR-15 CR-6 GE—1
Calculated a=0 59.4% 64.2% 64.9% 64.3%
results (1:0.37 58.4% 62.7% 63.3% 62.8
Expenmenta' 1500'" 59.8% 52.5% 53.3% 52.7%
results vrbratlon

 

To attain the maximum compaction density from the experiments, 39 of each
powder was vibrated for 150min and then compacted to 220MPa. After 180MPa
compaction, the relative densities were convergent to maximum values. Those
experimental maximum relative densities are also listed in Table 3.2. For CR-15,
CR6, and GE-1 powder, the experimental values are less than the calculated
values. Two reasons contribute to the lower experimental results, 1) the (I1 and
[3 may not be exact for our powders, and 2) the agglomerates presented in the
powders and the non-perfect spherical-shaped powder particles [113]. However,
the order of the relative density/compaction capability among these three powders
is the same in both the calculation of Brouwers’ equation and the experiments.
From this point, the Brouwers” equation has an excellent potential for predicting

the compaction capability of various powders.

Contrary to CR—15, CR-6, and GE-1 powders, the experimental result for
TMDAR is larger than the calculated result. As mentioned before, Brouwers’

equation is suitable for the powder systems with lognonnal particle distribution.

58

However, the particle size distribution of TMDAR is not lognormal. Thus, the
Brouwers’ equation is not suitable to calculate its compaction capability. The
non-lognonnal size distribution powder systems have increased maximum
packing fractions than lognorrnal distributed powders [113]. Thus, the compaction
capability of TMDAR is improved compared to the other three powders. Therefore,
when using Brouwers’ equation to evaluate the compaction capability of powders,

the particle size distribution of each powder should be Iognonnal.

3.1.7. Conclusions

Several groups of powder mixtures were produced by mixing four alumina
powders. After investigating their compact density versus stress and strain
relationships, the initial relative density was determined to be appropriate for
quantifying the compaction capability of each powder mixture. The powder mixing
process changes the compaction capability of the powder mixtures. The shape of
the initial relative density versus proportion of coarse powder curve depends on
the ratio of average particle size, and the difference in the initial density of two
powders. If the average particle size ratio is less than 3.6, or the average particle
size ratio is larger than 3.6 but the initial relative density different is higher than
10%, the curve is linear. If the average particle size ratio is larger than 3.6 and the
initial relative density difference is smaller than 10%, the curve is parabolic. The

triangle enclosed by the line intersecting the relative density of the fine powder

59

‘1

and the maximum relative density of the coarse powder, the line intersecting the
relative density of the coarse powder and the maximum relative density of the fine
powder as well as the line connecting the relative density of the fine and coarse
powder form the boundary of the initial relative density-proportion of coarse
powder curve. The experimental results also show Brouwers’ equation has
excellent potential for comparing the compaction capability of different powders

with lognonnal particle size distribution.
3.2 DIMENSIONAL VARIATION BY COMPACTION

In Section 1.3.2.3, it has been introduced that due to the series of operation
steps of compaction, the green samples contain two structural inhomogeneities:
density distributions as the variation of the internal form and the dimensional
variability as manifest in the external shape of the compact [78-80, 82-84]. To
investigate the dimensional variation as well as the powder mixing effect on the
dimensional variability, the external shapes of several green samples achieved in
Section 3.1.1 were measured. The measurements were preformed by
VeeIo-DEKTAK 6M Stylus Profiler at center for coating and laser application, CCL
Fraunhofer. The profilometer is with 0.5nm resolution. A specially designed
sample holder was used to support samples as Fig.3.8 shown. The diameter of
cave in the holder is the same to the inner diameter of the die. After a sample

“sitting” in the sample holder, the probe of the profiler touched the external surface

60

oi the

front

 

 

 

61686

perfo

 

Hg,“

of the sample. A 3mg force was applied on the probe and then the probe moved
from one edge to the other edge to measure the external surface profile. After one
measurement, the sample was rotated 90° and another measurement was
performed. Totally four measurements were performed for each sample.

Probe of the
profiler

  
 
    
   

Probe movement

Sample direction

Sample holder/
base

Figure 3.8 The schematics of external shape measurement.

ll

 

 

Thickness position (mm)
A

 

 

 

 

0" u
-11.13-11'.10 -11.05 11.00 11.05 11.101113

Diameter encing position (mm)

Figure 3.9 The diameter variation along the thickness direction of GE-1 samples

By taking average value of four measurements, the diameter variation along

61

the thickness direction was obtained for each sample. Fig.3.9 shows the
dimensional variation of GE-1 sample. All samples feature the similar barrel
lateral shape, which is a result of release of larger residual radial stress at about

the middle of the compact after ejection [80].

For GE-1 sample, the difference between the largest diameter and smallest
one is 20.631 pm. This difference varies among samples. Fig.3.10 shows the

diameter difference dependence on the powder component for the CR15+GE1

 

    
 

 

 

and TMDAR+CR15 groups.
24
’5 A 21-
9’ £5. .
a V
3 5 184
ea .
s e 15-
2 *5 -
0 0
g: 12.
s .
g; 9. +cr15+ee1
g g ‘ —o—TMDAR+CR15
'u
6 - I ' I ' l ' fi ‘ I

 

0 20 40 60 a) 100
Proportionofooarsepowder(%)

Figure 3.10 Dependence of largest and smallest diameter difference on the
powder proportion.

If one compares Fig.3.10 to the lines of corresponding powder groups in Fig.
3.2, it is easy to see that powder mixtures with better compaction capability are
with smaller diameter difference. Powders with better compaction capability

results shorter green samples if the powder masses are same, resulting a smaller

62

 

reside
ihenr

isah

usng
by8v
pail
sbpe
(GI.

Iset

 

residue stress distribution difference insider the green samples hold by the die.
Therefore, after the residue stress release by the ejection, the diameter difference

is also smaller.

The TMA unit offers a facility to measure Young’s modulus of materials (E)
using the three-point bending method. The Young’s modulus of CR-15 compact
by 80MPa is 1031.3 MPa, and that of TMDAR is 2155 MPa. The elastic unloading
part of the stress-strain curves for the powders is linear, as Fig 3.11 shown. The
slope of the elastic unloading part (m), the bulk modulus (K), the shear modulus
(G), the Young’s modulus (E) and the Poisson's ratio (v) have relationship as

listed in Equations 3.10-3.12 [114].

 

80.

- 13

Stress (MPa)
2.3

5

L

 

 

 

0'l r W f r ' I ' l
0.00 0.05 0.10 0.15 0.20 0.25 0.30
Strain

 

Figure 3.11 Stress-strain curve of TMDAR

 

m =K+§G (3.10)
= 90K (3.11)
3K+G

63

also
madl
alurr

rifle

to;

 

Sail
”10
San
the

SI];

 

 

V_ 3K-2G
2(3K+G)

 

(3.12)

Therefore, by measured Young’s modulus and the calculated slope value, the
other moduli and Poisson’s ratio can be obtained, as listed in Table 3.3. Table 3.3
also presents the corresponding values by Aydin et al. [78-80]. The samples
made by Aydin et al. have much higher moduli than ours. In their experiments, the
alumina powders were mixed with poly PVA bind to enhance the strength. The

different processes explain the value difference.

Table 3.3 Material properties for several alumina compacts

 

Powder TMDAR CR-15 Aydin et al. [78]
Young’s modulus (MPa) 2155.1 1031.3 9027.4
Unloading slope (MPa) 2498.3 1250.4 11485.9

 

 

 

 

 

 

 

 

 

 

 

Shear modulus (MPa) 876.1 410.8 3531.9
Bulk modulus (MPa) 1329.9 702.3 6677.4
Poisson’s ratio 0.23 0.255 0.278*
* assumed value

By Fig. 3.10 one can see the diameter difference for our sample varies from 7
to 23 pm. This value in the report of Aydin et al. is only 4 pm [80]. Since our
samples have much lower moduli than theirs, once the die wall restraint was
moved, the dimension recovery at radial direction should be larger for our
samples. Then with the same residue stress difference along the axial direction,
the final dimension recovery difference at the center and the top/bottom surface

should be also larger for our samples.

More interesting, the curves in Fig.3.10 have a “mirror image” relationship to
the responding curves in Fig.3.2. This relationship is very important, since we can
estimate the dimension variation of green samples made by powder mixtures
based on the compaction capability relationship in Fig.3.2 and the tested diameter

difference of the two ending powders.
3.3 DENSITY DISTRIBUTION BY COMPACTION

3.3.1 Experimental Design

The densities of a green compact are not even everywhere, but with a density
distribution. To detect the density distribution insider a compact, Aydin et al [78, 79]
designed an experiment, in which they used lead balls as tracers. However, this
method only put the tracers in several positions, not in a continuous way. To
overcome this disadvantage, we used colored powder as tracer to investigate the

density distribution insider green compacts by Powder Metallurgy.

In Section 3.1, we already discovered that powder mixing changes the
compaction capability. Therefore, we dyed several powder mixtures by stamp-ink
(2000 plus, Red, COSCO, Germany). The mixtures then were put into a furnace
(Carbolite-HTF1700, UK) for 4 hours at 70°C to dry out. The remained solids were
put into bottles with 12mm diameter alumina mixing media. The bottles were on a

jar mill (U.S. Stoneware 764AVM, USA.) for 48 hours to break the solids. Then

65

the powders were sifted to get colored powder with size less than 0.3mm.

The colored powders were compacted to 0.5MPa to get the initial densities as
mentioned in Section 3.1.1. Then the values were compared with five different
main powder (mixture): TMDAR, 50/50 TMDAR/CR15, CR15, 50l50 CR15/GE1,
and GE1, respectively. The colored powder with the same compaction capability

to a powder (mixture) will be used as its compaction indicator.

To investigate the density distribution insider a green compact, the height of
the green sample cannot be too small. Otherwise, the density distribution will be in
a small range, hard to identify. So in this study, we keep the height/diameter ratio
of each green sample around 1.1-1.2. The diameter of the samples is 19.04 mm.
In the experiments, we kept the thickness of each main powder layer are identical,
also each colored powder layer. And the thickness of colored powder layer is
around 1/15 of the main powder layer. Based on these requirements, the powder
mass of each layer can be calculated. The main powder is 1.59 for each layer and

the colored powder mass is 0.129 for each layer.

Similar to the compaction procedure in Section 3.1.1, the first layer powder,
which always is main powder, was pour into the die, which was lubricated with
graphite powder (Panef Corp., USA). Then a pre-load of 0.5MPa was applied to
compact the first layer to obtain enough stiffness. After the pre-compaction, the

die set was moved from the MTS (MTS Insight 300, MTS Systems Corp., USA).

66

The layer thickness, measured by subtracting the height of the two punches from
the total height of the two punches and the pre-loaded compact inside the die,
was recorded. The top punch was then dragged out of the die slowly and then the
second layer powder (colored powder) was pour into the die. Flatting the surface
of the new layer powder and putting the top punch back to the die, the 0.5 MPa
pre-Ioad was applied on the both layer again. Repeat the procedure till the last
layer was pre-loaded. Finally the load of 80MPa was applied to compact the

whole multi-layered samples.

The green samples were then took out of the die and polished carefully on the
lateral surface till to the middle section. Then each sample was placed on the
sample holder mentioned in Section 3.2 for photo taking. The photos were taken

by a dissection microscope (Wild M5A, Wild Heerbrugg Ltd, Switzerland).

3.3.2 Measurement Results and Discussion
The representative picture of the middle section is shown in Fig. 3.12. Due to
the axial symmetric characteristics of the density distribution in the compact, the

broken parts in the left edge shown in Fig. 3.12 do not influence the calculation of

the density distribution contour.

67

 

Figure 3.12 The photo of the middle section of a TMDAR sample. The bottom side
in the picture is also the side contact to the bottom punch in the compaction.
Based on Equations 3.6 and 3.7 in Section 3.1.3, the relative density pt can be

calculated as:

mtg.)

 

 

pt = pie (3.13)
where p,- is the initial density after 0.5MPa, which already is presented in Section
3.1.2 for each main powder. The final height of a position, ht, is obtained by
analyzing the photo by software Image G Since each indicator layer is curved

after compaction as shown in Fig.3.14, the ht varies by positions. Therefore,

different position is with different density.

68

 

‘54

Helght (cm)
-.~ ;

 

0.8 .

 

0.6 .

0.4 *

 

 

 

 

o 0.2 0.4 0.6 0.8
Radius (cm)

Figure 3.13 The density distribution of TMDAR green sample, zero position is the

radial symmetric axel in Fig.3.12.

The density distribution contour was plotted by MatLab, Fig.3.13 shows the
contour of TMDAR, in which the 0 position is corresponding to the center axial in
the Fig.3.12. All the other four powder compacts feature similar density
distribution contour as shown in Fig.3.13, but the density distribution range varies
as different powders, as listed in Table 3.4. Similar to the average density
relationship in Fig.3.2, powders with better compaction capability have both larger
lowest density and highest density. From Fig. 3.13, one can see that the
high-density regions exist at the near the bottom central region and on the central

axis. And the low-density regions are at the bottom edges and near the top center.

69

Our results are similar to Aydin et al [78, 79] and others’ report [82-84]. However,
our samples are with much larger density range than others’ report. This should
also relate to the lower modulus our samples have. But the material cohesion and
internal friction angle difference may also contribute to the density distribution

range. This needs to be investigated later.

Table 3.4 The lowest and highest density in various samples

 

 

 

 

 

 

Powder Lowest density (g/cm3) Highest density (glcm3)
TMDAR 1 .618 2.462
CR—15 1.199 1.662
GE-1 1.203 1.671
50/50 TMDAR/CR15 1.409 2.064
50/50 CR15/GE1 1.414 1 .867

 

 

 

 

 

7O

CHAPTER 4

THE PHYSICS OF POWDER METALLURGY: SINTERING

Sintering kinetics is dependent on many variables, including material
components, green density, porosity, impurities, phase transition, and particle size
distribution, and so on [92]. This chapter will focus on how these factors affect
sintering kinetics for alumina and zirconia, especially the powder mixing effect on

the sintering.

4.1 EXPERIMENTS AND DATA CALCULATION

Two Al203 powders, TMDAR and CR—15, as well as two ZrOz powders,
TZBYS and CERAC-2003 were investigated in this chapter. The particle volume
distribution curve of each size class is presented in Fig. 4.1. As shown in Fig. 4.1,
both TMDAR and CERAC-2003 powders feature a single-peak powder size
distribution profile and the plots of both CR-15 and TZ3YS powders exhibit a
dual-peak profile. The second peak of these two plots results from the
agglomerates present in these powders. The particle size distribution results are

consistent to the Micrograph observation in Fig. 2.2.

A series of alumina and zirconia powder mixtures was produced, with the

proportion of TMDAR in alumina system and CERAC-2003 in zirconia system

71

ranging 0% to 100% in 10% intervals, resulting in a total of 22 powder mixture
samples in this study. The powders were mixed using 12mm diameter alumina or
zirconia mixing media in a jar mill (U.S. Stoneware 764AVM, USA.) for 48 hours
and then compacted in a single-action die under a load producing the pressure of
60MPa. The green samples were 7.94mm in both diameter and height. The real
time sintering testing was performed using the TMA (Setaram 95, France) with a
protective environment of argon gas. The heating rate was 10°Clmin and the final
soak temperature was 147500. The soak duration was 2 hours. The volume of the
fully-sintered pieces was measured in water by Archimedes’ principle. To attain
clear micrographs, the fully-sintered samples were polished (Abramin, Denmark)
and thermal-etched in a box furnace at 14200C. The microstructure was observed

by Scanning Electron Microscopy (JEOL 6400V, Japan).

 

 

 

 

 

20
——TMDAR - - ~CR—15
- - - - TZ3YS --- CERAC-2003
15 - /.\.
A /' \
g .
7510 - .’ ‘.
E \
a O
‘5 \
> I \ '
5 l- .’ ’ \ ‘
1 \ \.
b . \ \
| . -\.L
0.1 1 5
Particle Size (pm)

Figure 4.1. Particle size distributions of the four powders used in this Chapter.

From the TMA testing results, we calculated and plotted densification

72

rate-relative density curves to describe the sintering kinetics of each powder
mixture. Since the TMA can measure the length change in only one direction, to
calculate the densification rate based on the results of TMA, Lance et al. [70]

defined an anisotropic shrinkage factor a:

a: (¢f-¢0)Lo
(Lf‘Lo)¢0

 

(4.1)

where Lo and Lf are the initial and final height of the specimen, and (pa and ¢f are
the initial and final mean diameters of a specimen. For each of our experimental
results, a was almost 1 (>0.991). It is therefore reasonable to consider the
sintering process for our samples to be a self-similar (isotropic) one. Thus, with
the 1:1 height to diameter ratio, the temperature dependent relative density can

be calculated from the following expression:

 

 

 

 

 

_ 13
Mali—[19- Lf 3
D”): 1+AL(T) Df {roman} Df (4'2)
Lo

where Df is the relative density of the fully-sintered sample, AL(17 is the
displacement at temperature T, so the LO+AL('D represents the height of the
sample at temperature T. Using formulas (1.16) and (4.2), it is relatively easy to

derive the expression of densification rate:

15m: —AL‘(T)

ism = 00‘) 20[L0 + Mm]

(4.3)

 

73

where the coefficient 1/20 (3/60) is a result of the conversion to SI units, since the

TMA counts time in minutes instead of seconds.

4.2 POWDER MIXING EFFECT ON PARTICLES AND SINTERED SAMPLES

Powder mixing can manipulate the initial powder characteristics and finally

affect the dimensions and microstructures of sintered samples.

4.2.1 Powder Mixing Effect on Particle Size Distribution Profile

 

20
I
,\ - - - 10010 TMDAR/CR-15
,,..._‘ ----------- 80l20 TMDAR/CR-15
§ 15' 1 '3‘, —50150 TMDAR/CR-15
E 1,513,}, ------~ 30170 TM DAR/CR4 5
1,3 1,1‘-.‘-., -----011oo TMDAR/CR-15
3. :5
O
‘5.
0
s
3
§
‘2 . -

 

 

 

 

1
Particle size (um)

Figure 4.2. Particle size distribution profiles of Al203 powder mixtures.

Fig. 4.2 shows the particle size distribution testing results of the representative
alumina powder mixtures. Obviously, particle size distribution profiles vary as the
proportion of CR-15ITMDAR in the powder mixtures. The width of the particle size
distribution increases with the increasing of the proportion of CR-15. As shown in

Fig. 4.1, CR-15 has much larger particle size distribution range than TMDAR.

74

Therefore, increasing the pr0portion of CR-15 in alumina powder system would
resufts in a wider particle size distribution profile. However, due to the vibration
and impact by the medium in the mixing, the large agglomerates were broken.
Thus, the width of particle size distribution for TMDAR+CR-15 mixtures is less

than that of as-received CR-15.

The particle size distribution of the nine TMDAR+CR-15 mixtures features two
peaks. The area fraction of the second peak changes with the varying powder
proportions, as seen in Fig. 4.3. This area fraction change corresponds to a
change in the volume fraction of agglomerates. Fig. 4.3 shows that the
agglomerate volume fraction in the TMDAR/CR-15 powder mixtures increases as
the increase of CR—1 5 at first, once the volume proportion of CR-15 reaches 40%,
the agglomerate volume begins to drop as the increase of CR-15 till the volume

proportion of CR-15 reaches 90%.

For zirconia powder mixtures, since TZBYS and CERAC-2003 are different in
particle size (Fig. 4.1), the particle size distribution of zirconia powder mixture also
changed with the proportion of CERAC-2003/TZ3YS. However, the change is not
as obvious as alumina mixtures. The particle size distribution width increases with
the increasing of the proportion of CERAC-2003 until 40% CERAC-2003 and then

decreases.

75

 

«h 0" 0| 0)
01 C U'I o
1 V T v 1 V r

ch
0
' I

 

 

The second peak area fraction (%)

0.)
01

20.40460A80‘100
The proportion of CR-15 (%)

 

C

Figure 4.3 The area fraction of the second peak in the particle size distribution

curves for varying alumina powder mixtures.

4.2.2 Powder Mixing Effect on Microstructures of Sintered Samples

For the two alumina powders, TMDAR has as low as 920°C sintering initiating
temperature; on the other hand, CR-15, generally used as polishing media, has a
much, higher sintering-beginning temperature (above 107000). Because of these
distinct powder characteristics, the sintering capability should increase with the
increase of the TMDAR proportion in the powder mixtures. The powder mixing

results in the variation of the microstructure of alumina powder mixtures.

Fig. 4.4 shows SEM micrographs of fully-sintered TMDAR and CR-1 5 samples.

From these graphs, one can find:

Average grain size: Pure CR-15 sample shows smaller average grain size
than TMDAR sample. Fig. 4.5 shows the dependence of average grain size of all

11 fully-sintered alumina samples on the proportion of TMDAR. Because TMDAR

76

is a low-temperature sintering powder, it has a greater potential for grain growth
than CR-15 in sintering. Therefore, the final average grain size increases as the

proportion of TMDAR powder increases as shown in Fig. 3.5.

 

Figure 4.4 SEM micrographs of fully-sintered a) TMDAR, and b) CR-15

(Acceleration voltage: 15kV, Working distance: 15mm ).

4.0

3.5- I/.

 

3.0- /I

\.
\.

1.0-

Average Grain Size (pm)

.‘3
or

 

 

i:

 

o '2'0'4'0'6107837100
Percentage of TMDAR (%)

Figure 4.5. Average grain size of fully-sintered alumina samples.

Pores: Pure TMDAR sample has only few inter-grain pores, while a lot of inter

and inner grain pores left in fully-sintered samples containing CR-15. With CR-15

77

increases, the quantity of pores increases. This phenomenon also related to the
high sintering capability of TMDAR. As introduced in Section 1.3.3.1, the single
inter-grain pores prove that the sintering of TMDAR has been into the final stage,

but all powder mixture with CR-15 only sintered in the intermediate stage.

Grain size distribution: Pure TMDAR sample has very narrow grain size
distribution, while fully-sintered samples containing CR—15 have large grain size
distribution range. Two reasons result in the large grain size distribution for
powder mixture containing CR—15: 1) agglomerates in CR—15 and 2) CR-15
contains very high promoting grain growth elements: Na, K and Si, which are not

evenly distributed (Table 2.1).

 

Figure 4.6. The micrograph of a fully-sintered 40/60 CERAC—2003+T23YS

sample (Acceleration voltage: 15kV, Working distance: 15mm).

For zirconia system, because T23YS and CERAC-2003 have very similar

sintering capability, the final sintered zirconia samples have similar microstructure.

78

Fig. 4.6 shows the micrograph of a fully-sintered 40/60 CERAC-2003/TZ3YS
samples. Comparing Figs. 4.4 and 4.6, one can see that under the same sintering
path, the grain size of zirconia is much smaller than that of alumina. Also the
sintered zirconia samples show a relatively uniform grain size, while the alumina

powders with CR-15 feature a wide distribution of grain size.
4.2.3 Powder Mixing Effect on Dimensions of Sintered Samples

The content of powder mixture dictates its compactability and sinterability,
ultimately changing the diameter of the final piece. Fig. 4.7 shows the variation of

final diameter with respect to the powder mixtures of alumina and zirconia.

 

 

      

 

  
 
 

 

 

 

 

 

 

a b
18.0
17.8
A173 A
1
£17.44 E
.. 1 7:
$17.2 g
3110'. +90MPa =6
5163- +1zom=a E ,
“-163: +150”?! “13,4. +120MP0 +150|Pa
, -—e—180MPa . —e—1GOMPa —¢—210MPa
13,4. —e—210MPa 16.2-
6‘23'4B‘ebTaB'1éo oizfi'k'eb'e’o'Too
The proportion of CR-15 in the alumina system The proportlon of CERAC-Zooa ht zlrconla system

Figure 4.7. The relationship between the final diameters and the percentage of a)

CR-15 in alumina system and b) CERAC-2003 in zirconia system under varying

compaction load.

Two characteristics of the powder mixtures that influenced the shrinkage of the

compacts were the packing density of contents and the particle size distribution.

79

With a higher proportion of more compactible powders and the optimum particle
size distribution, the initial green compacts will attain a higher green density under
the same compaction load. They thus shrink less, resulting in a larger final

diameter.

For the alumina powders, TMDAR has a much higher compactibility than
CR-15 as discussed in Section 3.1. This means that powder compacts containing
a higher proportion of TMDAR lead to a larger final diameter under the same load.
It is seen from Fig. 4.7(a) that the final diameter of alumina samples increased
significantly when the proportion of TMDAR was raised from 0% to 10%. As the
proportion of TMDAR increases further, the final diameter increased almost

linearly.

In zirconia system, the situation is quite different since the CERAC-2003 and
TZ3YS powders have a very similar compactibility. Thus the particle size
distribution will be the main factor in determining the final diameter. Table 2.1
shows that CERAC-2003 has a much larger average particle size than TZ3YS. It
follows that, in some combination of these two powders, the small T23YS
particles will fill in the interstitial spaces among the larger CERAC-2003 particles.
Powder combinations meeting this criterion have a higher compactibility than
either of the pure powders as discussed in Section 3.1.4. As can be seen in Fig.

4.7(b), when the proportion of CERAC-2003 was between 30 and 80%, the final

80

diameter of full-sintered zirconia pieces was much larger than others.

4.3 DENSIFICATION RATE-RELATIVE DENSITY CURVES

4.3.1 Alumina Powder System

Fig. 4.8 shows the representative densification rate-relative density curves
observed in the alumina powder mixtures. Because of the similarity of the curves
for 1) 10%-30% TMDAR powder mixtures, 2) 60%-90% TMDAR powder mixtures,
only six densification curves including 0% and 100% TMDAR powders are shown

to enhance the clarity of the plots.

 

0.40 - —— 0% TMDAR- - ~10%TMDAR
035; ----40%TMDAR--- 50%TMDAR
E ' _ ----60%TMDAR ----- 100%TMDAR
0')
'2 0.30 :-
‘g 0.25 - , .. l‘~
“ t J” T .e \
E 0.20 - .’ i‘ ’\ ‘.‘~
/ )l ‘ . ‘
:g '00, v \ \
8 0.15 b 43:, \K“ e ‘g
F h lie", \‘\ .\ ‘9
g 0.10 L" ’1’," \s:\..\‘“
3 0.05 - 1”" \‘:(:.\‘.,
000 . In... 1.... I L I \.‘°.l

 

 

 

0.4 0.5 0.6 0.7 ‘ 0.8 ‘ 0.9 1.0
Relative density

Figure 4.8 Densification rate as a function of relative density for TMDAR+CR-15

alumina powder mixtures.

As shown in Fig. 4.8, increasing the proportion of TMDAR enhances both the
green density and the final density of the samples. With the exception of the pure

CR—15 sample, all of the specimens are nearly fully-sintered (D > 95%). Due to

81

the high sintering capability of TMDAR, the samples containing a higher

proportion TMDAR have higher fully-sintered densities.

In the densification rate—relative density curve, one point of critical importance
is the maximum densification rate point. Prior to reaching this point, there is no
grain growth and the pores among the grains are parts of interconnected
networks. These networks begin to collapse into isolated pores after the powder
compact reaches its maximum densification rate, and rapid grain growth begins to
occur [74]. From Fig. 4.8, the maximum densification rate for the alumina powder
mixtures occurs within the relative density range of 70-84%, consistent with the
results of Lance et al. [70] and Lange [115]. Another point of interest is that the
increase in the proportion of TMDAR also increases the relative density at which
the maximum densification rate occurs. This change is also a result of the

increased green density of the samples caused by increased TMDAR proportion.

The ascending and descending parts of a densification curve are the
segments before and after the maximum densification point, respectively. Fig. 4.8
shows that the powder mixtures with higher CR—15 proportions have higher
densification rates in the ascending section and lower rates in the descending
section of the curve. Ting et al. [74, 75] concluded by theoretical calculation that
“Prior to the occurrence of grain growth, a maximum densification rate exists as

the starting particle size distribution width increases, During grain growth, the

82

 

incrs

(Fig

d9?

one
sinf
cle.r

sir

Y'- — — ' — ' _

 

model predicts decreasing densification rate with increasing starting particle size
distribution width.” Our experimental observations match this conclusion since the
increase in the proportion of CR-15 increases the particle size distribution width

(Fig. 4.2)

Depending on the powder mixture system, the ascending section for the
densification rate-relative density curves can be closely approximated by either
one or two straight lines. The 100% TMDAR, agglomerate-free sample, exhibits a
single linear segment with one slope. In contrast, systems containing CR-15
demonstrate two linear segments with distinct slopes. Lance et al. [70] obtained
similar results by stating, “Agglomerates free alumina powder shows a single

slope linear segment and powders with agglomerates show two linear segments.”

The length of the first linear part of the curves in Fig. 4.8 varies depending on
the proportion of CR-15. It decreases as the proportion of CR-15 decreases from
100% to 90%, then slowly increases until the proportion of CR—15 reaches 40%,
then decreases again until the proportion of CR-15 reaches 10%. This length
change in relation to the CR-15 proportion is the same as the one outlined
previously for the change in the area fraction of the second peak in the particle
size distribution for alumina powder mixtures (Fig. 4.3). This similarity can be

explained.

Many researchers [104, 116] have pointed out that densification rate is

83

 

will

when

me

and

the

the

inversely proportional to a power of grain size in the initial stage:

1

éS(T) at a (4.4)

where G is the grain size and n is a positive constant that depends on the diffusion
mechanism. Therefore, we infer that the small particles within the agglomerates
and other free small particles dominate the beginning of the sintering process as
they begin to consolidate together. This consolidation causes the first linear part of
the curves in Fig. 4.8. The compaction causes contact between the particles
within the agglomerates. Once the compaction of the particles inside the
agglomerates reaches a critical point, the agglomerates begin to assume the
dominant role in the sintering process and the second linear part would begin.
Therefore, greater quantity and size of agglomerates will require more time for the
agglomerates to finish the consolidation. Hence, the first linear part of the

densification curve is extended.

Another important aspect of the densification curves in Fig. 4.8 is that the
slope of the first linear segment in the ascending part is nearly constant for all our
alumina powder mixtures. It is independent of the green density and the amount
of agglomeration in the sample. This result is similar to that of Lance et al. [70],
but different from that of Rahaman et al. [117]. It is believed that the slope of the
first linear part of the densification curve is related to the pore size/particle size

ratio [70, 98]. From this result, the pore size/particle size ratio for our CR—15 and

84

TMDAR powder system is concluded to be the same under the same compaction
load. In Lance's experiments, he used several powders with similar pore
size/particle size ratio. In Rahaman’s study, the compaction load used on a
particular powder was varied to achieve the samples with a variety of green
densities, and this process changed the pore size/particle size ratio in each
sample. The processing method and powders used in each study explains the

difference in the three results.

Each powder mixture containing CR-15 features a plateau in the ascending
portion in Fig. 4.8. Even though the relative density and densification rate value
are different for each powder mixture, the temperature at which the plateau occurs
is within the same temperature range (1150-120000). This plateau is a result of
y- to o-phase transition of alumina [96], since 10% y-phase alumina is present in
CR-15 (Table 2.1). TMDAR powder contains only a-phase alumina and no plateau

in the pure TMDAR densification rate-relative density curve.

A plateau in descending section of a densification rate-relative density curve
signifies the occurrence of abnormal grain growth [70]. It can be seen that no
plateaus exist in that region for any curves in Fig. 4.8. This holds true even for a
powder system with agglomerates (such as CR-15), which is known to cause
abnormal grain growth. The micrographs in Fig. 4.4 also provide evidence that no

abnormal grain growth occurred.

85

4.3.2 Zirconia Powder System

Fig. 4.9 shows the seven representative curves obtained for our zirconia
powder system. The 10% and 20% CERAC-2003 systems as well as all the
powder mixture systems between 50% and 80% CERAC-2003 exhibit very similar
densification rate—relative density curves. The 'densification rate-relative density

curve for each group is presented in Fig. 4.9 as a single curve to allow for clarity.

 

 

 

 

 

0.40
0.35 1-
.193 0.30 -
O
50.25 - . . z
9 ’ ’ ' I}. \c
80.20 ' ’,:' ." ‘$.\
5 . , (,1, .’o/ 0% CERAC \
z: 0.15 - g1," 1/ - - 10% CERAC
,8; 1 .5.: .’, - - ~ -30% CERAC 1.3
‘as 0.10 - ;,,~,'. -.—40% CERAC '
o r, .5,- :,’ - - - -60% CERAC
0 0.05 1' .1, ..... 90% CERAC '- .\
0 00 ’ - 1:11”. ':""“°.'1°9%S>ER6¢ . t.

 

0.4 0.5 0.6 0.7 0.8 0.9 1.0
Relative density

Figure 4.9 Densification rate as a function of relative density for representative

TZ3YS+CERAC-2003 zirconia system.

Fig. 4.9 shows that the green density of zirconia samples increases when the
proportion of CERAC-2003 is between 0% and 40%, and begins to decrease
beyond 40%. This is because the small T23YS particles fill in the interstitial
spaces among the larger CERAC-2003 particles as well as the powders of the

zirconia system feature very similar compactibility. The similarity in the

86

sinteribilities of CERAC-2003 and TZ3YS results in a similar final density for

various zirconia powder mixtures.

The maximum densification rate for each of our zirconia powder mixtures
occurs within the relative density range of 74—82%. This result is consistent with
the report of Trunec et al. [118]. The higher the green density of a powder mixture,
the higher the relative density at which the maximum densification rate occurs.
This is the same result found with our alumina powder mixtures. The densification
rate in ascent and descent part changes as the proportion of CERAC-2003, which
also fit to the Trng’s calculation [74]. However, unlike the sintering curves of
alumina system, the ascending section of the curves for zirconia powders in Fig.
4.9 cannot be approximated by straight line(s). Using the linear approximation and
relating the length of the first linear part to the agglomeration present in the green
sample are methods that only apply to alumina powder mixtures. The shapes of
densification rate-relative density curves for zirconia system are found to be

semi-ellipse.

4.4 PHENOMENOLOGICAL CONSTITUTIVE MODELS FOR ALUMINA AND

ZIRCONIA SINTERING CURVES

4.4.1 Model Equation and Calculation Procedure

As mentioned in Section 1.3.3.2, one can fit analytical expressions directly

87

des

moi

alu

wt

8f

 

from the results of sintering experiments to set a phenomenological model to
describe the densification kinetics. In this section, the Hsueh’s phenomenological
model [107] is used to describe the densification rate — relative density curves of

alumina and zirconia shown in Fig. 4.8 and 4.9.

The equation of Hsueh’s model is:

1%“ = Q(T)[Doo(T) —D]" (1.18)
where D..(T) is the theoretically possible fully-sintered density at temperature T

and 0(1) is related to grain size and activation energy.

To fit the densification rate - relative density curves to Equation (1.18),
part-isothennal heating cycle sintering of samples is needed. The part-isothermal
heating cycle sintering was first utilized by Dom in 1957 [119]. The part-isothermal

heating cycle used in this study is shown in Fig. 4.10.

 

1600

1200 -

 
 
  
 

Temperature (°C)
8
0

.§

 

 

 

_8 1'2 ' 1'6
Sintenng time (hour)

Figure 4.10 The part-isothermal ramp/soak sintering cycle used in this study to

calculate the phenomenological constitutive models.

88

Fig. 4.11 shows the part-isothermal sintering test result for 100% TMDAR
powder. Each “descending part” is from the isothermal sintering. If one extends
each descending part and intersects the extension with the relative density axis,

the intersection point gives the Doc for the temperature at which the isothermal

sintering performed.

 

100% TMDAR

.0 .° .°
C O
1: 2" 8

  

 

 

 

Densiflcatlon rate (10313)
P
O
‘f’ .

 

 

 

0.6 f 0T7 ' 0T8 ' 0T9 ' 1T0
Relative density

Figure 4.11 The densification rate — relative density relationship of the 100%
TMDAR powder under the part-isothermal sintering path described in Fig. 4.10.

After obtaining a series of values of D..(T), the following steps are used to
calculate the phenomenological constitutive model for each powder mixture in

Figs. 4.8 and 4.9:

1. Taking the natural logarithm for the both sides of Eq. (1.18), a linear

relationship can be found:

ln(és)=nln([Doo(T)-D])+ln(Q(T)) (4.5)

89

2. Calculating D..(T) - D for the relative density data of each isothermal
sintering testing part and then taking the natural logarithm for the

densification rate data and the D..(T) — D.

3. Using the linear function to fit the terms 1n(é‘)and ln(D..(T) — D), a series
of linear equations, each of which relates to a specific isothermal sintering
temperature are obtained. Table 4.1 shows the linear equations calculated

for pure TMDAR powder.

Table 4.1. The linear equations calculated for pure TMDAR powder

 

 

 

 

 

 

lsothennal temperature (°C) Linear fitting equations
102° 111(1):")=l.6381n[0.6118-D]-1.6439
1080 111(3) =1.65210[0.6802—D]+0.3165
"40 111(3) =1.648ln[0.792—D]—0.0657
120° 111(3) =1.6551n[0.973-D]-0.5173
1260

 

 

 

ln(és) = 1.6351n[0.995 — D] — 1.059

 

4. The coefficients in front of |n(D..(T) — D) give the value of n in Eq.(1.18).
From Table 4.1 we can see that the n value is nearly constant for a powder

system under different temperature. The n for TMDAR is around 1.65.

5. The. entries in Table 4.1 give a series value of ln(O(T)). Thus we can get a
relationship between ln(D(T)) and temperature T, then use a polynomial to

relate (1(7) and T. For pure TMDAR, the 0(7) can be expressed as:

90

0(7) = —1.3799 x 10"1 17:4 + 6.0705 x10m8T3

(4.6)
- 8.719 x10—5T2 + 0.0370797 + 5.2474

6. A series D..(T) values at different temperature Tare also obtained. we can
fit D..(T) into a hyperbolic tangent function. For the pure TMDAR powder,
the expression is:

Doo(T) = {0.2224 tanh[8.3785 x10_3T — 9.4498]} + 0.7776 (4.7)

7. Combining the result of steps 4—6, The final phenomenological constitutive

model for each powder mixture is obtained.

4.4.2 Models for Alumina Powder Mixtures
The calculated phenomenological constitutive function for 100% TMDAR:

a" = {-1.138 ><10—11(T)4 + 0.503408 x10"7(T)3
— 0.72765 ><10"4(T)2 + 0.0319064(T) + 3.5792] (4.8)
x { {0.2224tanh[8.3785 x10-3(T +40) —9.4498]} + 0.7776-D}1'5

Fig. 4.12 shows the comparison of the experimental measurement and the
calculated result by Equation (4.8) for both the non-isotherrnal and part-isothermal
heating cycles. The correlation between the calculated and experimental results
remains very high for both two figures. The errors between the experimental data

and the calculated results are less than i6%.

The constitutive equations for other alumina powder mixtures were also

calculated and several relationships were found.

91

1.

The value of n is constant for any alumina powder mixture. That is, n is

only affected by material, and it is a material parameter.

(1(7) should be influenced by the apparent activation energy [104].
However, the (1(7) values for different alumina powder mixture with a
different percentage of TMDAR are very similar, the same 0(7) in Equation

(4.6) was used to simulate other alumina powder mixtures and showed a

very good correlation too.

 

 

 

 

 

 

 

 

 

 

 

 

 

3. Since D..(T) is influenced by the green density, D..(T) changes with
respect to the proportion of TMDAR present in the powder system. For
example, the D..(T) for 50% TMDAR system becomes:

Doo(T) = {0.2464 tanh[8.2135 x 10'3 (T + 30) — 7.1422]} + 0.7536 (4.9)

0.06 0.30

— Experimental result ,
E 0.05- ‘ ' “WW ”5“" ’5 0.251
a? ‘ \ 4
g 0.044 99 0.20.
gcm- 30w:
g 0.02- a; 0.10:
. . E ,
. 3 —Ca lated s lt
g 0.01, 8 005-1 , . , _ Exggfimeng, 3,5,,"
0.00 W000...1.....
0.5 0.6 0.7 0.8 0.9 1.0 0.6 0,7 03 0_9 1,0
Relative density Relativebdensity
a
Figure 4.12 Comparison of the experimental and calculated results for 100%

TMDAR under a) non-isothennal and b) part-isothermal heating circle.

92

phi

 

It should also be pointed out that the simulation result from the
phenomenological constitutive model does not contain the plateau that occurs in

conjunction with the phase change.

4.4.3 Models for Zirconia Powder Mixtures

The Hsueh’s formula also can be applied to zirconia powder systems. The
phenomenological constitutive equations for all zirconia powder mixtures are
obtained. For example, the equation to describe the sintering kinetics of pure

TZ3YS is:

$5 = [1.00465 x 10‘9 (T -150)4 + 5.83063 x10.6(T --150)3
— 1.26736 x 10‘2 (T -150)2 +12.2284(T - 150) + 51384] (4.10)
x { {0.2409 tanh[9.5305 x 10‘3(T) - 12.2591} + 0.7444 — 0}“
0.40

0.35-

75 t
«r 0.30-

 

, — Experimental result
8 0.054 - - - - Calculated result

 

 

 

0-00 T fl r fi F f I ' I '
0.5 0.6 0.7 0.8 0.9 1.0
Relative density

 

Figure 4.13 Comparison of the experimental and calculated results for 100%

T23YS under a non-isothermal heating circle.

93

Fig. 4.13 shows the comparison of the experimental and the calculated results
by Equation (4.10) during the non-isothermal heating cycle. The errors between

the experimental data and the calculated results are less than i4%.

Comparing all 11 equations for zirconia, we can find that the n value for
zirconia is 2.1. The function, (1(T), for all zirconia powder mixtures is nearly the

same too. And D.o(T) changes with respect to the proportion of TZ3YS present in

the powder system.

4.5 CONCLUSIONS

1. Mixing powders is an effective approach to manipulating the
characteristics of raw powders, such as compactibility, sinteribility and
agglomerates. These parameters finally influence the green and final
densities, the sintering kinetics of powder system and the final

microstructures.

2. Each material has a unique densification rate-relative density curve.
The ascent parts of the curves for alumina can be approximated by
straight line(s), while the shapes of zirconia powder densification

rate-relative density curves are found to be semi-ellipse.

3. The powder with wider particle size distribution shows a higher

densification rate before the occurrence of grain growth and a lower

94

6.

7.

one after the densification rate point. This finding verified Tlng’s

theoretical calculation [74, 75].

Phase transition add a kinetic mechanism for sintering, results in a

suddenly change in densification rate.

Using the part-isothermal heating method, phenomenological
constitutive sintering equations were derived for our alumina and

zirconia powder mixtures by Hsueh's model [107].

The variable n in Hsueh’s model is a material parameter. Even though
0(7') should be influenced by the apparent activation energy, its
difference for the powder mixtures in our CR-15ITMDAR alumina
system or TZ3YS/CERAC-2003 zirconia system can be ignored. Doo(T)
is influenced by green density, D.o(T) changes with respect to the
proportion of TMDAR or CERAC-2003 present in the alumina or

zirconia powder system.

The basic equation of Hsueh's model does not reflect any phase
changes that may occur. Despite of the shortcoming, the constitutive
models used in this study will be effective in describe most powder

sintering processes.

95

CHAPTER 5

ZrOz-Ale3 STEPWISE FGM:
MANUFACTURING AND CRACKS PREVENTION

Considering the severe temperature gradients a TPS experiences, FGM is an
important candidate for the core material of Perspirable Skin. The first material we
considered is ZrOz-AI203 FGM. The difficulty remaining in the manufacturing of
ZrOz-Al203 FGM by PM is the formation of cracks and/or distortion in the
samples. Several reports show that the number of cracks can be reduced by
controlling some factors such as heating and cooling rates, layer composition [58,
62]. However, none of these works provided any method to eliminate cracks and
camber. Torrecillas et al. [65] studied an FGM system featuring zircon and
molybdenum, concluding that a nearly similar transient shrinkage state for each

layer can lead to the final fully-sintered specimen being free of cracks.

In this study, the sintering kinetics results for various alumina and zirconia
powder mixtures obtained in Chapter 4 were compared. By referring the
conclusion made by Torrecillas et al. [65]. Ideal powder mixtures to prevent the
cracks and camber in ZrOz-AI203 FGM were identified. Other factors affecting the
formation of cracks and camber in an Al203JZr02 FGM, including the compaction

load, interface profiles, and ramp/soak sintering cycle, were also varied in order to

96

determine the optimal experimental parameters. Finally, flat, crack-free

three-layered Al203/Zr02 FGM samples were fabricated.

5.1 EXPERIMENTAL PROCEDURES

The chosen powder mixtures based on the sintering kinetics curves were
compacted in a single-action die and sintered to construct FGM specimens
featuring three layers of equal thickness. The top layer is 100% zirconia (denoted
as layer Z), the bottom layer is 100% alumina (layer A), and the middle layer is a
mixture of 50% by volume of the alumina powder and zirconia powder (layer M).
The interface profiles between the layers can be controlled, which will be
discussed in Section 5.4. In order to ensure that each layer has the same volume,
the mass of alumina and zirconia to be present in each layer needed to be
calculated using the theoretical densities, which are 6.05g/cm3 for Zr02 and
3.87-3.989/cm3 for Al203 layer depending on the content of CR-15 powder. The

mass ratio for each layer can be described as follows.
mAzmMszz1:1.24:l.478 (5.1)

Naturally, in the powder mixture of layer M, the mass ratio of alumina to

zirconia is nearly 1:1.478.

The load to compact powder stacks was in the range of 60 to 210MPa. The

green samples were of 22.02mm diameter and had a height between 4.2 and

97

4.75mm depending on the compaction load used. Green compacts were sintered
in air at 147500 (Carbolite-HTF1700, UK). Several different ramp/soak sintering
cycles were used in order to determine the influence of heating/cooling rate on the
sintering process. The microstructure of final samples was observed by Scanning

Electron Microscopy (JEOL 6400V, Japan).

A flow chart summarizing the experimental processing is shown in Fig. 5.1.

Measure Mix powders: Add, 1,0de
[2 Z1'02 powders to d1e,glvmg
[2 Al203 powders rolling machine, prescribed interface
amounts 48 hours
between each layer

 

 

 

 

 

 

 

 

 

 

 

 

Examine sample: Sinter using Form green sample
are there cracks using uniaxial
or camber? ramp/soakbe‘l profile compaction
Examine
Hmicrostructure]

 

Figure 5.1 Flow chart detailing the manufacturing process used in this chapter.

5.2 POWDERS SLECTION BASED ON SINTERING KINETICS

To achieve the flatness in the FGM specimen (no significant camber), the
essential requirement is that the final diameter of each layer should remain at a
similar value. This does not guarantee, however, the survivability of the FGM

specimen during co-sinteling, since the final diameter of each layer may be the

98

same but the shrinkage rate at each layer during the co-sintering process can be
substantially different. Definitely, a large difference in the final diameter between
two layers induces residual stress, resulting in either cracks or camber.
Comparing Fig. 4.7 (a) and 4.7 (b), it can be seen that the final diameters of
alumina are most often larger than those of zirconia compacted at a same load;
only when the proportion of CR—15 in alumina system is higher than 82%, it was
possible to achieve similar dimensions of the alumina and zirconia layers. Since
the powder combination of 40% CERAC-2003 and 60% T23YS yields the largest
final diameter for zirconia layer, we fixed this proportion for layer 2 in this study.
Also, from Figs. 4.8 and 4.9, one can find that most zirconia powder mixtures
have higher densification rates than the alumina powder mixtures. In contrast to
this trend, the curve of 40%CERAC-2003+60%T23YS (Powder Z), the zirconia
powder system with the lowest densification rate, lies between 100%CR-15 and

90% CR-15+10%TMDAR curves.

Based on these two comparison results, several alumina powder mixtures
were tested with the CR-15 powder varying between 100% and 85%. The TMA
testing results revealed that the alumina powder mixtures containing 94% CR-15
and 6% TMDAR (Powder A) has very similar densification rate curve as Powder 2
(Fig. 5.2). Also, sintered samples by Powder A and Powder Z had almost the

same final diameter. These two powders were mixed in equal volume. The

99

resulting powder mixture yielded a similar, not exactly the same, densification
curve as Powders A and Z. This should be due to the change in the particle size
distribution. However, considering the excellent sinterability of TMDAR, by making
a small adjustment in the TMDAR proportion, the powder system with 46%
CR-15, 4% TMDAR, and 20% CERAC-2003, 30% T23YS by volume (Powder M)
shows a nearly same sintering behavior as Powder A and Powder 2 (Fig. 5.2) as

well as almost the same final diameter.

 

 

 

 

 

0.5 0.6 05 ' 03 ' 0T9 '
Relative density

0.25-
3 4
«,3 0,204
2 .
o
E 0.15d
c 4
E 0.10-
55 . —LayerA ‘
: ——LayerM
3 0.05- _ _ LayerZ I.
l
0.00 1 1. f . .
1

Figure 5.2. The densification rate-relative density curves of the three chosen

powder mixtures (ramp rate: 10°C/min).

The shape of the three curves in Fig. 5.2 is very similar. One obvious
difference is located around 0.22-10-3/s densification rate in the ascending
portion. The corresponding sintering temperature range is 1150-120000. There is
a plateau for layer A and a drop in slope for layer M, but there is no noticeable

change for layer Z near this region. As explained in Section 4.3.1, the change in

100

densification rate for layers A and M is a result of y- to cr-phase transition of
alumina [20] since 10% v-phase alumina is present in CR-15. However, since
layer 2 does not contain CR-15, there is no plateau or abrupt slope change in its

dens'rfication rate curve.

The similarity among the sintering kinetics of the three powders results in no
obvious difference in shrinkage rate and final diameter among layers during the
co-sintering of a FGM sample. Therefore, the Powder A, Z. and M are the
potential powders to achieve flat, crack-free three-layered Al203/Zr02 FGM

samples.
5.3 THE INFLUENCE OF COMPACTION LOAD

The compaction load also affects the final diameter. Fig. 4.7 also depicts this
relationship. For any given powder combination, the final diameter and the
compaction load are can be seen to be directly proportional. As the compaction
load increases, the particles in each specimen pack together more tightly,
resulting in an increase in the green density [76]. This decreases the shrinkage,
ultimately leading to a larger diameter on the fully sintered samples. However, for
a material system under varying compaction loads, the plots seem to display a

“parallel characteristic’, suggesting that the change in the compaction load does

101

nc

 

 

not impact the relation between the final diameter and the content of the powder

mixture.

As the compaction load increases, the normal stress being exerted on the
powder by the die will increase. Therefore, in the ejection step, there is a larger
friction force between the die and the powder. The increase in friction raises the
possibility of camber or cracks. In addition, beyond a critical load the yield surface
of ceramic powders move out to the shear failure surface [89]. The particles slide
against each other, resulting in micro-cracks, which may eventually lead to a

crack in the sample.

Table 5.1 The damage characteristics of FGM samples experienced different

compaction load

Load (MPa) Structural Characteristics
>160 Cracks between layers M and A and camber in shape
100—160 Camber in shape, no cracks
60—100 Flat and no cracks
<40 Too fragile to handle for the green piece

 

 

 

 

 

 

 

 

 

In this study, we found that the change in compaction load resulted in various
damage characteristics in the sample, as shown in Table 5.1. These observations
suggest that it is reasonable to consider that a low compaction load is preferable
in order to achieve Undamaged and undistorted FGM samples. However, the use
of a compaction load lower than 40MPa causes the green bodies to be very weak:

either they fracture during ejection from the forming die or they are too fragile to

102

handle. Due to these findings, we considered a compaction load of 60MPa to be

the optimized compaction load.
5.4 THE INFLUENCE OF INTERFACE PROFILE

In the processing of multi-layered FGMs, typically a free and flat interface
(natural interface) is used between two successive layers. However, this study
finds that with the natural interfaces of the Al203/Zr02 FGM sample, cracks were
formed between layer A and layer M despite of no apparent camber on the
sample. This crack formation necessitated the investigation into using more

complex interfaces.

Two additional interface profiles were investigated in this study: smooth and
occlusive. The smooth profile is obtained by lightly rotating the regular flat punch
without any pressure. The smooth interface has a smaller interface area than the
natural interface. The occlusive interface profile, so named because it resembles
the way in which the cusps of molars from the upper and lower jaw fit together,
yields an increase in the interface area. This profile will be obtained by pressing
the lower powder layer with a punch featuring a jagged surface as shown in Fig.

5.3 and pouring the powder for the subsequent layer.

Considering the structure of our FGM sample, each interface requires its

distinct profile to prevent the formation of cracks. The interfacial crack between

103

the layers A and M indicates that the bonding between A and M was weaker. The
interlock structure of the occlusive interface would increase the bonding between
these two layers. In addition, the occlusive interface creates a quasi-continuous
intergradation, which provides a more continuous material properties transition
between these two layers when compared to the other two interface profiles. At
the same time, the interface between M and Z was much stronger as no interfacial

crack has been detected.

 

Figure 5.3 The punch featuring a jagged surface for making the occlusive

interface.

For our powder systems, we found that only the combination of a smooth
interface between the layers M and Z and an occlusive one between the layers A
and M prevents the formation of cracks. At this time, the exact reason for this
particular interface combination to work is not known. Fig. 5.4 shows the BSE

(Back Scatter Electron) micrographs for the two modified interfaces.

104

 

Figure 5.4 BSE Micrographs of the two interfaces used in this study, a) the
occlusive interface between layer A and layer M and b) the smooth interface
between layer Z and layer M (Acceleration voltage: 25kV, Working distance:

39mm).

5.5 THE INFLUENCE OF RAMP/SOAK PROFILE

The mixing proportions of powder have been determined in order to achieve
nealiy equal final diameters. However, the transient diameter change during the
sintering process is also important to yield samples without camber and cracks.
Fig. 5.5 shows the change in the shrinkage rate of powder mixture for layer A and
layer 2 under an isothermal experiment at 125000. It is clear that the shrinkage
rate of layer 2 is higher than that of layer A at this temperature. In fact, this
conclusion is suitable for the whole sintering temperature range we used. This
sintering mismatch contributes the most important factor in creating cracks or

camber as mentioned above.

105

 

 

0.00055 - - - °LaverZ

. —LayerA

0.0 ' 0T2 10:4. ' 0T6 ' 0:8 ' 1:0 ' 1.2
Slntenng tlme (hour)

 

 

 

Figure 5.5 Shrinkage ratio changing profile of Powders A and Z under an
isothermal sintering experiment at 1250°C (dh(t) is the height changing ratio and

h(t) is the height of sample at time t).

However, considering that alumina has much higher thermal conductivity than
zirconia [120, 121], with a faster ramp rate, alumina can be heated up more
quickly and may catch up to the shrinkage of zirconia in the co-sintering process.
This results in a reduction in the transient mismatch of shrinkage between
different layers. From our observation, if the previously determined optimal
system of powder mixtures is sintered with a lower ramp rate (less than '7 OCImin),
cracks formed on the surface of layer A. Final samples were free of cracks and
camber if the ramp rate was higher than 10°C/min and a two-hour soak interval
was used. This ramp rate is exactly used for the sintering curves shown in Fig.

5.2. However, considering the low thermal conductivity of ceramics, the ramp rate

106

cannot be set too high. This would cause a large temperature difference within a

sample and may create a condition for cracks [58].

Because of the difference in the CTE between layers of a fully sintered
sample, a lower cooling rate was preferred to avoid cracks, since the residual
stresses can be relaxed in the initial period of cooling [58]. In our experiments, the
cooling rate of 4°C/min is low enough to prevent cracks caused by CTE

mismatch. The final optimized ramp/soak sintering cycle is shown in Fig. 5.6.

 

 

Temperature (°C)

 

 

 

 

Sintering time (hour)

Figure 5.6 Optimal ramp/soak sintering profile for this study.

5.6 SHRINKAGE RATE-SINTEIRNG TEMPERATURE CURVES OF CHOSEN

POWDERS UNDER OPTIMIZED CONDITIONS

Table 5.2 summarizes the discussion of Sections 5.2 to 5.5 and provides the

optimal parameters to yield undistorted, flat three-layered A|203IZr02 FGM

samples without cracks.

107

Table 5.2 Summary of optimized experimental conditions for a 3-layered

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Alea/ZrOz F GM.
Layer Z 60% TZ3YS, 40%CERAC-2003
Interface Z/M Smooth
20% CERAC-2003, 30% TZ3YS
Structure LayerM
46% CR-lS, 4% TMDAR
Interface M/A Occlusive
Layer A 94% CR-IS, 6%TMDAR
Compaction load 60 MPa
Rate 0f temperature Change 10°C/min for heating: 4°C/min for coolinL
1 .00 -I
0.95 -
£0 J
E 0.90 d
. LayerA
0.85 _ _ . Layer M
- - - - Layer Z
0.80 1 . v . . I v r .
0 300 600 900 1200 1 500
Temperature (0C)

Figure 5.7 Shrinkage ratio-temperature curves for chosen three powder-mixtures
under optimized experimental condition (h1- is the height of sample at temperature

Tand ho is the height of the corresponding green sample).

The densification rate-relative density curves of the three chosen powder
mixtures under the optimal parameters have been shown in Fig. 5.2. Alternatively,
the shrinkage ratio-sintering temperature curve was also used to express the
sintering kinetics of Powders A, M and 2, which is shown in Fig. 5.7. The similarity

of the curves can be directly observed, where all three powder mixtures begin

108

sintering at about 1050°C, and that similar transient shrinkage behavior is
exhibited above 105000. The similarity of shrinkage rate for those chosen powder
mixtures ensures that no significant dimensional mismatch could occur at any
time during sintering, thus reducing the possibility to form cracks or camber. The

present work verifies the conclusion by Torrecillas et al. [65].

 

Figure 5.8. A representative Backscattered Electron image (BSEI) of the
three-layered Al203lAl203+Zr02/Zr02 FGM (Acceleration voltage: 22kV, Working

distance: 15mm).

Fig. 5.8 shows a representative microstructure of the cut cross-section of the
three-layered FGM. Obviously no debonding cracks happened between the
conjoint layers. The microstructure observation of the surfaces showed neither
channeling in the layer with tensile stress (in this study, alumina layer) nor
edge-effect cracks described by Cal [58]. In this study, we fabricated 15 FGM
samples by the chosen powder mixtures under the described ramp/soak path, 14

of which are totally crack and camber free. The other one has a small crack

109

between mixture layer and alumina layer, which may be a result from carelessly

handling of the green sample from the die.
5.7 PHENOMENOLOGICAL CONSTITUTIVE MODELS

Due to the similarity of the densification rate-relative density curves shown in
Fig. 5.2, it is intuitive to investigate and compare the Hsueh’s constitutive model
[107] describing these three curves. Based on the calculation steps mentioned in
Section 4.4.1, we obtain the phenomenological constitutive functions for those
three sinter plots.

We a little changed the entire phenomenological constitutive model expression

to the form of:
6'“ = 0(T + Ta)[Doo(T + 77)) — D]" (5.2)
By calculation, the 0(T + Ta) is a 4th order polynomial and can be written as:'
9(2‘ + Ta) = a(T + Ta)4 + b(T + Ta)3 + C(T + Ta)?” + d(T + Ta) + e (5.3)

and Doo(T+Tb), the theoretically possible full-sintered density at temperature T, is

a hyperbolic tangent function of the form:
Doo(T + 77)) = f tanh[g(T + 77)) - h]} + i (5.4)

Table 5.3 summarizes the coefficients for all three powder mixtures.
From Table 5.3, we can find that the exponent index n is different in each

powder mixture. However, the n for layer M is close to the average of the n values

110

for layer A and layer Z. As of now we cannot give the physical explanation for this
relationship. Because the content of layer M is almost equal to the mixture of half

layer A and half layer Z, the near-average value of n for layer M seams logical.

Table 5.3 The coefficients used to construct the phenomenological constitutive

models for the chosen powder mixtures.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Layer Ta (0C) a (~10-10) b (~10-7) c (103) d e
A -80 -1.707 7.55112 4.091475 0.478596 53.688
M -40 -3.5278 15.60565 2.224715 0.9891 110.955
2 .20 -5.69 25.1704 -3.63825 1.59532 178.96
Layer Tb (0C) f g (-10‘3) h i n
A 0.2365 0.7435 1.65
M -460 0.2449 8.3885 9.4498 0.7551 1.88
2 0.2325 0.7675 2.1

 

 

 

 

 

 

 

 

Using Table 5.3 and formula (5.3), we can find that 0(1) is entirely different for
each layer. This difference is a result of variation of each powder combination’s
apparent activation energy [104], which is determined by the content of the
powder system. By Table 5.3 and formula (5.4), we can find that the coefficient f
and i are different for each layer too. The two coefficients are calculated by the

relative green density 09 and the final relative full density Dfoo in the following

way:

{f+i=Dfoo=l (5.5)

-f+i=Dg

111

Since the green density varies for different layer like discussed in Section 4.3,

coefficient f and ialso must vary with the powder mixture.

In contrast, the coefficients 9, h and Tb were found to be constant for all three
powder mixtures. This results in the terms inside the hyperbolic tangent function
being identical for all three cases. In the simulation process, we find that these
three coefficients significantly influence the shape of the calculated curve. The

similarity of shape of the three plots in Fig. 5.2 results in the same values for g, h

 

  

 
  
       

 

 

 

and T1,.
0.25s .
.O
3 ‘ .
4 0.20. \ -.
9:, l \ ‘.
§0.15- I \ ‘.‘
.5, / .'—R5for layerA \ i,
g 0.10- I ,’ —RcforlayerA \ '.
”é . / 3 — -REf0rlayerM I
8 035‘ .0 — - -RcforlayerM \ '.
‘ I ’1' . . oREforlayerZ \ L
a... .1.: . ~: - -.Rct°r'a.v°r5 . . ..
0.5 0.6 0.7 0.8 0.9 1.0
Relative density

Figure 5.9 The comparison of experimental and calculated densification rate vs.

relative density curves (RE gives the experimental result and R0 represents the

calculated result).

Fig. 5.9 shows the comparison of the experimental and the calculated

densification rate by formula (5.2) for all three powder mixtures. The errors

112

between the experimental data and the calculated results are less than -|_-6%. It
should also be pointed out that the simulation result from the phenomenological
constitutive model does not display the plateau that occurs in conjunction with the

phase change.
5.8. CONCLUSIONS

In the co-sintering of multi-layered FGMs, matching the compaction and
sintering behavior of two distinct materials, each from one type of powder, is not
possible. This has been proved by the research of Cal et al. [58]. Mixing powders
is an effective approach to manipulating the characteristics of raw powders, such
as compactibility, sinterability and agglomerates ratio. These parameters finally
influence the sintering kinetics of powder system. By comparing the densification
rate-relative density curves as well as the final diameter-powder ratio curve of an
alumina powder system containing TMDAR and CR-15 and a zirconia powder
system containing TZ3YS and CERAC-2003, we found that 94% CR-15 and 6%
TMDAR alumina powder has very similar densification rate curve and final
diameter to the 40% CERAC-2003+60% TZ3YS zirconia powder. By mixing these
two powders and slightly adjusting the content of TMDAR, we produced a 50 vol%
alumina 50 vol% zirconia powder mixture with the similar densification
rate-relative density curve and diameter as the other two pure powders. The

content of the 50 alumina l50 zirconia mixture is 46% CR—15 and 4% TMDAR/

113

20% CERAC-2003 and 30% TZ3YS by volume. The shrinkage ratio curves of
these three powder mixtures were found to be almost identical. The similarity in
the shrinkage ratio for those chosen powder mixtures ensures that no significant
dimensional mismatch could occur at any time during sintering, thus reducing the
possibility for cracks and camber in the sample. In addition, the effect of the
compaction load, interface profiles and temperature ramp/soak cycles were
studied. Through a series of experimental processing, the optimal processing
parameters were then obtained, which enabled us to produce flat 3—layered
Al203/Zr02 FGMs without cracks. Decreasing the compaction load, increasing
the ramp rate, selecting an appropriate mixture combination and modifying the
interface profile have been found to produce FGM samples free of defects. The
shrinkage curves were found to be almost identical. The almost identical
densification rate curves of the chosen powder mixtures under the optimized
sintering conditions feature the same hyperbolic tangent term in the

corresponding three phenomenological constitutive models.

After we successfully fabricated Al203/ ZrOz FGMs, we considered replacing

reinforced carbon-carbon composite (RCC) by Mullite for the skin of a space

shuttle, and manufacturing a ZrOz-Al203 FGM core + Mullite skin Perspirable
Skin. However, the total weigh of the TPS will increase a lot. If keeping RCC as

skin material, because the CTE of either alumina or zirconia is larger than that of

114

RCC, there is no gas channel forming at high temperature for a ZrOz-AI203 FGM
core+ RCC skin structure. Therefore, ZrOz-Al203 FGMs are not suitable for the
core material of Perspirable Skin. So ceramic with lower CTE is necessary to be

investigated for the Perspirable Skin project.

115

CHAPTER 6

ZrWan and ZrWan-Zroz COMPOSITES:
lN-SITU REACTION AND PHYSICAL PROPERTIES

Since ZrOz-Al203 FGMs are not suitable for the core material of Perspirable
Skin, ceramic with lower CTE is necessary to be investigated for the Perspirable
Skin project. This chapter will present our investigation on ZrW203, a material
featuring isotropic negative thermal expansion over the whole solid state, as well

as its composites with ZrOz.
6.1 EXPERIMENTAL PROCEDURES

Four powders, W-Fluka, ZW-OR, CERAC-2003, and TMDAR, were used in
this study. These powders were mixed in varying proportions as described later
using 12mm diameter zirconia media in a mixing jar mill (U.S. Stoneware 764AVM,
USA.) for 48 hours. The powder mixtures were compacted in a single-action die
under the load producing 80MPa compaction pressure. The green samples for
CTE testing were cylindrical with 7.94mm diameter and 6mm height while the
green samples for Young’s modulus testing were rectangular parallelepipeds
Whose dimension is 16.5mmX5.05mmX3.5mm. Green compacts were sintered in

a fumace (Carbolite-HTF1700, UK) under the atmospheric condition in a covered

116

platinum crucible, which can decrease the sublimation of W03 at temperatures
above 800°C [122]. Several ramp/soak profiles were used in the experiments,
which will be described in the following sections. However, a quenching process is
necessary for each ramp/soak profile to prevent the decomposition of ZrW203 [25,
123]. The volume of each fully-sintered sample was measured in water using

Archimedes’ principle, which was then used to calculate the relative densities.

Before testing CTE and Young’s modulus, the samples were heat-treated (3°C
[min for both heating and cooling cycles, and soaking for 60 minutes at 300°C) to
cure microcracks induced by the quenching process [25]. The CTE and Young’s
modulus of the sintered samples were measured using the TMA with the heating
and cooling rates of 1°C /min in an argon gas environment. Three samples
produced for each material were tested for CTE and Young’s modulus. The CTE
variation is less than 5% and the maximum discrepancy in the Young’s modulus
data is 6% in the three samples. Therefore, we considered that the CTE and
Young’s modulus test results for each material are consistent and each reported
value in the paper is the average of the corresponding results of three samples.
The sintered samples were then polished (Abramin, Denmark) and thermal
etched in the furnace at 600°C for the microstructure observation. The
microstructure of each sample was observed using Scanning Electron Microscopy

(JEOL 6400V, Japan).

117

4.41.41 HI!

6.2 SYNTHESIS OF ZrW203 SUBSTRATE

From the W03 and ZrOz bi-phase diagram [123], ZrW203 is only present at a
temperature higher than 1110°C and stable in the temperature range of 1110 -
126000. Therefore, in the processing of ZrW203 substrate, the final soaking

temperature must be higher than 1110°C and a quenching step is necessary to
prevent the decomposition of ZrW203. Based on these two requirements, the
ramp/soak profile shown in Fig. 6.1 was used to produce ZrW203. The
stoichiometric ratio of W03 and ZrOz in the reactant is 2:1, which translated into

the mass ratio of 1:0.266. The reaction can be expressed as follows:

ZrOz + 2W03 —>ZrW203 (6.1)

 

 

13%?

Sintering temperature (°C)
A O)
. .8 . .3

19’

L

 

O

 

' V ' V ' V f U

2 4 6 8 10
Sintering time (hours)

0

Figure 6.1 The ramp/soak path used for producing ZrW203.

After quenching in open air, the surfaces of the samples featured small

micro-cracks. These micro-cracks disappeared completely after the cure

118

treatment cycle mentioned above.

 

 

 

 

 

 

 

 

 

 

 

..n 1400
120 1200
100 1000
. 3800-
8” 8
060- 9600-
5
4o. -' 400-
lil llll I I'M
A I I ll 9 l I. l I" III I I ll
' 2'0 ' 3'0 ' 4'0 50 60 2° 3° 4° 5° 60
20(0) 29(0)
a b

Figure 6.2 a) The XRD pattern of the reaction product and b) the standard powder

diffraction file of ZI‘W203 (JCPDS 13-557).

Fig. 6.2 (a) shows the XRD pattern of the reaction product. The XRD testing
was executed with a Scintag XDSZOOO 4-angle pole figure diffractometer. This
pattern was observed to be nearly the same as the standard powder diffraction file
of ZrW208 (Fig. 6.2 (b), JCPDS 13—557). This verifies that the compound

produced is pure ZrW203.

 

Figure 6.3 The microstructure of the ZrW203 substrate.

119

The final dimensions of the cylindrical ZrW203 we have produced were

7.51 mm in diameter and 5.68mm in height and the final relative density was 90%.

The microstructure of the resulting ZrW203 is shown in Fig. 6.3.

 

 

. —- ZrW208

 

 

 

0 '100'200j300'400'500'600‘700
Testing temperature (°C)

Figure 6.4 The temperature dependence of CTEs of ZrW203 and CERAC-2003

sintered by ramp/soak path in Fig. 6.1.

The CTE-temperature relationship of the ZrW203 substrate was measured
and presented in Fig. 6.4. The CTE-temperature relationship of the partially
sintered CERAC-2003 sample utilizing the ramp/soak path shown Fig. 6.1 is also
presented in Fig. 6.4. These two ceramics are the main components for the
composites in this study. As expected, the CTE of ZrW203 is negative and
uniform for a wide range of temperature except with a sharp change around
160°C due to the a- to [3- ZrW203 phase transition. The CTE of the ZrW203 at
room temperature is —8.1 X10-5K-1, which matches the report by Mary at al. [20].

The CTE of the partially sintered CEREAC-2003 is 8.6><10-5K-1 at room

120

temperature.

 

..L
o
C

1 fl-
‘ ./
0.90 d l
0 ' 150300 ' 300103500 ' 600 ' 700'800
Testing temperature (°C)

. A

P .0
8 a

I A

Thermal conductivit (Wm'1K'1)
o .o
(O CO
I? h

 

 

 

Figure 6.5 The temperature dependence of thermal conductivity of ZrW203.

The high temperature thermal conductivity of ZrW203 was measured using

the laser flash method (FlashLine 5000, USA) from room temperature to 710°C.
The results are shown in Fig. 6.5. Around 160°C, a sharp peak, corresponding to
the d to [3 ZrW203 phase transition can be observed. The room temperature
phase is phase a, and its thermal conductivity is around 0.89 Wm-1K-1, a result
that is very close to the reported value of 0.82 Wm-1K-1 [124]. The high
temperature phase 8 features a nearly constant thermal conductivity at 0.985
Wm-1K-1 between 500 to 710°C. Our data indicates that the thermal conductivity
of the phase [3 is higher than the phase a. It is known that ZrW203 exhibits a
crystalline structure, and usually a crystalline material possesses a high thermal
conductivity. However, our data show the thermal conductivity of ZrW203 is very

low (even lower than that of glasses). From the report of Mary et al. [20], the

121

dimension of the unit cell ZrW203 is extremely large when compared with
common ceramics. This structural characteristic provides more phonon vibration
modes to hinder the heat flow in solid. Consequently, the thermal conductivity of

ZrWzog is thus very low.
6.3. ZrIleOgIZroz COMPOSITES

6.3.1 Manufacturing and CTEs

With the ramp/soak path shown in Fig. 6.1 and a higher proportion of ZrOz, a
ZrW203/Zr02 composite instead of 211N203 can be fabricated. Thus, by varying
the ratio of W03 to ZrOz, the resulting composites feature varying ratio between
ZrW203 and ZrOz. Table 6.1 shows several W03/Zr02 mass ratios used in this
study and the corresponding resultant ZrW203/Zr02 volume ratios in the sintered

samples.

Table 6.1 The WOg/ZrOz mass ratios of various green samples and the

corresponding resultant ZrVVzongrOz volume ratios in the sintered samples.

 

W03/Zr02 mass ratio ZrW203/Zr02 volume Final relative

 

# in reactant powder ratios in sintered sample density
1 0.159:1 20:80 77%
2 O.264:1 30:70 79%
3 0.38:1 38.9:61.1 80%
4 0.593:1 51 5:485 82%
5 1.096:1 70:30 83%
3 2.30721 90:10 84%

 

122

The temperature—dependent CTE value of each sintered sample is shown in
Fig. 6.6. As shown, both Samples 1 and 2 feature positive CTEs, Samples 4—6
exhibit negative CTEs, and the CTE of Sample 3 is nearly zero. Fig. 6.6 shows
that the CTE-temperature curves of the composites feature a shape that is very
similar to that of pure ZrW203. However, the peak caused by phase transition
occurs at a lower temperature for the composites. This “peak shift" is possibly a
result of phase transition from a- ZrW203 (low pressure phase) to y— ZrW203
(high pressure phase) [125] due to the thermal stress induced by the CTE

mismatch between ZrW203 and ZrOz.

 

 

 

 

 

 

6
31 fl// ____________
0; ..... \l . °°°°°°°°°°°°°°°°°
A « . 0' .’ -----------------
4‘ 4’11 ----------------------
‘0- '6.‘ .“'°’.o” ........................
E -9«3 E31?
012; '53,: -—#1 - - -#2
' . in" - #3 —-- #4
-15: -~-o#5 ----- #6
13: .; .......... er208
0 '100'200fi300'400‘500'600'700
Testing temperature (00)

Figure 6.6 The temperature dependent CTEs of the various ZrW203IZr02

composite samples.

The relationship between the CTEs of various samples and the corresponding

volume fractions of ZrW203 for both room temperature and 500°C testing

123

conditions is plotted in Fig. 6.7(a) and 6.7(b), respectively. It can be observed that
the CTE values continuously decrease as the volume fraction of ZrW208
increases in the composites. For the zero CTE ZrW203/Zr02 composite, the

volume fraction of ZrW203 in the final product is about 38.9% (Sample 3).

 

 

    

 

 

 

 

 

 

 

A 5- A
43‘ 4‘
g 01 g
LU . I.I.I
5 ..... 0
‘5 ' Q“e.\.
' --------- Rose fiadillwper) ~~~~~~~~
—-——— Roeen-Hadh 0m) ‘
1 n —>—Experknenlal
0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0
Volume Fraction of ZrW208 Volume Fraction of ZrW208
a b

Figure 6.7 The CTEs of the ZrW203/Zr02 composite samples and corresponding
calculated values from several prediction models at a) room temperature and b)

500°C.

As mentioned in Section 1.2.3.3, the ROM is the simplest method to calculate
the effective CTE of a composite. By using the CTE testing results of ZrW203 and
Zr02 shown in Fig. 6.4, the effective CTEs of ZrW208/Zr02 composites were
calculated based on the ROM and presented in Fig. 6.7. Large discrepancy exists
between the experimental results and the calculated values from the ROM for
both room temperature and 500°C testing conditions. In fact, the ROM predicts

that Sample 4 has a room temperature CTE of nearly zero, but the experimental

124

data showed its CTE to be —2.14><10-5K-1. This discrepancy is due to the porosity
of the resulting composites. At the same time, the ROM to predict affective CTE

does not include the elastic constants that account for the thermal stress influence

between ZrW203 and ZrOz.

The calculated CTE as a function of v% of ZrW203 results from Turner model
[37], Kemer model [38], Rosen-Hashin Bounds model [39] and Levin model [40]
(Equations (1.6-1.9)) also are shown in Fig. 6.7, which take into account the
elastic constants into the calculation of CTEs. The values of various elastic
constants of ZrW203 and ZrOz necessary for the CTE calculation are calculated
based on the experimental data of Young’s modulus and the assumed Poisson’s

ratio. This will be discussed in Section 6.3.2.

Clearly, Equations (1 .6-1.9) result in better predictions than the ROM. Among
these, the Levin model [40] produces CTE values that are the most similar to the
experimental data. The maximum error of Levin model was found to be less than
8%. By studying the series of Al203/NiAl composites, Hsieh et al. [126] concluded
“the Kemer [38] and Turner [37] models can be used as the upper and lower
bounds for the CTE of two-phase materials, respectively.” This conclusion also
matches the results from our ZrW203/Zr02 composites. Another interesting

finding is that the upper boundary predicted by the Rosen-Hashin Bounds model

125

[39] almost superimposes on the curve form Kemer model [38] for the
ZrW203/Zr02 composites.

All of the ZrW203/Zr02 composites maintained their initial cylindrical shape,
with final diameter and height around 7.35mm and 5.57mm, respectively, and
they featured final relative densities in the 77—84% range (see Table 6.1). This low
density persists mainly because Zr02 has not been fully sintered by the
ramp/soak path shown in Fig. 6.1. In the representative micrograph of the
composites (Fig. 6.8), the large particles surrounded by small Zr02 particles are
ZrW203. The abundance of pores remaining between the ZrOz particles is due to
the fact that ZrOz is far from fully sintered. In addition, cracks are observed to
exist between ZrW203 and ZrOz grains, resulting from the considerable
difference in CTEs for these two component materials. These cracks also

contribute to the low final density.

 

Figure 6.8 The microstructure of a ZrW20312r02 composite (Sample 3).

126

6.3.2. Young’s Modulus

The TMA unit offers a facility to measure Young’s modulus of materials using
the three-point bending method. After sintering and polishing, the samples used in
Young’s modulus testing are rectangular parallelepipeds (cuboids) with edge
lengths 12.6mm, 4.2mm and 2.5mm. The temperature dependent Young’s moduli
of the fabricated composites as well as that of ZrW203 and Zr02 are shown in

Fig. 6.9.

:5
01

 

New»
U‘IOU'IO
.AlA.A.-

 

 

—L
01
L
1
ll
Ii
(1
ll
ll
Ii
ll
ll
ll
ll

A

e e
o
l

—4—#6—+—#5—-—#4
—n-—#3—o—#2—-—#1

—e—ZrW208 —o—Zr02

Young's modulus (GPa)
N
O

p
U'I
I .

0.0' . .fi . . r . -
0 100 200 300 400 500 600 700
Testing temperature (°C)

 

 

 

' I 1 I '

Figure 6.9. Young’s modulus - temperature curves for composites as well as for
ZrW203 and ZrOz sintered by ramp/soak path in Fig.6.1.
Since the ZrOz in the composites is processed by the ramp/soak path shown

in Fig. 6.1, the CERAC-2003 for Young’s modulus testing was also partially

sintered by the same ramp/soak path. Microcracks formed in the ZrOz samples

due to the quenching process. The highest testing temperature was set as 650°C

127

in order to avoid the decomposition of ZrW203. The room temperature Young’s
modulus of pure ZrWzOg was found to be 4.31GPa, which nearly matches the
value of 4.22GPa reported by Chen et al. [25]. However, these values quite
different from the single crystal value of 88.3GPa reported by Drymiotis et al.
[127]. Since the ZrOz sample was only partially sintered and contains
microcracks, its Young’s modulus is much lower than that of a fully-sintered

sample (~2006Pa) and it does not feature a large decrease from 100 to 400°C,

which is typical for fully-sintered ZrOz [128]. As happened with CTEs, the Young’s
moduli of the composites and the ZrW203 feature a value change around 160°C

due to the a to [3 phase transition.

 

 

  
  
   

5 5
---M—Twichr02asmatrix ---M-Twlchr02asmatrix
1..-. M-TwichrWZOBasmatrix ‘---- M-TwichrWZOBasmatrix
a 4,, — Kwon revised M-T model a? 4. --- Kwon revised M-T model
{5 4 Experimental data {3 V Experimental data
3 7 8
5 3. 3 3‘
3 8
5 2
.g a
c 2. c 2..
g 3
>. >-
1 f f 1 fl

 

 

 

 
   

 

 

 

0.0 7 072 7 074 7 076 078 1.0 0.0 072 7 074 7 076 7 07a 7
Volume fraction of ZrW208 Volume fraction of ZrW208
a b

Figure 6.10. The calculated Young’s modulus of ZrW20312r02 composites by
Mori-Tanaka model and the experimental measurement of composites at a) room

temperature, b) 500°C.

128

1.0

From the reports of Drymiotis [127] and Holcome [129], we took the Poison’s
ratio is 0.3 for both 211N203 and ZrOz. Therefore, with the Young’s modulus
values for ZrW203 and partially sintered ZrOz, we calculated the elastic constants
needed for Mori-Tanaka method (Equation 1.1) and Equations (1.6-1.9) and the
Young’s moduli of ZrW20312r02 composites by the Mori-Tanaka method. These
results are shown in Fig. 6.10 along with the experimental Young’s modulus of the
composites. It can be seen that the experimental data lies between the two curves
predicted by the Mori-Tanaka method. Based on the definition of continuity by
Nishimatsu and Gurland [47], we calculated four different continuity values. Since
the pores of ZrW203 is much less that that of ZrOz, only three microstructural
interfaces of ZrW203-ZrW203, ZrW203-pores, and ZrW203-Zr02 are needed in
the calculation. The summation of interface number of ZrW203-pores and
ZrW203-ZrOz results in the interface number of ZrW203-porous ZrOz. The

calculation formula we used is

_ 2Nzw/zw
2Nzw/zw+ lep + Nzw/zo

 

C (62)

where, Nzw/zw, Nzw/p, and Nzw/zo represent the number of interfaces of
ZrW203-ZrW203, ZrWZOB-pores, and ZrW203-Zr02 that crosses the unit line,
respectively.

The continuity values are listed in Table 6.2. The curve by Kwon et al. [42]

revised Mori-Tanaka method represented in Fig. 6.10 too. As can be seen, the

129

revised Mori-Tanaka method shows a much better fit to experimental data, even '

when the volume fraction of ZrW203 is higher than 0.6. The maximum error of

Mori-Tanaka method revised by Kwon et al. [42] was found to be only 4%.

Table 6.2 The continuity values obtained by the microstructure observation for

ZrW203-Zr02 composite samples with different ZrW203 volume frictions.

 

ZrW203 volume proportion range (%) Continuity

 

0-20 0
20-45 0.3
45-65 0.5
65-90 0.75

90-1 00 0.98

 

Here, one point need to be emphasized is that there are voids in the
ZrW203/Zr02 composites. If the Young’s moduli of the single crystal ZrW203 and
fully-sintered ZrOz are used for the Mori-Tanaka method. The third phase of void
need to be considered too. However, in our calculation, by taking the measured
Young’s modulus values of ZrW203 and ZrOz sintered by the same ramp/soak
profile to produce the ZrW203/Zr02 composites as the two boundary values, the
effect of voids on the Young’s modulus has been included. Because the baundary
values are exactly for the components of all ZrW203/Zr02 composites in this
paper, the calculated curves in Fig. 6.10 can be used to predict the Young’s

moduli of any other ZrW203IZr02 composites.

130

min

6.4 ZERO CTE COMPOSITES CONTAINING ZrWan

Fig. 6.6 shows Sample 3 with nearly zero CTE. The dimensions of this
composite do not change with the temperature changing. Therefore, it can be
used as the ceramic substrate of Optical fiber Bragg gratings and some
components of microelectronics. One advantage of this kind of composites is to
reduce the thermal stress due to the temperature gradient or transient
temperature change. Several fabrication methods were developed to produce the

ZrW203-containing composites with zero CTE. These methods were then
evaluated based on the microstructure, final density, mechanical strength of the

sintered samples, and the ability to maintain the shape during the processing.

6.4.1 Method l: In-Situ Reaction of ZrOz-I-W03

By Table 6.1, the reaction of powder mixture of W-Fluka and CERAC-2003
with the 1:2.62 mass ratio produced a ZrW203/Zr02 composite with nearly zero
CTE. The volume fraction of ZrW203 in the final product is 38.9% and the mass
ratio between ZrW203 and ZrOz expected to be around 121.86. The
ZrW203/Zr02 composite fabricated by Method l maintained its cylindrical shape
with the final diameter and height of 7.35mm and 5.57mm respectively, and the
final relative density of the composite was only 81%. Its Young’s modulus at room
temperature is 22610.01 GPa. The CTE measurement for this composite is

shown in Fig. 6.11.

131

 

0.0 .

q

 

 

 

 

 

 

-4.0'
'¥ ..................
co -8.0- ----- .
2 .
:2 -12 " Methods I," 8: Optimal
o ........... Method III
16 ‘ 2: Method IV
' " - - - - ZrW208
0 710072017300'400'500'600'700
Testing temperature (°C)

Figure 6.11 CTE-temperature curves for nearly zero CTE composites fabricated
by various processing methods; each data point represents an average of test

results for three samples.

6.4.2 Method II: Cosintering of ZrOz and erzos

Considering that no reaction occurs between ZrW203 and ZrOz, ZW-OR and
CERAC-2003 powders were mixed with the mass ratio of 121.86. This mass ratio
was chosen based on the experimental results of Section 6.4.1. The powder
mixture was sintered by the ramp/soak path from Fig. 6.1. The produced
ZrW203/Zr02 composite also exhibits near zero CTE. Fig. 6.11 shows that the
CTE curves of the composites fabricated by Methods l and II are almost identical.
Fig. 6.12 (b) displays the micrograph of the composite fabricated by Method II. By
comparing Figs. 6.12 (a) and 6.12 (b), it can be seen that the microstructures for
both composites are very similar. Therefore, Method II produces a very similar

composite as Method l. The Young’s modulus at room temperature of the

132

composite by Method II is 2.27:l:0.01 GPa. However, due to the relatively high cost
of commercially available ZrW203 powder, Method II is a more expensive

process than Method l.

 

Figure 6.12 Micrographs of near-zero CTE composites made by Method a) l b) II,
C) III and d) IV. The larger grains are ZrW208 and the smaller grains are

Zr02/Al203 Marking distance: 15mm, acceleration voltage: 15KV).

6.4.3 Method III: In-Situ Reaction of ZrOz+WO3+AI203

In sintering a powder mixture containing ZrOz, W03, and Al203, a complex

chemical reaction occurs when the temperature exceeds 1100°C

133

ZrOz + W03 + AI203 -> Zr'WzOg + A|2(WO4)3 + ZrOz + AI203 (6.3)

The melting point of Al2(WO4)3 is 113500 [130]. Therefore, a liquid phase

exists if the soaking temperature is set at 119000. The presence of the liquid will

promote the densification kinetics, improving the final relative density.

Based on several experiments, one mixture of ZrOz, W03, and Al203 powders
used to produce a near-zero CTE ZrW203/AI2(WO4)3/Zr02IAl203 composite was

with the mass ratio:

mwo3:m2r02:mA|203=1:0.266:1.53 (6.4)

The CTE curve for this composite is also presented in Fig. 6.11. The
ramp/soak path used in this method is the same as that of Fig. 6.1. The final
relative density of the composite is greater than 95%, which is much higher than
those of Methods l and II (81%). The microstructure of the composite produced by
Method lll (Fig. 6.12 (c)) shows much more compact structure than the
microstructures shown in Figs. 6.12 (a) and (b). Very few pores are left among
ZrOz and Al203 grains in Fig. 6.12 (c), a characteristic attributed to the infiltration
of the liquid AI2(WO4)3 phase. The average grain size of Al2(WO4)3 and ZrW203
in Fig. 6.12 (c) is much less than those in Figs. 6.12 (a) and (b). The liquid phase
produced in the sintering process for Method "I mainly promotes sintering kinetics
of Zr02 and AI203, resulting a solid ZrOz+Al203 matrix with few pores. In

comparison to the porous zirconia matrix produced by Methods l and II, the

134

Al2(WO4)3 and ZrW203 phases are tightly integrated into the solid zirconia matrix
produced by Method III, which contributes to the small grain growth of AI2(WO4)3
and ZrW203. The Young’s modulus at room temperature of the composite by

Method III is also higher than that by Method l or II. The value is 38.791:0.03 GPa.

However, the critical problem for Method III is the powder mixture resulting in
excessive liquid phase, AI2(WO4)3, which caused the geometric distortion of the
samples. The final shape of the composites fabricated by this method changed

substantially from their original cylindrical shape.

6.4.4 Method IV: In-Sltu Reaction of Zr02+W03: Another Ramp/Soak Path

Method IV used the same powder mixture to produce pure ZrW203 (see
Section 6.2) with a changed ramp/soak path as shown in Fig. 6.13. The cooling
down and the second isothermal soaking part in Fig. 6.13 causes a partial
decomposition of ZrW203, resulting in a ZrW203/Zr02NV03 composite. By using
a 2°Clmin cooling rate and soaking at 952°C for 37 minutes, a
ZrWZOg/ZrozNVO3 composite with nearly zero CTE was fabricated, as shown in
Fig. 6.11. The final relative density of the composite fabricated by Method IV is
only 73%, and the room temperature Young’s modulus is 1.89:0.01 GPa. Each
value is much lower than the corresponding value of the other three methods. Fig.
6.12 (d) shows the microstructure of the composite fabricated by Method IV,
which is less dense than those of the other composites. Because of its loose

microstructure, most of the thermal stress due to the CTE mismatch among

135

ZrW203, ZrOz, and W03 has been released into the larger cracks and pores.
Upon heating the composite, only a smaller magnitude of the thermal stress is
induced, which deters the a-to-y phase transition. Therefore, no obvious “peak
shift" is observed on the CTE-testing temperature curve for this particular
composite as shown in Fig. 6.11. This composite retained the cylindrical shape

with the final diameter of 7.49mm and the final height of 5.65mm.

\

 

 

    
 
 

1200-

.s
O
O
O
l

800-
1

600 -

400 -

 

Sintering temperature (°C)

 

 

 

0'2'4'6'8'1‘0'1‘2
Sintering time (hours)

Figure 6.13 The ramp/soak path used in Method IV.

Besides the low final density, another obvious disadvantage of Method IV is
the requirement of a very precise control of sintering temperature and time. A
small change in the cooling rate or in the duration of the final isothermal cycle (see

Fig. 6.13) yields an entirely different CTE result.

6.4.5 Optimal Fabrication Method and Density Improvement

By comparing the four methods, the optimal method is determined for the

production of zero CTE composite containing ZrW203. Methods l and II produce

136

very similar results, where Method II is much more expensive. Method |I| yields
the highest Young's modulus and relative density. However, it could not maintain
the sample’s shape during sintering. Method lV yields the lowest relative density
and Young’s modulus. Therefore, it was concluded that the composite is best
produced by a new method that combines Methods I and Ill. By the in-situ
reaction of the powder mixture of W03, Al203 and Zr02 with mass ratio
1:0.03:2.61, the optimal nearly zero CTE composite containing

ZrW203/AI2(WO4)3/Zr02/AI203 was obtained.

 

Figure 6.14 The micrograph of near-zero CTE composite made by optimal
method (With 0.07 wt% alumina, Working distance: 15mm, acceleration voltage:

15KV).

The CTE-temperature relationship of the optimal composite is almost the
same as those of Methods l and II (Fig. 6.11). The optimal composite retains its
cylindrical shape and reaches a final relative density of 90%. Its Young's modulus

at room temperature is 11.19GPa, which is higher than that of the composites

137

fabricated by Methods l and II. The microstnlcture of the composite fabricated by
the new optimal method is shown in Fig. 6.14. The microstructure is similar to
Figs. 6.12 (a) and (b). However, due to the flow of the liquid phase, the pores

among Zr02 grains in Fig. 6.14 are much reduced than those in Figs. 6.12 (a) and
(b).

Similar method was used to improve density and final mechanical properties of
other composites. The 0.07wt% Al203 was added into our W03+Zr02 powder
system, which caused the final relative density to increase from 80 to 90%.
Furthermore, the minute amount of TMDAR allowed the samples to maintain their

cylindrical shape. The microstructure of these improved-density composites far

fewer pores exist between ZrOz grains, similar to Fig.6.14.

6.5 CRACKS PROPAGATION?

There are cracks between ZrW203 and ZrOz grains in erzoaeroz
composites as shown in Figs. 6.8, 6.12, and 6.14. An important problem is ifthose
cracks propagate in the thermal cycles a TPS will experience? If the cracks do
propagate by the thermal stress, then ZrW203/Zr02 composites cannot be used
for the Perspirable Skin. To investigate this issue, we heated and cooled the
Sample 3 by the thermal cycles shown in Fig. 6.15 many times. And measured

the CTE and Young’s modulus of the sample after each thermal cycle.

138

    
   

 

 

 

 

 

 

 

 

 

 

1200- 4.
1000-
3: 800-
2 6004
a a:
it . l] l
400-
g .
" 200-
0. . 7-7—1——r—U-7’h-—
0 1 2 n
Thermal Cycle

Figure 6.15 Thermal cycles used to investigate the crack propagation.

From the test results, the CTE of the composite does not change after each
thermal cycle. Each measurement is the same to the corresponding curve in Fig.
6.6. There is only very small change of Young’s modulus after the first thermal

cycle, and then the Young’s modulus keeps constant as shown in Fig. 6.16.

 

 

 

 

A 104

G

% 4

v 8*

(I)

2 .

.§ 6- +Wlthout Al203
E —e—VVlth Al203
.0)

U)

c

3

>-

2 l I

0 272'67871'0'15'12'16'1'8'20
Thennalecle

Figure 6.16 Young’s modulus evolution with the thermal cycles.

139

The measured CTE and Young’s modulus values proof that no obvious
physical properties decay by thermal cycles. Therefore, we can conclude that
cracks between er203 and ZrOz may grow, but porous structure of the
ZrW203I2r02 composites prevent cracks propagate, since once the tips of the
cracks reach the porous ZrOz region, the energy/stress will release into the

grain-bridges.
6.6. CONCLUSIONS

By the in-situ synthesis of W03 and ZrOz in a mass ratio of 1:0.266. a ZrW203
substrate was fabricated. By increasing the ratio of Zr02 in the reactants, the
product was found to be ZrW203/Zr02 composites. Both the CTE and Young’s
modulus of various samples were measured, and those data were compared with
several model predictions, including the rule of mixture (ROM), the Turner model,
the Kemer model, the Rosen-Hashin bounds model, the Levin model and the
Mori-Tanaka method. Among the model predictions, the revised Mori-Tanaka
method by Kwon et al. offers a high degree of agreement to the experimental
Young’s modulus values and the Levin model shows best correlation to the CTE
testing values. To the knowledge of the authors, this research is the first time to
apply CTE prediction models to composites containing negative CTE materials.
Adding a small amount of AI203 into the W03+Zr02 reaction system was found to

effectively increase the final density of the sintered composites. The controllable

140

CTE characteristics formulated in this study can be used to fabricate a specific
ZrW203/Zr02 composite in order to meet given requirements for thermal
expansion in an industrial process. Also, Zr02l(WO3)/(AI2(WO4)3)/
(Al203)/ZrW203 composites with nearly zero CTE can be fabricated by various
methods. Each method yields some uniqueness in the microstructure, final
density, mechanical strength, and ability to maintain shape. By comparing the four
methods, the optimal method is found to be the in-situ reaction of powder mixture
of W03, AI203, and ZrOz with mass ratio 1:0.03:2.61. The final relative density of
the composite made by this optimal method is around 90%, and the room
temperature Young’s modulus is 11.196Pa and the sintered sample retains the
shape of the green sample. The main advantage of this material is the zero CTE,
which reduces the thermal stress under thermal gradient loading and transient

temperature change in a structure.

Due to the negative thermal expansion, pure ZrW203 and some ZrW203/Zr02
composites can be used as the core of Perspirable Skin. However, to
accommodate for the temperature gradient 3 TPS will experiment at reentry, the
geometry of a ZrW203 core or a ZrW203/Zr02 composite core can not to be a
simple cylindrical shape. It has to be one that has a bigger radius at the top
surface and a smaller radius at the bottom part. The resulting geometry consisted

of a frustum of a cone at the top half portion and a cylinder at the bottom half

141

portion. When such geometry experiences a temperature gradient, the top
surface of the core will shrink significantly due to the endured high temperature,
resulting in a large gap at the top surface, while the bottom part of the core will still
maintain contact with the RCC skin because of the lower bottom temperature.

This designed shape for the core made by ZrW208 is shown in Fig. 6.17 [131].

 

Figure 6.17 Designed geometry for the ZrW203 core [131].

The complex shape shown in Fig. 6.17 is hard to achieve by Powder
Metallurgy method. Considering the gradient temperature a TPS will experiment
at reentry, a cylinder-shaped FGM containing ZrW203 and Zr02 might be better

core material, if the fabrication is possible.

142

 

 

she

H0

me

FE

ho

lur

del

DIE

mi

dis

7.1

 

CHAPTER 7

ZrWan-Zroz CONTINUOUS FGMs: FABRICATION AND
THERMAL EXPANSION GRADIENT CONTROL

As discussed in Section 6.6, the geometry of the ZrW203 core or
ervzongroz composite core for Perspirable Skin needs to be with very complex
shape to accommodate for the temperature gradient it will experiment at reentry.
However, it is hard to achieve the complex shape sample by Powder Metallurgy
method. Therefore, it is necessary to investigate the possibility of fabrication of
FGM containing ZrW203. We employed the same method to that in Chap. 5 and
hoped to produce multi-layer FGMs containing ZrW203. Surprisingly, the products
turned to be ZrW203-Zr02 continuous FGMs. In the following sections, the
detailed processing steps and the measurement techniques used will be
presented together with the mechanisms that contribute to the formation of the
continuous structure. In addition, the influence of the soaking duration on the
microstructures, the method used to reduce the distortion in the final FGMs will be

discussed.
7.1 EXPERIMENTAL PROCEDURES

The four raw powders used in this study were W-Fluka, CERAC-2003, TZ3YS,

143

and TMDAR. A WO3+Zr02 powder mixture and ZrOz powder were stacked
layer-by-layer in a single-action die and then compacted under the compaction
pressure of 80MPa to form two-layer Zr02/Zr02+W03 and three-layer
Zr02/Zr02+W03/Zr02 green bodies. Each ZrOz layer was composed of 0.49 of
zirconia powder. With out special explanation, the W03+Zr02 powder mixture is
the one to produce pure ZrW203 (Powder A). The stoichiometric ratio of W03 and
ZrOz was 2:1 (the mass ratio is mwo3: eroz =1:0.266) in the W03+Zr02
powder mixture as discussed in Section 6.2. All powder mixtures were mixed
using 12mm-diameter zirconia media in a jar mill (U.S. Stoneware 764AVM,
USA.) for 48 hours. Four samples were produced, each featuring a unique mass
ratio between the layers as shown in Table 7.1. Samples 1, 2 and 3 featured a
symmetric Zr02/Zr02+W03/Zr02 stacking structure and the only variation among
them was the mass of the mixture layer. Sample 4 was designed to have an

asymmetric Zr02/Zr02+WO3 stacking structure.

Table 7.1 The mass ratio for each green sample and theoretical thickness/volume

ratio and erzog volume fraction in the sintered samples.

 

 

 

 

 

# Mass ratio Thickness/volume ratio Theoretical Zl‘Wan
Zriconia1:Mixture:Zirconia2 Zriconia1:Mixture:Zirconia2 volume fraction

1 1:1.78:1 1:2.13:1 51.5%

2 1:1.08:1 1:1.28:1 38.9%

3 1:0.65:1 1:0.77:1 29%

4 1:0.54:0 1 :O.64:0 38.9%

 

The diameter of the green compacts was 7.94mm after compaction. Because

144

the processing ZrW203 requires the final soaking temperature higher than
1110°C and a quenching step necessary to prevent the decomposition of ZrW203,
as discussed in Section 6.2, these green compacts were sintered in a covered
platinum crucible under atmospheric conditions in a furnace (Carbolite-HTF1700,
UK). The covered cmcible provided a nearly sealed environment in order to
decrease the sublimation of W03 at temperatures higher than 800°C [122]. The
ramp/soak profile used in this study is similar to Fig. 6.1, but the soaking durations
was varied from 3.5 hours, 6 hours and 14 hours to investigate its influence on the
final microstructures. The volumes of the fully-sintered pieces were measured in

water using Archimedes’ principle for the calculation of the relative density.

Before the CTE testing, the samples were heat treated (3°Clmin for both

heating and cooling cycles, and soaking for 60 minutes at 300°C) to cure

microcracks induced by the quenching process [25]. The CTE measurements of
sintered samples were performed using the Therrnomechanical Analyzer (TMA:
Setaram 95, France) with argon gas providing a protective environment and using
heating and cooling rates of 1°C/min. Three specimens produced for each
sample were tested for their CTEs. The CTE variation in the measurement is less
than 5%. Therefore, we considered that the CTE testing results for each sample
are consistent and each reported value in the paper is the average of the

corresponding results of three specimens. The sintered samples were polished

145

(Abramin, Denmark) and thermally etched in a furnace at 600°C. Then the

microstructure of samples was observed using Scanning Electron Microscopy

(JEOL 6400V, Japan).

7.2 CONTINUOUS GRADIENT

In the first attempt to fabricate ZrW203-2r02 FGMs, we used exactly the same
ramp/soak path in Fig. 6.1. If the sintering of the green stacks produces multiple
layers of Zr02/ZrW203 or Zr02/ZrW208/Zr02, as expected, the sintered samples
should feature a white/green or white/greenlwhite color distribution since pure
erzoa is green and pure ZrOz is white. However, the sintered samples were
found to exhibit a gradual change in yellow color along the axial direction. This
color distribution indicates that ZrW203 has infiltrated into the layers that were
initially pure ZrOz. To investigate the materials distribution, the samples were
polished down to observe the cross-sectional microstructures at several positions.
The sintered Samples 1, 2 and 3 featured a symmetric microstructure about the
mid-plane along the axial direction and Sample 4 remained asymmetric. Also, the
proportion of ZrW203 was found to vary continuously along the axial direction in
each of the four samples. Fig. 7.1 shows the micrographs of several
cross-sections of Sample 2. The large ZrW203 grains are sunounded by the
much smaller ZrOz grains. Fig. 7.1 clearly demonstrates the continuous decrease

in the concentration of ZrW203 from the mid-plane shown in Fig. 7.1 (f) to the

146

outer surfaces shown in Fig. 7.1 (a). By the cross section observed, the area
fraction of ZrW208 is estimated to be around 70% at the mid-plane, but only

around 20% on both the top and bottom surfaces.

"1"“

 

.2)/u

Figure. 7.1 Micrographs of several cross-sections for sintered Sample 2 with
height of 6.2mm from the position of a) the outer surface, b) 2.6mm away neutral
plane, 6) 1.8mm away neutral plane, (I) 1.2 mm away neutral plane, e) 0.6mm
away neutral plane and f) the neutral plane. The larger grains are ZrW203, which

are surrounded by ZrOz (Working distance 15mm, acceleration voltage: 15KV).

Samples 1, 2 and 3 have a similar gradient microstmcture. However, the area

147

9X3

190

die

fractions of ZrW203 at the same positions in Samples 1 and 3 differ from those
examined in Sample 2. In Sample 4, the proportion of ZrW203 continually

decreases from the surface initially composed of WO3+ ZrOz to the one initially

composed of ZrOz,

Fig. 7.1 shows the existence of cracks between ZrOz and ZrW203 grains, a
direct consequence of the significant difference in CTE between the two
constituent materials. However, it is important to point out that the interfacial

debonding, a typical defect found in multi-layered materials [58], does not appear

 

   
 

 

 

in our FGMs.
4
.9 2*
7x .
“a 0-
m I
5 -2-
a 1
"g Sample 1
0: -4 - —-o—Sample 2
. —*—Sample 3
-6 —->(—Sample 4

 

4-37-2-1012 3 4
Position (mm)

Figure. 7.2 The radial thermal expansion-position relationship for sintering FGMs
at room temperature. The 0 position is defined as the mid-plane for Sample 1-3

and the initial WO3+Zr02 surface for Sample 4 (Soaking duration: 6 hours).

The radial surface of each sample was polished to achieve two parallel planes.

148

The radial thermal expansions of each sample were then measured at several
locations for each sample. It can be seen in Fig. 7.2 that the radial thermal
expansions feature a continuously changing profile, providing additional evidence

of a continuous gradient of the sintered FGMs.

However, the radial expansions presented in Fig. 7.2 are not the physical
properties of cross-sectional CTEs since the values include both the thermal
expansion effect and the mechanical constraints exerted from the adjacent parts
of the sample. After observing the microstructure of the cross-sections at each
testing position, the corresponding ZrWZOBIZroz area ratio at each position was
estimated. Using Fig. 6.7, the corresponding cross-sectional CTE of each testing
position was obtained. Fig. 7.3 shows both the radial thermal expansion and the
corresponding cross-sectional CTEs for Sample 4. Clearly, the discrepancy
between two data is insignificant. However, since the adjacent parts have less
ZrW203 proportion, the radial thermal expansion of the layers near the initial
WO3+ ZrOz mixture surface show a slightly higher value then the cross-sectional
CTEs due to the tension from the adjacent parts. The radial thermal expansion of
the parts near the initial ZrOz surface are lower than the corresponding
cross-sectional CTEs due to the compaction from the adjacent parts, which have
more ZrW203 proportion. Due to the same reason, for Samples 1, 2 and 3, the

central portions’ radial CTEs are slightly higher than the cross-sectional CTEs and

149

the outer surface parts’ radial CTEs are a little lower.

Corresponding ZrW208 volume fraction

 

    
 

 

 

0.69 0.615 0.52 0.37 0.33 0.28 0245
4 I l l l l I I I
0.312
2.
7x
‘9 0-
o
C
l‘—‘ -2-
0
.4 . + "Radial CTE”
-—x—- Cross-sefional CT E

 

0.0 0.5 1.0 1.5 2.0 2.5 3.0 73.5
Position (mm)

Figure 7.3 The radial thermal expansion and the corresponding cross-sectional
CTEs for Sample 4 at room temperature. The sample height is 6.21mm. The 0

position is defined as the initial W03+ ZrOz surface and the soaking duration was

6 hours.

There are several key processing factors that contribute to the fabrication of
continuous FGMs. First, the soaking time was extended to 6 hours in order to fully
react the constituent powders, W03 and ZrOz. This ensures that the W03
powders have enough time to diffuse into the zirconia layer(s). Another major
contributing factor that is essential to understanding this process is the
sublimation of W03 at temperatures above 800°C [122]. The sublimation causes
the W03 gas to diffuse into the whole crucible, providing an additional transport

mechanism to form the continuously varying microstructures. The resulting

150

transport of W03 coupled with the chemical reaction between W03 and Zr02
enables the ZrW203 grains to appear not only in the initial W03+Zr02 mixture
layer but also in the ZrOz layer(s). In addition, the symmetric distribution of W03
about the mid-plane in the green body for Samples 1, 2 and 3 contributed to the

final symmetric distribution of ZrW203 throughout the sintered samples.

7.3 EFFECT OF SOAKING DURATION ON MICROSTRUCTURES

Considering that the diffusion of W03 is one of the major contributing factors in
the development of the continuous microstructure of the FGMs, the soaking
duration must have a significant influence on the final microstructure. Therefore,
two additional soaking durations, 3.5 and 14 hours, were evaluated. The samples
sintered in these two new ramp/soak paths were also polished to observe the
cross-sectional microstructures at several locations. For the samples sintered with
the 3.5-hour soak time, the surfaces also show a gradual change in yellow along
the axial direction, similar to the sample processed with the 6 hours soak duration.
The outermost surfaces of the initial ZrOz layers are now ZrW203/Zr02
composite structure in yellow color. However, most the other part of the initial
Zr02 layers exhibited white circular regions sunounded by a yellow ring, in
contrast to the whole yellow cross-section found in the previous samples. The
microstnlcture observation showed that the outer ring is composed of both ZrOz

and ZrW203 grains while the white center is composed of only zirconia. For

151

Sample 2, the location of these “white circle + yellow ring” parts is between
+2.4mm and +2.8mm and also between -2.4mm and -2.8mm along the axial
direction using the origin of the coordinate defined at the center of the mid-plane.
The whole height of the sample is 6.2mm and the sample occupies the space
between -3.1mm and 3.1mm in the axial direction, and the initial W03+Zr02
powder mixture occupies the space between -1.21 mm and 1.21 mm. The white
circle features a diameter of 6.91mm while the diameter of Sample 2 is 7.44mm.
The pure Zr02 region indicates that the central W03 did not diffuse into the whole
ZrOz layer(s) with the 3.5-hour soaking duration. The average single-direction
diffusion path of W03 in the Zr02 layer(s) for all four samples is only 1.2mm for
the 3.5-hour soaking duration. Therefore, the average single-direction diffusion
speed of W03 from the center part (initial mixture part) to the outer part (initial
ZrOz part) is 0.343mm/hour. However, as pointed out above, the sublimation
provides an additional transport mechanism for WO3. This additional transport
mechanism induces the formation of the yellow-colored ZrW203+Zr02 ring and

the ZrW203/Zr02 composite structure for the outermost surfaces.

For the samples sintered with the 14—hour soaking time, the color distribution
of the surfaces is even. The microstructure of each cut surface features a
ZrW203/Zr02 composite structure and has nearly the same area fraction of

ZrW203. This microstructural characteristic indicates the sintered samples are the

152

even-distributed ZrW203IZr02 composites. The volume fraction of ZrW203 for
each sample is near to the theoretical value calculated by the mass ratio of ZrOz

and W03 in Table 7.2.

Table 7.2 The room temperature axial CTE of each samples under different
soaking durations and of the CTE of the ZrW203er02 composites with the
theoretical volume fraction of ZrW203 calculated by the mass ratio of ZrOz and

W03 in Table 7.1.

oaklng tlme 2 6 14 Theoretical
Sample #

 

1 -2.11 -2.13 -2.1 -2.14
2 0 0 0.04 0
3 1.87 1.86 1 .89 1 .86
4 0.02 0 0.05 0

 

The measured radial thermal expansion also changed with the soaking
duration. Fig. 7.4 shows the radial thermal expansion for Sample 2. For the
3.5-hour soaking time, the "flat” sections represent no thermal expansion gradient.
These ‘flat” portions occur at the locations similar to the “white circle + yellow
ring.” Therefore, the ‘flat" sections consist of the nearly pure ZrOz component.
The decrease in the thermal expansion, the radial coordinates between +2.8mm
and +3.2mm and also between -3.2mm and -2.8mm, occurs due to the ZrWzOg
from the reaction of ZrOz and sublimated W03. The radial thermal expansion of
the samples with the 14-hour soaking time is nearly constant, which provides

further evidence that the samples are evenly distributed ZrW203/Zr02

153

composites. Another important aspect to point out is that the radial thermal
expansion values of the samples with the 14—hour soaking time are only slightly
larger than the testing results for corresponding ZrWzoa/ZrOz composites with
theoretical ZrW203 volume fraction calculated by the mass ratio of ZrOz and W03
(Table 7.1). This is due to the W03 that escaped the system as a gas produced by

sublimation, resulting in a slight decrease of ZrW203 fraction in the samples.

 

       
   

6
7 —0—3.5h soaking
4- +6h soaking
‘9 1 +14h soaking
7! 2 .,
‘2 .
a: 0-
u.l .
'—
0 .2 .
.4.

 

 

 

Null
(9.

-3 7 -2 -71 7 0 7 1
Position (mm)

Figure 7.4 The CTE-position relationship of Sample 2 for various soaking

durations.

7.4 POWDER COMPONENT EFFECT

Varying the component of each layer can also change the microstructure and
CTE distribution. For example, we changed the pure ZrOz layer to be powder
mixture of Zr02 and W03 with mwo3: erOZ =1:0.38 (Powder 8), which produces

a composite of ZrW203 and ZrOz with 0 CTE as shown in Section 6.3. And 1.39

154

PowderA and 1.79 Powder B were measured and stacked together. With 6 hours

soak duration, the produced continuous ZrW203+Zr02 FGM (Sample 5) was with

height of 7.7mm and the he axial CTE of the sample is shown in Fig. 7.5.

 

o.

.2.

CTE (10'6K’1)
(in _ L

 

 

 

U ''''' I ' I ' I ' I ' l ‘ I

o 1 2 3 4 5 6 7 8
Measurement position (mm)

Figure 7.5. The CTE-position relationship of Sample 5.

7.5 DISTROTION CONTROL

Initially, only CERAC-2003 powder was used as the zirconia component of the
WO3+Zr02 powder mixture and ZrOz layer(s). For the 3.5-hour and 6-hour
soaking cases, after sintering, the original cylindrical shape of the green bodies
changed to a shape similar to a barrel for Samples 1, 2 and 3 and the frustum of a
cone for Sample 4. This distortion is a result of the final dimensional mismatch
between the two materials. For the cylindrical green body with 7.94mm diameter
sintered in the ramp/soak path from Fig. 6.1, the ZrW203 produced by the in-situ

reaction of W03 and ZrOz mixture (with the Stoichiometric ratio of 2:1) has a final

155

diameter of 7.51mm while the pure CERAC-2003 yields only a 7.28mm diameter.
Due to the variation in the proportion of ZrW203 along the axial direction, the
diameter of the sample changes from the mid-plane (initial W03+Zr02 surface) to

the outer surfaces (initial Zr02 surface).

In Section 4.2.3, we have demonstrated that the final diameters of the sintered
samples vary as the content of powder mixtures changes. Based on this finding,
CERAC-2003 powders were mixed with TZ3YS in a variety of proportions to form
zirconia powder mixtures. And the corresponding final diameters of sintered
zirconia samples were compared to the diameter of pure erzog, 7.28mm. The

relationship is shown in Fig. 7.6.

 

r1 >1
O N
AAL‘Al-A..A-Al

7‘
on

P‘
L
I ‘4‘ I A

+ Zr02 diameter
—ZrW208 diameter-7.51mm

 

 

7‘
U
A I I

 

' 2? ' 4'0 ' e'o ' e'o ' 160
Proportion of Cerac-2003 (%)

Diameter sintered at 1200°C (mm)

94

Figure. 7.6 The relationship between the diameters of zirconia samples sintered
by the ramp/soak path of Fig.6.1 and the percentage of Cerac-2003 in zirconia

powder mixtures (the diameter of green bodies was 7.94mm).

Fig. 7.6 shows that two mixtures of zirconia have a similar final diameter to the

156

pure ZrW203 when the proportion of CERAC-2003 in zirconia system is around
8% or 91%. Through several attempts, the exact proportion of CERAC-2003 in the
CERAC-2003+TZ3YS powder mixture has been refined to 11% in order to prevent

the distortion in the sintered FGMs.

7.6 DENSITY IMPROVEMENT

The final relative density of all four FGM samples was found to be only near
80%. As discussed in Section 6.3.1, the samples exhibit this low density mainly

because Zr02 is far from fully-sintered when the final soaking temperature is only

119000. This is evidenced by the sample micrograph (Fig. 7.1) from which one

can observe that numerous pores remain among the Zr02 particles. In addition,
the cracks between the Zr02 and ZrW203 grains due to the significant difference
in CTEs between two component materials contribute to the low final density.
Similar to the density-improvement method in Section 6.4.5, 0.07% mass ratio of
the alumina powder TMDAR was added to each powder mixture. The melting
point of AI2(WO4)3 is 113500 [130] and therefore a liquid phase exists at the soak
temperature of 119000. The presence of this liquid will promote the densification
kinetics, resulting in an increase in the final relative density from 80 to 90%.
Furthermore, the final shape of the samples was not affected, since the added

TMDAR only comprises 0.07% of the total mass. The microstructure of the FGMs

with 0.07% of AI203 remains very similar to that of Fig. 7.1. However, far fewer

157

pores among Zr02 grains are evident, which can be attributed to the presence of

the liquid Al2(WO4)3 phase during sintering.
7.7 AXIAL CTES

The axial CTE — temperature relation for all four samples (with 0.07% mass
ratio TMDAR powder and 6 hours soaking duration) was measured and the data

are presented in Fig. 7.7 together with the CTE curve of pure ZrW203.

10 __.

 

5.

‘5’
I
l
2
\

CTE 00-6101)
'1
!
!
!
l
I
!
I
I

-15. 7‘I 83 7 7 7 7
’c Zr\N208 ----
207 Zr02 -----
0 10072007300 400750076007700
Testing temperature (°C)

 

 

 

Figure. 7.7 The axial CTE vs. temperature curve for pure ZrW203 and samples

1-4 (with 0.07 wt% TMDAR powder by mass and 6 hours soaking duration).

As can be seen, the macroscopic axial CTE is negative for Sample 1, positive
for Sample 3 and nearly zero for Samples 2 and 4. The difference in the axial
CTEs is due to the thickness variations in each layer for various samples. The

CTE curves for all FGMs as well as the pure ZrW203 feature a sharp change near

160°C due to the a- to 8- ZrW203 phase transition [20]. However, similar to the

158

ZrWzongroz composites, the peak caused by phase transition occurs at a lower
temperature for the FGMs comparing to pure an208. This “peak shift” is possibly
a result of phase transition from a-ZrW203 (low pressure phase) to v-ZrW203
(high pressure phase) [125] due to the thermal stresses caused by the CTE

mismatch between Zr02 and ZrW203.

The axial CTEs of the samples processed under various soak durations are all
close to the theoretical CTEs as shown in Table 7.2, which indicates that the
average distribution ratio of erzog along the axial direction does not change for
each soak duration. Based on this observation, we can conclude that even for
3.5-hour soak duration, all W03 have already reacted with Zr02 mainly in the
W03+Zr02 layer, thus generating a sharp boundary between ZrW203+Zr02 and
pure Zr02. For Sample 2, the boundaries were at the 12.4mm position as
discussed before. As the soak duration increases, due to the different
concentration of Zr02 across the boundary, the ZrW203 in the ZrW203+Zr02
layer partially decomposes and produces W03. The new W03 diffuses toward the
pure Zr02 layer and reacts with the Zr02 to produce new ZrW203. With this
decomposition-reaction mechanism, ZrW203 advances toward the outer surfaces
of Zr02 layer(s). Therefore, the processing technique in the fabrication of fully
continuous FGMs requires appropriately adjusting soaking duration. However, the

gradient of Zr02 in the FGMs will drive the decomposition-reaction mechanisms

159

to continue if the soak duration continually increases until the sample becomes
the evenly distributed ZrW203IZr02 composite, as evident by the 14-hour soak
duration case. However, due to the loss of W03 by sublimation, the CTE values of
the samples after the 14~hour soak duration are slightly larger than the theoretical

values.

The continuous radial thermal expansion variation of the FGMs can be utilized
to reduce the thermal stress induced from a thermal gradient loading that may
exist in a structure. Considering the processing method described in this paper,

several other ceramic mixture systems such as ZnO+Nb205 and Sb203+Al203

may also have the potential to produce continuous FGMs.

7.8 CONCLUSIONS

Some research [29-31] on ZrW203/Zr02 composites had been published prior
to the work described in this paper. This particular study distinguishes itself from
the previous works by reporting on the processing of continuous FGMs containing
ZrW203 and Zr02. The green sample used in this study is not a well-mixed
W03+Zr02 powder compact, but rather multiple layers consisting of Zr02 and a
WO3+Zr02 powder mixture. Due to the diffusion and sublimation of W03 as well
as the reaction between W03 and Zr02 during sintering, continuous FGMs made

of ZrW203 and Zr02 were fabricated instead of the expected multi-layer FG Ms for

160

several different soaking durations. The continuous structure of the FGM is
evidenced by the microstructure observation and the measurement of the radial
CTEs. Soaking time influences the final microstructures, mainly the result of the
balance between the decomposition of ZngOg, the reaction of W03 and Zr02 as
well as the diffusion of W03. With a short soaking duration, the central W03
cannot diffuse throughout the whole structure, leaving some parts as a near pure
Zr02 structure and others are ZrW203/Zr02 composite structure. Appropriately
adjusting soaking duration will result the final sintered samples being fully
continuous FGMs. When the soaking time is long enough, the sintered sample
converts to an evenly distributed ZrW203/Zr02 composite. In addition, a small
additional amount of alumina powders results in an FGM with a significantly larger
final relative density while avoiding shape transformation in the FGM. The
thickness of each layer in the processing of FGMs can be varied in order to

achieve a variety of gradient in physical properties.

 

Figure 7.8 Designed core shape of Perspirable Skin with ZrW203-Zr02 FGM.

161

-.1 02E-03
-.907E-04

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.154E+07
.204E+07
.254E+07
.305E+07
.355E+07
.406E+07
.456E+07

IIDEIIIII

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C

Figure 7.9 The FEA results for the best FGM core design a) gap distance at
working condition b) Von Mises stress at working condition 0) first stress at room
temperature.

The continuous variation in radial thermal expansion of the FGMs can be
utilized to reduce the thermal stress induced from a thermal gradient loading.

Therefore, continuous ZrW203-Zr02 FGMs are ideal candidates for the core

162

material of Perspirable Skin. We applied Sample 5 into the design of the
Perspirable Skin. The shape of the core is a simple cylinder with semi-circular

channels [131], which can be manufactured by PM directly.

The gap distance and stress analysis for Perspirable Skin with cores shown in
Fig. 7.8 were analyzed by finite element software ANSYS. The results are shown
in Fig. 7.9 [131]. A larger gap distance at the top surface, 97.7pm, produced, while
the bottom part of the core remains in contact with the RCC skin at working

condition. The maximum stress at contact is 4.25MPa at room temperature.

163

CHAPTER 8

SUMMARY

8.1 CONTRIBUTIONS

The main contributions of this study are listed below,

1. The powder mixing process changes the compaction capability of the
powder mixtures. The shape of the initial relative density versus proportion
of coarse powder curve depends on the ratio between the average particle
sizes as well as the difference in the initial density of two powders. If the
average particle size ratio is less than 3.6, or the average particle size ratio
is larger than 3.6 but the initial relative density different is higher than 10%,
the curve is linear. If the average particle size ratio is larger than 3.6 and
the initial relative density difference is smaller than 10%, the curve is

parabolic.

2. The triangle enclosed by the line intersecting the relative density of the fine
powder and the maximum relative density of the coarse powder, the line
intersecting the relative density of the coarse powder and the maximum
relative density of the fine powder as well as the line connected the relative

density of the fine and coarse powder forms the boundary of the initial

164

relative density-proportion of coarse powder curve.

. After compaction, green samples feature a barrel lateral shape, which is a
result of release of larger residual radial stress at about the middle of the

compact after ejection than the top/bottom.

. The density distribution in a green compact is not even. The high-density
regions exist at near the bottom central region and on the central axis. And

the low-density regions are at the bottom edges and near the top center.

. Mixing powders is an effective approach to manipulate the sinteribility and
the final microstructures of raw powders. Each powder mixture has a
unique densification rate-relative density curve. The ascent parts of the
curves for alumina can be approximated by straight line(s). while the
shapes of densification rate-relative density curves of zirconia powders are

semi-ellipse.

. Using the part-isothermal heating method, phenomenological constitutive
sintering equations were derived for our alumina and zirconia powder
mixtures by Hsueh’s model [107]. The variable n in Hsueh’s model is a
material parameter and Doo(T) changes with respect to the proportion of
TMDAR or CERAC-2003 present in the alumina or zirconia powder system.
The shortcoming of Hsueh’s model is it does not reflect any phase

changes that may occur.

165

7. By comparing the densification rate-relative density curves as well as the
final diameter-powder ratio curves of an alumina powder system containing
TMDAR and CR-15 and a zirconia powder system containing TZ3YS and
CERAC-2003, we found that 94% CR-15 and 6% TMDAR alumina powder
has very similar densification rate curve and final diameter to the 40%
CERAC-2003+60% T23YS zirconia powder. By mixing these two powders
and slightly adjusting the content of TMDAR, we produced a 50 vol%
alumina + 50 vol% zirconia powder mixture with the similar densification
rate-relative density curve and diameter as the other two pure powders.
The content of the 50 alumina /50 zirconia mixture is 46% CR-15 and 4%
TMDAR] 20% CERAC-2003 and 30% TZ3YS by volume. The shrinkage
ratio curves of these three powder mixtures were found to be almost
identical. The similarity in the shrinkage ratio for those chosen powder
mixtures ensures that no significant dimensional mismatch could occur at
any time during sintering, thus reducing the possibility for cracks and
camber in the sintered sample. In addition, the effect of the compaction
load, interfacial profiles and temperature ramp/soak cycles were studied.
Through a series of experiments, the optimal processing parameters were
then obtained, which enabled us to produce flat 3—layered Al203IZr02
FGMs without cracks. Decreasing the compaction load, increasing the

ramp rate, selecting an appropriate mixture combination and modifying the

166

interfacial profiles have been found to produce FGM samples free of
defects. The shrinkage curves were found to be almost identical. The
almost identical densification rate curves of the chosen powder mixtures
under the optimized sintering conditions feature the same hyperbolic
tangent term in the corresponding three phenomenological constitutive

models.

. By the in-situ synthesis of W03 and Zr02 in a mass ratio of 1:0.266. a
ZrW203 substrate was fabricated. By increasing the ratio of Zr02 in the
reactants, the product was found to be ZrW203/Zr02 composites. Both the
CTE and Young’s modulus of various samples were measured, and those
data were compared with several model predictions, including the rule of
mixture (ROM), the Turner model, the Kemer model, the Rosen-Hashin
bounds model, the Levin model and the Mori-Tanaka method. Among the
model predictions, the revised Mori-Tanaka method by Kwon et al. offers a
high degree of agreement to the experimental Young’s modulus values and
the Levin model shows best correlation to the CTE testing values. To the
knowledge of the authors, this research is the first time to apply CTE
prediction models to composites containing negative CTE materials.
Adding a small amount of Al203 into the WO3+Zr02 reaction system was

found to effectively increase the final density of the sintered composites.

167

The controllable CTE characteristics formulated in this study can be used

to fabricate a specific ZrW203/Zr02 composite in order to meet given

requirements for thermal expansion in an industrial process.

9. Zr02/(W03)I(AI2(WO4)3)I(Al203)IZrW203 composites with nearly zero
CTE can be fabricated by various methods. Each method yields some
uniqueness in the microstmcture, final density, mechanical strength, and
ability to maintain shape. By comparing the four methods, the optimal
method is found to be the in-situ reaction of powder mixture of W03, AI203,
and Zr02 with mass ratio 1:0.03:2.61. The final relative density of the
composite made by this optimal method is around 90%, and the room
temperature Young’s modulus is 11 .19GPa and the sintered sample retains
the shape of the green sample. The main advantage of this material is the
zero CTE, which reduces the thermal stress under thermal gradient

loading and transient temperature change in a structure.

10. Continuous FGMs containing ZrW203 and Zr02 were fabricated. The
green sample used is made of multiple layers consisting of Zr02 and a
W03+ Zr02 powder mixture. Due to the diffusion and sublimation of W03
as well as the reaction between W03 and Zr02 during sintering,
continuous FGMs made of Zr02 and ZrW203 were fabricated instead of

the expected multi-layer FGMs for several different soaking durations. The

168

11.

continuous structure of the FGM is evidenced by the microstructure
observation and the measurement of the radial CTEs. Soaking time
influences the final microstructures, mainly the result of the balance
between the decomposition of ZrW203, the reaction of W03 and Zr02 as
well as the diffusion of W03. With a short soaking duration, the central
W03 cannot diffuse throughout the whole structure, leaving some parts as
a near pure Zr02 structure and others are ZrW203/Zr02 composite
structure. Appropriately adjusting soaking duration will result the final
sintered samples being fully continuous FGMs. When the soaking time is
long enough, the sintered sample converts to an evenly distributed
ZrW203/Zr02 composite. The thickness of each layer in the processing of
FGMs can be varied in order to achieve a variety of gradient in physical
properties. The continuous variation in radial thermal expansion of the
FGMs can be utilized to reduce the thermal stress induced from a thermal

gradient loading.

Continuous ZrW203-Zr02 FGMs are ideal candidates for the core material
of Perspirable Skin. The shape of a ZrW203-Zr02 FGM core is a simple
cylinder with semi-circular channels, which can be manufactured by PIM

directly.

169

8.2 SUGGESTIONS FOR NEXT STEP RESEARCH

As mentioned in Section 1.1, from the design idea to the application of
Perspirable Skin on the space vehicles, a series of researches are needed: 1)
core material selection, 2) materials fabrication, 3) materials properties test, which
will be used as the input parameter of Finite Element Analysis (FEA), 4) structure
design by FEA, including gap and stress analysis, 5) core pieces and RCC panel

assembly, and 6) simulated temperature environment test.

After three and half years, now Steps 1-3 are achieved as discussed in this
dissertation. The shape of the core made by ZrW208-Zr02 FGMs was also
determined. However, the core dimensions depend on the calculation of
thermodynamics and heat transfer. This should be an important research part in

the future.

After the determination of core dimensions, the assembly and
true-environment test need to be performed to verify the suitability of Perspirable

Skin as next-generation TPS.

170

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