• TABLE OF CONTENTS
HIDE
 Title Page
 Dedication
 Acknowledgement
 Table of Contents
 List of Figures
 List of Tables
 Abstract
 Introduction
 Glass-ceramics
 Fracture mechanics
 Materials preparation and...
 Test techniques
 Dynamic fatigue: results and...
 Crack velocity experiments
 Discussion
 Conclusions and suggestions for...
 Reference
 Biographical sketch
 Copyright














Title: Fracture mechanics and failure predictions for glass, glass-ceramic, and ceramic systems
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Table of Contents
    Title Page
        Page i
    Dedication
        Page ii
    Acknowledgement
        Page iii
    Table of Contents
        Page iv
        Page v
    List of Figures
        Page vi
        Page vii
        Page viii
    List of Tables
        Page ix
        Page x
    Abstract
        Page xi
        Page xii
    Introduction
        Page 1
        Page 2
        Page 3
        Page 4
        Page 5
    Glass-ceramics
        Page 6
        Page 7
        Page 8
        Page 9
        Page 10
        Page 11
        Page 12
        Page 13
        Page 14
        Page 15
        Page 16
        Page 17
    Fracture mechanics
        Page 18
        Page 19
        Page 20
        Page 21
        Page 22
        Page 23
        Page 24
        Page 25
        Page 26
        Page 27
        Page 28
        Page 29
        Page 30
        Page 31
        Page 32
        Page 33
        Page 34
        Page 35
        Page 36
        Page 37
    Materials preparation and characterization
        Page 38
        Page 39
        Page 40
        Page 41
    Test techniques
        Page 42
        Page 43
        Page 44
        Page 45
        Page 46
        Page 47
    Dynamic fatigue: results and discussion
        Page 48
        Page 49
        Page 50
        Page 51
        Page 52
        Page 53
        Page 54
        Page 55
        Page 56
        Page 57
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        Page 108
        Page 109
        Page 110
        Page 111
        Page 112
        Page 113
        Page 114
    Crack velocity experiments
        Page 115
        Page 116
        Page 117
        Page 118
        Page 119
        Page 120
        Page 121
        Page 122
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        Page 125
        Page 126
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        Page 128
        Page 129
        Page 130
        Page 131
    Discussion
        Page 132
        Page 133
        Page 134
        Page 135
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        Page 137
        Page 138
        Page 139
        Page 140
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        Page 142
        Page 143
        Page 144
        Page 145
        Page 146
    Conclusions and suggestions for future work
        Page 147
        Page 148
        Page 149
        Page 150
        Page 151
    Reference
        Page 152
        Page 153
        Page 154
        Page 155
    Biographical sketch
        Page 156
        Page 157
        Page 158
    Copyright
        Copyright
Full Text











FRACTURE MECHANICS AND FAILURE PREDICTIONS
FOR GLASS, GLASS-CERAMIC, AND CERAMIC SYSTEMS












By
RONALD A. PALMER












A DISSERTATION PRESENTED TO THE GRADUATE COUNCIL OF
THE UNIVERSITY OF FLORIDA
IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE
DEGREE OF DOCTOR OF PHILOSOPHY



UNIVERSITY OF FLORIDA


1981








































To EZZen













ACKNOWLEDGEMENTS


The author thanks those who served on his committee,

R. W. Gould, C. S. Hartley, L. E. Malvern, and G. Y. Onoda, Jr.,

for their assistance and academic instruction. Thanks are also due

his head professor, L. L. Hench, who provided the opportunity to

perform this study as well as advice and encouragement throughout.

S. W. Freiman (of NBS) gave invaluable assistancelin sample

preparation and experimental technique.

Before returning to graduate school (and since), the author

received greatly appreciated support from D. C. Greenspan, D. Cronin,

R. V. Caporali, and R. A. Ferguson. Discussions with S. Bernstein,

F. K. Urban, J. W. Sheets, W. J. McCracken, C. L. Beatty and many

others also contributed to this work.

Before finishing this dissertation, the author began working

for Rockwell Hanford Operations in Richland, Washington. The patience

shown by his supervisors, F. M. Jungfleisch, M. J. Kupfer, and

L. P. McRae is greatly appreciated.

Finally, the author wishes to thank his wife, Ellen, for her

love and support during this time.

This work was supported by the Air Force Office of Scientific

Research.









TABLE OF CONTENTS


ACKNOWLEDGEMENTS....................................

LIST OF FIGURES.........................................

LIST OF TABLES.........................................

ABSTRACT...............................................

CHAPTER


I INTRODUCTION .............................. .....

II GLASS-CERAMICS... ............................

A. General .....................................
B. Nucleation and Crystallization..............
C. Applications and Advantages.................
D. The Lithia-Silica System....................

III FRACTURE MECHANICS.............................

A. Historical Background...........................
B. Static Fatigue in Glasses and Ceramics......
C. Fracture Mechanics of Glasses and Ceramics..
D. Lifetime Predictions........................
E. Methods Used for this Study.................

IV MATERIALS PREPARATION AND CHARACTERIZATION.....

A. Melting and Casting .........................
B. Annealing, Nucleation, and
Crystallization Schedule .................
C. Final Sample Preparation....................
D. Characterization ...........................

V TEST TECHNIQUES ...............................

A. Biaxial Flexure. ......................... .
B. Double Cantilever Beam Testing.............


Pace

iii

vi

ix

xi



1

6

6
7
12
12

18

18
21
29
33
36

38

38

38
39
40

42

42
44









Page

VI DYNAMIC FATIGUE: RESULTS AND DISCUSSION...... 48

A. Quantitative Microscopy.................... 48
B. Dynamic Fatigue Testing of 33L-Glass....... 48
C. Dynamic Fatigue Testing of 33L-92%......... 68
D. Dynamic Fatigue Testing of 33L-7%.......... 82
E. Dynamic Fatigue Testing of 33L-57%......... 99
F. The Effect of Crystallization on Strength.. 108
G. The Effect of Crystallization on N......... 110
H. The Effect of Crystallization on
Lifetime Predictions..................... 113
I. Summary.. ................................. 114

VII CRACK VELOCITY EXPERIMENTS.................... 115

A. General ................................... 115
B. 33L-Glass ................................ 117
C. 33L-Partially Crystallized...... .......... 117
D. 33L-92% Crystalline........................ 127

VIII DISCUSSION..... .............................. 132

A. Dynamic Fatigue............................ 132
B. Slow Crack Growth........................ .. 142
C. Comparing Dynamic Fatigue and
Slow Crack Growth........................ 143

IX CONCLUSIONS AND SUGGESTIONS FOR FUTURE WORK... 147

A. Conclusions................................ 147
B. Suggestions for Future Work................ 148

REFERENCES............................................. 152

BIOGRAPHICAL SKETCH .................................. 156








LIST OF FIGURES


Figure Page
1 Two stage and isothermal heat treatments
for processing a glass-ceramic 9

2 Tammann curves (nucleation or growth rates
vs. temperature) for controlled and uncon-
trolled crystallization 11

3 Phase diagram of the Li2O-Si02 system 14

4 Three modes of failure: I, normal or opening
mode; II, sliding mode; III, tearing mode 20

5 Possible reactions between water and segments
of the glass network 23

6 Hypothetical changes in crack tip geometry
due to stress corrosion 26

7 Universal fatigue curve developed by Mould
and Southwick (1959) 28

8 Equation 19 plotted for 33L-Glass tested in
air 35

9 Lifetime prediction diagram using equation 22
for 33L-Glass 37

10 Specimen configuration for double cantilever
beam constant moment crack growth experiment 41

11 Biaxial flexure test jig 43

12 Constant moment double cantilever beam test
apparatus 45

.13 Representative microstructure of 33L-7%
crystalline 51

14 Representative microstructure of 33L-57%
crystalline 52

15 Representative microstructure of 33L-92%
crystalline 53

16 Dynamic fatigue results for 33L-Glass tested
in air 55

17 Dynamic fatigue results for 33L-Glass tested
in water 57









Figure Page

18 Dynamic fatigue results for 33L-glass tested
after aging one day in water 59

19 Weibull plot for some 33L-92% crystalline
material 66

20 LPD for 33L-glass 67

21 Dynamic fatigue results for 33L-92% crystalline
tested in air 70

22 Dynamic fatigue results for 33L-92% crystalline
tested in water 72

23 Dynamic fatigue results for 33L-92% crystalline
tested after aging one day in water 74

24 Dynamic fatigue results for 33L-92% crystalline
tested after aging one week in water 76

25 LPD for 33L-92% crystalline 83

26 Dynamic fatigue results for 33L-7% crystalline
tested in air 85

27 Dynamic fatigue results for 33L-7% crystalline
tested in water 87

28 Dynamic fatigue results for 33L-7% crystalline
tested after aging one day in water 89

29 Dynamic fatigue results for 33L-7% crystalline
tested after aging one week in water 91

30 LPD for 33L-7% crystalline 98

31 Dynamic fatigue results for 33L-57% crystalline
tested after aging one day in water 101

32 Dynamic fatigue results for 33L-57% crystalline
tested after aging one week in water 103

33 LPD for 33L-57% crystalline 104

34 Theoretical crack velocity vs. stress intensity
factor relationship for brittle materials 116









Figure


V-K relationship for 33L-glass tested in air


V-K relationship for

V-K relationship for
samples

V-K relationship for
samples

Region of slow crack

Region of fast crack

V-K relationship for

Region of slow crack

Region of fast crack


33L-glass tested in water

33L-low crystallinity


33L-high crystallinity


growth in 33L-5% crystalline

growth in 33L-5% crystalline

33L-92% crystalline

growth in 33L-92% crystalline

growth in 33L-92% crystalline


123

125

126

128

130

131


133


Growth of a gel layer at the surface of a glass
containing two depths of flaws

A comparison of the Method of Maximum Likelihood
and the Monte Carlo method for predicting N


viii


Page









LIST OF TABLES


Table Page

1 Commercial Glass-Ceramics 13

2 Results of Quantitative Microscopy for
Determining Per Cent Crystallinity 49

3 Dynamic Fatigue Data for 33L-Glass
Tested in Air 60

4 Dynamic Fatigue Data for 33L-Glass
Tested in Water 61

5 Dynamic Fatigue Data for 33L-Glass
Tested After Aging 1 Day in Water 62

6 Liquid Nitrogen Strength of 33L-Glass 63

7 Dynamic Fatigue Data for 33L-92%
Crystalline Tested in Air 77

8 Dynamic Fatigue Data for 33L-92%
Crystalline Tested in Water 78

9 Dynamic Fatigue Data for 33L-92$
Crystalline Tested After Aging
1 Day in Water 79

10 Dynamic Fatigue Data for 33L-92%
Crystalline Tested After Aging
1 Week in Water 80

11 Liquid Nitrogen Strength of 33L-92%
Crystalline 81

12 Dynamic Fatigue Data for 33L-7%
Crystalline Tested in Air 92

13 Dynamic Fatigue Data for 33L-7%
Crystalline Tested in Water 93

14 Dynamic Fatigue Data for 33L-7%
Crystalline Tested After Aging
1 Day in Water 94

15 Dynamic Fatigue Data for 33L-7%
Crystalline Tested After Aging
1 Week in Water 95









Table Page

16 Liquid Nitrogen Strength of 33L-7%
Crystalline 96

17 Dynamic Fatigue Data for 33L-57%
Crystalline Tested After Aging
1 Day in Water 105

18 Dynamic Fatigue Data for 33L-57%
Crystalline Tested After Aging
1 Week in Water 106

19 Liquid Nitrogen Strength of
33L-57% Crystalline 107

20 Strength of 33L-Glass and Glass-
Ceramics 109

21 Fracture Parameters and (oo/aa) from
Dynamic Fatigue Data 111

22 33L-Glass Fracture Parameters as
Determined by Slow Crack Growth 118

23 33L-Partially Crystalline Fracture
Parameters as Determined by Slow
Crack Growth 121

24 33L-92% Crystalline Fracture Parameters
as Determined by Slow Crack Growth 129

25 Effect of Surface Finish on Aged
Strength of Sodium Disilicate Glass 135













Abstract of Dissertation Presented to the Graduate Council
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Doctor of Philosophy


FRACTURE MECHANICS AND FAILURE PREDICTIONS
FOR GLASS, GLASS-CERAMIC, A?!D CERAMIC SYSTEMS


By

Ronald A. Palmer

June, 1981

Chairman: Larry L. Hench
Major Department: Materials Science and Engineering


State-of-the-art fracture mechanics techniques are used to determine

the fatigue parameters for the lithium disilicate glass/glass-ceramic

system. Glass-ceramics are ideal materials for examining the effects

of crystallization on fatigue behavior. Two methods (dynamic fatigue

and slow crack growth) were employed and were found to produce different

values for the fatigue parameters. These parameters are used to design

lifetime prediction diagrams and, theoretically, should be independent

of the method of determination.

It was found that aqueous corrosion has a severe effect on the

fatigue parameters, as measured in dynamic fatigue, especially after

aging for up to one week in distilled water. The lithium disilicate

glass, which is known to readily form a gel layer in water, exhibits

the most rapid change in parameters.









The most crystalline composition (92% crystalline) shows the

greatest strength loss due to aging. This is attributed to water

migration along a network of microcracks into the grain boundaries.

At low volume fraction of crystals (7%) a residual stress in

the glassy matrix effects a strength increase and a decrease in the

environmental sensitivity which disappears with aging in water.

No effect of aging in water was found in the slow crack growth

studies. In all cases, the environmental sensitivity was found to

be much higher in these experiments than in dynamic fatigue. The

reasons for the difference are discussed in later chapters.

The limitations of the present fracture mechanics theory are

discussed in the light of the inconsistencies found between these

methods. It is recommended that a combination of techniques be used

when reliable lifetime predictions are required. A matrix of tests,

including static and dynamic fatigue and proof tests, is proposed

as an improved method of characterizing the fatigue behavior of a

material.








CHAPTER I-INTRODUCTION


Since the beginning of the twentieth century, the growth of techno-

logy has put increasingly more stringent demands on materials and

material properties. Advances in the fields of transportation (automo-

biles to aircraft to spacecraft), energy (coal and oil to nuclear and

solar), and others have necessitated improvements in existing materials

and the development of new materials in order to meet the high-performance

requirements of these technologies. The investigation of how to make

materials stronger with lighter weight has been advanced by studying

how materials fail. Macroscopic observation of the growth of cracks

combined with microscopic examination has been the most fruitful method

of learning the mechanisms of material failure. Studies of this type

have led to improvements in both the strength and toughness of materials

through the design and control of specific microstructures which impeded

initiation and/or propagation of cracks.

Recently, concern with the conservation or security of complex sys-

tems has placed additional emphasis on determining how long materials

will survive under-various environmental conditions. Thus,the field of

fracture mechanics has expanded from relatively simple measurement-

taking to making failure or lifetime predictions from those measurements.

In order to make meaningful predictions, parameters such-as-or-iginal

flaw size, critical flaw size, and stress corrosion susceptibility

become important. Also, there is a need to know what happens as a flaw

grows from a relatively insignificant stress concentration to some

critical size where catastrophic failure occurs. This process is termed








subcritical crack growth. Characterization of a mater ial.s_s.ub-r.t-i-t-cal

crack growth behavior and knowledge of the distribution of flaw sizes

permits prediction of the lifetime of a component in a given situation.

In order to predict and subsequently to guarantee the lifetime of

a component, some method of non-destructive evaluation is required.

Proof tests can be designed, in which all components are subjected to

a stress far beyond that expected in service, such that survivors are

assured some minimum service lifetime. By performing a proof test,

the need for large safety factors is reduced and overdesigning can be

avoided.

It is essential that the effect of the service environment on

time to failure be completely and correctly accounted for in fracture

mechanics theories if lifetime predictions are to be realistic. Thus,

a deeper understanding of the physical implications of the stress

corrosion susceptibility parameters is important. The combined effects

of aqueous environment and stress state on the subcritical growth of

flaws of various sizes need to be understood in order to ensure that

aging effects are correctly modeled and/or simulated in the proof

test design.

Therefore, one major objective of this thesis is to examine the

relative importance of aqueous environments, including time-dependent

effects, on the lifetime predictions for a brittle material. In order

to achieve this objective, it is necessary to study a more chemically

reactive material system than has heretofore been examined in lifetime

prediction investigations. By testing a material with known mechanisms

of chemical attack it is hoped that the critical reaction phenomena

for deterioration of mechanical performance can be elucidated.




3



In order for lifetime prediction theories to be of general use,

they must be equally applicable to polycrystalline ceramics, glasses,

and glass-ceramics. The accuracy of predicted lifetimes or their

validity should be independent of the wide range of microstructure

encountered in technical ceramics. Thus,a second major objective of

this thesis is to investigate the effect of microstructure on the

fracture behavior and time to failure of a glass-ceramic possessing

a wide range of crystallinity.

Of particular concern in the thesis is the possible interaction

between microstructural and environmental effects in fracture behavior.

Many technical ceramics are multiphased and the environmental suscepti-

bility of interphase boundaries is the potential "weak link" of their

long term performance. A unique feature of this study is the simulta-

neous examination of both major variables, microstructure and environ-

ment, in the same composition of material.

Glass-ceramics are ideal materials for studying the effects of

microstructure on mechanical properties. By varying the heat treatment,

fully glassy or fully crystalline materials may be fabricated, as well

as partially crystalline materials. The grain size of the crystalline

phase can be varied as well as the volume fraction of crystallinity.

In this thesis, the lithium disilicate system was chosen for

study because the nucleation and crystallization kinetics are well-

documented. The mechanical behavior of this system is also known,

although the environmental effects are not yet understood. Also of

initial importance is the ability to produce a fully crystallized

material having the same composition as the glass. Lithium disilicate

glass and glass-ceramics also fulfill the prime requirement of this

thesis --they react readily with water compared with other materials








which have been examined previously for their fracture behavior.

Studies by Sanders (1973), Ethridge (1977), and Dilmore (1977)

have established the details of aqueous attack of lithium disilicate

glasses. Recently, McCracken (1981) has conducted a parallel corrosion

study on lithium disilicate glass-ceramics of variable fraction of

crystals and determined the mechanisms of corrosion of the two-phased

glass-ceramic materials.

Thus, the lithiumdisilicate glass-ceramic system satisfies criteria

for studying both the effect of microstructure and aging in water on

the strength and fatigue behavior of a material of homogeneous composition.

Results obtained on the synergistic effects of subcritical crack growth

and aqueous corrosion should be important in extending the fracture

mechanics principles utilized in predicting lifetimes. By concurrently

studying the corrosion and fatigue mechanisms of this material system,

it is hoped that new insights will be gained in order to more reliably

predict lifetimes of brittle materials in general.

During this investigation quantitative microscopy was used to

monitor the volume fraction of crystallinity. Strength testing was

done with an Instron machine on discs, using the biaxial flexure test

and fracture mechanics tests were performed using the double cantilever

beam technique. Both optical and scanning electron microscopy were used

for examination of fracture surfaces.

Heat treatments were devised to achieve four microstructures: fully

glassy, 5 percent and 50 percent crystalline, and fully crystalline.

For each, both strength tests and fracture mechanics tests were made

in order to determine the nature of the sub-critical crack growth in




5




the material. Ideally, the two methods should yield identical results.

Where they did not, microstructural analysis of the fracture surfaces

was used to interpret the differences. A statistical analysis of the

strength data is also important in determining the accuracyof these

results and is an important part of this investigation.

Chapters II and III introduce the topics of glass-ceramics and

fracture mechanics, respectively. Chapter IV describes the prepara-

tion and characterization of materials used in this investigation.

Chapter V discusses the mechanical testing methods employed. Chapters

VI and VII discuss the results and the analyses of the fatigue

parameters and lifetime prediction diagrams. Finally, conclusions

and suggestions for future work are presented in Chapters VIII and IX.







CHAPTER II-GLASS CERAMICS


A. General

Glass-ceramics may be described as polycrystalline solids which have

been formed from a glassy melt by carefully controlled heat treatments.

In order for crystals to form, nuclei must be present. The nucleation

may be homogeneous (self-nucleating) or heterogeneous (by addition of

nucleating agents). The crystallization process may be controlled or

uncontrolled. Uncontrolled crystallization is termed devitrification

and is generally though of as a process to avoid. Controlled crystalli-

zation of glasses produces materials known as glass-ceramics. Glass-

ceramics have also been referred to as "vitrocerams," "devitrocerams,"

"sitalls," and "melt-formed ceramics." (See Stewart, 1972.)

Glass makers through the ages have struggled to avoid the destruc-

tive effects of devitrification. However, occasionally attempts were

made to crystallize glass purposely. Reaumur (1739) in the early 1700's

crystallized soda-lime-silica glass bottles by packing them in sand and

gypsum and heating them for a long time. Unfortunately, the crystals

nucleated at the surface, resulting in weak and deformed pieces.

The classical work on nucleation and crystallization was done by

Tammann (1925) in the 1920's. His theoretical and experimental investi-

gations laid the foundation for our present knowledge of these processes.

In the 1940's photosensitive glasses were developed by Stookey (1947)

at the Corning Glass Works. Colloidal dispersants of metals (gold,

copper, or silver) added as nucleants were shown to be activated by

exposure to ultra-violet light. Subsequent heat treatments resulted in







.ne nucleation and growth of crystals. By masking portions of the glass,

intricate and precise patterns could be produced. As the crystalline

phase is less durable than the glassy phase, hydrofluoric acid could

dissolve away the more soluble phase, resulting in a glass part or

pattern made more precisely than any other conventional glass forming

method.

Later, reputedly by accident, Stookey allowed a sample of one of

his glass compositions to be heated too long, resulting in complete

crystallization of the sample. It was found to be remarkably fine

grained and harder and stronger than the parent glass. This led to

the development of PyroceramR and many of the other commercial glass-

ceramics we know today. The various families of glass-ceramic composi-

tions and their applications will be discussed later in the chapter.


B. Nucleation and Crystallization

After the formation of the parent glass, the glass-ceramic process

required a two-step heat treatment. Figure 1 is a schematic of the

treatment. The first step is at a relatively low temperature (about

50-100C above the annealing point) and allows for the formation of

nuclei. In general, more nuclei form with time, so in order to obtain

a fine-grained material, longer times may be utilized. (The mathematics

of nucleation and growth have been well developed and will not be dis-

cussed here. See Bergeron, 1973).

Nucleating agents are generally noble metals or refractory oxides.

Materials which have been used as nucleating agents include Au, Pt, Ag,


R Corning Glass Works, Corning, NY.























Figure 1. Two stage and isothermal heat treatments for
processing a glass-ceramic









(1) Two Stage Heat Treatment


(2) Isothermal Heat Treatment
I


TIME









Cu, TiO2, and P205. It is recognized that there are certain key

characteristics for a nucleating agent to be effective. For nucleus

formation, it is important for the nucleant to be very soluble at

melting and forming temperatures while barely soluble at low temperatures,

to have a low free energy of activation for homogeneous nucleating, and

to be very mobile compared to the major components of the glass at low

temperatures. For the nucleant to promote crystal growth effectively,

there must be a low interfacial energy between it and the glass and

its crystal structure and lattice parameters should be similar to that

of the crystal phase.

Glass-in-glass phase separation has been found to promote glass-

ceramic formation without any nucleating agents. Agents which promote

phase separation, such as P205, are very effective in this manner.

Nucleation may occur either at the phase boundary or within one of the

phases (most likely the one most resembling the crystalline phase.)

The second step in the so-called "ceraming" process is the crystal-

lization treatment. For materials where only one crystalline phase develops,

the crystal growth may be a very simple process. However, if several phases

are developing, all different from the composition of the homogeneous glass,

the composition at the crystal-glass interface is constantly changing and

the growth process becomes exceedingly complex.

Figure 2 shows the Tammann curves (nucleation or growth rate vs.

temperature) for controlled and uncontrolled systems. For a controlled

system, it is easy to find nucleation and growth temperatures (ideally

at the maximum rates) where the other process does not occur. This type

allows the experimenter to have great control over the microstructure



























TEMPERATURE


TEMPERATURE


Tammann curves (nucleation or growth rates vs. temperature)
for controlled and uncontrolled crystallization


Figure 2.










of the final material. In the uncontrolled system, the nucleation and

growth curves overlap considerably, making it very difficult to get

appreciable nucleation without some crystallization and vice versa.

Control over the final microstructure is impossible in this system.

C. Applications And Advantages

Table 1 lists a number of commercial glass-ceramics, their major

crystalline phases, important properties, and applications. The wide

variety of materials and applications are discussed in detail by

Pincus (1972).

The advantages of glass-ceramics over conventionally processed

(slip cast, sintered, etc.) ceramics are listed below:

1. Because the microstructure can be controlled to a certain

extent, properties such as electrical properties, transparency,

and chemical durability can be tailored to specific applications.

2. Glass-forming techniques (blowing, pressing, drawing, and

casting) can be used, providing economical, high-speed,

automatic production.

3. Small dimensional changes during crystallization.

4. Zero porosity.

5. The homogeneity of the melt and the nucleation process leads

to uniform microstructure and properties.

6. Crystalline phases otherwise unattainable can be produced.

D. The Lithia-Silica System

Figure 3 shows the phase diagram for the lithia-silica system. The

composition chosen for this study was the 33.3 mole percent lithia composi-

tion. (This will be referred to as the 33L composition.) Previous work

done on this system has shown that the crystals which form this composition






Table 1

Commercial Glass-Ceramics


Designation

Corning 8603


Corning 9606


Corning 9615


G.E. Re-X


0-I CerVit


Pflaudler
Nucerite



PPG Hercuvit
101


Major Phases

Li20-Si02
Li20-Si02

2MgO-2A1203.5Si02

SiO2
Ti02

B-spodumene solid
solution


Li20-2Si02


B-quartz S.S.


alkali silicates




B-quartz S.S.


Properties

Photochemically
machineable

Transparent to
microwaves
Erosion and
Thermal Shock
resistance

Low T.E., strong,
thermally and
chemically stable,
easy to clean

Sealable to metals
Dielectric

Low T.E.
Polishability

Coating of steel
Chemical durability
Impact resistance
Abrasion resistance

Transparent


Application

Fluidics devices
Printing plate molds


Radomes


Range tops


Housings
Bushings


Telescopic mirrors


Chemical process equipment




High temperature windows
Infrared transparencies





14










L.i,0- Si O,
ico After Kracek, Holmquist.
and Glassor.
16oo a Quartz
\ Cristubalite
1 00__ y Tridymite
I Li;O.2SiO, 11:21
00- o LiO SiO, 11:11

1300


u Ioo I







oo-

,00.

E00- --
0)---*o -- \----\- \ I











Li-O ImoloI1


-igure 3. Phase diagram of the Li20-Si02 system









are solely lithium-disilicate (Li20-2Si02). There has been much work

done on both the binary system and systems with additions of nucleating

agents and aluminum oxide. As presented in Table 1, Li20-2SiO2 is the

major phase in many commercially important glass-ceramic compositions.

For this reason, study of the 33L composition will provide a basis on

which the characterization of the whole family of lithia-silica glass-

ceramics can be done.

The photo-chemically machineable glass-ceramics which first appeared

in the 1940's are lithia-silica based materials. Stookey's (1947, 1950a,

1950b, 1954, 1956) work on these materials is found in the patent literature.

Rindone (1958, 1962)studied the addition of platinum to a Li20.4Si02

glass. He measured (using x-ray diffraction) the amount of Li20-2Si02

crystallized from the glass as a function of time (10 minutes to 32 hours)

and the amount of Pt added (zero to 0.025%). Rindone proposed that lithium-

rich clusters surrounding the Pt form as nuclei for the Li20-2Si02 which

precipitates out. Later, Kinser (1968) showed that a metastable lithium-

metasilicate phase (Li20.Si02) is the precursor to the disilicate crystals

in the 33L glass.

Glasser (1967) studied binary lithium silicates ranging in composi-

tion from 80 to 88 weight percent Si02. He concluded that under certain

conditions a two-stage heat treatment schedule would improve the strength

of the crystallized composition. While accepting the explanation that

the formation of a large number of nuclei results in a fine-grained material,

Glasser also proposed another mechanism. He suggested that the lower

temperature treatment yields a metastable solid solution that is later









exsolved at higher temperatures. This results in a fine-grained

precipitate within the host crystals. Whether this mechanism would

actually occur in complex commercial compositions has yet to be shown.

Freiman (1968) studied the crystallization kinetics of several

lithia-silica compositions including 33L. He showed that an increase

in the nucleation time from three to 24 hours decreased the activation

energy for crystallization and increased the crystallization rate.

He found that the Li20.2SiO2 crystal growth was spherulitic in nature

and that small angle x-ray scattering confirmed the presence of a

metastable phase after nucleation at 4750C.

Freiman (1968) also studied the strength of the glass-ceramics he

produced. He found the strength to be lower than that predicted by

theory due to cracking in the composite because of the stresses set up

between the glass and the crystals during crystallization. He was able

to reduce the cracking by increasing the nucleation time, providing

better bonding between the glassy and crystalline phases.

Kinser(1968) also found the metastable lithium metasilicate phase

present in various lithia-silica compositions. A similar precursor

phase was found in a soda-silica composition.

Nakagawa and Izumitani (1969) studied a: Li20-2.5Si02 glass and a

Li20-Ti02-Si02 glass containing 22.5 weight percent Ti02. In the

binary glass, they found droplets due to liquid-liquid phase separation

occurring independently from the nucleation of Li20-2SiO2 crystals.

The droplets did not act as nuclei for crystallization. In the ternary

glass, they found that similar droplets deposited lithium titanate

crystals which then act as nuclei for crystallization.









Harper, James, and McMillan (1970) studied a lithia-silica glass

(30 percent Li20) with and without P205 as a nucleating agent. Nucleation

due to glass-in-glass phase separation as well as homogeneous nucleation

of lithium disilicate was discussed, but neither mechanism was firmly

established as correct. The reasons for the action of P205 as a nucleant

were discussed (surface energy effects, formation of lithium phosphates,

and more extensive phase separation), but were also left unresolved.

Doremus and Turkalo (1972) studied a lithium silicate glass (-26-27

mole percent lithia) with and without P205 also. They found that the

phosphorous slows the growth rate of the lithium disilicate crystals,

but that both produced similar microstructures. Spherulitic crystals

were also found, as in previous works, but some question was raised as

to whether they are true spherulites or not. No sheaf-like structures

have been shown for Li20.2Si02 crystals, such as can be found in so-called

spherulitic polymers, liquid crystals, and complex minerals.

The choice of 33L as the composition to study in this investigation

was based on the detailed microstructural and kinetic information of the

previous work and the fact that the glass and crystalline phases have

the same composition. A two-stage heat treatment with a long nucleation

time was also selected based upon Freiman's (1968) studies. Optical

and electron microscopy were used to confirm the attainment of materials

described previously.







CHAPTER III -FRACTURE MECHANICS


A. Historical Background

It is generally recognized that Griffith (1921) is the father of

fracture mechanics. He was the first to show a relationship between the

measured strength of a material, its material properties, and the length

of the pre-existing crack responsible for failure. The existence of pre-

existing cracks as precursors to failure had been proved by Inglis (1913)

some years before. Inglis showed that the stress near an elliptical hole

(resembling a crack) would be greater than the applied stress by

o = 2aa(a/p)T (1)

where oa is the applied stress, a is the half-crack length, and p is the

crack tip radius.

Griffith reasoned that the free energy of a cracked body and the

applied forces should not change during crack extension.. That is, the

amount of energy put into breaking the material should be equivalent to

the amount of energy required to create two new surfaces, or

dU dW (2)
da da

where U is the-strain energy due to the crack, W the energy required for

growth, and a the half-crack length.

Griffith calculated the strain energy to be
-2
U f a (3)
E

where E is Young's modulus, and the energy required for growth to be

W = 4ay (4)

where y is the surface energy. Inserting Eqs. (3) and (4) into (2)

gives the Griffith criterion for fracture of an infinite sheet with a







slit crack in plane stress:
= 2yE-y
=f (5)
where of is the stress at the crack tip resulting in failure.
There are three different modes in which a solid may be stressed
(Fig. 4). Mode I is the normal or opening mode; mode II is the sliding
mode; mode III is the tearing mode. The mode I stress field at the
crack tip has been determined by Irwin (1958) to be

aij (27 ) fij() (6)

where r and e define a coordinate system at the crack tip, f.i(e) is a
function accounting for the angular dependence of the stress about the
crack tip, and K is the stress intensity factor. For mode I,

KI =a (a)2 (7)

Failure then will occur at some critical stress intensity factor

KIc = of(wa) (8)

Combining Eqs. (5) and (8)

KIc = (2yE) (9)

We may now define G = 2yas the crack extension force such that
the critical value of G is
K2
G c (10)

for plane stress and for plane strain
K2
G Ic 2c
c (1 2)E

where v is Poisson's ratio. (The crack extension force is also called

the strain energy release rate, havingdimensionsof energy per unit
plate thickness and per unit crack extension which are the same as force



























































Three modes of failure: I, normal or opening
mode; II, sliding mode; III, tearing mode


Figure 4.








per unit crack extension. See Broek (1974).)

Because of the dominant tensile nature of the failure of glasses

and ceramics, only mode I failure under plane stress will be considered

in the following discussions.

B. Static Fatique In Glasses And Ceramics

Among the first to notice the detrimental effects of water on the

strength of glass were Preston and his co-workers (1946). They observed

a decrease in strength under a static load over intervals from minutes

to days for soda-lime and borosilicate glasses and several porcelain

compositions. The loss in strength was observed in tests conducted in

humid air and water, but the effect was more pronounced in water. No

loss in strength was noted when testing in a vacuum or at low temperatures.

Charles (1958) and his co-workers (Charles and Fisher, 1960 and

Hillig and Charles, 1964) introduced the chemical aspects of the delayed

failure problem. Figure 5 shows four reactions between water and segments

of the glass network. Reaction (a) demonstrates the replacement of an

alkali ion (M) with a hydrogen ion at a nonbridging oxygen site. In

his original work, Charles (1958) found that the temperature dependence

of the corrosion rate was identical with the temperature dependence of

alkali ion diffusion, which lends support to this mechanism.

Reaction (b) is less important. It shows aqueous attack on the

covalent bridging oxygen site. As fused silica and crystalline quartz

are relatively insoluble at moderate temperature and neutral pH, this

reaction is much less likely to cause significant damage to the glass

network.

























Figure 5. Possible reactions between water and segments
of the glass network







I I
(a) [-Sli-- [M]] + H20 + [-SiOGH] + M + OH

I I I
(b) E -S*i-O-Si + H 4 -2 2 [-SiOH]

(c) [-Si--O-Si-] + OH [-SiOH] + [-Si-0-]
I I I I

(d) [-Si-O-] + H 0 + [-Si--OH] + OH
I 2 I









Reactions (c) and (d) show a two-step breakdown of the covalent

chain initiated by the OH" ion. As reactions (a) and (d) produce the

same OH ion, the attack of water on a binary alkali silicate glass should

be autocatalytic.

Figure 6 shows the changes in crack tip geometry due to the

corrosion reactions and the presence or absence of stress. From Eq. (1),

we know that as the crack tip sharpens (p-o) the stress at the tip

increases. Figure 6(a) shows the crack tip sharpening under an applied

stress in a corrosive medium (i.e., water), causing weakening or fatigue

in the material. Figure 6(c) shows the crack tip rounding by corrosion

with little or no applied stress, which strengthens the material as it

ages in a corrosive medium. Figure 6(b) demonstrates the concept of a

fatigue limit, where the crack tip undergoes growth and rounding concur-

rently, resulting in no change in the stress at the crack tip.

Mould and Southwick (1959) performed an extensive study on the

strength and static fatigue of soda-lime-silica glass microscope

slides. They developed the concept of a universal fatigue curve.

By plotting a normalized strength (strength/low temperature strength,

a/aN) versus the logarithm of the normalized time to failure (time to

failure/time at which the strength is one-half the low temperature

strength, t/t0.5), it was found that for various abrasion treatments,

all of the data normalized in this manner fell on the same curve, such

that

a log t (12)
N t0.5


Their results are plotted in Figure 7.


























Figure 6. Hypothetical changes in crack tip geometry due to
stress corrosion









(a)


(h) (c)
I I
I
I I I
I I
I
r r
( I
r/ I
(I IL I
c,/


























Figure 7. Universal fatigue curve developed by Mould
and Southwick (1959a)







1.0


0.90


0.8

0.7


0.6


0.5


0.4

0.3

0.2.

0.1


0


-4 -3 -2 -1 0 1 2 3 4 5


log0 (t/t0.5)







Mould and Southwick (1959) also determined the value for the

breaking stress times the square root of the crack depth, a Ya7, which,

according to the Griffith criterion (Eq. 5), should be constant

(assuming constant y). Their value was 280-320 psi-in(0.31-0.35

MPam), which compares well with Griffith's value of 240 psi-in

(0.26 MPam).

Mould and Southwick (1959) also studied the effect of aging in

various media on strength and static fatigue. Water was found to be

as effective as HCL or NaOH in strengthening the glass. Approximately

a 30 percent increase in strength was observed. Very little effect was

observed in the static fatigue behavior, other than the general strength-

ening.

C. Fracture Mechanics of Glasses and Ceramics

Bradt, Hasselman, and Lange (1974) have edited a four volume

series on fracture mechanics of ceramics, which contains papers present-

ing an overview of the subject as well as specific problems. Lange (1974)

introduces the subject and traces the development of fracture mechanics

from the early theories to its present-day use as a tool in materials

development.

Evans (1974a) discusses the techniques used for fracture mechanics

determinations, including the advantages and pitfalls of each method.

The methods outlined (with references to more complete descriptions)

are three-point bend, single edge cracked tension, compact tension,

double cantilever beam (four variations), and double torsion.







Wiederhorn (1974) discusses subcritical crack growth and the

methods of obtaining crack velocity data. In addition to the direct

methods, such as described by Evans (1974a),Wiederhorn outlines the

indirect methods of obtaining the same data by constant load (static

fatigue) and constant strain rate (dynamic fatigue) experiments.

It has been shown (Evans, 1974b) that the crack velocity(V) may

be expressed as a power function of the applied stress intensity

factor(K):

V = AKN (13)

where A and N are constants to be determined experimentally. The

constant N is termed the stress corrosion susceptibility and is used

as a measure of a material's resistance to sub-critical crack growth

in corrosive environments.

By defining the crack velocity as

V dt (14)

and assuming a relationship between the stress, flaw size, and stress

intensity factor

K = aYa (15)

where Y is a constant which depends on crack and loading geometry, a

relationship may be derived giving the time to failure under a constant

load. (Note that Eq. 7 is the same as Eq. -15 with Y = ir.)

An equation defining the time to failure under a constant load may

be derived from Eqs. 13-15. From Eqs. 14-15,

da = 2K dK
02y2

and

Vdt 2K dK
a2y2








Using Eq. 13,

AKNdt = 2K dK
2y2

or
2KI-
dt = dK
2 2
AY 2c

Integrating now from zero to tf (corresponding to Ki, the initial stress

intensity factor, to Kc, the critical stress intensity factor) gives

2 22-N
f AY2(2-N)o2 -c i 2N

where a. is some applied stress. Since N is large and positive and
2-N 2-N
Ki>K This leads, finally, to the equation for the time
1 c 1 c
to failure under a constant applied load,

2-N
2K-N
t = (16)
AY2(N-2)co
a

From Eq. 15,
/ \
Ki a Kc (17)


where ac and Kc are the critical fracture stress and stress intensity

factor in an inert environment respectively. Then we have:
2-N
2(K /ac) -N (18)
f AY2(N-2) a


Kc and ac are determined by testing in liquid nitrogen, so that a

logarithmic plot of t vs. aa gives a straight line with a slope of -N

and an intercept which gives A.








Similarly, an equation relating the fracture strength to the

loading or stressing rate may be derived. (Details of the derivation

are given by Greenspan, 1977.) The equation is


N+1 2(N+1)(K /a )2-N
=- 2 a (19)
AY2(N-2)


where & is the stressing rate, do/dt. Now a logarithmic plot of a vs

a gives a straight line of slope 1+N and an intercept which gives

A. Ritter and co-workers (1971, 1974, 1978, 1979) have used Eqs. 18

and 19 extensively to determine these parameters for various glasses

and ceramics.

Usually, the crack propagation parameters obtained using the

static and dynamic fatigue methods agree with those obtained from

crack velocity experiments. However, several instances have occurred

where the data did not agree (Ritter and Manthuruthil,. 1973). The

materials involved are Pyrex and silica glasses. .Differences in the

chemical environment at the crack tip may account for the discrepancy.

The crack velocity experiments utilize a macroscopic crack to determine

the parameter, while the indirect methods initiate failure at micro-

scopic flaws, so that it is not unusual to imagine different chemistries

at the crack tip. Because the parameters are used for estimating failure

times, there is a practical need to resolve these differences in fracture

behavior.








D. Lifetime Predictions

Using Eqs. 18 and 19 we may construct diagrams to demonstrate

graphically the relationships between time to failure and applied

stress and failure stress and stressing rate. Figure 8 shows the

experimental results for 33L glass tested in air using Eq. 19.

Detailed discussion of this type of diagram is found in Chapter VI.

Rearranging Eq. 19 and taking the logarithm yields

noa = (Nl) [n B + zn (N+1) + (N-2) knoc] + TN?1 zno& (20)

where
2
B 2=
AY2 (N 2)K N-2

and the other terms have been previously defined. This now explicitly

defines the straight line relationship between an6 and an&. In this

case N = 30.5 and kn B = -2.07. (At this point, it is convenient to

express B in a logarithm, and A must be determined after a separate

experiment to find K .)

Because ceramics and glasses exhibit a wide spread in strength

values, lifetime predictions must use the lowest values to assure some

minimum lifetime. In order to increase the confidence in the minimum

lifetime prediction and to allow glasses and ceramics to be designed

to sustain greater loads, a proof test may be performed. In a proof

test, each sample is subjected to a stress greater than that expected

in service. This eliminates the weak ones and assures that every survivor

has some minimum strength or service life. This minimum service life

(tmin) is given by
SB N-2 -N \
t = B P2 aC (21)
min P a



























Figure 8. Equation 19 plotted for 33L-glass tested in
air





c (MPa-s- )


1 6 7.9 16 79 158
---- I-----------1----L1 1____________ L


33L Glass Air


5.00














S4.75














4.50


In c (MPa-s-)


N = 30.5

In B = -2.07


- -----------


r








which is simply Eq. 18 with a the proof test stress, substituted for

the inert strength, a.

A design diagram for lifetime predictions may now be constructed

by rearranging Eq. 21:


tmn = B(ap/a)N 2 (22)
min a p a

Using the crack growth parameters B and N and knowing the desired life-

time at an applied stress, a proof test ratio (a p/a) may be determined

in order to design a suitable proof test. Figure 9 shows the design

diagram for 33L glass tested-in air based on the data shown in Fig. 8.

As an example, if a component is expected to last ten years at

50MPa (horizontal line in diagram), a proof test ratio of 2.81 is needed.

Therefore, samples which had survived a proof test of 140 MPa would be

expected to survive the above conditions.

E. Methods Used For This Study

Both direct and indirect methods are used in determining the crack

growth parameters for the lithium disilicate glass-ceramic system. The

constant moment double cantilever beam method is used to measure the

crack velocity directly. The constant stressing rate method is used for

comparison. Chapters VI and VII will compare the results of the two

methods.









op/. a
1.5 2.0 3.0
-t -- f


4.0 5.0
I f


10 years, 50 MPa


33L-GLASS


TESTED IN AIR


0.5 1.0 1.5


In ( p/oa)


Lifetime prediction diagram using equation 22
for 33L-Glass


34





30






26


C-J


(\J ro
r
o


E
.Fa


22






18


14 -






10


Figure 9.


I I







CHAPTER IV-MATERIALS PREPARATION AND
CHARACTERIZATION


A. Melting and Casting

The parent glass was made by mixing reagent grade Li2CO3 and 5 lm

Min-U-Sil silica sand for one hour on a roller mill in a plastic jar.

Each batch weighed 200-250 g and was melted in a covered platinum crucible

for 24 hours in air in a electric muffle furnace at 13500C.

Casting was done in a graphite mold or graphite forms. Discs

required for the biaxial flexure test were made as follows: Cylinders

25 mm in diameter and about 50 mm long were formed and subsequently cut

into 2 mm thick slices with a diamond wheel. For double cantilever beam

specimens, bricks 20 mm x 25 mm x 80 mm were poured and subsequently cut

into plates with a diamond saw.


B. Annealing, Nucleation, and Crystallization Schedule

The completely glassy specimens were annealed immediately after

casting for four hours at 3500C and allowed to furnace cool. Qualitative

analysis of residual stresses was made using a polariscope with a tint

plate. Samples showing excessive stress were remelted and recast.

Those samples to be crystallized were placed in a tube furnace

directly after casting and held at the nucleation temperature. For all

levels of crystallinity, the nucleation treatment was 24 hours at 4750C.

This treatment was selected based on the work of Freiman (1968). The

size of the samples was also a factor. Because they were so large, a

long nucleation time was required to assure a consistent microstructure

throughout each specimen as well as from specimen to specimen. Two

cylinders or one brick could be treated at a time. To minimize thermal

38







gradients, the specimens were held in steel wire mesh boats and set on

an aluminum block in the center of the furnace.

To crystallize the specimens, the furnace was turned up to 5500C

and left for various periods of time. The furnace reached 5500C from

4750C in 15-20 minutes. Two hours resulted in about 7 percent crystal-

linity; four hours gave about 55 percent; fully crystallized specimens

were obtained by leaving them at 5500C for 24 hours.

After crystallization, the specimens were removed from the tube

furnace and placed in a small furnace at 2000C to prevent thermal shock

and allowed to furnace cool to room temperature.


C. Final Sample Preparation

Discs for biaxial flexure were cut from the cylinders with a high

speed diamond saw. Water was used as a coolant. Because of the rough

finish and reactivity of the materials with water, each disc was polished

dry with SiC paper to a 320 grit finish. The final discs were.about

2.5 mm thick. Discs were kept in dessicator to prevent atmospheric water

attack before testing.

Plates for double cantilever beam (DCB) testing were cut from the

bricks to the approximate dimensions 1 mm x12 mm x 75 mm. These were

cut using a low speed diamond watering saw, with mineral oil or Isocut*

fluid as a coolant. Although surface finish is not important in this

test, care was taken to avoid contact with water. A groove roughly half

the thickness of the specimen was machined down the center. This gives

the propagating crack an easy path to follow. The groove was made using


*Buehler and Co., Evanston, IL.







a milling machine and a diamond tool. Figure 10 shows the shape and

representative dimensions of the DCB specimens.


D. Characterization

Volume fraction crystallinity was evaluated by quantitative micro-

scopy (DeHoff and Rhines, 1968) using a petrographic microscope. A

121 point grid was placed 10 times on each sample measured at 200X to

obtain sufficient data for analysis.

The samples to be evaluated were polished sections, polished using

SiC paper to 600 grit, followed by 6 pm and 1 pm diamond paste. The

microstructure was made visible using an etch in 5 percent HF for one

minute. (See Chapter VI for examples of the microstructures.)
































bi
A j


F--2 h-


SECTION
A-A

0.5mm

1.0mm

6.0mm

18.0mm


Figure 10. Specimen configuration for double cantilever
beam constant moment crack growth experiment


L








CHAPTER V-TEST TECHNIQUES


A. Biaxial Flexure

Figure 11 shows the test jig for the biaxial flexure test. The

sample cup, which is mounted on the load cell of an Instron* testing

machine, has three press-fitted ball bearings which define a support

circle for the disc samples and also allows liquids or gases to be added

for testing in various reactive or non-reactive environments. The

loading pin is mounted on the crosshead of the testing machine and is

centered with respect to the circle defined by the ball bearings.

Detailed stress analysis of this method can be found in the work

of Kirstein and Woolley (1967). More recently, Wachtman, Capps, and

Mandel (1972) evaluated this method in a thirteen-laboratory round-

robin test. For small deflections, the strength, S, in this con-

figuration is

S 3 P(X Y) (23)
d
where

X = (1 + v) ln + -1 2 B\2

Y = (1 + v) [1 + ln ] + (1 ()

A = radius of support circle
B = radius of loaded area
C = radius of specimen
P = load
d = specimen thickness
v = Poisson's ratio.


* Instron Corp., Canton, MA.



























RAM-




3 STEEL BALL-
BEARINGS 120
APART




TO LOAD CELL-


UPPER CROSSHEAD


STEEL PIN


HOLDER


Figure 11. Biaxial flexure test jig








The dimensions used in our testing are A = 9.5 mm, B = 0.8 mm, and

C = 12.7 mm. A Poisson's ratio of 0.24 was used for all materials

studied (Freiman, 1968). These values reduce Eq. 23 to


S = -1.8689 2 (24)
d

Samples were tested in biaxial flexure at five cross head speeds

over three decades (0.2, 0.1, 0.02, 0.01 and 0.002 inches per minute)

in three atmospheres (air, water, and liquid nitrogen). Some samples

were also tested after aging one day or one week in water.

Testing in air was straightforward (22C, 65-70% relative humidity).

Care was taken when testing in water to ensure that the samples tested

at the fastest rate were in water about the same length of time as those

tested at the slowest rate (about two minutes).

In the aging experiments, samples were placed in plastic vials

with sufficient water to achieve a surface area to volume ratio (SA/V)

of 1 cm-1. Discs were then tested in the same water in which they were

aged.

Samples tested in liquid nitrogen were pre-cooled to avoid thermal

shock failure. The test jig was cooled with liquid nitrogen and filled

with the liquid during testing. Because of the absence of static

fatigue at liquid nitrogen temperatures, testing was done only at one

rate of 0.02 inches per minute. The average strength from the liquid

nitrogen testing was used as the ac value in Eqs. 17-20.

B. Double Cantilever Beam Testing

Freiman, Mulville, and Mast (1973) give a detailed analysis of the

constant moment double cantilever beam technique. Figure 12 shows the




































~I


I S.


*1





Ipi


'...-A

IJ
i;






1-V
i
| r
*^ '


.- v- ^
^- *I


Constant moment double cantilever beam test apparatus


Figure 12.








test apparatus for this technique. The test specimen is cemented

using epoxy to the loading arms in a pair of slotted inserts to insure

proper alignment. All the pivot points have suitably low friction

provided by bearings. The load is applied by means of a weight

pan connected through a triangular piece (assuring equal load

distribution) to the loading arms. A constant load provides a

constant moment applied by the arms to the specimen. This yields

a constant stress intensity factor, defined by


K TL (25)



where

T = load

L = moment arm length

I =- b h3 = moment of inertia of the beam

t = web thickness,

as defined in Figure 10.

A starter crack is initiated at the base of the slot in the groove

by tightening a sharp screw against the ungrooved side. The crack will

grow at a constant velocity under a constant load. The range of

velocities measured was from 10-10 to 10-4.m/s. With proper care,

multiple measurements may be made on one sample by changing the load

after taking sufficient readings at one load. Measurements were made

every few hours for very slow velocities and every half minute for

fast velocities. Again, testing was done in air and water at room

temperature (%220C).








Measurement of the crack velocity was made with a traveling

microscope.* The magnification was 32X. The accuracy of the

microscope was 0.0005 mm. Readings were made to the nearest

micrometer.

The above procedure will provide crack velocity data for stress

intensity factors less than Kc. Values for Kc, the critical stress

intensity factor, were determined using this apparatus attached to

an Instron** machine. An initial load was applied to begin the crack

propagation, then the cross head was turned on at a constant speed

of 0.02 inches per minute and the crack then propagated to failure.

The highest value of the load (T) then is substituted into Eq. 25,

and the value for Kc determined.


* Gaertner Scientific Corp., Chicago, IL.

** Instron Corp., Canton, MA.







CHAPTER VI-DYNAMIC FATIGUE: RESULTS AND DISCUSSION


A. Quantitative Microscopy

For the dynamic fatigue specimens, at least ten different discs

representing about half of the cylinders were examined for percent

crystallinity. Table 2 is a compilation of these results.

Figures 13-15 are optical micrographs of representative micro-

structures produced by each treatment. For the remainder of the work,

the nomenclature for the various microstructures will be as follows:

Crystallization Treatment Nomenclature

2 hours 33L- 7% Crystalline

4 hours 33L-57% Crystalline

24 hours 33L-92% Crystalline

For the 33L-92%, the remaining 8 percent is not a glassy phase

but open porosity. The porosity is a result of extensive microcracking

which occurs as the crystalline phase shrinks away from the less dense

glassy phase. Evidence of this microcracking can also be seen in 33L-7%

and 33L-57%. (See Figures 13-14.) There appears to be little if any

residual glassy phase in 33L-92%.

B. Dynamic Fatigue Testing of 33L-Glass

Figures 16-18 are plots of Eq. 20 for 33L-Glass testing in air,

in water, and after aging one day in water. The accompanying tables

(Tables 3-5) show the raw data for each plot. The straight lines in

Figures 16-18 are least squares fits using all data points obtained

in the testing. Table 6 shows the inert strength data from testing

samples as prepared and after aging one day in water.
48









TABLE 2

Results of Quantitative Microscopy for
Determining Per Cent Crystallinity


24 Hour Crystallization Treatment


% Crystalline
92.34
97.14
80.77
87.51
93.68
94.04
93.96
96.87
88.44
95.69
90.11
92.64


Average, x


Std., Dev., s



s/x


4 Hour Crystallization Treatment


Average, x


Std., Dev., s



s/x


Sample
308X
412X
507X
605X
804X
1006X
1102X
1310X
1402X
1907X
2303X
1508X


91.93%


4.65%



5.06%


203Z
402Z
409Z
603Z
704Z
709Z
802Z
907Z
1003Z
1309Z


57.14%


55.08
56.28
52.31
60.37
59.13
56.57
60.29
57.02
63.80
50.58


3.95%



6.91%









Table 2 Continued

2 Hour Crystallization Treatment


% Crystalline
5.08
9.05
9.09
7.93
7.07
6.61
6.41
6.07
5.46
5.54
5.54
6.61
7.27


Average, x



Std. Dev., s


Sample
602W
611W
807W
901W
1101W
111OW
1201W
1209W
1307W
1405W
1608W
1807W
2110W


6.79%



1.27%



18.64%


























or p
o
1)
45
9
r
bBO
*Cn d


.1,

I S


0.


C
"



.

*4 *

-g -


&Ar
4 r *
V~~a 9 .f
*'^' '" ,:


S S
9 B

j *8%


i'(


" cr
6 <


e6


.. i
A3


0
A




A' '6

S5

e~

S -V


Figure 13. Representative microstructure of

33L-7% crystalline


I

$sUI


,i' 8'
r-9 5 i
P


1.


ib ab
%" a


t 8


4]







































I 1Oum ,

Figure 14. Representative microstructure of
33L-57% crystalline











































Figure 15. Representative microstructure of
33L-92% crystalline

























Figure 16. Dynamic fatigue results for 33L-glass tested
in air






(MPa-s 1)


33L Glass Air


5.00












r-

S4.75














4.50


In 0 (MPa-s-l)


N = 30.5

In B = -2.07


-100


I I I r - :'
























Figure 17. Dynamic fatigue results for 33L-glass tested
in water






S(MPa-s1 )


33L Glass H20


N = 11.0


In B = 4.23


-150




-125


U ,
t(>I) -


In o (MPa-s-1)


5.20-





5.00-


4.80-





4.60-


4.40





4.20


)


~I


1 - . .ai-r;
























Figure 18. Dynamic fatigue results for 33L-glass tested
after aging one day in water




. (MPa-s-l)


33L Glass Aged 1 Day


5.50





5.25





5.00





4.75






4.50


In o (MPa-s-1)


N = 37.4

In B =-30.73


-200


S175


150 ,


.125





-100


I -


1_--~-









Table 3


Dynamic Fatigue Data for
Tested in Air


Stressing Rate


158

136
20
15%
32
136
7.4


79

131
13
10%
30
132
11.2


= average strength
= standard deviation
= coefficient of variation
= sample size
= median strength
= Weibull modulus


33L-Glass


(MPa-s1I)


S(MPa)
s(MPa)
s/S
n
S (MPa)
m '


16

125
29
23%
32
123
4.9


7.9

135
37
28%
31
125
4.0


1.6

113
19
17%
32
112
6.7


S
s
s/S
n
S
m
m


I





61



Table 4


Dynamic Fatigue
Tested


Data for 33L-Glass
in Water


Stressing


Rate (MPa-s-1)


158

123
16
13%
32
124
8.0


79

137
30
22%
32
S135
5.1


average strength
standard deviation
coefficient of variation
sample size
median strength
Weibull modulus


16

112
19
17%
26
111
6.2


7.9

100
16
16%
32
101
6.6


S(MPa)
s(MPa)
s/S
n
Sm(MPa)
m



S=
s =
s/ =
n =
S =
m =


1.6

91
22
24%
33
91
4.2









Table 5

Dynamic Fatigue Data for 33L-Glass
Tested After Aging 1 Day in Water


Stressing Rate (MPa-s-1)


158

124
8
7%
9
125
14.5


79

157
49
31%
31
.145
3.6


16

129
37
29%
15
120
3.7


7.9

133
46
35%
31
121
3.3


average strength
standard deviation
coefficient of variation
sample size
median strength
Weibull modulus


S(MPa)
s(MPa)
s/S
n
Sm(MPa)
m



=
s =
s/ =
n =
S =
m =
M


1.6

125
42
33%
31
112
4.0
















Table 6


Liquid Nitrogen Strength of 33L-Glass


As Prepared


S(MPa)

s(MPa)

s/S

n

Sm(MPa)

m


Aged 1 Day


179

3.4

19%

11

178

5.0


211

61

29%

10

224

3.1


= average strength

= standard deviation

= coefficient of variation

= sample size

= median strength

= Weibull modulus


S

s

s/S

n

Sm

m








The decrease in strength when tested in water and subsequent

increase after aging are consistent with previous works on glass

(Mould and Southwick, 1959, and others). However, the change in

stress corrosion susceptibility, N, from 30.5 (in air) to 11.0 (in

water) to 37.4 (after aging) was not anticipated. Because the

mechanism of stress corrosion (aqueous attack at the crack tip) is

the same in air and in water, the N values are expected to remain

constant. This large variation in N suggests that the kinetics of

aqueous corrosion are also involved in stress corrosion.

When testing is performed in air, the concentration of water at

the crack tip is low compared to that when testing in water. Less H

would then be available for ion exchange with Li slowing the reaction

and allowing less stress corrosion (giving a higher N value).

The conditions at the crack tip are altered drastically by aging

in water. The strength increases due to a rounding of the crack tip,

which, from Eq. 1, lowers the amount of stress concentration. During

the aging period, a reaction layer forms on the surface which is

depleted in lithium (due to ion exchange). In order for the flaw to

grow, it must first penetrate the reaction layer before entering the

bulk glass. This reaction layer, even after the flaw has grown through

it, protects the bulk from the aqueous environment. The protection

thus afforded raises the N value to one even higher than that in air.

Weibull Statistics

In the tables showing the raw data, m is a parameter called the

Weibull modulus. This parameter is obtained from (Wiederhorn, 1974)

ln In(l-F)-1 = m In (Si/So) (26)








where F is the failure probability for each strength value S.. The

parameters m and So are the Weibull modulus and scale parameter

respectively. The amount of scatter in the data can be quantified

in terms of m. As m increases the scatter becomes less (the slope of

Eq. 26 increases). Figure 19 is an example of a Weibull plot for

33L-92% crystalline material.

For 33L-Glass, the m value ranges from 3.1 to 14.5, depending

on environment, stressing rate, and aging, but mostly ranging from

about three to eight. This is very low and indicates a large range

of flaw sizes controlling the strength of the glass.

Ideally, the sample size for an adequate Weibull analysis should

be thirty or more. Although this study rarely meets that requirement,

the m values are still reported, but should be taken only as an indica-

tion of the true Weibull modulus of the material.

Lifetime Prediction Diagrams

Figure 20 is the lifetime prediction diagram (LPD) based on Eq. 22

for 33L-Glass. It can be seen that for a component to survive ten years

at 50MPa, different proof test levels are necessary depending on the

environment. In air, a proof test ratio of about 2.81 (140MPa) is

needed; in water, 13.46 (673 MPa); after aging one day, 5.21 (260 MPa).

Obviously, no 33L-Glass component would survive a proof test of

673 MPa, so that a different design level (shorter lifetime or lower







Si (MPa)
290


175


2g5


158 MPa-s '
16 MPa-s-
1.6 MPa-s


.0


33L-92% CRYSTALLINE

TESTED IN WATER


5.2


In S.
*1


5.3


(MPa)


Weibull plot for some 33L-92% crystalline material


0.5





0.0-





-0.5-


-1.0 -


-1.5





-2.0


-0.90





-0.75







.0.50


-0.25











-0.10





Figure 19.






ap/ a


1.5 2.0 2.5


in (ap/aa)


Figure 20. LPD for 33L-Glass


r<)
0.
t~

S26
E

r-



24





22





20


1.0








stress) is mandatory for 33L-Glass in water. However, if the data from

the aged samples are used, a proof test of only 260 MPa is necessary.

There is still a need to lower the design level, but not nearly as much.

The problem is, which data are relevant?

This situation illustrates the dynamics of the problem which have

yet to be discussed, let alone resolved. In order to make reliable

lifetime predictions, the conditions that a component sees must be known

(or assumed). It is also assumed (Wiederhorn 1973) that there is no

change in the flaw during or after proof testing. It is evident from

this work that a corrosive environment will have some effect on the flaw

and its immediately surroundings in the bulk. It would seem, then, that

no reliable predictions can be made using this procedure for materials

in corrosive environments due to the changing character of the flaws.

More discussion will follow after presenting the crack velocity

studies.


C. Dynamic Fatigue Testing of 33L-92%

Figures 21-24 present the dynamic fatigue results for 33L-92% and

Tables 7-10 give the raw data. Tests were conducted in air, in water,

and in water after aging for one day and one week. Table 11 shows the

results of the inert environment testing.

There was the expected decrease in strength when tested in water,

but no increase after aging. After aging one day, there was little

change over testing in water, but after one week, there was substantial

decrease in strength. This decrease can be attributed to the pervasive

attack of the water throughout the continuous microcrack network.

Similar effects have been seen in other porous ceramics (Frakes, Brown,

and Kenner 1974).























Figure 21. Dynamic fatigue results for 33L-92% crystalline
tested in air







S(MPa-s-)

1.6 7 9 1 79 158

5.60

33L 92% Crystalline Air



250
5.50





-. 225
5.40




N = 70.6

5.30 In B =- 5.66 200






5.20

0 1 2 3 4 5


In o (MPa-s-1)
























Figure 22. Dynamic fatigue results for 33L-92% crystalline
tested in water





; (MPa-s-1)
0, (MPa-s )


5.50






5.40







C
5.30






5.20-






5.10


In a (MPa-s-1)
























Figure 23. Dynamic fatigue results for 33L-92% crystalline
tested after aging one day in water






o (MPa-s1)

11.6 7.9 1( 77 158
225
5.40

33L 92% Crystalline.- Aged 1 Day




5.30- 200






5.20-
N = 27.6
175
In B = 0.73 175



5.10





5.00

---5


In o (MPa-s-1)
























Figure 24. Dynamic fatigue results for 33L-92% crystalline
tested after aging one week in water







o (MPa-s- )
\.6 7.9 16 79 15,8

5.25

33L 92% Crystalline Aged I Week

175







5/ 150
c 5.00 *


N = 22.3

In B = 2.37



125




4.75 ",

b 2 5 3 5


In c (MPa-s- )









Table 7


Dynamic Fatigue Data for 33L-92% Crystalline
Tested in Air


Stressing


158

226
9
4%
11
225
24.3


79

228
11
5%
11
227
21.1


Rate (MPa-s-1)


16

226
14
6%
9
226
14.7


7.9

226
18
8%
13
219
11.7


average strength
standard deviation
coefficient of variation
sample size
median strength
Weibull modulus


S(MPa)
s(MPa)
s/5
n
Sm
m




S=
s =
s/S =
n =

Sm =
m=


1.6

209
18
9%
10
205
11.2









Table 8


Dynamic Fatigue Data for 33L-92% Crystalline
Tested in Water


Stressing Rate


158

213
14
7%
8
208
13.8


79

214
10
5%
10
213
20.6


16

199
10
5%
11
196
17.9


(MPa-s- )


7.9

193
6
3%
9
196
29.3


average strength
standard deviation
coefficient of variation
sample size
median strength
Weibull modulus


S(MPa)
s(MPa)
s/S
n
Sm
m






s/ =
n=
S
m =


1.6

181
7
4%
10
180
24.0









Table 9


Dynamic Fatigue Data for 33L-92% Crystalline
Tested After Aging 1 Day in Water


Stressing Rate (MPa-s-1)


158

207
9
5%
6
208
19.9


79

206
6
3%
15
*207
33.7


16

203
10
5%
4
200
15.7


7.9

187
8
5%
15
187
22.7


average strength
standard deviation
coefficient of variation
sample size
median strength
Weibull modulus


S(MPa)
s(MPa)
s/S
n
Sm(MPa)
m



S=
s =
s/S =
n =
S =
m =
M


1.6

179
7
4%
6
181
22.3









Table 10


Dynamic Fatigue Data for 33L-92% Crystalline
Tested After Aging 1 Week in Water


Stressina Rate


158

175
18
10%
14
169
9.8


79

169
15
9%
14
165
11.0


16

160
17
11%
13
156
9.4


(MPa-s-1)


7.9

156
18
11%
14
152
8.9


= average strength
= standard deviation
= coefficient of variation
= sample size
= median strength
= Weibull modulus


S(MPa)
s(MPa)
s/S
n
Sm(MPa).
m


1.6

141
15
11%
14
137
9.6


S
s
s/S
n
Sm
m











Table

Liquid Nitrogen Strength


11

of 33L-92% Crystalline


As Prepared

274

19

7%

9

282

12.7


Aged 1 Day

280

20

7%

15

276

14.2


Aged 1 Week

221

26

12%

10

213

8.1


= average strength

= standard deviation

= coefficient of variation

= sample size

= median strength

= Weibull modulus


S(MPa)

s(MPa)

s/S

n

Sm(MPa)

m


s

s/S

n

Sm

m








The stress corrosion susceptibility again changes with environment.

In air, N = 70.6, but in water it drops to the mid-twenties. Because

the lithium disilicate crystals are much more durable than the glass

(McCracken 1981), the N value is very high compared with the glass.

There is virtually no change in N after aging of this glass-ceramic.

This can be explained by the lack of an extensive glassy phase. The

water attacks the grain boundaries where the glassy phase exists. But

because the glassy phase is so limited in size and extent, no protective'

layer builds up, only dissolution occurs. Therefore, no matter how long

the aging period, the mechanism and the associated kinetics change very

little.

The Weibull moduli for 33L-92% range from 8.9 to 33.7. These are

much higher than those for 33L-Glass, indicating a narrower distribution

of strength controlling flaws.

Figure 25 is the lifetime prediction diagram for 33L-92%. The

lines for the material tested in water are grouped together, again indi-

cating little difference in mechanism or kinetics. The aged one week

line is off-set slightly because of the large decrease in strength

observed. For this material in air, a proof test ratio of 1.62 (81MPa)

is needed to assure a lifetime of ten years at 50 MPa. This is much

lower than that for glass under equivalent conditions. (Note different

scales in Figs. 20 and 25.) For an aqueous environment, the ratio

ranges from 2.91 (145 MPa) to 3.39 (169 MPa).


D. Dynamic Fatigue Testing of 33L-7%

Figures 26-29 are plots of the dynamic fatigue data listed in

Tables 12-15. Table 16 shows the inert strength data for 33L-7%.




83


p/.,5
2.,5


33L 92% Crystalline


70





60 -





50 -





40





30





20


Years, 50 MPa


Aged 1 Week


0.4


0.6


0.8


1.6


In ( pI/a)
pa"


Figure 25. LPD for 33L-92% crystalline


3r0 3.5 4,0 4r5 5,0


Z.0


Air



















Aged 1 Day


m i I m m


1 r _ _
























Figure 26.


Dynamic fatigue results for 33L-7% crystalline
tested in air





o (MPa-s1 )


33L 7% Crystalline Air


N = 116.1

In B = -34.43


In 6 (MPa-s-1)


5.40


5.20 -


a0
?5.00 -

c




4.80






4.60


-200




.175


.150 c
O-
s:
10


125







r100


t -I--


___ Jf
























Figure 27. Dynamic fatigue results for 33L-7% crystalline
tested in water






o (MPa-s-1)


33L 7% Crystalline H20


N = 136.0


In B = -53.93


-200


-175




-150
I/)


-125






-100


0 1 2 3 4 5

In o (MPa-s1)


5.40-


5.20-


5.00-


4.80-






4.60-


. .. ..


----L---------
























Figure 28. Dynamic fatigue results for 33L-7% crystalline
tested after aging one day in water




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