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The fracture mechanics of lithium disilicate glass and glass-ceramics Rao, Avaral S. 1977

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THE FRACTURE MECHANICS OF LITHIUM DISILICATE GLASS AND GLASS-CERAMICS by AVARAL S. RAO B.Sc. U n i v e r s i t y of Mysore, 1965 B.E. Indian I n s t i t u t e of Science, 1969 M.A.Sc. Un i v e r s i t y of B r i t i s h Columbia, 1971 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY i n the Department of Metallurgy We accept t h i s thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA May, 1977 © Avaral S. Rao, 1977 In p r e s e n t i n g t h i s t h e s i s in p a r t i a l f u l f i l m e n t o f the r e q u i r e m e n t s f o r an advanced degree at the U n i v e r s i t y o f B r i t i s h Co lumb ia , I ag ree that the L i b r a r y s h a l l make i t f r e e l y a v a i l a b l e f o r r e f e r e n c e and s tudy . I f u r t h e r agree t h a t p e r m i s s i o n f o r e x t e n s i v e c o p y i n g o f t h i s t h e s i s f o r s c h o l a r l y purposes may be g r a n t e d by the Head o f my Department o r by h i s r e p r e s e n t a t i v e s . It i s u n d e r s t o o d tha t c o p y i n g o r p u b l i c a t i o n o f t h i s t h e s i s f o r f i n a n c i a l g a i n s h a l l not be a l l o w e d w i thout my w r i t t e n p e r m i s s i o n . Department o f Metallurgy  The U n i v e r s i t y o f B r i t i s h Co lumbia 2075 Wesbrook Place Vancouver, Canada V6T 1W5 Date July 15 , 1977 i ABSTRACT The dependence of f r a c t u r e strength upon the time of loading i s commonly termed s t a t i c f a t i g u e or delayed f a i l u r e . This has been a t t r i b u t e d to the growth of s u b c r i t i c a l flaws under s t r e s s . Hence the study of s u b c r i t i c a l crack growth i s important i n p r e d i c t i n g the l i f e expectancy of a material when i t i s subjected to a s t r e s s . S u b c r i t i c a l crack growth of glass and glass-ceramics, at room temperature and i n two d i f f e r e n t environments (toluene and water) was studied. Glass containing 17.8 wt% I ^ O - 82.2 w t % SiO^ and c r y s t a l l i z e d glasses (glass-ceramics) were chosen. The double t o r s i o n technique was used to determine crack v e l o c i t y at various s t r e s s i n t e n s i t y f a c t o r s . I t was shown that the slopes of the v e l o c i t y - s t r e s s i n t e n s i t y f a c t o r diagrams f o r glass and glass-ceramics (having d i f f e r e n t volume f r a c t i o n s of c r y s t a l l i n e phase) tested i n water, remained constant. However, these p l o t s s h i f t e d to the higher s t r e s s - i n t e n s i t y region, as the degree of c r y s t a l l i n i t y i n the glass increased. The crack v e l o c i t y - s t r e s s i n t e n s i t y f a c t o r p l o t s of glass and glass-ceramics tested i n toluene have shown a s i m i l a r behaviour but the slope of these p l o t s increased as the degree of c r y s t a l l i n i t y i n the glass increased. A m o d i f i c a t i o n of the s t r e s s -23 corrosion model of H i l l i g and Charles i s proposed. Crack v e l o c i t y data of glass and glass-ceramics tested i n water agreed w e l l with the proposed model. Crack v e l o c i t y data of glass and glass-ceramics tested i n toluene i i are discussed.in terms of the " l a t t i c e trapping theory".. An equation i s presented to p r e d i c t . t h e l i f e expectancy under s t r e s s of these materials from crack growth data. The transverse rupture t e s t was used to determine the f r a c t u r e strength of glass and glass-ceramics. These r e s u l t s have shown that the f r a c t u r e strength of glass-ceramics i s increased mainly due to the increase i n the f r a c t u r e surface energy. The c r i t i c a l s t r e s s i n t e n s i t y f a c t o r of glass-ceramics increases as the degree of c r y s t a l l i n i t y increases. The f r a c t u r e surface. energy of these materials was c a l c u l a t e d from the knowledge of the c r i t i c a l , s t r e s s i n t e n s i t y f a c t o r and i t was shown that the f r a c t u r e surface energy of glass-ceramics containing up to 0.5 volume f r a c t i o n of. c r y s t a l l i n e phase i s r e l a t e d to the i n t e r -p a r t i c l e spacing. This observation i s f u r t h e r substantiated by f r a c t o -graphic examination. The k i n e t i c s of c r y s t a l l i z a t i o n of l i t h i u m d i s i l i c a t e from 17.8wt% L i 2 0 - 82.2 wt % S i 0 2 glass was studied by c r y s t a l l i z i n g t h i s glass at 530°C f o r various lengths of time. I t was shown that the c r y s t a l l i z a t -i o n of l i t h i u m d i s i l i c a t e i s a d i f f u s i o n c o n t r o l l e d r e a c t i o n . I t was found that the d i f f u s i v i t y f o r t h i s process i s much lower than the d i f f u s i o n c o e f f i c i e n t of l i t h i u m ion. i i i ACKNOWLEDGEMENT I would l i k e to thank my research supervisor Dr. J. S. Nadeau for h i s advice and assistance throughout the course of t h i s research project. Thanks are also due to other members of the department and fellow graduate students with s p e c i a l appreciation to Mr. R. Bennett and Dr. M. A. Clark. F i n a n c i a l assistance i n the form of a National Research Council Research Assistantship i s greatly acknowledged. iv TABLE OF CONTENTS Page CHAPTER 1 INTRODUCTION 1 1.1 Previous Work on S t a t i c Fatigue of Glass 3 1.2 S t a t i c Fatigure Models and Mechanisms 15 1.3 Summary of the The o r e t i c a l Models .. 24 1.4 Estimation of Time-To-Failure from Growth 26 Ki n e t i c s 1.5 Objectives of the Present Work 27 CHAPTER 2 EXPERIMENTAL PROCEDURE 2.1 Ma t e r i a l Preparation 28 2.1.1 Glass Preparation 28 2.1.2 Specimen Preparation .. .. 29 2.1.3 Heat Treatment 29 2.2 Sample Characterization 30 2.2.1 D i f f e r e n t i a l Thermal Analysis 30 2.2.2 Density Measurement 30 2.2.3 Metallography 31 2.2.3.1 O p t i c a l Microscopic Examination .. 31 2.2.3.2 Petrographic Examination 33 2.2.3.3 Transmission Electron 34 Microscopy (TEM) 2.2.4 Determination of Degree of C r y s t a l l i n i t y ..34 2.2.4.1 Point-Count Method 34 2.2.4.2 X-ray Method 35 V Page 2.3 K i n e t i c s of C r y s t a l l i z a t i o n 37 2.4 Measurement of E l a s t i c Constants .. 38 2.4.1 Young's Modulus 38 2.4.2 Poisson's Ratio 40 2.5 Measurement of Mechanical Properties 41 2.5.1 Microhardness Measurement 41 2.5.2 Transverse Rupture Strength 41 2.6 Slow Crack Growth Tests 42 2.6.1 Slow Crack Growth of Annealed Glass . . . . 42 2.6.2 Slow Crack Growth of Glass-ceramics . . . . 49 2.7 C r i t i c a l Stress Intensity Factor Measurement .. 49 2.8 Fractographic Examination 50 CHAPTER 3 RESULTS 3.1 D i f f e r e n t i a l Thermal Analysis 51 3.2 Density Study 51 3.3 K i n e t i c s of C r y s t a l l i z a t i o n 57 3.4 Microhardness 63 3.5 E l a s t i c Constants 63 3.6 Transverse Rupture Tests 68 3.7 Slow Crack Growth Tests 77 3.7.1 Crack Velo c i t y - S t r e s s Intensity Factor 77 Diagrams 3.7.1.1 Annealed Glass 77 v i Page 3.7.1.2 Glass-Ceramics up to 50% of C r y s t a l l i n e Phase 80 3.7.1.3 Glass-Ceramics above 50% C r y s t a l l i n e Phase .. 80 3.8 C r i t i c a l Stress I n t e n s i t y Factor ( K ^ ) 8 8 3.9 Fracture Surface Energy 8 8 3.10 Fractography 91 CHAPTER 4 DISCUSSION 4.1 C r y s t a l l i z a t i o n of Lithium D i s i l i c a t e Glass ..107 4.2 Mechanical Properties .. . . H 8 i 4.2.1 Microhardness .. .. .. H 8 4.2.2 E l a s t i c Moduli . . 1 2 1 4.2.3 Fracture Strength . . . . . . . . 1 2 5 4.3 Fracture Surface Energy .. .. ..134 4.4 S t a t i c Fatigue ..137 4.4.1 Model f o r Slow Crack Growth i n Corrosive Environment (water) .. . . . . . . . . . . .. 137 4.4.2 Slow Crack Growth i n Non-Corrosive Environment (toluene) 144 4.5 P r e d i c t i o n of L i f e Expectancy .7".. .. .. ..155 CHAPTER 5 SUMMARY AND CONCLUSIONS ..162 APPENDICES 164 BIBLIOGRAPHY • - 1 7 6 v i i LIST OF FIGURES Figure Number Page 1 Stress-time c h a r a c t e r i s t i c s of annealed soda lime galss-rods V i n diameter, i n bending (After Shand 7) . . . . . . . . 2 2 Fatigue of glass and p o r c e l a i n under steady loads (After -Preston^) , 4 3 Weakening of glass rods during f r a c t u r e as computed from stress-time c h a r a c t e r i s t i c s curve (A), a 1 = 5500 p s i (B), a i = 10,000 p s i (After Shand 8) 6 4 Fracture time as a function of reduced strength S/Sn for d i f f e r e n t surface treatments of soda-lime glass (After Mould and Southwick 1 2) 8 5 Uni v e r s a l f a t i g u e curve f o r glass abraded i n various ways (After Mould and Southwick"'-2) .. 9 6 E f f e c t of time and temperature on r e l a t i v e • strength (After Mould 1 3) .. . . . . . . . . . . . . . . 10 7 , Reduced strength Vs load duration (log scale) f o r specimens tested immersed i n d i s t i l l e d water and i n nitrogen atmospheres of 0.5% and 43% r e l a t i v e humidity (After M o u l d 1 1 ) . . . . . . . . .. 12 8 Schematic st r e s s i n t e n s i t y f a c t o r - c r a c k v e l o c i t y diagram f o r a m a t e r i a l i n a co r r o s i v e environment . . . . . . . . . . . . . . . . 13 9 Dependence of crack v e l o c i t y on s t r e s s i n t e n s i t y f a c t o r , K j i n s o d a - l i m e - s i l i c a glass (After Wiedernorn 2^) .. .. .. .. .. .. 14 10 Dependence of crack v e l o c i t y on s t r e s s i n t e n s i t y f a c t o r , K j , and temperature i n s o d a - l i m e - s i l i c a glass (After Wiederhorn ) .. .. 20 11 Photograph of Automatic Lapping Machine . . . . .. 32 12 Por t i o n of the phase diagram of I ^ O - S i t ^ system .. . . . . . . . . . . . . 36 v i i i Figure Number Page 13 Photograph of s t a t i c e l a s t i c moduli measurement set up 39 14 Specimen used i n double t o r s i o n test ^ 15 Loading f i x t u r e used i n double t o r s i o n test .. 16 Schematic drawing of humidity chamber 17 Flow diagram of humidity c o n t r o l l i n g set up 18 D i f f e r e n t i a l thermal analysis of annealed glass 19 Dependence of heating rate on peak c r y s t a l l i z a t -ion temperature 21 Volume f r a c t i o n of c r y s t a l l i n e phase i n glass-ceramics as a function of time at 530°C . . . . . 22 O p t i c a l micrograph of glass-ceramic containing (a) .05 volume f r a c t i o n of c r y s t a l l i n e phase.. (b) .15 to .20 volume f r a c t i o n of c r y s t a l l i n e phase 23 Relative degree of c r y s t a l l i n i t y as a function . of time at 530°C 24 Microhardness of glass-ceramic as a function of volume f r a c t i o n of c r y s t a l l i n e phase .. 46 47 52 53 20 Densities of the glass-ceramics as a function of volume f r a c t i o n of c r y s t a l l i n e phase .. ,. J J 58 60 60 (c) .35 volume f r a c t i o n of c r y s t a l l i n e phase • • • • 61 (d) .55 volume f r a c t i o n of c r y s t a l l i n e phase 61 (e) .75 volume f r a c t i o n of c r y s t a l l i n e phase . . • D Z (f) .90 volume f r a c t i o n of c r y s t a l l i n e phase 62 64 65 Young's modulus of glass—ceramics as a function of "volume f r a c t i o n of c r y s t a l l i n e phase Poisson's r a t i o of glass-ceramics as a function of volume f r a c t i o n of c r y s t a l l i n e phase Shear modulus of glass-ceramics as a function of volume f r a c t i o n of c r y s t a l l i n e phase Fracture stress (af) and c r i t i c a l - s t r e s s i n t e n s i t y factor (K-TQ) of glass-ceramics as a function of volume f r a c t i o n of c r y s t a l l i n e phase Relative f r a c t u r e stress of glass-ceramics as a function of volume f r a c t i o n of c r y s t a l l i n e phase .. E f f e c t of mean free path between spherulites on fract u r e stress (tested i n toluene) of glass-ceramics E f f e c t of mean free path between spherulites on fra c t u r e stress (tested i n water) of glass-ceramics V e l o c i t y - s t r e s s i n t e n s i t y f a c t o r diagrams f or annealed glass at room temperature V e l o c i t y - s t r e s s i n t e n s i t y factor diagrams f or glass-ceramic containing .15 ± .05 volume f r a c t i o n of c r y s t a l l i n e phase at room temperature V e l o c i t y - s t r e s s i n t e n s i t y factor diagrams f or glass-ceramic containing .30 ± .05 volume f r a c t i o n of c r y s t a l l i n e phase at room temperature V e l o c i t y - s t r e s s i n t e n s i t y factor diagrams for glass-ceramic containing .50 ± 5 volume f r a c t i o n of c r y s t a l l i n e phase at room temperature V e l o c i t y - s t r e s s i n t e n s i t y factor diagrams for glass-ceramic containing .70 ± .05 volume f r a c t i o n of c r y s t a l l i n e phase at room temperature V e l o c i t y - s t r e s s i n t e n s i t y f a c t o r diagrams for glass-ceramic containing .85 + .05 volume f r a c t i o n of c r y s t a l l i n e phase at room temperature X Figure Number Page 38 V e l o c i t y - s t r e s s i n t e n s i t y f a c t o r diagrams f o r glass and glass-ceramics tested i n water at room temperature 86 39 V e l o c i t y - s t r e s s i n t e n s i t y factor diagrams f or glass and glass-ceramics tested i n toluene at room temperature 89 40 E f f e c t of mean free path between spherulites on fra c t u r e surface energy of glass-ceramic 92 41 SEM fractograph of sample (used i n transverse rupture tests) of (a) Glass-ceramic containing l e s s than .05 volume f r a c t i o n of c r y s t a l l i n e phase 94 (b) Glass-ceramic containing .15 ± .05 volume f r a c t i o n of c r y s t a l l i n e phase 95 (c) Glass-ceramic containing .50 ± .05 volume f r a c t i o n of c r y s t a l l i n e phase 96 (d) Glass-ceramic containing .85 ± .05 volume f r a c t i o n of c r y s t a l l i n e phase 97 42 SEM fractograph of sample (used i n double t o r s i o n tests) of (a) Glass-ceramic containing l e s s than .05 volume f r a c t i o n of c r y s t a l l i n e phase 98 (b) Glass-ceramic containing .05 volume f r a c t i o n of c r y s t a l l i n e phase 99 (c) Glass-ceramic containing .15 ± .05 volume f r a c t i o n of c r y s t a l l i n e phase 100 . (d) Glass-ceramic containing .30 ± .05 volume f r a c t i o n of c r y s t a l l i n e phase 101 (e) Glass-ceramic containing .50 ± .05 volume f r a c t i o n of c r y s t a l l i n e phase .. 102 •(f) Glass-ceramic containing .70 ± .05 volume f r a c t i o n of c r y s t a l l i n e phase 103 XX Page (g) Glass-ceramic containing .85 ± .05 volume f r a c t i o n of c r y s t a l l i n e phase 104 (h) Glass-ceramic containing .85 ± .05 volume f r a c t i o n of c r y s t a l l i n e phase(magnified view) [Arrow indicates the d i r e c t i o n of crack propagation] 105 (a) TEM photograph of i n d i v i d u a l l i t h i u m d i s i l i c a t e s p herulite 109 (b) TEM photograph of i n d i v i d u a l l i t h i u m d i s i l i c a t e s p herulite HO (c) TEM photograph of i n d i v i d u a l l i t h i u m d i s i l i c a t e spherulite H I (a) SEM photogtaph of p a r t i a l l y c r y s t a l l i z e d glass-ceramic H 5 (b) T y p i c a l s p h e r u l i t i c microstructure of p a r t i a l l y c r y s t a l l i z e d glass-ceramic from petrographic section (crossed n i c o l s ) H 6 Diameter of the l i t h i u m d i s i l i c a t e s p h e r u l i t e versus r e c i p r o c a l of square root of time of c r y s t a l l i z a t i o n at 530°C 1 1 7 Fracture stress and microhardness of glass-ceramics versus volume f r a c t i o n of c r y s t a l l i n e phase 120 E f f e c t of composition on e l a s t i c modulus of glasses i n system: x Me20 (100 - x) Si02 where Me2 i s Li20 (after Kozlovskaya35) 122 Comparison of values of Young's modulus of glass-ceramics with the t h e o r e t i c a l models 12^ Comparison of values of Poisson's r a t i o of glass-ceramics with the t h e o r e t i c a l models -^6 V e l o c i t y versus Stress i n t e n s i t y f a c t o r C r i t i c a l stress i n t e n s i t y factor diagram for glass and glass-ceramics (tested i n water at room temperature) 143 x i i Figure Number Page 51 Graphical representation of the slow crack growth regime r e s u l t i n g from l a t t i c e trapping (After Thompson 5 7) 146 52 Velocity-square of stress i n t e n s i t y factor diagram for (tested i n toluene at room temperature) (a) Annealed Glass 148. (b) Glass-ceramic containing .15 ± .05 volume f r a c t i o n of c r y s t a l l i n e phase 149 (c) Glass-ceramic containing .30 ± .05 volume f r a c t i o n of c r y s t a l l i n e phase 150 (d) Glass-ceramic containing .50 ± .05 volume f r a c t i o n of c r y s t a l l i n e phase 151 (e) Glass-ceramic containing .70 ± .05 volume f r a c t i o n of c r y s t a l l i n e phase 152 (f) Glass-ceramic containing .85 ± .05 volume f r a c t i o n of c r y s t a l l i n e phase 153 53 (a) L i f e expectancy versus volume f r a c t i o n of c r y s t a l l i n e phase at a 157 — 2 - = 1.1 a app (b) L i f e expectancy versus volume f r a c t i o n of c r y s t a l l i n e phase at a 158 — B - - 1.5 a app .(c) L i f e expectancy versus volume f r a c t i o n of c r y s t a l l i n e phase at a 1 5 9 a app (d) L i f e expectancy versus volume f r a c t i o n of 3 c r y s t a l l i n e phase at a 160 a app (e) L i f e expectancy versus volume f r a c t i o n of c r y s t a l l i n e phase at a ^ app x i i i Figure Number Page A l V e l o c i t y - s t r e s s i n t e n s i t y f a c t o r diagrams f o r : (a) Annealed glass at room temperature 170 (b) Glass-ceramic containing .15 ± .05 volume f r a c t i o n of c r y s t a l l i n e phase at room temperature 171 (c) Glass-ceramic containing .30 ± .05 volume f r a c t i o n of c r y s t a l l i n e phase at room temperature 172 (d) Glass-ceramic containing .50 ± .05 volume f r a c t i o n of c r y s t a l l i n e phase at room 1 7 ^ temperature (e) Glass-ceramic containing .70 ± .05 volume f r a c t i o n of c r y s t a l l i n e phase at room temperature 174 (f) Glass-ceramic containing .85 ± .05 volume f r a c t i o n of c r y s t a l l i n e phase at room 1 7 S temperature • L / J x i v LIST OF TABLES Table Page 1 Summary of DTA of the glass 54 2 Density of the glass and glass-ceramics 56 3 Volume f r a c t i o n of c r y s t a l l i n e phase i n glass-ceramics a f t e r heat-treating for various lengths of time at 530 ± 5°C 59 4 E f f e c t of degree of c r y s t a l l i n i t y on micro-hardness 66 5 E f f e c t of degree of c r y s t a l l i n i t y on e l a s t i c moduli . . . . . . . . 70 6 E f f e c t of degree of c r y s t a l l i n i t y on frac t u r e stress 73 7 E f f e c t of environment upon slopes and intercepts of log V - log diagrams of annealed glass 79 V = AK n 8 E f f e c t of degree of c r y s t a l l i n i t y upon slopes and intercepts of log V - log diagrams (tested i n water) 87 V = AK» 9 E f f e c t of degree of c r y s t a l l i n i t y upon slopes and intercepts of log V - log diagrams (tested i n toluene) 90 V = AK* 10 C r i t i c a l stress i n t e n s i t y factors and fracture surface energies of glass and glass-ceramics . . . . 93 11 Summary of ( ) and ( — — ) 2 f o r glass °GC EGC ceramics 1 2 8 XV LIST OF TABLES Table Page 12 Summary of ( ) and ( ) for glass-°GC YGC ceramics 131 13 C r i t i c a l flaw size in samples used in transverse rupture tests 133 2 2 y o f 14 Summary of activation energy calculated from crack velocity data 154 1 1. INTRODUCTION The most c h a r a c t e r i s t i c mechanical property of glass and glass-ceramics i s b r i t t l e n e s s . These materials deform e l a s t i c a l l y up to a c e r t a i n stress and then suddenly break. The fracture strength i s extremely s e n s i t i v e to the surface conditions and i s usually determined by the s i z e of surface flaws. The fracture strength i s r e l a t e d to flaw dimension c by a modified G r i f f i t h ' s equation''": _ 1 ( 2 E "± )H (1) Fr y c where y = A geometrical factor E = Young's modulus = E f f e c t i v e surface energy. For a long period of time, fracture i n glass was assumed to depend upon flaw geometry. Later i t was r e a l i z e d that fracture was also affected by active environments. The f i r s t evidence for strength reduction i n glass by an external 2 environment was found by Grenet . Glass laths loaded r a p i d l y were stronger than those loaded slowly. In addition, a time delay to f a i l u r e was observed i n which glass laths would support a load for a period of time before f a i l u r e . This dependence of fracture strength upon the time of loading has been termed S t a t i c Fatigue or Delayed F a i l u r e and i s observed i n many ceramic s o l i d s . S t a t i c fatigue data are commonly expressed as stress versus time to f a i l u r e as shown i n Figure 1. A stress below which f a i l u r e w i l l not occur i s c a l l e d the s t a t i c fatigue l i m i t . 2 16,-DURATION OF LOAD (sec) Figure 1 Stress-time c h a r a c t e r i s t i c s of annealed soda lime glass-rods V i n diameter, i n bending (after Shand 7). 3 1.1 Previous Work on S t a t i c Fatigue of Glass 4 Preston observed that glass can carry a heavier load f o r a few seconds than i t can carry f o r a minute; i t can carry a heavier load for a minute than f o r an hour. He c a l c u l a t e d a fatigue curve f o r annealed s o d a - l i m e - s i l i c a t e glass and p o r c e l a i n as shown i n Figure 2. Strength measurements were done by using rods of 8.35 mm (V1) diameter. Later Baker and Preston"* i n v e s t i g a t e d the phenomenon of strength decay or s t a t i c f a t i g u e i n more d e t a i l . They examined soda-lime gla s s , Pyrex gla s s , s i l i c a glass and p o r c e l a i n . They measured the t e n s i l e strength of these materials i n various surrounding media and found that the t e n s i l e strength of glass i n vacuum i s f a i r l y independent of the time of loading. However, i f the glass were exposed to moisture, i t r a p i d l y l o s t i t s strength under s t r e s s . I t was concluded that the strength decay i s mainly due to chemical attack i n the flaws of glass by water and p o s s i b l y by CO^. They found a r e l a t i o n -ship between t i m e o f f a i l u r e and s t r e s s as shown below: S = [Cj/log C 2 t] + C 3 , (2) where S = Breaking s t r e s s t = Time of f a i l u r e and are a r b i t r a r y constants. 3 Orowan observed a s i m i l a r phenomenon. He found that glass can be broken by stresses f a r below the ordinary breaking s t r e s s as measured i n short-time t e s t s , provided that the load i s applied f o r a s u f f i c i e n t l y long time. He observed that about a t h i r d of the short-time breaking s t r e s s 4 Figure 2 Fatigue of glass and porcelain under steady loads (after Preston^). 5 i s s u f f i c i e n t to produce f r a c t u r e , i f i t i s sustained for a number of weeks. Gurney and Pearson performed both c y c l i c and s t a t i c fatigue experiments on s o d a - l i m e - s i l i c a t e glass and concluded that an important point i n delayed f a i l u r e was the time of loading (duration) and not whether the loading was c y c l i c or s t a t i c . 7 8 Shand ' , i n reviewing the work on s t a t i c fatigue, calculated the weakening of t y p i c a l specimens during the loading period. A mean stress-time curve was determined for a group of 8.35 mm (V) diameter rods of annealed soda-lime glass and the r e s u l t s are shown i n Figure 1. From these r e s u l t s he correlated the weakening of a specimen to the growth of a flaw under a constant applied stress as follows. From Figure 1 i t i s found that the breaking stress for a period of loading of t, seconds i s a p s i , then the r e l a t i v e remaining strength a f t e r a period of loading of t seconds may be represented by a Relative Remaining Strength = — (3) b where i s the breaking stress for a period of loading of ( t ^ - t) seconds as taken from Figure 1. The corresponding graph f o r 2 applied s t r e s s e s , 10000 p s i and 5500 p s i i s as shown i n Figure 3. This shows that the weakening (or rate of flaw growth) i s small u n t i l a large f r a c t i o n of the breaking time i s reached. At t h i s point flaw growth accelerates and s t r e s s -flaw geometry condition approaches the c r i t i c a l value given by Griffith"'" f o r 8 spontaneous crack propagation. Therefore Shand concluded, that stresses i n glass w i l l cause slow propagation of flaws and the rate of propagation w i l l increase as the condition of rupture i s approached. 6 Figure 3 Weakening of glass rods during fracture as computed from stress-time c h a r a c t e r i s t i c s curve (A), c?i = 5500 p s i (B) , oi = 10,000 p s i (After Shand 8) 7 Mould:*'"LU'"LJ''X':> and Southwick"""^ studied the strength of glass (S) as a function of f i v e v a r i a b l e s : time, temperature, ambient humidity of the atmosphere, abrasion depth and abrasion age. The specimens were microscope s l i d e s of s o d a - l i m e - s i l i c a t e glass abraded i n s i x d i f f e r e n t ways and broken i n flexure so that a l l f r a c t u r e originated i n the abraded area. They found that there was no change i n strength with time at l i q u i d nitrogen temperature (-196°C). Hence the breaking strength at l i q u i d nitrogen temperature (S ) provided a normalizing f a c t o r . When the r a t i o n S/S n was plotted as a function of log f a i l u r e time at stress S for d i f f e r e n t surface treatments, a s e r i e s of curves of the same shape were found, as shown i n Figure 4. The average f a i l u r e time at S/S = % c a l l e d tj was a n -3 strong function of surface treatments. One of the most f a s c i n a t i n g r e s u l t s of Mould's work i s the "Universal Fatigue Curve" (UFC) as shown i n Figure 5. Here reduced strengths, S/Sn are plotted against reduced time log t / t T . Despite a wide v a r i e t y of abrasive treatments, a l l the data are w e l l represented by a s i n g l e smooth curve. Figure 6 shows the e f f e c t of temperature on r e l a t i v e strength (S/S ) for several fixed f a i l u r e times. Mould and Southwick divided t h i s plot into 4 zones namely A, B, C and D as shown i n Figure 6 and q u a l i t a t i v e l y explained t h i s phenomenon as follows. At low temperature and very short f a i l u r e time, (Zone A), f a i l u r e stress i s nearly independent of time and temperature. This i s believed to be due to the fact that s i g n i f i c a n t chemical i n t e r a c t i o n with the environment i s not possible under these conditions. In Zone B, chemical i n t e r a c t i o n or stress-enhanced chemical reaction begins to dominate and hence s t a t i c fatigue i s very pronounced. Zone C probably 8 LOAD DURATION (sec.) a Severe g r i t b l a s t b Mild g r i t b l a s t Emery clpt h perpendicular to stress d 600 g r i t e 320 g r i t f 150 g r i t p a r a l l e l to stress c 150 g r i t Figure 4 Fracture time as a function of reduced strength S/Sn for d i f f e r e n t surface treatments of soda-lime glass (After Mould and Southwick x ). 9 a Severe g r i t b l a s t b Mild g r i t b l a s t Emery Cloth perpendicular to stress d 600 g r i t e 320 g r i t f 150 g r i t p a r a l l e l to stress c 150 g r i t Figure 5 Universal fatigue curve for glass abraded ^ i n various ways (After Mould and Southwick ) 10 U 1 1 100 200 300 400 500 600 700 800 900 TEMPERATURE (°KJ Figure 6 E f f e c t of time and temperature on r e l a t i v e strength (After M ould 1 3). 11 r e f l e c t s the e f f e c t s of a counter process such as desorption of water. In Zone D, the glass becomes s o f t enough f o r f a i l u r e by viscous flow. They also found that the s t a t i c fatigue l i m i t i s about one t h i r d of the normally measured short time strength. The e f f e c t of the surrounding 13 medium on s t a t i c f a t i g ue behaviour i s shown i n Figure 7 .; I t can be seen that the f a t i g u e curves under the d i f f e r e n t conditions studied are e s s e n t i a l l y p a r a l l e l to one another. An a l t e r n a t i v e way of i l l u s t r a t i n g s t a t i c fatigue i s by p l o t t i n g v e l o c i t y (V) of a s u b c r i t i c a l crack as a function of the s t r e s s i n t e n s i t y 14 f a c t o r (Kj) . A schematic lnV-K^ diagram i s shown i n Figure 8. Three c h a r a c t e r i s t i c regions of crack growth are apparent from t h i s f i g u r e . At low values of the s t r e s s i n t e n s i t y f a c t o r region I, crack growth i s exponentially dependent on the .stress i n t e n s i t y f a c t o r and also dependent on the environment as shown i n Figure 9. In the plateau region (region II) the crack v e l o c i t y i s nearly independent of the applied s t r e s s - i n t e n s i t y . In region I I I , the crack v e l o c i t y i s again exponentially dependent on K^ . U n i v e r s a l fatigue curves can be c a l c u l a t e d from lnV-I?_ data by 17 assuming the crack s i z e and geometry . For a shallow surface crack whose length along the surface i s much greater than i t s depth L , = a* /TrL~. Since the s t r e s s i n t e n s i t y f a c t o r i s proportional to the load, K^/K^, = a^ aN where i s the c r i t i c a l s t r e s s i n t e n s i t y f a c t o r and i s the breaking strength at l i q u i d nitrogen temperature. The logarithm of reduced time to f a i l u r e , l o g ( t / t ^ ) i s obtained by numerical i n t e g r a t i o n of lriV-K^. data or a n a l y t i c a l i n t e g r a t i o n of the equation of v e l o c i t y and s t r e s s i n t e n s i t y f a c t o r . Wiederhorn and Bolz"^ found the data of v e l o c i t y and 12 1 0 , i c 3 icr2 io"' i IO too icoo io * LOAD D U R A T I O N (sec) Figure 7 Reduced strength Vs load duration (log scale) for specimens tested immersed i n d i s t i l l e d water and i n nitrogen atmospheres of 0.5% and 43% r e l a t i v e humidity (After Mould J-1) Figure 8 Schematic stress i n t e n s i t y factor-crack v e l o c i t y diagram for a material i n a corrosive environment. 14 Figure 9 Dependence of crack v e l o c i t y on stress i n t e n s i t y f a c t o r , i n soda-lime s i l i c a glass (After Wiederhorn 25). 15 stress i n t e n s i t y f a c t o r to f i t into an equation, V = V exp [ (-E* + b K ) /RT] (4) o 1 at stage I Integration of equation (4) gives K /K = 2_ = 0.5 - ( ) log ( t / t ^ ) (5) The r e s u l t s of Wiederhorn and h i s coworkers"^ were obtained by 18 the double c a n t i l e v e r beam (DCB) technique. In t h i s technique i t i s d i f f i c u l t to control crack v e l o c i t y because of increasing stress i n t e n s i t y 19 with crack length. Recently Williams and Evans showed how the double 20 torsion (DT) technique could be used i n crack v e l o c i t y measurements. With t h i s specimen, i s independent of crack length and hence i t i s easy to produce a stable crack. The theory of the double tor s i o n technique i s given i n Appendix 1. 1.2 S t a t i c Fatigue Models and Mechanisms The e a r l i e s t attempt to investigate the mechanism of s t a t i c fatigue 3 1 was by Orowan . He approached the problem by considering the G r i f f i t h ' s r e l a t i o n : where a = Breaking stress E = Young's modulus 16 Y = Surface energy C = Depth of the most severe surface crack. He proposed that a decrease i n surface energy caused by the adsorption of species from the environment was responsible for lowering the breaking stress i n an active environment. If fracture occurs r a p i d l y , the adsorbed f i l m cannot advance as f a s t as the crack t i p . The stress necessary to produce such a rapid fracture i s obtained from equation (6) by using the surface energy which i s obtained i n vacuum measurement. If on the other hand the crack propagates very slowly,the adsorbed species have plenty of time to d i f f u s e and to reduce the surface energy at the t i p of the crack. This reduces the fracture strength of the glass according to equation (6). The r a t i o of breaking stress f o r very rapid and very slow fracture i s then equal to the square root of the r a t i o of the two surface energies. 21 Charles also adopted G r i f f i t h ' s flaw theory as the s t a r t i n g point for a theory of s t a t i c fatigue of glass. He assumed that p r e - e x i s t i n g cracks grow under stress-enhanced corrosion. When one of these cracks reaches the c r i t i c a l s i z e , the material f a i l s . He proposed that the flaw growth process should involve a chemical reaction and should be activated by both temperature and stress. The f i n a l expression for t i m e - t o - f a i l u r e i s Log t : = n log 1/a - log K" ' (7) 9. where t = Time of f a i l u r e a = Applied stress n, K''' are constants 17 21 Based on t h i s theory Charles calculated the a c t i v a t i o n energy for s t a t i c fatigue i n soda-lime glass and found that i t i s equal to the a c t i v a t i o n energy for Na + ion d i f f u s i o n . The theory that has been most successful i n explaining s t a t i c fatigue i n many ceramic materials i s the one proposed by Charles and H i l l i g 22 23 ' i n the early 1960's. They also assumed that s t a t i c fatigue i s caused by a stress-enhanced chemical reaction that occurs at crack t i p s where the stress i s high. The s t a r t i n g point f o r t h i s theory i s the absolute reaction rate theory. If a chemical reaction i s con t r o l l e d by an activated process, then the rate of reaction w i l l be kT K = ( — ) [ e x p (-AF*/RT) - exp (-AF*/RT)] (8) where k = Boltzman's constant h = Planck's constant R = Gas constant T = Temperature AF* = Free energy of formation of the activated complex from the reactant AF* = Free energy of formation of the activated complex from P reaction products. For a glass surface undergoing chemical attack i n a corrosive environment, the rate or v e l o c i t y of recession of the surface, V, w i l l be proportional to the reaction rate, K. If AF* >> AF* the v e l o c i t y of recession i s V exp (-AF*/RT) (9) o r IB Assuming that the a c t i v a t i o n energy, AF* may be expanded i n a Taylor's s e r i e s as a function of s t r e s s and taking the f i r s t two terms of s e r i e s gives: AF* , " = AF* (a = o) + 6AF* N r ( a ) r 6a 1 a=o 22 23 Charles and H i l l i g ' c a l l e d AF* (a = o) = E* SAF* . , _ . •' -r(a) I - V* Sa a=o E*~ =• A c t i v a t i o n energy of the chemical r e a c t i o n i n the absence o of s t r e s s . V* = A c t i v a t i o n volume. By taking curvature i n t o account, the v e l o c i t y of recession of the crack t i p under the combined e f f e c t of s t r e s s and chemical re a c t i o n i s Y V V = V exp - [(E* - V*a + )/RT] (10) O O P where a = T e n s i l e s t r e s s at the t i p of the crack Y = Surface energy Y = Molar volume of the s o l i d m p = Radius of curvature of the crack t i p Y V m. — = Free energy d i f f e r e n c e between a f l a t and a curved surface. I f the crack shape i s assumed to be e l l i p t i c a l , then a, the s t r e s s of the 24 crack t i p i s given by the I n g l i s r e l a t i o n o = 2 S /T7P" -(H) S = Applied s t r e s s L = Length of surface crack 19 and also K = S / TTL (12) = Stress intensity factor Substituting equations (11) and (12) in equation (10) gives 2V*K Y V V = V exp - [ (E* — — - + )/RT] (13) o o / p / up Equation (13) may be used directly to obtain an approximation for 25 the static fatigue limit . A reasonable criterion for the static fatigue limit is that the velocity of the crack tip should be equal to the, general rate of recession i.e. 2V*K Y V - = / up Rearranging equation (14) K. I 2V* / p (15) 22 23 A more exact procedure is followed by Charles and H i l l i g ' . They found that the static fatigue limit should occur when d(L/p)/dt = 0 and the fin a l form of their equation is T T _ 3 y Vm /T (16) I ' 4V* / p Wiederhorn"^^further refined Charles and H i l l i g ' s theory to find out the dependence of crack growth rate on environment and crack tip stress. The equation obtained by Widerhorn i s : V* K y V V = A p° exp {[2/3 - ]/RT} (17) A / P v Up where p. is the concentration of the active species at the crack tip and A is a constant. Wiederhorn's results are shown in Figures 9 and 10. Figure 10 Dependence of crack v e l o c i t y on stress i n t e n s i t y f a c t o r , K j , and temperature 25 i n soda-lime s i l i c a glass (After Wiederhorn ). 21 A more detai l e d understanding of s t a t i c fatigue was done by 15 16 Wiederhorn e t . a l . ' They hypothesized that the crack t i p environment plays a major r o l e i n crack growth. The environment of a crack t i p i s characterized by (1) the large r a t i o of the surface area of the crack to volume within the crack (2) the leaching action of the environment on the fresh fracture surface as the crack propagates. In an e f f o r t to duplicate these two conditions, studies with ground glass water s l u r r i e s 16 were conducted . The pH of the s l u r r y was measured either with narrow range i n d i c a t o r paper or with a glass electrode. The pH of the glass s l u r r i e s was found to be dependent on the glass composition. The pH for s i l i c a glass was low (- 4), suggesting that an a c i d i c environment ex i s t s at the t i p s of cracks i n t h i s glass. This low pH i s the r e s u l t of a reaction between water and s i l a n o l groups on the glass surface. High pH s l u r r i e s (- 12) were obtained with glass containing large concentration of a l k a l i ions ( s o d a - l i m e - s i l i c a t e ) , the high pH being p r i m a r i l y due to alkali-hydrogen ion exchange between the s o l u t i o n and the glass. A f t e r e s t a b l i s h i n g the nature of the crack t i p environment, 15 Wiederhorn and h i s coworkers studied the e f f e c t of pH of the environment on crack propagation i n glass. They chose three glass compositions, soda-l i m e - s i l i c a t e , vitreous s i l i c a and low a l k a l i b o r o s i l i c a t e and used buffered solutions ranging i n pH from -0.8 to 14.8. In general, the pH influenced the slope of the crack propagation curve. They found that the slope of lnV-K^ plots decreases with increasing pH of the. test invironments. They also found that the e f f e c t of pH was more pronounced i n the low crack v e l o c i t y region than i n the high crack v e l o c i t y region. As t^ he crack moves, 22 the crack t i p continuously exposes fresh fracture surface. This leads to an i o n i c reaction at the crack t i p between the s o l u t i o n and the glass. Hence the composition of the s o l u t i o n at the crack t i p can be d i f f e r e n t from that of the bulk s o l u t i o n . This leads to d i f f u s i o n between the bulk e l e c t r o l y t e and the crack t i p s o l u t i o n . The rafe of d i f f u s i o n depends upon the concentration difference between these two solutions and time. Hence at low crack v e l o c i t i e s , there i s enough time for d i f f u s i o n to take place and the composition of the s o l u t i o n at the crack t i p becomes s i m i l a r to that of the bulk e l e c t r o l y t e . However at high crack v e l o c i t i e s , there i s not enough time for t h i s d i f f u s i o n to occur and the concentration or pH of the crack t i p s o l u t i o n i s determined by the glass composition. Hence two regimes of behaviour are expected for a moving crack: at slow v e l o c i t i e s the composition and pH of the crack t i p s o l u t i o n should be dominated by the external environment; at high crack v e l o c i t i e s the composition and pH of the crack t i p s o l u t i o n should be determined by the glass composition. Wiederhorn"'"'' also found that the slope of In V-K^ plots obtained i n water for soda-lime glass and s i l i c a glass coincided with the slope of pH = 12 and pH - 4 r e s p e c t i v e l y . This r e s u l t supports the 16 s l u r r y methods of determining pH to approximate the pH at the t i p of a crack i n water. Thp low slope of crack propagation curve at Stage I I , shown i n Figure 10 i s a t t r i b u t e d to the severe environment (high pH) at the crack t i p as explained above. 26 27 Metcalfe e t . a l . ' pointed out that the mechanism proposed by 21 Charles cannot apply to high strength glass filaments because the sharp-ended cracks would need to be u n r e a l i s t i c a l l y small to be consistent with 23 the high strength and small diameters of filaments. They proposed an a l t e r n a t i v e mechanism of s t a t i c fatigue i n these glass f i b e r s which involved an ion exchange between a l k a l i metal ions i n the glass and hydrogen ions from either adsorbed moisture or aqueous s o l u t i o n . This reaction reduces the molecular volume at the surface layer and thus 26 27 generates a t e n s i l e stress at the surface. Metcalfe ' has shown that t h i s t e n s i l e stress would reach very high value so that the glass filaments cracked spontaneously i n the absence of stresses applied externally. These regions of high i n t e r n a l stress are believed to constitute the basic type of G r i f f i t h flaw, rather than the submicroscopic, sharp-ended cracks generally assumed. These workers have also shown that the a c i d i c solutions of low pH were more detrimental to strength than a l k a l i n e s olutions. Additions of sodium ion to an a c i d i c s o l u t i o n reduced the detrimental strength e f f e c t s , and strength l o s t i n acid could be restored by subsequent immersion i n a s o l u t i o n containing sodium ions. 28 R i t t e r and Sherburne have shown that the stress-enhanced corrosion model cannot account for the s t a t i c fatigue of p r i s t i n e s i l i c a t e glasses. They concluded that t h i s inadequacy i s probably related to a difference between the fatigue processes that occur at the.tips of deep cracks as opposed to shallow cracks i n r e l a t i v e l y flaw-free surfaces. They have also proposed that i t i s e n t i r e l y possible that stress-corrosion and Na +-H + exchange occur simultaneously. 29 Cox has developed an atomistic theory which i s based on the weakening of Si-0 bond by mobile sodium ions due to e l a s t i c s t r a i n when these mobile sodium ions occupy i n t e r s t i t i a l s i t e s . Fracture i s i n i t i a t e d 24 by the probability that a number of adjacent Si-0 bond are broken simultaneously to form a self-generating flaw. Time, humidity, temperature and severity of surface flaws expl i c i t l y enter into the strength expression. The weakness of this theory is the questionable assumption that the migrating cation weakens the Si-0 network. It would also be necessary for the cations to overcome a large electrostatic energy barrier in coming together to form the self generating flaw. 30 Recently Doremus objected to the assumption of H i l l i g and 23 30 Charles that the slope of lnV-K^ plot is independent of stress. Doremus argued that there are no experimental facts to support this and also that the activation volume is rarely independent of pressure. Alternatively 30 Doremus found that static fatigue data also f i t an inverse relation between log crack velocity and load better than direct proportionality. Hence an equation of the following form is proposed. V = V exp (-a /a ) (18) T • where V and a are stress-independent coefficients and a is the applied T stress. V is the limiting reaction rate at high stress and where B is a constant which is proportional to the activation energy for the reaction of water with the oxide network, E is Young's modulus, R is the gas constant and T is temperature. 1.3 Summary of the Theoretical Models 3 1. Orowan proposed that static fatigue is caused by a decrease 25 i n surface energy r e s u l t i n g from the adsorption of species from the environment. According to t h i s theory the t h e o r e t i c a l strength of the material w i l l decrease due to environment. 21 2. The theory of Charles describes a crack growth mechanism and a t t r i b u t e s the loss of strength to the slow growth of a crack u n t i l i t reaches the c r i t i c a l s i z e . Growth of the s u b c r i t i c a l crack to c r i t i c a l s i z e was a t t r i b u t e d to a stress-enhanced chemical reaction at the t i p of the crack. 15 16 3. Wiederhorn ' hypothesized that the crack t i p environment played a major r o l e i n crack growth. He showed that the crack t i p environment was d i f f e r e n t from the bulk e l e c t r o l y t e . At high crack v e l o c i t i e s , the concentration or pH of crack t i p s o l u t i o n was c o n t r o l l e d by the glass composition and at slow crack v e l o c i t i e s the pH of crack t i p s o l u t i o n was co n t r o l l e d by the external environment. Wiederhorn has also shown that the pH of the test environments co n t r o l l e d the slope of crack propagation plots (InV -K-j. diagrams) and found that the slope decreased with increasing pH. 26 27 4. Metcalfe ' proposed an ion exchange mechanism for the s t a t i c fatigue i n p r i s t i n e glass f i b e r s . Ion exchange between a l k a l i metal ions i n the glass and hydrogen ions from either adsorbed moisture or aqueous s o l u t i o n , generates a t e n s i l e s t r e s s at the surface. When t h i s t e n s i l e stress reaches a very high value,the glass filaments crack spontaneously 26 i n the absence of external s t r e s s . 29 5. Cox proposed that the Si-0 bond w i l l be weakened by the movements of the migrating a l k a l i ion and f r a c t u r e w i l l be i n i t i a t e d by the number of simultaneously broken Si-0 bonds to form a self-generating flaw. 30 6. Doremus derived a s t a t i c fatigue equation based on stress-23 enhanced corrosion at the crack t i p . The f i n a l expression r e l a t e s InV to the Inverse of stress, 1. 4 Estimation of Time-to-Failure from Growth K i n e t i c s Crack growth k i n e t i c s can be used to measure t i m e - t o - f a i l u r e under constant load. This involves an i n t e g r a t i o n of the V-K^ plot from K-^, i n i t i a l stress i n t e n s i t y factor to K , f i n a l stress i n t e n s i t y f a c t o r . The l c d e t a i l e d d e s c r i p t i o n of t h i s method i s given i n Appendix II. The f i n a l form of equation i s [K ( 2 " n ) - K T J(2-n). " ~ 2 2 A(2-n) L ~ I C " y ] (20) o : y app °a K I i Introducing ~ aPP = ^ — i n the above equation a p l c 1 » fey t ( ^ - ) " - 2 - i ] (2i) a y v / app 3Pp H H 27 where n and A corresppnd to the slope and the intercept of log V - log p l o t s , a i s the applied stress and a i s the proof stress, app p 1.5 Objectives of the Present Work The main aim of the present study was to obtain some understanding of s t a t i c fatigue phenomenon i n glass-ceramics containing d i f f e r e n t volume fr a c t i o n s of c r y s t a l l i n e phase. Crack growth k i n e t i c s for these materials were measured by the double t o r s i o n technique. One objective of t h i s work was to test the d i f f e r e n t s u b c r i t i c a l crack growth models. A c a r e f u l fractographic study was conducted to reveal the mechanism of fracture i n glass-ceramics. Other mechanical properties such as fracture strength, microhardness and e l a s t i c moduli ( s t a t i c method) were also measured i n order to understand fr a c t u r e i n more d e t a i l . Growth-kinetics,density and d i f f e r e n t i a l thermal analysis were also measured i n order to characterise the structure of these glass-ceramics. 28 2. EXPERIMENTAL PROCEDURE 2.1 Ma t e r i a l Preparation 2.1.1 glass Preparation A batch of 495 gms of L i 2 C 0 3 * powder, 933.75 gms of S i 0 2 * * powder and 5 gms of LiNO^*** f i n e c r y s t a l s was prepared and mixed thoroughly i n a b a l l m i l l . This mixture was then heated i n a Platinum -3% Rhodium c r u c i b l e at 1450°C i n a furnace**** to produce glass of compos-i t i o n 17.8 wt% Li 20-82.2 wt% S i 0 2 . The molten glass was s t i r r e d with a long s i l i c a rod to produce thorough mixing. Subsequently f.he molten glass was refined (to remove bubbles) at 1450°C for 24 hours. It was then cast into heated graphite moulds to form rectangular blocks 69.9 mm x 25.4 mm x 50.8 mm (2.75" x 1" x 2") or cylinders of diameter 50.8 mm (2") and height 38.1 mm (1.5"). These blocks were annealed at 470°C for 48 hours and furnace cooled. * Reagent grade supplied by CENCO of Canada Limited. ** Pure grade ground s i l i c a f l o u r supplied by Ottawa S i l i c a Co. Ottawa, I l l i n o i s , U.S.A. *** Reagent grade supplied by A l l i e d Chemicals Canada Limited. **** Super Kanthal Muffle Furnace. 29 2.1.2 Specimen Preparation Rectangular bars 4 0 m m x 3 m m x 3 m m (1.575" x 0.118" x 0.118") were cut from the cast blocks of glass i n a diamond impregnated saw. These specimens were used to measure density and transverse rupture strength. Cylinders 10.2 mm (0.4") diameter and 38.1 mm (1.5") long were d r i l l e d i n a v e r t i c a l core d r i l l i n g machine using a 9.53 mm (0.375") diameter diamond impregnated core d r i l l from the cast c y l i n d e r . These samples were used f o r e l a s t i c moduli measurements. Specimens 69.9 mm x 25.4 mm x 1.5 mm (2.75" x 1" x 0.060") were s l i c e d from the block using a diamond impregnated saw. These specimens were polished with 270 g r i t SiC i n an automatic lapping machine to achieve p a r a l l e l surfaces. These plates were used i n crack v e l o c i t y studies by 19 the Double Torsion Technique 2.1.3 Heat-Treatment A portion of the samples was given a c r y s t a l l i z a t i o n treatment by heating at 530±5°C for d i f f e r e n t lengths of time to produce glass-ceramics having d i f f e r e n t degrees of c r y s t a l l i n i t y . This heat treatment was performed i n a small nichrome wound muffle furnace. A l l these samples were heated from room temperature to 530°C and held at t h i s temperature for the desired lengths of time and then furnace cooled. 30 2.2 Sample Characterization 2.2.1 D i f f e r e n t i a l Thermal Analysis Thermal analyses were performed on powder (-325 mesh s i z e ; 30 to 40 mgm) obtained from as-cast samples i n a d i f f e r e n t i a l thermal analyser*. Pure alumina powder (-325 mesh s i z e ; 30 to 40 mgm) was used as the standard sample and heating rates of 5, 10, 15, 20 and 25°C/min were used. The s t a r t i n g temperature was room temperature (25°C). 2.2.2 Density Measurement The bulk density of the glass and glass-ceramics was calculated by the conventional method. The samples were small rectangular bars 40 mm long 3 mm wide and 3 mm thick (1.575" x 0.118" x 0.118"). A l l four sides of these samples were ground on 240 g r i t SiC p o l i s h i n g paper to remove a thi n layer of the surface which might have a d i f f e r e n t degree of c r y s t a l l i n -i t y than the bulk. The specimens were subsequently f i n i s h e d on 400 g r i t SiC p o l i s h i n g paper to produce smooth surfaces. Care was taken to keep the surfaces of these samples p a r a l l e l . The hand grinding operation was r done so that the surface scratches on the samples lay JL to the length of the sample. These samples were then cleaned i n the u l t r a s o n i c v i b r a t o r * Dupont 900 D i f f e r e n t i a l Thermal Analyser. 31 and l a t e r with water. Samples were then thoroughly rinsed i n e t h y l a l c o h o l d r i e d and stored i n a desiccator. The weight of these samples was recorded by using a balance*. The volume was determined by measuring the dimensions of the samples. The dimensions of the samples were measured with a micrometer. The r a t i o of weight to volume y i e l d s the bulk density. 2.2.3 Metallography 2.2.3.1 O p t i c a l Microscopic Examination The samples were mounted on a 165.1 mm(6.5") diameter and 12.7 mm (0.5") t h i c k brass p l a t e using thermoplastic cement**. Then the samples were ground on an automatic lapping machine as shown i n Figure 11. Coarse grinding was done using 240 g r i t SiC powder and f i n e grinding was accomplished using 400 and 1000 g r i t SiC powder on 3 d i f f e r e n t cast i r o n laps. The p o l i s h i n g was done i n the same automatic lapping machine by using cerium oxide*** as the abrasive. Three to four hours of p o l i s h i n g was required to obtain a scratch f r e e polished surface. These samples * Sartorius s i n g l e pan balance (Model 2432). ** No 7 0C Lakeside Brand supplied by Hugh Courtright & Co., Chicago, U.S.A. *** Cerium oxide "C" supplied by Micometallurgical Limited. 32 Figure 11 Photograph of Automatic Lapping Machine 33 were removed from the brass p l a t e and washed i n ethyl a l c o h o l to get r i d of the thermoplastic cement. Later they were etched i n 3% HF, 2% HC1 and 95% water s o l u t i o n f o r 0.5 minute to 1.5 minute depending on the degree of c r y s t a l l i n i t y i n the sample. The etched samples were subsequently plated with a 60-40 gold-palladium a l l o y i n a D.C. Sputtering System* to improve the r e f l e c t i v i t y of the etched surface. O p t i c a l photomicrographs i n bright f i e l d and dark f i e l d i l l u m i n a t i o n were prepared to characterise the structure. 2.2.3.2 Petrographic Examination A t h i n s e c t i o n was s l i c e d from the o p t i c a l metallographic examination specimen using a diamond impregnated saw.• These t h i n sections were cemented on 'Well petrographic s l i d e s ' with thermoplastic cement. Subsequently these t h i n sections were ground on a m u l t i p l e stage wet hand grinder. This operation gave a very t h i n .section of 0.05 mm ( 0 . 0 0 2 " ) thickness. The samples were removed from the 'Well petrographic s l i d e s ' and washed thoroughly with e t h y l a l c o h o l . They were then sandwiched between a cover p l a t e and a petrographic s l i d e using Canada Balsam and were viewed i n a petrographic microscope. * . HUMMER. . Hummer i s a D.C. sputtering system. A negative p o t e n t i a l i s applied to the 60 - 40 gold-palladium cathode which i s enclosed i n the process chamber at a pressure; 50-500 m i l l i t o r r . This was supplied by Technics Inc., Alexandria, V i r g i n i a 22304, U.S.A. 34 2.2.3.3 Transmission Electron Microscopy (TEM) Part of the sample used in petrographic microscopy was thinned in a micro ion m i l l * u n t i l the specimen had a small hole in i t . These specimens were coated with carbon and used for TEM studies. 2.2.4 Determination of Degree of Crystallinity 31 2.2.4.1 Point-Count Method The basic principle of the point-count method depends on the fact that the proportion of a random array of points on a micrograph which w i l l f a l l on a specific phase is equal to the proportion by volume of that phase. In practice, i t is generally found to be inconvenient to project a random array of points onto a microstructure. A regular array of points is used and i t is assumed that the microconstituents are randomly distributed. It is important that the spacing of the rectangular grid be large with respect to the microstructural features- The volume fraction p^ of the a phase is given by p a = n a/n (22) where is the number of points occurring in the a phase and n is the total number of points. * Micro Ion M i l l produced by Technics Inc., Alexandria, U.S.A. 35 A 3 mm x 3 mm square grid was superimposed on the o p t i c a l micrograph and the number of points ( n a) i n t e r s e c t i n g the c r y s t a l l i t e s were recorded. The t o t a l number of points (n) on the microstructure was 806. The r a t i o of these two number gave the volume f r a c t i o n of c r y s t a l l i n e phase i n the glass-ceramic. An average value of f i v e such readings was taken. 2.2.4.2, X-Ray Method 32 A standard quantitative analysis by the X-ray technique was used. An X-ray diffTactometer* f i t t e d with a goniometer and a proportional counter was used. According to the phase-diagram of the Li^O - SiO^ system shown i n Figure 12, glass having a composition 17.8 wt% li 2 ° ~ 8 2 - 2 w t ^ s i n 2 c a n n a v e maximum of 90% c r y s t a l l i n e Li20.2Si02 i f the glass i s c r y s t a l l i z e d at 530°C. This sample i s taken as the standard sample. It was prepared by c r y s t a l l i z i n g the annealed glass at 530°C for a very long time (48 hours). It was then crushed to powder with the help of a percussion hammer and a small b a l l m i l l . A powder sample of -325, +400 mesh s i z e was taken. The integrated peak area between 22.66° to 26° was taken into consideration. Background i n t e n s i t y close to these peaks (21° - 22.66°and 26° - 27.66°) was measured * P h i l l i p s PW 1009 water cooled X-ray d i f f r a c t i o n unit f i t t e d with North American P h i l l i p s 42 202 type wide range goniometer and Xenon f i l l e d proportional counter. 36 9501 I H 1 1 —I Li 2 0 7 5 8 0 8 5 Si02 W E I G H T % Figure 12 Portion of the phase diagram of L i 2 0 -SiO„ system. 37 and subtracted from the integrated peak to obtain the actual peak area. An average of 20 readings was taken. In order to make sure that the standard sample was f u l l y c r y s t a l l i n e (90% Li^O 2Si02) , the sample was c r y s t a l l i z e d for a d i f f e r e n t length of time at 530°C u n t i l the peak area remained constant. The peak area remained constant a f t e r 22 hours c r y s t a l l i z a t i o n treatment at 530°C. The actual peak area for a l l of the glass-ceramics containing d i f f e r e n t volume fr a c t i o n s of c r y s t a l l i n e phase was calculated by repeating the above procedure. The r a t i o of actual peak area of the standard sample to that of the glass-ceramics containing d i f f e r e n t volume f r a c t i o n s of c r y s t a l l i n e phase, m u l t i p l i e d by 0.9 gave the weight f r a c t i o n of l i t h i u m d i s i l i c a t e present i n each sample. 2.3 K i n e t i c s of C r y s t a l l i z a t i o n The refined molten glass was cast into a heated graphite mold of 152.4 mm long, 12.7 mm wide and 12.7 mm deep. (6" x 1/2" x 1/2"). These bars were annealed at 470°C for 48 hours. Samples 25.4 mm x 12.7 mm x 12.7 mm (1" x 1/2" x 1/2") were cut from the longer glass bars. Twelve of these samples were c r y s t a l l i z e d at 530°C for twelve d i f f e r e n t lengths of time, 30, 60, 90, 120, 190, 240, 300, 390, 495, 660, 1045 and 1320 minutes. Each of these samples was cut into two pieces, 6.35 mm x 12.7 mm x 12.7 mm (1/4" x 1/2" x 1/2") and 19 mm x 12.7 mm x 12.7 mm (3/4" x 1/2" x 1/2") in the diamond impregnated saw. The small samples were used for o p t i c a l 38 metallographic examination to evaluate the degree of crystallinity by the point-count method and subsequently used for microhardness measurement. The large samples were used for X-ray studies to obtain the degree of cr y s t a l l i n i t y . 2.4 Measurement of Elastic Constants 2.4.1 Young's Modulus Glass cylinders of diameter 10.2 mm (0.4") and 38.1 mm (1.5") long (which were prepared by the technique described in Specimen Preparation) were crystallized at 530°C for various lengths of time to obtain the desired degree of cr y s t a l l i n i t y . The ends of these samples were sliced in the diamond impregnated saw to obtain parallel surfaces. They were then com-pressed in a universal testing machine* to 60 MPa and 120 MPa between parallel loading anvils made out of hardened steel as shown in Figure 13. A 12.7 mm (1/2") strain gauge extensometer was used to measure longitudinal strain. In order to obtain reliable results in this procedure the direction of loading should be parallel to the centre line of the sample. This is possible only i f the samples have parallel surfaces and the surfaces of the loading anvils are parallel to each other. Setting up of the loading anvils for parallelism was accomplished with the help of Instron Testing Machine supplied by Instron of Canada Limited. 3 9 Figure 13 Photograph of s t a t i c e l a s t i c moduli measurement set up. 40 a standard sample whose Young's modulus was well known. Here a mild s t e e l cylinder 12.7 mm (1/2") diameter and 25.4 mm (1") long having p a r a l l e l surfaces was used as standard sample. This sample was compressed to 120 MPa and the l o n g i t u d i n a l s t r a i n was determined at 4 postions 90° apart by using the s t r a i n gauge extensometer. The Young's modulus calculated by t h i s process at 4 positions (90° apart) was compared to the known value of 207 GPa (30 x 10 p s i ± 1%). If the loading anvils were p a r a l l e l to each other, a l l the four values of Young's modulus calculated should be equal to 207 GPa. If not the loading a n v i l s were shimmed by 0.025 mm (0.001") brass shim sheets u n t i l the values of Young's modulus calculated by t h i s procedure equalled 207 GPa. Annealed glass samples and glass-ceramics containing low volume fractio n s of c r y s t a l l i n e phase were compressed to 453.6 kgs. Glass ceramics having higher degrees of c r y s t a l l i n i t y were compressed to 907.2 kgs. An average of eight values was taken. 2.4.2 Poisson's Ratio The samples used for the determination of Young's modulus were . also used for t h i s purpose. The l a t e r a l elongation was measured by using 12.7 mm (0.5") s t r a i n gauge extensometer which was connected d i a m e t r i c a l l y by a s p e c i a l f i x t u r e . The l a t e r a l elongation was measured at 4 d i f f e r e n t positions (90° apart) and an average of eight values was taken. The samples were compressed to the same load as that used for the Young's 41 modulus measurements. 2.5 Measurement of Mechanical Properties 2.5.1 Microhardness Measurement Samples used for o p t i c a l metallography were also used to determine the microhardness. A Diamond Pyramid Hardness(DPH) indentor i n combination with a Tukon hardness tester was used at a load of 50 gms. A l l the indentations were made on the i n t e r - c r y s t a l l i n e phase i n the samples containing up to 50% c r y s t a l l i n e phase. Above 50%, the indentations were i n the c r y s t a l l i n e phase. An average of f i f t e e n values was taken on each sample. 2.5.2 Transverse Rupture Strength Samples used for density measurements were also used to determine the transverse rupture strength of the glass and glass-ceramics. Transverse rupture tests were performed using a universal t e s t i n g machine* with each sample r e s t i n g i n a three point bending f i x t u r e . The three loading points were sapphire rods. The span was 25.4 mm ( l 1 ) long. Samples were loaded at a constant crosshead speed of 4.2 x 10 ^ m.sec ^ (0.01"/min) to f a i l u r e . The load was applied to the f i x t u r e by means of a compression cage. The tests were performed i n toluene and i n water. * Instron Testing machine. 42 The fracture s t r e s s , o\_ , of a bar fractured i n three-point bending i s a Fr 3 PL 2 b d 2 (23) where P = Fracture load L Span length (25.4 mm) b = Breadth of specimen d = Depth of specimen An average of eight to ten values was taken. The fractured samples were thoroughly rinsed i n ethyl a l c o h o l , dried and stored i n a desiccator for fractographic examination. Slow crack growth tests were performed i n four environments, toluene,nitrogen at 30% r e l a t i v e humidity (rh), 70% rh and water. The 19 double tor s i o n technique was used i n t h i s study. The theory underlying the double tor s i o n technique has been described i n Appendix 1. The specimens consisted of rectangular s l i d e s 69.85 mm long, 25.4 mm wide and 1.52 mm thick (2.75" x 1" x 0.06") grooved along one side to leave approximately h a l f the specimen thickness. A notch was 2.6 Slow Crack Growth Tests 2.6.1 Slow Crack Growth of Annealed Glass 43 then introduced to a depth of 15.00 mm (0.595") to i n i t i a t e the crack. A t y p i c a l specimen i s shown i n Figure 14. The dimension W was measured using a vernier c a l i p e r , t was measured using a micrometer and t was n measured with a t r a v e l l i n g microscope. The loading f i x t u r e i s depicted i n Figure 15. The sample was supported on two p a r a l l e l s t a i n l e s s s t e e l r o l l e r s and the load was applied v i a two hemispheres attached to the f i x t u r e ' s upper p l a t e . The whole assembly was placed i n a 166.00 mm (7 1/2") diameter, 90.00 mm (3 1/2") t a l l and 3.00 mm (0.11") thick glass d i s h that rested on a 'D' compression load c e l l . This set up was used for both the water and toluene environ-ments . The study of slow crack growth for annealed glass at 30% rh and 70% rh was done i n a small p l e x i - g l a s s chamber (12.70 mm diameter) as shown i n Figure 16. Humidity i n t h i s chamber was c o n t r o l l e d by mixing known volumes of water vapour and nitrogen gas i n the apparatus, shown i n Figure 17. The volume of gas i n the chamber was c o n t r o l l e d by a set of manometers. Humidity i n the chamber was measured according to the ASTM^ method. The samples were e q u i l i b r a t e d f o r 4 hours. For a l l samples the following procedure was used to measure the crack v e l o c i t y as a function of stress i n t e n s i t y . a. The specimen was loaded incrementally at a crosshead speed of 4.25 x 10 ^ m sec (0.001" min "*") u n t i l a rapid load drop and r e l a x a t i o n curve was obtained. This indicated the formation of a sharp crack. 44 < w Figure 14 Specimen used i n double t o r s i o n t e s t . gure 15 Loading f i x t u r e used i n double Figure 16 Schematic drawing of humidity chamber. NITROGEN LONG GRADUATED CYLINDERS WATER I iff 1 MANOMETER U TO ACRYLIC BOX •MANOMETER IMMERSION TUBE Figure 17 Flow diagram of humidity c o n t r o l l i n g set up 48 b. The load was increased at a crosshead speed of 8.5 x 10 m sec (0.002" min "*") to accelerate the crack and a second load r e l a x a t i o n curve was produced. c. When the load had decreased to a nearly constant value, the specimen was unloaded and removed from the f i x t u r e . d. The f i n a l crack length was measured by using a dead weight loading apparatus to open the crack and a t r a v e l l i n g microscope. Measurement was performed by t o r s i o n a l l y loading the specimen to a load below the value at the end of load r e l a x a t i o n . e. Load relaxations due to the f i x t u r e and machine were evaluated by using a dummy specimen. The dimensions of t h i s specimen were the same as the test sample but without the centre groove and the notch. The loading sequence f or th i s sample was exactly the same as that of the test specimens. f. A new load-relaxation curve e n t i r e l y due to the crack growth i n the sample.was obtained by subtracting the back ground relaxation (load r e l a x a t i o n due to f i x t u r e and load c e l l ) from the load r e l a x a t i o n curve obtained i n b. A f u l l scale load of 1.83 Kgs(4 lbs)with a load suppression -4 -1 scale was used to measure the load. A chart speed of 8.5 x 10 m sec (2" min "*") was used throughout the experiment. The crack v e l o c i t y at any point on the load r e l a x a t i o n curve was obtained by s u b s t i t u t i n g the value of the slope at that point ( )» the load (P), the f i n a l length of crack dt (a^) and the f i n a l load at the end of load r e l a x a t i o n (P^) into equation A(11)[Appendix 1]. The corresponding stress i n t e n s i t y was computed from 49 the load (P) and the dimensions of sample and f i x t u r e according to equation (A6) [Appendix 1] Three to four experiments were performed to obtain one v e l o c i t y s t r e s s - i n t e n s i t y curve. 2.6.2 Slow Crack-Growth of Glass-Ceramics Glass specimens 68.95 mm long 25.4 mm wide and 1.52 thick (2.75" x 1" x 0.060") were c r y s t a l l i z e d at 530°C for various lengths of time to obtain the desired degree of c r y s t a l l i n i t y . These specimens were polished with 270 g r i t - S i C p o l i s h i n g paper to eliminate any surface c r y s t a l l i z a t i o n . The procedure which was used for annealed glass was followed here to obtain v e l o c i t y - s t r e s s - i n t e n s i t y curves. Two environ-ments, toluene and water were used. 2.7 C r i t i c a l Stress Intensity Factor Measurement The c r i t i c a l s tress i n t e n s i t y f actor (Kj^) f ° r the glass and 19 glass-ceramics was obtained by the double torsion technique . Double torsi o n samples which were used i n slow crack growth measurements were reassembled i n the same f i x t u r e as described i n Section 2.6 and f a s t - 4 - 1 -1 loaded at a crosshead speed of 2.1 x 10 m sec (0.5" min - ) to f a i l u r e i n a toluene environment. The f a i l u r e load (P ) was substituted c i n equation (A6) [Appendix 1] to obtain Kjr,. The fr a c t u r e samples 50 were thoroughly rinsed i n et h y l a l c o h o l , dried and stored i n a desiccator f o r fractographic examination. 2.8 Fractographic Examination Fractured surfaces of transverse rupture test samples and slow crack growth measurement samples were coated with a 60-40 gold-palladium a l l o y i n a D.C sputtering system and these surfaces were examined by scanning electron microscopy. 51 3. RESULTS 3.1 D i f f e r e n t i a l Thermal Analysis (DTA) DTA plots for 82.2 wt% SiC>2 - 17.8 wt% L i 2 0 glass are shown i n Figure 18. The number printed on each of the plots corresponds to the heating rate (h) used. Conventional extrapolation methods were used to determine the annealing temperature and also the peak temperature (T^) that corresponds to the maximum d e f l e c t i o n . The annealing temperature* was found to be 470°C. The peak temperatures at various heating rates are l i s t e d i n Table 1. The thermogram at a given heating rate was found to be the same for a bulk piece of the material as for the crushed powder. The a c t i v a t i o n energy for the c r y s t a l l i z a t i o n process was calculated from the slope of the plot ln(h/T ) Vs 1/Tp, where h = heating rate i n °C/min and T = temperature at which the maximum d e f l e c t i o n occurs. The plot of P 2 33 ln(h/T ) versus 1/T i s shown i n Figure 19. The a c t i v a t i o n energy for P P c r y s t a l l i z a t i o n was found to be 180 KJ/mole (43 Kcal/mole). 3.2 Density Study The de n s i t i e s of the glass and glass-ceramics are l i s t e d i n Table 2. Figure 20 shows the t h e o r e t i c a l density based on a simple r u l e of mixtures and the experimentally determined values. A reasonable f i t i s * Approximately the glass t r a n s i t i o n temperature. 0 \00 200 300 400 500 600 700 TEMPERATURE , DEG. c. Figure 18 D i f f e r e n t i a l thermal analysis of annealed glass. Table 1 SUMMARY OF DTA OF THE GLASS Heating Rate <j>,, °C/min. Peak Temperature T °C(°K) P 1/T , 10 3 */T , 10~ 6 V. -1 mm In (cf./T 2) P 5 580 (853) 1.1723 6.8718 - 11.88 10 605 (878) 1.1390 12.972 - 11.25 15 614 (887) 1.1274 19.065 - 10.86 20 627 (900) 1.1111 24.691 - 10.60 25 634 (907) 1.025 30.390 - 10.40 0 2 -4 -6 -8 I VOLUME FRACTION Figure 20 Densities of the glass-ceramics as a function of volume f r a c t i o n of c r y s t a l l i n e phase. Table 2 DENSITY OF THE GLASS AND GLASS-CERAMICS Volume Fract i o n of C r y s t a l l i n e Phase 3 3 Bulk Density 10 kg/m 0 2.323 0.1 2.326 0.2 2.338 0.4 2.346 0.5 2.356 0.7 2.361 0.85 2.383 a-* 57 seen between the t h e o r e t i c a l curve and experimental points. The calculated porosity was found to be les s than 2%. 3.3 K i n e t i c s of C r y s t a l l i z a t i o n The percentage of c r y s t a l l i n e phase a f t e r various times of annealing at 530 ± 5° C i s given i n Table 3. At low percentage of c r y s t a l l i n e phase (< 5%) i t i s d i f f i c u l t to measure the volume f r a c t i o n by the X-ray method. At very high degree of c r y s t a l l i n i t y i t becomes d i f f i c u l t to measure the volume f r a c t i o n by the point count analysis. Figure 21 shows the dependence of f r a c t i o n c r y s t a l l i z e d on the time of annealing at 530°C. The corresponding microstructures are shown i n Figure 22. 34 Morgan has shown that the time dependence of volume c r y s t a l l i z a t i o n i s described by the equation a = a Q [1 - exp ( - K t n ) ] (24) where a = Saturation value of c r y s t a l l i z a t i o n o t = Time of c r y s t a l l i z a t i o n K = Constant n = Constant determined by the shape of the i n d i v i d u a l c r y s t a l s The above equation can be written as a In In ( — ) = In K + n In t (25) a - a o Ln In ( o ) i s plotted as a function of In t for the glass-ceramic, a - a o Figure 21 Volume f r a c t i o n of c r y s t a l l i n e phase i n g l ceramics as a function of time at 530°C. Table 3 VOLUME FRACTION OF CRYSTALLINE PHASE IN GLASS-CERAMICS AFTER HEAT-TREATING FOR VARIOUS LENGTH OF TIME OF 530 ± 5°C Time, Minutes X-ray Method Point-Count Analysis Weight Fraction Volume Fr a c t i o n Volume F r a c t i o n 30 — - 0 60 - - 0 90 - - 0.02 20 - - ^ 0.04 190 - - 0.05 240 0.164 0.169 0.186 300 0.377 0.386 0.37 390 0.605 0.613 0.550 495 0.784 0.789 -666 0.816 0.821 -1045 0.889 0.893 -1320 0.894 0.897 — 60 10 ym Figure 22 Optical micrograph of glass-ceramic containing: (a) .05 volume fraction of crystalline phase. Figure 22(b) 0.15 to 0.20 volume fraction of crystalline phase. Figure 22(c) M 10 ym 0.35 volume f r a c t i o n of c r y s t a l l i n e phase. I — I 10 um Figure 22(d) 0.55 volume f r a c t i o n of c r y s t a l l i n e phase. 63 as shown i n Figure 23. Here a i s taken as 0.90. A good linear-dependence o i s seen as predicted by the above equation and the stra i g h t l i n e has a slope equal to 2.56. The slope of th i s l i n e i s s e n s i t i v e to the shape of the i n d i v i d u a l c r y s t a l l i t e s . A slope of 1, 2, or 3 corresponds r e s p e c t i v e l y to p l a t e , cylinder and sphere. 3.4 Microhardness Figure 24 shows the microhardness as a function of degree of c r y s t a l l i n i t y . The indentations were made on the glassy phase except at higher degree of c r y s t a l l i n i t y , > 50%, where they were made on the c r y s t a l l i n e phase. Figure 24 shows a sharp r i s e i n the hardness at the early stage of the c r y s t a l l i z a t i o n and a plateau region beyond 0.2 volume f r a c t i o n of c r y s t a l l i n e phase. Hardness values are also compiled i n Table 4. 3.5 E l a s t i c Constants Figure 25 shows the Young's modulus as a function of the degree 47 of c r y s t a l l i n i t y . Young's modulus values obtained by Freiman and Hench are also shown i n t h i s f i g u r e . Even though the actual values of the Young's modulus obtained i n the present work and that by Freiman and 47 Hench are d i f f e r e n t , both show a s i m i l a r increase as the degree of c r y s t a l l i n i t y increases. The Young's modulus value obtained by Kozlovskaya' for the ~ 5 ^ ® 2 &^ass i s a ^ s o shown i n Figure 25. This value i s i n close agreement with the present r e s u l t s . Figure 23 Relative degree of c r y s t a l l i n i t y as a function of time at 530°C. Figure 24 Microhardness of glass-ceramics as a function of volume f r a c t i o n of c r y s t a l l i n e phase. ON Table 4 EFFECT OF DEGREE OF CRYSTALLINITY ON MICROHARDNESS Volume Fraction of C r y s t a l l i n e Phase Mean DPH (kg/mm2) Standard Deviation 0 496.9 18.7 0.02 603.0 10.6 0.05 643.9 13.4 0.18 677.3 22.5 0.35 690.0 25.2 0.55 689.0 28.2 0.75 713.0 16.7 ON ON VOLUME FRACTION Figure 25 Young's modulus of glass-ceramics as a function of volume f r a c t i o n of c r y s t a l l i n e phase. 68 Poisson's r a t i o as a f u n c t i o n of the volume f r a c t i o n of c r y s t a l l i n e phase i s shown.in Figure 26. From the values of Young's modulus and Poisson's r a t i o the shear moduli were ca l c u l a t e d . These are l i s t e d i n Table 5. Figure 27 shows the v a r i a t i o n of shear modulus with respect to the volume f r a c t i o n of c r y s t a l l i n e phase. The values of Young's modulus, shear modulus and Poisson's r a t i o are also l i s t e d i n Table 5. 3.6 Transverse Rupture Tests Figure 28 and Table 6 show the v a r i a t i o n of mean f r a c t u r e s t r e s s with respect to the volume f r a c t i o n of c r y s t a l l i n e phase i n two d i f f e r e n t environments, water and toluene. The v a r i a t i o n of the f r a c t u r e s t r e s s r a t i o i n the two environments i s shown i n Figure 29. As seen from t h i s f i g u r e the r a t i o remained constant over the whole range of c r y s t a l l i z a t i o n . I t i s also seen from t h i s f i g u r e that the f r a c t u r e s t r e s s of the glass and glass-ceramic tested i n water i s 80% of that i n toluene. The square of the f r a c t u r e s t r e s s i s p l o t t e d as a function of the r e c i p r o c a l of the mean free path between c r y s t a l s i n Figures 30 and 31. This dependency i s seen i n both water and toluene. These values are l i s t e d i n Table 6. Figure 26 Poisson's r a t i o of glass-ceramics as a function of volume f r a c t i o n of c r y s t a l l i n e phase. ON Table 5 EFFECT OF DEGREE OF CRYSTALLINITY ON ELASTIC MODULI Volume Fraction of Crystalline Phase Young's Modulus lO^N/m* (Mean Value) Shear; Modulus I-'.-1010N/m2(Mean Value) Poisson's Rate (Mean Value) 0 7.209 2.854 0.2.63 0.1 7.606 3.0.06 0.2.65 0.25 8.2.21 3.240 0.268 0.4 9.200 3.616 0.2.72 0.5 9.990 3.920 0.274 0.65 10.294 4.027 0.2.78 0.8 10.4.11 4.063. 0.281 0.9 11.280 4.392 0.284 I 50 T VOLUME FRACTION Figure 27 Shear modulus of glass-ceramics as a function volume f r a c t i o n of c r y s t a l l i n e phase. 72 CM •s. 10 I—I 0 - 0 — K —A--©— 0~ (WATER) ic O- (TOLUENE) 0 0 - 4 0-3 0-2 o-o •4 -6 -8 VOLUME FRACTION 0 Figure 28 Fracture stress (a f) and c r i t i c a l stress i n t e n s i t y factor ( K I C ) of glass-ceramics as a function of volume f r a c t i o n of c r y s t a l l i n e phase. Table 6 EFFECT OF DEGREE OF CRYSTALLINITY ON FRACTURE STRESS Volume Fraction of C r y s t a l l i n e Phase Fracture Stress, of, N/m2, (psi) In Toluene In Water 0 1.01 x 10 8 8.25 x 10 7 (14.666 x 10 ) (11.975 x 10 ) 0.10 1.125 x 10 8 9.163 x 10 7 (16.319 x 103) (13.390 x 10 3) 0.20 1.509 x 10 8 1.069 x 10 8 (21.89 x 10 3) (15.514 x 10 3) 0.40 1.837 x 10 8 1.266 x 10 8 (26.642 x 10 3) (22.717 x 10 3) 0.50 2.126 x 10 8 1.735 x 10 8 (30.847 x 10 3) (25.167 x 10 3) 0.60 2.417 x 10 8 2.016 x 10 8 (35.065 x 10 3) (29.249 x 10 3) 0.90 3.115 x 10 8 2.4256 x 10 8 (45.182 x 10 3) (35.181 x 10 3) •25 -5 -75 VOLUME FRACTION Figure 29 Relative fracture stress of glass-ceramics as a function of volume f r a c t i o n of c r y s t a l l i n e phase. Figure 30 E f f e c t of mean free path between spherulites on fracture stress (tested i n toluene) of glass-ceramics. 76 Figure 31 E f f e c t of mean free path between spherulites on fracture stress (tested i n water) of glass-ceramics . 77 3.7 Slow Crack Growth Tests 3.7.1 Crack V e l o c i t y - S t r e s s Intensity Factor Diagrams Since the i n i t i a l values of the exponential function describing crack v e l o c i t y coincide with the power function, crack v e l o c i t y during s u b c r i t i c a l flaw growth can often be expressed as a power function of 3 6 the applied stress V = A K i n (26) where V i s crack v e l o c i t y , A and n are constants • In the present study a l l the crack propagation data were plotted i n accordance with the above equation. 3.7.1.1 Annealed Glass Figure 32 shows log V - log K^ . diagrams obtained for annealed glass from load-relaxation curves, i n d i f f e r e n t environments, water, 70% rh, 30% rh, and toluene. Stage II i s observed i n the tests done at 30% relative-humidity. Table 7 gives the slopes and intercepts of these p l o t s . The slopes of log V - log diagrams of the annealed glass tested i n water, 70% rh, 30% rh remained f a i r l y constant at a value of 19 ± 4. However the slope corresponding to the tests done i n toluene was much higher (65). I t appeared that the log V - log K p l o t s of glass tested 6 0 2 Figure 32 Velocity-stress intensity factor diagrams for annealed glass at room temperature. 00 Table 7 EFFECT OF ENVIRONMENT UPON SLOPES AND INTERCEPTS OF LOG V-LOG Kj DIAGRAMS OF ANNEALED GLASS V = AK^ Test Conditions Slope n Intercept Log A Cor r e l a t i o n C o e f f i c i e n t r Toluene 64.3 - 388.76 .995 30% Relative 14.6 - 91.11 .982 Humidity 70% 14.56 - 90.38 .991 Humidity Water 19.00 - 115.89 .992 80 i n toluene were i n the Stage III region. As seen from Figure 32 the log V - log K^ . diagrams move to higher s t r e s s - i n t e n s i t y as the water content i n the environment decreases. These r e s u l t s were also plotted as InV Vs and presented i n Appendix 3. A l i n e a r dependency i s also seen between InV Vs (The two functions are s u f f i c i e n t l y s i m i l a r that the data f i t either p l o t equally w e l l ) . 3.7.1.2 Glass-Ceramics up to 50% of C r y s t a l l i n e Phase Figures 33, 34 and 35 show the log V- log K pl o t s f or 15 ± 5%, 30 ± 5%, and 50 ± 5% c r y s t a l l i n e glass-ceramics. Tables 8 and 9 give the values of slope and intercept of these pl o t s for tests i n water and toluene re s p e c t i v e l y . The slopes of the log V- log pl o t s for tests i n water are about 1/3 of those for tests i n toluene. 3.7.1.3 Glass-Ceramics above 50% of C r y s t a l l i n e Phase Plots of log V versus log f o r 70 ± 5% and 85 ± 5% c r y s t a l l i z e d glass-ceramics are shown i n Figures 36 and 37. The corresponding slopes and intercepts of these pl o t s are l i s t e d i n Tables 8 and 9. These r e s u l t s are also p l o t t e d as InV Vs K^ . i n Appendix 3 i n order to f a c i l i t a t e com-22 23 parison with one of the stress-enhanced corrosion theories ' Figure 38 shows the e f f e c t of the degree of c r y s t a l l i n i t y on the s t a t i c fatigue behaviour of glass i n water. As seen from Figure 38, the - 3 51 0 = WATER A = TOLUENE i • o U l _A CO ^ •5 O' GT .0° / O' o - 5 - 5 0° / - 6 - 5 , i A A / A A / A A' A* A/ A/ / K IC 5 - 9 5 - 9 4 5 - 9 8 6 0 2 L O G K j , 6 0 6 6 1 0 •,. _3/2 N.m 6 1 4 6 1 8 Figure 33 Ve l o c i t y - s t r e s s i n t e n s i t y factor diagrams f o r glass-ceramic containing .15 ± .05 volume f r a c t i o n of c r y s t a l l i n e phase at room temperature. oo o o - WATER A - T O L U E N E / o Ul (S) / o K I C - 6 G J / 5 92 6 0 6 0 8 6 1 6 6 2 0 — 3 / 2 LOG KT , N. m Figure 34 V e l o c i t y - s t r e s s i n t e n s i t y factor diagrams for glass-ceramic containing .30 ± .05 volume f r a c t i o n of c r y s t a l l i n e phase at room temperature. E - 6 1 1 1 1-o - W A T E R . j A - T O L U E N E ' / / a A i UJ I O A / ! o / o -51- o * O I I K I C 1 A' / 1 - A I I I L ? T T 4 6 ^ 2 2 6 3 0 L O G K j , N . m Figure 35 Ve l o c i t y - s t r e s s i n t e n s i t y f a c t o r diagrams f o r glass-ceramic containing . 5 0 + 5 volume f r a c t i o n of c r y s t a l l i n e phase at room temperature. oo oo O-WATER H A ~ TOLUENE o UJ (/> 3 -6 1 _ L J. 622 630 6 38 LOG Kx , N. -3/2 m K i c _ L 6 46 Figure 36 V e l o c i t y - s t r e s s i n t e n s i t y f a c t o r diagrams f o r glass -ceramic containing .70 ± .05 volume f r a c t i o n of c r y s t a l l i n e phase at room temperature. oo T o - W A T E R A - T O L U E N E o o ' / A -5 -6 o / / A A A A A A A A' KIC A 628 636 _ L 6 4 4 652 6 60 L O G K x , N m -3/2 Figure 37 Ve l o c i t y - s t r e s s i n t e n s i t y factor diagrams for glass -ceramic containing .85 + .05 volume f r a c t i o n of c r y s t a l l i n e phase at room temperature. -3-5 L O G K I t N . m -3/2 Figure 38 Velocity-stress intensity factor diagrams for glass and glass-ceramics tested in water at room temperature. 00 ON Table 8 EFFECT OF DEGREE OF CRYSTALLINITY UPON SLOPES AND INTERCEPTS OF LOG V-LOG K^ . DIAGRAMS (TESTED IN WATER) V = AK^ Volume Fraction of C r y s t a l l i n e Phase Slope n Intercept Log A Co r r e l a t i o n C o e f f i c i e n t , r 0 19.00 - 115.89 .992 .15 ± .05 17.9 - 111.60 .996 .30 ± .05 22.3 - 138.88 .997 .50 ± .05 25.86 - 164.65 .987 .70 ± .05 18.4 - 121.36 .996 .85 ± .05 16.9 - 112.92 .985 88 slopes of log V - log p l o t s remains f a i r l y constant, however the plots move to a higher stress i n t e n s i t y as the degree of c r y s t a l l i n i t y increases The e f f e c t of the degree of c r y s t a l l i n i t y on the s t a t i c fatigue behaviour of glass i n the toluene environment i s shown i n Figure 39. The slopes of these plots increase as the degree of c r y s t a l l i n i t y increases. 3.8 C r i t i c a l Stress Intensity Factor ( K J r ) The c r i t i c a l s tress i n t e n s i t y factors (K.^) as measured by f a s t loading [11.25 x 10 ^ m/sec (0.05"/min)]the double tor s i o n samples a f t e r completion of the load r e l a x a t i o n tests are l i s t e d i n Table 10. Figure 28 shows the K , c r i t i c a l stress i n t e n s i t y factor,as a function of the volume f r a c t i o n of c r y s t a l l i n e phase. From t h i s f i g u r e i t i s c l e a r that K^, increases as the degree of c r y s t a l l i n i t y increases. The value of f o r the 85 ± 5% c r y s t a l l i z e d glass-ceramic i s about 3.5 times that of the annealed glass. The trend of increase of i s s i m i l a r to that of the fracture s t r e s s . 3.9 Fracture Surface Energy The fracture toughness equation can be written as K i c • ( 2 7 ) -3-5^ o UJ in <s> O LOG K T , N.nrT .3/2 6-5 Figure 39 V e l o c i t y - s t r e s s i n t e n s i t y factor diagrams f o r glass and glass-ceramics tested i n toluene at room temperature. oo Table 9 EFFECT OF DEGREE OF CRYSTALLINITY UPON SLOPES AND INTERCEPTS OF LOG V-LOG K DIAGRAMS (TESTED IN TOLUENE) V = AK* Volume Fraction Slope Intercept C o r r e l a t i o n of C r y s t a l l i n e Phase n Log A C o e f f i c i e n t r 0 64.30 - 388.76 .992 .15 ± .05 60.31 - 369.56 .979 .30 ± .05 105.74 - 649.46 .962 .50 ± .05 67.93 - 429.53 .983 .70 ± .05 92.50 - 598.90 .968 .85 ± .05 156.10 -1011.60 . 98 91 Substituting G IC = 2y i n the above equation: K. IC / 2 Ey (28) where K. IC = The C r i t i c a l stress i n t e n s i t y f a c t o r = C r i t i c a l S t r a i n energy release rate Y = Fracture surface energy E = Young's modulus Knowing K and E one can calculate y, the frac t u r e surface energy by using equation 28, Table 10 gives the frac t u r e surface energy calculated by the above method. Fracture surface energy i s plotted as a function of r e c i p r o c a l mean free path i n Figure 40. A l i n e a r dependency i s observed up to about 0.5 volume f r a c t i o n of c r y s t a l l i n e phase. 3.10 Fractography transverse rupture specimens are shown i n Figures 41(a) to 41(d). Figures 42(a) to 42(h) show scanning electron micrographs of fracture surfaces of double t o r s i o n specimens. Glass-ceramics containing a low volume f r a c t i o n of c r y s t a l l i n e phase (up to 20%) show i n t e r p a r t i c l e f r a c t u r e with c h a r a c t e r i s t i c fracture steps along the d i r e c t i o n of the crack growth. Figures 42(d) and 42(e) show a mixture of i n t e r p a r t i c l e and t r a n s p a r t i c l e f r a c t u r e . Glass-ceramics containing higher volume f r a c t i o n s of c r y s t a l l i n e phase (> 50%) show t r a n s p a r t i c l e fracture. Cleavage steps Scanning electron micrographs of fracture surfaces of various Figure 40 E f f e c t of mean free path between spherulites on fracture surface energy of glass-ceramic. Table 10 CRITICAL STRESS INTENSITY FACTORS AND FRACTURE SURFACE ENERGIES OF GLASS AND GLASS-CERAMICS Volume Fraction of C r y s t a l l i n e Phase Mean C r i t i c a l Stress Intensity Factor, N.m-3'2 Fracture Surface Energy, J.m2 1 , tim-1 Mean Free Path 0 1.015 x 10 6 6.650 0 .10 ± .01 1.137 x 10 6 7.901 .019 .15 ± .05 1.328 x 10 6 10.251 .032 .30 ± .05 1.55 x 10 6 13.046 .045 .50 ± .05 2.02 x 10 6 18.91 .076 .70 ± .05 2.98 x 10 6 39.115 .139 .85 ± .05 3.53 x 10 6 51.397 .314 VO 1 10 ym Figure 41 SEM fractograph of sample(used In transverse rupture tests) of (a) Glass-ceramic containing le s s than .05 volume f r a c t i o n of c r y s t a l l i n e phase. 95 I 1 10 ym Figure 41(b) Glass-ceramic containing .15 ± .05 volume f r a c t i o n of c r y s t a l l i n e phase. 96 I 1 10 ym Figure 41(c) Glass-ceramic containing .50 ± .05 volume f r a c t i o n of c r y s t a l l i n e phase. I 1 10 ym Figure 41(d) Glass-ceramic containing .85 ± .05 volume f r a c t i o n of c r y s t a l l i n e phase. 98 I 1 10 ym Figure 42 SEM fractograph of sample(used i n double to r s i o n tests) of (a) Glass-ceramic containing l e s s than .05 volume f r a c t i o n of c r y s t a l l i n e phase. [Arrow indicates the d i r e c t i o n of crack propagation]. 99 I 1 10 ym Figure 42(b) Glass-ceramic containing .05 volume f r a c t i o n of c r y s t a l l i n e phase. [Arrow indicates the d i r e c t i o n of crack propagation]. I — I 10 ym Figure 42(c) Glass-ceramic containing .15 ± .05 volume f r a c t i o n of c r y s t a l l i n e phase. [Arrovr indicates the d i r e c t i o n of crack propagation]. I — I 10 ym Figure 42(d) Glass-ceramic containing .30 ± .05 volume f r a c t i o n of c r y s t a l l i n e phase. [Arrow indicates the d i r e c t i o n of crack propagation]. 102 I 1 10 ym Figure 42(e) Glass-ceramic containing .50 ± 0.05 volume fraction of crystalline phase. [ A r r o w indicates the direction of crack propagation]. 103 I 1 10 ym Figure 42(f) Glass-ceramic containing .70 ± .05 volume f r a c t i o n of c r y s t a l l i n e phase. 104 I 1 10 ym Figure 42(g) Glass-ceramic containing .85 ± .05 volume f r a c t i o n of c r y s t a l l i n e phase. 105 1 10 ym Figure 42(h) Glass-ceramic containing .85 ± .05 volume fraction of crystalline phase (magnified view) 106 are seen (area A i n Figure 42(h))in t r a n s p a r t i c l e fractured samples. The fractured surfaces of samples tested i n water did not d i f f e r from samples tested i n toluene. 107 4. DISCUSSION 4.1 C r y s t a l l i z a t i o n of Lithium D i s i l i c a t e Glass 37 It has been established by Hench et a l that c r y s t a l l i z a t i o n i n l i t h i u m d i s i l i c a t e glass proceeds i n the following stages. 1. Formation of metastable l i t h i u m m e t a s i l i c a t e at the end of a nucleation treatment. The formation of these m e t a s i l i c a t e c r y s t a l l i t e s i s due to an ordering of extremely small regions i n the glass containing randomly d i s t r i b u t e d I ^ O - Si02 chains. The + ordering probably involves short range migration of L i ions to be incorporated into a me t a s i l i c a t e structure. 2. When the same sample i s given a c r y s t a l l i z a t i o n t r e a t -ment at higher temperature, Li20 groups apparently d i f f u s e out of the met a s i l i c a t e n u c l e i producing the l i t h i u m d i s i l i c a t e structure. 3. When a c r i t i c a l s i z e of d i s i l i c a t e region i s reached, the growth proceeds towards completion. 4. While the l i t h i u m d i s i l i c a t e c r y s t a l l i t e i s growing, Li20 groups are rejected at the growing front and as a r e s u l t protrusions are sent out from t h i s c r y s t a l l i t e i n search of l i t h i u m 108 m e t a - s i l i c a t e regions. These protrusions grow r a d i a l l y from the c e n t r a l c r y s t a l l i t e producing a s p h e r u l i t i c structure. A c h a r a c t e r i s t i c feature of the s p h e r u l i t i c structure i s the 38 presence of fibrous sub-units c a l l e d f i b r i l s . It has been shown that the f i b r i l l a r development i s a fundamental process i n s p h e r u l i t i c growth i n the c r y s t a l l i z a t i o n of polymers. F i b r i l s are also seen i n the present study. Figures 43(a), 43(b), 43(c) and 44(a) show f i b r i l s extending r a d i a l l y from the c e n t r a l nucleus. It i s also seen from these figures that the f i b r i l s branch out as they grow; t h i s helps to f i l l the space between two main f i b r i l s , as the spherulite expands. From these micrographs i t i s also seen that there exists a low angle grain boundary between the f i b r i l s . Hence a sp h e r u l i t e i s not a si n g l e c r y s t a l . In the early stages of growth, a sp h e r u l i t e probably develops from a si n g l e c r y s t a l and becomes aggregates of f i b r i l s as branching eventually sets i n . In the present study a separate nucleation treatment was not used. However, p r i o r to the c r y s t a l l i z a t i o n treatment, the samples 37 were annealed to r e l i e v e stresses, at 470°C. Hench chose 475°C as the nucleation temperature for 33.3 mole% L ^ O and 66.6 mole% S102 39 glass. On the other hand Hing and McMillan chose 500°C as the nucleation temperature for 30 L i 2 0 . 69 S i 0 2 . l P 2°5 § l a s s ' Hence i n the present study the annealing treatment might also have produced 109 Figure 43(a) TEM photograph of i n d i v i d u a l l i t h i u m d i s i l i c a t e spherulite. 110 Figure 43(b) TEM photograph of individual lithium d i s i l i c a t e spherulite. gure 43(c) TEM photograph of i n d i v i d u a l l i t h i u m d i s i l i c a t e spherulite. 112 nucleation. However, t h i s treatment did not a l t e r the transparency of the glass, i n d i c a t i n g the absence of phase separation. The proper annealing temperature for the present work was determined by d i f f e r e n t i a l thermal a n a l y s i s . A small exothermic peak between 458°C and 486°C (Figure 18) reveals the annealing point of t h i s glass. This peak i s 40 believed to be due to an adjustment i n the glass structure The present study on c r y s t a l l i z a t i o n showed an incubation period of 40 minutes when the glass was given a heat-treatment at 530°C. This shows that the c r y s t a l l i z a t i o n of t h i s glass i s a d i f f u s i o n controlled reaction to further confirm the d i f f u s i o n c o n t r o l l e d nature of the reaction, the data for the growth of the spherulites was f i t t e d to 41 42 Zener and Frank's model. Figure 45 shows the p l o t of the diameter of the s p h e r u l i t e as a function of the square root of time. This p l o t shows a l i n e a r dependency as predicted by the theory. The d i f f u s i v i t y 41 of the process i s determined as follows: According to Zener R = L / Dt (29) d = 2L / Dt (30) where L = F(f) R = Radius of the spherulite d = Diameter of the spherulite t = Time i n sec f = Supersaturation D = D i f f u s i o n c o e f f i c i e n t of the d i f f u s i n g speciess 113 If the process has an incubation period of t o , then equation (30) can be written as d = 2L • D(t - t o ) (31) The corresponding pl o t f o r equation (31) i s shown i n Figure 45. Experimental points up to 70% c r y s t a l l i n i t y l i e i n a s t r a i g h t l i n e . The slope of t h i s l i n e corresponds to 2L / D. L was calculated from 42 the graph of L versus f . Assuming s p h e r i c a l p a r t i c l e s , D, the -13 2 d i f f u s i o n c o e f f i c i e n t was calculated to be 6.7 x 10 cm /sec. I f the p a r t i c l e s are assumed to be c y l i n d r i c a l , t h e corresponding value of D i s -12 2 1.1 x 10 cm /sec. Each of these values i s small compared to the expected d i f f u s i o n c o e f f i c i e n t of L i + (- 1 x 10 ^cm^/sec)^. 43 In an atomistic approach the d i f f u s i o n c o e f f i c i e n t can be related to the mean free path (A^), the average distance of successive jumps of d i f f u s i n g ions, frequency of atomic v i b r a t i o n (v) and the a c t i v a t i o n energy (AF*) i n the following form D = * i / - AF* . , q o . — v exp( — ) (32) kT and v = ;— h where k = Boltzman's constant h = Planck's constant T = Temperature R = Gas constant Assuming A_ = 5A° and s u b s t i t u t i n g AF* as 42 Kcal/mole ( t h i s value was 114 obtained from d i f f e r e n t i a l thermal a n a l y s i s ) , the value of D i s 1.2 x -12 2 10 cm /sec. This value i s i n close agreement with the experimentally -12 2 obtained value of 1.1 x 10 cm /sec. Thus the c r y s t a l l i t e s obey the growth law for c y l i n d r i c a l p a r t i c l e s . The dependence of volume f r a c t i o n of c r y s t a l l i n i t y upon the c r y s t a l l i z i n g time i s given by equations (24) and (25). Figure 23 a o shows a l i n e a r dependency between l n . l n ( ) versus Int. The slope a Q- a of this s t r a i g h t l i n e corresponds to 2.5. Thus according to Morgan's 34 analysis the shape factor of the p a r t i c l e s l i e s between that for spheres and that for rods. As explained e a r l i e r , a s p h e r u l i t i c structure has both s p h e r i c a l and r o d - l i k e c h a r a c t e r i s t i c s . Figures 43(a) to 43(c) and 44(a) show that the spherulite i s composed of f i b r i l s which have r o d - l i k e shape extending r a d i a l l y outwards from the c e n t r a l nucleus. Microstructures observed i n the petrographic study are shown i n Figure 44(b). These microstructures show sp h e r i c a l shaped p a r t i c l e s . Thus there i s a c o r r e l -ation between the structure predicted from growth k i n e t i c s and the observed 37 microstructure. Hench has obtained s i m i l a r r e s u l t s . The a c t i v a t i o n energy for the growth of spherulites i n 33.33 37 mole% L^O - 66.66 mole% Si02 glass was determined by Hench . He concluded that the a c t i v a t i o n energy for bulk c r y s t a l l i z a t i o n i s strongly dependent on p r i o r nucleation treatment. The a c t i v a t i o n energy f o r the samples with 24 hours nucleation treatment was 52 Kcal mole ^ while for a sample with only 3 hours nucleation treatment i t was 92 Kcal mole Figure 44(a) SEM photograph of p a r t i a l l y c r y s t a l l i z e d glass-ceramic. 116 Figure 44(b) T y p i c a l s p h e r u l i t i c microstructure of p a r t i a l l y c r y s t a l l i z e d glass-ceramic from petrographic section (crossed n i c o l s ) 117 Figure 45 Diameter of the l i t h i u m d i s i l i c a t e spherulite versus r e c i p r o c a l of square root of time of c r y s t a l l i z a t i o n at 530°C. 118 In studying the d e v i t r i f i c a t i o n behaviour of 30 mole% Ll^O - 70 mole% 44 -1 Si02» Jaccodine obtained a value of 49 Kcal/mole for the growth of I^Si^O,. sphe r u l i t e s . In the present study the a c t i v a t i o n energy f o r the growth of L i ^ S i ^ O ^ spherulties was determined by d i f f e r e n t i a l thermal analysis as described i n the experimental section and the value i s 42 Kcal mole \ This agrees very well with the values obtained by 44 37 Jaccodine and Hench . The present value of a c t i v a t i o n energy i s considerably higher than the a c t i v a t i o n energy for the d i f f u s i o n of l i t h i u m ions (19.1 Kcal mole and for the d i f f u s i o n of oxygen ions (32.4 Kcal -1 45 mole ) . This shows that the growth of the l i t h i u m d i s i l i c a t e spherulite i s not due to d i f f u s i o n of l i t h i u m ion or oxygen ion and i s due to s ome other species. This d i f f u s i o n species may be I ^ O groups i n an i o n i c 37 form as hypothesized by Hench 4.2 Mechanical Properties 4.2.1 Microhardness As seen from Figure 24 the microhardness of the glassy-ceramic increases as the degree of c r y s t a l l i n i t y increases. The increase i s rapid i n the early stage of c r y s t a l l i z a t i o n and much slower i n the l a t e r stages. In order to determine the deformation mechanism i n the microhardness t e s t the hardness value i s compared with the fr a c t u r e 119 strength. In Figure 46 the f r a c t u r e strength and microhardness are plotted against volume f r a c t i o n of c r y s t a l l i n e phase. From t h i s f i g u r e i t i s seen that the trends of the increases i n f r a c t u r e strength and microhardness are not the same. This shows that the mechanism of increase i n hardness i s not the same as that of fracture strength. 46 Ernsberger showed that the microhardness of glass may be regarded as a measure of the pressure required for i n i t i a t i n g d e n s i f i c a t i o n or volumetric y i e l d . He suggested that t h i s d e n s i f i c a t -ion involves simply a collapse of the structure under the indenter into a more close packed arrangement by a process of minor bond r o t a t i o n . By measuring the r e f r a c t i v e index around the indentation i n an i n t e r -ference microscope, he came to the conclusion that p l a s t i c i t y does not e x i s t i n s i l i c a t e glass even on a microscopic scale. When the present glass i s undergoing the c r y s t a l l i z a t i o n treatment, the l i t h i u m d i s i l i c a t e s p herulite nucleates and tends to grow. But at the same time the structure i n the i n t e r - s p h e r u l i t i c glass tends to become more dense. If most of t h i s rearrangement i n the structure occurs i n the early stages of c r y s t a l l i z a t i o n , then t h i s would account for the rapid r i s e of hardness. Once t h i s rearrangement i s complete, the hardness i n the i n t e r - s p h e r u l i t i c region would remain the same and t h i s would account for the plateau region. Figure 46 Fracture stress and microhardness of glass-ceramics versus volume f r a c t i o n of c r y s t a l l i n e phase. 121 4.2.2 E l a s t i c Moduli The v a r i a t i o n of Young's modulus of glass-ceramics containing d i f f e r e n t volume f r a c t i o n s of c r y s t a l l i n e phase i s shown i n F i g . 25. In 47 35 the same fi g u r e the data of Freiman and Kozlovskaya are also shown. Present r e s u l t s were determined by using a s t a t i c method while most of the other data were obtained by a dynamic method. The Young's modulus obtained for the glass i n the present study agrees very well with that 35 of Kozlovskaya . Eventhough the actual values of the Young's modulus 47 are d i f f e r e n t i n the present experiments from those of Freiman , the 47 trend of increase i s apparently s i m i l a r . Freiman obtained h i s data on glass of 33.33 mole% 1*2^ ~ 66.66 mole% SiC^ and the present study 35 was done on 30 mole% I ^ O - 70 mole% Si02 glass. Kozlovskaya showed the dependence of Young's modulus of I ^ O - Si02 binary glass on % Si20 content i n the glass, as shown i n Figure 47. The value of Young's modulus (E) for 33.33 mole% I ^ O - 66.66 mole% Si02 glass obtained from 47 th i s f i g u r e did not agree with Freiman's data, eventhough both used a dynamic method i n measuring the Young's modulus. The Young's modulus for f u l l y c r y s t a l l i n e material was calculated 4 from Figure 25 by extrapolation and the corresponding value i s 12.6 x 10 MPa. From Figure 20, the density of 100% c r y s t a l l i n e material was also calculated by extrapolation. By comparing t h i s density value with the t h e o r e t i c a l v a l u e , i t was found that the sample was 98% dense . The Young's 122 CJ .—i 3 T3 O s cj 7} Hi 70 h 6.0 5.0 • a o b 20 M o l a r 7C Figure 47 E f f e c t of composition on e l a s t i c modulus of glasses i n system: x Me20 (100 - x) Si02 where Me 2 i s L i 2 0 (after Kozlovskaya 35) (1) L i 2 0 (2) Na 20 (3) K 20 (a) experimental values (b) calculated values 123 modulus value of 100% c r y s t a l l i n e m a terial was corrected f o r p o r o s i t y by using Hasselman's^ a n a l y s i s . The corrected value i s 13.12 x 10^ MPa. From the knowledge of Young's moduli f o r the f u l l y c r y s t a l l i z e d glass-ceramic and f o r the annealed gla s s , the e l a s t i c behaviour of the two phase m a t e r i a l was analysed. T h i s i s shown i n Figure 48. Here the top s o l i d l i n e corresponds to the Voight model and the bottom s o l i d l i n e corresponds to the Reuss model. The top and bottom dotted l i n e s 49 correspond to Hashxn's upper and lower bound models r e s p e c t i v e l y . As seen from Figure 48, the Young's modulus agrees very w e l l 49 with the p r e d i c t i o n of Hashin's t h e o r e t i c a l mixing model up to 0.5 volume f r a c t i o n of c r y s t a l l i n e phase. Above 0.5 the experimental values are below the t h e o r e t i c a l mixing model. As the degree of c r y s t a l l i n i t y increases the matrix (glass) 35 becomes r i c h e r i n Si02 content. According to Kozolvskaya the increase of Si02 content i n L i 2 0 ~ SiO2 binary glass tends to decrease the Young's modulus. Hence as the degree of c r y s t a l l i n i t y i n these glass-ceramics increases, Young's modulus of the matrix becomes lower than the s t a r t i n g g l a s s . This e f f e c t may be pronounced i n glass-ceramics containing more than 0.5 volume f r a c t i o n of c r y s t a l l i n e phase. However, i n the t h e o r e t i c a l p r e d i c t i o n i t was assumed that the Young's modulus of the matrix remains constant f o r a l l concentrations. This may be responsible 0 -2 4 -6 -8 VOLUME FRACTION Figure 48 Comparison of values of Young's modulus of glass-ceramics with the t h e o r e t i c a l models. r—1 125 for the discrepancy between the t h e o r e t i c a l curve and the experimental points. The Poisson's r a t i o of the glass-ceramics was also analysed 49 according to Hashin's model and the r e s u l t s are shown i n Figure 49. Although the f i t i s reasonably good, there i s enough scatter i n the experimental r e s u l t s that no conclusions can be drawn. 4.2.3. Fracture Strength The r e l a t i o n between the fra c t u r e strength and the other fracture parameters i s given by equation (1). When attempting to explain the increase i n strength of glass-ceramics i t i s reasonable f i r s t to consider the contribution from the increase i n Young's modulus. Frey and Mackenzie"^ have argued that i n dispersions of A^O^ or ZrC^ i n a glass matrix, the increase i n fra c t u r e strength i s caused by the increase i n the Young's modulus of the mixture. A c t u a l l y t h e i r data show that for a low volume f r a c t i o n of ZrC^ (20%) the strength decreases. For the same volume f r a c t i o n of Al^O^ the strength increases s l i g h t l y . The dif f e r e n c e would appear to be due to the d i f f e r e n c e i n i n t e r n a l stress a r i s i n g from thermal contraction mismatch rather than the increased e l a s t i c modulus. According to equation (1), the r a t i o of the strength of a glass-ceramic to that of a glass should be given by: VOLUME FRACTION Figure 49 Comparison of values of Poisson's r a t i o of g l ceramics with the t h e o r e t i c a l models. 127 where a = Fracture strength of annealed glass G a = Fracture strength of glass-ceramic GO E = Young's modulus of annealed glass G E_ = Young's modulus of glass-ceramic GC C = I n i t i a l flaw si z e i n annealed glass G C„„ = I n i t i a l flaw s i z e i n glass-ceramic When the glass and the glass-ceramics were given the same abrasion treatment (C_ = C ), equation (33) becomes (34) Table 11 shows the r a t i o gG calculated from equation (34) and experi-°GC mentally obtained values. The experimental values are considerably lower than the values calculated by the above method. The f r a c t u r e strength of glass-ceramic containing .90 volume f r a c t i o n of c r y s t a l l i n e phase (calculated according to equation (34)) shows a value of 1.25 times that of annealed glass, but i t was found experimentally that the fracture strength of glass-ceramic containing .90 volume f r a c t i o n of c r y s t a l l i n e phase was about 3 times that of annealed glass. JGC GC (33) Table 11 a E h SUMMARY OF ( — ) AND ( ) FOR GLASS-CERAMICS °GC EGC Volume Fraction of C r y s t a l l i n e Phase GC Toluene > GC Water ( ) v E ' GC .1 0.897 0.902 0.973 .2 0.669 0.771 0.949 .4 0.549 0.526 0.885 .5 0.475 0.476 0.8495 .6 0.417 0.409 0.836 .9 0.324 0.340 0.8038 129 Hasselman and F u l r a t h also proposed a f r a c t u r e theory for a composite system. They hypothesized that hard c r y s t a l l i n e dispersions within the glass matrix l i m i t the s i z e of G r i f f i t h flaws and strengthen the composite. They observed strength enhancement i n a glass - Al^O^ composite and concluded that strengthening resulted whenever the i n t e r p a r t i c l e distance (X) became small enough to l i m i t the s i z e of the surface flaws to l e s s than that present i n the glass containing no p a r t i c l e s . They also concluded that the strengthening was very small whenever the i n t e r p a r t i c l e distance (X) was bigger than the surface flaws introduced during processing. In the present case, a l l of the transverse rupture samples were abraded with a 400 g r i t SiC (- 25 ym) and hence the samples contain 62 flaws of approximately 25 ym. According to Hasselman and F u l r a t h , the strength of glass-ceramics having an i n t e r p a r t i c l e distance (X) higher than 25 ym should remain approximately constant. However i n the present case substantial strengthening i s seen i n glass-ceramics having X larger than 25 ym (Figures 30 and 31). From equation (1) i t can be seen that the f r a c t u r e strength can be increased by an increase i n the f r a c t u r e surface energy. If the strength enhancement of glass-ceramics i s only a t t r i b u t e d to the increase i n f r a c t u r e surface energy, one can write 130 a~ = (35) GC TGC Table 12 compares the ratio °G calculated from equation (35) and °GC experimentally obtained values. The experimental values agree reasonably well with the ratio of 2 • Thus the increased fracture surface energy appears to be the maxn contributing factor i n the strength enhancement" of glass-ceramics. 52 Lange has shown that the fracture surface energy of a composite material can be expressed i n terms of the matrix and the interparticle distance (A). The detailed analysis of this theory i s discussed in the next section. The above -relation i n glass-ceramics can be written as Y = Y + T/X (36) GC G where y = Fracture surface energy of glass-ceramics GC Y = Fracture surface energy of annealed glass G' T = Line tension of the crack A = Inter-spherulitic distance Substituting equation (36) in equation (1) and rearranging 4 - ^ EGC 1 \ + ^ <37> 2 1 According to this relation a Vs - r - should give a straight li n e i f the contribution from the increase in Young's modulus to strengthening Table 12 SUMMARY OF ( ) AND ( ) FOR GLASS-CERAMICS °GC YGC Volume Fraction of C r y s t a l l i n e Phase GC Toluene GC Water Y G h  YGC .10 0.897 0.902 0.917 .2 0.669 0.771 0.805 .4 0.549 0.526 0.714 .5 0.475 0.476 0.593 .6 0.417 0.409 0.506 .7 0.374 0.375 0.412 .9 0.324 0.340 0.359 132 of the glass-ceramics i s n e g l i g i b l e . Figures 30 and 31 show the r e l a t i o n 2 between a Vs 1/X f o r tests i n toluene and water. A s t r a i g h t l i n e f i t GC i s seen up to - 50% c r y s t a l l i n e phase as predicted by equation (37). Equation (1) can be expressed i n terms of the c r i t i c a l s tress i n t e n s i t y f a c t o r (K ) as follows ±.\j 1 K I C (38) From t h i s equation the c r i t i c a l flaw s i z e can be calculated when a^, K and Y are known. Brown and Strawley"^ have shown that Y f o r three point bending i s approximately 2.0. Table 13 l i s t s the value of c r i t i c a l flaw s i z e for glass and glass-ceramics tested i n toluene and water. The c r i t i c a l flaw si z e i n the samples tested i n toluene i s approximately 25 ym. This corresponds to the s i z e of the 400 g r i t SiC powder used i n abrading the samples. This suggests that while the sample i s loading i n the three point bending test i n toluene, the sample does not undergo s u b c r i t i c a l crack growth. The apparent c r i t i c a l flaw s i z e i n g l a s s -ceramics containing 90% c r y s t a l l i n e phase was 33 ym. This value was higher than the other glass-ceramics possibly due to the porosity i n those containing 90% c r y s t a l l i n e phase. From Table 13 i t i s seen that the c r i t i c a l flaw s i z e i n the samples tested i n water i s approximately 40 ym. This value i s higher than the i n i t i a l flaw s i z e i n the samples (- 25 ym) ; suggesting that while the sample i s loading i n the three Table 13 CRITICAL FLAW SIZE IN SAMPLES USED IN TRANSVERSE RUPTURE TESTS K 2 - IC 2 2 y a f Volume Fraction of C r y s t a l l i n e Phase C, ym(in Toluene) C, ym(in Water) 0 26 • 39 10 26 40 20 24 40 50 24 36 60 26 37 90 33 55 134 point bending test i n water, i t undergoes s u b c r i t i c a l crack growth. Hence these samples r e g i s t e r lower f r a c t u r e strengths than those tested i n toluene. The discrepancy of the glass-ceramics containing 90% c r y s t a l l i n e phase may again be due to porosity. 4.3 Fracture Surface Energy The fr a c t u r e surface energy of the glass-ceramics increased as the f r a c t i o n of c r y s t a l l i n e phase increased as shown i n Table 10. A factor of 3 increase i n fr a c t u r e surface energy was obtained at 50% 52 c r y s t a l l i n e phase and a f a c t o r of 8 at 90%. Lange has proposed a theory for the increase i n the f r a c t u r e energy of b r i t t l e matrix composites. This involves an i n t e r a c t i o n of the crack front with the second phase. The theory i s based on the observation that the length of a crack front increases when i t i s impeded by second phase p a r t i c l e s within a b r i t t l e matrix. Using the concept that the crack front has a l i n e energy, such an increase i n the crack front length should require 52 energy, thus increasing the energy to propagate the crack. Lange found that the f r a c t u r e energy i s l i n e a r l y r e l a t e d to the r e c i p r o c a l of the mean free path given by equation (36). In the present case the pinning of the crack front might have been caused by stresses at the 63 p a r t i c l e - m a t r i x i n t e r f a c e . Borom et a l have shown that i n t h e i r glass-ceramic, the c r y s t a l l i n e phase has a higher thermal contraction 135 c o e f f i c i e n t than the parent glass and they concluded that there existed 47 a hoop compressive stress at the i n t e r f a c e . Frieman and Hench have shown that the thermal contraction c o e f f i c i e n t of the c r y s t a l l i n e phase i n t h e i r glass-ceramic was lower than that of the parent glass. According to t h i s condition the p a r t i c l e w i l l be i n a state of hydrostatic compression and the i n t e r f a c e w i l l also experience a compressive s t r e s s . In the present experiments, the composition of the glass used and the 47 microstructure obtained was s i m i l a r to that used i n Frieman 1s work. Hence i t i s believed that the p a r t i c l e ( l i t h i u m d i s i l i c a t e ) produced stresses that impeded crack propagation. In the present study i t was found that the data agreed with 52 Lange's analysis up to = 50% c r y s t a l l i n e phase.Figure 40 shows a l i n e a r r e l a t i o n s h i p between the fr a c t u r e surface energy and the r e c i p r o c a l of the i n t e r c r y s t a l l i n e path. The slope of t h i s l i n e which corresponds to -2 2 the l i n e energy according to the theory,is 1.924 x 10 J/m (19.24 ergs/ 2 52 cm ). This value i s within the l i m i t s of the values reported by Lange for a sodium b o r o - s i l i c a t e g l a s s and alumina composite. The intercept of t h i s l i n e ( F ig. 40) corresponds to the surface energy of the annealed 2 glass. The intercept i s 4.1 J/m . This value i s i n f a i r agreement with 2 the experimentally obtained value for the annealed glass (6.7 J/m ) The i n t e r a c t i o n between the crack and the p a r t i c l e i s also revealed by fractographs. In Figures 42(a) to 42(c), a c h a r a c t e r i s t i c fracture step i s seen perpendicular to the p o s i t i o n of the general crack 136 front. These f r a c t u r e steps are due to the bowing of the crack front between the l i t h i u m d i s i l i c a t e spherulites. Since the s i z e of these spherulites i s very small (2 to 5 ym), the pinned portion of the crack front finds i t easier to pass between the spheru l i t e s . When i t does t h i s and j o i n s with the bowed crack f r o n t , i t leaves a fractured step. When the si z e of sphe r u l i t e i s large (the spacing between them i s small) the pinned portion of the crack front finds i t more d i f f i c u l t to push between the sphe r u l i t e . Hence t h i s crack front breaks through the spherulites. Thus there i s more t r a n s p a r t i c l e fracture as the degree of c r y s t a l l i n i t y increases. Part of the increase i n fr a c t u r e energy i n glass-ceramics containin a high volume f r a c t i o n of c r y s t a l l i n e phase i s due to the random o r i e n t a t i o n of the li t h i u m d i s i l i c a t e c r y s t a l s . Lithium d i s i l i c a t e has an orthorhombic 37 c r y s t a l structure with a we l l defined cleavage along the (010) plane As explained i n the beginning of t h i s Chapter, the sphe r u l i t e i s not a single c r y s t a l . I t consists of f i b r i l s r a d i a t i n g out from a ce n t r a l nucleus. When the cracks i n t e r a c t with the spherulite the crack tends to propagate along th (010) planes. Cracks f i n d i t easier to propagate i n the f i b r i l s having an (010)plane p a r a l l e l to the plane of crack propagation. But the crack encounters more resistance i n propagating i n the f i b r i l s having cleavage planes normal to the plane of crack propagation. Hence the crack tends to rupture other high index planes. A l t e r n a t i v e l y the crack can also propagate along i n t e r - f i b r i l l a r paths. However, the crack has to rupture the cent r a l 137 core from which the f i b r i l s radiate. Both the above mentioned processes would require a d d i t i o n a l energy. Hence glass-ceramics have higher fracture surface energy than glass because the f r a c t u r e path i s more tortuous and high energy surfaces are exposed. The type of f r a c t u r e described above i s shown i n Figures 42(f) to 42(h). These figures shown very rough surfaces composed of mountain and v a l l e y l i k e structures due to the p u l l out of f i b r i l s from the c e n t r a l core of the spherulites. They also show smooth f l a t surfaces which correspond to cleavage planes. Cleavage steps are also seen.(Figure 42(h) area A) 4.4 S t a t i c Fatigue 4.4.1 Model for Slow Crack Growth i n Corrosive Environment (water) The rate of corrosion can be expressed as the v e l o c i t y (V) of 23 attack, normal to the surface by V = 2A Sinh exp ( - ) (39) r AF* - h A F i , / n v = A exp - [ — J (40) where A F = Free energy of the corrosion reaction A F * = A c t i v a t i o n energy A = Constant R = Gas constant T = Temperature °K 138 23 H i l l i g and Charles have shown that the re a c t i o n can be described by the following equation. 2 t; v V cr V AF = AF - ' m + app m T - 2E " ( 4 1 ) where y = Surface free energy p = Radius of curvature of surface crack undergoing corrosion V = Molar volume of the material m a = Applied stress app E = Young's modulus of the material 23 The H i l l i g and Charles theory can be more r e a d i l y adapted to the experimental observations i f the following d e f i n i t i o n i s employed. o . c = ty °th where o ~ Stress at the t i p of the surface crack c o"t^ = Theoretical strength of the material 54 Orowan has shown that o t h = PET <42) where r Q i s the distance between two cleaving planes. The stress at the t i p of the crack can be rel a t e d to the applied stress 24 and the dimensions of the crack f o r an e l l i p t i c a l l y shaped crack by a = 2 a V L/p (43) c app 139 where L = Length of the surface crack Irwin"*"' has shown for an e l l i p t i c a l l y shaped crack, K, CT / irL app (44) where K = Stress i n t e n s i t y f a c t o r Substituting equation (44) i n (43) 2 K_ TTp Expressing the c r i t i c a l s tress i n t e n s i t y factor (K^^,) as (45) K. IC (2 E Y) CT (46) By using equations(42),(45)and (46), can be expressed as th K, l c _ 2/2 . /r7 1J_ G t h /r- / p K i c (47) The a c t i v a t i o n energy of a chemical reaction i s expected to be stress-dependent and i n the present case AF* i s dependent on ty. The a c t i v a t i o n energy can be expanded i n Taylor's series as a function of i> by AF A F , _ + 1 ip=0 2 2 * 3 AF , t a xp2 ij; = o (48) Let AF = AF i(j=0 ° 140 3AF and — 2ty n has the same units as AF, and hence i t i s c a l l e d the ty = 0 ty Decremental energy factor and can he written as 3AF t •bty ty = 0 = - A (49) Substituting equation (47) , (48), (49) and (41) i n (40) and rearranging V Y V v - , « p [( - S g - i -• - j j S + A ,* 2 V 2 / TT K, K. IC 2 * .2 3 AF 2 2 ty = 0 )/RT] (50) a V app m _ ty^ 4E 0 A 2 3 A F , Zty can be taken as zero. ty = 0 Hence equation (50) becomes V = V 0 exp ( A * 2 /~2~ V 0 K, K /RT) (51) IC Y V where V Q = exp (- 2 p m ) = corrosion of unstressed material at a crack with radius of curvature p and V.. = A exp [-( A F P - H A F 0 RT •)] Taking the natural logarithm of equation (51) 1 * 2 J~2 InV = lnV 0 + jfi [ A K, K (52) IC 141 According to equation (52) J M - ^ ( A* — / ^ ) (") 3 W " R T v " / i t / p The l e f t hand side of the equation (53) corresponds to the slope of a plot of InV versus K /K . If the crack v e l o c i t y data are p l o t t e d i n t h i s manner a s t r a i g h t l i n e should be obtained. The slope of t h i s 1 ^ 2 v2 / r l i n e should correspond to — [ A — / —4- ]. With the /tt / P r * knowledge of slope, R, T and assuming— - = 1, the value of A can be P calculated. Eventhough equation (51) i n many respects resembles H i l l i g ' s and Charles's equation f o r stress-corrosion of the material, there i s a subtle d i f f e r e n c e . In the f i n a l form of H i l l i g ' s and Charles's equation (equation 13) i t was found that the a c t i v a t i o n volume (V ) i s s t r e s s -30 independent. This observation was c r i t i c i z e d by Doremus because there are no experimental fa c t s to support t h i s idea. I t i s also noted that the a c t i y a t i o n volume i n a chemical reaction i s r a r e l y independent of 30 pressure . However i n the present analysis the decremental energy factor (A*) can be considered constant since the v a r i a b l e \> or K^/K^ i s dimensionless. Equation (51) has also been used by Sines i n deriving the time to f a i l u r e expression. He pointed out that the crack growth data 142 should be f i t t e d to an equation having the form of equation (51) i n order to be dimensionally correct f or a t i m e - t o - f a i l u r e equation. A l l of the crack v e l o c i t y data f o r samples tested i n water were plotted as InV Vs K /K in order to t e s t the above model. This i s shown i n Figure 50. This f i g u r e shows a s t r a i g h t l i n e f i t . In the same 25 19 f i g u r e crack v e l o c i t y data of Wiederhorn and Williams et a l f o r soda -3/2 lime s i l i c a t e glass were also plotted. (Here K = 0.74 MN.m i s 19 taken ). As seen from Figure 50 these two l i n e s agree reasonably well with the present set of data. The slopes of the l i n e s correspond to the present set of data and the l i n e s corresponding to s o d a - l i m e - s i l i c a t e glass are approximately the same. This was not s u r p r i s i n g since l i t h i u m s i l i c a t e glass and s o d a - l i m e - s i l i c a t e glass are s i m i l a r . Hence i t suggests that the mechanism of s t r e s s - c o r r o s i o n i s also s i m i l a r i n these glasses. The value of the slope of the l i n e i n Figure 50 i s 21. Substituting t h i s value i n equation (53) and assuming —— = 1, at 25°C P * the value of A i s 7.5 Kcal/mole. Hence i n the present a n a l y s i s , the a c t i v a t i o n energy for the stress-corrosion of glass and glass-ceramics * 2 /2 K I i n water can be taken as (AF Q - 7.5 — — — — ), AF Q being the A K I C a c t i v a t i o n energy for the chemical r e a c t i o n between glass, g l a s s -ceramics ancj water i n the absence of s t r e s s . I t was well established 21 25 + by Charles and by Wiederhorn that d i f f u s i o n of Na ions i s responsible 143 1 0 " 1 0 " o lxl cn > 1 0 ' O o _l LU > / 0 =r ANNEALED a = -is + — -30 v — 50 © = -70 -SODA LIME GLASS 2 4 , 2 5 + - I - . / ' +•/ o ° / 10" 0-5 0-8 Figure 50. Velocity versus Stress intensity factor C r i t i c a l stress intensity factor diagram for glass and glass-ceramics (tested in water at room temperature). 1 4 4 f o r the corrosion of s o d a - l i m e - s i l i c a t e glass i n water. Generalizing t h i s concept f o r a l l a l k a l i s i l i c a t e glasses, i t can be assumed, that a s i m i l a r mechanism i s responsible f o r the corrosion o f . l i t h i u m 4 5 d i s i l i c a t e glass and. glass-ceramics i n water. Mohyddin has shown that the a c t i v a t i o n energy f o r the l i t h i u m ion d i f f u s i o n i n l i t h i u m s i l i c a t e glass i s 1 9 Kcal/mole. Hence the a c t i v a t i o n energy f o r the s t r e s s - c o r r o s i o n of l i t h i u m d i s i l i c a t e glass and glass-ceramics i n water i s ( 1 9 - 1 2 K j / K j . ) . • At = 0 . 5 K ^ , , t h i s i s 1 3 Kcal/mole. Thus i t i s seen that f o r a low value of K^/K^, the a c t i v a t i o n energy f o r the s t r e s s -corrosion i s almost equal to that of corrosion. These_low values of K j V K ^ - q can be considered as the s t a t i c f a t i g u e l i m i t . Hence the s t a t i c fatigue l i m i t can be considered as a threshold l i m i t of K j / K - j - q above which K^. decreases the a c t i v a t i o n energy f o r the process. 4 . 4 . 2 Slow Crack Growth i n a Non-Corrosive Environment (Toluene) 5 3 I t has been established by Wiederhorn that slow crack growth i n s o d a - l i m e - s i l i c a t e glass i n vacuum i s congruent with the data from region I I I on the V-K^ p l o t , Figure 8 . In the present study, a l l the crack v e l o c i t y data from te s t s i n toluene resembled that of region I I I . As seen from Figures 3 2 to 37 the l o g V Vs l o g p l o t s were very c l o s e to K and the slopes of these l i n e s were much higher than f o r specimens tested i n water. 145 Wiederhorn"'"' has analysed %he crack growth data f o r d i f f e r e n t glasses i n vacuum and concluded that crack growth i n the absence of a corrosive environment cannot be explained by either the a l k a l i ion d i f f u s i o n theory or the viscous flow theory. He suggested that a thermally activated crack growth process proposed by Thomson 57 58 and h i s co-workers and elaborated by Lawn can q u a l i t a t i v e l y explain the crack propagation data i n vacuum. The theory of Thomson^7 i s c a l l e d the " L a t t i c e Trapping Theory". It r e l a t e s crack t i p structure to crack propagation rate. He has shown that the discreteness of the atomic or molecular l a t t i c e can trap a cleavage crack i n a manner analogous to the trapping of a d i s l o c a t i o n by the P e i e r l ' s v a l l e y s . Using several s i m p l i f i e d mathematical models, i t has been demonstrated that near the c r i t i c a l G r i f f i t h s t r e s s , a range of stresses e x i s t s for crack s t a b i l i t y . Within t h i s range the crack i s " l a t t i c e trapped". This i s i l l u s t r a t e d i n Figure 51. Instead of one p o s i t i o n of crack s t a b i l i t y as predicted by the G r i f f i t h theory, several pos i t i o n s exist at which a crack can be arrested. However with s u f f i c i e n t thermal energy, thermally activated crack growth can occur by movement of the crack from one point of s t a b i l i t y to the next. Within t h i s range the a c t i v a t i o n energy for forward (AG^) and backward (AG^) motions of the crack vary between a maximum and zero.. Assuming a l i n e a r approximation of a c t i v a t i o n energy 59 with s t r a i n energy release rate Tyson and h i s co-workers derived an FORCE ON CRACK UNSTABLE REGION STABLE REGION UNSTABLE REGION CRACK HEALING | CRACK IS LATTICE TRAPPED DYNAMIC FRACTURE GRIFFITH CRACK LENGTH LENCTH ure 51 Graphical representation of the slow crack growth regime r e s u l t i n g from l a t t i c e trapping (after Thomson-*7) 147 equation for the crack v e l o c i t y . The f i n a l form of t h e i r equation i s InV = l n V 0 - [ AG 0 (1 - K ^ / K ^ )/RT] (54) where V 0 = Nav N = Number of stretched bonds a = L a t t i c e parameter v = Attack frequency AG„ = A c t i v a t i o n energy for the bond rupture under zero stress R = Gas constant T = Temperature °K 2 From equation (54), a p l o t of InV Vs K^ should give a s t r a i g h t l i n e AG and the slope of t h i s l i n e should corresponds to ~ j — 9 — • Figures 52(a) K K RT 2 52(f) are pl o t s of InV Vs for the materials used i n t h i s study and tested i n toluene. Experimental points show a good l i n e a r dependency 2 between InV and K^ .. From the slopes of these pl o t s AG 0, the a c t i v a t i o n energy for bond rupture under zero stress was calculated and the values are l i s t e d i n Table 14. The value of AG0 remained approximately constant up to a volume f r a c t i o n at which l i t h i u m d i s i l i c a t e spherulites began to overlap (> 50%). The corresponding value of A G D i s clpse to 125.5 KJ/mole (30 Kcal/mole). This value i s lower than the value obtained 53 59 for s o d a - l i m e - s i l i c a t e glass tested i n vacuum ' . However t h i s value agrees reasonably with the bond strength of l i t h i u m o x i d e ^ . However, since only one temperature was used i n the present study, i t i s not possible to place much confidence i n arguments based upon a c t i v a t i o n 148 Figure 52 Velocity-square of stress i n t e n s i t y factor diagram for (tested i n toluene at room temperature) (a) annealed glass Figure 52(b) Glass-ceramic containing .15 ± .05 volume f r a c t i o n of c r y s t a l l i n e phas 150 O LU CO >-H ( J O _) UJ > 20 K 2 -3 T N m Figure 52(c) Glass-ceramic containing .30 + f r a c t i o n of c r y s t a l l i n e phase. . 05 volume 151 Figure 52(d) Glass-ceramic containing .50 ± .05 volume f r a c t i o n of c r y s t a l l i n e phase. 152 Figure 52(e) Glass-ceramic containing .70 + .05 volume f r a c t i o n of c r y s t a l l i n e phase. 153 Figure 52(f) Glass-ceramic containing .85 ± .05 volume f r a c t i o n of c r y s t a l l i n e phase. Table 14 SUMMARY OF ACTIVATION ENERGY CALCULATED FROM CRACK VELOCITY DATA Volume Fract i o n of C r y s t a l l i n e Phase Slope K T C, N/m3 / 2 AG 0, KJ7Mole (Kcal/Mole) 0 3.8741 x 1 0 " 1 1 1.013 x 10 6 99.18 (23.69) .15 ± .05 2.4145 x I O " 1 1 1.328 x 10 6 106.22 (25.37) .30 ± .05 3.359 x I O " 1 1 1.55 x 10 6 201.39 (48.1) .50 ± .05 1.0763 x I O " 1 1 2.02 x 10 6 109.57 (26.17) .70 ± .05 6.9155 x 10~ 1 2 2.98 x 10 6 153.24 (36.60) .85 ± .05 9.9881 x 10~ 1 2 3.53 x IO 6 310.53 (74.17) Ln 4>-155 energies. Crack v e l o c i t y studies at d i f f e r e n t temperatures i n vacuum w i l l reveal more about the mechanism of crack growth i n non-corrosive environments. As seen from Table 14, a glass-ceramic containing 90% of c r y s t a l l i n e phase has a higher a c t i v a t i o n energy ( A G 0 ) . This value i s i n reasonable agreement with the value obtained for soda-lime-53 59 s i l i c a t e glass ' . Hence i n t h i s m aterial, i t appears that crack propagation i n toluene i s c o n t r o l l e d by the bond rupture of the Si-0 bonds. 4.5 P r e d i c t i o n of L i f e Expectancy stress-corrosion can be determined by integ r a t i n g the v e l o c i t y - s t r e s s i n t e n s i t y curve between the l i m i t s RV . and K _ as shown i n Appendix 2. I i IC n Here the V = A K r e l a t i o n i s assumed. I f t h i s r e l a t i o n i s changed to V = V 0 exp ( 6 K /K ) and the same procedure of i n t e g r a t i o n i s followed, one a r r i v e s at The t i m e - t o - f a i l u r e of a b r i t t l e material which undergoes t a. app 2 2 2 y IC I i K. K. IC I i + 1) - e (B + 1) ] (55) 156 where a = Applied stress app y = Geometrical factor t = Time to f a i l u r e a Sines has shown that equation (55) can be modified by using i n K I i P the place of — — and the f i n a l equation i s K I C 2 K I C 2 r - B ^ E £ f r gapp , n t >. 2-^- [e a (6 -f^ + 1) •a y V 0 3 P app - e" P (B + 1)] where o p i s a proof stress and a p > a a p p ' (56) The l i f e expectancy p l o t s f o r l i t h i u m d i s i l i c a t e glass and 5 2 6 2 glass-ceramics under two applied stresses (10 N/m and 10 N/m ) and f i v e a d i f f e r e n t values of . — (1.1, 1.5, 2, 3, A) are shown i n Figures 53(a) a app to 53(e). These plo t s are v a l i d only f o r specimens having a flaw s i z e l i k e those used i n the rupture test and water environment. From these figures i t i s c l e a r that the l i f e expectancy increases with increasing r a t i o of a p — . I t i s also seen that the l i f e expectancy increases with increasing app volume f r a c t i o n of c r y s t a l l i n i t y i n glass at a given stress. This behaviour i s very c l e a r l y indicated by equation (56) where t i s d i r e c t l y proportional he2' 157 VOLUME FRACTION Figure 53(a) L i f e expectancy versus volume f r a c t i o n of c r y s t a l l i n e phase at a - £ — = 1.1 a app 158 159 VOLUME FRACTION Figure 53(c) L i f e expectancy versus volume f r a c t i o n of c r y s t a l l i n e phase at a ^ app 160 VOLUME FRACTION Figure 53(d) L i f e expectancy versus volume f r a c t i o n of c r y s t a l l i n e phase at a = 3 a app 1 6 1 VOLUME FRACTION Figure 53(e) L i f e expectancy versus volume f r a c t i o n of c r y s t a l l i n e phase at a 162 5. SUMMARY AND CONCLUSIONS 1. The strength of glass-ceramics can be explained i n terms of the fracture surface energy. The increase i n e l a s t i c modulus has very l i t t l e e f f e c t i n strengthening of glass-ceramics containing low volume f r a c t i o n s of c r y s t a l l i n e phase. 2. Crack v e l o c i t y data f o r glass and glass-ceramics tested i n water can be analysed by a stress-corrosion model based on the expression V = V 0 exp ( A — ). K I C 3. The fracture surface energy of glass-ceramics tends to 52 follow Langes r hypothesis based on the pinning of the crack front by second phase p a r t i c l e s , up to about 0.5 volume f r a c t i o n of c r y s t a l l i n e phase. 4. The c r i t i c a l stress i n t e n s i t y factor of glass-ceramics increases as the degree of c r y s t a l l i n i t y increases. The c r i t i c a l stress i n t e n s i t y factor of glass-ceramics having .85 ± .05 volume f r a c t i o n of c r y s t a l l i n e phase i s about 3.5 times that of the annealed glass. 5. Crack v e l o c i t y data of glass and glass-ceramics tested i n toluene can be explained i n terms of the " l a t t i c e trapping" model"'7. 163 6. The l i f e expectancy (time-to-failure) of glass-ceramics increases as the degree of c r y s t a l l i n i t y increases and t h i s increase i s mainly due to the c r i t i c a l s tress i n t e n s i t y . 7. The a c t i v a t i o n energy f o r c r y s t a l l i z a t i o n of l i t h i u m d i s i l i c a t e from 17.7 wt% L i 2 0 - 82.2 wt% S i 0 2 glass at 530°C was found to be 180 KJ/mole (43 Kcal/mole). 8. The Young's Modulus of glass-ceramics tends to follow 49 Hashin's model of e l a s t i c behaviour of a two phase material, up to 0.5 volume f r a c t i o n of c r y s t a l l i n e phase. 164 APPENDICES 165 APPENDIX 1 Theory of Double Torsion Technique The double tor s i o n method f o r measuring slow crack growth i s 20 based on a technique suggested by Outwater and Jerry and further 19 developed by Williams and Evans . Figure 14 shows a t y p i c a l specimen which can be considered as two t o r s i o n bars each having a rectangular cross-section, loaded to P/2. For small d e f l e c t i o n s , y and for bars having a width very much larger than the thickness, the t o r s i o n a l s t r a i n , 6 i s given by 6 P/2 • W a 9 - y/Vl - — (Al) W t 3 G where P/2 = Total load applied to one bar P/2 • W = Torsional moment m G = Shear modulus of the material a = Crack length t = Bar thickness W/2 = Bar width W = Moment arm m If c i s the e l a s t i c compliance, then on rearranging 3 W 2 a c = y/P = 2 ( A 2 ) W t G 166 If the crack p r o f i l e i s independent of the crack length, the s t r a i n -energy release r a t e , ^ may be given by £ P 2 , dc , P 2 , dc . , x ^ = = ^ ( d A ) = 2 r - ( d A ) ( A 3> n where A = Crack area t = Web thickness i n the plane of the crack, n D i f f e r e n t i a t i n g equation (A2) with respect to A and s u b s t i t u t i n g into equation (A3) 2 2 3P W s = 3 (A4) 2W t t G n Substituting the following plane s t r a i n equation for , the s t r a i n -energy release rate for crack opening mode 6 2G K I ( A 5 ) where v = Poisson's r a t i o Kj. = S t r e s s - i n t e n s i t y factor Then equation (A4) reduces to K = W ( = - ) -P (A6) 1 m W t 3 t n (1 - v) From equation (A6) i t can be seen that the stress i n t e n s i t y factor (K^ .) i s a function of the applied load, specimen dimensions and e l a s t i c constant and i t i s independent of the crack length. 167 The compliance f o r the double t o r s i o n specimen may be given by y/P = (Ba + D) ( A 7 ) dc where B = — = Slope of the experimental compliance - crack length curve. D = Intercept of the experimental compliance - crack length curve. D i f f e r e n t i a t i o n of equation ( A 7 ) with respect to time at constant displace-dy ment ( = 0 ) gives v . ( £ . ) . _ ( » t ± j > , ( - » , ( A 8 ) y y Also at constant displacement P(Ba + D) = p i ( B a i + D) = P f ( B a f + D) ( A 9 ) where subscripts i and f r e f e r to the values at the beginning and end of rel a x a t i o n . Substituting equation ( A 9 ) i n equation ( A 8 ) and rearranging V - <<jf )' = (a +D/B) ( £ ) (A10) y P ' y where V = V e l o c i t y of the crack If B >> D, the —• i s n e g l i g i b l e and hence v = - !±*f ( a ) . ( g ) ( A 1 1 ) 168 APPENDIX 2 An Estimate of Time-To-Failure From Crack Growth K i n e t i c s Under constant applied stress a , of i n t e r e s t i n a delayed r app fracture t e s t , the t i m e - t o - f a i l u r e , t i s given by 'Ic t = | f- (A12) / C. 1 where C. = I n i t i a l flaw s i z e x C, = C r i t i c a l Flaw s i z e Ic V = Crack v e l o c i t y h The time for C > C T i s n e g l i g i b l e . Since K_^ = Y a C T Ic IC app Ic 2K dC = ~ 2 — • dK (A13) Y a app Substituting equation (A13) i n equation (A12) t = f ^ . dh (A14) Y a J app * K I i For a material undergoing stress-corrosion, the crack v e l o c i t y i n region 36 I and region II can be written as V x = A^Kj 1 1 (A15) 169 V 2 = A 2 (A16) Substituting equation (A15 and (A16) i n (A14) K T t = ±- r K T ( 1 " n ) dK Y 2 a 2 A l ' 1 1 app / K I i + j~ f K r dK x (A17) 2 *T1 where K T = stress i n t e n s i t y factor at the i n f l e c t i o n between region I and region I I . A t h i r d term corresponding to region I I I may be added but t h i s i s generally n e g l i g i b l e . Depending on the environment, the second term i s often n e g l i g i b l e . Hence equation (A17) reduces to 2 < K i i 2 ~ n " K i c 2 " n > t = i L (A18) (n-2) A, Y a 1 app 170 APPENDIX 3 1(5* UJ O o i i o 5 lO61 O - WATER 0 -70% RELATIVE HUMIDITY • - 30% " A - TOLUENE 10 Figure A l V e l o c i t y - s t r e s s i n t e n s i t y factor diagrams for : (a) Annealed glass at room temperature 171 io-, , , _ , _ O to 10 ' I 0 7 L t A 1 I. I A I A I A I A i A J J _3/2 KT , MN.m Figure A l (b) Glass-ceramic containing .15 ± .05 volume f r a c t i o n of c r y s t a l l i n e phase at room temperature. t o 3 10 !— O - WATER A -TOLUENE / / o o' / o » O A / J A > I 0 5 L 0 ° o / o / o / o / 10 1-2 1-4 Kt , MN.ml Figure A l (c) Glass-ceramic containing .30 ± .05 volume f r a c t i o n of c r y s t a l l i n e phase at room temperature. 173 1 0 6 1 0 o - WATER A - TOLUENE /A /A A / A A / 1 0 c7 1 - 3 1 -5 1-7 i M N.m"2 1 9 Figure A l (d) Glass-ceramic containing .50 ± .05 volume f r a c t i o n of c r y s t a l l i n e phase at room temperature. 10 I <J e o - WATER A - T O L U E N E / c_> o t I 0 6 ' P 6 _L 1 6 1-8 2 0 2 2 _ 3 M Nm 2 2 4 2 6 Figure A l (e) Glass-ceramic containing .70 ± .05 volume f r a c t i o n of c r y s t a l l i n e phase at room temperature. •p> o - W A T E R /O A - T O L U E N E / ° OS / o /° J L K T , M N . m 2 / / A A / A A 'O A / A 20 2-2 24 2-6 28 30 3 Figure A l (f) Glass-ceramic containing .85 ± .05 volume f r a c t i o n of c r y s t a l l i n e phase at room temperature. 176 BIBLIOGRAPHY 1. 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