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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. I n d i a n I n s t i t u t e o f S c i e n c e , 1969 M.A.Sc. U n 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 M e t a l l u r g y  We accept  t h i s t h e s i s as conforming  to the r e q u i r e d standard  THE UNIVERSITY OF BRITISH COLUMBIA May, ©  1977  A v a r a l S. Rao, 1977  In  presenting  this  an a d v a n c e d  degree  the  shall  I  Library  further  for  agree  scholarly  by  his  of  this  written  at  purposes  for  freely  permission may It  is  British  July  15,  1977  of  Columbia,  British  by  for  gain  Columbia  shall  the  that  not  requirements I  agree  r e f e r e n c e and copying  t h e Head o f  understood  Metallurgy of  of  for extensive  permission.  University  fulfilment  available  be g r a n t e d  financial  2075 Wesbrook Place Vancouver, Canada V6T 1W5  Date  it  representatives. thesis  in p a r t i a l  the U n i v e r s i t y  make  that  Department o f The  thesis  of  this  be a l l o w e d  or  that  study. thesis  my D e p a r t m e n t  copying  for  or  publication  without  my  i  ABSTRACT  The  dependence of f r a c t u r e s t r e n g t h upon t h e time of l o a d i n g i s  commonly termed s t a t i c f a t i g u e o r d e l a y e d  failure.  T h i s has  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 f l a w s under s t r e s s . study o f s u b c r i t i c a l c r a c k growth i s i m p o r t a n t expectancy  i n two  g l a s s - c e r a m i c s , a t room  d i f f e r e n t environments ( t o l u e n e and water)  G l a s s c o n t a i n i n g 17.8  wt%  I^O  ( g l a s s - c e r a m i c s ) were chosen.  - 82.2  w  t % SiO^ and  The double  t o r s i o n technique  shown t h a t the s l o p e s o f the v e l o c i t y - s t r e s s i n t e n s i t y  diagrams f o r g l a s s and  glass-ceramics  was  crystallized  used t o d e t e r m i n e c r a c k v e l o c i t y a t v a r i o u s s t r e s s i n t e n s i t y I t was  life  of a m a t e r i a l when i t i s s u b j e c t e d t o a s t r e s s .  temperature and  glasses  Hence t h e  i n p r e d i c t i n g the  S u b c r i t i c a l c r a c k growth o f g l a s s and  studied.  been  was  factors. factor  ( h a v i n g d i f f e r e n t volume f r a c t i o n s  o f c r y s t a l l i n e phase) t e s t e d i n w a t e r , remained c o n s t a n t .  However, t h e s e  plots shifted  to the h i g h e r s t r e s s - i n t e n s i t y r e g i o n , as t h e degree o f  crystallinity  i n the g l a s s i n c r e a s e d .  f a c t o r p l o t s o f g l a s s and s i m i l a r behaviour  but  The  crack v e l o c i t y - s t r e s s  intensity  g l a s s - c e r a m i c s t e s t e d i n t o l u e n e have shown a  the s l o p e of t h e s e p l o t s i n c r e a s e d as the d e g r e e  o f c r y s t a l l i n i t y i n the g l a s s i n c r e a s e d .  A m o d i f i c a t i o n o f the  stress-  23 c o r r o s i o n model of H i l l i g and of g l a s s and model.  Charles  i s proposed.  Crack v e l o c i t y  data  g l a s s - c e r a m i c s t e s t e d i n water agreed w e l l w i t h the proposed  Crack v e l o c i t y d a t a o f g l a s s and  glass-ceramics t e s t e d i n toluene  ii  a r e d i s c u s s e d . i n terms of the " l a t t i c e t r a p p i n g t h e o r y " . . presented  to predict.the l i f e  from c r a c k growth  The  t e s t was  glass-ceramics.  i s i n c r e a s e d m a i n l y due  i n c r e a s e i n the f r a c t u r e s u r f a c e energy. f a c t o r of glass-ceramics  used to determine the f r a c t u r e  These r e s u l t s have shown t h a t  t h e f r a c t u r e s t r e n g t h of g l a s s - c e r a m i c s  The  critical  i n c r e a s e s as the degree of  shown t h a t the f r a c t u r e s u r f a c e energy o f g l a s s - c e r a m i c s  calculated  graphic  L i 0 - 82.2 at ion  was up  inter-  i s f u r t h e r s u b s t a n t i a t e d by f r a c t o -  examination.  The 2  it  containing  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 This observation  the  crystallinity  f r a c t u r e s u r f a c e . energy of t h e s e m a t e r i a l s was  p a r t i c l e spacing.  to  stress intensity  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  to 0.5  is  expectancy under s t r e s s of t h e s e m a t e r i a l s  transverse rupture  The  equation  data.  s t r e n g t h o f g l a s s and  increases.  An  wt  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% % Si0  530°C f o r v a r i o u s  2  glass lengths  was  s t u d i e d by c r y s t a l l i z i n g  o f time.  I t was  this  shown t h a t the  crystallizat-  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 .  found t h a t the d i f f u s i v i t y f o r t h i s p r o c e s s 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 i o n .  glass  i s much lower than  It the  was  iii  ACKNOWLEDGEMENT  I would l i k e for h i s advice project.  to thank my r e s e a r c h  s u p e r v i s o r Dr. J . S. Nadeau  and a s s i s t a n c e throughout t h e course of t h i s  research  Thanks a r e a l s o due to o t h e r members o f t h e department and  f e l l o w graduate students  with  s p e c i a l a p p r e c i a t i o n t o Mr. R. Bennett  and Dr. M. A. C l a r k .  F i n a n c i a l a s s i s t a n c e i n t h e form of a N a t i o n a l C o u n c i l Research A s s i s t a n t s h i p i s g r e a t l y acknowledged.  Research  iv  TABLE OF CONTENTS  Page CHAPTER 1  CHAPTER 2  INTRODUCTION  1  1.1  P r e v i o u s Work on S t a t i c F a t i g u e of G l a s s  3  1.2  S t a t i c F a t i g u r e Models and Mechanisms  1.3  Summary of t h e T h e o r e t i c a l Models  1.4  E s t i m a t i o n of T i m e - T o - F a i l u r e Kinetics  1.5  O b j e c t i v e s o f t h e P r e s e n t Work  15 .. 24  from Growth  26  27  EXPERIMENTAL PROCEDURE 2.1  2.2  Material Preparation  28  2.1.1  Glass Preparation  28  2.1.2  Specimen P r e p a r a t i o n  2.1.3  Heat Treatment  .. .. 29 29  Sample C h a r a c t e r i z a t i o n  30  2.2.1  D i f f e r e n t i a l Thermal A n a l y s i s  30  2.2.2  D e n s i t y Measurement  30  2.2.3  Metallography  31  2.2.4  2.2.3.1  O p t i c a l M i c r o s c o p i c Examination .. 31  2.2.3.2  Petrographic Examination  33  2.2.3.3  Transmission E l e c t r o n Microscopy (TEM)  34  Determination  of Degree o f C r y s t a l l i n i t y  2.2.4.1  Point-Count  2.2.4.2  X-ray Method  Method  ..34 34 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  2.4  Measurement of E l a s t i c Constants  2.5  2.6  CHAPTER 3  37 ..  38  2.4.1  Young's Modulus  38  2.4.2  Poisson's Ratio  40  Measurement o f M e c h a n i c a l P r o p e r t i e s  41  2.5.1  M i c r o h a r d n e s s Measurement  41  2.5.2  T r a n s v e r s e Rupture S t r e n g t h  41  Slow Crack Growth T e s t s  42  2.6.1  Slow Crack Growth of Annealed G l a s s  ....  42  2.6.2  Slow Crack Growth of G l a s s - c e r a m i c s  ....  49  ..  49  2.7  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 Measurement  2.8  F r a c t o g r a p h i c Examination  50  RESULTS 3.1  D i f f e r e n t i a l Thermal A n a l y s i s  51  3.2  D e n s i t y 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  T r a n s v e r s e Rupture T e s t s  68  3.7  Slow Crack Growth T e s t s  77  3.7.1  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 Diagrams  77  3.7.1.1  77  Annealed G l a s s  vi  Page 3.7.1.2  3.7.1.3  G l a s s - C e r a m i c s up t o 50% of C r y s t a l l i n e Phase  80  G l a s s - C e r a m i c s 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 Intensity Factor  3.9  F r a c t u r e S u r f a c e Energy  (K^)  3.10 F r a c t o g r a p h y CHAPTER 4  8  8  8  8  91  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  4.2  Mechanical Properties  ..107 ..  ..H  8  i  Microhardness  .. .. .. H  4.2.2  E l a s t i c Moduli  4.2.3  Fracture Strength  4.3  F r a c t u r e S u r f a c e Energy  4.4  Static Fatigue  4.5 CHAPTER 5  4.2.1  .. ........  8  1 2 1  1 2  5  .. .. ..134 ..137  4.4.1  Model f o r Slow C r a c k Growth i n C o r r o s i v e Environment (water) .. . . . . . . . . . . .. 137  4.4.2  Slow C r a c k Growth i n N o n - C o r r o s i v e Environment ( t o l u e n e )  P r e d i c t i o n o f L i f e Expectancy  SUMMARY AND CONCLUSIONS  .7".. .. .. ..155 ..162  APPENDICES BIBLIOGRAPHY  144  164 •  -  1 7  6  vii  LIST OF FIGURES Figure Number 1  Page S t r e s s - t i m e 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  F a t i g u e o f g l a s s and p o r c e l a i n under s t e a d y l o a d s ( A f t e r -Preston^) ,  3  4  Weakening o f g l a s s rods d u r i n g f r a c t u r e as computed from s t r e s s - t i m e c h a r a c t e r i s t i c s c u r v e ( A ) , a = 5500 p s i ( B ) , a i = 10,000 p s i ( A f t e r Shand 8) 1  4  F r a c t u r e time s t r e n g t h S/Sn treatments of and S o u t h w i c k  5  as a f u n c t i o n o f reduced for d i f f e r e n t surface s o d a - l i m e g l a s s ( A f t e r Mould )  1 2  8  U n i v e r s a l f a t i g u e c u r v e f o r g l a s s abraded i n v a r i o u s ways ( A f t e r Mould and Southwick"'- ) 2  6  6  ..  E f f e c t o f time and temperature on r e l a t i v e • strength (After Mould ) .. . . . . . . . . . . . . . .  10  Reduced s t r e n g t h Vs l o a d d u r a t i o n ( l o g s c a l e ) f o r specimens t e s t e d immersed i n d i s t i l l e d water and i n n i t r o g e n atmospheres o f 0.5% and 43% r e l a t i v e h u m i d i t y ( A f t e r M o u l d ) . . . . . . . . ..  12  Schematic s t 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 for a material i n a c o r r o s i v e environment . . . . . . ....  13  1 3  7  ,  1 1  8  9  ......  Dependence o f c r a c k v e l o c i t y on s t r e s s intensity factor, Kj i n soda-lime-silica glass ( A f t e r Wiedernorn ^) .. .. .. ..  .. ..  Dependence o f c r a c k 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 g l a s s ( A f t e r Wiederhorn  ) .. ..  2  10  9  ....  14  2  0  11  Photograph o f Automatic L a p p i n g Machine  ..  32  12  P o r t i o n o f t h e phase diagram o f I ^ O - S i t ^ system .. . . . . . . . . . . . .  36  viii  Figure Number 13  Page Photograph of s t a t i c e l a s t i c m o d u l i measurement s e t up  39  14  Specimen used i n double t o r s i o n  test  ^  15  L o a d i n g f i x t u r e used i n double t o r s i o n  16  Schematic drawing of h u m i d i t y chamber  17  Flow diagram of h u m i d i t y c o n t r o l l i n g  18  Differential glass  19  Dependence of h e a t i n g r a t e on peak c r y s t a l l i z a t i o n temperature  20  D e n s i t i e s of the g l a s s - c e r a m i c s as a f u n c t i o n of volume f r a c t i o n of c r y s t a l l i n e phase .. ,.  test  .. 46 47  s e t up  thermal a n a l y s i s of annealed  52  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 a s s ceramics as a f u n c t i o n of time at 530°C .. . . .  22  O p t i c a l micrograph of g l a s s - c e r a m i c c o n t a i n i n g (a)  .05 volume f r a c t i o n  (b)  .15 t o .20 volume f r a c t i o n c r y s t a l l i n e phase  (c)  .35 volume f r a c t i o n phase  of  .55 volume f r a c t i o n phase  of  .75 volume f r a c t i o n phase  of  .90 volume f r a c t i o n phase  of  (d)  (e)  (f)  of c r y s t a l l i n e  phase..  of  53  J J  58  60  60  crystalline •• ••  61  crystalline 61 crystalline . .•  D  Z  crystalline 62  23  R e l a t i v e degree of c r y s t a l l i n i t y as a f u n c t i o n . of time at 530°C  64  24  M i c r o h a r d n e s s of g l a s s - c e r a m i c as a f u n c t i o n of volume f r a c t i o n of c r y s t a l l i n e phase ..  65  Young's modulus o f g l a s s — c e r a m i c s as a f u n c t i o n of "volume f r a c t i o n of c r y s t a l l i n e phase P o i s s o n ' s r a t i o o f g l a s s - c e r a m i c s as a f u n c t i o n of volume f r a c t i o n o f c r y s t a l l i n e phase Shear modulus of g l a s s - c e r a m i c s as a f u n c t i o n o f volume f r a c t i o n of c r y s t a l l i n e phase F r a c t u r e s t r e s s ( a f ) and 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 (K-TQ) of g l a s s - c e r a m i c s as a f u n c t i o n o f volume f r a c t i o n o f c r y s t a l l i n e phase R e l a t i v e f r a c t u r e s t r e s s of g l a s s - c e r a m i c s as a f u n c t i o n o f volume f r a c t i o n o f c r y s t a l l i n e phase  ..  E f f e c t of mean f r e e path between s p h e r u l i t e s on f r a c t u r e s t r e s s (tested i n toluene) of g l a s s ceramics E f f e c t of mean f r e e path between s p h e r u l i t e s on f r a c t u r e s t r e s s ( t e s t e d i n water) o f g l a s s 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 o r annealed g l a s s a t 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 f o r g l a s s - c e r a m i c c o n t a i n i n g .15 ± .05 volume f r a c t i o n of c r y s t a l l i n e phase a t 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 f o r g l a s s - c e r a m i c c o n t a i n i n g .30 ± .05 volume f r a c t i o n of c r y s t a l l i n e phase a t 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 f o r g l a s s - c e r a m i c c o n t a i n i n g .50 ± 5 volume f r a c t i o n of c r y s t a l l i n e phase a t 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 f o r g l a s s - c e r a m i c c o n t a i n i n g .70 ± .05 volume f r a c t i o n of c r y s t a l l i n e phase a t 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 f o r g l a s s - c e r a m i c c o n t a i n i n g .85 + .05 volume f r a c t i o n of c r y s t a l l i n e phase a t room temperature  X  Figure Number 38  39  40  41  Page 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 g l a s s and g l a s s - c e r a m i c s t e s t e d i n water a t room temperature  86  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 g l a s s and g l a s s - c e r a m i c s t e s t e d i n t o l u e n e a t room temperature  89  E f f e c t of mean f r e e p a t h between s p h e r u l i t e s on f r a c t u r e s u r f a c e energy o f g l a s s - c e r a m i c  92  SEM f r a c t o g r a p h of sample (used i n t r a n s v e r s e r u p t u r e t e s t s ) of (a)  (b)  (c)  (d)  42  G l a s s - c e r a m i c c o n t a i n i n g l e s s than f r a c t i o n of c r y s t a l l i n e phase  .05 volume 94  Glass-ceramic c o n t a i n i n g .15 ± .05 volume f r a c t i o n o f c r y s t a l l i n e phase  95  G l a s s - c e r a m i c c o n t a i n i n g .50 ± .05 volume f r a c t i o n o f c r y s t a l l i n e phase  96  G l a s s - c e r a m i c c o n t a i n i n g .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  SEM f r a c t o g r a p h of sample (used i n double t e s t s ) of (a)  (b)  (c)  (d)  (e)  •(f)  G l a s s - c e r a m i c c o n t a i n i n g l e s s than f r a c t i o n o f c r y s t a l l i n e phase G l a s s - c e r a m i c c o n t a i n i n g .05 volume of c r y s t a l l i n e phase  torsion  .05 volume 98 fraction 99  G l a s s - c e r a m i c c o n t a i n i n g .15 ± .05 volume f r a c t i o n o f c r y s t a l l i n e phase  100 .  G l a s s - c e r a m i c c o n t a i n i n g .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  G l a s s - c e r a m i c c o n t a i n i n g .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  G l a s s - c e r a m i c c o n t a i n i n g .70 ± .05 volume f r a c t i o n o f c r y s t a l l i n e phase  103  XX  Page (g)  G l a s s - c e r a m i c c o n t a i n i n g .85 ± .05 volume f r a c t i o n of c r y s t a l l i n e phase  (h)  G l a s s - c e r a m i c c o n t a i n i n g .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 i n d i c a t e s the d i r e c t i o n of c r a c k propagation]  105  TEM photograph of i n d i v i d u a l l i t h i u m spherulite  disilicate 109  TEM photograph of i n d i v i d u a l l i t h i u m spherulite  disilicate  TEM photograph of i n d i v i d u a l l i t h i u m spherulite  disilicate  (a)  (b)  (c)  (a)  (b)  104  HO  HI  SEM photogtaph of p a r t i a l l y c r y s t a l l i z e d g l a s s ceramic  H5  T y p i c a l s p h e r u l i t i c m i c r o s t r u c t u r e of p a r t i a l l y c r y s t a l l i z e d g l a s s - c e r a m i c from p e t r o g r a p h i c section (crossed n i c o l s )  H6  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 v e r s u s r e c i p r o c a l of square r o o t of time of c r y s t a l l i z a t i o n at 530°C  1  1  7  F r a c t u r e s t r e s s and microhardness of g l a s s - c e r a m i c s v e r s u s 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 c o m p o s i t i o n on e l a s t i c modulus of g l a s s e s i n system: x Me20 (100 - x) Si02 where Me2 i s L i 2 0 ( a f t e r Kozlovskaya35)  122  Comparison of v a l u e s of Young's modulus of g l a s s - c e r a m i c s w i t h the t h e o r e t i c a l models 12^ Comparison of v a l u e s of P o i s s o n ' s r a t i o of g l a s s - c e r a m i c s w i t h the t h e o r e t i c a l models -^6 V e l o c i t y versus  Stress intensity factor C r i t i c a l stress intensity factor  diagram f o r g l a s s and at room temperature)  glass-ceramics (tested  i n water 143  xii  Figure Number 51  Page G r a p h i c a l r e p r e s e n t a t i o n of the slow c r a c k growth regime r e s u l t i n g from l a t t i c e t r a p p i n g ( A f t e r Thompson ) 57  52  V e l o c i t y - s q u a r e of s t r e s s i n t e n s i t y f a c t o r diagram f o r ( t e s t e d i n t o l u e n e a t room temperature) (a)  Annealed  (b)  G l a s s - c e r a m i c c o n t a i n i n g .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  G l a s s - c e r a m i c c o n t a i n i n g .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  G l a s s - c e r a m i c c o n t a i n i n g .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  G l a s s - c e r a m i c c o n t a i n i n g .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  G l a s s - c e r a m i c c o n t a i n i n g .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  (c)  (d)  (e)  (f)  53  146  (a)  (b)  Glass  148.  L i f e expectancy v e r s u s volume f r a c t i o n of c r y s t a l l i n e phase a t a — 2 - = 1.1 a app L i f e expectancy v e r s u s volume of c r y s t a l l i n e phase at a  — B - a .(c)  (d)  (e)  fraction 158 1.5  app  L i f e expectancy v e r s u s volume f r a c t i o n of c r y s t a l l i n e phase a t a a  157  1 5  9  app  L i f e expectancy v e r s u s volume f r a c t i o n of c r y s t a l l i n e phase a t a 3 a app L i f e expectancy v e r s u s 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  xiii  Figure Number Al  Page 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 g l a s s a t room temperature  170  (b)  G l a s s - c e r a m i c c o n t a i n i n g .15 ± .05 volume f r a c t i o n of c r y s t a l l i n e phase a t room temperature  171  G l a s s - c e r a m i c c o n t a i n i n g .30 ± .05 volume f r a c t i o n of c r y s t a l l i n e phase a t room temperature  172  (c)  (d)  G l a s s - c e r a m i c c o n t a i n i n g .50 ± .05 volume f r a c t i o n o f c r y s t a l l i n e phase a t room temperature  (e)  (f)  G l a s s - c e r a m i c c o n t a i n i n g .70 ± .05 volume f r a c t i o n o f c r y s t a l l i n e phase at room temperature G l a s s - c e r a m i c c o n t a i n i n g .85 ± .05 volume f r a c t i o n of c r y s t a l l i n e phase a t room temperature  17^  174  17S  •  L / J  xiv  LIST OF TABLES Table  Page  1  Summary o f DTA o f t h e g l a s s  54  2  D e n s i t y of t h e g l a s s  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 g l a s s ceramics a f t e r h e a t - t r e a t i n g f o r v a r i o u s l e n g t h s of time a t 530 ± 5°C  59  E f f e c t o f degree o f c r y s t a l l i n i t y hardness  on m i c r o 66  E f f e c t o f degree o f c r y s t a l l i n i t y moduli  on  E f f e c t of degree o f c r y s t a l l i n i t y stress  on f r a c t u r e  4  5  6  7  11  =  AK  70  73  79  n  =  87  AK»  E f f e c t of degree of c r y s t a l l i n i t y upon s l o p e s and i n t e r c e p t s of l o g V - l o g diagrams (tested i n toluene) V  10  .. .. .. ..  E f f e c t o f degree of c r y s t a l l i n i t y upon s l o p e s and i n t e r c e p t s of l o g V - l o g diagrams ( t e s t e d i n water) V  9  elastic  E f f e c t of environment upon s l o p e s and i n t e r c e p t s o f log V - log diagrams of annealed g l a s s V  8  and g l a s s - c e r a m i c s  =  AK*  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 s and f r a c t u r e s u r f a c e e n e r g i e s o f g l a s s and g l a s s - c e r a m i c s Summary of (  90  ) and ( — — °GC GC  ....  93  ) f o r glass 2  E  ceramics  1  2  8  XV  LIST OF TABLES  Table 12  Page Summary of (  ) and  (  °GC 13  ) Y  f o r glass-  GC  ceramics  131  C r i t i c a l flaw size i n samples used i n transverse rupture tests  133  2 2 y o f  14  Summary of a c t i v a t i o n energy calculated from crack v e l o c i t y data  154  1  1. INTRODUCTION  The  most c h a r a c t e r i s t i c mechanical p r o p e r t y  ceramics i s b r i t t l e n e s s . c e r t a i n s t r e s s and  These m a t e r i a l s deform e l a s t i c a l l y up  then suddenly break.  s e n s i t i v e to the s u r f a c e c o n d i t i o n s and of s u r f a c e  flaws.  by a m o d i f i e d  The  1 y  Fr  (  The  fracture strength  glass-  to a i s extremely  i s u s u a l l y determined by  the  size  f r a c t u r e s t r e n g t h i s r e l a t e d to flaw dimension  Griffith's  _  of g l a s s and  2 E  c  equation''":  "± )  (1)  H  c  where y  =  A geometrical  factor  E  =  Young's modulus  =  E f f e c t i v e surface  energy.  For a l o n g p e r i o d of time, f r a c t u r e i n g l a s s was depend upon flaw geometry.  L a t e r i t was  realized  assumed to  t h a t f r a c t u r e was  also  a f f e c t e d by a c t i v e environments. The  first  evidence f o r s t r e n g t h r e d u c t i o n i n g l a s s by an  external  2 environment was  found by Grenet  than those loaded  slowly.  .  Glass  l a t h s loaded  In a d d i t i o n , a time d e l a y  i n which g l a s s l a t h s would support  r a p i d l y were  stronger  to f a i l u r e was  observed  a l o a d f o r a p e r i o d of time b e f o r e  failure.  T h i s dependence of f r a c t u r e s t r e n g t h upon the time of l o a d i n g has  been termed  S t a t i c Fatigue  solids.  or Delayed F a i l u r e and  i s observed i n many ceramic  S t a t i c f a t i g u e data are commonly expressed as s t r e s s versus to f a i l u r e as shown i n F i g u r e 1. occur  i s c a l l e d the  A s t r e s s below which f a i l u r e w i l l  static fatigue limit.  time  not  2  16,-  DURATION OF LOAD (sec)  Figure 1  S t r e s s - t i m e c h a r a c t e r i s t i c s of annealed soda lime g l a s s - r o d s V i n diameter, i n bending ( a f t e r Shand ). 7  3  1.1  Previous  Work on  Static Fatigue  of  Glass  4 Preston  observed t h a t g l a s s can c a r r y a h e a v i e r  seconds t h a n i t can  c a r r y f o r a minute; i t can  a minute t h a n f o r an hour.  He  s o d a - l i m e - s i l i c a t e g l a s s and  Preston"*  porcelain.  i n various  load  for  p o r c e l a i n as shown i n F i g u r e mm  (V ) 1  2.  Strength  diameter.  Later  i n v e s t i g a t e d the phenomenon o f s t r e n g t h decay o r  f a t i g u e i n more d e t a i l . g l a s s and  carry a heavier  static  They examined s o d a - l i m e g l a s s , Pyrex g l a s s ,  They measured the  s u r r o u n d i n g media and  i n vacuum i s f a i r l y  few  c a l c u l a t e d a f a t i g u e c u r v e f o r annealed  measurements were done by u s i n g rods of 8.35 Baker and  load f o r a  t e n s i l e strength of these  found t h a t the t e n s i l e s t r e n g t h  independent of the  time o f l o a d i n g .  silica  materials of  glass  However, i f the  g l a s s were exposed t o m o i s t u r e , i t r a p i d l y l o s t i t s s t r e n g t h under s t r e s s . I t was  c o n c l u d e d t h a t the  i n the f l a w s  s t r e n g t h decay i s m a i n l y due  of g l a s s by water and  s h i p between t i m e o f  S  =  f a i l u r e and  [Cj/log C  2  where S  =  Breaking s t r e s s  t  =  Time o f and  t]  +  p o s s i b l y by CO^.  to c h e m i c a l  They found a  attack relation-  s t r e s s as shown below:  C  , (2)  3  failure are  arbitrary  constants.  3 Orowan be broken by  He  s t r e s s e s f a r below the o r d i n a r y b r e a k i n g  i n short-time l o n g time.  observed a s i m i l a r phenomenon.  He  t e s t s , provided  found t h a t g l a s s  can  s t r e s s as measured  t h a t the l o a d i s a p p l i e d f o r a  observed t h a t about a t h i r d o f the s h o r t - t i m e  sufficiently breaking  stress  4  Figure 2  F a t i g u e of g l a s s and p o r c e l a i n under steady l o a d s ( a f t e r P r e s t o n ^ ) .  5  is  sufficient  to produce f r a c t u r e , i f i t i s s u s t a i n e d  f o r a number of  weeks. Gurney and  Pearson  performed both c y c l i c and  experiments on s o d a - l i m e - s i l i c a t e g l a s s and p o i n t i n d e l a y e d f a i l u r e was whether the l o a d i n g was  concluded t h a t an  the time of l o a d i n g  c y c l i c or  static  (duration)  fatigue important  and  not  static.  7 8 Shand ' , i n r e v i e w i n g  the work on s t a t i c  the weakening of t y p i c a l specimens d u r i n g stress-time  curve was  the l o a d i n g p e r i o d .  determined f o r a group of 8.35  of annealed soda-lime g l a s s and these r e s u l t s he  fatigue, calculated  mm  (V)  A mean diameter rods  the r e s u l t s are shown i n F i g u r e 1.  From  c o r r e l a t e d the weakening of a specimen to the growth of  a flaw under a constant From F i g u r e  a p p l i e d s t r e s s as  follows.  1 i t i s found t h a t the b r e a k i n g  of l o a d i n g of t , seconds i s a  stress for a period  p s i , then the r e l a t i v e remaining  a f t e r a p e r i o d of l o a d i n g of t seconds may R e l a t i v e Remaining S t r e n g t h  be r e p r e s e n t e d  strength  by  a —  =  (3) b  where  i s the b r e a k i n g  as taken from F i g u r e 1. 10000 p s i and  s t r e s s f o r a p e r i o d of l o a d i n g of The  ( t ^ - t ) seconds  c o r r e s p o n d i n g graph f o r 2 a p p l i e d  5500 p s i i s as shown i n F i g u r e  3.  stresses,  T h i s shows t h a t  the  weakening (or r a t e of flaw growth) i s s m a l l u n t i l a l a r g e f r a c t i o n of breaking  time i s reached.  At  t h i s point  f l a w growth a c c e l e r a t e s and  f l a w geometry c o n d i t i o n approaches the c r i t i c a l v a l u e 8 spontaneous c r a c k p r o p a g a t i o n . glass w i l l  Therefore  cause slow p r o p a g a t i o n of flaws  i n c r e a s e as the c o n d i t i o n of r u p t u r e  Shand and  the stress-  g i v e n by G r i f f i t h " ' " f o r  concluded, t h a t s t r e s s e s i n the r a t e of p r o p a g a t i o n  i s approached.  will  6  Figure 3  Weakening o f g l a s s rods d u r i n g f r a c t u r e as computed from s t r e s s - t i m e 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 ( A f t e r Shand ) 8  7  Mould *'" '" '' ' :  LU  LJ  X  and  :>  Southwick"""^ s t u d i e d  the s t r e n g t h  (S) as a f u n c t i o n of f i v e v a r i a b l e s : time, temperature, ambient of the atmosphere, a b r a s i o n  depth and  abrasion  age.  The  of  glass  humidity  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 g l a s s abraded i n s i x d i f f e r e n t ways and area.  broken i n f l e x u r e so t h a t a l l f r a c t u r e o r i g i n a t e d i n the  They found t h a t t h e r e was  no  abraded  change i n s t r e n g t h w i t h time at  nitrogen  temperature  (-196°C).  nitrogen  temperature  (S ) p r o v i d e d n  S/S  p l o t t e d as a f u n c t i o n of l o g f a i l u r e time at s t r e s s S f o r d i f f e r e n t  n  was  surface  The  factor.  average f a i l u r e time at S/S  s t r o n g f u n c t i o n of s u r f a c e One  at  liquid  When the  ratio  Curve"  are p l o t t e d a g a i n s t  abrasive  = % called  (UFC)  as shown i n F i g u r e  reduced time l o g t / t . T  5.  a  strengths,  a wide v a r i e t y of  by  a s i n g l e smooth  6 shows the e f f e c t of temperature on r e l a t i v e s t r e n g t h  f o r s e v e r a l f i x e d f a i l u r e times. 4 zones namely A,  B, C and  t h i s phenomenon as f o l l o w s . (Zone A ) ,  Here reduced  Despite  t r e a t m e n t s , a l l the d a t a are w e l l r e p r e s e n t e d Figure  was  -3  n  treatments.  tj  as  o f the most f a s c i n a t i n g r e s u l t s o f Mould's work i s the  "Universal Fatigue  curve.  a normalizing  strength  t r e a t m e n t s , a s e r i e s of curves of the same shape were found,  shown i n F i g u r e 4.  S/Sn  Hence the b r e a k i n g  liquid  At low  to be due  temperature and  qualitatively  very  short  independent of time and  to the f a c t  )  Southwick d i v i d e d t h i s p l o t i n t o  D as shown i n F i g u r e 6 and  f a i l u r e stress i s nearly  This i s believed  Mould and  (S/S  explained  failure  time,  temperature.  that s i g n i f i c a n t chemical i n t e r a c t i o n  w i t h the environment i s not p o s s i b l e under these c o n d i t i o n s .  In Zone B,  c h e m i c a l i n t e r a c t i o n or s t r e s s - e n h a n c e d c h e m i c a l r e a c t i o n b e g i n s to dominate and hence s t a t i c f a t i g u e i s v e r y  pronounced.  Zone C  probably  8  LOAD DURATION (sec.)  Figure 4  a  Severe g r i t  b  M i l d g r i t b l a s t Emery c l p t 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 s t r e s s  c  150 g r i t  F r a c t u r e time s t r e n g t h S/Sn treatments o f and S o u t h w i c k x  blast  as a f u n c t i o n of reduced for d i f f e r e n t surface soda-lime g l a s s ( A f t e r Mould ).  9  a  Severe g r i t  b  M i l d g r i t b l a s t Emery C l o t h perpendicular to s t r e s s  d  600  grit  e  320  grit  f  150 g r i t p a r a l l e l to s t r e s s  c  150  Figure 5  blast  grit  U n i v e r s a l f a t i g u e curve f o r g l a s s abraded i n v a r i o u s ways ( A f t e r Mould and Southwick  ^ )  10  100  Figure 6  200  300 400 500 600 TEMPERATURE (°KJ  U  1  1  700  800  900  E f f e c t of time and temperature on r e l a t i v e strength (After M o u l d ) . 1 3  11  r e f l e c t s t h e e f f e c t s of a c o u n t e r p r o c e s s such as d e s o r p t i o n o f water. In Zone D,  the g l a s s becomes s o f t enough f o r f a i l u r e by v i s c o u s f l o w .  They a l s o found  t h a t the s t a t i c f a t i g u e l i m i t  n o r m a l l y measured s h o r t time s t r e n g t h .  The  i s about one  e f f e c t of the  t h i r d o f the surrounding  13 medium on s t a t i c  f a t i g u e behaviour  i s shown i n F i g u r e 7  .;  I t can  be  seen t h a t t h e f a t i g u e c u r v e s under t h e d i f f e r e n t c o n d i t i o n s s t u d i e d a r e essentially parallel An velocity  t o one  a l t e r n a t i v e way  another. of i l l u s t r a t i n g s t a t i c f a t i g u e i s by  (V) o f a s u b c r i t i c a l c r a c k as a f u n c t i o n of the s t r e s s  plotting  intensity  14 factor  (Kj)  .  A schematic  lnV-K^ diagram i s shown i n F i g u r e 8.  c h a r a c t e r i s t i c r e g i o n s o f c r a c k growth a r e apparent  Three  from t h i s f i g u r e .  At  low v a l u e s o f the s t r e s s i n t e n s i t y f a c t o r r e g i o n I , c r a c k growth i s e x p o n e n t i a l l y dependent on the .stress i n t e n s i t y f a c t o r and a l s o dependent on the environment as shown i n F i g u r e 9. the c r a c k v e l o c i t y i s n e a r l y independent  In the p l a t e a u r e g i o n ( r e g i o n I I ) of the a p p l i e d s t r e s s - i n t e n s i t y .  In r e g i o n I I I , the c r a c k v e l o c i t y i s a g a i n e x p o n e n t i a l l y dependent on U n i v e r s a l f a t i g u e curves can be c a l c u l a t e d from 17 assuming the c r a c k s i z e and  geometry  .  lnV-I?_ d a t a by  F o r a s h a l l o w s u r f a c e c r a c k whose  l e n g t h a l o n g the s u r f a c e i s much g r e a t e r than i t s depth L ,  = a* TrL~. S i n c e /  the s t r e s s i n t e n s i t y f a c t o r i s p r o p o r t i o n a l t o the l o a d , K^/K^, = 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  s t r e n g t h a t l i q u i d n i t r o g e n temperature. to f a i l u r e ,  The  l o g a r i t h m o f reduced  d a t a or a n a l y t i c a l i n t e g r a t i o n of t h e e q u a t i o n o f v e l o c i t y and Wiederhorn and B o l z " ^ found  a  ^ N a  i s the breaking  l o g ( t / t ^ ) i s o b t a i n e d by n u m e r i c a l i n t e g r a t i o n o f  intensity factor.  K^.  time  lriV-K^. stress  the d a t a o f v e l o c i t y  and  12  10,  ic  3  icr  2  io"' LOAD  Figure 7  i  IO  too  icoo  io*  D U R A T I O N (sec)  Reduced s t r e n g t h Vs l o a d d u r a t i o n ( l o g s c a l e ) f o r specimens t e s t e d immersed i n d i s t i l l e d water and i n n i t r o g e n atmospheres of 0.5% and 43% r e l a t i v e h u m i d i t y ( A f t e r Mould J-) 1  Figure 8  Schematic s t 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 for a material i n a c o r r o s i v e environment.  14  Figure 9  Dependence of c r a c k v e l o c i t y on s t r e s s intensity factor, i n soda-lime s i l i c a glass (After Wiederhorn 5). 2  15  s t r e s s i n t e n s i t y f a c t o r to f i t i n t o an  V  =  V  exp  o  [ (-E*  +  equation,  b K ) /RT] 1  (4)  at stage I I n t e g r a t i o n of e q u a t i o n  (4) g i v e s  K /K  -  The  =  2_  =  0.5  (  ) log (t/t^)  (5)  r e s u l t s of Wiederhorn and h i s coworkers"^ were o b t a i n e d  by  18 the double difficult  c a n t i l e v e r beam (DCB)  technique.  In t h i s t e c h n i q u e i t i s  to c o n t r o l c r a c k v e l o c i t y because of i n c r e a s i n g s t r e s s  intensity  19 with crack length.  R e c e n t l y W i l l i a m s and Evans  showed how  the  double  20 torsion  (DT)  With t h i s  technique c o u l d be used  specimen,  i s independent  to produce a s t a b l e c r a c k . g i v e n i n Appendix 1.2  of c r a c k l e n g t h and hence i t i s easy  t h e o r y of the double  t o r s i o n technique i s  1.  S t a t i c F a t i g u e Models and Mechanisms  The was  The  i n c r a c k v e l o c i t y measurements.  e a r l i e s t attempt  3 by Orowan .  He approached the problem by c o n s i d e r i n g the  relation:  where  t o i n v e s t i g a t e the mechanism of s t a t i c  a  =  Breaking  stress  E  =  Young's modulus  fatigue  Griffith's  1  16  Y  =  S u r f a c e energy  C  =  Depth of the most severe s u r f a c e c r a c k . He proposed t h a t a decrease  i n s u r f a c e energy caused  by  the  a d s o r p t i o n of s p e c i e s from the environment was  responsible f o r lowering  the b r e a k i n g s t r e s s i n an a c t i v e environment.  I f f r a c t u r e occurs  the adsorbed necessary  f i l m cannot advance as f a s t as the c r a c k t i p .  The  rapidly,  stress  to produce such a r a p i d f r a c t u r e i s o b t a i n e d from e q u a t i o n  (6)  by u s i n g the s u r f a c e energy which i s o b t a i n e d i n vacuum measurement. I f on the other hand the c r a c k propagates have p l e n t y of time to d i f f u s e and of  the c r a c k .  to  equation  T h i s reduces  (6).  The  v e r y s l o w l y , t h e adsorbed  species  to reduce the s u r f a c e energy at the t i p  the f r a c t u r e s t r e n g t h of the g l a s s a c c o r d i n g  r a t i o o f b r e a k i n g s t r e s s f o r v e r y r a p i d and  slow f r a c t u r e i s then equal t o the square  very  r o o t of the r a t i o of the  two  surface energies. 21 Charles  a l s o adopted G r i f f i t h ' s  p o i n t f o r a t h e o r y of s t a t i c  f a t i g u e of g l a s s .  c r a c k s grow under stress-enhanced reaches  the c r i t i c a l  growth p r o c e s s  f l a w t h e o r y as the  corrosion.  s i z e , the m a t e r i a l f a i l s .  He  assumed t h a t p r e - e x i s t i n g  When one  stress.  The  final  of these  cracks  He proposed t h a t the  should i n v o l v e a chemical r e a c t i o n and  by both temperature and  starting  flaw  should be a c t i v a t e d  expression for time-to-failure  is Log t : =  n l o g 1/a  - log K" ' 9.  where  t  = Time of  failure  a  = Applied  stress  n, K'''  are  constants  (7)  17  Based on t h i s theory C h a r l e s static  21  c a l c u l a t e d the a c t i v a t i o n energy f o r  f a t i g u e i n soda-lime g l a s s and found t h a t i t i s equal t o the  a c t i v a t i o n energy f o r N a The  +  ion diffusion.  theory t h a t has been most s u c c e s s f u l  f a t i g u e i n many ceramic m a t e r i a l s  i n explaining  i s t h e one proposed by C h a r l e s  static and H i l l i g  22 23 '  i n t h e e a r l y 1960's.  They a l s o assumed t h a t  s t a t i c f a t i g u e i s caused  by a s t r e s s - e n h a n c e d c h e m i c a l r e a c t i o n t h a t o c c u r s a t c r a c k t i p s where the stress  i s high.  rate theory.  The s t a r t i n g p o i n t  f o r t h i s t h e o r y i s the a b s o l u t e  I f a chemical r e a c t i o n i s c o n t r o l l e d by an a c t i v a t e d  then the r a t e o f r e a c t i o n w i l l be kT K = (— ) [ e x p (-AF*/RT) where  k  =  Boltzman's constant  h  =  Planck's constant  R  =  Gas c o n s t a n t  T  =  Temperature  AF*  =  =  exp (-AF*/RT)]  process,  (8)  F r e e energy o f f o r m a t i o n o f the a c t i v a t e d complex from the  AF* P  -  reaction  reactant  F r e e energy o f f o r m a t i o n of the a c t i v a t e d complex from r e a c t i o n products.  For a g l a s s s u r f a c e undergoing c h e m i c a l a t t a c k environment, the r a t e or v e l o c i t y of r e c e s s i o n proportional  t o the r e a c t i o n r a t e , K.  i n a corrosive  o f the s u r f a c e , V, w i l l be  I f AF* >> AF* the v e l o c i t y of r e c e s s i o n  is  V  o  exp (-AF*/RT) r  (9)  IB  Assuming t h a t  the a c t i v a t i o n energy, AF*  s e r i e s as a f u n c t i o n o f s t r e s s and  may  taking  be  the  expanded i n a  f i r s t two  Taylor's  terms of  series  gives: 6AF* AF* , " r(a)  =  AF* r  (a = o) 22  C h a r l e s and  Hillig  +  N  6a  23 '  c a l l e d AF*  (a = o) =  SAF* . r(a)  ,  I  Sa  E*~ o  =•  A c t i v a t i o n energy o f the of  V* By tip  taking  =  the  absence  stress.  combined e f f e c t of s t r e s s and  =  V  exp O  -  [(E* O  -  V*a  o f the  crack  chemical r e a c t i o n i s V  +  (10)  )/RT]  P  a  =  T e n s i l e s t r e s s a t the  Y  =  S u r f a c e energy  =  M o l a r volume o f the  p  =  Radius o f c u r v a t u r e o f the c r a c k t i p  Y —  V .  m  •' V*  c h e m i c a l r e a c t i o n i n the  Y  Y  .  c u r v a t u r e i n t o a c c o u n t , t h e v e l o c i t y of r e c e s s i o n  V  If  _ a=o  E*  A c t i v a t i o n volume.  under the  where  a=o  1  t i p of the  crack  solid  m  =  F r e e energy d i f f e r e n c e between a f l a t  c r a c k shape i s assumed t o be  elliptical,  and  then a,  a curved  the  surface.  s t r e s s of  the  24 c r a c k t i p i s g i v e n by  the I n g l i s r e l a t i o n  o  =  2 S  S  =  Applied  L  =  L e n g t h of s u r f a c e  /T7P"  -(H)  stress crack  19  and also  K  =  S / TTL  =  Stress i n t e n s i t y factor  Substituting equations  (12)  (11) and (12) i n equation (10) gives 2V*K  V  =  V  exp -  o  [ (E* o  Y V  +  — — -  / / up  )/RT]  p  (13)  Equation (13) may be used d i r e c t l y to obtain an approximation for 25 the s t a t i c fatigue l i m i t  . A reasonable c r i t e r i o n f o r the s t a t i c fatigue  l i m i t i s that the v e l o c i t y of the crack t i p should be equal to the, general rate of recession i . e .  -  2V*K  YV  =  / up  Rearranging equation (14) K.  I  2V*  / p  (15) 22 23  A more exact procedure i s followed by Charles and H i l l i g  '  . They found  that the s t a t i c fatigue l i m i t should occur when d(L/p)/dt  =  0  and the f i n a l form of t h e i r equation i s  ym V  TT  _  3  I  ' 4V*  /T  (16)  / 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 t i p stress. The equation obtained by Widerhorn i s : V* K V  where  =  A p° exp {[2/3 A  /  v  Up  -  y V P  ]/RT}  (17)  p. i s the concentration of the active species at the crack t i p and A  i s a constant.  Wiederhorn's results are shown i n Figures 9 and 10.  F i g u r e 10  Dependence of c r a c k 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 25 i n soda-lime s i l i c a g l a s s ( A f t e r Wiederhorn ).  21  A more d e t a i l e d u n d e r s t a n d i n g of s t a t i c 15 Wiederhorn e t . a l .  They h y p o t h e s i z e d  p l a y s a major r o l e i n c r a c k growth.  to  done by  16 '  c h a r a c t e r i z e d by  f a t i g u e was  The  t h a t the c r a c k t i p environment environment of a c r a c k t i p i s  (1) the l a r g e r a t i o of the s u r f a c e area of the c r a c k  volume w i t h i n the c r a c k  (2) the l e a c h i n g a c t i o n of the environment  on the f r e s h f r a c t u r e s u r f a c e as the c r a c k propagates. d u p l i c a t e these two  c o n d i t i o n s , s t u d i e s w i t h ground  In an e f f o r t  g l a s s water  to  slurries  16 were conducted  .  The pH of the s l u r r y was  measured e i t h e r w i t h narrow  range i n d i c a t o r paper o r w i t h a g l a s s e l e c t r o d e . s l u r r i e s was  found t o be dependent on the g l a s s c o m p o s i t i o n .  s i l i c a g l a s s was at  The pH of the g l a s s  low  The pH f o r  (- 4 ) , s u g g e s t i n g t h a t an a c i d i c environment  the t i p s of c r a c k s i n t h i s g l a s s .  exists  T h i s low pH i s the r e s u l t of a  r e a c t i o n between water and s i l a n o l groups on the g l a s s s u r f a c e . High slurries of  pH  (- 12) were o b t a i n e d w i t h g l a s s c o n t a i n i n g l a r g e c o n c e n t r a t i o n  a l k a l i i o n s ( s o d a - l i m e - s i l i c a t e ) , the h i g h pH b e i n g p r i m a r i l y due  a l k a l i - h y d r o g e n i o n exchange between the s o l u t i o n and  to  the g l a s s .  A f t e r e s t a b l i s h i n g the n a t u r e of the c r a c k t i p environment, 15 Wiederhorn and h i s coworkers on c r a c k p r o p a g a t i o n i n g l a s s .  s t u d i e d the e f f e c t  of pH of the environment  They chose t h r e e g l a s s c o m p o s i t i o n s ,  l i m e - s i l i c a t e , v i t r e o u s 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  b u f f e r e d s o l u t i o n s r a n g i n g i n pH from -0.8  t o 14.8.  i n f l u e n c e d the s l o p e of the c r a c k p r o p a g a t i o n curve. s l o p e of  They a l s o found  t h a t the e f f e c t of pH was  used  In g e n e r a l , the They found  lnV-K^ p l o t s decreases w i t h i n c r e a s i n g pH of the. t e s t  pH  t h a t the invironments.  more pronounced i n the low  v e l o c i t y r e g i o n than i n the h i g h c r a c k v e l o c i t y r e g i o n .  soda-  crack  As t^he c r a c k moves,  22  the c r a c k t i p c o n t i n u o u s l y exposes f r e s h f r a c t u r e s u r f a c e .  This leads  to an i o n i c r e a c t i o n a t the c r a c k t i p between the s o l u t i o n and  the g l a s s .  Hence the c o m p o s i t i o n of the s o l u t i o n at the c r a c k t i p can be from t h a t of the b u l k s o l u t i o n . e l e c t r o l y t e and  different  T h i s l e a d s t o d i f f u s i o n between the b u l k  the c r a c k t i p s o l u t i o n .  The  r a f e of d i f f u s i o n depends upon  the c o n c e n t r a t i o n d i f f e r e n c e between these two  s o l u t i o n s and  time.  Hence  at low c r a c k v e l o c i t i e s , t h e r e i s enough time f o r d i f f u s i o n to take p l a c e and  the c o m p o s i t i o n of the s o l u t i o n a t the c r a c k t i p becomes s i m i l a r to  that of the b u l k e l e c t r o l y t e .  However a t h i g h c r a c k v e l o c i t i e s , t h e r e i s  not enough time f o r t h i s d i f f u s i o n to occur and the c r a c k t i p s o l u t i o n i s determined regimes of behaviour  are expected  the c o n c e n t r a t i o n or pH of  by the g l a s s c o m p o s i t i o n .  Hence  f o r a moving c r a c k : a t slow v e l o c i t i e s  the c o m p o s i t i o n and pH o f the c r a c k t i p s o l u t i o n s h o u l d be dominated the e x t e r n a l environment; a t h i g h c r a c k v e l o c i t i e s the c o m p o s i t i o n of the c r a c k t i p s o l u t i o n should be determined Wiederhorn"'"'' a l s o found i n water f o r soda-lime slope  of  two  plots  glass coincided with  pH = 12 and pH - 4 r e s p e c t i v e l y .  and  pH  by the g l a s s c o m p o s i t i o n .  t h a t the s l o p e of In V-K^  g l a s s and s i l i c a  by  obtained  the  This r e s u l t supports  the  16 s l u r r y methods  of d e t e r m i n i n g pH to approximate the pH at the t i p of a  c r a c k i n water.  Thp  low s l o p e of c r a c k p r o p a g a t i o n curve at Stage I I ,  shown i n F i g u r e 10 i s a t t r i b u t e d to the severe environment  (high pH)  at  the c r a c k t i p as e x p l a i n e d above. Metcalfe e t . a l .  26  '  27  p o i n t e d out t h a t the mechanism proposed  by  21 Charles  cannot  a p p l y to h i g h s t r e n g t h g l a s s f i l a m e n t s because the  ended c r a c k s would need to be u n r e a l i s t i c a l l y  sharp-  s m a l l to be c o n s i s t e n t w i t h  23  the h i g h  s t r e n g t h and s m a l l diameters o f f i l a m e n t s .  They proposed an  a l t e r n a t i v e mechanism o f s t a t i c f a t i g u e i n these g l a s s f i b e r s which i n v o l v e d an i o n exchange between a l k a l i metal i o n s i n the g l a s s and hydrogen i o n s from e i t h e r adsorbed m o i s t u r e or aqueous s o l u t i o n . reaction  reduces the m o l e c u l a r volume a t t h e s u r f a c e  This  l a y e r and thus  26 27 generates a t e n s i l e s t r e s s a t the s u r f a c e .  Metcalfe  that t h i s t e n s i l e s t r e s s would r e a c h v e r y h i g h v a l u e filaments  cracked  externally.  '  has shown  so t h a t the g l a s s  spontaneously i n the absence o f s t r e s s e s  These r e g i o n s  of high  applied  i n t e r n a l s t r e s s are b e l i e v e d to  c o n s t i t u t e the b a s i c type o f G r i f f i t h f l a w , r a t h e r than the s u b m i c r o s c o p i c , sharp-ended c r a c k s  g e n e r a l l y assumed.  These workers have a l s o shown t h a t  the a c i d i c s o l u t i o n s o f low pH were more d e t r i m e n t a l alkaline solutions. the d e t r i m e n t a l  Additions  strength  to strength  o f sodium i o n to an a c i d i c s o l u t i o n reduced  e f f e c t s , and s t r e n g t h l o s t  i n a c i d c o u l d be  r e s t o r e d by subsequent immersion i n a s o l u t i o n c o n t a i n i n g 28 R i t t e r and Sherburne  sodium i o n s .  have shown t h a t the s t r e s s - e n h a n c e d  c o r r o s i o n model cannot account f o r the s t a t i c glasses.  than  f a t i g u e of p r i s t i n e  silicate  They concluded t h a t t h i s inadequacy i s p r o b a b l y r e l a t e d t o a  d i f f e r e n c e between the f a t i g u e p r o c e s s e s t h a t occur a t t h e . t i p s of deep cracks  as opposed t o s h a l l o w c r a c k s  i n relatively  flaw-free  surfaces.  They have a l s o proposed t h a t i t i s e n t i r e l y p o s s i b l e t h a t s t r e s s - c o r r o s i o n and  Na -H +  +  exchange occur  simultaneously.  29 Cox  has developed an a t o m i s t i c theory  which i s based on the  weakening o f S i - 0 bond by mobile sodium i o n s 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 initiated  24  by the p r o b a b i l i t y 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 e x p l i c i t l y enter into the strength expression. The weakness of this theory i s the questionable assumption that the migrating cation weakens  the Si-0 network.  It would also be necessary for the cations  to overcome a large e l e c t r o s t a t i c energy barrier i n coming together to form the s e l f generating flaw. 30 Charles  Recently Doremus  23  objected to the assumption of H i l l i g and  that the slope of lnV-K^ plot i s independent of stress. Doremus  30  argued that there are no experimental facts to support this and also that the activation volume i s rarely independent of pressure.  Alternatively  30 Doremus  found that s t a t i c fatigue data also f i t an inverse r e l a t i o n  between log crack v e l o c i t y and load better than direct proportionality. Hence an equation of the following form i s proposed. V = V exp (-a /a )  (18)  T •  where V  and a are stress-independent c o e f f i c i e n t s and a i s the applied T  stress.  V  i s the l i m i t i n g reaction rate at high stress and  where B i s a constant which i s proportional to the a c t i v a t i o n energy for the reaction of water with the oxide network, E i s Young's modulus, R i s the gas constant and T i s  1.3  temperature.  Summary of the Theoretical Models  3 1.  Orowan  proposed that s t a t i c fatigue i s caused by a decrease  25  in  s u r f a c e energy  environment.  r e s u l t i n g from the a d s o r p t i o n of s p e c i e s from  the  A c c o r d i n g to t h i s theory the t h e o r e t i c a l s t r e n g t h o f the  m a t e r i a l w i l l decrease  due  to environment.  21 2.  The  theory of C h a r l e s  d e s c r i b e s a c r a c k growth mechanism  and a t t r i b u t e s the l o s s of s t r e n g t h to the slow growth of a c r a c k u n t i l it  reaches  s i z e was  the c r i t i c a l  size.  Growth of the s u b c r i t i c a l c r a c k to  a t t r i b u t e d to a stress-enhanced  critical  c h e m i c a l r e a c t i o n at the t i p of  the crack.  15 16 3.  Wiederhorn  '  hypothesized  p l a y e d a major r o l e i n c r a c k growth. environment was  different  He  t h a t the c r a c k t i p environment showed t h a t the c r a c k t i p  from the b u l k e l e c t r o l y t e .  the c o n c e n t r a t i o n or pH of c r a c k t i p s o l u t i o n was c o m p o s i t i o n and  At h i g h c r a c k v e l o c i t i e s ,  c o n t r o l l e d by the g l a s s  at slow c r a c k v e l o c i t i e s the pH of c r a c k t i p s o l u t i o n  c o n t r o l l e d by the e x t e r n a l environment.  was  Wiederhorn has a l s o shown t h a t  the pH of the t e s t environments c o n t r o l l e d the s l o p e of c r a c k p r o p a g a t i o n plots  (InV -K-j. diagrams) and  found  t h a t the s l o p e decreased w i t h  increasing  pH.  26 27 4.  Metcalfe  '  proposed  fatigue i n p r i s t i n e glass fibers. in  an i o n exchange mechanism f o r the Ion exchange between a l k a l i metal  the g l a s s and hydrogen i o n s from e i t h e r adsorbed  s o l u t i o n , generates  moisture  a t e n s i l e s t r e s s a t the s u r f a c e .  ions  or aqueous  When t h i s  s t r e s s reaches a v e r y h i g h v a l u e , t h e g l a s s f i l a m e n t s c r a c k  static  tensile  spontaneously  26  i n the absence of e x t e r n a l  stress.  29 5.  Cox  proposed t h a t  movements of the m i g r a t i n g a l k a l i  the  S i - 0 bond w i l l be weakened by  i o n and  f r a c t u r e w i l l be  the number of s i m u l t a n e o u s l y broken Si-0 bonds to form a  initiated  the by  self-generating  flaw. 30 6.  Doremus  derived  a static  f a t i g u e e q u a t i o n based on  stress-  23 enhanced c o r r o s i o n InV  to the  1. 4  at the  I n v e r s e of  Estimation  crack t i p .  of T i m e - t o - F a i l u r e  initial  This  f i n a l expression r e l a t e s  stress, from Growth K i n e t i c s  Crack growth k i n e t i c s can be constant load.  The  involves  an  used to measure t i m e - t o - f a i l u r e under  i n t e g r a t i o n of the V-K^  s t r e s s i n t e n s i t y f a c t o r to K  p l o t from  K-^,  , f i n a l stress intensity factor.  The  lc  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 g i v e n i n Appendix I I .  The  final  of e q u a t i o n i s "  Introducing  ~  2 2 o :y app  °a ~ PP p  K  =  a  a  1  »  a  y 3Pp  A(2-n)  I i ^ — lc  L  [K ~I  ( 2  "  n )  - K (2-n). " ] T J  C  y  (20)  i n the above e q u a t i o n  fey v  /  t ( ^ - ) " app H H  2  - i ]  (2i)  form  27  where n and A corresppnd to the s l o p e and the i n t e r c e p t of l o g V - l o g plots, a  1.5  app  i s the a p p l i e d s t r e s s and a  p  i s the p r o o f  stress,  O b j e c t i v e s of the P r e s e n t Work  The main aim of the p r e s e n t study was of s t a t i c  t o o b t a i n some u n d e r s t a n d i n g  f a t i g u e phenomenon i n g l a s s - c e r a m i c s c o n t a i n i n g d i f f e r e n t  f r a c t i o n s of c r y s t a l l i n e phase.  volume  Crack growth k i n e t i c s f o r these m a t e r i a l s  were measured by the double t o r s i o n t e c h n i q u e .  One o b j e c t i v e o f t h i s work  was to t e s t the d i f f e r e n t s u b c r i t i c a l c r a c k growth models. A c a r e f u l f r a c t o g r a p h i c study was conducted of f r a c t u r e i n g l a s s - c e r a m i c s . s t r e n g t h , microhardness i n o r d e r t o understand  t o r e v e a l the mechanism  Other mechanical p r o p e r t i e s such as f r a c t u r e  and e l a s t i c moduli  ( s t a t i c method) were a l s o measured  f r a c t u r e i n more d e t a i l .  G r o w t h - k i n e t i c s , d e n s i t y and d i f f e r e n t i a l thermal a n a l y s i s were  also  measured i n o r d e r t o c h a r a c t e r i s e the s t r u c t u r e of these g l a s s - c e r a m i c s .  28  2. EXPERIMENTAL PROCEDURE  2.1  Material Preparation  2.1.1  glass Preparation  A b a t c h of 495 gms o f L i C 0 * 2  3  powder, 933.75 gms o f 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 .  T h i s m i x t u r e was then heated i n a P l a t i n u m -  3% Rhodium c r u c i b l e at 1450°C i n a f u r n a c e * * * * t o produce g l a s s o f composi t i o n 17.8 wt% L i 0 - 8 2 . 2 wt% S i 0 2  2  .  The molten g l a s s was s t i r r e d w i t h  a l o n g s i l i c a rod to produce thorough m i x i n g . g l a s s was r e f i n e d  ( t o remove b u b b l e s ) a t 1450°C  Subsequently f.he molten f o r 24 hours.  I t was  then c a s t i n t o heated g r a p h i t e moulds t o form r e c t a n g u l a r b l o c k s 69.9 mm x 25.4 mm x 50.8 mm  (2.75" x 1" x 2") o r c y l i n d e r s o f diameter 50.8 mm  (2") and h e i g h t 38.1 mm  (1.5").  These b l o c k s were annealed a t 470°C f o r  48 hours and f u r n a c e c o o l e d .  *  Reagent  grade s u p p l i e d by CENCO o f Canada L i m i t e d .  **  Pure grade ground s i l i c a f l o u r s u p p l i e d by Ottawa Ottawa,  I l l i n o i s , U.S.A.  ***  Reagent  grade s u p p l i e d by A l l i e d  ****  Super K a n t h a l M u f f l e Furnace.  S i l i c a Co.  Chemicals Canada L i m i t e d .  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 c a s t b l o c k s o f g l a s s i n a diamond impregnated saw. These specimens were used t o measure d e n s i t y and t r a n s v e r s e r u p t u r e strength. C y l i n d e r s 10.2 mm (0.4") diameter and 38.1 mm (1.5") l o n g were drilled  in a vertical  c o r e d r i l l i n g machine u s i n g a 9.53 mm  diameter diamond impregnated c o r e d r i l l  (0.375")  from the c a s t 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 sliced  69.9 mm x 25.4 mm x 1.5 mm (2.75" x 1" x 0.060") were  from the b l o c k u s i n g a diamond impregnated saw.  These  specimens  were p o l i s h e d w i t h 270 g r i t SiC i n an automatic l a p p i n g machine t o a c h i e v e parallel the  surfaces.  These p l a t e s were used i n c r a c k v e l o c i t y  Double T o r s i o n Technique  2.1.3  s t u d i e s by  19  Heat-Treatment  A p o r t i o n o f the samples was g i v e n a c r y s t a l l i z a t i o n by h e a t i n g a t 530±5°C  for different  ceramics h a v i n g d i f f e r e n t was  l e n g t h s o f time t o produce  degrees o f c r y s t a l l i n i t y .  treatment glass-  T h i s heat treatment  performed i n a s m a l l nichrome wound m u f f l e f u r n a c e .  A l l these  were heated from room temperature t o 530°C and h e l d a t t h i s f o r the d e s i r e d l e n g t h s o f time and then f u r n a c e c o o l e d .  samples  temperature  30  2.2  Sample C h a r a c t e r i z a t i o n  2.2.1  D i f f e r e n t i a l Thermal A n a l y s i s  Thermal a n a l y s e s were performed on powder (-325 mesh s i z e ; 30 to 40 mgm) analyser*.  o b t a i n e d from a s - c a s t samples i n a d i f f e r e n t i a l thermal  Pure alumina powder (-325  mesh s i z e ; 30 to 40 mgm)  as the s t a n d a r d sample and h e a t i n g r a t e s of 5, 10, 15, 20 and were used.  2.2.2  The s t a r t i n g temperature was  25°C/min  room temperature (25°C).  D e n s i t y Measurement  The b u l k d e n s i t y o f the g l a s s and g l a s s - c e r a m i c s was by the c o n v e n t i o n a l method. long 3 mm  was used  wide and 3 mm  thick  calculated  The samples were s m a l l r e c t a n g u l a r b a r s 40 (1.575" x 0.118" x 0.118").  of these samples were ground on 240 g r i t  A l l four  mm  sides  SiC p o l i s h i n g paper t o remove a  t h i n l a y e r of the s u r f a c e which might have a d i f f e r e n t degree o f c r y s t a l l i n ity  than the b u l k .  The specimens were s u b s e q u e n t l y f i n i s h e d on 400  SiC p o l i s h i n g paper to produce smooth  surfaces.  the s u r f a c e s o f these samples p a r a l l e l .  Care was  grit  taken to keep  The hand g r i n d i n g o p e r a t i o n  was  r done so t h a t the s u r f a c e s c r a t c h e s on the samples l a y JL to the l e n g t h of the sample.  *  Dupont  These samples were then cleaned i n the u l t r a s o n i c  900 D i f f e r e n t i a l Thermal A n a l y s e r .  vibrator  31  and  l a t e r w i t h water.  a l c o h o l d r i e d and The  Samples were t h e n t h o r o u g h l y r i n s e d i n e t h y l  stored i n a desiccator.  weight of t h e s e samples was  recorded  by u s i n g a b a l a n c e * .  The  volume was  determined by measuring the dimensions o f the  The  dimensions of the samples were measured w i t h a micrometer.  o f weight to volume y i e l d s the b u l k  2.2.3  Metallography  2.2.3.1  Optical Microscopic  The 12.7  mm  The  ratio  density.  Examination  samples were mounted on a 165.1  (0.5") t h i c k b r a s s  samples.  mm(6.5")  plate using thermoplastic  diameter  cement**.  and Then  the  samples were ground on an a u t o m a t i c l a p p i n g machine as shown i n F i g u r e C o a r s e g r i n d i n g was accomplished using laps. using was  The  done u s i n g 400  and  p o l i s h i n g was  cerium oxide***  required  1000  240  grit  grit  done i n the  SiC powder and  same a u t o m a t i c l a p p i n g machine by Three t o f o u r hours of p o l i s h i n g  to obtain a scratch f r e e polished  S a r t o r i u s s i n g l e pan  **  No  ***  Cerium o x i d e "C"  balance  was  SiC powder on 3 d i f f e r e n t c a s t i r o n  as the a b r a s i v e .  *  fine grinding  11.  surface.  These samples  (Model 2432).  7 0C L a k e s i d e Brand s u p p l i e d by Hugh C o u r t r i g h t & Co., s u p p l i e d by M i c o m e t a l l u r g i c a l  Limited.  C h i c a g o , U.S.A.  32  Figure 11  Photograph of Automatic Lapping Machine  33  were removed from t h e b r a s s p l a t e and washed i n e t h y l a l c o h o l t o g e t rid  o f the t h e r m o p l a s t i c cement.  HC1  and  L a t e r they were etched i n 3% HF,  95% water s o l u t i o n f o r 0.5  the degree of c r y s t a l l i n i t y  minute t o 1.5  i n t h e sample.  The  minute depending  O p t i c a l photomicrographs i l l u m i n a t i o n were p r e p a r e d  2.2.3.2  Petrographic  0.05  mm  field  sliced  from t h e o p t i c a l m e t a l l o g r a p h i c saw.• These  thin  'Well p e t r o g r a p h i c s l i d e s ' w i t h t h e r m o p l a s t i c  T h i s o p e r a t i o n gave a v e r y t h i n . s e c t i o n o f  thickness.  petrographic s l i d e s '  field  t h e s e t h i n s e c t i o n s were ground on a m u l t i p l e  hand g r i n d e r .  (0.002")  and d a r k  structure.  specimen u s i n g a diamond impregnated  Subsequently  s t a g e wet  i n bright  Examination  s e c t i o n s were cemented on cement.  Sputtering  of the e t c h e d s u r f a c e .  to c h a r a c t e r i s e the  A t h i n s e c t i o n was examination  on  etched samples were  s u b s e q u e n t l y p l a t e d w i t h a 60-40 g o l d - p a l l a d i u m a l l o y i n a D.C. System* t o improve t h e r e f l e c t i v i t y  2%  The  samples were removed from t h e  'Well  and washed t h o r o u g h l y w i t h e t h y l a l c o h o l .  They  were t h e n sandwiched between a c o v e r p l a t e and  a petrographic s l i d e  u s i n g Canada Balsam and were viewed i n a p e t r o g r a p h i c m i c r o s c o p e .  * . HUMMER. . Hummer i s a D.C. s p u t t e r i n g system. A n e g a t i v e p o t e n t i a l i s a p p l i e d to the 6 0 - 4 0 g o l d - p a l l a d i u m cathode which i s e n c l o s e d i n t h e p r o c e s s chamber a t a pressure; 50-500 m i l l i t o r r . T h i s was s u p p l i e d by T e c h n i c s Inc., A l e x a n d r i a , 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 i n petrographic microscopy was  thinned  in a micro ion m i l l * u n t i l the specimen had a small hole i n i t .  These  specimens were coated with carbon and used for TEM studies.  2.2.4  Determination  of Degree of C r y s t a l l i n i t y  2.2.4.1  Point-Count Method  31  The basic p r i n c i p l e 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 s p e c i f i c phase i s equal to the proportion by volume of that phase.  In practice, i t i s generally found to be inconvenient to  project a random array of points onto a microstructure.  A regular array  of points i s used and i t i s assumed that the microconstituents randomly distributed.  It i s important  are  that the spacing of the rectangular  grid be large with respect to the microstructural features-  The volume  f r a c t i o n p^ of the a phase i s given by  p  where  a  =  n /n a  i s the number of points occurring i n the a phase and n i s the  t o t a l number of points.  *  (22)  Micro Ion M i l l produced by Technics Inc., Alexandria, U.S.A.  35  A 3 mm x 3 mm square g r i d was superimposed micrograph  and the number o f p o i n t s (  were r e c o r d e d . was  806.  n a  on the o p t i c a l  ) intersecting  the c r y s t a l l i t e s  The t o t a l number o f p o i n t s (n) on the m i c r o s t r u c t u r e  The r a t i o o f these two number gave the volume f r a c t i o n o f  c r y s t a l l i n e phase i n the g l a s s - c e r a m i c .  An average v a l u e o f f i v e  such  r e a d i n g s was taken.  2.2.4.2,  X-Ray Method  32 A s t a n d a r d q u a n t i t a t i v e a n a l y s i s by the X-ray was  used.  An X-ray d i f f T a c t o m e t e r * f i t t e d w i t h a goniometer  p r o p o r t i o n a l counter was used. Li^O  - SiO^ system  17.8  wt% l i ° ~ 2  8  2  -  and a  A c c o r d i n g t o t h e phase-diagram o f the  shown i n F i g u r e 12, g l a s s having a c o m p o s i t i o n 2 w  t  ^  s  i  n  c  a  n  2  n  a  v  e  maximum o f 90% c r y s t a l l i n e  L i 2 0 . 2 S i 0 2 i f the g l a s s i s c r y s t a l l i z e d taken as the standard sample. annealed  technique  at 530°C.  T h i s sample i s  I t was prepared by c r y s t a l l i z i n g the  g l a s s a t 530°C f o r a v e r y l o n g time  (48 h o u r s ) .  I t was then  crushed t o powder w i t h the h e l p o f a p e r c u s s i o n hammer and a s m a l l b a l l mill.  A powder sample o f -325, +400 mesh s i z e was taken.  peak a r e a between 22.66° t o 26° was taken i n t o intensity  *  c l o s e t o these peaks  The i n t e g r a t e d  consideration.  Background  (21° - 22.66°and 26° - 27.66°) was measured  P h i l l i p s PW 1009 water c o o l e d X-ray d i f f r a c t i o n u n i t f i t t e d w i t h North American P h i l l i p s 42 202 type wide range goniometer and Xenon f i l l e d p r o p o r t i o n a l counter.  36  9501 Li 0 2  I  75  H 80 WEIGHT  F i g u r e 12  1  1  85 %  P o r t i o n of the phase diagram of L i 0 SiO„ system. 2  -  —I  Si0  2  37  and  s u b t r a c t e d from the i n t e g r a t e d peak to o b t a i n the a c t u a l peak a r e a .  An average of 20 r e a d i n g s was standard  sample was  crystallized  In o r d e r to make sure t h a t the  fully crystalline  for a different  remained c o n s t a n t .  (90% L i ^ O 2Si02) , the sample  l e n g t h of time at 530°C u n t i l  was  the peak a r e a  The peak a r e a remained c o n s t a n t a f t e r 22 hours  c r y s t a l l i z a t i o n treatment The  taken.  a t 530°C.  a c t u a l peak area f o r a l l of the g l a s s - c e r a m i c s c o n t a i n i n g  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 was the above procedure.  The  c a l c u l a t e d by r e p e a t i n g  r a t i o of a c t u a l peak a r e a of the standard  sample  to t h a t of the g l a s s - c e r a m i c s c o n t a i n i n g 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 d i s i l i c a t e present  2.3  of 152.4  mm  Crystallization  r e f i n e d molten g l a s s was  l o n g , 12.7  mm  These b a r s were annealed x 12.7  mm  lithium  i n each sample.  K i n e t i c s of  The  gave the weight f r a c t i o n of  (1" x 1/2"  wide and  c a s t i n t o a heated  12.7  mm  deep.  at 470°C f o r 48 hours.  x 1/2")  g r a p h i t e mold  (6" x 1/2" Samples 25.4  x 1/2"). mm  x 12.7  were cut from the l o n g e r g l a s s b a r s .  Twelve  of these samples were c r y s t a l l i z e d a t 530°C f o r twelve d i f f e r e n t  lengths  of time,  1320  30,  60,  90,  120,  Each of these samples was (1/4" x 1/2"  x 1/2")  and  190,  240,  300,  cut i n t o two 19 mm  i n the diamond impregnated saw.  x 12.7 The  390,  495,  p i e c e s , 6.35 mm  x 12.7  mm  660,  1045  and  mm  x 12.7  mm  (3/4" x 1/2"  minutes.  x 12.7 x  mm  mm  1/2")  s m a l l samples were used f o r o p t i c a l  38  metallographic  examination to evaluate the degree of c r y s t a l l i n i t y 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 c r y s t a l l i n i t y .  2.4  Measurement of E l a s t i c 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 i n Specimen Preparation) 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 .  The ends of these samples were s l i c e d i n the  diamond impregnated saw to obtain p a r a l l e l surfaces. pressed i n a universal testing machine* to 60 MPa  They were then com-  and 120 MPa  between  p a r a l l e l loading anvils made out of hardened s t e e l as shown i n Figure A 12.7 strain.  mm  13.  (1/2") s t r a i n gauge extensometer was used to measure longitudinal In order to obtain r e l i a b l e r e s u l t s i n this procedure the  d i r e c t i o n of loading should be p a r a l l e l to the centre l i n e of the sample. This i s possible only i f the samples have p a r a l l e l surfaces and surfaces of the loading anvils are p a r a l l e l to each other. of the loading anvils for p a r a l l e l i s m was  the  Setting up  accomplished with the help of  Instron Testing Machine supplied by Instron of Canada Limited.  39  F i g u r e 13  Photograph of s t a t i c e l a s t i c measurement s e t up.  moduli  40  a standard sample whose Young's modulus was s t e e l c y l i n d e r 12.7  mm  (1/2") diameter  p a r a l l e l s u r f a c e s was  used  compressed to 120 MPa  and  and  w e l l known. 25.4  as s t a n d a r d sample.  mm  Here a m i l d  (1") l o n g h a v i n g  T h i s sample  the l o n g i t u d i n a l s t r a i n was  determined  4 p o s t i o n s 90° a p a r t by u s i n g the s t r a i n gauge extensometer. modulus c a l c u l a t e d by t h i s p r o c e s s at 4 p o s i t i o n s to the known v a l u e of 207  GPa  (30 x 10  p s i ± 1%).  was at  The Young's  (90° a p a r t ) was  compared  I f the l o a d i n g a n v i l s  were p a r a l l e l to each o t h e r , a l l the f o u r v a l u e s of Young's modulus c a l c u l a t e d should be equal t o 207 shimmed by 0.025 mm  GPa.  (0.001") b r a s s shim sheets u n t i l the v a l u e s of Young's  modulus c a l c u l a t e d by t h i s procedure Annealed  I f not the l o a d i n g a n v i l s were  g l a s s samples and  e q u a l l e d 207  GPa.  g l a s s - c e r a m i c s c o n t a i n i n g low volume  f r a c t i o n s of c r y s t a l l i n e phase were compressed t o 453.6 kgs. G l a s s h a v i n g h i g h e r degrees average  An  taken.  Poisson's Ratio  The a l s o used 12.7  of c r y s t a l l i n i t y were compressed to 907.2 kgs.  of e i g h t v a l u e s was  2.4.2  ceramics  mm  samples used  f o r t h i s purpose.  f o r the d e t e r m i n a t i o n of Young's modulus were . The l a t e r a l e l o n g a t i o n was  (0.5") s t r a i n gauge extensometer which was  by a s p e c i a l f i x t u r e . positions  The  l a t e r a l e l o n g a t i o n was  (90° a p a r t ) and an average  measured by u s i n g  connected  diametrically  measured at 4 d i f f e r e n t  of e i g h t v a l u e s was  samples were compressed t o the same l o a d as t h a t used  taken.  The  f o r the Young's  41  modulus measurements.  2.5  Measurement of M e c h a n i c a l P r o p e r t i e s  2.5.1  M i c r o h a r d n e s s Measurement  Samples used f o r o p t i c a l m e t a l l o g r a p h y were a l s o used to determine the microhardness.  A Diamond Pyramid Hardness(DPH) i n d e n t o r  i n combination w i t h a Tukon hardness t e s t e r was All  the i n d e n t a t i o n s were made on the i n t e r - c r y s t a l l i n e phase  samples  c o n t a i n i n g up to 50% c r y s t a l l i n e phase.  i n d e n t a t i o n s were i n the c r y s t a l l i n e phase. was  used a t a l o a d of 50  taken on each  2.5.2  Above 50%,  gms.  i n the  the  An average of f i f t e e n v a l u e s  sample.  T r a n s v e r s e Rupture S t r e n g t h  Samples used f o r d e n s i t y measurements were a l s o used to determine the t r a n s v e r s e r u p t u r e s t r e n g t h of the g l a s s and g l a s s - c e r a m i c s . T r a n s v e r s e r u p t u r e t e s t s were performed u s i n g a u n i v e r s a l t e s t i n g machine* w i t h each sample r e s t i n g i n a t h r e e p o i n t bending f i x t u r e . were s a p p h i r e r o d s .  The span was  25.4  at a c o n s t a n t crosshead speed of 4.2 The l o a d was  mm  ( l ) long. 1  Samples were loaded  x 10 ^ m.sec ^ (0.01"/min) to f a i l u r e .  a p p l i e d to the f i x t u r e by means of a compression cage.  t e s t s were performed i n t o l u e n e and i n water.  *  The t h r e e l o a d i n g p o i n t s  I n s t r o n T e s t i n g machine.  The  42  The  f r a c t u r e s t r e s s , o\_ , of a bar  fractured i n three-point  bending i s a  where P  3 PL Fr  =  2  bd  (23)  2  Fracture load Span l e n g t h  L  (25.4  mm)  b  =  Breadth of specimen  d  =  Depth of specimen An  average of e i g h t to t e n v a l u e s was  samples were thoroughly  taken.  The  r i n s e d i n e t h y l a l c o h o l , d r i e d and  fractured stored i n  a d e s i c c a t o r f o r f r a c t o g r a p h i c examination.  2.6  Slow Crack Growth T e s t s  2.6.1  Slow Crack Growth of Annealed  Glass  Slow c r a c k growth t e s t s were performed i n f o u r environments, toluene,nitrogen  at 30%  r e l a t i v e humidity  ( r h ) , 70%  r h and water.  The  19 double t o r s i o n technique  was  the double t o r s i o n technique The 25.4  mm  used i n t h i s study.  The  theory  has been d e s c r i b e d i n Appendix  underlying  1.  specimens c o n s i s t e d of r e c t a n g u l a r s l i d e s 69.85 mm  wide and  1.52  mm  t h i c k (2.75" x 1" x 0.06") grooved a l o n g  s i d e to l e a v e approximately  h a l f the specimen t h i c k n e s s .  A notch  long, one was  43  then i n t r o d u c e d  to a depth of 15.00  mm  (0.595") to i n i t i a t e the  A t y p i c a l specimen i s shown i n F i g u r e 14. u s i n g a v e r n i e r c a l i p e r , t was  The  dimension W was  crack. measured  measured u s i n g a micrometer and  t  was n  measured w i t h  a t r a v e l l i n g microscope.  The supported v i a two  l o a d i n g f i x t u r e i s d e p i c t e d i n F i g u r e 15.  on two  hemispheres a t t a c h e d  assembly was tall  and  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  load c e l l .  mm  (7 1/2")  sample  the l o a d was  t o the f i x t u r e ' s upper p l a t e .  p l a c e d i n a 166.00 mm  3.00  The  The  diameter, 90.00 mm  T h i s s e t up was  used f o r both the water and  applied  whole (3  (0.11") t h i c k g l a s s d i s h t h a t r e s t e d on a 'D'  was  1/2")  compression  toluene  environ-  ments . The and  70%  study of slow c r a c k growth f o r annealed g l a s s at 30%  r h was  done i n a s m a l l p l e x i - g l a s s chamber  as shown i n F i g u r e 16.  Humidity i n t h i s chamber was  known volumes of water vapour and F i g u r e 17.  The  volume of gas  n i t r o g e n gas  diameter)  c o n t r o l l e d by m i x i n g  i n the apparatus,  i n the chamber was  shown i n  c o n t r o l l e d by a s e t of  manometers.  Humidity i n the chamber was  method.  samples were e q u i l i b r a t e d f o r 4 hours.  The  (12.70 mm  rh  measured a c c o r d i n g to the A S T M ^  For a l l samples the f o l l o w i n g procedure was  used to measure  the c r a c k v e l o c i t y as a f u n c t i o n of s t r e s s i n t e n s i t y . a. of 4.25  The  specimen was  x 10 ^ m sec  r e l a x a t i o n curve was crack.  loaded  (0.001" min obtained.  i n c r e m e n t a l l y at a crosshead  "*") u n t i l a r a p i d l o a d drop  T h i s i n d i c a t e d the f o r m a t i o n  speed  and of a sharp  44  <  w  F i g u r e 14  Specimen used i n double t o r s i o n  test.  gure 15  L o a d i n g f i x t u r e used i n double  F i g u r e 16  Schematic drawing of h u m i d i t y chamber.  MANOMETER  TO ACRYLIC BOX  NITROGEN  LONG GRADUATED CYLINDERS  I iff 1  U  •MANOMETER  WATER IMMERSION TUBE  F i g u r e 17  Flow diagram of h u m i d i t y c o n t r o l l i n g  s e t up  48  b. m sec  The l o a d was i n c r e a s e d  a t a crosshead speed o f 8.5 x 10  (0.002" min "*") to a c c e l e r a t e t h e c r a c k  and a second  load  r e l a x a t i o n curve was produced. c.  When the l o a d had decreased to a n e a r l y constant  value,  the specimen was unloaded and removed from t h e f i x t u r e . d.  The f i n a l c r a c k l e n g t h was measured by u s i n g a dead  weight l o a d i n g apparatus t o open the c r a c k  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 l o a d i n g the specimen t o a l o a d below the v a l u e e. evaluated  a t the end of l o a d r e l a x a t i o n . Load r e l a x a t i o n s due t o the f i x t u r e and machine were  by u s i n g  a dummy specimen.  The dimensions o f t h i s  were the same as the t e s t sample but without the c e n t r e notch.  specimen  groove and the  The l o a d i n g sequence f o r t h i s sample was e x a c t l y the same as t h a t  of the t e s t  specimens.  f.  A new l o a d - r e l a x a t i o n curve e n t i r e l y due t o the c r a c k  growth i n the sample.was o b t a i n e d  by s u b t r a c t i n g the back ground r e l a x a t i o n  (load r e l a x a t i o n due to f i x t u r e and l o a d c e l l ) from t h e l o a d r e l a x a t i o n curve obtained  i n b.  A full  s c a l e l o a d o f 1.83 Kgs(4 l b s ) w i t h a l o a d  suppression -4  s c a l e was used to measure the l o a d .  A chart  speed o f 8.5 x 10  (2" min "*") was used throughout the experiment.  -1 m sec  The c r a c k v e l o c i t y a t any  p o i n t on the l o a d r e l a x a t i o n curve was o b t a i n e d by s u b s t i t u t i n g the v a l u e o f the s l o p e a t t h a t p o i n t ( )» t h e l o a d ( P ) , the f i n a l l e n g t h o f c r a c k  dt (a^) and t h e f i n a l l o a d a t the end o f l o a d r e l a x a t i o n (P^) i n t o e q u a t i o n A(11)[Appendix 1 ] .  The c o r r e s p o n d i n g s t r e s s i n t e n s i t y was computed from  49  the l o a d  (P) and the dimensions o f sample  equation  (A6) [Appendix 1]  and f i x t u r e a c c o r d i n g  Three t o f o u r experiments were performed t o o b t a i n velocity stress-intensity  2.6.2  one  curve.  Slow Crack-Growth  G l a s s specimens  to  of G l a s s - C e r a m i c s  68.95 mm  l o n g 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 f o r v a r i o u s l e n g t h s of time to o b t a i n the d e s i r e d degree of c r y s t a l l i n i t y . were p o l i s h e d w i t h crystallization.  These  270 g r i t - S i C p o l i s h i n g paper to e l i m i n a t e any The procedure which was  2.7  surface  used f o r annealed g l a s s  f o l l o w e d here to o b t a i n v e l o c i t y - s t r e s s - i n t e n s i t y c u r v e s . ments, toluene  specimens  Two  was  environ-  and water were used.  Critical  S t r e s s I n t e n s i t y F a c t o r Measurement  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 (Kj^) f °  r  the g l a s s and 19  glass-ceramics  was  obtained  by the double t o r s i o n t e c h n i q u e  .  Double  t o r s i o n samples which were used i n slow c r a c k growth measurements were reassembled i n the same f i x t u r e as d e s c r i b e d i n S e c t i o n 2.6 and f a s t - 4 - 1 -1 loaded a t a crosshead speed o f 2.1 x 10 m sec (0.5" min - ) t o f a i l u r e i n a toluene i n equation  environment.  The f a i l u r e l o a d  (A6) [Appendix 1] to o b t a i n K ,. jr  (P ) was c  substituted  The f r a c t u r e samples  50  were thoroughly r i n s e d i n e t h y l a l c o h o l ,  d r i e d and s t o r e d i n a  d e s i c c a t o r f o r f r a c t o g r a p h i c examination.  2.8  Fractographic  Examination  F r a c t u r e d s u r f a c e s o f t r a n s v e r s e r u p t u r e t e s t samples and slow c r a c k growth measurement samples were coated w i t h a 60-40 g o l d p a l l a d i u m a l l o y i n a D.C s p u t t e r i n g system and these s u r f a c e s were examined by scanning e l e c t r o n  microscopy.  51  3.  3.1  D i f f e r e n t i a l Thermal A n a l y s i s  DTA i n F i g u r e 18. the  RESULTS  p l o t s f o r 82.2 wt%  SiC>  2  (DTA)  - 17.8 wt% L i 0 g l a s s a r e shown 2  The number p r i n t e d on each of the p l o t s corresponds to  heating rate  (h) used.  C o n v e n t i o n a l e x t r a p o l a t i o n methods were used  to determine the a n n e a l i n g temperature and a l s o the peak temperature that corresponds to the maximum d e f l e c t i o n .  (T^)  The a n n e a l i n g temperature*  was  found t o be 470°C.  The peak temperatures a t v a r i o u s h e a t i n g r a t e s  are  listed  The thermogram at a g i v e n h e a t i n g r a t e was  i n T a b l e 1.  found  to be the same f o r a b u l k p i e c e of the m a t e r i a l as f o r the crushed powder. The a c t i v a t i o n energy f o r the c r y s t a l l i z a t i o n p r o c e s s was the  s l o p e of the p l o t l n ( h / T  and T  P  ln(h/T  ) Vs 1/T , p  calculated  where h = h e a t i n g r a t e i n °C/min  = temperature at which the maximum d e f l e c t i o n o c c u r s . 2 P  ) v e r s u s 1/T  c r y s t a l l i z a t i o n was  3.2  P  from  i s shown i n F i g u r e 19.  The p l o t of  The a c t i v a t i o n energy  33  for  found to be 180 KJ/mole (43 K c a l / m o l e ) .  D e n s i t y Study The d e n s i t i e s of the g l a s s and g l a s s - c e r a m i c s are l i s t e d i n  T a b l e 2.  F i g u r e 20 shows the t h e o r e t i c a l d e n s i t y based on a s i m p l e r u l e  of m i x t u r e s and the e x p e r i m e n t a l l y determined v a l u e s . A r e a s o n a b l e f i t i s  *  Approximately the g l a s s t r a n s i t i o n  temperature.  0  \00 200  Figure  18  300 400 500 600 TEMPERATURE , DEG. c.  Differential  700  thermal a n a l y s i s of annealed  glass.  Table 1 SUMMARY OF DTA OF THE GLASS  H e a t i n g Rate <j>,, °C/min.  Peak Temperature T °C(°K) P  1/T , 10  3  */T , 1 0 ~ . -1 mm V  6.8718  6  In (cf./T ) P 2  - 11.88  5  580 (853)  1.1723  10  605 (878)  1.1390  12.972  - 11.25  15  614 (887)  1.1274  19.065  - 10.86  627 (900)  1.1111  24.691  - 10.60  634 (907)  1.025  30.390  - 10.40  20 25  0  F i g u r e 20  2  -4 VOLUME  -6 FRACTION  -8  D e n s i t i e s of the g l a s s - c e r a m i c s as a f u n c t i o n of volume f r a c t i o n of c r y s t a l l i n e phase.  I  Table 2 DENSITY OF THE GLASS AND  Volume F r a c t i o n  of C r y s t a l l i n e  Phase  GLASS-CERAMICS  Bulk D e n s i t y 10  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  3  kg/m  3  a-*  57  seen between the t h e o r e t i c a l curve and e x p e r i m e n t a l p o i n t s .  The c a l c u l a t e d  p o r o s i t y was found to be l e s 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 v a r i o u s times of a n n e a l i n g a t 530 ± 5° C i s g i v e n i n T a b l e 3. 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 by the X-ray method. difficult  A t low percentage  t o measure the volume  At v e r y h i g h degree of c r y s t a l l i n i t y  t o measure the volume f r a c t i o n by the p o i n t count  of fraction  i t becomes analysis.  F i g u r e 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 o f a n n e a l i n g at 530°C.  The c o r r e s p o n d i n g m i c r o s t r u c t u r e s are shown i n  F i g u r e 22. 34 Morgan  has shown t h a t the time dependence of volume  c r y s t a l l i z a t i o n i s d e s c r i b e d by the e q u a t i o n  a where  a  =  a  [1 - exp ( - K t ) ] n  Q  (24)  = S a t u r a t i o n v a l u e of c r y s t a l l i z a t i o n  o  t  = Time o f 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  crystals  The above e q u a t i o n can be w r i t t e n as  a In  Ln In (  In ( —  o  a  o  - a  a  o  - a  )  =  I n K + n In t  (25)  ) i s p l o t t e d as a f u n c t i o n of In t f o r the g l a s s - c e r a m i c ,  F i g u r e 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 f u n c t i o n 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  Point-Count  X-ray Method  Time, Minutes Weight  Fraction  Volume F r a c t i o n  Analysis  Volume F r a c t i o n  30  —  -  0  60  -  -  0  90  -  -  20  -  -  190  -  -  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  0.02 ^  0.04 0.05  —  60  10 ym Figure 22  Optical micrograph of glassceramic containing: (a)  Figure 22(b)  .05 volume f r a c t i o n of c r y s t a l l i n e phase.  0.15 to 0.20 volume f r a c t i o n of c r y s t a l l i n e phase.  M 10 ym F i g u r e 22(c)  0.35 volume f r a c t i o n phase.  of c r y s t a l l i n e  I—I  F i g u r e 22(d)  10 um 0.55 volume f r a c t i o n phase.  of c r y s t a l l i n e  63  as shown i n F i g u r e 23.  Here a i s taken as 0.90. o  A good  linear-dependence  i s seen as p r e d i c t e d by t h e above e q u a t i o n and t h e s t r a i g h t l i n e has a s l o p e equal t o 2.56.  The s l o p e o f t h i s l i n e i s s e n s i t i v e t o t h e shape o f t h e  individual crystallites.  A s l o p e o f 1, 2, or 3 corresponds  respectively  to p l a t e , c y l i n d e r and sphere.  3.4  Microhardness  F i g u r e 24 shows the microhardness  as a f u n c t i o n o f degree  of c r y s t a l l i n i t y . The i n d e n t a t i o n s were made on t h e g l a s s y phase at h i g h e r degree o f c r y s t a l l i n i t y , c r y s t a l l i n e phase.  except  > 50%, where they were made on t h e  F i g u r e 24 shows a sharp r i s e i n t h e hardness  at t h e  e a r l y stage o f the c r y s t a l l i z a t i o n and a p l a t e a u r e g i o n beyond 0.2 volume f r a c t i o n o f c r y s t a l l i n e phase.  Hardness v a l u e s a r e a l s o compiled i n  Table 4.  3.5  Elastic  Constants  F i g u r e 25 shows t h e Young's modulus as a f u n c t i o n o f t h e degree of c r y s t a l l i n i t y .  Young's modulus v a l u e s o b t a i n e d by Freiman and Hench  are a l s o shown i n t h i s f i g u r e .  47  Even though t h e a c t u a l v a l u e s o f the  Young's modulus o b t a i n e d i n the p r e s e n t work and t h a t by Freiman and 47 Hench  a r e d i f f e r e n t , b o t h show a s i m i l a r i n c r e a s e as t h e degree of  c r y s t a l l i n i t y increases. f o r the  ~ ^ ® 2 &^ 5  ass  The Young's modulus v a l u e o b t a i n e d by Kozlovskaya' i  s  a  ^  s  o  c l o s e agreement w i t h the p r e s e n t  shown i n F i g u r e 25. results.  This value i s i n  Figure  23  R e l a t i v e degree of c r y s t a l l i n i t y f u n c t i o n of time at 530°C.  as a  F i g u r e 24  Microhardness of g l a s s - c e r a m i c s as a f u n c t i o n 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 F r a c t i o n of C r y s t a l l i n e Phase  Mean DPH (kg/mm ) 2  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  F i g u r e 25  FRACTION  Young's modulus of g l a s s - c e r a m i c s as a f u n c t i o n of volume f r a c t i o n of c r y s t a l l i n e phase.  68  P o i s s o n ' 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 F i g u r e  26.  From the v a l u e s o f Young's modulus and P o i s s o n ' s r a t i o shear m o d u l i were c a l c u l a t e d .  These a r e l i s t e d  i n Table  the  5.  F i g u r e 27 shows the v a r i a t i o n of shear modulus w i t h r e s p e c t t o the volume f r a c t i o n o f c r y s t a l l i n e phase.  The v a l u e s o f Young's modulus,  shear modulus and P o i s s o n ' s r a t i o a r e a l s o l i s t e d  3.6  Transverse  i n Table  5.  Rupture T e s t s  F i g u r e 28 and T a b l e 6 show the v a r i a t i o n o f mean f r a c t u r e s t r e s s w i t h r e s p e c t t o the volume f r a c t i o n o f c r y s t a l l i n e phase i n two different  environments,  s t r e s s r a t i o i n the two  water and  toluene.  The v a r i a t i o n of t h e  environments i s shown i n F i g u r e 29.  As  fracture seen  from t h i s f i g u r e the r a t i o remained c o n s t a n t over t h e whole range o f crystallization.  I t i s a l s o seen from t h i s f i g u r e t h a t the  s t r e s s of the g l a s s and  fracture  g l a s s - c e r a m i c t e s t e d i n water i s 80% o f t h a t i n  toluene. The  square of t h e 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 f u n c t i o n o f  the r e c i p r o c a l of the mean f r e e p a t h between c r y s t a l s i n F i g u r e s 30 31.  T h i s dependency i s seen i n b o t h water and t o l u e n e .  are l i s t e d  i n Table  6.  and  These v a l u e s  F i g u r e 26  P o i s s o n ' s r a t i o of g l a s s - c e r a m i c s as a f u n c t i o n 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 C r y s t a l l i n e Phase  Young's Modulus lO^N/m* (Mean Value)  Shear; Modulus I-'.10 N/m2(Mean Value) 10  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  F i g u r e 27  FRACTION  Shear modulus of g l a s s - c e r a m i c s as a f u n c t i o n volume f r a c t i o n of c r y s t a l l i n e phase.  72  0-4 - 0 —  K  —A-  O-  (TOLUENE)  -©—  0~  (WATER)  ic  0-3  CM •s.  10  0-2 I—I  o  o-  0  0  •4 VOLUME  F i g u r e 28  -6  -8  0  FRACTION  F r a c t u r e s t r e s s ( a ) and 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 ( K ) of glass-ceramics as a f u n c t i o n o f volume f r a c t i o n o f c r y s t a l l i n e phase. f  I C  Table 6 EFFECT OF DEGREE OF CRYSTALLINITY ON FRACTURE STRESS  F r a c t u r e S t r e s s , of, N/m , ( p s i ) 2  Volume F r a c t i o n of C r y s t a l l i n e Phase  In  In Toluene  Water  0  1.01 x 1 0 (14.666 x 10 )  8.25 x 1 0 (11.975 x 10 )  0.10  1.125 x 1 0 (16.319 x 103)  9.163 x 1 0 (13.390 x 1 0 )  1.509 x 1 0  1.069 x 1 0  0.20  8  8  8  1.266 x 1 0 (22.717 x 1 0 )  2.126 x 1 0 (30.847 x 1 0 )  1.735 x 1 0 (25.167 x 1 0 )  2.417 x 1 0 (35.065 x 1 0 )  2.016 x 1 0 (29.249 x 1 0 )  3.115 x 1 0 (45.182 x 1 0 )  2.4256 x 1 0 (35.181 x 1 0 )  8  8  8  3  0.90  8  1.837 x 1 0 (26.642 x 1 0 ) 3  0.60  3  (15.514 x 1 0 )  3  0.50  7  (21.89 x 1 0 ) 3  0.40  7  8  3  3  8  3  8  3  8  3  8  3  •25 VOLUME  F i g u r e 29  Relative function  -5 FRACTION  -75  f r a c t u r e s t r e s s of g l a s s - c e r a m i c s as a 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 f r e e path between s p h e r u l i t e s on f r a c t u r e s t r e s s ( t e s t e d i n toluene) of glass-ceramics.  76  F i g u r e 31  E f f e c t of mean f r e e path between s p h e r u l i t e s on f r a c t u r e s t r e s s ( t e s t e d i n water) of g l a s s ceramics .  77  3.7  Slow Crack Growth T e s t s  3.7.1  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 Diagrams  Since the i n i t i a l v a l u e s of the e x p o n e n t i a l f u n c t i o n d e s c r i b i n g c r a c k v e l o c i t y c o i n c i d e w i t h the power f u n c t i o n , c r a c k v e l o c i t y s u b c r i t i c a l f l a w growth can o f t e n be expressed  during  as a power f u n c t i o n of  36 the a p p l i e d s t r e s s V  =  A K  (26)  n i  where V i s c r a c k v e l o c i t y , A and all  n a r e c o n s t a n t s • In the p r e s e n t  the c r a c k p r o p a g a t i o n data were p l o t t e d  i n accordance  study  w i t h the above  equation.  3.7.1.1  Annealed  Glass  F i g u r e 32 shows l o g V - l o g K^. diagrams o b t a i n e d g l a s s from l o a d - r e l a x a t i o n c u r v e s , i n d i f f e r e n t r h , 30% r h , and  toluene.  relative-humidity. plots.  The  Stage I I i s observed  annealed  environments, water, i n the t e s t s done at  T a b l e 7 g i v e s the s l o p e s and  s l o p e s of l o g V - l o g  for  i n t e r c e p t s of  diagrams of the annealed  70% 30%  these glass tested  i n water, 70% r h , 30% r h remained f a i r l y c o n s t a n t a t a v a l u e of 19 ± 4. However the s l o p e c o r r e s p o n d i n g higher  (65).  to the t e s t s done i n t o l u e n e was  I t appeared t h a t the l o g V - l o g K  much  p l o t s of g l a s s t e s t e d  602  Figure 32  Velocity-stress intensity factor diagrams f o r annealed glass at room temperature.  00  Table 7 EFFECT OF ENVIRONMENT UPON SLOPES AND INTERCEPTS OF LOG V-LOG K j DIAGRAMS OF ANNEALED GLASS V = AK^  Correlation  Coefficient  Test Conditions  Slope n  Intercept Log A  Toluene  64.3  - 388.76  .995  30% R e l a t i v e Humidity  14.6  -  91.11  .982  70% Humidity  14.56  -  90.38  .991  Water  19.00  - 115.89  .992  r  80  i n t o l u e n e were i n the Stage III r e g i o n .  As seen from F i g u r e 32  the  l o g V - l o g K^. diagrams move to h i g h e r s t r e s s - i n t e n s i t y as the water content i n the environment d e c r e a s e s . as InV Vs  These r e s u l t s were a l s o  and p r e s e n t e d i n Appendix 3.  seen between InV Vs  (The two  plotted  A l i n e a r dependency i s a l s o  f u n c t i o n s are s u f f i c i e n t l y  s i m i l a r that  the d a t a f i t e i t h e r p l o t e q u a l l y 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  F i g u r e s 33, 34 and 35 show the l o g V- l o g K 30 ± 5%,  and  50 ± 5% c r y s t a l l i n e g l a s s - c e r a m i c s .  v a l u e s of s l o p e and respectively. a r e about 1/3  3.7.1.3  The  T a b l e s 8 and  s l o p e s of the l o g V- l o g  5%,  9 g i v e the  i n t e r c e p t of these p l o t s f o r t e s t s i n water and  toluene  p l o t s f o r t e s t s i n water  of those f o r t e s t s i n t o l u e n e .  Glass-Ceramics  above 50% of C r y s t a l l i n e Phase  P l o t s of l o g V v e r s u s l o g  f o r 70 ± 5% and 85 ± 5%  g l a s s - c e r a m i c s are shown i n F i g u r e s 36 and and  p l o t s f o r 15 ±  i n t e r c e p t s of these p l o t s are l i s t e d  37.  The  crystallized  corresponding  i n T a b l e s 8 and 9.  These r e s u l t s  are a l s o 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 22 p a r i s o n w i t h one  of the stress-enhanced  corrosion theories  of g l a s s i n water.  com-  23 '  F i g u r e 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 the s t a t i c f a t i g u e behaviour  slopes  on  As seen from F i g u r e 38,  the  - 3 51 0 = WATER A = TOLUENE  i  o  Ul  CO  i  O'  •  GT  _A ^•5  A  /  A / A  .0° O'  K  A / A A' A*  o  /  - 5 - 5  0°  IC  A/ A/  / -6-5,  5 - 9  5 - 9 4  5 - 9 8  L O G  F i g u r e 33  6  0  K j  6 0 6  2  ,  6 1 0  6 1 4  6 1 8  •,. _3/2 N.m  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 g l a s s ceramic c o n t a i n i n g .15 ± .05 volume f r a c t i o n o f c r y s t a l l i n e phase a t room temperature. oo  o - WATER A-TOLUENE  / /  o Ul  (S)  o K  IC  o G  J  /  -6  5 92  6 0  6 08  LOG  F i g u r e 34  616  K , N. m —  6 20  3/2  T  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 g l a s s ceramic c o n t a i n i n g .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.  1  1  o  -  W A T E R  A  -  T O L U E N E  1  1-  .  j  '  /  / a  /  i  I  UJ  A  !  O  A  E  -51-  o  * I  O  o /  I IC K  1 A'  - 6  o  /  1-A ?  I T  T  4 L O G  F i g u r e 35  I 6 K j  ^  2  ,  N.  I  2  6  L  3  0  m  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 g l a s s - c e r a m i c c o n t a i n i n g . 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 a t room temperature.  oo oo  O-WATER H  A  ~ TOLUENE  o UJ  (/>  Ki c  3  -6  622  1  630  _L  LOG  F i g u r e 36  J.  6 38 -3/2 K , N. m  _L  6 46  x  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 g l a s s ceramic c o n t a i n i n g .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  A  o' /  / A A  -5 o  A A A A'  -6  _L  6 44  636 L O G  F i g u r e 37  A  A A  /  628  KIC  K  x  ,  652  6 60  -3/2  N m  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 g l a s s ceramic c o n t a i n i n g .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  LOG  Figure 38  K  I t  N.  m  -3/2  Velocity-stress intensity factor diagrams f o r glass and glass-ceramics tested i n 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^  Correlation Coefficient, r  Slope n  Intercept Log A  0  19.00  -  115.89  .992  ± .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  Volume F r a c t i o n of C r y s t a l l i n e Phase  .15  88  slopes  of l o g V - l o g  move to a h i g h e r The  p l o t s remains f a i r l y c o n s t a n t ,  s t r e s s 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  environment i s shown i n F i g u r e  of these p l o t s i n c r e a s e as the degree of c r y s t a l l i n i t y  3.8  Critical  The  Stress Intensity Factor  plots  increases  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  behaviour of g l a s s i n the toluene slopes  however the  fatigue 39.  The  increases.  (K ) J r  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 s (K.^)  as measured by  fast  l o a d i n g [11.25 x 10 ^ m/sec (0.05"/min)]the double t o r s i o n samples a f t e r c o m p l e t i o n of the l o a d r e l a x a t i o n t e s t s are l i s t e d shows the K  From t h i s f i g u r e i t i s c l e a r t h a t  as the degree of c r y s t a l l i n i t y i n c r e a s e s .  the 85 ± 5%  Figure  c r y s t a l l i z e d glass-ceramic  annealed g l a s s .  The  i s about 3.5  t r e n d of i n c r e a s e of  The  value  K^,  of  times that of  for the  i s s i m i l a r to t h a t of  the  fracture stress.  3.9  28  , 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 , a s 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. increases  i n T a b l e 10.  Fracture  The  Surface  Energy  f r a c t u r e toughness e q u a t i o n can be w r i t t e n K  ic  •  as ( 2 7 )  -3-5^  o UJ  in  <s> O  LOG  F i g u r e 39  K  .3/2  T  6-5  , N.nrT  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 g l a s s and g l a s s - c e r a m i c s t e s t e d i n t o l u e n e 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*  Slope n  Intercept Log A  Correlation Coefficient 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  Volume F r a c t i o n of C r y s t a l l i n e Phase  91  Substituting  G  IC  =  2y  i n the above e q u a t i o n :  / 2 Ey  K. IC  (28)  =  The C r i t i c a l s t r e s s i n t e n s i t y  factor  =  C r i t i c a l S t r a i n energy r e l e a s e  rate  Y  =  Fracture  E  =  Young's modulus  where K. IC  Knowing K  surface  energy  and E one can c a l c u l a t e y,  the f r a c t u r e s u r f a c e  e q u a t i o n 28, T a b l e 10 g i v e s the f r a c t u r e s u r f a c e above method.  Fracture  surface  mean f r e e path i n F i g u r e 40.  energy by u s i n g  energy c a l c u l a t e d by the  energy i s p l o t t e d as a f u n c t i o n  of r e c i p r o c a l  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  Scanning e l e c t r o n micrographs of f r a c t u r e s u r f a c e s of v a r i o u s t r a n s v e r s e r u p t u r e specimens a r e shown i n F i g u r e s 41(a) t o 4 1 ( d ) . 42(a)  Figures  t o 42(h) show scanning e l e c t r o n micrographs o f f r a c t u r e s u r f a c e s o f  double t o r s i o n  specimens. G l a s s - c e r a m i c s c o n t a i n i n g  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 w i t h c h a r a c t e r i s t i c f r a c t u r e s t e p s a l o n g the d i r e c t i o n of the c r a c k growth. F i g u r e s 42(d) and 42(e) show a m i x t u r e o f 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 fracture.  Glass-ceramics containing  h i g h e r volume f r a c t i o n s o f  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 f r a c t u r e .  Cleavage s t e p s  Figure  40  E f f e c t of mean f r e e path between s p h e r u l i t e s on f r a c t u r e s u r f a c e energy of g l a s s - c e r a m i c .  T a b l e 10 CRITICAL STRESS INTENSITY FACTORS AND FRACTURE SURFACE ENERGIES OF GLASS AND GLASS-CERAMICS  Volume F r a c t i o n of C r y s t a l l i n e Phase  Mean C r i t i c a l Stress Intensity F a c t o r , N.m ' -3  Fracture Surface Energy, J.m 2  1  Mean F r e e  Path  , tim-1  2  0  1.015 x 1 0  6  6.650  0  .10 ± .01  1.137 x 1 0  6  7.901  .019  .15 ± .05  1.328 x 1 0  6  10.251  .032  .30 ± .05  1.55 x 1 0  6  13.046  .045  .50 ± .05  2.02 x 1 0  6  18.91  .076  .70 ± .05  2.98 x 1 0  6  39.115  .139  .85 ± .05  3.53 x 1 0  6  51.397  .314  VO  1 10 F i g u r e 41  ym  SEM f r a c t o g r a p h of sample(used t r a n s v e r s e r u p t u r e t e s t s ) of (a)  In  Glass-ceramic c o n t a i n i n g 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.  95  I F i g u r e 41(b)  1  10 ym G l a s s - c e r a m i c c o n t a i n i n g .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  Figure  41(c)  1  10 ym G l a s s - c e r a m i c c o n t a i n i n g .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 F i g u r e 41(d)  10  ym  1  G l a s s - c e r a m i c c o n t a i n i n g .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  F i g u r e 42  1  10 ym SEM f r a c t o g r a p h of sample(used i n double t o r s i o n t e s t s ) of (a)  G l a s s - c e r a m i c c o n t a i n i n g 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 i n d i c a t e s the d i r e c t i o n of crack propagation].  99  I  F i g u r e 42(b)  1  10 ym G l a s s - c e r a m i c c o n t a i n i n g .05 volume f r a c t i o n of c r y s t a l l i n e phase. [Arrow i n d i c a t e s the d i r e c t i o n of crack propagation].  I—I  F i g u r e 42(c)  10 ym G l a s s - c e r a m i c c o n t a i n i n g .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 i n d i c a t e s the d i r e c t i o n of crack propagation].  I—I  F i g u r e 42(d)  10 ym G l a s s - c e r a m i c c o n t a i n i n g .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 i n d i c a t e s the d i r e c t i o n o f crack p r o p a g a t i o n ] .  102  I 1 Figure 42(e)  10 ym Glass-ceramic containing .50 ± 0.05 volume f r a c t i o n of c r y s t a l l i n e phase. [ A r r o w indicates the d i r e c t i o n of crack propagation].  103  I  10 Figure 42(f)  1 ym  G l a s s - c e r a m i c c o n t a i n i n g .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 F i g u r e 42(g)  ym  G l a s s - c e r a m i c c o n t a i n i n g .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 Figure 42(h)  10 ym 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)  106  are seen (area A i n F i g u r e 4 2 ( h ) ) i n t r a n s p a r t i c l e f r a c t u r e d The f r a c t u r e d s u r f a c e s samples  of samples  tested i n toluene.  samples.  t e s t e d i n water d i d not d i f f e r  from  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 I t has been e s t a b l i s h e d by Hench  e t a l that  i n l i t h i u m d i s i l i c a t e g l a s s proceeds i n t h e f o l l o w i n g 1.  crystallization  stages.  Formation o f m e t a s t a b l e l i t h i u m m e t a s i l i c a t e a t t h e end  of a n u c l e a t i o n treatment.  The f o r m a t i o n  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 t o an o r d e r i n g o f extremely s m a l l r e g i o n s g l a s s c o n t a i n i n g randomly d i s t r i b u t e d I ^ O - Si02 c h a i n s .  i n the  The  + ordering probably incorporated  i n v o l v e s s h o r t range m i g r a t i o n  When the same sample i s g i v e n a c r y s t a l l i z a t i o n t r e a t -  ment a t h i g h e r  temperature, L i 2 0 groups a p p a r e n t l y  m e t a s i l i c a t e n u c l e i producing  d i f f u s e out o f t h e  the l i t h i u m d i s i l i c a t e s t r u c t u r e .  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 r e g i o n i s reached,  the growth proceeds towards  4.  i o n s t o be  into a metasilicate structure.  2.  3.  of L i  completion.  While t h e 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,  L i 2 0 groups a r e r e j e c t e d a t t h e growing f r o n t and as a r e s u l t protrusions  a r e sent out from t h i s c r y s t a l l i t e i n s e a r c h  of l i t h i u m  108  meta-silicate regions. c r y s t a l l i t e producing  These p r o t r u s i o n s grow r a d i a l l y from the a spherulitic  central  structure.  A c h a r a c t e r i s t i c f e a t u r e of the s p h e r u l i t i c s t r u c t u r e i s the  38 presence of f i b r o u s s u b - u n i t s c a l l e d the f i b r i l l a r in  development i s a fundamental  the c r y s t a l l i z a t i o n of polymers.  study.  fibrils.  t h a t the f i b r i l s  F i b r i l s are a l s o seen i n the p r e s e n t  micrographs  show f i b r i l s  extending  I t i s a l s o seen from t h e s e f i g u r e s  branch out as they grow; t h i s h e l p s to f i l l  between two main f i b r i l s ,  that  p r o c e s s i n s p h e r u l i t i c growth  F i g u r e s 4 3 ( a ) , 4 3 ( b ) , 43(c) and 44(a)  r a d i a l l y from the c e n t r a l n u c l e u s .  I t has been shown  as the s p h e r u l i t e expands.  the space  From these  i t i s a l s o seen t h a t t h e r e e x i s t s a low angle g r a i n boundary  between the f i b r i l s .  Hence a s p h e r u l i t e i s not a s i n g l e c r y s t a l .  In  the e a r l y stages of growth, a s p h e r u l i t e p r o b a b l y develops from a s i n g l e c r y s t a l and becomes aggregates o f f i b r i l s  as b r a n c h i n g e v e n t u a l l y  sets  in.  In used.  the p r e s e n t study a s e p a r a t e n u c l e a t i o n treatment was  not  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  were annealed to r e l i e v e s t r e s s e s , a t 470°C. the n u c l e a t i o n temperature  Hench  f o r 33.3 mole% L ^ O  37  chose 475°C as  and 66.6  mole%  S102  39 glass.  On  the o t h e r hand Hing and M c M i l l a n  n u c l e a t i o n temperature  f o r 30 L i 0 . 2  chose 500°C as the  69 S i 0 . l P ° 5 § l 2  the p r e s e n t study the a n n e a l i n g treatment might  2  a s s  '  Hence i n  a l s o have produced  109  F i g u r e 43(a)  TEM photograph of i n d i v i d u a l d i s i l i c a t e spherulite.  lithium  110  Figure 43(b)  TEM photograph of i n d i v i d u a l 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 d i s i l i c a t e spherulite.  lithium  112  nucleation.  However, t h i s treatment d i d not  a l t e r the  transparency  of the g l a s s , i n d i c a t i n g the absence of phase s e p a r a t i o n . annealing  temperature f o r the p r e s e n t  thermal a n a l y s i s . ( F i g u r e 18)  work was  The  determined by  A s m a l l exothermic peak between 458°C and  r e v e a l s the a n n e a l i n g  p o i n t of t h i s g l a s s .  proper  differential 486°C  T h i s peak i s  40 believed  to be due  The  to an adjustment i n the g l a s s  present  structure  study on c r y s t a l l i z a t i o n showed an  p e r i o d of 40 minutes when the g l a s s was  incubation  g i v e n a heat-treatment at 530°C.  T h i s shows t h a t the c r y s t a l l i z a t i o n of t h i s g l a s s 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 to f u r t h e r c o n f i r m  the d i f f u s i o n c o n t r o l l e d n a t u r e of  r e a c t i o n , the d a t a f o r the growth of the s p h e r u l i t e s was  41  the  fitted  to  42  Zener  and  Frank's  model.  F i g u r e 45  shows the p l o t o f the  of the s p h e r u l i t e as a f u n c t i o n of the square r o o t of time. shows a l i n e a r dependency as p r e d i c t e d by  the theory.  of the p r o c e s s i s determined as f o l l o w s :  According  The  diameter This plot  diffusivity  41  where  to Zener  R  =  L  / Dt  (29)  d  =  2L / Dt  (30)  L  =  F(f)  R  =  Radius of the  d  =  Diameter of the  t  =  Time i n sec  f  =  D  =  spherulite spherulite  Supersaturation 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 s p e c i e s s  113  I f the p r o c e s s has an i n c u b a t i o n p e r i o d of t , then e q u a t i o n o  (30)  can  be w r i t t e n as d The  corresponding p l o t  =  2L • D ( t - t )  f o r equation  E x p e r i m e n t a l p o i n t s up to 70% The  diffusion  42  .  c o e f f i c i e n t was  (31) i s shown i n F i g u r e 45.  c r y s t a l l i n i t y l i e i n a straight  s l o p e of t h i s l i n e corresponds  the graph of L v e r s u s f  t o 2L / D.  Assuming s p h e r i c a l calculated  to be 6.7  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 -12 1.1  x 10  expected  (31)  o  L was  calculated  p a r t i c l e s , D, x 10  line.  -13  cm  2  from  the  /sec.  I f the  c o r r e s p o n d i n g v a l u e of D i s  2 cm  /sec.  diffusion  Each of these v a l u e s i s s m a l l compared t o the c o e f f i c i e n t of L i  +  (- 1 x 10  ^cm^/sec)^.  43 In an a t o m i s t i c approach related  to the mean f r e e path  ( A ^ ) , the average  jumps of d i f f u s i n g i o n s , frequency activation  energy  (AF*)  and  D  v  be  (v) and  the  , . (32) q o  kT ;— h  =  Boltzman's constant  h  =  Planck's  T  =  Temperature  R  =  Gas =  of atomic v i b r a t i o n  =  =  can  d i s t a n c e of s u c c e s s i v e  i n the f o l l o w i n g form * i / - AF* . — v exp( — )  where k  Assuming A_  the d i f f u s i o n c o e f f i c i e n t  constant  constant 5A° and  substituting  AF* as 42 Kcal/mole  (this value  was  114  o b t a i n e d from d i f f e r e n t i a l thermal a n a l y s i s ) , the v a l u e of D i s 1.2 -12 10  x  2 cm  /sec.  T h i s v a l u e i s i n c l o s e agreement w i t h the e x p e r i m e n t a l l y -12  o b t a i n e d v a l u e of 1.1  x 10  growth law f o r c y l i n d r i c a l  The  2 cm  /sec.  Thus the c r y s t a l l i t e s obey the  particles.  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 g i v e n by equations  (24) and  (25).  F i g u r e 23  a shows a l i n e a r  dependency between  o  ln.ln(  ) versus Int.  The  slope  a - a Q  of t h i s s t r a i g h t l i n e corresponds  t o 2.5.  Thus a c c o r d i n g t o Morgan's  34 analysis and  the shape f a c t o r of the p a r t i c l e s l i e s between t h a t f o r spheres  that f o r rods.  As e x p l a i n e d e a r l i e r , a s p h e r u l i t i c s t r u c t u r e 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 . 44(a)  F i g u r e s 43(a)  t o 43(c)  and  show t h a t the s p h e r u l i t e i s composed of f i b r i l s which have r o d - l i k e  shape e x t e n d i n g r a d i a l l y outwards from the c e n t r a l n u c l e u s . observed  Microstructures  i n the p e t r o g r a p h i c study a r e shown i n F i g u r e 44(b).  m i c r o s t r u c t u r e s show s p h e r i c a l shaped p a r t i c l e s .  These  Thus t h e r e i s a c o r r e l -  a t i o n between the s t r u c t u r e p r e d i c t e d from growth k i n e t i c s and 37 microstructure. Hench has o b t a i n e d 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  the  observed  f o r the growth of s p h e r u l i t e s i n 33.33 37  mole% L ^ O concluded  - 66.66 mole% Si02 g l a s s was t h a t the a c t i v a t i o n energy  determined  by Hench  .  He  f o r 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 n u c l e a t i o n treatment.  The a c t i v a t i o n energy  samples w i t h 24 hours n u c l e a t i o n treatment was a sample w i t h o n l y 3 hours n u c l e a t i o n treatment  f o r the  52 K c a l mole ^ w h i l e f o r i t was  92 K c a l mole  F i g u r e 44(a)  SEM photograph of p a r t i a l l y glass-ceramic.  crystallized  116  Figure  44(b)  T y p i c a l s p h e r u l i t i c m i c r o s t r u c t u r e 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 p e t r o g r a p h i c s e c t i o n ( c r o s s e d n i c o l s )  117  F i g u r e 45  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 v e r s u s r e c i p r o c a l of square r o o t of time of c r y s t a l l i z a t i o n at 530°C.  118  In s t u d y i n g the d e v i t r i f i c a t i o n b e h a v i o u r Si02» J a c c o d i n e  44  of 30 mole% Ll^O  o b t a i n e d a v a l u e of 49 Kcal/mole  I^Si^O,. s p h e r u l i t e s .  -1  - 70 mole%  f o r the growth of  In the p r e s e n t study the a c t i v a t i o n energy  the growth of L i ^ S i ^ O ^ s p h e r u l t i e s was  determined  by  differential  thermal a n a l y s i s as d e s c r i b e d i n the e x p e r i m e n t a l s e c t i o n and i s 42 K c a l mole \  ions (19.1 K c a l mole  .  The p r e s e n t v a l u e of a c t i v a t i o n energy i s  .  and f o r the d i f f u s i o n of oxygen i o n s (32.4  T h i s shows t h a t the growth of the l i t h i u m d i s i l i c a t e to d i f f u s i o n of l i t h i u m i o n or oxygen i o n and  other s p e c i e s .  T h i s d i f f u s i o n s p e c i e s may  form as h y p o t h e s i z e d by Hench  4.2.1  f o r the d i f f u s i o n of l i t h i u m Kcal  45 )  i s not due  4.2  by  37 and Hench  c o n s i d e r a b l y h i g h e r than the a c t i v a t i o n energy  -1  the v a l u e  T h i s agrees v e r y w e l l w i t h the v a l u e s o b t a i n e d  44 Jaccodine  mole  for  be I ^ O  i s due  groups i n an  spherulite to s ome ionic  37  Mechanical P r o p e r t i e s  Microhardness  As seen from F i g u r e 24 the microhardness  of the glassy-ceramic  i n c r e a s e s as the degree of c r y s t a l l i n i t y i n c r e a s e s . The  increase i s rapid i n  the e a r l y 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  In o r d e r to determine microhardness  t e s t the hardness  stages.  the d e f o r m a t i o n mechanism i n the v a l u e i s compared w i t h the  fracture  119  strength.  In F i g u r e 46  the f r a c t u r e s t r e n g t h and microhardness  are  p l o t t e d a g a i n s t 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 t h a t the t r e n d s microhardness are not increase  of the i n c r e a s e s  the same.  i n hardness i s not  i n fracture strength  and  T h i s shows that the mechanism of  the same as t h a t of f r a c t u r e  strength.  46 Ernsberger  showed t h a t the microhardness of g l a s s may  regarded as a measure of the p r e s s u r e d e n s i f i c a t i o n or v o l u m e t r i c i o n i n v o l v e s simply  yield.  He  required  for  be  initiating  suggested t h a t t h i s d e n s i f i c a t -  a c o l l a p s e of the s t r u c t u r e under the i n d e n t e r  into  a more c l o s e packed arrangement by a p r o c e s s 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 i n d e n t a t i o n  i n an  inter-  f e r e n c e microscope, he came to the c o n c l u s i o n  t h a t p l a s t i c i t y does  e x i s t i n s i l i c a t e g l a s s even on a m i c r o s c o p i c  scale.  When the p r e s e n t  g l a s s i s undergoing the  crystallization  treatment, 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 n u c l e a t e s grow.  But  at the same time the s t r u c t u r e i n the  g l a s s tends to become more dense.  and  tends to  inter-spherulitic  I f most of t h i s rearrangement  i n the s t r u c t u r e o c c u r s i n the e a r l y stages of c r y s t a l l i z a t i o n , t h i s would account f o r the r a p i d r i s e of hardness. rearrangement i s complete, the hardness i n the r e g i o n would remain the same and region.  not  then  Once t h i s  inter-spherulitic  t h i s would account f o r the  plateau  Figure  46  F r a c t u r e s t r e s s and microhardness of g l a s s - c e r a m i c s v e r s u s 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  Elastic  Moduli  The v a r i a t i o n o f Young's modulus o f g l a s s - c e r a m i c s c o n t a i n i n g d i f f e r e n t volume f r a c t i o n s o f c r y s t a l l i n e phase i s shown i n F i g . 25. I n the same f i g u r e the d a t a o f Freiman P r e s e n t r e s u l t s were determined  47  and K o z l o v s k a y a  35  a r e a l s o shown.  by u s i n g a s t a t i c method w h i l e most o f  the other d a t a were o b t a i n e d by a dynamic method.  The Young's modulus  o b t a i n e d f o r t h e g l a s s i n t h e p r e s e n t study agrees v e r y w e l l w i t h t h a t 35 of K o z l o v s k a y a  .  Eventhough t h e a c t u a l v a l u e s o f t h e Young's modulus 47 are d i f f e r e n t i n the p r e s e n t experiments from those of Freiman , the trend of increase i s apparently s i m i l a r .  Freiman  47  obtained h i s data  on g l a s s o f 33.33 mole% 1*2^ ~ 66.66 mole% S i C ^ and t h e p r e s e n t  study  35 was done on 30 mole% I ^ O - 70 mole% Si02 g l a s s .  Kozlovskaya  showed  the dependence of Young's modulus of I ^ O - Si02 b i n a r y g l a s s on % Si20 content i n the g l a s s , as shown i n F i g u r e 47.  The v a l u e o f Young's  modulus (E) f o r 33.33 mole% I ^ O - 66.66 mole% Si02 g l a s s o b t a i n e d 47 t h i s f i g u r e d i d not agree w i t h Freiman's  from  d a t a , eventhough both used a  dynamic method i n measuring t h e Young's modulus. The Young's modulus f o r f u l l y c r y s t a l l i n e m a t e r i a l was c a l c u l a t e d 4 from F i g u r e 25 by e x t r a p o l a t i o n and t h e c o r r e s p o n d i n g v a l u e i s 12.6 x 10 MPa.  From F i g u r e 20, the d e n s i t y o f 100% c r y s t a l l i n e m a t e r i a l was a l s o  c a l c u l a t e d by e x t r a p o l a t i o n . t h e o r e t i c a l v a l u e , i t was found  By comparing t h i s d e n s i t y v a l u e w i t h t h e t h a t t h e sample was 98% dense .  The Young's  122  • a  CJ  o b  70 h .—i 3  T3  O  s  6.0  cj 7}  Hi  5.0  20  M o l a r 7C F i g u r e 47  E f f e c t of c o m p o s i t i o n on e l a s t i c modulus of g l a s s e s i n system: x Me20 (100 - x) Si02 where Me i s L i 0 (after Kozlovskaya 5) 3  2  2  (2) N a 0  (1)  Li 0  (a) (b)  experimental values calculated values  2  2  (3) K 0 2  123  modulus v a l u e o f 100%  c r y s t a l l i n e m a t e r i a l was  by u s i n g H a s s e l m a n ' s ^ a n a l y s i s .  corrected f o r porosity  The c o r r e c t e d v a l u e i s 13.12  From t h e knowledge o f Young's m o d u l i  f o r the f u l l y  x 10^  MPa.  crystallized  g l a s s - c e r a m i c and f o r t h e annealed g l a s s , t h e e l a s t i c b e h a v i o u r o f t h e two phase m a t e r i a l was  analysed.  T h i s i s shown i n F i g u r e 48.  Here t h e  top s o l i d l i n e c o r r e s p o n d s t o the V o i g h t model and t h e bottom s o l i d c o r r e s p o n d s t o the Reuss model. c o r r e s p o n d t o Hashxn's  49  The  line  top and bottom d o t t e d l i n e s  upper and lower bound models r e s p e c t i v e l y .  As seen from F i g u r e 48, t h e Young's modulus agrees v e r y w e l l 49 w i t h the p r e d i c t i o n o f Hashin's  t h e o r e t i c a l m i x i n g model up t o  volume f r a c t i o n o f c r y s t a l l i n e phase.  Above 0.5  0.5  the e x p e r i m e n t a l v a l u e s  a r e below the t h e o r e t i c a l m i x i n g model.  As t h e degree of c r y s t a l l i n i t y i n c r e a s e s the m a t r i x  (glass)  35 becomes r i c h e r i n Si02 c o n t e n t .  According to Kozolvskaya  the i n c r e a s e  o f Si02 c o n t e n t i n L i 0 ~ SiO2 b i n a r y g l a s s tends t o d e c r e a s e t h e Young's 2  modulus.  Hence as the degree of c r y s t a l l i n i t y  i n these glass-ceramics  i n c r e a s e s , Young's modulus o f the m a t r i x becomes lower than t h e glass.  T h i s e f f e c t may  more than 0.5  be pronounced  m a t r i x remains  i n glass-ceramics containing  volume f r a c t i o n o f c r y s t a l l i n e phase.  t h e o r e t i c a l p r e d i c t i o n i t was  starting  However, i n the  assumed t h a t t h e Young's modulus o f t h e  c o n s t a n t f o r a l l c o n c e n t r a t i o n s . T h i s may  be r e s p o n s i b l e  0  -2  4 VOLUME  F i g u r e 48  -6 FRACTION  -8  Comparison of v a l u e s of Young's modulus of g l a s s - c e r a m i c s w i t h the t h e o r e t i c a l models. r—  1  125  f o r the d i s c r e p a n c y between the t h e o r e t i c a l curve and the e x p e r i m e n t a l points.  The P o i s s o n ' s r a t i o o f the g l a s s - c e r a m i c s was a l s o a n a l y s e d 49 a c c o r d i n g t o Hashin's Although  the f i t i s r e a s o n a b l y  experimental 4.2.3.  model and the r e s u l t s a r e shown i n F i g u r e 49. good, t h e r e i s enough s c a t t e r i n the  r e s u l t s t h a t no c o n c l u s i o n s can be drawn.  Fracture Strength  The r e l a t i o n between the f r a c t u r e s t r e n g t h and the o t h e r f r a c t u r e parameters i s g i v e n by e q u a t i o n  ( 1 ) . When attempting t o  e x p l a i n the i n c r e a s e i n s t r e n g t h of g l a s s - c e r a m i c s i t i s r e a s o n a b l e  first  to c o n s i d e r the c o n t r i b u t i o n from the i n c r e a s e i n Young's modulus.  Frey  and Mackenzie"^ have argued t h a t i n d i s p e r s i o n s of A ^ O ^ glass matrix,  or Z r C ^ i n a  the i n c r e a s e i n f r a c t u r e s t r e n g t h i s caused  i n the Young's modulus of the m i x t u r e .  by the i n c r e a s e  A c t u a l l y t h e i r d a t a show t h a t  f o r a low volume f r a c t i o n o f ZrC^ (20%) the s t r e n g t h d e c r e a s e s .  For  the same volume f r a c t i o n of A l ^ O ^ the s t r e n g t h i n c r e a s e s s l i g h t l y . d i f 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 a r i s i n g from thermal e l a s t i c modulus.  The  stress  c o n t r a c t i o n mismatch r a t h e r than the i n c r e a s e d  According  to e q u a t i o n  ( 1 ) , the r a t i o of the  of a g l a s s - c e r a m i c t o t h a t of a g l a s s should be g i v e n by:  strength  VOLUME  F i g u r e 49  FRACTION  Comparison of v a l u e s of P o i s s o n ' s r a t i o of g l ceramics w i t h the t h e o r e t i c a l models.  127  J  GC  (33)  GC  where a  =  F r a c t u r e s t r e n g t h of annealed  =  F r a c t u r e s t r e n g t h of g l a s s - c e r a m i c  =  Young's modulus of annealed  E_ GC  =  Young's modulus of g l a s s - c e r a m i c  C  =  Initial  f l a w s i z e i n annealed  =  Initial  flaw s i z e i n glass-ceramic  a  G GO  E  G  G  C„„  glass  glass  glass  When the g l a s s and the g l a s s - c e r a m i c s were g i v e n the same a b r a s i o n treatment  (C_  =  C  ), equation  (33) becomes  (34)  T a b l e 11 shows the r a t i o G g  c a l c u l a t e d from e q u a t i o n  (34) and e x p e r i -  °GC mentally obtained v a l u e s .  The e x p e r i m e n t a l v a l u e s a r e c o n s i d e r a b l y  lower than the v a l u e s c a l c u l a t e d by the above method.  The f r a c t u r e  s t r e n g t h of g l a s s - c e r a m i c c o n t a i n i n g .90 volume f r a c t i o n of c r y s t a l l i n e phase ( c a l c u l a t e d a c c o r d i n g t o e q u a t i o n t h a t of annealed  g l a s s , but i t was found  (34)) shows a v a l u e of 1.25  times  e x p e r i m e n t a l l y t h a t the f r a c t u r e  s t r e n g t h of g l a s s - c e r a m i c c o n t a i n i n g .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 t h a t of annealed  glass.  SUMMARY OF  Volume F r a c t i o n of C r y s t a l l i n e Phase  a (— °GC  )  T a b l e 11 E AND ( GC  h )  FOR GLASS-CERAMICS  E  GC  Toluene  ( v  >  GC  Water  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 composite system.  a l s o proposed a f r a c t u r e t h e o r y f o r a  They h y p o t h e s i z e d  t h a t hard c r y s t a l l i n e d i s p e r s i o n s  w i t h i n the g l a s s m a t r i x l i m i t the s i z e of G r i f f i t h flaws and the composite.  They observed  strengthen  s t r e n g t h enhancement i n a g l a s s -  Al^O^  composite and  concluded  t h a t s t r e n g t h e n i n g r e s u l t e d whenever the  interparticle  d i s t a n c e (X) became s m a l l enough to l i m i t the s i z e of  s u r f a c e flaws to l e s s than t h a t p r e s e n t particles.  They a l s o concluded  the  i n the g l a s s c o n t a i n i n g no  t h a t the s t r e n g t h e n i n g was  whenever the i n t e r p a r t i c l e d i s t a n c e (X) was  very  small  b i g g e r than the s u r f a c e  flaws i n t r o d u c e d d u r i n g p r o c e s s i n g .  In the p r e s e n t were abraded w i t h a 400  case, a l l of the t r a n s v e r s e r u p t u r e g r i t SiC  (- 25 ym)  samples  and hence the samples c o n t a i n  62 flaws of a p p r o x i m a t e l y  25 ym.  A c c o r d i n g to Hasselman and F u l r a t h  s t r e n g t h of g l a s s - c e r a m i c s h a v i n g an i n t e r p a r t i c l e d i s t a n c e (X) than 25 ym  should remain a p p r o x i m a t e l y  constant.  ( F i g u r e s 30 and From e q u a t i o n  higher  However i n the p r e s e n t  case s u b s t a n t i a l s t r e n g t h e n i n g i s seen i n g l a s s - c e r a m i c s h a v i n g than 25 ym  , the  X larger  31).  (1) i t can be seen t h a t the f r a c t u r e s t r e n g t h  can be i n c r e a s e d by an i n c r e a s e i n the f r a c t u r e s u r f a c e energy.  If  the s t r e n g t h enhancement of g l a s s - c e r a m i c s i s o n l y a t t r i b u t e d to the increase  i n f r a c t u r e s u r f a c e energy, one  can w r i t e  130  a~  (35)  =  GC  T  Table 12 compares the r a t i o  °G  GC  calculated from equation  (35)  and  °GC  experimentally obtained values.  The experimental values agree reasonably  w e l l with the r a t i o of  Thus the increased fracture surface  2  •  energy appears to be the maxn contributing f a c t o r i n the strength enhancement" of glass-ceramics.  52 Lange  has shown that the f r a c t u r e surface energy of a  composite material can be expressed i n t e r p a r t i c l e distance (A).  i n terms of the matrix and  the  The d e t a i l e d analysis of t h i s theory i s  discussed i n the next section.  The above -relation i n glass-ceramics  can be written as Y where  y  GC  =  Y  G  +  T/X  (36)  =  Fracture surface energy of  =  Fracture surface energy of annealed glass  T  =  Line tension of the crack  A  =  I n t e r - s p h e r u l i t i c distance  GC  Y  glass-ceramics  G'  Substituting equation  (36) i n equation  4  According to t h i s r e l a t i o n a  (1) and  GC 1 \  - ^  E  2  1  +  rearranging  ^  <> 37  Vs - r - should give a straight l i n e i f  the contribution from the increase i n Young's modulus to strengthening  T a b l e 12  SUMMARY OF (  ) AND °GC  Volume F r a c t i o n of C r y s t a l l i n e Phase  (  ) Y  FOR GLASS-CERAMICS  GC  Y  GC  Toluene  GC  Water  Y  G  h  GC  .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 g l a s s - c e r a m i c s i s n e g l i g i b l e .  between a  2 GC  Vs 1/X  F i g u r e s 30 and 31 show the  f o r t e s t s i n t o l u e n e and water.  A straight line f i t  i s seen up to - 50% c r y s t a l l i n e phase as p r e d i c t e d by e q u a t i o n  Equation intensity factor  (1) can be expressed  (K  relation  (37).  i n terms of the c r i t i c a l  stress  ) as f o l l o w s ±.\j  1  K  IC  (38)  From t h i s e q u a t i o n the c r i t i c a l  f l a w s i z e can be c a l c u l a t e d when a^,  K  S t r a w l e y " ^ have shown t h a t Y f o r t h r e e  and Y a r e known.  p o i n t bending critical The  T a b l e 13 l i s t s  the samples.  T h i s suggests  s u b c r i t i c a l c r a c k growth.  grit  The  apparent  those c o n t a i n i n g 90% c r y s t a l l i n e phase.  (- 25  SiC powder used i n  t e s t i n t o l u e n e , the sample does not undergo critical  flaw s i z e i n g l a s s -  33 ym.  h i g h e r than the other g l a s s - c e r a m i c s p o s s i b l y due  40 ym.  approximately  t h a t w h i l e the sample i s l o a d i n g  c o n t a i n i n g 90% c r y s t a l l i n e phase was  the c r i t i c a l  the v a l u e of  g l a s s - c e r a m i c s t e s t e d i n t o l u e n e and water.  to the s i z e of the 400  the t h r e e p o i n t bending  ceramics  2.0.  f l a w s i z e i n the samples t e s t e d i n t o l u e n e i s  T h i s corresponds  abrading in  i s approximately  f l a w s i z e f o r g l a s s and  critical  25 ym.  Brown and  This value  to the p o r o s i t y i n  From T a b l e 13 i t i s seen t h a t  f l a w s i z e i n the samples t e s t e d i n water i s  approximately  T h i s v a l u e i s h i g h e r than the i n i t i a l f l a w s i z e i n the ym) ;  was  s u g g e s t i n g t h a t w h i l e the sample i s l o a d i n g i n the  samples three  T a b l e 13 CRITICAL FLAW SIZE IN SAMPLES USED IN TRANSVERSE RUPTURE TESTS K  -  2  IC  2 2 y a f  Volume F r a c t i o n of C r y s t a l l i n e Phase  C, ym(in Toluene)  •  C, ym(in Water)  39  0  26  10  26  40  20  24  40  50  24  36  60  26  37  90  33  55  134  p o i n t bending  t e s t i n water, i t undergoes s u b c r i t i c a l c r a c k growth.  Hence these samples r e g i s t e r lower f r a c t u r e s t r e n g t h s than tested i n toluene. 90%  The  d i s c r e p a n c y of the g l a s s - c e r a m i c s c o n t a i n i n g  c r y s t a l l i n e phase may  4.3  those  a g a i n be due  to p o r o s i t y .  F r a c t u r e S u r f a c e Energy  The  f r a c t u r e s u r f a c e energy of the g l a s s - c e r a m i c s i n c r e a s e d  as the f r a c t i o n of c r y s t a l l i n e phase i n c r e a s e d as shown i n T a b l e A f a c t o r of 3 i n c r e a s e i n f r a c t u r e s u r f a c e energy was  10.  o b t a i n e d 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 a t 90%.  Lange  has proposed a  t h e o r y f o r the i n c r e a s e i n the f r a c t u r e energy of b r i t t l e composites. second phase.  matrix  T h i s i n v o l v e s an i n t e r a c t i o n of the c r a c k f r o n t w i t h The  the  t h e o r y i s based on the o b s e r v a t i o n t h a t the l e n g t h  of a c r a c k f r o n t i n c r e a s e s when i t i s impeded by second phase p a r t i c l e s w i t h i n a b r i t t l e matrix.  U s i n g the concept  t h a t the c r a c k f r o n t has  a  l i n e energy, such an i n c r e a s e i n the c r a c k f r o n t l e n g t h should r e q u i r e 52 energy, thus i n c r e a s i n g the energy to propagate the c r a c k . found  Lange  t h a t 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 f r e e path g i v e n by e q u a t i o n  (36).  In the p r e s e n t  p i n n i n g of the c r a c k f r o n t might have been caused 63 particle-matrix interface.  Borom e t a l  g l a s s - c e r a m i c , the c r y s t a l l i n e phase has  case  by s t r e s s e s a t  the the  have shown t h a t i n t h e i r a h i g h e r thermal c o n t r a c t i o n  135  c o e f f i c i e n t than the p a r e n t g l a s s and  they concluded  that there existed 47  a hoop compressive  s t r e s s a t the i n t e r f a c e .  Frieman and Hench  have  shown t h a t the thermal c o n t r a c t i o n 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 g l a s s - c e r a m i c was  lower  than t h a t of the parent g l a s s .  According  to t h i s c o n d i t i o n the p a r t i c l e w i l l be i n a s t a t e of h y d r o s t a t i c compression and  the i n t e r f a c e w i l l a l s o e x p e r i e n c e a compressive  p r e s e n t experiments,  stress.  the c o m p o s i t i o n of the g l a s s used and  m i c r o s t r u c t u r e o b t a i n e d was  s i m i l a r t o t h a t used  Hence i t i s b e l i e v e d t h a t the p a r t i c l e  In the  the 47  i n Frieman s 1  (lithium d i s i l i c a t e )  work.  produced  s t r e s s e s t h a t impeded c r a c k p r o p a g a t i o n . In the p r e s e n t study i t was  found  t h a t the data agreed  with  52 Lange's  a n a l y s i s up t o = 50% c r y s t a l l i n e p h a s e . F i g u r e  r e l a t i o n s h i p between the f r a c t u r e s u r f a c e energy the i n t e r c r y s t a l l i n e path.  and  40 shows a  linear  the r e c i p r o c a l of  The  s l o p e of t h i s l i n e which corresponds t o -2 2 the l i n e energy a c c o r d i n g t o the t h e o r y , i s 1.924 x 10 J/m (19.24 e r g s / 2 52 cm ) . T h i s v a l u e i s w i t h i n the l i m i t s of the v a l u e s r e p o r t e d by Lange f o r a sodium b o r o - s i l i c a t e g l a s s and alumina of t h i s l i n e glass.  The  ( F i g . 40) corresponds i n t e r c e p t i s 4.1  2  t o the s u r f a c e energy  The  intercept  of the  annealed  T h i s v a l u e i s i n f a i r agreement w i t h 2 the e x p e r i m e n t a l l y o b t a i n e d v a l u e f o r the annealed g l a s s (6.7 J/m )  The  J/m  composite.  .  i n t e r a c t i o n between the c r a c k and  r e v e a l e d by f r a c t o g r a p h s .  In F i g u r e s 42(a)  the p a r t i c l e i s a l s o  to 4 2 ( c ) , a c h a r a c t e r i s t i c  f r a c t u r e step i s seen p e r p e n d i c u l a r to the p o s i t i o n of the g e n e r a l c r a c k  136  front.  These f r a c t u r e steps a r e due t o t h e bowing of t h e c r a c k f r o n t  between t h e 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 s . spherulites  i s v e r y s m a l l (2 t o 5 ym), t h e pinned  front finds i t easier and  S i n c e t h e s i z e o f these portion  t o pass between t h e s p h e r u l i t e s .  of the crack  When i t does t h i s  j o i n s w i t h the bowed c r a c k f r o n t , i t l e a v e s a f r a c t u r e d  the s i z e of s p h e r u l i t e pinned  portion  i s large  spherulites.  When  (the s p a c i n g between them i s s m a l l ) t h e  o f t h e c r a c k f r o n t f i n d s i t more d i f f i c u l t  between the s p h e r u l i t e .  step.  Hence t h i s c r a c k f r o n t breaks  t o push  through t h e  Thus t h e r e i s more t r a n s p a r t i c l e f r a c t u r e as t h e degree  of c r y s t a l l i n i t y  increases.  P a r t o f t h e i n c r e a s e i n f r a c t u r e energy i n g l a s s - c e r a m i c s a h i g h volume f r a c t i o n o f c r y s t a l l i n e phase i s due t o t h e random of t h e l i t h i u m d i s i l i c a t e c r y s t a l s .  L i t h i u m d i s i l i c a t e has an  containin  orientation  orthorhombic 37  c r y s t a l s t r u c t u r e w i t h a w e l l d e f i n e d c l e a v a g e a l o n g t h e (010) As e x p l a i n e d i n t h e b e g i n n i n g of t h i s Chapter, crystal.  I t consists  of f i b r i l s  an  planes.  (010)plane  encounters  Cracks  find i t easier  t h e c r a c k tends  t o propagate i n t h e f i b r i l s  i n propagating  r u p t u r e o t h e r h i g h index p l a n e s . along i n t e r - f i b r i l l a r paths.  having  But t h e c r a c k  i n the f i b r i l s having  planes normal t o t h e plane o f c r a c k p r o p a g a t i o n .  When  to propagate along t h  p a r a l l e l to the p l a n e o f c r a c k p r o p a g a t i o n .  more r e s i s t a n c e  i s not a s i n g l e  r a d i a t i n g out from a c e n t r a l n u c l e u s .  the c r a c k s i n t e r a c t w i t h t h e s p h e r u l i t e (010)  the s p h e r u l i t e  plane  cleavage  Hence t h e c r a c k tends to  A l t e r n a t i v e l y t h e c r a c k can a l s o  propagate  However, t h e c r a c k has t o r u p t u r e t h e c e n t r a l  137  c o r e from which the f i b r i l s  radiate.  would r e q u i r e a d d i t i o n a l energy.  Both the above mentioned  processes  Hence g l a s s - c e r a m i c s have h i g h e r  f r a c t u r e s u r f a c e energy than g l a s s because the f r a c t u r e path i s more t o r t u o u s and h i g h energy s u r f a c e s a r e exposed.  The  type of  d e s c r i b e d above i s shown i n F i g u r e s 4 2 ( f ) to 4 2 ( h ) . shown v e r y rough s u r f a c e s composed of mountain due  to the p u l l out of f i b r i l s  They a l s o show smooth f l a t  These f i g u r e s  and v a l l e y l i k e s t r u c t u r e s  from the c e n t r a l c o r e of the  s u r f a c e s which correspond  Cleavage steps a r e a l s o s e e n . ( F i g u r e 42(h)  fracture  area  spherulites.  to c l e a v a g e  A)  4.4  Static  4.4.1  Model f o r Slow Crack Growth i n C o r r o s i v e Environment  The  Fatigue  r a t e of c o r r o s i o n can be expressed  a t t a c k , normal to the s u r f a c e V  where  planes.  23  as the v e l o c i t y  2A Sinh  =  A exp -  exp  [  r  AF* —  h  ( -  AF  AF  =  Free energy of the c o r r o s i o n r e a c t i o n  AF*  =  A c t i v a t i o n energy  A  =  Constant  R  =  Gas  T  =  Temperature  °K  (V)  by  =  constant  (water)  )  i J  (39)  , v (40) / n  of  138  Hillig  and C h a r l e s  23  have shown t h a t the r e a c t i o n can be d e s c r i b e d by  the f o l l o w i n g e q u a t i o n . 2  AF  where  y  Surface free  =  p  =  =  AF  v V ' m T -  -  +  t;  cr V app m 2E "  (  4  1  )  energy  Radius of c u r v a t u r e of s u r f a c e c r a c k undergoing corrosion  V  m  a  app  E  =  Molar volume of the m a t e r i a l  =  Applied  =  Young's modulus of the m a t e r i a l  stress  23 The H i l l i g  and C h a r l e s  experimental  t h e o r y can be more r e a d i l y adapted to the  o b s e r v a t i o n s i f the f o l l o w i n g d e f i n i t i o n i s employed.  o  .  c °th where  o  ~  c  o" ^ = t  ty  =  S t r e s s a t the t i p of the s u r f a c e c r a c k T h e o r e t i c a l s t r e n g t h of the m a t e r i a l  54 Orowan  has shown t h a t o  where r  Q  t h  =  PET  <42)  i s the d i s t a n c e between two c l e a v i n g p l a n e s .  The s t r e s s a t the t i p of the c r a c k can be r e l a t e d to the a p p l i e d s t r e s s and the dimensions o f the c r a c k a  c  =  24  f o r an e l l i p t i c a l l y  2 a  app  V L/p  shaped c r a c k by  (43)  139  where L  =  Length  of t h e s u r f a c e c r a c k  Irwin"*"' has shown f o r an e l l i p t i c a l l y  CT  K, where K  =  Stress intensity  shaped c r a c k ,  / irL  (44)  app factor  S u b s t i t u t i n g e q u a t i o n (44) i n (43) 2 K_  (45)  TTp E x p r e s s i n g the c r i t i c a l  stress intensity factor K. IC  By u s i n g e q u a t i o n s ( 4 2 ) , ( 4 5 ) a n d  (K^^,) as (46)  (2 E ) Y  CT (46),  can be expressed as th  lc_ G  The  be s t r e s s - d e p e n d e n t a c t i v a t i o n energy  i>  /r-  th  a c t i v a t i o n energy  K,  . / r 7 1J_  2/2  /  p  K  (47)  i c  of a c h e m i c a l r e a c t i o n i s expected t o  and i n the p r e s e n t case AF* i s dependent on ty. The  can be expanded i n T a y l o r ' s s e r i e s as a f u n c t i o n of  by AF  AF,  _  1  +  ip=0 2 * 3 AF  2  Let  AF  i(j=0  =  AF  °  ,  a xp  2  t  ij; =  o  (48)  140  and  3AF —  has the same u n i t s as AF,  ty = 0  2ty  ty  n  and hence i t i s c a l l e d the  Decremental energy f a c t o r and can he w r i t t e n as 3AF  t  •bty ty = 0 S u b s t i t u t i n g equation  (47) , (48), (49) and  « p  ,  2  3 AF  .2 2  a  ty = 0  2V  K,  2  K. IC  / TT  (50)  )/RT]  3 AF,  _ ty^2  can be taken as z e r o .  ty = 0  Zty  Hence e q u a t i o n  V  =  (50) becomes  V  0  exp ( A  =  exp (-  K,  * 2 /~2~  V0  Y V Q  A ,*  *  2  4E  where V  +  0 A  V m  app  -•  [( - S g - i  (41) i n (40) and r e a r r a n g i n g  Y V -jjS  V  -  v  (49)  = - A  2 p  m ) =  K IC  c o r r o s i o n of u n s t r e s s e d m a t e r i a l at a  c r a c k w i t h r a d i u s of c u r v a t u r e p and V..  =  Taking  (51)  the n a t u r a l l o g a r i t h m of e q u a t i o n  InV  = lnV  0  +  1 * jfi [ A  (51)  /RT)  2 J~2  A exp  [-(  AF  P  -  RT  HAF  0  •)]  K, K  (52) IC  141  A c c o r d i n g to e q u a t i o n  J 3  The  (52)  -  M  "  W  ^  R T  v  ( A* —  "  / i t /  /  ^  p  )  l e f t hand s i d e of the e q u a t i o n (53) corresponds  p l o t of InV v e r s u s K /K  .  1 —  to  to the s l o p e of a  I f the c r a c k v e l o c i t y d a t a a r e 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 o b t a i n e d . l i n e s h o u l d correspond  (")  [ A  ^2 —  v2  /  /  /tt  r knowledge of s l o p e , R, T and a s s u m i n g — P  /  r —4P  The s l o p e of ].  this  With the  = 1, the v a l u e of A  *  can  be  calculated.  Eventhough e q u a t i o n  (51) i n many r e s p e c t s resembles  Hillig's  and C h a r l e s ' s e q u a t i o n f o r s t r e s s - c o r r o s i o n of the m a t e r i a l , t h e r e i s a subtle difference.  In the f i n a l form of H i l l i g ' s and C h a r l e s ' s e q u a t i o n  ( e q u a t i o n 13)  i t was  found  t h a t the a c t i v a t i o n volume (V ) i s s t r e s s -  independent.  T h i s o b s e r v a t i o n was  c r i t i c i z e d by Doremus  are no e x p e r i m e n t a l f a c t s to support t h i s i d e a .  30  because t h e r e  I t i s a l s o noted  that  the a c t i y a t i o n volume i n a chemical r e a c t i o n i s r a r e l y independent  of  30 pressure factor is  .  However i n the p r e s e n t a n a l y s i s the decremental  energy  (A*) can be c o n s i d e r e d constant s i n c e the v a r i a b l e \\> or  K^/K^  dimensionless. Equation  (51) has a l s o been used by Sines  time to f a i l u r e e x p r e s s i o n .  i n deriving  He p o i n t e d out t h a t the c r a c k growth d a t a  the  142  should be f i t t e d  t o an e q u a t i o n h a v i n g the form of e q u a t i o n  to be d i m e n s i o n a l l y c o r r e c t f o r a t i m e - t o - f a i l u r e  (51) i n o r d e r  equation.  A l l of the c r a c k v e l o c i t y d a t a f o r samples t e s t e d i n water were p l o t t e d as InV Vs K /K shown i n F i g u r e 50.  i n order t o t e s t the above model.  T h i s f i g u r e shows a s t r a i g h t l i n e f i t .  f i g u r e c r a c k v e l o c i t y d a t a of Wiederhorn  25  This i s  In the same  and W i l l i a m s et a l  19  f o r soda  -3/2 l i m e s i l i c a t e g l a s s were a l s o p l o t t e d .  (Here K  = 0.74  MN.m  is  19 taken  ).  As seen from F i g u r e 50 these two  w i t h the p r e s e n t s e t of d a t a .  The  l i n e s agree r e a s o n a b l y w e l l  s l o p e s of the l i n e s correspond  to the  p r e s e n t s e t of d a t a and  the l i n e s c o r r e s p o n d i n g t o s o d a - l i m e - s i l i c a t e  g l a s s are a p p r o x i m a t e l y  the same.  T h i s was  not s u r p r i s i n g s i n c e l i t h i u m  s i l i c a t e g l a s s and s o d a - l i m e - s i l i c a t e g l a s s a r e s i m i l a r . suggests  Hence i t  t h a t the mechanism o f s t r e s s - c o r r o s i o n i s a l s o s i m i l a r i n these  glasses. The v a l u e of the s l o p e of the l i n e i n F i g u r e 50 i s 21. S u b s t i t u t i n g t h i s value i n equation  (53) and assuming ——  = 1, a t 25°C  P  * the v a l u e of A  i s 7.5  a c t i v a t i o n energy  Kcal/mole.  Hence i n the p r e s e n t a n a l y s i s ,  f o r the s t r e s s - c o r r o s i o n of g l a s s and  i n water can be taken as  (AF  * Q  - 7.5  2 /2 — —  A a c t i v a t i o n energy  I —— IC  the  glass-ceramics  K  ), AF  Q  being  the  K  f o r the c h e m i c a l r e a c t i o n between g l a s s ,  glass-  ceramics ancj water i n the absence o f s t r e s s . I t was w e l l e s t a b l i s h e d 21 25 + by C h a r l e s and by Wiederhorn t h a t d i f f u s i o n of Na ions i s r e s p o n s i b l e  143  10"  0 =r ANNEALED  a = -is  + — -30 v — 50 © = -70  /  -SODA LIME G L A S S  24,25  +  -I-  .  /  '  10"  +•/  o  lxl  o °  /  cn  >  10'  O  o _l LU >  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 i n water at room temperature).  144  for  the c o r r o s i o n of s o d a - l i m e - s i l i c a t e g l a s s 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 g l a s s e s , i t can be assumed, t h a t a s i m i l a r mechanism i s r e s p o n s i b l e  f o r the c o r r o s i o n o f . l i t h i u m 45  d i s i l i c a t e g l a s s and. g l a s s - c e r a m i c s  i n water.  Mohyddin  has  shown  t h a t the a c t i v a t i o n energy f o r the l i t h i u m i o n 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 g l a s s i s 19 Kcal/mole.  Hence the a c t i v a t i o n energy f o r  s t r e s s - c o r r o s i o n o f l i t h i u m d i s i l i c a t e g l a s s and is  (19  -  12 K j / K j .  ) . • At  = 0.5  seen t h a t f o r a low v a l u e  K ^ , , t h i s i s 13 Kcal/mole.  limit  considered can be  as the  considered  static  fatigue limit.  as a t h r e s h o l d  d e c r e a s e s the a c t i v a t i o n energy f o r the  4.4.2  i n water  Thus i t i s  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 -  c o r r o s i o n i s almost e q u a l t o t h a t of c o r r o s i o n . can be  glass-ceramics  the  of K j V K ^ - q  These_low v a l u e s Hence the s t a t i c  fatigue  l i m i t o f K j / K - j - q above which K^. process.  Slow C r a c k Growth i n a N o n - C o r r o s i v e Environment  (Toluene)  53  I t has  been e s t a b l i s h e d by Wiederhorn  t h a t slow  crack  growth i n s o d a - l i m e - s i l i c a t e g l a s s i n vacuum i s congruent w i t h the from r e g i o n I I I on the V-K^  p l o t , Figure 8.  I n the p r e s e n t  the c r a c k v e l o c i t y d a t a from t e s t s i n t o l u e n e As  seen from F i g u r e s  to K  and  the s l o p e s  t e s t e d i n water.  32  to 37  the l o g V Vs  log  data  study, a l l  resembled t h a t o f r e g i o n I I I . p l o t s were v e r y  of t h e s e l i n e s were much h i g h e r  close  t h a n f o r specimens  145  Wiederhorn"'"' has a n a l y s e d %he c r a c k growth d a t a f o r d i f f e r e n t g l a s s e s i n vacuum and concluded  t h a t c r a c k growth i n t h e  absence of a c o r r o s i v e environment cannot be e x p l a i n e d by e i t h e r t h e a l k a l i i o n d i f f u s i o n theory or the v i s c o u s flow theory.  He  t h a t a t h e r m a l l y a c t i v a t e d c r a c k growth p r o c e s s proposed  by Thomson  and h i s co-workers  57  and e l a b o r a t e d by Lawn  58  suggested  can q u a l i t a t i v e l y  e x p l a i n t h e c r a c k p r o p a g a t i o n d a t a i n vacuum.  The Theory".  theory o f Thomson^  7  i s called  the " L a t t i c e  I t r e l a t e s crack t i p s t r u c t u r e to crack propagation  He has shown t h a t the d i s c r e t e n e s s of t h e atomic can t r a p a cleavage c r a c k i n a manner analogous 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 . mathematical  or molecular  Trapping rate. lattice  t o the t r a p p i n g of a  Using s e v e r a l s i m p l i f i e d  models, i t has been demonstrated t h a t 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 o f s t r e s s e s e x i s t s f o r c r a c k s t a b i l i t y . t h i s range the c r a c k i s " l a t t i c e t r a p p e d " . F i g u r e 51.  This i s i l l u s t r a t e d i n  I n s t e a d o f one p o s i t i o n o f c r a c k s t a b i l i t y as p r e d i c t e d by  the G r i f f i t h arrested.  Within  theory, s e v e r a l p o s i t i o n s e x i s t  However w i t h s u f f i c i e n t  a t which a c r a c k can be  thermal energy,  thermally activated  c r a c k growth can occur by movement o f t h e c r a c k from one p o i n t o f s t a b i l i t y to the next. forward  (AG^)  W i t h i n t h i s range t h e a c t i v a t i o n energy f o r  and backward  (AG^)  motions o f t h e c r a c k v a r y between a  maximum and zero..  Assuming a l i n e a r a p p r o x i m a t i o n  of a c t i v a t i o n  w i t h s t r a i n energy  r e l e a s e r a t e Tyson and h i s co-workers  59  energy  d e r i v e d an  FORCE ON CRACK UNSTABLE REGION CRACK HEALING |  STABLE REGION CRACK IS LATTICE TRAPPED  UNSTABLE REGION DYNAMIC FRACTURE  GRIFFITH LENGTH ure 51  CRACK LENCTH  G r a p h i c a l r e p r e s e n t a t i o n of the slow c r a c k growth regime r e s u l t i n g from l a t t i c e t r a p p i n g ( a f t e r Thomson-* ) 7  147  e q u a t i o n f o r the c r a c k v e l o c i t y .  InV where  V  0  =  =  lnV  -  0  [ AG  0  (1 - K ^ / K ^  )/RT]  (54)  Nav  N  = Number of s t r e t c h e d 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 R  = Gas  T  = Temperature °K  From e q u a t i o n and  The f i n a l form of t h e i r e q u a t i o n i s  f o r the bond r u p t u r e under zero  stress  constant  (54), a p l o t of InV Vs K^  2  should g i v e a s t r a i g h t l i n e AG the s l o p e of t h i s l i n e should corresponds t o ~ j — — • F i g u r e s 52(a) K RT 9  K  2  5 2 ( f ) a r e p l o t s of InV Vs tested i n toluene.  f o r the m a t e r i a l s used  i n t h i s study  and  E x p e r i m e n t a l p o i n t s show a good l i n e a r dependency  2 between InV and K^.. energy  From the s l o p e s of these p l o t s AG ,  f o r bond r u p t u r e under zero s t r e s s was  are l i s t e d  the  activation  c a l c u l a t e d and  the v a l u e s  0  i n T a b l e 14.  The v a l u e of AG  0  remained a p p r o x i m a t e l y  constant  up to a volume f r a c t i o n a t which 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 s began to o v e r l a p (> 50%). 125.5  The  c o r r e s p o n d i n g v a l u e of A G  KJ/mole (30 K c a l / m o l e ) .  i s c l p s e to  T h i s v a l u e i s lower than the v a l u e o b t a i n e d 53 59  f o r s o d a - l i m e - s i l i c a t e g l a s s t e s t e d i n vacuum agrees  D  '  .  However t h i s v a l u e  r e a s o n a b l y w i t h the bond s t r e n g t h of l i t h i u m o x i d e ^ .  s i n c e o n l y one  temperature  was  used  However,  i n the p r e s e n t study, i t i s not  p o s s i b l e to p l a c e much c o n f i d e n c e i n arguments  based  upon a c t i v a t i o n  148  F i g u r e 52  V e l o c i t y - s q u a r e of s t r e s s i n t e n s i t y f a c t o r diagram f o r ( t e s t e d i n t o l u e n e at room temperature) (a)  annealed  glass  F i g u r e 52(b)  G l a s s - c e r a m i c c o n t a i n i n g .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  F i g u r e 52(c)  T N  2  m  -3  G l a s s - c e r a m i c c o n t a i n i n g .30 + . 05 volume f r a c t i o n of c r y s t a l l i n e phase.  151  Figure  52(d)  G l a s s - c e r a m i c c o n t a i n i n g .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  F i g u r e 52(e)  G l a s s - c e r a m i c c o n t a i n i n g .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)  G l a s s - c e r a m i c c o n t a i n i n g .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  of  Volume F r a c t i o n C r y s t a l l i n e Phase  K ,  Slope  T C  N/m  3/2  0  3.8741 x 1 0 "  1 1  1.013 x 1 0  6  .15 ± .05  2.4145 x I O "  1 1  1.328 x 1 0  6  .30 ± .05  3.359 x I O "  .50 ± .05  1.0763 x I O "  .70 ± .05  .85 ± .05  1.55 x 1 0  6  1 1  2.02 x 1 0  6  6.9155 x 1 0 ~  1 2  2.98 x 1 0  6  9.9881 x 1 0 ~  1 2  3.53 x I O  6  1 1  AG , KJ7Mole (Kcal/Mole) 0  99.18 (23.69) 106.22 (25.37) 201.39 (48.1) 109.57 (26.17) 153.24 (36.60) 310.53 (74.17)  Ln 4>-  155  energies.  Crack v e l o c i t y s t u d i e s a t d i f f e r e n t  temperatures  i n vacuum  w i l l r e v e a l more about the mechanism of c r a c k growth i n n o n - c o r r o s i v e environments.  As seen from T a b l e 14, a g l a s s - c e r a m i c c o n t a i n i n g 90% of  c r y s t a l l i n e phase has a h i g h e r a c t i v a t i o n energy  (AG ).  i s i n r e a s o n a b l e agreement w i t h the v a l u e o b t a i n e d f o r 53 silicate  glass  This value  0  soda-lime-  59 '  .  Hence i n t h i s m a t e r i a l , i t appears  that crack  p r o p a g a t i o n i n t o l u e n e i s c o n t r o l l e d by the bond r u p t u r e of the S i - 0 bonds.  4.5  P r e d i c t i o n of L i f e  The  Expectancy  t i m e - t o - f a i l u r e of a b r i t t l e m a t e r i a l which undergoes  s t r e s s - c o r r o s i o n can be determined  by i n t e g 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 Ii IC n Here the V to  V  = V  followed,  = 0  exp  A K  r e l a t i o n i s assumed.  ( 6 K /K  one a r r i v e s a t 2 t  a. app - e  ) and  I f t h i s r e l a t i o n i s changed  the same procedure Ii  2  y  2  (B + 1) ]  2.  IC  of i n t e g r a t i o n i s K. Ii K. IC  +  1)  (55)  156  where a  =  Applied  y  =  Geometrical  t  =  Time to  app  Sines  stress factor  failure  a  has  shown t h a t e q u a t i o n (55) can be m o d i f i e d by u s i n g Ii the p l a c e of — — and the f i n a l e q u a t i o n i s IC K  in P  K  t  2  >. •a  app  - e"  where o  p  K  2-^y  P  The  life  V  (B +  i s a p r o o f s t r e s s and  a  2 r  - B ^ E £ [e a  3  0  -f^ , +  app (6 g  f r  n  p  >  1)  P  (56)  1)]  expectancy  g l a s s - c e r a m i c s under two  IC  a a  p  p  '  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 g l a s s and  a p p l i e d s t r e s s e s (10  5  N/m  2  and 10  6  N/m  2  ) and  five  a  d i f f e r e n t v a l u e s of  . —  (1.1, 1.5,  2, 3, A) a r e shown i n F i g u r e s  53(a)  a  app  to  53(e).  These p l o t s a r e v a l i d o n l y f o r specimens h a v i n g a f l a w s i z e  those used i n the r u p t u r e t e s t and water environment. it  i s c l e a r t h a t the l i f e  expectancy  From t h e s e  like  figures  i n c r e a s e s w i t h i n c r e a s i n g r a t i o of  a  p  —  .  I t i s a l s o seen t h a t 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 g l a s s a t a g i v e n s t r e s s .  he ' 2  i s v e r y c l e a r l y i n d i c a t e d by e q u a t i o n  This  behaviour  (56) where t i s d i r e c t l y p r o p o r t i o n a l  157  VOLUME  F i g u r e 53(a)  FRACTION  L i f e expectancy v e r s u s volume of c r y s t a l l i n e phase at a -£— a  app  fraction =  1.1  158  159  VOLUME F i g u r e 53(c)  FRACTION  L i f e expectancy v e r s u s volume f r a c t i o n c r y s t a l l i n e phase at a  app  ^  of  160  VOLUME  Figure 53(d)  FRACTION  L i f e expectancy v e r s u s volume of c r y s t a l l i n e phase a t a  a  app  fraction =  3  161  VOLUME  F i g u r e 53(e)  FRACTION  L i f e expectancy v e r s u s volume of c r y s t a l l i n e phase at a  fraction  162  5. SUMMARY AND CONCLUSIONS  1. of  The s t r e n g t h o f g l a s s - c e r a m i c s can be e x p l a i n e d i n terms  the f r a c t u r e s u r f a c e energy.  very l i t t l e  The i n c r e a s e i n e l a s t i c modulus has  e f f e c t i n s t r e n g t h e n i n g of g l a s s - c e r a m i c s c o n t a i n i n g 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 g l a s s and g l a s s - c e r a m i c s t e s t e d  i n water can be a n a l y s e d by a s t r e s s - c o r r o s i o n model based on the expression  V = V  0  exp ( A  — IC  ).  K  3.  The f r a c t u r e s u r f a c e energy o f g l a s s - c e r a m i c s tends t o 52  follow Langes  r  h y p o t h e s i s based on the p i n n i n g of the c r a c k f r o n t by  second phase p a r t i c l e s , up t o 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  s t r e s s i n t e n s i t y f a c t o r of glass-ceramics  i n c r e a s e s as the degree of c r y s t a l l i n i t y i n c r e a s e s . i n t e n s i t y f a c t o r of glass-ceramics having  The c r i t i c a l  .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 t h a t o f the annealed  5.  stress  glass.  Crack v e l o c i t y data o f g l a s s and g l a s s - c e r a m i c s t e s t e d i n  t o l u e n e can be e x p l a i n e d i n terms o f the  " l a t t i c e trapping"  model"' . 7  163  6. increases  The l i f e  expectancy  ( t i m e - t o - f a i l u r e ) of g l a s s - c e r a m i c s  as the degree o f c r y s t a l l i n i t y i n c r e a s e s  and t h i s  increase  i s m a i n l y due t o the c r i t i c a l s t r e s s 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 0 - 82.2 wt% 2  Si0  2  g l a s s a t 530°C was  found  to be 180 KJ/mole (43 K c a l / m o l e ) .  8.  The Young's Modulus o f g l a s s - c e r a m i c s tends t o f o l l o w  49 Hashin's  model of e l a s t i c b e h a v i o u r of a two phase m a t e r i a l , up t o  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 T o r s i o n Technique  The  double t o r s i o n method f o r measuring slow c r a c k growth i s  based on a technique  suggested by Outwater and  Jerry  20  and  further  19 developed by W i l l i a m s  and  which can be c o n s i d e r e d c r o s s - s e c t i o n , loaded having  Evans  as two  .  F i g u r e 14  t o r s i o n bars  to P/2.  shows a t y p i c a l  each having  specimen  a rectangular  For s m a l l d e f l e c t i o n s , y and  f o r bars  a w i d t h v e r y much l a r g e r than the t h i c k n e s s , the t o r s i o n a l  6 i s given  by 6 P/2  9 where P/2  -  • W  y/Vl  • W  a  — W t G T o t a l l o a d a p p l i e d to one  =  P/2  (Al)  3  =  m  -  bar  T o r s i o n a l moment  G  =  Shear modulus of the m a t e r i a l  a  =  Crack l e n g t h  t  =  Bar  W/2 W  m  = =  strain,  thickness  Bar  width  Moment  arm  I f c i s the e l a s t i c compliance, 3 W c = y/P  =  2  then on a  2 W t  rearranging  ( A 2 )  G  166  If the c r a c k p r o f i l e i s independent energy  release r a t e , ^  £ ^ where  P =  A t  =  ^  (  = Crack =  n  2  o f the c r a c k l e n g t h , the s t r a i n -  may be g i v e n by  , dc , d A )  P  2  2 r n  =  (  , dc . d A  , >  )  x  ( A 3  area  Web  t h i c k n e s s i n the p l a n e of t h e c r a c k ,  D i f f e r e n t i a t i n g equation  (A2) w i t h r e s p e c t to A and s u b s t i t u t i n g  into  e q u a t i o n (A3)  3P  s  =  2  2  W  3 2W t t  (A4)  G  n  S u b s t i t u t i n g the f o l l o w i n g p l a n e s t r a i n e q u a t i o n f o r energy  release  v  2G  =  Poisson's  Kj. =  ( A 5 )  ratio factor  (A4) reduces to  K  = 1  From e q u a t i o n  I  K  Stress-intensity  Then e q u a t i o n  W m  (  = W t t  -  3  n  )  -P  (A6)  (1 - v )  (A6) i t can be seen t h a t the s t r e s s i n t e n s i t y f a c t o r  a f u n c t i o n of the a p p l i e d l o a d , specimen dimensions and  the s t r a i n -  r a t e f o r c r a c k opening mode  6 where  ,  i t i s independent  of the c r a c k l e n g t h .  and e l a s t i c  (K^.) i s  constant  167  The  compliance  f o r the double  t o r s i o n specimen may  be  given  by y/P  =  (A7)  (Ba + D)  dc where  B  =  —  = Slope of the e x p e r i m e n t a l  compliance  - c r a c k l e n g t h curve. D  =  I n t e r c e p t of the e x p e r i m e n t a l  compliance  - crack length curve. ( A 7 ) w i t h r e s p e c t to time a t c o n s t a n t  D i f f e r e n t i a t i o n of e q u a t i o n  displace-  dy ment (  = 0 ) gives  .  v  (£.)._  (  »t±j>, - » , (  y Also at constant  ( A 8 )  y  displacement  P(Ba + D)  =  p i  where s u b s c r i p t s i and  (Ba  i  + D)  =  P (Ba f  f  (A9)  + D)  f r e f e r to the v a l u e s at the b e g i n n i n g and  end  of  relaxation. S u b s t i t u t i n g equation  V  where  V  I f B >> D,  -  (A9)  <<jf )' y  (A8)  i n equation  =  (a P  and r e a r r a n g i n g  +D/B) '  ( £ )  (A10) y  = V e l o c i t y of the c r a c k the  v  =  —•  i s n e g l i g i b l e and  - !±*f  ( a  ) . ( g )  hence  ( A 1 1 )  168  APPENDIX 2  An E s t i m a t e of T i m e - T o - F a i l u r e From Crack Growth K i n e t i c s  Under c o n s t a n t a p p l i e d s t r e s s a r  app  , of i n t e r e s t  i n a delayed  f r a c t u r e t e s t , the t i m e - t o - f a i l u r e , t i s g i v e n by 'Ic  t  /  =  f-  |  (A12)  C. 1  where C. x  =  Initial  flaw  size  C, Ic  =  C r i t i c a l Flaw s i z e  V  =  Crack  velocity  h The time f o r C > C  i s negligible.  T  Ic dC  S u b s t i t u t i n g equation  t  =  T  2K ~ 2 — • Y a app  dK  (A13) i n e q u a t i o n  =  a  Y  J  app  For a m a t e r i a l undergoing  f  x  (A12)  ^  .d  h  (A14)  Ii  s t r e s s - c o r r o s i o n , the c r a c k v e l o c i t y i n r e g i o n  can be w r i t t e n as V  (A13)  *  K  I and r e g i o n I I  S i n c e K_^ = Y a C IC app I c  =  A^Kj  36  11  (A15)  169  V  Substituting  equation  = A  2  (A15  (A16)  2  and  (A16) K  t  = Y a 2  2  A  app  ±l  2  K  /  '  f  j~  (A14)  T r  K  +  in  ( 1 T  "  dK  n )  1  1  Ii  K  dK  r  (A17)  x  *T1 where K I and  T  = stress  i n t e n s i t y f a c t o r at the  i n f l e c t i o n between r e g i o n  region II.  A t h i r d term c o r r e s p o n d i n g to r e g i o n I I I may generally i s often  negligible.  Depending on  negligible.  Hence e q u a t i o n  2  t  the  =  < ii ~ K  2  n  "  K  ic " > 2  (n-2)  A,  1  Y  a app  added but  environment, the  (A17)  i L  be  reduces  this is second term  to  n  (A18)  170 APPENDIX 3  1(5*  O - WATER 0 - 7 0 % RELATIVE HUMIDITY • - 30% " A - TOLUENE  UJ  O o  iio  lO  5  61  10  Figure A l  Velocity-stress for : (a)  intensity factor  Annealed g l a s s  a t room  diagrams  temperature  171  io-,  ,  ,  _ , _  t  A  1 I.  O  to  I  10 '  A  I A  I  A I A i A  J  J  I0  7 L  K  T  F i g u r e A l (b)  ,  _3/2  MN.m  G l a s s - c e r a m i c c o n t a i n i n g .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.  to  !—  3  O - WATER A -TOLUENE  /  /  o  »  O  o o'  A  /  J A  / >  I0 L  0°  5  10  o / o / o / o  / 10  1-2  K , t  F i g u r e A l (c)  1-4  MN.ml  G l a s s - c e r a m i c c o n t a i n i n g .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  o - WATER A - TOLUENE /A  /A 6  10  A / A A /  c7  10  1-3  1-5  1-7  i M N.m" 2  F i g u r e A l (d)  G l a s s - c e r a m i c c o n t a i n i n g .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.  1 9  10 o - WATER A - TOLUENE I <J  /  e c_>  o  t  I0 ' 6  P  6  _L 16  1-8  2 0  2 2  2 4  2 6  _3  M Nm F i g u r e A l (e)  2  G l a s s - c e r a m i c c o n t a i n i n g .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  A  -  T O L U E N E  /O /  °  /  OS /  /°  o  /  A A  /  A A A / A  'O  20  2-2 K  T  J  L  24  2-6  ,  MN.m  28  3 2  F i g u r e A l ( f ) G l a s s - c e r a m i c c o n t a i n i n g .85 ± .05 volume f r a c t i o n o f c r y s t a l l i n e phase at room temperature.  30  176  BIBLIOGRAPHY  1.  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