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Effect of environment on the fracture of brittle solids MacMillan, Robin Frederick George 1968

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THE EFFECT OF ENVIRONMENT ON THE ' FRACTURE OF BRITTLE SOLIDS by R. F. G. Mac MIL.'..AN B tSc. University of Natal, South A f r i c a B.Sc. (HONS) University of Natal, South A f r i c M.Sc. University of Natal, South A f r i c a A thesis submitted in p a r t i a l fulfilment of the requirements for the degree of D.OCTOR OF PHILOSOPHY in the Department of M i n e r a 1 Enginee r i rt g We accept t h i s thesis as conforming to the required standard THE UNIVERSITY. OF BRITISH COLUMBIA February, 195 8 In p r e s e n t i n g t h i s t h e s i s in p a r t i a l f u l f i l m e n t o f the r e q u i r e m e n t s f o r an advanced deg ree at the U n i v e r s i t y o f B r i t i s h C o l u m b i a , I a g ree t h a t the L i b r a r y s h a l l make i t f r e e l y a v a i l a b l e f o r r e f e r e n c e and s t u d y . I f u r t h e r ag ree t h a t p e r m i s s i o n f o r e x t e n s i v e c o p y i n g o f t h i s t h e s i s f o r s c h o l a r l y pu rpo se s may be g r a n t e d by the Head o f my Department o r by h i s r e p r e s e n  t a t i v e s . I t i s u n d e r s t o o d t h a t c o p y i n g o r p u b l i c a t i o n o f t h i s t h e s i s f o r f i n a n c i a l g a i n s h a l l not be a l l o w e d w i t h o u t my w r i t t e n p e r m i s s i o n . Depa r tment The U n i v e r s i t y o f B r i t i s h Co l umb i a Vancouve r 8, Canada Date 2o / ^ / -ABSTRACT The e f f e c t of s p e c i f i c active environment on the fracture strength of glass and polymethyl methacrylate was investigated using an i n d i r e c t t e n s i l e t e s t i n g technique. The strength of glass was not affected by exposure to dry gaseous and CO^i At low water vapour coverages, (<l/3 monolayer), the te n s i l e strength of glass was reduced by approximately 50%. Further increase i n water vapour pressure did not weaken the s o l i d to a much greater extent. The existence of surface microcracks governs the absolute t e n s i l e fracture strength, and any process which varies the flaw geometry acts to vary t h e t e n s i l e fracture strength. Soaking in the l i q u i d has the same e f f e c t as adsorption from the vapour phase near saturation. A l l vapour adsorbates caused a weakening, the magnitude of the decrease increasing with increasing a b i l i t y of the adsorbate to screen the surface Si cores. Moisture was the most active environ ment encountered. Polymethyl methacrylate did not weaken i n the vapour phase despite multilayer adsorption, but stressing i n i i . w e t t i n g l i q u i d s d i d c a u s e d r a s t i c f a i l u r e , w i t h a 5 7% de c r e a s e i n t e n s i l e s t r e n g t h . N o n - w e t t i n g l i q u i d s do n o t a f f e c t t h e s t r e n g t h o f t h e a c r y l J . c p l a s t i c s . F r a c t u r e e x p e r i m e n t s on a q u a r t z i t i c r o c k i n aqueous s o l u t i o n s o f • s u r f a c t a n t , ( q u a r t e n a r y ammonium s a l t s ) , show t h a t t h e w e a k e n i n g due t o s u r f a c t a n t a d s o r p t i o n i s n e g l i g i b l e , s i n c e w a t e r i t s e l f c a u s e s t h e maximum s t r e n g t h r e d u c t i o n , . The a d s o r p t i o n o f s u r f a c t a n t i s o n l y a s e c o n d a r y e f f e c t . A mechanism has been p r o p o s e d f o r t h e s t r e s s - e n v i r o n m e n t a l f a i l u r e o f b r i t t l e s o l i d s . T h i s mechanism r e c o g n i z e s t h e e x i s t e n c e o f m i c r o - c r a c k s , r e g a r d s t h e s t a b l e c r a c k p r o p a g a t i o n s t a g e o f t h e f r a c t u r e p r o c e s s t o be e n  v i r o n m e n t s e n s i t i v e , and i n v o l v e s t h e s t r a i n - a c t i v a t e d a d  s o r p t i o n r e s u l t i n g i n a d e c r e a s e i n c o h e s i o n a t t h e f l a w apex. The m a g n i t u d e o f t h e 'weakening i s c r i t i c a l l y d e p e n d e n t on t h e n a t u r e o f t h e b o n d i n g i n t h e s o l i d s u r f a c e . A l i t e r a t u r e r e v i e w o f s t r e s s - s o r p t i o n c r a c k i n g , w i t h an e m p h a s i s on n o n - m e t a l l i c s y s t e m s , i s i n c l u d e d . J. Leja, Professor, Supervisor. ACKNOWLEDGEMENTS / The guidance and friendship of my research supervisor, Dr. J. Leja, throughout the course of t h i s study are g r a t e f u l l y acknowledged. I wish to thank the various members of the Department of Mineral Engineering and rny colleagues for many he l p f u l discussions. The construction of the vacuum c e l l by Mr. P. Sunderland i s greatly appreciated, as i s the typing of t h i s thesis by Mrs. C. Guarnaschelli. A special vote of thanks to my wife Lynne, for her patience and support over the years leading to t h i s d i s s e r t a t i o n . The following scholarships are g r a t e f u l l y acknowledged, Giant Yellowknife Mines Limited . (1965-66) Shell Canada Scholarship for Research (1966-6 7) National Research Council Studentship (1967-68). TABLE OF CONTENTS Page ABSTRACT i ACKNOWLEDGEMENTS i i i LIST OF FIGURES. i v LIST OF TABLES . . . . . . . . v i i CHAPTER I INTRODUCTION 1 1:1 General -. 1 1:2 Statement of the Problem . . . . . 1 1:3 The Approach and Scope of the Problem. . . . . . 3 1:4 H i s t o r i c a l Review. . 5 CHAPTER 2 EXPERIMENTAL 13 2 :1 Materials. 13 2:2 Specimen Preparation 15 2 :3 Fracture Measuring Technique . . . 17 2:'} Preliminary Experiments 23 • 2 : 5 Fracture Apparatus 24 2 :6 Experimental Procedure 33 2 : 7 The Adsorption Apparatus 36 2 :3 Adsorption Procedure 39 CHAPTER 3 THE THEORY OF BRITTLE FRACTURE 41 3:1 The Properties of the Solid. . . . 41 (a) Glass . . . . . . . . . . . . 41 Page ' (b) P l a s t i c s 49 3:2 B r i t t l e Fracture 55 (a) G r i f f i t h 58 (b) Poncelet . 67 CHAPTER 4 ADSORPTION. 77 4:1 Introduction . . . . . . . . . . . 77 4:2 Definitions . 78 4:3 Surface Tension, Surface Free Energy Concept 78 4:4 Surface Stress, Surface Tension Concept. . 79 4:5 The' Effect of Adsorption 33 CHAPTER 5 RESULTS AMD DISCUSSION 8 7 5:1 Interpretation of Results, . . . . 87 5:2- Vycor Glass ^ 90 5:3 Fracture Isotherms on Kimble Glass. 114 5:4 Polymethyl Methacrylate 118 ' 5:5 The Effe c t of Immersion 124 5:6 The Spreading or Wetting Effect.' . 130 5:7 Quar t z i t i c Rock Specimen 140 5:8 Fractography 141 • -5,:9 Environmental Stress Cracking Mechanism 147 5:10 A Proposed Mechanism for Stress Sorption Cracking of B r i t t l e Solids ' 151 Page CHAPTER 6 SUMMARY AND CONCLUSIONS. . . . . . . . . " . 1 5 5 BIBLIOGRAPHY 1 6 8 APPENDICES • . 1 7 5 A Description of Apparatus Components... . 1 7 5 B Calibration of Load C e l l 1 7 7 C B.E.T. Calibrations. . . . 1 7 9 D B.E.T. Isotherm.Calculations 1 8 5 E Tensile Fracture Strength Calculations . 1 9 3 iv. LIST OF FIGURES Figure _ ' Page 1 Activation of Vycor Glass ' 16 2 The B r a z i l i a n Test 20 3 Tensile Fracture across C y l i n d r i c a l Specimens 22 4 High Vacuum Pumping System. . . . . . . . . . . 26 5 High Vacuum Fracture Apparatus. . . 3 0 6 High Vacuum Ce l l . . 31 7 Specimen in Fracture Position . . . . . . . . . . 34 8 Containers f o r Fracture in the Liquid Phase . . 34 9 The Adsorption Apparatus . -38 10 The Sample Vessels 3 8 11 Schematic Picture of the Fracture of S i l i c a 44 12 The Structure of Polymethyl Methacrylate. . . . 44 13 Crazing of Polymethyl Methacrylate . 5 2 14 E f f e c t of Temperature on the Stress-Strain Curve of Polymethyl Methacrylate 54 '15(a) Crack Velocity Related to Crack Length Ratio . 6 5 (b) Maximum Crack Velocity versus Stress 65 16 The Morse Curve . . 68 17 P r i n c i p a l Bond Diagram . 6 8 18(a) Cycle r e l a t i n g Surface Tension and Surface Stress ' . ' 80 V. LIST OF FIGURES (Continued) Figure Page 18(b) Model of the Silanol Surface 89 19 Adsorption Isotherm on Vycor Glass CN and CO2) 92 2 0 Adsorption Isotherms on Vycor Glass (Water Vapour and n-Butylamine 93. 21 Adsorption Isotherms on Vycor Glass (Acetone and Benzene) . 94 22 B.E.T. Linear Plots ... : ....... . 96 23 Vads versus log P/Po 100 24 Change in Surface Tension with Increase in Vapour Pressure (Water Vapour and n-Butyl amine) 101 25 Change in Surface Tension with Increase in Vapour Pressure (Acetone and Benzene).'. 102 26 Predicted Shape of Fracture Isotherms from Surface Tension Changes 103 2 7 Tensile Fracture Strength versus Relative Pressure for Vycor Glass (Water Vapour and n-Rutylamine) 106 2 8 Tensile Fracture Strength versus Relative Pressure for Vycor Glass (Acetone and Benzene) . . . 108 29 Volume Changes of Vycor Glass with Adsorption 112 30(a) Enthalpy Changes in Surface Formation, Adsorption and Compound Formation '84 (b)- Surface Tension Changes on Adsorption 85 31 Fatigue Curve for Polymethyl Methacrylate. . . 121 32 Tensile Fracture Strength versus Relative Pressure (Water Vapour and n-Butylamine). . 115 ' 33 Tensile Fracture.Strength versus Relative Pressure (Acetone and Benzene) . 116 v i . LIST OF FIGURES (Continued) Figure Page 34 Electron Micrograph of Vycor Glass . . . . . . . . 125 35 Effect of Soaking Time on Tensile Fracture Strength 126 36 Tensile Fracture Strength versus Surface Tension of the Wetting Liquid 135 " 37(a) Model for I n t e r f a c i a l Attractions . . 133 (b) Tensile Fracture Strength versus I n t e r f a c i a l A t t r a c t i v e Forces . . . . . . . . 139 38(a) Fracture Surface of Glass in Water Vapour. . . . 142 (b) Fracture Surface of Glass in Vacuo 14 2 3 9 Fracture Surface of. Polymethyl Methacrylate in A i r , . , 14.3 4 0 Electron Micrograph of the Mirror Region . . . . 143 41 Electron Micrograph of the Fine Hackle Region . . . . . . . . 144 . 42 Electron Micrograph of the Coarse Hackle Region , 14 4 4 3 Model of the Ionic Rigid S o l i d 14 9 44„ Model of the Covalent Semi~3rittle Solid . . . . 149 4 5 Morse Curve for Ionic Soli d , , 15 3 4 6 Morse Curve for Covalent Soli d 159 47 Load C e l l Calibration. . . 178 •48 Adsorption Apparatus C a l i b r a t i o n . 183 v i i o LIST OF TABLES Table Page 1 Bending Test versus B r a z i l i a n Test 25 2 S t a t i s t i c a l Analysis 89 3 E f f e c t of Strain Rate on Tensile Fracture Strength on Kimble Glass 8 9 4 S h i f t s in Frequency of Surface OH groups on Porous Glass 95 5 Equilibrium Adsorption Rates on Vycor Glass 98 . 6 Relative Vapour Pressures at Monolayer Volumes . . . . . . . 97 7 The E f f e c t of Dry N~ and C0? on the Tensile Fracture Strength of Vycor Glass. . . . . . 105 8 The E f f e c t of Adsorption from Aqueous Solution 117 9 The E f f e c t of Vapour Environment on the Tensile Strength of Polymethyl. Methacrylate. . 119 1.0 The E f f e c t of Immersion on.the. Tensile .Strength of Polymethyl Methacrylate . . . . 120 11 The E f f e c t s of A l k a l i Solutions. 129 12 ' The E f f e c t of Strain Rate on the Fracture of Polymethyl Methacrylate 129 13 The Ef f e c t of Paraffin O i l on the Tensile Strength of Kimble Glass 136 14 Polar I n t e r f a c i a l Interactions at Solid/Liquid Interfaces . . . . . . . . . . 133 15 The Effect of Environment on Tensile Strength of Rock • •'. • '•• -141 16 Bulb Cali b r a t i o n 180 v i i i . LIST OF TABLES (Continued) Table Page 17 Volume Calibrations . 182 18 Adsorption Isotherm Data on Vycor Glass . . . . 187 19 B.E.T. Linear Plots 188 20 Monolayer Volumes from B.E.T. Linear Plots. . . 188 21 Surface Energy Plots 192 2 2 Surface Tension Reductions on Adsorption. . . . 194 2 3 Fracture Isotherms 194 1. CHAPTER ONE INTRODUCTION 1:1 General The use of an active chemical environment to promote cracking would be extremely b e n e f i c i a l i n any a p p l i  cation where the fracture of a s o l i d i s required (e.g. crush ing and grinding). Much e f f o r t has been expended i n devising methods to prevent stress accelerated f a i l u r e , p a r t i c u l a r l y i n m e t a l l i c systems, but l i t t l e thought has been applied to i t s constructive use. Recent aspects of lunar d r i l l i n g ^ 1 ^ have led to the r e a l i z a t i o n that stress environmental cracking i s being subconsciously applied i n most fracture operations, although l i t t l e i s known of the mechanism. 1 :^ Statement of the Problem Stress environmental cracking i s a study of funda- i mental, as well as p r a c t i c a l i n t e r e s t , since i t involves a unique interplay of surface chemistry, electrochemistry and s o l i d state. The phenomenon may be defined as a process whereby f a i l u r e of a s o l i d occurs as a resu l t of an accelerat ed mechano-chemical reaction in a stressed region, in an active environment. Failure occurs at a strength l e v e l well below that which would be experienced in the absence of the environment. None of the investigations of stress cracking occurring in both met a l l i c and non-metallic systems, have led to a theory o r mechanism which adequately explains the peculiar s e l e c t i v i t y of the solid/environment system. Non- m e t a l l i c systems, in p a r t i c u l a r , have received very l i t t l e (2) attention. As early as 1864, Dupre' conceived that the fracture strength of s o l i d s might be related to the energy of the newly formed surfaces. Many theories have been forth coming involving the reduction of surface free energy r e s u l t ing from s p e c i f i c adsorption, thereby leading to a strength (3) reduction of the s o l i d ; e s p e c i a l l y since G r i f f i t h rephrased the Dupre' concept and formulated i t . However, deviat ions ^ 4 ^ 5 ^ ^  ^ are more the rule than the exception, de monstrating the need for a more complete mechanistic t r e a t  ment. Therefore, the purpose of t h i s d i s s e r t a t i o n is . to investigate possible stress-environmental cracking systems on non-metallic b r i t t l e materials, with a view to explaining the action of the environment and the s e l e c t i v i t y of the solid/environment system. 1: 3 -he„.,.Sc^pe ^ aJ2d Appr^oac"h o f t h e S t u d y The i n v e s t i g a t i o n was c a r r i e d o u t on f o u r b r i t t l e m a t e r i a l s . S i l i c a i s i d e a l l y s u i t e d f o r s t u d y i n g t h e c h e m i s t r y o f s u r f a c e s due t o i t s i s o t r o p i c n a t u r e and h i g h c h e m i c a l r e a c t i v i t y , t h e r e f o r e two i n o r g a n i c g l a s s e s were s e l e c t e d . F i r s t l y , a h i g h l y p o r o u s V y c o r g l a s s f o r a d  s o r p t i o n and f r a c t u r e s t u d i e s and, s e c o n d l y , a b o r o s i l i c a t e g l a s s t o c o u n t e r e f f e c t s w h i c h m i g h t r e s u l t f r o m t h e p o r o u s n a t u r e o f t h e V y c o r g l a s s . By way o f c o m p a r i s o n , a b r i t t l e a c r y l i c p l a s t i c was c h o s e n , b e c a u s e t h e f r a c t u r e p a t t e r n a t room t e m p e r a t u r e a p p e a r s s i m i l a r t o g l a s s . The c o v a l e n t b o n d i n g o f t h e p l a s t i c and i t s low e n e r g y s u r f a c e , m i g h t . b e e x p e c t e d t o y i e l d v a s t l y d i f f e r i n g e n v i r o n m e n t a l e f f e c t s f r o m t h e i o n i c s i l i c a s , . E x p e r i m e n t s on a q u a r t z i t i c r o c k were d e s i g n e d t o s o r t o u t some o f t h e c o n f u s i o n o c c u r r i n g i n r e p o r t e d e f f e c t s i n t h e l i t e r a t u r e , w h i l s t a l s o b r i e f l y c o n s i d e r i n g t h e p o s s i b i l i t i e s o f a p r a c t i c a l a p p l i c a t i o n . The u t i l i z a t i o n o f t e n s i l e s t r e s s e s i s n o t t o a r t i  f i c i a l l y r e s t r i c t t h e p r o b l e m , b u t a r i s e s f r o m t h e f a c t t h a t s t r e s s a c c e l e r a t e d f a i l u r e o n l y o c c u r s i n t e n s i o n . The i n d i r e c t t e n s i l e t e s t a f f o r d s a r a p i d c o m p a r a t i v e method f o r m e a s u r i n g t e n s i l e f r a c t u r e s t r e n g t h . The p r o j e c t h a s b een c o n d u c t e d i n f o u r p h a s e s , as f o l l o w s : CD H i s t o r i c a l r e v i e w o f t h e p r o b l e m (2) P r e l i m i -n a r y e x p l o r a t i o n o f t h e c r a c k i n g t e c h n i q u e s . (3) C o n t r o l l e d e x p e r i m e n t a t i o n . (4) T h e o r e t i c a l e v a l u a t i o n and t h e p o s t u - l a t i o n o f a f r a c t u r e mechanism. E x p e r i m e n t a l l y the. i n v e s t i g a t i o n i s c o m p r i s e d o f two main s e c t i o n s . (1) A d s o r p t i o n S t u d i e s The d e t e r m i n a t i o n o f a d s o r p t i o n i s o t h e r m s l e d t o c a l c u l a t e d s u r f a c e f r e e e n e r g y c h a n g e s and s u r f a c e c o v e r a g e v a l u e s . (2) F r a c t u r e S t u d i e s (a) F r a c t u r e o f t h e s o l i d s i n c o n t r o l l e d v a p o u r and l i q u i d e n v i r o n m e n t . (b) E x a m i n a t i o n o f t h e f r a c t u r e s u r f a c e s by o p t i c a l m i c r o s c o p y and t r a n s m i s s i o n e l e c t r o n m i c r o s c o p y u s i n g a r e p l i c a t e c h n i q u e , The r e s u l t s o f t h e s e e x p e r i m e n t s , t o g e t h e r w i t h t h e v a r i o u s a c c e p t e d f r a c t u r e t h e o r i e s , were u s e d t o i n t e r p r e t t h e f r a c t u r e mechanism i n t h e v a r i o u s s y s t e m s . I n p a r t i c u l a r , a mechanism b a s e d on t h e b o n d i n g o f t h e s o l i d s u r f a c e i s s u g g e s t e d as an e x p l a n a t i o n f o r t h e s t r e s s e n v i r o n m e n t a l c r a c k i n g i n b r i t t l e m a t e r i a l s . 5. 1: 4 Ms^orj.cal Review ( 7 ) Preliminary investigations by Rehbinder et a l in 1944, showed that the addition of small amounts of surface active agents to the surrounding l i q u i d medium, re s u l t i n g i n adsorption on the s o l i d surfaces, i s capable of reducing the resistance of the s o l i d to stress. This phenomenon termed the "Rehbinder E f f e c t " may be used to f a c i l i t a t e the boring of hard rocks, disintegration of solids i n m i l l i n g , and in abrasion. Rehbinder added e l e c t r o l y t e s , (,01-.1%), to the f l u s h i n g water for rotary d r i l l s and found an increase in d r i l l i n g speed of as much as 20-60%. - "The mechanism.is associated with the penetration of the surface active species into the strained s o l i d along the surface of the microcracks, which develop in the course of deformation. Due to the reciprocating nature of the b i t the stress imparted to the s o l i d i s periodic. When the stress ceases to act, the 'embryo-microcracks' tend to heal. The cohesive forces are however, bound to the adsorbed layer, coating the surfaces of the minute cracks and the crack i s prevented from 'healing'"^ 7). These investigations on the change in mechanical properties of a material, which accompanies the adsorption of surface active agent, opened the door to a very obscure and controversial f i e l d . In 194 9 Von Szantho v ' published the f i r s t detailed investigation on the e f f e c t of additives in wet grinding. His r e s u l t s showed that the addition of a f l o t a t i o n c o l l e c t o r considerably lowered the amount of energy required for grind-ing of quartz. Using cement bricks in a dry grinding c i r c u i t Gotte and Z i e g l e r v showed an increase of 20-100%, in grind ing capacity ( i . e . reduction i n energy), when non-polar sur face active gases and vapours were admitted to the system. W. von Engelhardt^ 1 0^ (1943) found that certain polar l i q u i d s had a softening e f f e c t on quartz being ground with a widia tipped wheel. He showed that small additions of surface active agents such as f a t t y acids, produce higher hardness values f o r quartz, but with increased concentrations the hardness f e l l appreciably. An 80% sulphite lye increases the amount of quartz ground in standard time by it-3 per cent, as compared to values in water. Engelhardt's r e s u l t s i n d i  cated that certain organic l i q u i d s such as hexane and benzol increased quartz hardnessj whilst others such as acetic a c i d , pentanols and cetyl alcohol had a softening e f f e c t . It appeared that non-polar l i q u i d s produced an increase in hardness, whilst polar/non-polar l i q u i d s reduced the hardness, the e f f e c t increasing with molecular chain length. Moorthy and Tooley^ 1 1^ determined the e f f e c t s of cert a i n organic l i q u i d s on the strength properties of glass. In a l l cases, except nitrobenzene, breaking strengths were higher under the organics than in water, ranging from a 36% to 19% increase for alcohols to values of 90% for heptane, benzene and toluene. The strength of a l l specimens was lower in water than in a i r . 7. In Japan a th e o r e t i c a l treatment of the ef f e c t of (12) environment was carried out by M. Sato . He developed an equation f o r the surface tension of a s o l i d Yg> Ys = -Y^Af/f) where y^= Surface Tension of the wetting l i q u i d f = Breaking Stress in the dry state Af = Change in f due to adsorption. His experiments showed that the t e n s i l e strength decreases in a bending test with the presence of wetting l i q u i d , regardless of the type of material. The decrease was dependent on y^. The greater the w e t t a b i l i t y (the difference between y s and y^), the lower the decrease in strength, i . e . a l i n e a r r elationship exists between Af/f and y^. Frangiskos and Smith* 1 3*, (1957), studied the action of e l e c t r o l y t e s , NaCl and N^COg, and surface active agents such as s i l i c o n e s , on quartz, using a laboratory stamp m i l l to duplicate the reciprocating nature of a percussion d r i l l . In a l l cases the e f f i c i e n c y of the grind, i n the presence of the additive, increased. The e f f i c i e n c y i s 'measured by the surface area of the product as measured by a i r permeability t e s t s . The ef f e c t was concentration de pendent, (14) An attempt was made by Ghosh, Harris and Jowett , at Leeds University in 1960 , to repeat the work of Frangiskos and. Smith. The r e s u l t s , based on the new surface area pro-duced, showed that whenever an additive i s used,there i s an o v e r a l l increase in the surface area on grinding. (15) In 1963 Hammond and Ra'itz , measuring the fracture strength of fused s i l i c a rods found the decrease in the fracture strength and the corresponding decrease in'the surface free energy to be consistent with the G r i f f i t h theory of b r i t t l e fracture. The fracture strength decreases as the environmental vapours become more polar. (1 6 ) A patent by Siebel and Zeisel claimed the use of various additives in grinding and gave some figures for the grinding of a s i l i c e o u s lead-zinc ore in a laboratory rod m i l l . For a feed size of 0-7 mm the grinding e f f i c i e n c y was reported as the percentage material greater than a given size from 1 mm to .1 mm, for various grinding times. Calgon was one of the additives used, the improvement in the fineness of the grind being generally of the order of 30% at concen trations of .01-.04%. (17) In 1954 A l b e r t i was granted a patent on the use of dispersing agents as additives in grinding but no numerical results were l i s t e d . (18) Gilbert and Hughes experimented on the use of additives f o r improving the e f f i c i e n c y of wet grinding, I n i t i a l l y , t e sts on the grinding of quartz in a three-inch diameter ring b a l l m i ll.using a s i l i c o n e , showed no substantial improvement in the grinding performance. However f o r quart- z i t e a l e s s e r quantity of fines was produced. 9. Using a f i v e - i n c h diameter b a l l m i l l at two m i l l speeds and a s i l i c o n e additive, very s l i g h t improvements i n the grind were experienced, but these were well below those quoted by previous workers using s i m i l a r additives i n a stamp m i l l . On using a cat ionic wetting agent at varying concen trat i o n s and pH's, s l i g h t decreases in the grinding e f f i c i e n c y resulted. Addition of e l e c t r o l y t e s , sodium carbonate, sodium s i l i c a t e and sodium hexametaphosphate in a six-inch diameter rod -mill gave negative r e s u l t s . Only the l a t t e r had any e f f e c t on the fineness of the grind, producing a coarser product. The authors conclude that in conventional rod and b a l l m i l l s , the use of inorganic additives r e s u l t s only in a decrease in grinding e f f i c i e n c y , or has no e f f e c t at a l l . A number of references have been made as to the i n  fluence of moisture on the compressive strength of rocks, showing i n general that as the moisture content increases, the compression strength decreases. _ . ( 1 9 ) , O I L i J . , . . , ( 2 0 ) . . • _ Price ' and,•Colback. and Wild , i n a series of tests on rocks,. conclude that the reduction in strength from the "dry" to the saturated condition i s dependent on the re duction of the surface free energy of the specimen by the presence of a surface active l i q u i d . The l a t t e r also show a l i n e a r decrease of the strength with the surface tension (12) of the immersing l i q u i d , as calculated by M. Sato In a study on the causes"of rock deterioration ( 2 1 ) . Dr. T.R. Dunn at the Rensselaer Polytechnic I n s t i t u t e , 10. c o n c l u d e d t h a t breakdown o f t h e r o c k c o u l d be c a u s e d by " o r d e r i n g " o f p o l a r m o l e c u l e s In. a d s o r p t i o n s u r f a c e s , i n a warming and c o o l i n g e n v i r o n m e n t . U s i n g t h e method o f H e r v z f o r t h e cone f r a c t u r e o f (22) g l a s s , R o e s l e r * has shown .that t h e p r e s e n c e o f c h e m i c a l e n v i r o n m e n t a t t h e c r a c k t i p c a u s e d c r a c k p r o p a g a t i o n a t v e r y much s m a l l e r l e v e l s o f l o a d , t h a n i n a i r . (2 3) R e h b i n d e r and Aslanova r e p o r t t h a t i n t h e p r e s e n c e o f w a t e r v a p o u r , o r o f s u r f a c e a c t i v e s p e c i e s a d s o r b e d f r o m aqueous s o l u t i o n s , g l a s s f i b r e s show an e l a s t i c e f f e c t , w h i c h i n c r e a s e s as t h e s t r e s s a p p r o a c h e s t h e r u p t u r e s t r e s s . C h e m i c a l e t c h i n g o f t h e s u r f a c e l a y e r t o remove s u r f a c e f i s s u r e s i n c r e a s e d t h e f i b e r s t r e n g t h . A s i m i l a r e f f e c t , c a l l e d l i q u o s t r i c t i o n has been r e p o r t e d by B e n e d i c k s \ t h e phenomenon b e i n g t h e e x p a n s i o n (25) o f s o l i d due t o a d s o r p t i o n . B e n e d i c k s and Harden i n a p a p e r on t h e " w e t t i n g e f f e c t " , ( t h e change i n t h e s o l i d t e n s i l e s t r e n g t h r e s u l t i n g f r o m t h e w e t t i n g l i q u i d ) , showed b o t h p o s i t i v e and n e g a t i v e e f f e c t s i . e . w e a k e n i n g and s t r e n g t h e n i n g o f t h e s o l i d . ' G l a s s w e t t e d w i t h H 20 gave a d e c r e a s e o f a b o u t 4-0% • whereas t a r o i l gave an i n c r e a s e o f 30% f o r t h e same m a t e r i a l . They c o n c l u d e t h a t t h e e f f e c t i s a f u n c t i o n o f t h e l i q u i d s u r f a c e t e n s i o n , t h e m a g n i t u d e o f t h e e f f e c t b e i n g v e r y d i f f e r e n t f o r d i f f e r e n t s o l i d s . F o r i n c r e a s i n g s o l i d s h a r d n e s s , t h e r e l a t i v e d e c r e a s e i n t h e t e n s i l e s t r e n g t h d i m i n i s h e s . (122 ) In m e t a l l i c systems N.J. Petch has explained the fracture of steels containing.hydrogen by the surface d i f f u s i o n of hydrogen to the crack apex where i t adsorbs, reducing surface energy of metal atoms subject to a t e n s i l e force. Uhlig coined the phrase "stress-sorption cracking" (12 3) to apply to t h i s f a i l u r e mechanism . It was proposed that selective adsorption along the crack walls lowers the surface free energy, operating conjointly with e l e c t r o  chemical action along paths where defects predominate and where compositional gradients e x i s t . The cracking of mild (124) s t e e l i n b o i l i n g n i t r a t e solutions was discussed i n terms of the stress-sorption mechanism by adsorption of OH and NO ions along cracking paths, 'under tensional stresses. A series of experiments on the swelling of compacts of chalk, kaolin and coal , enhance the idea that ad sorption causes a reduction i n strength only i f accompanied by appreciable swelling, but not otherwise. A p a r t i c u l a r (26) coal showed marked swelling on adsorption of vapours of benzene, acetone and methanol, but only s l i g h t swelling in water vapour. The strength was correspondingly reduced in the organic solvents but not i n water, whilst the reduction in surface free energy as calculated by the Gibbs equation was appreciable in a l l three cases. . (28) . Flood and his collaborators in a thermodynamic treatment, have presented an expression which correlates the e l a s t i c p r o p e r t i e s and the a d s o r p t i o n p r o p e r t i e s . T h e i r t h e o r e t i c a l treatment allows the r e p r o d u c t i o n o f experimental volume changes due to a d s o r p t i o n to be made w i t h reasonable accuracy. Conclus ion There i s ample evidence o f a s t r e n g t h reducing, mechanism o f n o n - m e t a l l i c m a t e r i a l s i n a v a r i e t y o f e n v i r o n  ments. However, no s a t i s f a c t o r y e x p l a n a t i o n s have been g i v e n f o r the e f f e c t s , w h i l s t the t h e o r i e s o f b r i t t l e f r a c t u r e f a i l to e x p l a i n the s e l e c t i v i t y o f the phenomenon. There i s a l s o a great d e a l o f c o n t r o v e r s i a l data a r i s i n g from experiments on s i l i c i o u s m a t e r i a l , as to the d i r e c t i o n and magnitude o f . t h e . e f f e c t . A development, o f the t h e o r e t i c a l foundations i n v o l v e d i n a f r a c t u r e system may serve to e l u c i d a t e the problem. 13 CHAPTER TWO EXPERIMENTAL 2:1 Materials ( i ) Vycor Glass The Vycor glass was supplied by Corning Glass in the form of cylinders of height .5 inches and diameter .5 inches. Designated Corning No. 7930, t h i s glass approximates fused s i l i c a in many of i t s properties. It i s prepared by a process in which the r e l a t i v e l y high f l u x i n g oxide i s melted and formed to the desired shape, but somewhat oversize The fluxes are then removed by acid leaching. The leached material i s then f i r e d at high temperatures to consolidate the remaining porous s i l i c a structure,which causes i t to shrink to i t s f i n a l s i z e . Composition of Vycor No. 7 93 0 Si02 96% B 20 2 ' 3% Na20 0.4% A1 20 3 + Zr0 2 1% ( i i ) Kimble Glass Specimens of the b o r o s i l i c a t e glass were prepared from a .5 inch diameter glass rod by cutting on a diamond saw. The ends were then polished on a grinding wheel using carbo rundum paste. Although cutting and polishing do influence the t e n s i l e fracture strength, specimens prepared i n t h i s manner showed les s scatter i n strength values than the Vycor glass. Composition of Kimble Glass S i 0 2 75% B 20 3 10% Na20 7% A 1 2 ° 3 5 % BaO 2% CaO 1% ( i i i ) Polymethyl Methacrylate The p l a s t i c was obtained in the form of .5 inch diameter caste rods. Specimens were prepared by machining on a lathe. (iv) Chemicals A l l gases were p u r i f i e d by passing through a drying t r a i n consisting of s i l i c a g e l , ascarite (CC>2 removal), a heated copper f o i l i n a glass tube for oxygen removal, and anhydrous calcium sulphate, ( D r i e r i t e ) ; The water was double — 6 d i s t i l l e d with an equivalent conductance of 0.9x10" mhos. Technical grade mercury was used i n a l l manometers and cut-off valves. The organic solvents were reagent grade. Solvents were double d i s t i l l e d in an a l l glass s t i l l , the head and 15. t a i l f r a c t i o n s being rejected. Further drying was effected by storage over a suitable drying agent. To eliminate the E^O contamination of the hygroscopic solvents, adsorption was carried out by evaporating the solvent from the frozen l i q u i d . (v) Rock Specimens Any rock specimens were used in the "as i s " condition. To eliminate the moisture and grease contaminants the specimens were washed with carbon t e t r a c h l o r i d e , then methanol, oven dried at 60°C and stored in a dessicator. 2•^ Specimen^ Preparation (i) Vycor Glass Activation of the Vycor specimens was achieved by careful drying. The glass was oven dried at 60°C f o r one hour to prevent breakage from thermal shock. The specimens were then baked in a vacuum of 8x10 mm Hg i n the s p e c i a l l y designed vacuum c e l l , Fig. 6, for a period of H8 hours at approximately 100°C. The i n i t i a l pump-down must be extremely slow, since rapid evaporation of the water causes cracking due to thermal changes. Fig. 1 shows the e f f e c t of baking temperature on the absorptive capacity at a given vapour pressure. Thus for devices to be used at room temperature, 180°C i s the most ef fec t i v e a c t i v a t i n g temperature. _ Due to the size of the c e l l a temperature of only 100°C could be obtained with external heating. Wafer Pressure =0.1 n Temperature - 24°C 200 Activation Temperature ( ° C ) (a) Effect of Activation Temperature on Adsorptive Capacity at room tempera ture and a water , vapour pre ssure of 0,1 mm (b) Weight Loss vs. Time at an Activation Temperature of 180°C FIGURE 1. ACTIVATION OF VYCOR GLASS (Corning Glass Works, Corning N.Y.) 1 7 . ( i i ) Other Specimens Specimens of b o r o s i l i c a t e glass and rock were -7 evacuated at 8x10 mm Hg for 4 8 hours at 100°C p r i o r to the experiment, whilst with polymethyl methacrylate no external heating was used due to changes i n physical properties at low temperatures. ^ :^ Fracture Measuring Techniques A variety of techniques have been employed in the study of fracture of b r i t t l e s o l i d s . Impact tests on a notched bar u t i l i z e the conventional Charpy and Izod testing machines. In both systems the specimen i s struck by a swing ing pendulum and the energy required to cause fracture i s measured by the loss in energy of the pendulum/^*. Most comminution studies determine g r i n d a b i l i t y by measuring the surface area produced in a p a r t i c u l a r grinding test. The energy input to the m i l l i s then compared to the- surface area produced* 1 3*. Other techniques'^* involve free crushing conditions, y i e l d i n g a s i m i l a r r e s u l t of load versus p a r t i c l e size d i s t r i b u t i o n produced; or the propagating of + v + +. ( 3 0 ) e x i s t i n g cracks or notches in cleavage tests (31) (32) Compression tests on rocks , glass and more ( 3 3 ) generally concrete have been carried out to y i e l d compres sive •strength, but since environmental e f f e c t s occur only in tension t h i s type of test was not applicable. Tensile tests as applied to metals are frequently u t i l i z e d , but the problem of manufacturing specimens from b r i t t l e non-metallic materials precludes t h i s simple technique. Experiments have been attempted by p u l l i n g machined specimens, but specimen variations,, e s p e c i a l l y surface v a r i a t i o n s , make the results suspect. Fracture v e l o c i t i e s may be measured with u l t r a - (34 ) (35 ) sonic techniques or by high speed-photography . Roesler applied the technique of Hertz f o r controlled crack propa gation experiments. The technique involves the use of a c y l i n d r i c a l indenter to which a load i s applied. The spheric a l crack propagates in a conical fashion so that the crack area i s increasing continuously. Thus the crack w i l l stop propagating u n t i l the load i s increased further. The technique affords a useful means of studying environmental e f f e c t s since the chemical can be applied at the indenter t i p . However, for opaque sol i d s the method i s l i m i t e d . (38) Bending tests have been applied by many workers and prove to be simple and e a s i l y adaptable to vacuum systems. With glass specimens however the scatter i s f a i r l y high (+_ 29%) making results d i f f i c u l t to analyse. The B r a z i l i a n Test (37) As early as 1883, Hertz proposed a theory for the state of stress developed when a cylinder i s compressed across i t s diameter. The t h e o r e t i c a l basis has been dealt with by Timoshenko^ 3 8\ F r o c h t ^ 3 9 ^ and others. A B r a z i l i a n , .19. C a n i e r o * 4 0 * , proposed a method whereby the t e n s i l e strength of c y l i n d r i c a l specimens could oe determined. During recent years the method, which i s both rapid and simple, has been used to e s t a b l i s h a comparative t e n s i l e strength f o r rocks. Theory The B r a z i l i a n test i s based upon the state of stress developed when a c y l i n d r i c a l specimen i s compressed di a m e t r i c a l l y between platens as i l l u s t r a t e d in Fig. 2. Assuming plane stress and considering the disk, with concentrated load i n the diameter the following three general equations can be used to express the stress conditions at a l l points within the disk, x 2P ITt 2P l i t (R-y) 3 + (R+y) D J xy 2P (R-y) 2x _ (R+y) 2x where x 2+(R-y) 2 x 2+(R+y) 2 Of primary interest i s the maximum t e n s i l e stress 20. 1 X 1 FIGURE 2. THE BRAZILIAN TEST w h i c h o c c u r s n o r m a l t o t h e l o a d e d d i a m e t e r AB. T h i s , i n g e n e r a l , has a c o n s t a n t m a g n i t u d e . 1 TTDt where, ( Oj, = Maximum t e n s i l e s t r e s s P = A p p l i e d l o a d D = Specimen d i a m e t e r R = • D/2 . t = Specimen t h i c k n e s s I n a d d i t i o n t o t h i s t e n s i l e s t r e s s w i t h p o i n t l o a d i n g , c o m p r e s s i v e s t r e s s a c t s a l o n g t h e l o a d e d d i a m e t e r f r o m a minimum o f _JLIL a t t h e c e n t r e , t o an i n f i n i t e l y h i g h irDt v a l u e i m m e d i a t e l y u n d e r t h e l o a d i n g p o i n t s . I n p r a c t i c e i t i s r e q u i r e d t h a t f r a c t u r e be i n i t i  a t e d ' by t h e s e e v e n l y d i s t r i b u t e d t e n s i l e s t r e s s e s i f t h e t e s t i s t o y i e l d u s e f u l r e s u l t s . •Hence t h e h i g h c o m p r e s s i v e s t r e s s a t t h e l o a d i n g p o i n t s s h o u l d be d i s s i p a t e d . I t has been shown ^ t r"^'^" ^  t h a t t h e maximum s t r e s s a v n e a r t h e e n d s can be r e d u c e d by d i s t r i  b u t i n g t h e l o a d w i t h p a d s . However t h i s p a d d i n g w i l l change t h e a x f r o m t e n s i o n t o c o m p r e s s i o n i n t h e v i c i n i t y o f t h e p a d d i n g . I t can be shown t h a t t h e s t r e s s d i s t r i b u t i o n n e a r t h e c e n t r e i s u n a f f e c t e d by t h e s t r e s s r e d i s t r i b u t i o n due t o t h e pads. FIGURE 3 TENSILE FRACTURE OF CYLINDRICAL SPECIMENS (a) Vycor Glass (b) Kimble Glass (c) Polymethyl Methacrylate. 23. It has also been shown*43) that the t e n s i l e strength of a specimen decreases s l i g h t l y with an increasing t/D r a t i o . The selection of the B r a z i l i a n test for t h i s re search project resulted from the fact that corrosion cracking occurs in tension and the above test o f f e r s a simple, rapid method of obtaining r e s u l t s . Since comparative re s u l t s are desired for the t e n s i l e strength under varying environmental conditions, a fixed t/D r a t i o of 1 was selected and padding was not employed. Figs. 3a, b, and c, i l l u s t r a t e the t e n s i l e fracture occurring on the three types of specimens. In a l l cases the crack propagates • along the specimen diameter in. the di r e c t i o n of the maximum compressive force, i . e . at right angles to the maximum t e n s i l e l o a d . 2:4 Pre 1 imi n ar y. Ex peri men t s (a) Hydraulic Loading Tests C y l i n d r i c a l cor'e samples of rock with a height/ diameter r a t i o of 1 were compressed diametrically using an hydraulic jack and.press. Loading to f a i l u r e was applied at as constant a rate as possible. With the specimens immersed in a variety of aqueous solutions and organic solvents no pos i t i v e r e s u l t s were obtained in indicating sorption weaken ing systems. Two factors became apparent however. F i r s t l y , the need for an accurately controlled loading device. Secondly the ef f e c t s of surfactant environment would be a 24. function of the state of the o r i g i n a l surface. Clean, uncon- taminated, reproducible surfaces are e s s e n t i a l , (b) T r i p l e - p o i n t Bending Tests A series of t r i p l e point bending tests, were carried out on b o r o s i l i c a t e glass rods in a i r to give a d i r e c t com parison with the B r a z i l i a n t e s t . Table 1 shows that the B r a z i l i a n test gives r e s u l t s with very much l e s s scatter than the bending t e s t . (A coef f i c i e n t of v a r i a t i o n of 15.6% as opposed to 2 8.7% for the bend ing test.) This could be due to the effects of flaw geometry. In the bending test the tension i s over a smaller area and hence more c r i t i c a l l y affected by d i f f e r i n g flaw size. The s t a t i s t i c a l d i s t r i b u t i o n of the flaws over the smaller area also accounts f o r the r a t i o o f the t e n s i l e strength to be greater f o r the bending te s t than for the B r a z i l i a n test,by a f a c t o r of 1,8, 2:5 Fracture Apparatus The experimental apparatus consisted of the follow ing major components. (a) Constant Strain rate loading device. (b) Vacuum pumping system. (c) Load c e l l and s t r a i n indicator. (d) Vacuum c e l l , (e) Gas t r a i n . TABLE 1 Bending Test versus B r a z i l i a n Test Tensile Strength Rod Diam. No. in Test P.S.I. Coeff. of Variance Bending Test .5" 12 ' 10,315.4 28.7% B r a z i l i a n Test .5" 12 5,730.8 15.6% Ratio of Tensile Strengths.SSSl = 1 > 8 Braz A B C D E F • Rotary Vacuum Pump • Oil Diffusion Pump • Liquid Cold Trap • Vacuum Cell • Roughing Line - Bypass Line - Hot Filament Ion Gauge & G^  - Thermocouple Gauge - Foreline Valve - Roughing Value - Bypass Valve - Gate Valve & V6 - Cell Ports FIGURE 4. HIGH VACUUM PUMPING SYSTEM on (a) The Press Since t e n s i l e strength i s a function of s t r a i n rate i t i s e s s e n t i a l that the s t r a i n rate be known. For compara t i v e results employing a variety of chemical environments i t i s also necessary to use a reproducible constant s t r a i n rate for each series of t e s t s , A Wykeham Farrance Compression Testing Machine, Model T.57, with a load capacity of 5 tons, was selected for these experiments. The machine has a motorised feed and a gear box, which eliminates any hydraulic system. The gear box has six 5-1 reductions and additional change wheels, givi n g a t o t a l of t h i r t y d i f f e r e n t rates of feed, ranging from 0.3 inches/minute down to 0.000024 inches/minute. The ram has a 4 inch distance of travel and i s driven by a 1 H.P. e l e c t r i c motor. Manual adjustment of the i ram i s possible in both the coarse and fine ranges p r i o r to a c t i v a t i n g the motor. A reversible switch allows loading and unloading of the specimen at constant s t r a i n rate. (b) Vacuum System A schematic diagram of the vacuum system i s shown in Fig. 4. Details of the components are given in Appendix A. The pumping system consists of a forepump A, a f o r e l i n e valve V-^ , a 6 inch o i l d i f f u s i o n pump B, and a l i q u i d nitrogen trap C, coupled d i r e c t l y to the vacuum c e l l D.. The c e l l may be isolated from the d i f f u s i o n pump by the b u t t e r f l y valve V^, A roughing l i n e E v i a valve V 2 allows the c e l l to be "roughed out" p r i o r to opening the b u t t e r f l y valve to the. high vacuum l i n e . A separate by-pass l i n e F i s provided, to enable the low vacuum chamber to be maintained at roughing l i n e pressures during a run. A hot filament i o n i z a t i o n gauge G, i s used to measure high vacua (> 10~ 4 mm Hg), whilst thermocouple gauges at G 2 and G 3 give low vacuum readings. Valve V^ allows the vessel to be flushed with N 2, whilst also supplying an i n l e t port for the introduction of vapours. A mercury manometer, with one leg evacuated, allows vapour pressure differences within the c e l l to be measured through valve Vg. A separate pump i s used for lowering the mercury in the manometer. (c) Vacuum C e l l A schematic diagram of the high vacuum c e l l i s shown i n Fig. 6. Due to the lengthy pump-down times with ad- sorbants of high surface area, and the s t a t i s t i c a l nature of the experiment, the c e l l was designed to enable a sequence of twelve specimens to be fractured in ei t h e r high vacuum, or a controlled atmosphere. The specimens are mounted on sta i n l e s s steel buttons and held in place by l i g h t tension.clips (Fig. 7). A rotating specimen table holds twelve buttons -and can be turned, by 2 ° . means of handle H through a t r i p l e 0-ring seal. To avoid leakage around a piston moving in a r e c i  procating manner into the c e l l , a Bellofram r o l l i n g diaphragm was inserted. A s p l i t piston allowed the high vacuum chamber to be separated from a low vacuum chamber by the diaphragm. -3 The low vacuum chamber (10 mms Hg.), on the underside of the diaphragm, served a double purpose. F i r s t l y i t eliminat ed leakage into the high vacuum chamber and secondly i t re duced the pressure d i f f e r e n t i a l across the diaphragm. A device of t h i s nature proved successful in maintaining a -7 vacuum down to 8x10 mm, Hg., whilst allowing a piston motion of approximately 1 inch. Many e x i s t i n g problems in high vacuum experiments could be eliminated by t h i s technique since extremely careful machining i s not required. Details of the diaphragm are given in Appendix A. Unfortunately, as a result of the fracture experi ments, fine glass chips caused the diaphragm to tear between the piston and cylinder walls. Repeated attempts to prevent th i s tearing proved^unsuccessful and the design was abandoned. A s p l i t piston push rod was substituted, operating through a t r i p l e 0-ring seal. Due to the slow operation of the push rod, (.03 inches/min), no leakage occurred. The lew vacuum chamber was s t i l l incorporated to reduce possible leakage and to act as a v e r t i c a l guide for 1 the piston. The c e l l was constructed of heavy brass tubing of twelve inches diameter with 1/4 inch brass end plates.' A six FIGURE 5. HIGH VACUUM FRACTURE APPARATUS. 31. Ionization Guage Fixed Gas Inlet Valve Manometer FIGURE 6. HIGH VACUUM CELL 32. inch window allowed visual observation of the fracture procedure. The upper fixed a n v i l , specimen buttons and the piston were made of one inch s t a i n l e s s steel rod. A six inch diameter manifold provided connection to the high vacuum gate valve. The hot filament i o n i z a t i o n gauge was mounted on a one inch port on top of the c e l l by s i l v e r soldering the Kovar seal to the connecting flange. The piston was coupled to the ram of the constant s t r a i n rate machine by two l i g h t springs to counteract the e f f e c t of atmospheric pressure forcing the piston Into the c e l l . Vacuum Seals A l l elastomer seals used In the apparatus were standard 0-rings of buna-rubber or neoprene. Brass to brass connections were made by soft soldering the pickled components (d) Load Measurements A l l applied leads were measured using a stra i n gauge Indicator and load c e l l . The load c e l l u t i l i z e s the p r i n c i p l e that the e l e c t r i c a l resistance of very thin wires varies with.change i n length (strain) as imposed by an applied load. The read out measures the changes in resistance in terms of microstrain i. e . micro inches per inch. Details of the components and t h e i r c a l i b r a t i o n are given in Appendix A and B. 33. ^ :6 E x p e r i m e n t a l P r o c e d u r e The s p e c i m e n s were p r e p a r e d as p r e v i o u s l y d e s c r i b  ed. To a v o i d c o n t a m i n a t i o n when l o a d i n g t h e c e l l , s p e c i m e n s and b u t t o n s were h a n d l e d w i t h r u b b e r g l o v e s o r a d s o r b e n t t i s s u e . The c e l l was r o u g h e d o u t t o b a c k i n g pump p r e s s u r e s by o p e n i n g v a l v e V ? , t h e n f l u s h e d w i t h d r y n i t r o g e n . D u r i n g l o a d i n g a p o s i t i v e p r e s s u r e o f n i t r o g e n ' w a s m a i n t a i n e d i n t h e c e l l t o p r e v e n t a d s o r p t i o n o f m o i s t u r e on t h e s p e c i m e n s and w a l l s o f t h e s y s t e m . L o a d i n g o f t h e c e l l was most e a s i l y a c c o m p l i s h e d w i t h t h e c e l l f u l l y a s s e m b l e d and l o a d i n g t h r o u g h t h e 6 i n c h window p o r t . ^ . W i t h t h e window i n p o s i t i o n t h e c e l l was pumped down t o -2 0 m i c r o n s Hg t h r o u g h t h e r o u g h i n g l i n e E . The c e l l was t h e n f l u s h e d o nce w i t h d r y n i t r o g e n , by o p e n i n g v a l v e V^. The pump down p r o c e s s was r e p e a t e d t o 2 0u Hg, when t h e b u t t e r f l y v a l v e t o t h e h i g h vacuum l i n e was o p e n e d , a f t e r c l o s i n g and o p e n i n g b a c k i n g v a l v e . The e x t e r n a l h e a t  i n g c o i l s were a c t i v a t e d and t h e s y s t e m a l l o w e d t o pump f o r -7 4 8 h o u r s , r e s u l t i n g i n a vacuum o f t h e o r d e r o f 8x10 mm Hg. The p i s t o n was r a i s e d m a n u a l l y u n t i l a r e a d i n g r e g i s t e r e d on t h e s t r a i n i n d i c a t o r . W i t h t h e c l u t c h o f t h e c o n s t a n t s t r a i n r a t e machine e n g a g e d , t h e l o a d was a p p l i e d u n t i l f r a c t u r e o c c u r r e d . The t e n s i l e f r a c t u r e s t r e n g t h c o u l d be c a l c u l a t e d f r o m t h e o b s e r v e d s t r a i n r e a d i n g r e c o r d e d on FIGURE 7. SPECIMEN IN FRACTURE POSITION. FIGURE 3 . CONTAINERS FOR FRACTURE IN LIQUID PHASE. the s t r a i n i n d i c a t o r at f a i l u r e . (a) Adsorption from the vapour phase For vapour phase adsorption experiments the ad- sorbate was placed i n a vessel and subjected to vacuum through valve V^, before the c e l l was loaded. After pumping for a short while to remove entrained gases from the l i q u i d ad- sorbates, the l i q u i d was frozen i n a l i q u i d nitrogen dewar. The vessel and l i n e were pumped down during the evacuation of the specimens by opening valve with the adsorbate i n the frozen condition. The vapour could be introduced into the vessel by removing the dewar and warming with the heat of the hand. After the appropriate dosage, valve was closed. (b) Adsorption from sol u t i o n ; or experiments in the l i q u i d phase. ( i ) Treatment p r i o r to introduction to the c e l l . Specimens were evacuated as before. The c e l l was then f i l l e d with dry nitrogen and the specimens removed from the c e l l and placed in the test solution as quickly as possible. Fracture experiments were then c a r r i e d out i n a i r by removing the specimens one at a time from the solutions and f r a c t u r i n g in the c e l l . ( i i ) Liquid treatment within the c e l l . Small polythene cups were placed around each button. . Fig. 8. After specimen vacuum treatment as in previous runs, the cups were f i l l e d with solution whilst a positive nitrogen . 36 . p r e s s u r e was m a i n t a i n e d w i t h i n t h e c e l l . The s o l u t i o n :-;as a d m i t t e d t h r o u g h t h e window p o r t f r o m a p o l y t h e n e c o n t a i n e r v i a a l e n g t h o f p o l y t h e n e t u b i n g . F r a c t u r e e x p e r i m e n t s c o . i l d t h e n be c a r r i e d o u t w i t h t h e s p e c i m e n s immersed. 2 : 7 The A d s o r p t i o n A p p a r a t u s An a l l - g l a s s B.E.T. p r e s s u r e - v o l u m e a d s o r p t i o n a p p a r a t u s was c o n s t r u c t e d f o r t h e p u r p o s e o f d e t e r m i n i n g t h e a d s o r p t i o n p r o p e r t i e s . The u s e o f a h i g h s u r f a c e a r e a s o l i d ( V y c o r g l a s s ) , and g a s e s and v a p o u r s o f s u f f i c i e n t l y h i g h s a t u r a t e d v a p o u r p r e s s u r e s ( P o ) , a t t h e t e m p e r a t u r e o f t h e e x p e r i m e n t , make a method o f t h i s t y p e q u i t e s a t i s f a c t o r y . The d e t a i l s o f t h e a p p a r a t u s a r e shown i n F i g . 9. The main f e a t u r e s a r e , (a) Vacuum System The pumping s y s t e m c o n s i s t s o f two p a r t s : ( i ) H i g h vacuum w h i c h i s m a i n t a i n e d by a m e c h a n i c a l pump i n s e r i e s w i t h a s i x - i n c h o i l d i f f u s i o n pump. ( i i ) Low vacuum l i n e , m a i n t a i n e d by a m e c h a n i c a l pump. T h i s l i n e i s u s e d t o l o w e r t h e l e v e l s o f t h e m e r c u r y i n t h e gas b u r e t t e s and m e r c u r y c u t - o f f v a l v e s . (b) Vacuum M e a s u r i n g D e v i c e H i g h vacuum measurements a r e made on a h o t f i l a m e n t i o n i z a t i o n gauge i n t h e main m a n i f o l d . C h e c k i n g o f vacuum a t roughing pressure was c a r r i e d out using thermocouple gauges. (c) Gas Reservoirs Four 3 - l i t r e reservoirs made up the gas storage l i n e . One bulb was kept f u l l of He for c a l i b r a t i o n purposes. A l l gases were passed through a p u r i f i c a t i o n t r a i n before being admitted to the reservoir. To eliminate leakage the gases were stored at pressures close to atmospheric pressure. (d) Gas Burettes and Manometers The gas burettes are a series of bulbs connected by lengths of c a p i l l a r y tubing. Etch marks are made between the bulbs, whose volumes are calibrated p r i o r ' t o mounting in the apparatus. The size of the in d i v i d u a l bulbs i s of no consequence» but a large number of combination volumes are useful for a complete adsorption isotherm. Mercury cut-off manometers are used whenever possible to eliminate stop-cock grease. To maintain a constant internal volume the mercury in the manometers could be adjusted to fixed reference points a f t e r each gas dose and again before each pressure reading. (e) Sample Vessels To avoid lengthy pump down times before each de termination, three sample vessels were used (Fig. 10). These could be isola t e d during an adsorption run. FIGURE 9. THE ADSORPTION APPARATUS FIGURE 10. THE SAMPLE VESSELS 3 9 . (f) Furnace A two inch diameter tube furnace was used to outgas the specimens at an elevated temperature of 18 0°C. (g) Thermostating System The gas burettes were thermostated by c i r c u l a t i n g water from a constant temperature bath through the water jackets i n s e r i e s . A temperature drop of .5° was experienced across the l i n e . (h) Pressure Measurements - Pressure differences were read on a 50 cms cathe- tometer using a vernier scale to three decimal places,, i n cms. 2:8 Adsorption Procedure A precleaned weighed sample i s evacuated in a sample vessel. A known volume of vapour i s then admitted to the sample vessel and the volume not adsorbed i s determined from the pressure readings. Knowing the saturated vapour pressure of the vapour at the experimental temperature, allows the adsorption isotherm to be plotted according to the B.E.T. equation i n the form, P _ _1__ + C-l , _P V(Po-P) VmC VmC X Po P = Corresponding pressure Po = Sat. Vap. Pressure Vm = Monolayer Vol. C = Const, which i s a function of the heats of adsorption. P By p l o t t i n g — — — - as a function of P/Po a straight l i n e of V(Po-P) C - l 1 . . slope — and intercept i s obtained. VmC VmC The B.E.T. isotherm holds over the pressure range .05 < P'/p© < .35. Deviations from l i n e a r i t y are usually found outside t h i s range. The parameters of interest from a determination of t h i s type would be, (1) The volume of gas adsorbed at any equilibrium pressure P. (2) The monolayer volume (Vm), being the volume of ad- sorbate to form a mono-molecular layer over the surface.of adsorbent. (3) The surface area (S) obtained by converting Vm to the corresponding number of molecules and multiply in'g by the cross-sectional area. CHAPTER THREE THE THEORY OF BRITTLE FRACTURE ^ : 1 Th^ J?j?operties^of^the Solid (a) Glass The g l a s s - l i k e or vitreous state i s believed to be that of a s o l i d with, the molecular disorder of a l i q u i d frozen into i t s structure. Random Network Theory Glass appears to have many of the features of a normal s o l i d , v i z . , strength, hardness, e l a s t i c i t y etc., but further examination shows i t to have an extended melting range, whilst x-ray s t r u c t u r a l analysis indicates a molecular structure' akin to that of a l i q u i d at low temperatures. Zachariason, (1932 ) \ proposed that the atomic or molecular arrangement i n the glass l i k e state i s an ex tended network which lacks symmetry and p e r i o d i c i t y . He l a i d down a number of simple rul-es r e l a t i n g the way in which oxygen anions and the cations must l i n k together for an oxide to exist in the glassy state. B r i e f l y , the glass forming + + + 4 + 4.^ .4. + + + + cations ~(B , P , Si ) are surrounded by polyhedra o f o x y g e n i o n s i n t h e f o r m o f t e t r a h e d r a . The o x y g e n i o n s a r e o f two t y p e s v i z . , b r i d g i n g i o n s , e a c h o f w h i c h l i n k two p o l y h e d r a and non b r i d g i n g o x y g e n i o n s e a c h o f w h i c h b e l o n g to. o n l y one p o l y h e d r o n . Such a s y s t e m w o u l d p r o d u c e a p o l y  mer s t r u c t u r e w i t h l o n g c h a i n s c r o s s - l i n k e d a t i n t e r v a l s . In t h e s t r u c t u r e would be r e g i o n s o f u n b a l a n c e d n e g a t i v e c h a r g e where t h e o x y g e n i o n s a r e n o n - b r i d g i n g . C a t i o n s o f low p o s i t i v e c h a r g e and l a r g e s i z e ( N a + , K + , C a + + ) may e x i s t i n h o l e s i n t h e n e t w o r k , where t h e y compensate t h e e x c e s s n e g a t i v e c h a r g e . O x i d e s f o r m i n g t h e b a s i s o f t h e g l a s s a r e known a s n e t w o r k f o r m e r s and t h o s e s o l u b l e i n t h e n e t w o r k as n e t w o r k m o d i f i e r s . (45) In 194 7 Sun a d v a n c e d a t h e o r y t h a t g l a s s e s a r e o n l y f o r m e d from, t h o s e o x i d e s i n w h i c h t h e bond s t r e n g t h between t h e o x y g e n and t h e c a t i o n r e a c h e s a c e r t a i n minimum v a l u e . O x i d e s l o w e r i n g t h e bond s t r e n g t h may a c t as n e t  work m o d i f i e r s , o r i n t e r m e d i a t e s , but n o t as n e t w o r k f o r m e r s . The bond s t r e n g t h M + - 0~ o f a l l g l a s s f o r m e r s i s g r e a t e r t h a 80 K c a l s p e r A v o g a d r o number o f b o n d s , w h i l s t t h a t o f t h e m o d i f i e r s below 60 K c a l s . The c l a s s i f i c a t i o n i s a r b i t r a r y . U s i n g x - r a y a n a l y s i s Warren ^ has c o n f i r m e d t h e Z a c h a r i a s o n model on t h e s t r u c t u r e o f g l a s s . S c r e e n i n g Power When a group o f atoms i n t e r a c t c h e m i c a l l y , s i n g l e , m o l e c u l e s w i l l be f o r m e d o n l y i f v:he c a t i o n i s a p r o t o n (NH^), o r i f t h e number o f a n i o n s r e q u i r e d t o n e u t r a l i z e t h e c h a r g e o f t h e c a t i o n , a t t h e p a r t i c u l a r t e m p e r a t u r e , i s s u f f i c i e n t l y g r e a t t o p r o v i d e p r o p e r s h i e l d i n g o f t h e c a t i o n f o r c e f i e l d ( S i F g ) . U n l e s s b o t h c o n d i t i o n s , e l e c t r o n e u t r a l i t y and a d e q u a t e s c r e e n i n g a r e met, t h e i n t e r a c t i o n o f t h e atoms d o e s n o t l e a d t o t h e f o r m a t i o n o f m o l e c u l e s , but t o an i n d e f i n i t e a r r a y o f i o n s , i . e . a s o l i d . S i l i c a g l a s s i s t h e r e f o r e b e t t e r d e s c r i b e d by t h e f o r m u l a S i (0 / 2 ) ^ . T h i s e x p r e s s i o n i n d i c a t e s t h a t t h e 2- c a t i o n i s s c r e e n e d by f o u r 0 i o n s . S i n c e t h e c o m p o s i t i o n 2— + + + + i s S i 0 2 , e a c h 0 ' i o n i s s h a r e d by two S i , and i s t h e r e - 2 — .+ + + + . f o r e d e p i c t e d as 0 12 f o r e a c h S i i o n . T h i s f o r m u l a t i o n i n d i c a t e s t h e s c r e e n i n g o f t h e c o - o r d i n a t e r e q u i r e m e n t s o f •the c a t i o n s and t h e n a t u r e o f t h e b u i l d i n g u n i t s . The f r e s h l y f r a c t u r e d s u r f a c e w i l l be a r e g i o n o f i n c o m p l e t e s c r e e n i n g , r e s u l t i n g i n h i g h e r r e a c t i v i t y and a g r e a t e r e l e c t r o n r e d i s t r i b u t i o n i n l a t e r a l s u r f a c e bonds. A c o n t r a c t i o n o f t h e s e bonds r e s u l t s , t h e s u r f a c e r e m a i n i n g i n t e n s i o n . C e r t a i n s p o n t a n e o u s s u r f a c e r e a c t i o n s w i l l s e r v e t o w i t h d r a w e l e c t r o n s f r o m t h e s e l a t e r a l bonds, a r e l a x a t i o n and s w e l l i n g o f t h e s o l i d r e s u l t s . O b v i o u s l y t h e s t r o n g e r t h e s u r f a c e i n t e r a c t i o n , ( t h e s c r e e n i n g p o w e r ) , t h e g r e a t e r t h e FIGURE 11. SCHEMATIC PICTURE OF THE FRACTURE OF SI L I C A (a) Quartz (b) S i l i c a o Oxygen © S i l i c o n \ ". C o C CO c c CO o c c o CO c c c c c c c / \ c CO O c c o CO c / \ c c FIGURE 12. THE STRUCTURE OF POLYMETHYL METHACRYLATE.. 45. e l e c t r o n w i t h d r a w a l . The e f f e c t s o f t h e s c r e e n i n g o f t h e f o r c e f i e l d +-i • + + o f t h e S i c o r e s on the m e c h a n i c a l s t r e n g t h p r o p e r t i e s o f t h e m a t e r i a l j w i l l be d e a l t w i t h i n t h e s e c t i o n on a d s o r p t i o n . S u r f a c e S t r u c t u r e A f r e s h l y f o r m e d s u r f a c e o f s i l i c a c o n t a i n s two k i n d s o f s t r u c t u r a l u n i t s c a l l e d E - c e n t r e s and D - c e n t r e s ( F i g . 1 1 ) . The E - c e n t r e , ( e x c e s s o x y g e n c e n t r e ) , c o n s i s t s o f an S i + + + + i o n t h a t i s s c r e e n e d by f o u r i o n s . The S i + " * + ^ 2 - i o n s h a r e s o n l y t h r e e o f i t s f o u r 0 i o n s w i t h n e i g h b o u r i n g 2- t e t r a h e d r a , i t s f o u r t h 0 i o n i s n o t s h a r e d w i t h a n o t h e r c a t i o n . The s t r u c t u r a l u n i t may be w r i t t e n . + + + + o_ - The D - c e n t r e ( d e f i c i e n t o x y g e n u n i t ) has a p o s i t i v e + + + + e x c e s s c h a r g e . The S i i o n i s i n c o m p l e t e l y s c r e e n e d , h e n c e t h e s e u n i t s a r e r e s p o n s i b l e f o r t h e h i g h s u r f a c e e n e r g y o f s i l i c a s u r f a c e s . The s t r u c t u r a l u n i t has t h e f o r m u l a + ++•»• 2- + ( S l °1.5 ) I n t h e a b s e n c e o f r e a c t i v e m o l e c u l e s t h e s u r f a c e o f f r e s h l y b r o k e n s i l i c a c o n s i s t s o f an a r r a y o f E - u n i t s and D - u n i t s h a v i n g e x c e s s p o s i t i v e and n e g a t i v e c h a r g e s . The p o s s i b i l i t y of an electron t r a n s f e r from an E to a D u n i t - i s not l i k e l y , since t h i s would res u l t in the ++ + formation of S i ions having 8+1 outer electrons. Chemical Reactivity of the Glass Surface • 2 — An E-centre contains three bridging 0 ions . . .++++ . s t a b i l i z e d by two S i ions. In addition, the unit con- tains one 0 exposed to only one Si ion. This 0 ion has greater p o l a r i z a b i l i t y and screening power than the other two and i s termed a 'basic' active centre, with a negative excess charge. Thus the D-centre, or 'a c i d i c ' active centre i s .++++. p o s i t i v e , due to the .incompletely screened Si ion. The simultaneous occurrence of basic and a c i d i c s i t e s in the same surface leads to many i n t e r e s t i n g chemical reactions. ( i ) Water Vapour It i s a well established fact that the surface of glass i s covered with a layer of hydroxyl groups which a f f e c t many of the s o l i d ' s properties. This layer may be depicted as H H | I 0 0 1 I -'.Si - 0 - S i - and i s generally termed the "bound water". Many of the . 47. r e a c t i o n s o c c u r r i n g a t t h e glc\ss s u r f a c e i n v o l v e t h e s i l a n o l s u r f a c e . The work o f D z i s k o , ' V i s h r i e v s k d y a and C h d s a l O v a ^ 4 shows, (1) P h y s i c a l l y a d s o r b e d w a t e r i s removed by d r y i n g to c o n s t a n t w e i g h t a t 115°C. x (2) The bound w a t e r i s p r o p o r t i o n a l t o t h e s u r f a c e a r e a . > (3.) Between 115 °C and 6 00oCS t h e h y d r o x y l g r o u p s a r e e v o l v e d w i t h o u t s e r i o u s l o s s o f s u r f a c e a r e a . (4) Above 600°C s u r f a c e a r e a i s d e s t r o y e d . ( i i ) A d s o r p t i o n R e a c t i o n s Many o f t h e a d s o r p t i o n r e a c t i o n s w i t h g l a s s may be r e g a r d e d as s e c o n d a r y r e a c t i o n s s i n c e t h e s u r f a c e must f i r s t a d s o r b a h y d r o x y l i o n , o r l o s e a p r o t o n , i n o r d e r t o p r o v i d e a s i t e f o r c a t i o n i c a d s o r p t i o n . The f r a c t u r e d s u r f a c e i s u s u a l l y d i s t o r t e d i n s u c h a way as t o b r i n g the.more p o l a r i z - 2- a b l e 0 i o n s t o t h e s u r f a c e m o r d e r t o s c r e e n t h e s m a l l e r + + + + . • S i i o n s . Thus t h e s u r f a c e i s e s s e n t i a l l y n e g a t i v e l y c h a r g e d . N o n - i o n i c o r g a n i c compounds a r e a t t r a c t e d t o t h e s i l a n o l s u r f a c e , u s u a l l y i n t h e more s t a b l e m i c e l l a r f o r m ^ 4 ^ . The a d s o r p t i o n o f l o n g - c h a i n s u b s t i t u t e d ammonium i o n s has been e m p l o y e d f o r t h e f l o t a t i o n o f s i l i c a f r o m o r e s f o r many y e a r s , t h e a d s o r p t i o n t a k i n g p l a c e f r o m aqueous s o l u t i o n . A d s o r p t i o n f r o m s o l u t i o n i n v o l v e s a c o m p e t i t i o n f o r t h e s u r f a c e s i t e between t h e s o l v e n t and s o l u t e m o l e c u l e s . Thus i n general, the less polar the solvent the greater' the. adsorption of the active solute species. Amines are, how ever, strongly adsorbed from the gas phase, a monolayer being formed at very low p a r t i a l p r e s s u r e s ^ 4 9 ^ . Yates has demonstrated the importance of hydrogen bonding i n explaining volume changes accompanying adsorption on Vycor glass rods. The d i f f i c u l t i e s encountered i n studying i n t e r  actions on glass surfaces arise from the presence of water vapour and the extremely high r e a c t i v i t y of the surface. Stress Corrosion of Glass Mechanical forces acting on the s o l i d change the interatomic distances, causing the s o l i d to change i t s o p t i c a l and e l e c t r i c a l properties, as well as i t s chemical , + + + + r e a c t i v i t y . For s i l i c a s .under a t e n s i l e stress the Si ions are screened to a l e s s e r degree and are therefore more l i k e l y to increase t h e i r co-ordination by adding (OH) ions.' . . 2- . The pol a r i . z a b i l i t y of the 0 1 0 n s i s increased due to the increase Si-O-Si distance in the d i r e c t i o n of the force. A proton w i l l now p r e f e r e n t i a l l y enter the electron cloud of 2- the more polarizable 0 1 0 n s . Tnerefore the mechanical forces aid chemical c o r r o s i v i t y by increasing the internuclear distances. One would thus expect any environment with an a f f i n i t y f o r the glass surface to decrease the t e n s i l e strength by screening the e f f e c t s of a t t r a c t i v e cohesive 49. forces.; the greater the screening, the greater the decrease. (51) C.J. Culf has measured the e f f e c t of several l i q u i d s and dried gases upon the mechanical strength of plate glass. Moisture gave the major decrease in mechanical strength (a fracture energy of 2900 dynes/cms), with dry ammonia gas, (an e f f e c t i v e screener), having a l e s s e r e f f e c t , but s i m i l a r to many l i q u i d s , (4200 dynes/cms). The s t a t i c fatigue phenomenon, to be discussed subsequently, i s a direct consequence of the'mechanochemical reaction of the glass surface -with the ambient moist atmosphere, (b) P l a s t i c s - Polymethyl Methacrylate This a c r y l i c thermoplastic [-CH ~C(CH )COOCH,)-] J 3 3 i n possesses many remarkable properties and i s chosen for t h i s study for i t s b r i t t l e n e s s at room temperature. Polymethyl methacrylate has a molecular shape of long continuous carbon chains to which the methyl and ester groupings are attached. Fig.. 12 shows the structure, which i s large in the transverse d i r e c t i o n . There i s evidence that the polymer exists l a r g e l y in a c o i l e d configuration. Every second carbon of the chain is asymmetric, with r e s u l t i n g isomeric d and 1 arrangements randomly located down the chain. ' This randomness makes an ordered arrangement of the molecular chains d i f f i c u l t . Steric e f f e c t s associated with the ester grouping are also non-conducive to c r y s t a l l i z a t i o n . Thus polymethyl metha-crylate i s completely non-crystallirie. General Considerations in Polymer Failur e The forces of a t t r a c t i o n between the polymer molecules are of two types; hydrogen bonds and Van der Waal's forces. The Van der Waal's, or secondary forces, are due to a combination of several.forces, namely,the orientation e f f e c t (attraction between dipoles), the induction e f f e c t (attraction between a dipole and an induced di p o l e ) , and the London dispersion e f f e c t (attraction between non-polar molecules because of electron induced f l u c t u a t i n g dipole moments). The presence of polar groups in macro-molecules greatly increases t h e i r net a t t r a c t i o n . The point of i n i t i a t i o n of the fracture process may be quite a r b i t r a r y , usually commencing from s t r u c t u r a l imperfections. These imperfections are frequently at the surface and rupture i s usually a surface i n i t i a t e d e f f e c t . The t e n s i l e strength refers to the ultimate property of the material, normally expressed in terms of the t e n s i l e load at fracture divided by the i n i t i a l undeformed area of cross-section. Factors influencing the t e n s i l e strength of p l a s t i c s are, polymer co n s t i t u t i o n , c r y s t a l l i n i t y , degree of cross- l i n k i n g , molecular weight, temperature, rate of t e s t , geometry of the test piece and the type of surrounding environment. Fracture in the Glassy Region When the rate of the st r a i n becomes high, or the- test temperature s u f f i c i e n t l y low, a material that was for  merly rubbery, begins to behave as a glass. Due to the r e s t r i c t i n g e f f e c t of i n t e r n a l v i s c o s i t y , the chains of the network are unable to uncoil and stretch in a rubbery fashion. Under such conditions fracture i s of a b r i t t l e nature and the network chains are f a r from f u l l y extended at the moment of fracture. (52) Beuche has derived a t h e o r e t i c a l treatment for the b r i t t l e f a i l u r e of polymers using a s t a t i s t i c a l mechanic a l approach very s i m i l a r to that of Poncelet f o r glass. Environmental Stress-cracking of P l a s t i c s The term environmental stress cracking applies to accelei^ated surface i n i t i a t e d b r i t t l e f a i l u r e , which occurs when the material i s subjected to a t e n s i l e stress in an 'active environment'. The e f f e c t of t h i s environment i s to induce cracking which would not occur in i t s absence, or to cause f a i l u r e at lower st r e s s , or i n shorter times, than would normally be experienced i n an inactive environment. The molecular mechanisms involved in crack i n i t i  ation and propagation would be expected to be s i m i l a r to the non-environmental case, the d i s t i n c t i o n l y i n g in the cata strophic reduction i n crack resistance in the presence of an active environment. FIGURE 13 CRAZING OF POLYMETHYL METMACRYLATE ( 3 ) Richards v ' in 194 6 was the f i r s t to note the f a i l u r e of polyethenes of low molecular weight in soap solu tions. A review by Howard^1*' (1959) covers the studies to date 5 which mostly involve polyethylene. At the present time, t h e o r e t i c a l understanding of environmental stress cracking i s very sketchy, Hittmair and (55) Ullman report on the e f f e c t of c r y s t a l l i n i t y and molecular weight on stress cracking of polyethylene. The t h e o r e t i c a l reasons for the e f f e c t s are discussed i n terms of the G r i f f i t h theory of fracture, suggesting the role of the active species to be that of reducing the surface energy so that the stress at which b r i t t l e f a i l u r e occurs i s reduced. As discussed elsewhere, t h i s may be p a r t l y correct but i s obviously an i n s u f f i c i e n t reason f o r cracking. Polymethyl methacrylate exhibits the e f f e c t of crazing, i . e . the appearance of fine cracks on the surface in e i t h e r random or patterned formation, Fig. 13. The e f f e c t i s s i m i l a r to stress cracking since i t i s environment se n s i t i v e . ( i ) Structural E f f e c t s Average Molecular Weight i s known to be one of the major factors in determining stress cracking resistance. Howard^ 5 4 \ Spohn and F r e y ^ 5 6 \ and Lander^ 5 7^ have a l l shown the deleterious e f f e c t s of low molecular weight fracti o n s on crack resistance of polyethylene. Long chain networks with high degrees of cross- l i n k i n g serve to reduce the stress cracking e f f e c t s . 0 5 10 15 . 20 25 30 Elongation {%) FIGURE 14. EFFECT OF TEMPERATURE ON TENSILE STRESS-STRAIN CURVE OF POLYMETHYL METHACRYLATE (58) . ( i i ) Temperature Effects Fig. 14 shows the e f f e c t of temperature on the s t r e s s - s t r a i n curve of polymethyl methacrylate. In a group of specimens broken between 23°C and 80°C, Wo1cock et a l ^ 5 8 ^ have shown the nature of the fracture to go through a t r a n s i t i o n stage between 40°C and 50°C, Below 40°C the fracture surface i s f l a t and perpendicular to the faces of the specimen, i n d i c a t i n g e s s e n t i a l l y b r i t t l e f a i l u r e . Above 4 0°C there i s an i n d i c a t i o n of shear with the material becoming tougher and the c r i t i c a l crack size greater, so that the mirror area i s increased in size. The d u c t i l i t y also increases thereby reducing stress concentration at the t i p of the crack by flow. . It i s obvious from Fig. 14 that the elongation at f a i l u r e r i s e s sharply in the region 4 0°C-50°C. There would appear to be a change in the mechanism of f a i l u r e . i n t h i s region, as yet unexplained. ( i ) Introduction Metals, p l a s t i c s , concrete, ceramics, glass, wood, rocks etc., are a l l solids whose u t i l i z a t i o n i s governed by the presence of cracks or flaws within them. Some cracks are i n i t i a t e d by the concentration of stresses around flaws, that are either 1 natural to the material or b u i l t into i t inad vertently during manufacture or f a b r i c a t i o n . Others are i n i t i a t e d by p l a s t i c deformation o f the m a t e r i a l caused by the s t r e s s e s themselves. Under s t r e s s once a crack i s i n i  t i a t e d , i t grows slowly u n t i l the s t r a i n energy at the t i p reaches a l i m i t i n g v a l u e , at. which p o i n t the crack becomes uns t a b l e an^ propagates at h i g h v e l o c i t y o f i t s own accord. The nature o f t h i s process d i f f e r s from m a t e r i a l to m a t e r i a l but depends upon the manner i n which the l o a d i s a p p l i e d , as w e l l as the temperature and chemical environment. The l a t t e r two f a c t o r s are l e s s w e l l understood and i t i s the o b j e c t o f t h i s work to i n v e s t i g a t e f u r t h e r the r o l e o f chemical environment. To a v o i d c o n f u s i o n o c c u r r i n g from the use o f f r a c t u r e terminology, d e f i n i t i o n s o f the terms used i n the t h e s i s are given below, ( i i ) D e f i n i t i o n s F r a c t u r e i s d e f i n e d as the s e p a r a t i o n o r fragmenta t i o n o f a s o l i d body i n t o two o r more p a r t s under the a c t i o n o f a s t r e s s . The d i f f e r e n t types o f f r a c t u r e a r i s e from d i f f e r e n c e s i n the modes o f crack n u c l e a t i o n and crack pro p a g a t i o n ; these processes•depend on the nature o f the a p p l i e d s t r e s s , s t r a i n r a t e , temperature and specimen environment.^ F r a c t u r e may be e i t h e r d u c t i l e , where the s e p a r a t i o n occurs a f t e r e x t e n s i v e p l a s t i c deformation; o r b r i t t l e , with l i t t l e , o r i d e a l l y no p l a s t i c deformation accompanying the break. Various c o n d i t i o n s and stages o f f r a c t u r e may be 57. v i s u a l i z e d , (a) Crack I n i t i a t i o n . A f a i l u r e process by which one or more cracks are forrved in a material free from any cracks. (Poncelet) . (b) Fracture I n i t i a t i o n . A f a i l u r e process by which one or more e x i s t i n g cracks in the material begin . to extend. ( G r i f f i t h ) ( 3 5 . (c) Fracture Propagation. A f a i l u r e process subsequent to fracture i n i t i a t i o n in which the cracks are extending in the material. A d i s t i n c t i o n may be made between two types of fracture propagation: (i) Stable fracture propagation i s the f a i l u r e process in which crack extension i s a function of the applied load and can be controlled ac- cordingly. ( i i ) Unstable fracture propagation i s the f a i l u r e process in which crack extension i s governed by factors other than loading and thus becomes uncontrollable. ( i i i ) Fracture I n i t i a t i o n B r i t t l e f a i l u r e often, occurs at unpredictable l e v e l s of stress, by the suden propagation of a crack. It i s believed that i n c r y s t a l l i n e materials some dislocation process sets up stresses that are relieved by atomoc separation instead of atomic s l i p . A crack forms. The question i s then'whether the crack can spread cata s t r o p h i c a l l y across the cr y s t a l as a cleavage crack. If i t can, b r i t t l e fracture ensues. Amorphous-materials, such as glass, are completely b r i t t l e , whilst c r y s t a l l i n e materials usually exhibit some p l a s t i c deformation p r i o r to fracture. An approximate calc u l a t i o n of the t h e o r e t i c a l cohesive strength of a perfect material r e s u l t s in values several orders of magnitude l a r g e r than the measured values. The f i r s t explanation given for the discrepancy was derived (3) by G r i f f i t h from the assumption that a l l b r i t t l e materials contain a host of fine e l l i p t i c a l cracks. . The G r i f f i t h C r i t e r i o n Micro'cracks pre-existing on the surface, or i n the „ bulk of a material, act to concentrate applied stresses at the flaw apex'^ 1* . The G r i f f i t h . c r i t e r i o n f o r fracture i n i t i a t i o n predicts' that at a p a r t i c u l a r l e v e l of applied load, a c r i t i c a l energy .' value w i l l cause the crack to pro pagate. It should be noted that a fracture i n i t i a t i o n c r i t e r i o n i s not necessarily a strength f a i l u r e c r i t e r i o n . As a result of the stress concentration the cohesive strength of the material may be exceeded at t h i s l o c a l i z e d area at low applied loads. The c r i t i c a l stress value, as shown by O r o w a n ^ ° \ represents the molecular cohesive strength of the material« The Energy Approach The concept of the o r i g i n a l G r i f f i t h hypothesis i s based on the condition that the energy W applied by load ing a structure, i s balanced,by the e l a s t i c s t r a i n energy W stored in the structure and the surface energy W in the free faces of the e x i s t i n g cracks. W = VL + W e , s If the load i s increased the corresponding increase dW in the applied energy- W may be balanced eit h e r ( i ) by an increase dW in the st r a i n energy We only or, ( i i ) by an i n  crease dWs in the crack surface energy Ws or, ( i i i ) p a r t l y by an increase dW and p a r t l y by an increase dWs. In case ( i ) dW = dWe, dWs = 0 and the crack does not extend. In the other two cases dW can equal 0 and the era surface energy can only increase by extending the crack, i . e . i f the crack half-length c increases to (c + dc). Balancing the energies we have dW = dWe + dWs dc dc dc dW ^ e It can be shown that —- = 2—— . dc dc d W e a w s hence = . • dc dc For a thin plate G r i f f i t h gave* 3^ We = T T C 2 O 2 / E where o - Applied uniaxial' t e n s i l e stress, E = Modulus of E l a s t i c i t y . Y = Surface Energy per unit length of crack surface c = Crack half length. Solving by substitution we have, o = 2EY TTC 1/2 o i n (1) a. = Stress necessary f o r fracture i n i t i a t i o n in • We then have the G r i f f i t h c r i t e r i o n for fracture i n i t i a t i o n . For a <a- the crack does not extend (dW =0) i . e . ( i i ) For o > 0 £ n we have fracture propagation. Then the stress necessary to propagate a crack i s inversely proportional to the crack length. The t e n s i l e strength of a completely b r i t t l e material w i l l thus be de termined by the length of the largest crack e x i s t i n g p r i o r to loading, G r i f f i t h ' s experiments on glass f i b r e s showed that when surface cracks are absent,.an increase in strength r e s u l t s to values approaching the t h e o r e t i c a l cohesive s t r e n g t h . S i n c e t h e G r i f f i t h e q u a t i o n o n l y a p p l i e s t o comple t e l y b r i t t l e m a t e r i a l s , a new t r e a t m e n t must be u s e d f o r c r y s t a l l i n e m a t e r i a l s , w h i c h appeal- 1 t o f a i l i n a b r i t t l e f a s h i o n , b u t w h i c h u s u a l l y have an amount o f p l a s t i c d e f o r  m a t i o n n e x t t o t h e f r a c t u r e s u r f a c e . The t h e o r y must t h e r e  f o r e t a k e i n t o a c c o u n t n o t o n l y t h e e n e r g y n e c e s s a r y t o c r e a t e new s u r f a c e ( 2 y ) , but a l s o t o p r o d u c e p l a s t i c d e f o r m a t i o n i n t h e v i c i n i t y o f t h e c r a c k ( p ) . O r o w a n ^ ^ m o d i f i e d t h e G r i f f i t h e q u a t i o n t o , a- [ 2 ^ X 1 2 1 ] 1 / 2 ( 2 ) . uc J where p i s t h e work o f p l a s t i c d e f o r m a t i o n a t t h e t i p o f t h e g r o w i n g c r a c k . R o e s l e r has shown t h a t t h e e n e r g y d i s s i p a t e d i n p l a s t i c d e f o r m a t i o n i s much l a r g e r t h a n t h e s u r f a c e e n e r g y c h a n g e s u n l e s s t h e m a t e r i a l i s v e r y b r i t t l e . T h e r e f o r e , the. f u n c t i o n o f an e m b r i t t l i n g s p e c i e s i s n o t o n l y t o r e d u c e y, but a l s o t o d e c r e a s e p t o a v a l u e c l o s e t o z e r o . In a f r a c t u r e o f t h i s n a t u r e t h e s t r e s s c o n  c e n t r a t i o n a t t h e t i p o f t h e m i c r o c r a c k i s i n i t i a l l y accommo-' d a t e d by p l a s t i c d e f o r m a t i o n . When e q u a t i o n ( 2 ) i s s a t i s f i e d , t h e c r a c k w i l l p r o p a g a t e s p o n t a n e o u s l y . The s p e e d a t w h i c h t h i s s p o n t a n e o u s p r o p a g a t i o n o c c u r s i n c r e a s e s r a p i d l y f r o m z e r o t o a l i m i t i n g v a l u e , about o n e - t h i r d o f t h e speed o f l o n g i t u d i n a l sound waves i n t h e medium. S i n c e y i e l d s t r e s s i s s t r o n g l y d e p e n d e n t on s t r a i n r a t e , t h e v e l o c i t y o f t h e crack increases to the extent that p l a s t i c deformation cannot accommodate the stress concentration at the head of the crack, and the crack spreads in e. b r i t t l e manner. (iv) Fracture Propagation Subsequent to fracture i n i t i a t i o n i s fracture pro pagation, which consists of stable and unstable crack growth. As long as the condition a > a^ n i s maintained by a d e f i n i t e r e l a t i o n s h i p existing between c and the applied stress a the propagation i s controllable and stable. Irwin*^^* proposed the r e l a t i o n s h i p , / GE / TTC , (3) where G i s the energy released per unit crack area. Thus an amount of energy G i s released from the stored e l a s t i c s t r a i n energy We and used to form new surface. The s i m i l a r i t y between the G r i f f i t h and Irwin formulae i s obvious, but whilst equation (1) i s a formula specifying a. c r i t e r i o n , equation (3) constitutes a r e l a t i o n  ship between c and a When the unique relationship (3) between c and a ceases to e x i s t unstable propagation ensues. Stable propagation i s usually a slow process whilst (65) unstable propagation i s rapid Irwin postulated that when G attains a c r i t i c a l value GQ R )the t r a n s i t i o n from stable to unstable propagation ensues. GCR = ^ 2 C R CCR / E ( 4 ) Velocity of Crack Propagation Unstable fracture propagation occurs when other quantities, e.g. crack growth v e l o c i t y , play a contributing r o l e , and the fracture can no longer be controlled by the applied load. When a bond in the material breaks under the action of a t e n s i l e stress, the two freed atoms accelerate away from one another. Since they are part of the same body they cannot t r a v e l very f a r , each movement causing a di s t u r  bance to propagate through the body situated on ei t h e r side of the broken bond. This diturbance may be described by the theories of e l a s t i c i t y . Perpendicular to the free boundary the disturbance propagates as a lo n g i t u d i n a l wave, the front of which carries a displacement of the same orient a t i o n as the displacement of the freed p a r t i c l e , Along the free boundary the disturbance propagates as a transverse wave whose front c a r r i e s a d i s  placement that also has the orientation of the freed p a r t i c l e s . The l o n g i t u d i n a l waves superimpose a compression on the bonds of the body previously extended by the imposed t e n s i l e stress. They act therefore as a stress r e l i e v i n g mechanism l i b e r a t i n g the s t r a i n energy of the body as a consequence of the creation of new surface. As the r e f l e c t e d transverse waves on each s i d e o f t h e c r a c k r e a c h the c r a c k t i p s i m u l t a n e o u s l y , each c a r r y i n g d i s p l a c e m e n t s i n o p p o s i t e d i r e c t i o n s , t h e y super impose on t h e unbroken bonds at u.he edge o f t h e c r a c k , ( a l r e a d y e x t e n d e d by the t e n s i l e . s t r e s s ) , t h u s f u r t h e r i n g the break. The i r r e v e r s i b i l i t y o f the f r a c t u r e p r o c e s s r e s u l t s f r o m the e f f e c t s o f t h e s e emanating t r a n s v e r s e waves t h a t p r e v e n t the bond from r e f o r m i n g . By r e l a t i n g the k i n e t i c energy to the v e l o c i t y o f movement o f t h e m a t e r i a l on e i t h e r s i d e o f t h e p r o p a g a t i n g c r a c k d e r i v e d t h e e q u a t i o n i - t .a o c\2-]l/2 where V = C r a c k p r o p a g a t i o n v e l o c i t y = V e l o c i t y o f sound i n m a t e r i a l a c = C r i t i c a l s t r e s s l e v e l a = S t r e s s on p r e - e x i s t i n g f l a w . R o b e r t s and W e l l s * 6 3 * gave / ~ = B = .38 and ex- p r e s s e d V = .38 / - (1-c / c ) . / P Thus the t e r m i n a l v e l o c i t y w i l l be The t e r m i n a l v e l o c i t y i s t h u s a c h a r a c t e r i s t i c p r o p e r t y o f t h e m a t e r i a l , b e i n g .a f r a c t i o n o f t h e v e l o c i t y o f t h e l o n g i t u d i n a l wave i n a r o d -of t h i s m a t e r i a l . The v a l u e o f .38 f o r 3 compares w e l l w i t h S c h a r d i n and S t r u t h ' s * 5 ' 1 * value, o f .4 f o r v i t r e o u s s i l i c a . A s i m i l a r Stable frocture propagation Unstable frocture Forking and crog^ l . 500- h . p r o p a g a t i o n | coc ilescenco | — 1 l - J _ *s /I 1 1 1 1 1 10 Ratio 30 C. Original crack halHengtti Co 15 20 25 Crock half-length 35 40 45 FIGURE .15a-. CRACK VELOCITY RELATED TO CRACK-LENGTH RATIO ( 6 5 ) . ,....0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 ...... . .... Dimension'ess stress (cr/crc) FIGURE 15b« MAXIMUM CRACK VELOCITY VERSUS STRESS . (62). (6 S) resulv was obtained by Bieniawski ° f o r rocks. (65) Fig. 15a shows that fracture propagation s t a r t s with low v e l o c i t y which l a t e r increases rapidly to a constant value. The turning point in the curve marks the t r a n s i t i o n from stable to unstable propagation, i . e . when C / C q = c c ^ / c Q and G = G C R. Therefore, whilst the influence of crack v e l o c i t y i s small during stable propagation i t w i l l be a governing factor in the unstable fracture propagation process. Once the crack approaches i t s terminal, v e l o c i t y the k i n e t i c energy of crack extension must also approach a l i m i t i n g value. Since the released energy increases with crack length the crack tends to increase i t s surface area in order to dissipate the additional energy. Branching or forking occurs, (v) Alternatives to the G r i f f i t h Theory / r r \ (67) Various other t h e o r i e s K have arisen to explain b r i t t l e f a i l u r e s , many of which involve s l i g h t v a r i  ations of the basic G r i f f i t h hypothesis. The theory of Poncelet* 6 8*, however, does not u t i l i z e the concept of pre exi s t i n g cracks and warrants more detailed attention, This s t a t i s t i c a l mechanics approach states that nonequilibrium processes are determined by the difference between the f o r  ward and backward reaction rates, in t h i s case the difference between the rate at which bonds are broken and the rate at which these bonds are reformed. With no stress these rates O f . would be equal, but with stress the rates are biased; a process which i s stress and temperature s e n s i t i v e . (vi) The Poncelet Flaw Genesis Theory An ideal b r i t t l e s o l i d may be regarded as being composed of a c o l l e c t i o n of i d e n t i c a l p a r t i c l e s held together at d e f i n i t e spacings by bonds of an e l e c t r o s t a t i c nature. These bonds may be pictured in the usual way on a Morse diagram.- Fig. 16. E l e c t r o s t a t i c repulsions ex i s t between -the nuclei of both p a r t i c l e s and also between the electrons of both p a r t i c l e s , whilst e l e c t r o s t a t i c attractions occur between the electrons of one p a r t i c l e and the nucleus of the other. ' The equilibrium distance between the p a r t i c l e s i s stable, since the Morse resultant of the bond urges the p a r t i c l e s back toward t h e i r equilibrium spacing, no matter where, t h e i r actual spacing may momentarily be. Under the influence of these restoring bonds the p a r t i c l e s vibrate. The energy involved in these o s c i l l a t i o n s i s represented by the area subtended by arc AB or arc AC and i s usually referred to as the thermal energy l e v e l of the p a r t i c l e s . According to s t a t i s t i c a l mechanics the p r o b a b i l i t y that a given bond has a thermal v i b r a t i o n a l energy in excess of an a r b i t r a r y value E ( r ) i s given by P = e-E(r)/KT where T i s the temperature in degrees Kelvin and K i s 16 Boltzmann's constant (1.372x10" ergs/degree). FIGURE 17 PRINCIPAL BOND DIAGRAM While the energy l e v e l s of the various p a r t i c l e s are charging continuously and independently as the p a r t i c l e s i n t e r f e r e with one. another, the d i s t r i b u t i o n of the various le v e l s follows a well determined pattern referred to as the M ax we 11 - Bo 113 ina n n L aw. The.computations of the energy l e v e l of a p a r t i c l e i s a very complicated matter, but may be s i m p l i f i e d by c a l  c u l a t i n g the energy levels of the bonds rather than those of the p a r t i c l e s , a bond joi n i n g two p a r t i c l e s . The energy of a p a r t i c l e i s thus half the sum of the energy lev e l s of the bonds j o i n i n g i t to other p a r t i c l e s . The v i b r a t i o n a l energy levels of the various bonds of a p a r t i c l e do not depend solely on the vibration and energy l e v e l s of the p a r t i c l e being considered, but. also on the vibrations and energy lev e l s of the other p a r t i c l e s to ..which the one in question i s bound. It follows that the vibration and energy l e v e l s of any one bond varies independently of any other bond, and the bonds may thus be considered one at a time. The p r i n c i p a l bonds of a p a r t i c l e may be regarded a the 6 mutually perpendicular bonds l y i n g along the co-ordinat axis. The p r i n c i p a l stresses may be regarded as the vector- pairs of forces acting along the p r i n c i p a l bonds (Fig. 17). Since so l i d s f a i l , the p r i n c i p a l bonds must become unstable when subjected to s p e c i f i c stress tensors. Due to the increasingly steep nature of the negative Morse resultant the 1 70. continued contraction of bonds i s precluded. Unstable bonds must therefore keep on expanding. There may be nothing tc prevent the bond from reaching a t h i r d equilibrium spacing whilst expanding, which equilibrium would again be a stable equilibrium. On reaching such an equilibrium the bond st a r t s to o s c i l l a t e about i t and then becomes a "long" bond. It consequently ceases to be a p r i n c i p a l bond, some other bond becoming the p r i n c i p a l bond. Such bonds are termed "swapped" bonds. The f a i l u r e of so l i d s r e s u l t i n g in broken bonds we c a l l fracture, and the f a i l u r e giving swapped bonds, flow. Since b r i t t l e solids do show other phenomena than fracture when submitted to stress-tensors, we accept the p o s s i b i l i t y of flow, although not necessarily of a viscous or p l a s t i c nature. In the case of simple tension the stress acting along one axis i s p o s i t i v e , with both the other a x i a l stresses being zero. As.the vibrating bond reaches spacings greater than the' primary equilibrium spacing, i t s Morse re sultant, urging a contraction, at f i r s t increases from i t s value at B u n t i l a maximum spacing at point 0 i s reached. For greater bond expansions the Morse resultant de creases asymptotically to zero. As the spacing of the primary bond increases under the influence of i t s thermal energy there i s only one position greater, than the primary equilibrium for which the resultants and the.stress are again in equilibrium, as shown by D on the Morse curve. This i s an unstable equi librium and when the bond exceeds t h i s length, i t becomes a broken bond. The unstable equilibrium i s reached when the therma energy l e v e l .is s u f f i c i e n t , as given by the area under the Morse curve. This required energy l e v e l varies with the. t e n s i l e ' s t r e s s applied, and can therefore be expressed as a function of stress. The Maxwell-Boltzmann Law gives the time during which a bond possesses s u f f i c i e n t energy to overcome the energy b a r r i e r i n proportion to the t o t a l duration of the t e n s i l e load. I t i s found that the duration varies steeply with the stress. Theoretically the smallest t e n s i l e stress i s s u f f i c i e n t to break a bond but the required duration might be m i l l i o n s of years. At the surface where we have an absent bond the required energy would be appreciably less than i f a l l the p r i n c i p a l bonds were present. Thus the f i r s t bonds to break w i l l normally be surface bonds. At the t i p of an e x i s t i n g crack where the bond is perpendicular to the crack plane, the p r i n c i p a l bond in the crack plane cannot remain perpendicular to the v i b r a t i n g bond subject to the t e n s i l e stress, since the l i n k has been severed by the crack. As a r e s u l t t h i s bond becomes oblique and contributes to the applied stress. Thus bonds perpen-d i c u l a r to' a crack t i p v.'ill break even more readi l y than surface bonds. Physical Nature of Strength i n B r i t t l e Solids In b r i t t l e solids where the e l a s t i c flow in f a i l u r e i s very s l i g h t , the l i m i t i n g stress which may be applied to the s o l i d refers to the fracture stress. The fact that i d e n t i c a l b r i t t l e solids i n i d e n t i c a l tests w i l l not give i d e n t i c a l strengths follows from the v a r i a t i o n i n the energy l e v e l s of the various p a r t i c l e s . An average strength may however be computed on a s t a t i s t i c a l basis. Since the f i r s t bond to break sets the fracture phenomenon in motion the duration of a s p e c i f i c stress re quired to fracture i d e n t i c a l s o l i d s may vary greatly. The condition of the outer surface obviously a f f e c t s the strength considerably, as w i l l the surrounding atmosphere. It i s well established that the strength of so l i d s i s greater in vacuo or an atmosphere with no a f f i n i t y for the s o l i d . This aspect w i l l be discussed in further d e t a i l l a t e r . ( v i i ) A Comparison. Poncelet objected to the G r i f f i t h e x i s t i n g flaw hypothesis on the grounds that the i n i t i a t i o n of a crack i s an atomistic approach and not treatable by the macroscopic equations of thermodynamics. " I Jo Orowan approached the problem from an atomistic point of view and demonstrated that when the stress reaches a value- predicted by the Gr i f f i t h ' f o r m u l a the material w i l l break. In the Poncelet approach, although the crack geometry assumption i s removed, others are added in the form of a c t i v a t i o n energy and the manner'in which i n t r i n s i c energy i s biased by the macroscopic load. The i n t e r e s t i n g feature of the flaw genesis theory i s that i t leads to v i r t u a l l y the same conclusion as the pre e x i s t i n g flaw theory. Any disagreement i s a r e f l e c t i o n in the differences in the point of view between s t a t i s t i c a l mechanics and c l a s s i c a l thermodynamics. (a) Existence of Microcracks Gordon, Marsh and P a r r a t t * ^ * have presented ex perimental evidence that stress creates flaws. They also showed, using a sodium vapour decoration technique, that long (50y), narrow (200A°) and shallow (10 00A 0), cracks do exist i n glass p r i o r to the application of the stress. A further conclusion supporting the e x i s t i n g flaw hypothesis shows that low crack density results in the glass breaking at high stresses, E l l i o t t * showed that flaws no more" than several atomic diameter's would account for loss i n ( 71) strength. The res u l t s of Shand leave no doubt that the presence of minor surface flaws has .a dra s t i c e f f e c t on the strength of glass. No dire c t evidence for the.existence of surface flaws has resulted from electron microscopic exami- (72 nation, but the decoration techniques of Andrade and Tsien showed orientated cracks on the inside of glass tubes when abrasion was absent. Thus i t would appear that i n glass specimens cracks do exist and operate to reduce the strength. Bieniaskwi shows the existence of microcracks in rocks, the cracks l y i n g on grain boundaries between the constituent minerals, and concludes that t h e i r presence re sults in the modulus of e l a s t i c i t y of the material being lower.than that of a s o l i d continuum, (b) Crack Propagation Velocity (62) In comparing the equation of Mott (based on the i n i t i a l flaw concept of G r i f f i t h ) , with the Foncelet equation using the flaw genesis hypothesis, the differences are found to be very small, F i g . 15b, Poncelet assumes that there i s no flaw u n t i l i t i s created by a stress, at about . 7 a c v/hereupon i t spreads catastrophically to a l i m i t i n g value of .5 of the transverse wave ve l o c i t y . Thus the l i m i t i n g values of .38V and .5Vt in the case of Mott and Poncelet respectively, are reasonably close (in view of. the t h e o r e t i c a l assumptions made). 75. •(c) S t a t i c Fatigue S t a t i c Fatigue i s that phenomenon p a r t i c u l a r to inorganic- glass where the average breaking strength at constant load as opposed to alternating load i n c y c l i c fatigue, depends upon the time. From the pre-existing flaw point of view, the phenomenon can be related to slow fracture growth, i . e . the size of c Q depends on time.' The magnitude of c Q depends on the stress and atmosphere, such that a lower stress w i l l cause fracture a f t e r a longer time i n t e r v a l . Thus the stress-time equation results from the gradual penetration into the cracks of substances that w i l l be adsorbed on the crack walls. At a stress l e v e l of about 1/3 the breaking stress at rapid loading the glass appears to withstand fracture i n d e f i  n i t e l y . Orowan^ 6 0^ showed that the factor 1/3 was equal to the square root of the r a t i o of y i n moist atmosphere to y i n vacuum. Thus i t seemed that the change in y was responsible (74) for s t a t i c fatigue. Experiments of Gurney. and Pearson con- (75) firmed Orowan's prediction that s t a t i c fatigue w i l l not occur in vacuum. They were able to show that the fatigue e f f e c t could not be ascribed e n t i r e l y to gaseous attack on the crack, and i s possibly due to the atmospheric constituents in the surface layers. (66) E l l i o t t proposed that the crack depth may be deepened by the d i f f u s i o n of corrosion products at the crack t i p s . Thus the loss of strength with time may be due to the growth of the crack size or the decrease in the surface energy, o r both. In any event, the G r i f f i t h h y p o t h e s i s o f p r e - e x i s t i n g flaws seems to e x p l a i n adequately the phenomenon of s t a t i c f a t i g u e . 7 7 . CHAPTER FOUR ADSORPTION 4 :1 J:n.^roa\2£tion_ The s t u d y o f e n v i r o n m e n t a l e f f e c t s on f r a c t u r e i n - , v o l v e s the c o n t a c t o f s o l i d s u r f a c e s w i t h a gas o r l i q u i d p h a s e , r e s u l t i n g i n a d s o r p t i o n at the i n t e r f a c e . The ad s o r p t i o n c h a r a c t e r i s t i c s c o n s t i t u t e i m p o r t a n t p arameters i n d e d u c i n g t h e mechanism by which the f r a c t u r e t a k e s p l a c e . A d s o r p t i o n i n the s o l i d / v a p o u r system may be d e f i n e d as the c o n c e n t r a t i o n o f vapour at the s o l i d s u r f a c e r e s u l t i n g from t h e r e s i d u a l a t t r a c t i v e f o r c e s i n t h e s o l i d s u r f a c e . The phenomenon i s c u s t o m a r i l y d i v i d e d i n t o two br o a d c a t e g o r i e s o f p h y s i c a l a d s o r p t i o n and c h e m i s o r p t i o n . P h y s i c a l a d s o r p t i o n , b a r r i n g h y s t e r e s i s i n porous s o l i d s , i s r e v e r s i b l e and i n v o l v e s e s s e n t i a l l y n o n - s p e c i f i c f o r c e s . Chemical a d s o r p t i o n i n v o l v e s e l e c t r o n t r a n s f e r i n t h e f o r m a t i o n o f a c h e m i c a l bond and i s o f t e n r e f e r r e d t o as l o c a l i s e d o r f i x e d s i t e a d s o r p t i o n . The thermodynamic t e r m i n o l o g y o f s u r f a c e s i s n o r m a l l y a p p l i e d t o l i q u i d i n t e r f a c e s . When d e a l i n g w i t h s o l i d s misuse o f terms has l e d t o a gr e a t d e a l o f c o n f u s i o n ( 7 7 ' ( Q 9 ) • i n . the l i t e r a t u r e w / , The t e r m i n o l o g y t o be used i n t h i s t h e s i s i s d e f i n e d as f o l l o w s . ' l': 2 De f IjlJLtj-og^ ( i ) S u r f a c e f r e e energy. The work n e c e s s a r y t o form- u n i t a r e a of s u r f a c e by a p r o c e s s o f d i v i s i o n , i n vacuo. The 2 s p e c i f i c s u r f a c e f r e e energy i s the f r e e energy per i c m s . ( F ) . ( i i ) S u r f a c e T e n s i o n . (y) The work n e c e s s a r y t o form • u n i t a r e a o f s u r f a c e i n a multi-component system. ( i i i ) S u r f a c e S t r e s s . ( f ) L a t e r a l f o r c e s o p e r a t i n g i n the s o l i d s u r f a c e , which must be b a l a n c e d by e x t e r n a l f o r c e s , o r by volume s t r e s s e s i n the body. T h e r e f o r e , i n a one component system ( v a c u o ) , the s p e c i f i c s u r f a c e f r e e energy and s u r f a c e t e n s i o n a r e i d e n t i c  a l . In an environment we have, F = Y + u 3 r s where'u i s the c h e m i c a l p o t e n t i a l and T3 i s the c o n c e n t r a t i o n e x c e s s o f the adsorbed species,, i . e . y d e c r e a s e s due to the a d s o r p t i o n term u r _ . s ^ 4 : 3 The_ S u r f ace^ ^Tension, S u r f a c e Free Energy Concept C o n t r a r y to the s i t u a t i o n w i t h l i q u i d s the s u r f a c e t e n s i o n ( y ) and s u r f a c e f r e e energy (F) v a l u e s f o r s o l i d s a re not n e c e s s a r i l y e q u a l . G i b b s ^ 7 G ^ gave t h e r e l a t i o n s h i p between t h e q u a n t i t i e s , y = F + A dF/dA where A i s the s u r f a c e a r e a . The d i f f e r e n c e may be seen by i m a g i n i n g t h e p r o c e s s f o r c r e a t i n g f r e s h s u r f a c e t o be comprised o f two s t e p s . F i r s t l y t h e s o l i d o r l i q u i d .is c l e a v e d , k e e p i n g t h e atoms i n f i x e d p o s i t i o n s a s . t h e y appeared i n the b u l k and s e c o n d l y the atoms are a l l o w e d t o r e a r r a n g e t h e m s e l v e s t o t h e i r f i n a l e q u i l i b r i u m p o s i t i o n s , F o r l i q u i d s , due t o the h i g h m o b i l i t y o f the atoms, e q u i l i b r i u m i s e s t a b l i s h e d i m m e d i a t e l y and the two s t e p s o c c u r as one. In the case o f s o l i d s , the second s t e p may o c c u r o n l y s l o w l y and i n t h i s i n s t a n c e the s u r f a c e f r e e energy and s u r f a c e t e n s i o n w i l l not be e q u a l . T h e r e f o r e for. l i q u i d s dF/dA i s z e r o , and y = F, w h i l s t f o r s o l i d s ( 7 7 ) S h u t t l e w o r t n has shown t h a t F and dF/dA are o f the same (78) o r d e r o f magnitude, N i c o l s o n has c a l c u l a t e d t h e q u a n t i t i f o r NaCl and showed i t s s u r f a c e t e n s i o n to be about t h r e e t i m e s as l a r g e as i t s s u r f a c e f r e e energy. T y p i c a l s t u d i e s o f s o l i d s u r f a c e s are f r u s t r a t e d by t h e l a c k o f a s u i t a b l e a b s o l u t e t e c h n i q u e f o r measuring s o l i d s u r f a c e t e n s i o n s . Zero creep e x p e r i m e n t s conducted n e a r the m e l t i n g p o i n t would y i e l d v e r y d i f f e r e n t r e s u l t s from the non e q u i l i b r i u m c o n d i t i o n s w i t h i n c o m p l e t e r e l i e f o f s u r f a c e s t r e s s e s , Thjs^^arface__Str^ j 5 j,^S_urf^.ce_ T^ensa\on ^ Ccjicept The s u r f a c e s t r e s s e s ( f . ) are' f o r c e s a c t i n g 'within i t h e s u r f a c e o f a m a t e r i a l and are not to be c o n f u s e d w i t h 80. FIGURE 18a. CYCLE RELATING SURFACE TENSION AND SURFACE STRESS . (77) . b i o s u r f a c e t e n s i o n (Y). " C o n s i d e r a u n i t cube w i t h edges p a r a l l e l to the axes o f the C a r t e s i a n c o - o r d i n a t e system ' ' y» z x. F i g . 18a. The cube i s r e v e r s i b l y s t r e t c h e d a l o n g t h e x a x i s by an amount dx under the c o n s t r a i n t t h a t the. y edge (but not the z edge) m a i n t a i n s c o n s t a n t l e n g t h , w i t h t h e c o r r e s p o n d i n g work done b e i n g Wo. With the cube i n i t s o r i g i n a l p o s i t i o n l e t i t be s e p a r a t e d i n t o two h a l v e s a l o n g the x-y p l a n e , and l e t these h a l v e s be s t r e t c h e d by an amount (dx) under the same c o n s t r a i n t , as b e f o r e . I n g e n e r a l t h e work r e q u i r e d , W, , w i l l d i f f e r from Wo. T h i s d i f f e r e n c e i s a t t r i b u t e d t o a f o r c e component f x x w i t h i n t h e newly formed s u r f a c e a c t i n g i n the x d i r e c t i o n a c r o s s a u n i t l e n g t h normal t o the x a x i s . We have, xx 2dx X X where pure cube work the s e x x i s the l i n e a r s t r a i n * S i m i l a r l y the work r e q u i r e d t o p e r f o r m a sh e a r e Xy=dy on the same f a c e s o f the o r i g i n a l W' i n the y d i r e c t i o n o f the xy plan e and the W r e q u i r e d t o e f f e c t the same s h e a r on e o a r a t e d h a l v e s r e s u l t s i n a s t r e s s component, W-'1 - W' •xy " — 2e xy S i n c e the f ' s may be r e g a r d e d as the com ponents o f a t e n s o r i t may be c o n c l u d e d t h a t s u r f a c e s t r e s s and s u r f a c e t e n s i o n are not i n g e n e r a l even the same type o f p h y s i c a l q u a n t i t y ; t h e former i s a te n s o i ^ w h i l s t , the l a t t e r i s a s c a l a r . S h u t t l e w o r t h ^ 7 7 ^ e x p r e s s e d t h e r e l a t i o n  s h i p between f and Y by e q u a t i n g the work r e q u i r e d t o go from t h e o r i g i n a l u n s t r a i n e d cube to t h e f i n a l s t a t e o f two s e p a r a t e d h a l v e s ' s t r e t c h e d a l o n g the x - d i r e c t i o n by two d i f f e r e n t p a t h s . I The cube i s f i r s t s t r e t c h e d and the n s e p a r a t e d Wj = W + 2(l+e x x)(Y+ A y ) W q +2Y+ '2AY+2YC X X I I T h e c u b e i s f i r s t s e p a r a t e d a n d t h e n s t r e t c h e d E q u a t i n g W j a n d W-J-J w e g e t f = Y + x x d e C o n s i d e r i n g t h e s h e a r e a n d s i n c e t h e a r e a o f t h e x y p l a n e r e m a i n s u n c h a n g e d t h e e q u a t i o n f o r s h e a r i s f = _ i Y „ x y d e T h e g e n e r a l r e l a t i o n s h i p , X i l T i ] . 5c.. w h e r e 6 — = 1 i f i = J a n d z e r o o t h e r w i s e , a n d w h e r e a l l s t r a i n s e x c e p t e ^ j a r e h e l d c o n s t a n t i n t h e p a r t i a l d i f f e r e n  t i a t i o n . F o r t h e l i a u i d c a s e d y / d e - - w i l l b e . z e r o s i n c e n e w i l a t o m s a r e r e a d i l y s u p p l i e d t o t h e s u r f a c e a n d a c h a n g e i n a r e a w i l l n o t r e s u l t i n a c h a n g e i n s u r f a c e t e n s i o n , F o r s o l i d s h a v i n g l o n g r a n g e o r d e r t h e s t a t e o f t h e s u r f a c e w i l l d y b e a l t e r e d b y a n e x t e n s i o n a n d """" t 0 a n d t n e s u r f a c e s t r e s s 83. w i l l be d i f f e r e n t from the surface tension. Thus the surface tension.does not necessarily lead to surface stress.. Since f ^ j and dy/de— may have e i t h e r sign, compressive as well as t e n s i l e stresses are possible in the surface. In glass, both s o l i d - l i k e behaviour (dy/de i 0) and l i q u i d - l i k e behaviour (dy/de = 0) may be achieved by varying the temperature and the rate of s t r a i n . 4:5 The E f f e c t of Adsorption In the creation of fresh s o l i d surface the cohesive forces are disrupted, r e s u l t i n g in the surface i t s e l f con s t i t u t i n g a reactive or excited state. Vapour molecules reacting with the surface can again lower the surface tension. Obviously, the stronger the reaction the greater the decrease in surface tension, since adsorption i s a spontaneous exothermic event. Thus chemisorption would be more l i k e l y to influence the physical properties involving the s o l i d surface, (e.g. f r a c t u r e ) . Fig,; 30a shows the r e l a t i v e change in surface enthalpy for the events discussed. In general therefore, physical adsorption w i l l not greatly a f f e c t the surface configuration and influence surface sensitive properties. Once the surface i s covered with an adsorbed mono layer the stronger interactions must cease, unless new sur face i s created. The decrease in the surface tension w i l l , however, continue u n t i l a steady state i s reached at which 8 4 . the chemical potential of the adsorbate i s that of the con densed l i q u i d . The Gibbs adsorption isothernr ; relates the de crease i n the surface tension to the concentration excess of the adsorbed species, T, over the bulk, in equilibrium at any pressure p, by, - dy = RTTdlnp Physical Adsorption < t Chemisorption 1 Surface Formation S o l i d Compound Formation FIGURE 30a. ENTHALPY CHANGES IN SURFACE FORMATION, ADSORPTION AND COMPOUND FORMATION. 85. The change i n s u r f a c e t e n s i o n on a d s o r p t i o n i s i n d i c a t e d i n F i g . 30b where p 1 i s the h a l f - c o v e r a g e v a l u e and y Q i s the s u r f a c e t e n s i o n o f t h e c l e a n s o l i d s u r f a c e . For a c o n t i n u o u s curve o f t h i s n a t u r e i t i s assumed t h a t t h e h e a t s o f a d s o r p t i o n a re the same f o r a l l s u r f a c e s i t e s . 0^ Y I FIGURE 3 0b. SURFACE TENSION CHANGES ON ADSORPTION. The change i n s u r f a c e t e n s i o n accompanying ad s o r p t i o n may o r may not b r i n g about a change i n s u r f a c e s t r e s s . The change i n t h e s u r f a c e s t r e s s w i l l o c c u r when the a b s o l u t e v a l u e o f ~ i s d i f f e r e n t from y i n t h e e q u a t i o n Ae AY Y + 7 A e V a r i a t i o n s i n s u r f a c e s t r e s s w i l l be m a n i f e s t e d i n b u l k volume changes, e s p e c i a l l y i n i s o t r o p i c m a t e r i a l s . Bangham (79) and Razouk found the f r a c t i o n a l change i n l e n g t h , o f a c h a r c o a l r o d , t o be p r o p o r t i o n a l t o the r e d u c t i o n i n t h e s u r f a c e f r e e energy w i t h a d s o r p t i o n 86 d l / 1 = ir X c where ' = s u r f a c e p r e s s u r e and X i s a c o n s t a n t depending on the e l a s t i c p r o p e r t i e s o f t h e s o l i d . . I t s h o u l d be mentioned t h a t t h e i r c a l c u l a t i o n s i n v o l v e d t h e Gibbs a d s o r p t i o n e q u a t i o n and hence the c o n c l u s i o n , s h o u l d i n v o l v e the s u r f a c e t e n s i o n r e d u c t i o n and not s u r f a c e f r e e energy. (80) ' Maggs c o n c l u d e d t h a t i f l e n g t h . c h a n g e s be con f i n e d t o d i r e c t i o n s p a r a l l e l t o the a x i s o f the r o d then X i s s i m p l y r e l a t e d t o Young's modulus ( Y ) . . T h i s would be r e a s o n a b l e i f Young's modulus d i d not change w i t h a d s o r p t i o n . As y v a r i e s , t h e s u r f a c e s t r e s s may v a r y , and s i n c e Young's modulus i s a r e l a t i o n s h i p i n v o l v i n g s t r e s s and s t r a i n one ( 81) might e x p e c t Y t o v a r y . M, Sato has shown v a r y i n g m o d u l i w i t h a d s o r p t i o n . (82) Y a t e s c o n f i r m e d Bangham's e q u a t i o n , b u t by r e  g a r d i n g t h e g l a s s as an i s o t r o p i c s o l i d , found the b u l k modulus t o be a more r e a l i s t i c v a l u e , s i n c e Young's modulus o n l y t a k e s i n t o account a l i n e a r i n c r e a s e i n l e n g t h . ) 37 CHAPTER FIVE • RESULTS AND DISCUSSION ^ : ^  I n t e r p r e t a t i o'n__o f J R e s u I t s The t h e o r y o f the s t r e n g t h o f s o l i d s i n r e l a t i o n to s t r u c t u r e has always been u n s a t i s f a c t o r y . Large d i f f e r e n c e s r e s u l t between computed v a l u e s o f the m e c h a n i c a l s t r e n g t h from atomic and s t r u c t u r a l d a t a , and e x p e r i m e n t a l o b s e r v a t i o n s . G l a s s , which does not have a s i m p l e i o n i c c r y s t a l s t r u c t u r e , y i e l d s s t i l l g r e a t e r d i s c r e p a n c i e s i n e x p e r i m e n t a l r e s u l t s . A l t h o u g h the i d e a l m a t e r i a l f o r s t u d i e s o f b r i t t l e . f r a c t u r e , g l a s s would n ot appear to be s u i t a b l e f o r s t u d i e s i n m e c h a n i c a l s t r e n g t h . G.O. J o n e s ' 1 ^ * i n an e x c e l l e n t r e v i e w on the i n t e r  p r e t a t i o n o f d a t a on the s t r e n g t h o f g l a s s , has demonstrated the d i f f i c u l t i e s o f a n a l y s i s o f r e s u l t s on s t r e n g t h measure ments under p r o l o n g e d l o a d i n g c o n d i t i o n s , i . e . l o a d i n g o f the specimen- to some f r a c t i o n o f t h e u l t i m a t e b r e a k i n g l o a d and m e a s u r i n g t h e time to f a i l u r e . The v a r i a t i o n i n t i m e s w i l l be l a r g e due t o i n h e r e n t v a r i a t i o n s i n the s t r e n g t h p r o p e r t i e s . (Times v a r y from a f r a c t i o n o f a second t o thousands o f hours f o r the same t e s t ) . F a t i g u e t y p e s o f e x p e r i m e n t s s h o u l d be a v o i d e d i n t h e case o f g l a s s . G l a s s d i f f e r s i n s t r e n g t h p r o p e r t i e s from most m a t e r i a l s , p a r t i c u l a r l y p o l y c r y s t a l l i n e . m e t a l s , s i n c e , (1) S u r f a c e c o n d i t i o n i s o f major i m p o r t a n c e . (2) The s t r e n g t h i s reduced 3 to 4 t i m e s under c o n d i t i o n s o f p r o l o n g e d l o a d i n g . (3) The s t r e n g t h i s not s t r o n g l y t e m p e r a t u r e dependent i n the s o l i d s t a t e . (4) Heat t r e a t m e n t r e s u l t i n g i n s u r f a c e c o m p r e s s i o n i n c r e a s e s the s t r e n g t h . (5) S t r e n g t h depends on specimen s i z e . The' l a r g e r the s i z e t h e s m a l l e r t h e s t r e n g t h , (6) T h e i r f i b r e s show s t r e n g t h s o f 50 t o 100 t i m e s those o f "massive" g l a s s . Due to the wide v a r i a t i o n i n the e f f e c t i v e n e s s o f f l a w s - not always s u r f a c e - s t r e n g t h v a l u e s f o r g l a s s ex h i b i t c o n s i d e r a b l e s c a t t e r . E x p e r i m e n t s must be performed on a s t a t i s t i c a l b a s i s . .Table 2 g i v e s t h e r e s u l t s o f t h e s t a t i s t i c a l e v a l u  a t i o n o f t e n s i l e f r a c t u r e d a t a . A l l subsequent v a l u e s quoted i n the t e x t w i l l be the n u m e r i c a l mean o f t h r e e d e t e r m i n a t i o n s w i t h the s t a n d a r d d e v i a t i o n o c c u r r i n g i n T a b l e 2 b e i n g a p p l i e d . S i n c e the s t r e n g t h o f g l a s s i s s t r a i n r a t e dependent, the e f f e c t o f s t r a i n r a t e v a r i a t i o n was d e t e r m i n e d . Table 3 l i s t s the e f f e c t o f s t r a i n r a t e on the s t a t i s t i c a l s c a t t e r . At h i g h and low l o a d i n g r a t e s the s c a t t e r i s l a r g e s t , due TABLE 2 S t a t i s t i c a l A n a l y s i s S t r a i n Rate .0 3"/min, C o e f f . o f No. o f Mean S t r a i n S t d . V a r i a n c e S o l i d Environment Measurements u"/" Dev t % Vycor Vacuum G l a s s 8xl0- 7mm Hg 15 26 8 4 8 18 A i r 15 193 51 24 H„0 15 161 2 7 15 CCl- 4 . 15 216 37 17 Kimble Vacuum G l a s s 8x10-7mm Hg 15 2 94 44 15 A i r 15 165 . 2 8 17 H 20 15 138 15 11 P l e x i - Vacuum g l a s s 1 0 ~ 3 mm Hg 10 12 8 9 7 :. A i r 10' 132 12 9 TABLE 3 The E f f e c t o f S t r a i n Rate on the T e n s i l e F r a c t u r e S t r e n g t h o f Kimble G l a s s ( I n A i r ) S t r a i n Mean C o e f f . o f Rate No. o f S t r a i n S t d . V a r i a n c e "/Min. Measurements u"/" Dev. % 0.15 15 176 42 24 0.03 15 165 28 17 0.006 15 142 47 33 t o the c r i t i c a l dependence on f l a w geometry. An i n t e r m e d i a t e r a t e o f 0.03"/min was s e l e c t e d f o r a l l f u r t h e r measurements, u n l e s s o t h e r w i s e s t a t e d . 5 : 2 YJ19££L^\£££ The porous g l a s s , vacuum t r e a t e d and not h e a t e d above 200°C, w i l l have a s u r f a c e almost c o m p l e t e l y c o v e r e d w i t h h y d r o x y l groups. The hydrogen i n these h y d r o x y l s are (85) p a r t l y p r o t o n i z e d and are e l e c t r o n a c c e p t o r c e n t r e s T h i s r e s u l t s i n an i n c r e a s e d a d s o r p t i o n o f s u b s t a n c e s h a v i n g e l e c t r o n donor p r o p e r t i e s , such as w a t e r , a l c o h o l s , amines, and a r o m a t i c hydrocarbons.. Removal o f t h e s i l a n o l s u r f a c e s h a r p l y d e c r e a s e s the. a d s o r p t i o n o f t h e above (86) mentioned substan.ces . T c , ' 4 . n 4 . i ( 87) ( 88 ) I n i r a and s p e c t r a l s t u d i o s on porous g l a s s i n d i c a t e t h a t a l a r g e p e r c e n t a g e o f the s u r f a c e OH groups i n t e r a c t , w i t h o t h e r s r e s u l t i n g i n two t y p e s o f s u r f a c e h y d r o x y l groups, the f r e e groups and the hydrogen bonded groups. F i g . 181 shows a s u g g e s t e d model f o r the s u r f a c e FI \ 0---H — 0 0 K 1 . / X S i S i S i S i o ^ xo ^ 0 0 FIGURE 18.6. MODEL OF SILANOL SURFACE I f we. r e p r e s e n t a hydrogen bonded system as X-H...Y where H...Y i s the hydrogen bond and X-H the normal bond, then t h e s t r e n g t h o f the hydrogen b o n d i n g w i l l be g i v e n by a s h i f t to l o w e r f r e q u e n c i e s of the. X-H bond s t r e t c h i n g f r e q u e n c y . Table 4 g i v e s t h e r e s u l t s c f v a r i o u s workers i n o r d e r o f i n c r e a s i n g hydrogen bond s t r e n g t h f o r the systems s t u d i e s . A v a l u e f o r n - b u t y l a m i n e i s not a v a i l a b l e but might- be e x p e c t e d to be o f the same o r d e r as the ammonia group. The i m p o r t a n c e o f these r e s u l t s w i l l l i e i n the e f f e c t i v e s c r e e n i n g power o f the adsorbed s p e c i e s . The s t r o n g e r the i n t e r a c t i o n w i t h the s u r f a c e , t h e g r e a t e r . t h e s c r e e n i n g power. However the bond s t r e n g t h r e f e r s t o i n d i v i d u a l bonds formed and does n o t take i n t o a c c o u n t the a d s o r b a t e s i z e o r o r i e n t a t i o n on the s u r f a c e . Hence a more e f f e c t i v e s c r e e n e r might be a group o f l e s s e r hydrogen bond s t r e n g t h but c a p a b l e o f a d s o r b i n g on more a c t i v e s i t e s due to the p r o p e r s t e r i c f a c t o r s , e.g. w a t e r w i l l be a b e t t e r s c r e e n e r than a c e t o n e . The n a t u r e o f the a d s o r p t i o n p r o c e s s i s b e s t s t u d i e d through the a d s o r p t i o n i s o t h e r m . T h i s p l o t o f volume adsorbed at e q u i l i b r i u m p r e s s u r e p and c o n s t a n t t e m p e r a t u r e , may be c o m p r i s e d o f t h r e e phenomena; the i n c r e a s i n g a d s o r p t i o n to the monolayer, a m u l t i l a y e r b u i l d up, and a c o n d e n s a t i o n e f f e c t i n c a p i l l a r i e s o r p o r e s . ' (94) . Erunauer e t a l . c l a s s i f i e d the i s o t h e r m s m f i v e main t y p e s . T y p i c a l i s o t h e r m s on porous g l a s s e x h i b i t the o (a) Nitrogen 10 20 30 40 50 60 70 o |- (b) Carbon Dioxide 10 • 0 20 30 40 50 P cms Hg FIGURE 19' ADSORPTION ISOTHERMS ON VYCOR GLASS (25°C) FIGURE 20 ADSORPTION ISOTHERMS ON VYCOR GLASS (25°C) 9 5 . TABLE 4 S h i f t s i n Frequency o f S u r f a c e OH Groups on the A d s o r p t i o n o f Gases at Room Temperatures on. Porous G l a s s S h i f t A d s o r b a t e cms"-'- Re f e r e n c e N 2 24 (-170°C) 90 Benzene 110 91 Water 290 93 Acetone 330 89 Ammonia 820 89 s i g m o i d o r S-shaped, t y p e I I i s o t h e r m s , w i t h t h e e x c e p t i o n o f benzene, w h i c h appears to be more o f a type V, due to the s m a l l monomolecular f o r c e s o f a d s o r p t i o n ( F i g s . 19, 20, 21). A l l i s o t h e r m s were measured a t t h e r m o s t a t e d ambient t e m p e r a t u r e . In the case o f t h e gases and C 0 2 , p r e s s u r e s were i n c r e a s e d up to one atmosphere. S i n c e the s a t u r a t e d vapour p r e s s u r e o f these gases at 25°C i s g r e a t e r than 50 atmospheres, v e r y l i t t l e a d s o r p t i o n c o u l d be d e t e c t e d . 96. 97. TABLE 5 E q u i l i b r i u m A d s o r p t i o n Rates on Vycor G l a s s A d s o r b a t e Time to E q u i l i b r i u m Immediate c o 2 Immediate 2 0 minutes Benzene Immediate Acetone 1 0 minutes E t h a n o l 1 0 minutes n - B u t y l a m i n e 1 8 0 minutes E q u i l i b r i u m was a c h i e v e d when t h r e e c o n s e c u t i v e p r e s s u r e r e a d i n g s o v e r a p e r i o d o f 1 5 minutes were i d e n t i c a l , h a v i n g a l l o w e d a 1 5 minute p e r i o d f o r t h e r m a l e q u i l i b r i u m to be a c h i e v e d . Table 5 l i s t s t he v a r y i n g e q u i l i b r i u m t i m e s . P h y s i c a l a d s o r p t i o n i s n o r m a l l y r a p i d w h i l s t c h e m i s o r p t i o n may be r a p i d o r slow. The r a t e b e h a v i o u r i s i n d i c a t i v e o f t h e presence o f an a c t i v a t i o n energy, T a b l e 6 g i v e s the v a r i o u s parameters o f i n t e r e s t c a l c u l a t e d from t h e s e i s o t h e r m s . D e t a i l s o f the c a l c u l a t i o n s a re g i v e n i n Appendix D, The de c r e a s e i n s u r f a c e t e n s i o n on a d s o r p t i o n - may TABLE 6 R e l a t i v e V a p o u r P r e s s u r e s a t M o n o l a y e r Volumes (Vm) Vapour M o n o l a y e r V o l Vm c c s S.T.P. H 20 9 0.9 - B u t y l a m i n e 22.5 A c e t o n e 36.4 Benzene 17.0 FIGURE 23 V d vs log P/PQ (Vycor Glass) 80 0 .2 .4 -.6 .8 1.0 R/Po FIGURE 25 CHANGE IN SURFACE TENSION WITH INCREASE IN VAPOUR PRESSURE (Vycor Glass) be computed f r o m a p l o t o f Vads v e r s u s l o g Py/PQ by a p p l y i n g t h e G i b b s e q u a t i o n i n t h e f o r m * ^ * P/P, o r . _ RT -Ay - — MS V d l n P/P Q (See A p p e n d i x D f o r d e t a i l s o f t h e c o m p u t a t i o n ) . T y p i c a l p l o t s a r e shown i n F i g s . 24 and 25. Some u n c e r t a i n t y i n e s t i m a t i n g t h e a r e a u n d e r t h e c u r v e i s e v i d e n t s i n c e on a l o g s c a l e z e r o p r e s s u r e c o r r e s p o n d s t o minus i n f i n i t y . However e x t r a p o l a t i o n t o z e r o amount a d s o r b e d i s s u f f i c i e n t l y a c c u r a t e f o r t h e p u r p o s e o f t h i s work. Maximum d e c r e a s e o f s u r f a c e t e n s i o n ( y ) i s n o t r e a c h e d u n t i l w e l l i n t o t h e c o n d e n s a t i o n r e g i o n . A t low c o v e r a g e t h e l o w e r i n g o f y i s v e r y s m a l l . In t h e l i g h t o f th e G r i f f i t h e q u a t i o n i t m i g h t be e x p e c t e d t h a t maximum weaken i n g would o c c u r a t m u l t i l a y e r a d s o r p t i o n v a l u e s . F i g . 26 i l l u s t r a t e s t h e s h a p e s o f t h e p r e d i c t e d f r a c t u r e i s o t h e r m s c a l c u l a t e d f r o m t h e G r i f f i t h e q u a t i o n , by a s s u m i n g a c o n s t a n t c r i t i c a l c r a c k s i z e and u s i n g t h e s u r f a c e f r e e e n e r g y c h a n g e s computed a b o v e . The f r a c t u r e i s o t h e r m i s t h e v a r i a t i o n i n t e n s i l e f r a c t u r e s t r e n g t h w i t h i n c r e a s i n g c o n c e n t r a t i o n o f e n v i r o n m e n t . The f r a c t u r e d a t a were measured f o r t h e s y s t e m s s t u d i e d i n t h e a d s o r p t i o n e x p e r i m e n t s . The v a r i o u s r e s u l t s w i l l be d i s c u s s e d by c o r r e l a t i n g t h e d a t a f r o m (a) A d s o r p t i o n 10! TABLE 7 (a) The E f f e c t o f Dry N on the T e n s i l e 1 F r a c t u r e S t r e n g t h o f V y c o r G l a s s S t r a i n Rate 0.03"/Min. En v i ronment_ Vacuum 15 cms Hg 25 cms Hg 70 cms Hg T e n s i l e S t r e n g t h ( D . s . i . ) 86 9 2 8627 7968 8755 (b) The E f f e c t o f Dry C0 2 on the T e n s i l e F r a c t u r e S t r e n g t h o f Vyc o r G l a s s S t r a i n Rate 0.03"/Min. Environment Vacuum 2 5 cms Hg 40 cms Hg 70 cms Hg T e n s i l e S t r e n g t h ( p . s . i . ) 8692 7822 8055 7991 10 JZZ +-> c CD s_ +-> oo cu s- 4-> o ro S- CD I/) c cu I— ro i o i/) C L .1 x Water Vapour o n-Butylamine .4 .5 P/P .6 .7 o FIGURE 27 TENSILE FRACTURE STRENGTH vs. RELATIVE PRESSURE''F0R VYCOR GLASS 1.0 }-> o 107 S t u d i e s ; (b) S u r f a c e f r e e energy changes and, (c) F r a c t u r e . i s o t h e r m s . ( i ) Dry N i t r o g e n and Carbon D i o x i d e A t 25°C v e r y l i t t l e a d s o r p t i o n o c c u r s on t h e g l a s - I • s u r f a c e ( F i g . 19). The dry gases show no e f f e c t on.the f r a c t u r e s t r e n g t h t o a p r e s s u r e p f 1 atmosphere, [ T a b l e 7 and ( b ) ] . ( i i ) Benzene Benzene r e a c t s w i t h t h e s i l a n o l s u r f a c e by f o r m i n g ir-bonded complexes w i t h the a c i d h y d r o x y l s o f the s u r f a c e . 0 - H - . / V S i The i n t e r a c t i o n i s r e l a t i v e l y weak as e v i d e n c e d by the s m a l l r e d u c t i o n s i n s u r f a c e t e n s i o n o f t h e s o l i d s u r f a c e , ( F i g . 25). The r e l a t i v e d e c r ease i n t h e f r a c t u r e energy accompanying a d s o r p t i o n ( F i g . 2 8 ) , shows a s l i g h t g r a d u a l decrease t o a minimum c o r r e s p o n d i n g t o a r e l a t i v e p r e s s u r e o f = .8, F i g . 26 demonstrates the d e v i a t i o n P • ' 1 9 j from the e x p e r i m e n t a l c u r v e . Tensile Fracture Strength (p.s.i. x TO"3) CD a p o r o CO p o o p o m PO m CO < </> PO m m - u p o m o o o o PO m o p o - < o o p o CD > OO OO CO - p i 00 o — • — I — ro O J 4 > cn T 1 — — I 1— s X o D> 00 O r o f D P3 r + N O n> r p : f D 80 L 1C9. ( i i i ) Acetone S t r o n g hydrogen b o n d i n g , ( T a b l e 4 ) , r e s u l t s i n a l a r g e r s u r f a c e t e n s i o n r e d u c t i o n t h a n w i t h benzene. ( F i g . 2 5.) The maximum r e d u c t i o n o f t e n s i l e f r a c t u r e s t r e n g t h o c c u r r e d a t a p p r o x i m a t e l y P/P Q = .05, w h i c h c o r r e s p o n d s to a v a l u e o f o n l y 2 6 erg/cms i n t h e s u r f a c e t e n s i o n r e d u c t i o n . The s t r e n g t h o f the hydrogen bond formed ( a s h i f t o f Av= 350 cms "S i s s l i g h t l y g r e a t e r than t h a t formed w i t h w a t e r (290 cms-'1'). The s t r e n g t h r e d u c t i o n however i s o n l y 4 0% o f t h a t caused by 'water. T h i s i s p o s s i b l y due t o the l a r g e r acetone m o l e c u l e a d s o r b i n g on fewer Oil s i t e s and hence s c r e e n i n g the s u r f a c e to a l e s s e r degree. ( i v ) n - B utylamine The amine adsorbs s t r o n g l y from the vapour phase, f o r m i n g a m o n o l a y e r ' a t a very low r e l a t i v e p r e s s u r e (0.005) ( F i g . 20 and Table 5 ) . T r a c e s o f the amine cause a r e d u c t i o n i n t e n s i l e f r a c t u r e s t r e n g t h t o a v a l u e o f 75% o f the vacuum f r a c t u r e s t r e n g t h . Subsequent i n c r e a s e s i n vapour c o n c e n t r a  t i o n appear t o cause a s l i g h t s t r e n g t h e n i n g e f f e c t . L a t e r a l i n t e r a c t i o n o f t h e adsorbed s p e c i e s c o u l d e x p l a i n t h i s i n  c r e a s e , which i s not l a r g e enough t o l i e o u t s i d e o f t h e s t a n d a r d d e v i a t i o n f o r t h e measurements, and hence may be due t o s c a t t e r i n f r a c t u r e measurements. . . 110. (v) Water Water r e a c t s s t r o n g l y w i t h the s i l a n o l s u r f a c e . At a r e l a t i v e p r e s s u r e o f 0.05, the s t r e n g t h r e d u c t i o n has r e a c h e d 70% o f i t s maximum decrease ( F i g . 2 7 ) . A minimum t e n s i l e s t r e n g t h v a l u e i s re a c h e d a t ; P/P Q = .8. The s u r f a c e t e n s i o n r e d u c t i o n a t t h e p o i n t P/P Q = 0.05 i s o n l y a f r a c t i o n o f t h e maximum r e d u c t i o n c l o s e t o s a t u r a t e d ' v a p o u r p r e s s u r e ( F i g . 2H). A comparison between the f r a c t u r e i s o t h e r m s f o r water and n - b u t y l a m i n e , would l e a d one t o p r e d i c t , i n the l i g h t o f t h e G r i f f i t h e q u a t i o n , a f a r g r e a t e r s t r e n g t h decrease a t low cov e r a g e s f o r t h e amine vapour. R e s u l t s show' water t o g i v e t h e g r e a t e r s t r e n g t h d e c r e a s e . Thus a mechanism i n terms o f s u r f a c e energy r e d u c t i o n a l o n e would not be v a l i d . T h i s c o n c l u s i o n might be drawn by c o n s i d e r i n g t h e f r a c t u r e i s o t h e r m f o r water and comparing the s t r e n g t h v a l u e s w i t h the s u r f a c e t e n s i o n r e d u c t i o n at v a r i o u s r e l a t i v e p r e s s u r e s . Ob v i o u s l y the l a r g e s t d e c r e a s e would be e x p e c t e d i n the vapour phase at v a l u e s c l o s e t o s a t u r a t i o n pressure.. I t must be emphasized, however, t h a t g r e a t c a r e s h o u l d be e x e r c i s e d i n a p p l y i n g b u l k measurements t o f r a c t u r e t h e o r i e s . S i n c e t h e f r a c t u r e p r o c e s s i n a c t i v e e n vironment i n  v o l v e s a mechano-chemical mechanism, the p r o c e s s e s o c c u r r i n g i n the s t r e s s e d zone might be very d i f f e r e n t from t h o s e ' o c c u r r i n g i n the b u l k o f t h e s o l i d . . The c o n c e n t r a t i o n o f a d s o r b i n g s p e c i e s i n the s t r e s s e d zone w i l l be h i g h e r t h a n i n d i c a t e d from an ad-" • 111. s o r p t i o n i s o t h e r m a t t h e same r e l a t i v e p r e s s u r e . Hence the s u r f a c e t e n s i o n d e c r e a s e s i n t h e s t r e s s e d r e g i o n w i l l be v e r y much g r e a t e r than those i n d i c a t e d , s i n c e the r e l a t i v e p r e s s u r e i n a s u r f a c e f l a w may be c l o s e t o s a t u r a t i o n o r even t h a t o f the condensed l i q u i d phase. Hence a s u b s t i t u t i o n o f t h e s u r f a c e f r e e energy v a l u e s i n t o the G r i f f i t h e q u a t i o n and assuming a c o n s t a n t c r i t i c a l c r a c k s i z e , w i l l not be a v a l i d t e s t f o r the G r i f f i t h approach. F i r s t l y , the assumption o f a c o n s t a n t c r i t i c a l c r a c k s i z e i s e r r o n e o u s , s i n c e the en vironment i n f l u e n c e s the c r a c k growth phenomenon as w e l l as the specimen's l i m i t i n g s t r e n g t h . S e c o n d l y , f o r the reasons s t a t e d above, a comparison o f the c a l c u l a t e d s t r e n g t h v a l u e w i t h the measured s t r e n g t h , c o u l d not be e x p l a i n e d i n terms o f p l a s t i c f l o w at t h e c r a c k t i p . F o r w a t e r , t h e v a l u e of the t e n s i l e f r a c t u r e s t r e n g t h a t the s a t u r a t e d vapour p r e s s u r e i s the same as f o r s o a k i n g i n the l i q u i d , w h i l s t f o r a l l o t h e r a d s o r b a t e s measured, the vapour phase gave h i g h e r s t r e n g t h v a l u e s than t h e l i q u i d . Such d i f f e r e n c e s are a t t r i b u t e d t o t h e pr e s e n c e o f w a t e r i n t h e v a r i o u s s o l v e n t s . I n a l l e x p e r i m e n t s i n t h e vapour phase t h e e f f e c t o f t h e environment was v e r y much l e s s t han t h a t r e p o r t e d by v a r i o u s o t h e r w o r k e r s . I t i s f e l t t h a t the d i f f e r e n c e s a re caused by d i f f e r e n t l e v e l s o f m o i s t u r e c o n t a m i n a t i o n , s i n c e m o i s t u r e i s the dominant adsorbate, f o r g l a s s systems. 0 0 0 0 0 0 10 20 30 V, e r g s / c m ? (a) •  N i t r o g e n , Oxygen and Argon (b) Water Vapour ( c ) Acetone FIGURE 29. VOLUME CHANGES OF VYCOR GLASS WITH ADSORPTION. ( 8 4 } Volume Changes on A d s o r p t i o n (8 4) The work o f Y a t e s , i n s t u d y i n g volume changes on porous g l a s s accompanying a d s o r p t i o n , d e m o n s t r a t e s th e i m p o r t a n t a s p e c t s o f the depth a c t i o n o f c h e m i c a l b i n d i n g i n p h y s i c a l a d s o r p t i o n . Even n o b l e gases were c a p a b l e o f a d s o r p t i o n on t h e h i g h energy s u r f a c e and s c r e e n i n g t h e <.. + + + + S i c o r e s . F i g s . 29a,b,c show the l e n g t h changes o f porous ";:ycor g l a s s a f t e r the a d s o r p t i o n o f t h e c o r r e s p o n d i n g vapours ( 8 3 ) ( 84 ) used i n t h i s s t u d y , as o b t a i n e d by v a r i o u s workers The a d s o r p t i o n o f N 2 , C 0 o , and w a t e r r e s u l t i n e x p a n s i o n s which are a l i n e a r f u n c t i o n o f the f r e e energy l o w e r i n g . Acetone gave l a r g e c o n t r a c t i o n s i n t h e low c o verage r e g i o n s , f o l l o w e d by an e x p a n s i o n as a d s o r p t i o n i n c r e a s e d . One might t h e r e f o r e e x p e c t v e r y d i f f e r e n t s t r e n g t h p r o p e r t i e s i n t h e e x p a n s i o n and c o n t r a c t i o n r e g i o n s o f t h e " i s o t h e r m . Ad s o r p t i o n r e s u l t s i n a d e c r e a s e i n t h e s u r f a c e t e n s i o n b r i n g i n g about a change i n t h e s u r f a c e s t r e s s and t h e s o l i d expands. An e x p a n s i o n w i l l r e s u l t i n an i n c r e a s e i n the t e n s i l e s t r e s s e s a t an e x i s t i n g s u r f a c e c r a c k t i p , t h e r e b y r e s u l t i n g i n a weakening e f f e c t . C o n v e r s e l y a c o n t r a c t i o n , a l t h o u g h a r i s i n g from an i n c r e a s e i n s u r f a c e t e n s i o n , causes a com p r e s s i v e a c t i o n a c r o s s s u r f a c e s f l a w s and s h o u l d b r i n g about a s t r e n g t h increase-. As shown i n F i g s . 28, no such s t r e n g t h i n c r e a s e was e x p e r i e n c e d w i t h a c e t o n e . , The f o l l o w i n g c o u r s e I H . o f e v e n t s i s suggested. The volume changes measured are b u l k e f f e c t s ' r e  s u l t i n g f r om an o v e r a l l i n t e r a c t i o n o f t h e vapour w i t h the s o l i d . - At v e r y low coverages (<< V ) , m o l e c u l e s w i l l be ad- m s o r b e d a t p r e f e r e n t i a l h i g h energy s i t e s . S u r f a c e f l a w s would c o n s t i t u t e such s i t e s . I f a t e n s i l e l o a d i s a p p l i e d to the s o l i d , a c o n c e n t r a t i o n o f a d s o r b a t e w i l l o c c u r i n the s t r e s s e d r e g i o n , due to the i n c r e a s e d i n t e r a t o m i c d i s t a n c e s . The g r e a t e r t h e l o a d the g r e a t e r the r e a c t i v i t y o f t h i s s t r e s s e d zone. The c o n c e n t r a t i o n o f a d s o r b a t e i n t h i s zone w i i l then be v e r y much l a r g e r t h a n i n t h e b u l k specimen, t h e r e b y e x c l u d i n g any c o n t r a c t i o n s from o c c u r r i n g in- t h e s t r e s s e d r e g i o n , s i n c e c o n t r a c t i o n s were e x p e r i e n c e d a t v e r y low c o v e r a g e s . Thus w o r k i n g from an i d e a l vacuum c l e a n e d specimen, a l l a d s o r b a t e s w i l l r e s u l t i n a s t r e n g t h r e d u c t i o n mechanism. • , ' ' • • 5 : 3 F^racJLure I s o t h e r m s o n J 5 , , ^ ^ j : . ^ . - . ^ 2 ^ 1 ^ s The r e s u l t s e x p e r i e n c e d w i t h Kimble g l a s s a re shown i n F i g s . 32 and .33. In a l l c a s e s the e f f e c t s are s i m i l a r t o tho s e o b t a i n e d w i t h Vycor g l a s s , w i t h t h e e x c e p t i o n o f n - b u t y l a m i n e . Water, acetone and benzene r e s u l t e d i n l a r g e r d e c r e a s e s i n s t r e n g t h than w i t h t h e porous g l a s s . The d i f f e r e n c e may be a t t r i b u t e d t o two f a c t o r s . F i r s t l y , due - to the h i g h s u r f a c e a r e a o f t h e porous specimens, t h e removal o f s u r f a c e m o i s t u r e was i n c o m p l e t e . The vacuum.strength o n-Butylamine x Water Vapour 1 i i i ; i i i t i 0 • .1 .2 .3 .4 fy .5 . 6 . 7 .8 .9 IvO FIGURE"32 TENSILE FRACTION STRENGTH vs. RELATIVE PRESSURE FOR KIMBLE GLASS FIGURE 33 TENSILE FRACTURE STRENGTH.vs. RELATIVE PRESSURE FOR KIMBLE GLASS 117. TABLE 8 E f f e c t o f A d s o r p t i o n from Aqueous S o l u t i o n s Xl^JL-^3.s5 Kimble G l a s s T e n s i l e S t r e n g t h . T e n s i l e S t r e n g t h Environment p . s . i . Environment p . s . i . H 20 5096 H O 4368 10~ 4M C 1 2 T A 3 5262 10~ 4M C 1 2TAB . 4416 10~ 3M C 1 2TAB 5216 •10~ 3M C 1 2TAB 4343 v a l u e o f the Kimble g l a s s was g r e a t e r t h a n t h a t o f the ;/ycor c y l i n d e r s . The l a t t e r ' s s t r e n g t h c o u l d be i n c r e a s e d w i t h p r o l o n g e d pumping (8,800 p s i a f t e r 168 h r s . ) . S e c o n d l y , t h e h i g h s u r f a c e a r e a g l a s s would c o n t a i n a g r e a t e r number o f s u r f a c e f l a w s and t h e p r o b a b i l i t y o f b e i n g weaker would be h i g h , w h i l s t changes i n s u r f a c e s t r e s s would be c u s h i o n e d by the porous n a t u r e o f t h e m a t e r i a l . n - B u t y l a m i n e r e s u l t e d i n o n l y s m a l l r e d u c t i o n s i n s t r e n g t h o f : t h e Kimble g l a s s . The p r e s e n c e . o f the network m o d i f i e r s Na 20 and A ^ O g , might reduce t h e a d s o r p t i v i t y o f the s o l i d f o r t h e amine. A d s o r p t i o n from aqueous s o l u t i o n f a i l e d t o p r o v i d e any a d d i t i o n a l weakening o f e i t h e r the Kimble o r the V y c o r g l a s s (Table 8 ) . S i n c e the s o l v e n t , w a t e r , would be p r e  f e r e n t i a l l y a t t r a c t e d t o t h e s u r f a c e any a d d i t i o n a l s u r f a c e f r e e energy d e c r e a s e would be s m a l l . These r e s u l t s have been s u b s t a n t i a t e d on a q u a r t z i t i c r o c k specimen. 5:H Po1ymethyl Methacry1ate F r a c t u r e i s o t h e r m s were measured on p o l y m e t h y l m e t h a c r y l a t e as d e s c r i b e d e l s e w h e r e . Due t o the low energy s u r f a c e i t was found the h i g h vacuum p r e t r e a t m e n t was not n e c e s s a r y . T a b l e 9'gives the e f f e c t s o f f o u r vapours on the t e n s i l e f r a c t u r e s t r e n g t h . I n c r e a s i n g vapour c o n c e n t r a t i o n showed no measurable s t r e n g t h r e d u c t i o n compared w i t h t h e TABLE 1 E f f e c t o f V a p o u r E n v i r o n m e n t on t h e T e n s i l e S t r e n g t h o f P o l y m e t h y l M e t h a c r y l a t e E n v i r o n m e n t Benzene R e l a t i v e P r e s s u r e .15 .42 . 5-6 .84 T e n s i l e F r a c t u r e S t r e n g t h ( p . s . i . ) Vapour Load b e f o r e l o a d b e f o r e v a p o u r 4375 4288 4294 4316 4 326 4 2 94 A c e t o n e .08 4321 .36 ' 4311 4305 .59 4286 .79 4282 4301 C a r b o n T e t r a c h l o r i d e .17 ..33 .65 .77 4 314 4318 4297 4292 4296 4287 'Water . 15 .46 .68 .88 4 366 4305 4291 4361 4 2 94 4 311 120. TABLE 10 The E f f e c t o f Immersion on T e n s i l e S t r e n g t h o f P o l y m e t h y l M e t h a c r y l a t e ( S t r a i n Rate 0.03"/Min.) Immersion L i q u i d T e n s i l e F r a c t u r e S t r e n g t h 1 * S » 1 • Vacuum H 2 0 Ace tone Benzene Carbon T e t r a c h l o r i d e 4454 4362 1562 1634 1518 u-1 • Acetone x Benzene o Water © Air X — 4 5 6 Time to Failure (Mins,) 10 FIGURE 31 STATIC.FATIGUE CURVE FOR- POLYMETHYL METHACRYLATE ro c l e a n specimen (10~ mm Hg vacuum). I n each case t h e l o a d was a p p l i e d subsequent t o the i n t r o d u c t i o n o f t h e vapour. S i n c e p o l y m e t h y l m e t h a c r y l a t e i s known t o c r a z e under s t r e s s , a s e r i e s o f measurements were made by a p p l y i n g the l o a d b e f o r e i n t r o d u c i n g t h e vapour. A g a i n f a i l u r e d i d not o c c u r i n t h e vapour phase at r e d u c e d l o a d s . W i t h t h e n o t e d e x c e p t i o n o f w a t e r , immersion i n the l i q u i d r e s u l t e d i n f a i l u r e a t a p p r o x i  m a t e l y a 50% r e d u c t i o n i n Load ( T a b l e 1 0 ) . Water had no i n f l u e n c e on t h e s t r e n g t h p r o p e r t i e s , i l l u s t r a t i n g w e t t i n g t o be an i m p o r t a n t a s p e c t o f s t r e s s e n v i r o n m e n t a l c r a c k i n g . Water does not wet p o l y m e t h y l m e t h a c r y l a t e . F i g . 31, shows the r e s u l t s o f two t y p i c a l ' f a t i g u e c u r v e s . The specimens were l o a d e d to a f r a c t i o n o f t h e break i n g l o a d i n vacuum, and the time t o f a i l u r e measured on i n t r o  d u c i n g acetone and benzene. F a i l u r e t i m e s o f g r e a t e r than 10 m i n u t e s were not r e c o r d e d . Acetone w i t h a s t r o n g a f f i n i t y f o r the p l a s t i c , ( b e i n g a s o l v e n t f o r p o l y m e t h y l m e t h a c r y l a t e ) • F causes f a i l u r e w i t h e x p l o s i v e v i o l e n c e at h i g h e r l o a d s (- =.8 r v a c and i n s h o r t e r t i m e s than immersion i n benzene. At a r e l a t i v e l o a d o f .38 the c u r v e s i n t e r s e c t and benzene g i v e s f a i l u r e i n s h o r t e r t i m e s t h a n a c e t o n e . 'Due t o t h e s o l v a t i o n p r o c e s s i n a c e t o n e , l o n g e r immersion t i m e s l e a d to a c r a c k h e a l i n g mechanism, t h e J o f f e F e f f e c t . At low r e l a t i v e l o a d s (—=— •= .4) the c r a c k c o u l d be Fyac_ seen t o form on i n t r o d u c i n g the l i q u i d but the specimen d i d n o t f a i l w i t h i n t h e 10 minute p e r i o d . I t would appear under (a) Specimen Untreated (b) Specimen Soaked in 2N NaOH for 1HR FIGURE 34 ELECTRON MICROGRAPH OF END FACE OF VYCOR GLASS CYLINDER (X2.000) t h e s e c o n d i t i o n s t h a t the c r a c k p r o p a g a t i o n r a t e was s l o w e r t h a n the r a t e o f d i s s o l u t i o n o f t h e p l a s t i c , i n the s t r e s s e d r e g i o n , i n a c e t o n e . R e s u l t s p r e s e n t e d i n t h e s e c t i o n on t h e J o f f e e f f e c t r e i n f o r c e the above c o n c l u s i o n . The c r a c k p r o p a g a t i n g s t a & e . i s t h e r e f o r e t h e c r i t i c a l f a c t o r i n d e t e r m i n i n g t h e s t r e n g t h c h a r a c t e r i s t i c s . B e r r y * h a s shown t h a t p o l y m e t h y l m e t h a c r y l a t e undergoes p l a s t i c f l o w at t h e c r a c k t i p i n the p r o c e s s o f f r a c t u r e . A l a y e r o f m a t e r i a l w i t h a l t e r e d s t r u c t u r e i s c l e a r l y v i s i b l e and t h e a p p a r e n t s u r f a c e energy i s e x t r e m e l y h i g h . The c r a c k p r o p a g a t e s from the s u r f a c e i n t o t h e b u l k w i t h v e r y low v e l o c i t y compared w i t h t h e u n s t a b l e f r a c t u r e v e l o c i t y . The (97) low r a t e o f p r o p a g a t i o n i s a f u n c t i o n o f the. a p p l i e d l o a d ^ : ^ The E f f e c t o f Immersion The J o f f e E f f e c t J o f f e , i n 1 9 2 8 * ^ 8 \ demonstrated t h e 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 o f NaCl c r y s t a l s broken under w a t e r o r i n s a t u r a t e d NaCl s o l u t i o n . The e f f e c t i s a t t r i b u t e d to t h e de c r e a s e i n s t r e s s c o n c e n t r a t i o n a t the c r a c k t i p , by b l u n t i n g o f t h e t i p , i n one o f two ways. F i r s t l y , a d i s s o l u t i o n p r o c e s s i n the s t r e s s e d r e g i o n and s e c o n d l y , d e p o s i t i o n o f p r e c i p i t a t e from s o l u t i o n w i t h i n the c r a c k , b oth e f f e c t s r e  s u l t i n g i n a r e d u c t i o n i n s t r e s s c o n c e n t r a t i o n and i n c r e a s e i n s t r e n g t h . 3 o t h porous g l a s s and p o l y m e t h y l m e t h a c r y l a t e e x h i b i t the J o f f e " e f f e c t . 125. FIGURE 35 EFFECT OF SOAKING TIME ON TENSILE FRACTURE STRENGTH (VYCOR GLASS) 15 (a) +-> CD o> s - 4-> r o 00 I c OJ r— S- Z5 > o rci t- -r- 10 to c OJ •- n-Hexane H20 30 60 Time (Mins) 90 (b) 4-> CD OJ S- 4-> OO OO I o 0J i— s - 3 X 4-> o fO i~ -r- u_ 0J i — Q. CO C 0J 12 _L 2N NaOH 0.2N NaOH 30 60 Time (Mins) 90 FIGURE 35 (Cont'd) 15: TO Sodium Si 1icate II Sodium Silicate 0.11 30 60 Time (Mins) 90 127. ( i ) V y c o r G l a s s F i g . 35 shows t h e e f f e c t on t h e t e n s i l e s t r e n g t h p r o p e r t i e s o f t h e g l a s s on s o a k i n g i n v a r i o u s l i q u i d s . A l l •specimens were s o a k e d i n t h e s o l u t i o n and b r o k e n i n a i r . The i m m e d i a t e e f f e c t o f i m m e r s i o n i n w a t e r i s a d e c r e a s e i n s t r e n g t h f r o m t h e vacuum s t r e n g t h v a l u e . Hexane, h a v i n g no a f f i n i t y f o r t h e g l a s s , shows no s t r e n g t h c h a n g es w i t h t i m e . D i s t i l l e d w a t e r shows an i n c r e a s e o f a p p r o x i m a t e l y 45% a f t e r a s o a k i n g p e r i o d o f 1 h o u r . D i l u t e (0.2N) NaOH c a u s e s a r a p i d i n i t i a l i n c r e a s e f r o m t h e d i s t i l l e d w a t e r v a l u e , w i t h no f u r t h e r i n c r e a s e w i t h t i m e o c c u r r i n g . 2N NaOH, w h i c h c a u s e s t h e g l a s s t o f u s e , a d e q u a t e l y d e m o n s t r a t e s t h e i m p o r t a n c e o f s u r f a c e d e f e c t s . F i g . 34a i s - an e l e c t r o n m i c r o g r a p h o f t h e e n d f a c e o f t h e p o r o u s g l a s s p r i o r t o s o a k i n g i n 2H NaOH. F i g . 34b i l l u s t r a t e s t h e d i s  s o l u t i o n p r o c e s s r e s u l t i n g i n a b l u n t i n g o f s h a r p e d g e s . The o v e r a l l i n c r e a s e i n s t r e n g t h r e s u l t s f r o m r a p i d d i s s o l u t i o n i n t h e h i g h l y a l k a l i n e , medium. D i l u t e Na^O.SiO^ gave a s l i g h t d e c r e a s e i n s t r e n g t h w i t h t i m e . S i n c e a more c o n c e n t r a t e d s o l u t i o n (more a l k a l i n e ) r e s u l t e d i n a s t r e n g t h e n i n g e f f e c t , F i g . 3 5c, a wet t i n g mechanism s u g g e s t s i t s e l f i n t h e c a s e o f t h e d i l u t e s i l i c a t e . W e t t i n g and s p r e a d i n g w i l l be d e a l t w i t h s u b - , s e q u e n t l y . 128. •The Mechanism o f D i s s o l u t i o n The d i s s o l u t i o n o f s o l i d s i l i c a i n v o l v e s a s i m u l t a n e o u s h y d r a t i o n and d e p o l y m e r i z a t i o n . ( S i 0 2 ) n + 2nH 20 = n S i ( O H ) 4 A c h e m i c a l r e a c t i o n o f t h e s u r f a c e o f t h e s o l i d phase w i t h w a t e r r e s u l t s i n the h y d r a t i o n o f t h e s u r f a c e l a y e r o f S i 0 2 and as each s i l i c o n atom i s removed, t o g e t h e r w i t h i t s s u r r o u n d i n g oxygen atoms, f u r t h e r r e a c t i o n l e a d s to t h e f o r m a t i o n o f m o n o s i l i c i c a c i d . D i e n e r t and Wandenbulcke r e p o r t t h e d i s s o l u t i o n t o be c a t a l y s e d by bases and a l k a l i s a l t s , e s p e c i a l l y c a r b o n a t e s . A l e x a n d e r , K eston and I l e r ^ " ^ ^ r e p o r t a s l i g h t l y i n c r e a s e d s o l u b i l i t y i n the a c i d (pH < 4.2) and h i g h s o l u b i l i t y i n the a l k a l i n e r e g i o n s (pH > 9) . The' i n c r e a s e o f t e n s i l e f r a c t u r e s t r e n g t h o f V y c o r g l a s s , w i t h t i m e , i n v a r i o u s s o l u t i o n s , i s t h e r e f o r e a s s o  c i a t e d w i t h the d i s s o l u t i o n e f f e c t s r e s u l t i n g i n a decrease i n s t r e s s c o n c e n t r a t i o n at o p e r a t i v e f l a w s . Very s l i g h t i n  c r e a s e s i n t h e r a d i u s o f c u r v a t u r e at the f l a w apex w i l l g r e a t l y reduce i t s e f f e c t , as a s t r e s s c o n c e n t r a t o r ^ ' ' ^ , I t s h o u l d be emphasized t h a t b u l k d i s s o l u t i o n r a t e s may not be a p p l i e d , s i n c e the s t r e n g t h i s f l a w s e n s i t i v e . . R e a c t i o n s w i t h i n t h e f l a w may be v e r y d i f f e r e n t f r om r e a c t i o n s o f the b u l k s o l i d . 129. TA3LE 11 Eff e c t ' s o f A l k a l i S o l u t i o n s Environment HO. 0.2N NaOH 2N NaON N a 2 0 . S i 0 2 - -IN Load T e n s i l e S t r e n g t h 2250.0 5730.8 2125.0 5412.4 3700.0- 9423.9 1737.5 4425.5 Na 90.SiO - I N 2 2525.0 6685.9 Time o f s o a k i n g : 6 0 mins. S t r a i n r a t e : .03 i n c h e s / m i n . TABLE 12 E f f e c t o f S t r a i n Rate on F r a c t u r e o f P o l y m e t h y l M e t h a c r y l a t e Acetone Benzene S t r a i n Rate T e n s i l e S t r e n g t h S t r a i n Rate T e n s i l e S t r e n g t h "/Min p s i "/Min p s i .03 1562 .03 1634 .015 1615 .015 1752 .006 3774 .006 1761 . 0012 4154 . 0012 2019 130. ( i i ) P o l y m e t h y l M e t h a c r y l a t e The a c r y l i c p l a s t i c f r a c t u r e d i n l i q u i d acetone shows an i n t e r e s t i n g f e a t u r e o f the J o f f e e f f e c t . U s i n g r a p i d s t r a i n r a t e s • ( > .015 i n c h e s / m i n ) , c a t a s t r o p h i c f a i l u r e o f the s o l i d o c c u r s a t v e r y low l o a d s ( a p p r o x i m a t e l y 50% o f the l o a d r e q u i r e d t o f r a c t u r e i n a i r ) . At slow s t r a i n r a t e s (< .006 i n c h e s / m i n ) , s t r e n g t h e n i n g o c c u r s t o a v a l u e e q u i v a l e n t to the vacuum b r e a k i n g s t r e n g t h . (Table 1 2 ) . U s i n g benzene no s t r e n g t h e n i n g o c c u r s , s i n c e p o l y m e t h y l m e t h a c r y l a t e i s not s o l v a t e d . These r e s u l t s add f u r t h e r s u p p o r t t o the f l a w t h e o r y mechanism o f the J o f f e 1 e f f e c t , s i n c e the r a t e o f d i s  s o l u t i o n i s the c o n t r o l l i n g s t e p and must be a l l o w e d to pr o c e e d f a s t e r than t h e c r a c k p r o p a g a t i n g r a t e f o r the e f f e c t to be e v i d e n t . 5:6 The S p r e a d i n g o r W e t t i n g E f f e c t A l i q u i d w i l l wet a s o l i d when t h e work o f a d h e s i o n between t h e s o l i d and t h e l i q u i d i s g r e a t e r than t h e work o f c o h e s i o n i n t h e l i q u i d . S i n c e i t i s e s s e n t i a l f o r the e f f e c t s o f the environment to be f e l t at t h e c r a c k t i p f o r a r e d u c t i o n i n s t r e n g t h t o o c c u r , f o r l i q u i d a d s o r b a t e s s p r e a d  i n g o f t h e l i q u i d on the s o l i d i s a n e c e s s a r y a s p e c t o f s t r e s s - s o r p t i o n f a i l u r e . I t may r e a d i l y be shown t h a t n o n - s p r e a d i n g l i q u i d s do not causa f a i l u r e at l o w e r l o a d s , e.g. water and 131. p o l y m e t h y l m e t h a c r y l a t e . The t h e rmodynamic t r e a t m e n t o f Y o u n g a n d D u p r e * ^ 0 3 ^ i n d e r i v i n g t h e i r c l a s s i c a l w e t t i n g e q u a t i o n f r o m s u r f a c e t e n s i o n c o n c e p t s a l o n e , ( Y ^ C O S O = Y J - Y S L ^ > does n o t t a k e i n t o a c c o u n t t h e n a t u r e o f s u r f a c e s f o r c e s . Weyl e t a l * " * " 0 4 ^ were a b l e t o d e m o n s t r a t e t h a t i t i s n o t p o s s i b l e t o r e l a t e w e t t a b i l i t y o f h i g h e n e r g y s u r f a c e s t o t h e s u r f a c e t e n s i o n p r o p e r t i e s o f t h e l i q u i d . The modern a p p r o a c h * 1 0 ^ c o n c l u d e s t h a t c h e m i c a l bonds between t h e s o l i d and l i q u i d p h a s e s a r e r e s p o n s i b l e f o r a d e q u a t e w e t t i n g . R e c e n t l y Fowkes* 3"^ 5^ has shown t h e i m p o r t a n c e o f t h e London d i s p e r s i o n f o r c e s i n a d h e s i o n . R e g a r d l e s s o f t h e n a t u r e o f t h e s o l i d and o f t h e l i q u i d , t h e two p h a s e s w i l l a l w a y s a t t r a c t one a n o t h e r t h r o u g h t h e i r d i s p e r s i o n f o r c e s . S u p e r i m p o s e d on t h e s e f o r c e s w i l l be t h e s t r o n g e r mechanisms s u p p l y i n g c o h e s i o n . Thus t h e s u r f a c e t e n s i o n o f a l l m a t e r i a l s i s t h e sum o f t h e d i s p e r s i o n f o r c e s ( y ^ ) and o t h e r a t t r a c t i v e f o r c e s (y a)» F i g . . 3 7 a . i l l u s t r a t e s t h e model u s e d by Fowkes f o r p r e d i c t i n g w e t t i n g , s p r e a d i n g and a d s o r p t i o n b e h a v i o u r o f many f l u i d s . The s u r f a c e t e n s i o n s o f t h e p h a s e s a r e g i v e n by, T h us t h e i n t e r f a c i a l t e n s i o n between p h a s e s 1 and 2 w i l l be g i v e n by, -"1^0 , /~d d1 Y 1 2 = Y x + Y 2 - 2 A Y 2 The r e d u c t i o n i n s u r f a c e t e n s i o n on a d s o r p t i o n IT , a l l o w s an e v a l u a t i o n o f t h e p o l a r i n t e r a c t i o n s at t h e s o l i d / l i q u i d i n t e r f a c e ^ d - 1 where 2y/ Yg Y^ i s t h e d i s p e r s i o n f o r c e i n t e r a c t i o n and T r e + 2y^ i s a measure o f t h e p o l a r i n t e r a c t i o n s i n e r g s p e r square cms. Types o f A t t r a c t i v e F orces (a) Van d e r Waal's f o r c e s , w hich o p e r a t e between a l l atoms, i o n s , o r m o l e c u l e s , and are due t o a t t r a c t i o n s between o s c i l l a t i n g d i p o l e s i n a d j a c e n t atoms. They are r e l a t i v e l y weak f o r c e s . (b) Hydrogen'bonds. S i n c e the s i l a n o l s u r f a c e c o n t a i n s h y d r o x y l i o n s many o f t h e s u r f a c e p r o p e r t i e s w i l l be d e t e r m i n  ed by the a b i l i t y t o form hydrogen bonds. These are r e l a t i v e l y weak a t t r a c t i v e f o r c e s (2-7 K c a l s / m o l e ) , but t h e i r f o r m a t i o n i s a p r o c e s s r e q u i r i n g low a c t i v a t i o n e n e r g i e s . Hydrogen bonds form r a p i d l y a t room t e m p e r a t u r e . (c) D i p o l e - d i p o l e and E l e c t r o s t a t i c A t t r a c t i o n s . ' A s o l u t i o n p r o c e s s , i n v o l v e s a p e n e t r a t i o n o f exchanged c a t i o n s ( p r o t o n s ) i n t o t h e l a t t i c e , f o l l o w e d by an e x p u l s i o n o f c a t i o n s i n t o the l i q u i d . As opposed t o t h e p r e v i o u s l y mentioned t y p e s o f 133. FIGURE 3.7a. ATTRACTIVE FORCES AT THE INTERFACE. TABLE 14 P o l a r I n t e r f a c i a l I n t e r a c t i o n s a t S o l i d / L i q u i d I n t e r f a c e s . S o l i d L i q u i d V 2 Y L E x c e s s S i l i c a n - H eptane 10 0 100 0 ' Benzene 118 138 20 A c e t o n e 98 156 58 n - P r o p a n o l 98 182 84 Wate r 94 462 368 13k b o n d i n g , w h i c h are s t r i c t l y s u r f a c e e f f e c t s , t h e e l e c t r o  c h e m i c a l a t t a c k i s a depth p r o c e s s . Any one o f t h e s e r e a c t i o n s , o r c o m b i n a t i o n s o f "rhem, w i t h the s o l i d s u r f a c e , may r e s u l t i n a change i n s t r e n g t h p r o p e r t i e s by c h a n g i n g th e s t a t e o f s t r e s s o f t h e . s u r f a c e . T h i s s t r e n g t h change may be p o s i t i v e o r n e g a t i v e . Many r e s e a r c h e r s * 1 2 ^ 2 ^ ^ 2 0 ^ have shown t h a t a l i n e a r r e l a t i o n s h i p e x i s t s between t h e decrease i n t e n s i l e f r a c t u r e s t r e n g t h and the s u r f a c e t e n s i o n o f t h e w e t t i n g l i q u i d . C.J. C u l f * ^ 1 ^ has p o i n t e d o u t the d i f f i c u l t i e s i n removing w a t e r from the h y g r o s c o p i c s o l v e n t s used, e.g. a c e t o n e , benzene and e t h a n o l . To e l i m i n a t e t h i s u n c e r t a i n t y , v a l u e s o f t h e t e n s i l e f r a c t u r e s t r e n g t h o f Kimble g l a s s were measured by a d s o r b i n g from t h e vapour phase, at t h e s a t u r a t e d curve vapour p r e s s u r e o f t h e l i q u i d . F i g . 36(a) i l l u s t r a t e s the non l i n e a r i t y o f the r e s u l t s o b t a i n e d . For l i q u i d s i n v o l v i n g e s s e n t i a l l y t h e same type o f b o n d i n g , v i z . e t h a n o l , n - p r o p a n o l v and w a t e r , t h e curve does appear l i n e a r . L i q u i d s o f d i f f e r i n g p o l a r p r o p e r t i e s and s i m i l a r s u r f a c e t e n s i o n s y i e l d d i f f e r e n t s t r e n g t h d e c r e a s e s , a l t h o u g h each l i q u i d may be c l a s s e d as " w e t t i n g " the g l a s s s u r f a c e from s u r f a c e t e n s i o n c o n s i d e r a t  i o n s . Curve (b) and (c) i n F i g . 36 show the e f f e c t o f d r y i n g ( 24 ) the s o l v e n t s oh t h e r e l a t i v e s t r e n g t h changes. B e n e d i c k s showed a l a r g e i n c r e a s e i n t h e s t r e n g t h o f g l a s s ' u s i n g k e r o s e n e . I n t h e p r e s e n t s t u d y I have found l i g h t o i l s to cause o n l y s l i g h t e f f e c t s , always d e c r e a s i n g the t e n s i l e PO OO cn PO O —I PO m 2 5 oo CD CD ^_ cu PO m zz. OO o c n r— t—t cz »—1 Tensile Fracture Strength psi x 10"3 o ro o CO o oo c -s - h CU O ro ro l/l o 3 o o C I o o oo o; - n-Hexane< Ethanol Acetone - Benzene - Nitrobenzene Glycerol - Water 00 3> -5 Co O c ' o o >* / / o O x ° J & X / o o » / o I I I I I 1 d O cr cu I o a - J . cr 3 — • CQ CD 3> a CO r-J- CD in =5 c+ CD Cr. CU 3 Q- O O I I o cr o 3 c C L cr - j ro a . -•• r~ cn -J. r+ -O ->• C —j i( — ' C L TABLE 13 The E f f e c t o f P a r a f f i n O i l on T e n s i l e S t r e n g t h • o f Kimble G l a s s ( S t r a i n Rate .03"/Min.) S o l i d Treatment- Environment T e n s i l e F r a c t u r e S t r e n g t h ( p . s . i . ) Vacuum -7 8x10. mms Hg N i l P a r a f f i n O i l ( U n t r e a t e d ) P a r a f f i n O i l (Na m e t a l ) 9329 7354 8785 Vacuum th e n adsorbed v/ith H 20 vapour N i l 4 836 P a r a f f i n O i l 4 986 ( U n t r e a t e d ) P a r a f f i n O i l (Na m e t a l ) 5963 137. f r a c t u r e s t r e n g t h o f specimens which were vacuum t r e a t e d ( T a b l e 1 3 ) . For specimens p r e a d s o r b e d w i t h w a t e r vapour and u s i n g p a i ^ a f f i n o i l d r i e d -with Na m e t a l , s t r e n g t h i n c r e a s e s do o c c u r , a l t h o u g h o n l y a f r a c t i o n o f t h e v a l u e r e p o r t e d by B e n e d i c k s . The u n d r i e d o i l had l i t t l e e f f e c t . The i n c r e a s e i s t h e r e f o r e a s s o c i a t e d w i t h some d e h y d r a t i o n o f the s i l a n o l s u r f a c e due t o the s l i g h t s o l u b i l i t y o f w a t e r i n o i l . I t appears t h a t t h e s t r e n g t h r e d u c t i o n on Kimble g l a s s i s not a l i n e a r f u n c t i o n o f the w e t t i n g l i q u i d , but a more complex r e l a t i o n s h i p , i n v o l v i n g t h e s i z e f a c t o r and s t r e n g t h o f a t t r a c t i o n o f t h e a d s o r b i n g s p e c i e s . o The energy r e q u i r e d t o produce 1 cms o f new s u r f a c e must be g r e a t e s t i f t h e g l a s s i s broken i n vacuo, and w i l l d ecrease w i t h i n c r e a s i n g a b i l i t y o f t h e environment . ++ + + t o s c r e e n t h e f i e l d o f the S i i o n s as p r e v i o u s l y d e s c r i b e d , T h e r e f o r e depending on the s c r e e n i n g ' p o w e r o f t h e l i q u i d t h e t e n s i l e f r a c t u r e s t r e n g t h o f the g l a s s w i l l v a r y . The s c r e e n i n g e f f e c t i s d i f f i c u l t t o i n t e r p r e t i n terms o f s t e r l c f a c t o r s and s t r e n g t h s o f a d h e s i o n , s i n c e t h e c o m p l e x i t y o f t h e mechanism i s enhanced by the d i s t r i b u t i o n and v a r y i n g s i z e o f o p e r a t i v e f l a w s w i t h i n t h e specimen. The h i g h d i p o l e and s m a l l s i z e Of t h e water ^ ', (107) (1C m o l e c u l e cause the g r e a t e s t s t r e n g t h r e d u c t i o n o f g l a s s Due t o the r a p i d c o n t a m i n a t i o n o f a f r e s h l y formed s u r f a c e by h y d r o x y l i o n s the e f f e c t s o f o t h e r s p e c i e s may not be d e t e c t e d u n l e s s complete e l i m i n a t i o n o f a l l m o i s t u r e i s m a i n t a i n e d . C u l f ^ " ^ showed a 50% decrease i n f r a c t u r e energ; o f g l a s s i n dry gaseous NH^, whereas o n l y s m a l l d i f f e r e n c e s were found w i t h o t h e r gases ( C 0 2 , N 2 and S 0 2 ) . The h i g h s c r e e n i n g power and s m a l l s t e r i c f a c t o r for.NHg s a t i s f y the r e q u i r e m e n t s f o r an e f f e c t i v e s t r e n g t h r e d u c e r . F o l l o w i n g t h e t r e a t m e n t o f F o w k e s ( 1 0 5 ) , F i g . 3-7^  i n which the s u r f a c e t e n s i o n s o f t h e v a r i o u s phases are d i v i d e d i n t o two p a r t s , Table 14, shows the p o l a r i n t e r f a c i a l i n t e r a c t i o n s between s i l i c a and v a r i o u s l i q u i d s . The London d i s p e r s i o n c o n t r i b u t i o n f o r each o f . t h e l i q u i d s shown, [2 / Y^] i s a p p r o x i m a t e l y t h e same, w h i l s t t h e p o l a r / S L a t t r a c t i o n s v a r y v a s t l y . Water i s by f a r the most a c t i v e s p e c i e s . Fig.-. 37bshows the c o r r e l a t i o n between t h e s e v a l u e s and t h e decrease i n t e n s i l e , f r a c t u r e s t r e n g t h . A l t h o u g h not l i n e a r , p r o b a b l y due t o a s t e r i c e f f e c t , t h e curve does e x h i b i t a c o r r e l a t i o n f o r a l l p o i n t s . M i s s C u l f o b t a i n e d a c o r r e l a t i o n between t h e h e a t s o f w e t t i n g , a b u l k e q u i l i b r i u m e f f e c t , and the d e c r e a s e i n f r a c t u r e e n ergy, a dynamic event a t t h e e x i s t i n g f l a w . Acetone was the e x c e p t i o n . I t i s e v i d e n t t h a t t h e s t r e n g t h o f a t t r a c t i o n o f the a d s o r b e n t f o r t h e a d s o r b a t e i s o f p r i m a r y importance i n a s t r e n g t h r e d u c i n g mechanism. I t may be c o n c l u d e d t h a t w e t t a b i l i t y based on s u r f a c e t e n s i o n d i f f e r e n c e s a l o n e , i s not a c r i t e r i o n f o r s t r o n g i n t e r a c t i o n between t h e s o l i d and l i q u i d phases. T h e r e f o r e w e t t a b i l i t y i s a n e c e s s a r y but i n  s u f f i c i e n t c r i t e r i o n f o r s t r e s s - s o r p t i o n c r a c k i n g . 10 OJ c OJ OJ rO c c CL X OJ o o OJ rsl +-> s_ zc OJ Q. 1 O) (J 1 c CO t I Z L_ I I I • » ' |_ I I 50 100 150 200 250 300 350 400 450. '500 Interfacial Attractive Forces FIGURE 37b TENSILE FRACTURE STRENGTH VERSUS INTERFACIAL ATTRACTIVE FORCES 140. 5 :7 Q , i a r t z i t i c Rock Specimens A b r i e f s e r i e s o f e x p e r i m e n t s were c a r r i e d out t o t e s t the v a l i d i t y o f the f r a c t u r e p r o c e s s on r o c k s . A grano- d i o r i t e core o f 1" d i a m e t e r was f r a c t u r e d i n vacuum and i n s e l e c t e d e n v i r o n m e n t s , a f t e r p r e - t r e a t m e n t as d e s c r i b e d e l s e  where. • . The r e s u l t s shown i n T a b l e 15, l e a d t o the f o l l o w  i n g c o n c l u s i o n s : (1) M o i s t u r e e x h i b i t s the l a r g e s t r e d u c t i o n i n t e n s i l e f r a c t u r e s t r e n g t h o f any o f t h e environments t e s t e d . (2) A l l environments have a d e c r e a s i n g e f f e c t w i t h r e f e r e n c e t o a vacuum t r e a t e d specimen. (3) A d s o r p t i o n from aqueous s o l u t i o n has n e g l i  g i b l e e f f e c t due t o the major r e a c t i o n o f the w a t e r m o l e c u l e w i t h the s i l i c a s u r f a c e , (4) S t r e n g t h d e c r e a s e s i n v a r i o u s s o l v e n t s are o f t e n due to the presence o f m o i s t u r e i n the s o l v e n t . I t i s my e x p e r i e n c e t h a t the t e n s i l e f r a c t u r e s t r e n g t h v e r s u s s u r f a c e t e n s i o n p l o t i s not l i n e a r , e.g. n-hexane, w i t h a s u r f a c e t e n s i o n o f 18.4 dynes/cms. causes a p p r o x i m a t e l y the same decrease as g l y c e r o l (y = 63,4 dynes/cms.) i f the l i q u i d s a r e c a r e f u l l y d r i e d ( T a b l e 1 5 ) , (5) The c o n f u s i o n r e s u l t i n g i n the l i t e r a t u r e from a wide v a r i e t y o f e x p e r i m e n t s i s p r o b a b l y due t o the v a r i a t i o n i n s u r f a c e c o n d i t i o n s , b o t h p h y s i c a l and c h e m i c a l , of the s t a r t i n g . m a t e r i a l . A l l r e s u l t s s h o u l d c o n t a i n d e t a i l s of specimen h i s t o r y and p r e - t r e a t m e n t . . TA3LE 15 THE EFFECT OF ENVIRONMENT ON THE TENSILE STRENGTH OF ROCK T e n s i l e F r a c t u r e S t r e n g t h S u r f a c e T e n s i o n •Envi ronment p . s . i . dynes / cms. Vacuum 1 7290 Vacuum 2 7860 H 20 5540 72.8 n-Hexane 69 74 18.4 10~ 4M C 1 2TAB 5592 G l y c e r o l 6885 63.4 Ethane-1 6255 22 .8 C^2 TAB = Dodecyl trimethylammonium bromide -7 Vacuum 1 = 24 hours at 8x10 rams Hg _ 7 Vacuum 2 = 48 hours a t 8x10 mms Hg. 5 : 8 The Appearance _of Fr^cJ:u_re^_Surfaces - F r a c t o g r a p h y The f r a c t u r e s u r f a c e o f a c r a c k o p e n i n g under the i n f l u e n c e o f a s t e a d i l y i n c r e a s i n g c r a c k - t i p s t r e s s shows t h r e e d i s t i n c t zones , (1) A r e g i o n i n which the v e l o c i t y o f t h e c r a c k p r o p a g a t i o n i s i n c r e a s i n g r a p i d l y r e s u l t i n g i n a smooth m i r r o r on the f r a c t u r e s u r f a c e . FIGURE 38a FRACTURE SURFACE OF GLASS IN WATER VAPOUR ATMOSPHERE FIGURE 38b FRACTURE SURFACE OF GLASS IN VACUO FIGURE 39 FRACTURE SURFACE OF POLYMETHYL METHACRYLATE IN AIR FIGURE 40 ELECTRON MICROGRAPH OF THE MIRROR REGION (VYCOR GLASS X10,000) FIGURE 41 ELECTRON MICROGRAPH OF FINE HACKLE REGION (VYCOR GLASS XIO.OOO) FIGURE 42 ELECTRON MICROGRAPH OF COARSE HACKLE ZONE (VYCOR GLASS XIO.OOO) H5. (2) A f i n e h a c k l e zone i n which the v e l o c i t y r i s e s i m p e r c e p t i b l y , u s u a l l y a t the edge o f the m i r r o r zone. (3) A c o a r s e h a c k l e zone i n which the c r a c k i s t r a v e l l i n g a t maximum v e l o c i t y through the m a t e r i a l . The b r i t t l e s o l i d s s t u d i e J e x h i b i t these t h r e e zones, as i l l u s t r a t e d i n F i g s . 38 and 39. F o r g l a s s specimens broken i n vacuum the m i r r o r zone i s e i t h e r non e x i s t e n t o r ve r y s m a l l . Thus the e x t e n t o f c r a c k growth at slow v e l o c i t y i s l i m i t e d i n the absence o f environment. T h e r e f o r e the f u n c t i o n o f the environment on the f r a c t u r e p r o c e s s w i l l be t o c o n t r o l t h e i n i t i a l c r a c k p r o p a g a t i o n phenomenon. I t seems l o g i c a l t o expect t h a t a c r a c k r u n n i n g a t maximum v e l o c i t y w i l l not be a f f e c t e d by t h e p r e s e n c e o f an a c t i v e s p e c i e s . F i g s . 40 to. 42 are e l e c t r o n m i c r o - g r a p h s o f the f r a c t u r e s u r f a c e of the t h r e e r e g i o n s . In the m i r r o r zone the t e x t u r e i s e x t r e m e l y f i n e , ( F i g . 4 1 ) , becoming c o a r s e r as t h e c r a c k v e l o c i t y i n c r e a s e s t o the f i n e h e c k l e zone, F i g . 42. In the c o a r s e h a c k l e zone t h e crack, f r o n t i s smashing t h r o u g h t h e g l a s s at about one t h i r d o f t h e v e l o c i t y o f sound i n the m a t e r i a l , t e a r i n g p i e c e s o f g l a s s from the s u r f a c e and f o r m i n g l a r g e r i p p l e s t e p s , where the t r a n s v e r s e p u l s e s emanating from the c r a c k t i p i n t e r f e r e w i t h the p r o p a g a t i n g c r a c k f r o n t . With the g l a s s specimens i t i s s i g n i f i c a n t t h a t no d i f f e r e n c e s c o u l d be d e t e c t e d between the s i z e o f the m i r r o r formed i n v a r i o u s e n v i r o n m e n t s . I t might be e x p e c t e d 146. t h a t t h e g r e a t e r t h e w e a k e n i n g e f f e c t t h e g r e a t e r t h e e x t e n t o f t h e n i r r o r z o n e . T h i s may i n d e e d be s o , b u t a c l e a v a g e t e c h n i q u e w o u l d have t o be a d o p t e d t o e s t a b l i s h t h e f a c t . A f r a c t u r e t e c h n i q u e does n o t employ one s p e c i f i c s u r f a c e c r a c k , and f r a c t u r e may d e v e l o p f r o m a h o s t o f c o r r e c t l y o r i e n t a t e d f l a w s , r e s u l t i n g i n the c r a c k p r o p a g a t i n g f r o m more t h a n one s u r f a c e . Thus t h e s i z e o f t h e m i r r o r zone would n o t be i n d i c a t i v e o f t h e e f f e c t o f t h e e n v i r o n m e n t on c r a c k g r o w t h . P o l y m e t h y l m e t h a c r y l a t e shows a l a r g e m i r r o r s u r  f a c e e v e n when b r o k e n i n vacuum a t t e m p e r a t u r e s below 4 0°C. The e x t e n s i v e m i r r o r r e g i o n i s a s s o c i a t e d w i t h a l a r g e c r i t i c a l c r a c k s i z e . Thus t h e e f f e c t s o f e n v i r o n m e n t m i g h t be e x p e c t e d t o be more d r a s t i c i n t h e c a s e o f t h e s e m i - b r i t t l e p l a s t i c s t h a n w i t h t h e b r i t t l e g l a s s e s . S i n c e t h e c r a c k g r o w t h s t a g e i s v e r y p r o n o u n c e d , any phenomenon r e s u l t i n g i n an i n c r e a s e i n c r a c k v e l o c i t y d u r i n g t h i s g r o w t h , w i l l be m a n i f e s t e d i n a w e a k e n i n g and p o s s i b l e f a i l u r e o f t h e s p e c i m e n . 1 4 7 . ^"^ 'E n v i r o n m e n t a l S t r e s s Crack i n g Mechan ism I n many o f the s t u d i e s covered i n t h e l i t e r a t u r e r e v i e w the f o l l o w i n g e x p l a n a t i o n was g i v e n f o r t h e cause o f e n v i r o n m e n t a l s t r e s s c r a c k i n g . " S p e c i f i c a d s o r p t i o n l e a d s to a r e d u c t i o n i n s u r f a c e f r e e energy o f the s o l i d , t h e r e b y de c r e a s i n g the f o r c e n e c e s s a r y f o r f r a c t u r e , " T h i s mechanism has been pr o p o s e d f o r l i q u i d m e t a l e m b r i t t l e m e n t , weakening o f r o c k s and g l a s s e s , and s t r e s s c r a c k i n g o f p l a s t i c s . The e x p l a n a t i o n f o l l o w s d i r e c t l y from the c o n s i d e r a t i o n s o f t h e G r i f f i t h c r i t e r i o n , s i n c e • a decrease i n y must l e a d t o a r e - duct i o n i n a \ ( a °°Y ' T h i s h y p o t h e s i s i s i n c o m p l e t e i n t h a t , ( i ) I t f a i l s t o e x p l a i n the p e c u l i a r s e l e c t i v i t y o f the environment and t h e m a t e r i a l , ( i i ) P r o v i d e s no account o f t h e n a t u r e o f the e m b r i t t l i n g p r o c e s s on an at o m i c s c a l e , ( i i i ) E x p e r i m e n t a l r e s u l t s show poor c o r r e l a t i o n when f i t t e d t o the e q u a t i o n . • T h i s l a c k o f f i t i s o f t e n a t t r i b u t e d t o p l a s t i c f l o w i n t h e v i c i n i t y o f the c r a c k t i p , ( i v ) D u c t i l e m e t a l s f a i l s p o n t a n e o u s l y i n a b r i t t l e f a s h i o n . The t h e o r y o f f e r s no e x p l a n a t i o n f o r t h e r e d u c t i o n o f the p l a s t i c energy c o n t r i b u t i o n ( P ) . Gilman ( 1 9 5 9 ) C l l l ) , S t o l o f f and J o h n s t o n ( 1 9 5 3 ) ( 1 1 2 ) and l a t e r Westwood and Kamdar ( 1 9 6 4 ) ^ " * " ^ , adopted an approach 148 whereby t h e c o h e s i o n f o r c e s o f t h e atoms at t h e c r a c k t i p are c o n s i d e r e d . They c o n c l u d e d t h a t t h e r o l e o f t h e a d s o r p i n g s p e c i e s i s t o r e d u c e , i n some way, the bond s t r e n g t h , t h e r e b y c a u s i n g the c r a c k t o p r o p a g a t e . Westwood's t h e o r y was based on the c o n t i n u e d d i f f u s i o n o f the c r a c k i n g s p e c i e s a l o n g the c r a c k w a l l s , to m a i n t a i n p r o p a g a t i o n . Such a mechanism would l i m i t the use o f a u t o p h o b i c c r a c k i n g a g e n t s , i . e . those w h i c h w i l l not s p r e a d on t h e i r own monolayer, t h e r e b y o f f e r i n g a c e r t a i n s e l e c t i v i t y t o t h e p r o c e s s . A c o n s t a n t s u p p l y o f e m b r i t t l i n g atoms at the c r a c k t i p i s a l s o n e c e s s a r y and i t has i n d e e d been shown t h a t t h e r e must be a s u f f i c i e n t s u p p l y o f l i q u i d m e t a l t o m a i n t a i n l i q u i d m e t a l e m b r i t t l e m e n t \ N i e l s e n * ^ f i r s t demonstrated t h e d e p o s i t i o n o f c o r r o s i o n p r o d u c t s w i t h i n c r a c k s i n an 18Cr-8Ni s t a i n l e s s s t e e l . He su g g e s t e d t h a t t h e s e d e p o s i t s might e x e r t l a r g e h y d r o s t a t i c p r e s s u r e s , t h u s i n t r o d u c i n g the wedging mechanism ( i 16 ) o f c o r r o s i o n p r o d u c t s . P i c k e r i n g e t a l showed the wedging f o r c e t o be s u f f i c i e n t l y l a r g e t o propagate the c r a c k , but the e f f e c t i s l i m i t e d t o o n l y a few atomic d i a m e t e r ahead o f the c r a c k t i p . B r i t t l e systems i n v o l v i n g f r e e l y r u n n i n g c r a c k s are not l i k e l y t o i n v o l v e such a mechanism. In a l l mechanisms a t e n s i l e s t r e s s i s e s s e n t i a l t o f a c i l i t a t e c r a c k i n g . The s t r e s s need not be a p p l i e d e x t e r n a l  l y and may i n d e e d be an i n t e g r a l p r o p e r t y o f the s o l i d , c aus i n g spontaneous f a i l u r e on i n t r o d u c i n g the e n v i r o n m e n t , e.g. MgSn and H 2 0 ( 1 1 7 ) . Q-O-O-0 FIGURE 43 MODEL FOR THE IONIC RIGID SOLID FIGURE 44 MODEL FOR THE COVALENT SEMI-BRITTLE SOLID 1 5 0 . The e x i s t e n c e o f a ' t h r e s h o l d ' s t r e s s below w h i c h c r a c k i n g w i l l not o c c u r has been demonstrated f o r some m e t a l l i systems* 1" 1" 8^. T h e o r e t i c a l l y f o r g l a s s systems, which e x h i b i t s t a t i c f a t i g u e , no such t h r e s h o l d e x i s t s and t h e g l a s s w i l l e v e n t u a l l y f a i l , no m a t t e r how s m a l l the l o a d . The f u n c t i o n o f t h e t e n s i l e s t r e s s appears t o be to i n c r e a s e c h e m i c a l r e a c t i v i t y o f the s u r f a c e by t h r e e p o s s i b l e mechanisms. . ' ~ • ( i ) I n c r e a s e of. the s p a c i a l . a t o m i c arrangement, a l l o w  i n g p e n e t r a t i o n o f t h e c r a c k i n g s p e c i e s , ( i i ) To c o n t r i b u t e i n some way t o t h e s u r f a c e r e a c t i o n by s u p p l y i n g energy n e c e s s a r y f o r r e a c t i o n , ( i i i ) 3y e x p o s i n g f r e s h s u r f a c e t h r o u g h a s l i p mechanism o r by r u p t u r i n g o x i d e f i l m s , the s u r f a c e r e a c t i o n may be a c c e l e r a t e d -t i n t h e case o f m e t a l l i c systems. I n c r e a s e i n the magnitude o f t h e s t r e s s , above the t h r e s h o l d v a l u e , r e s u l t s i n a more r a p i d f a i l u r e , as does i n c r e a s e i n t e m p e r a t u r e . In comparing t h e r e s u l t s p r e s e n t e d on two ty p e s o f g l a s s and on a b r i t t l e p l a s t i c a f a i r l y complex mechanism s u g g e s t s i t s e l f f o r the s t r e s s - s o r p t i o n c r a c k i n g o f b r i t t l e m a t e r i a l s . I t i s l i k e l y t h a t a s i n g l e mechanism w i l l not s u f f i c e f o r a l l systems. Any adopted mechanism must e x p l a i n , i n t h e l i g h t o f the d a t a p r e s e n t e d , the f o l l o w i n g : ( i ) G l a s s i s i m m e d i a t e l y weakened i n t h e vapour phase w h i l s t the p l a s t i c i s n o t . 151 ( i i ) The r e d u c t i o n o f s t r e n g t h f o r the g l a s s i s t h e same i n c o n c e n t r a t e d vapour as i n t h e l i q u i d phase, w h i l s t the p l a s t i c i s c o n s i d e r a b l y weaker i n the l i q u i d phase. ( i i i ) G l a s s has a h i g h energy s u r f a c e (= 500 dynes/cms ), w h i l s t t h e p l a s t i c i s a low energy s u r f a c e (= 30 dynes/cms ). Thus from an a d s o r p t i o n p o i n t o f v i e w , t h e environment s h o u l d have a g r e a t e r e f f e c t on g l a s s t h a n on p l a s t i c s . G l a s s does not f a i l c a t a s t r o p h i c a l l y , whereas the p l a s t i c does. ( i v ) The mechanism m u s t . e x p l a i n the s e l e c t i v i t y o f the s o l i d / e n v i r o n m e n t system. (v) The n e c e s s i t y f o r the l i q u i d t o wet t h e s o l i d s u r f a c e and s p r e a d i s a n . i n h e r e n t a s p e c t o f the p r o c e s s . ( y i ) The p r o c e s s i s t e n s i l e s t r e s s dependent, ( v i i ) The mechanism must i n c l u d e an e x p l a n a t i o n f o r t h e functi.on o f an e m b r i t t l i n g s p e c i e s . ( v i i i ) The v a r i a t i o n o f s t r e n g t h p r o p e r t i e s w i t h s u r f a c e c o n d i t i o n , i n the presence o r absence o f e n v i r o n m e n t , must be e x p l a i n e d . ( i x ) The magnitude o f the e f f e c t , i n v a r y i n g from a s l i g h t weakening i n some systems, to c a t a s t r o p h i c f a i l u r e i n o t h e r s , must be i n c l u d e d i n the mechanism. 5:10 A Proposed Mechanism f o r S t r e s s S o r p t i o n C r a c k i n g o f . B r i t t l e S o l i d s . As a r e s u l t o f e x p e r i m e n t s such as those i n d i c a t e d i n the s e c t i o n on the J o f f e E f f e c t , i t appears o b v i o u s t h a t FIGURE 45 MORSE CURVE FOR THE IONIC SOLID 1 C I the e x i s t i n g s u r f a c e c r a c k s p l a y the major r o l e i n d e t e r m i n  i n g the t e n s i l e f r a c t u r e s t r e n g t h o f t h e b r i t t l e m a t e r i a l s . I n t h e model o f t h e s o l i d s u r f a c e , we t h e r e f o r e a c c e p t the presence o f s u r f a c e c r a c k s o r f l a w s , and r e g a r d t h e f a i l u r e as a c r a c k e x t e n s i o n phenomenon, p r o c e e d i n g from the t i p o f f l a w s o r i e n t a t e d i n d i r e c t i o n s at r i g h t a n g l e s t o t h e a p p l i e d t e n s i l e l o a d . T h e r e f o r e , we d i r e c t a t t e n t i o n t o the t i p o f an e x i s t i n g c r a c k and adopt an a t o m i c approach f o r d e t e r m i n i n g a mechanism. F or t h e c r a c k to e x t e n d r e p e a t e d b r e a k i n g o f bonds o f t h e ty p e B 2 _ S 3 e t c # a s s n o w n i n F i g * 4 3 would be n e c e s s a r y . The c o h e s i v e o r a t t r a c t i v e s t r e n g t h o f such bonds can be r e p r e s e n t e d on a Morse diagram ( F i g . 45) i n the u s u a l way. I n the absence o f environment t h e f u n c t i o n o f the t e n s i l e l o a d w i l l be t o i n c r e a s e the bond l e n g t h s BQ-H-^, ^2~^3* o r ^° m o v e U P ^ n e p o t e n t i a l energy curve i n the d i r e c t  i o n o f i n c r e a s i n g s e p a r a t i o n d i s t a n c e s . The s l o p e o f the Morse curve i n t h i s r e g i o n i s thus o f prime importance i n s t r a i n  i n g t h e s o l i d . F o r an e x t r e m e l y r i g i d i o n i c s o l i d the r a t e o f change o f p o t e n t i a l w i t h i n t e r n u c l e a r d i s t a n c e w i l l be h i g h , t h a t i s , d e f o r m a t i o n , o r i n c r e a s e i n bond l e n g t h w i l l o n l y be a c h i e v e d by the a p p l i c a t i o n o f h i g h l o a d s . There i s a p o i n t o f sec o n d a r y e q u i l i b r i u m P-on the Morse curve t o which t h e bond can be s t r e t c h e d w i t h o u t r e s u l t i n g i n f a i l u r e . Ex t e n s i o n beyond t h i s p o i n t i s accompanied by p a r t i n g o f the 155. bond. (P i s t h e p o i n t a t w h i c h d 2 U / d r 2 = 0 ) . F o r t h e r i g i d s o l i d , e x t e n s i o n t o t h i s p o i n t can o n l y be a c h i e v e d w i t h t h e a p p l i c a t i o n o f h i g h l o a d s , a l t h o u g h t h e s t r a i n n e c e s s a r y to c a u s e r u p t u r e m i g h t be v e r y s m a l l . The c u r v e i s v e r y s t e e p i n t h i s r e g i o n and s m a l l e x t e n s i o n s w i l l r e s u l t i n l a r g e r c h a n g e s i n a t t r a c t i v e f o r c e s , and s i n c e t h e p r o b a b i l i t y o f t h e s o l i d f a i l i n g i s b a s e d on t h e a c h i e v e  ment o f t h e p o t e n t i a l b a r r i e r E, s , any e x t e n s i o n w i l l ( a ) r e s u l t i n a h i g h e r p r o b a b i l i t y o f f a i l u r e . T h i s c a s e f o r t h e r i g i d i o n i c s o l i d e.g. g l a s s , o f f e r s an a d e q u a t e e x p l a n a t i o n f o r t h e s t a t i c f a t i g u e phenomenon, i . e . t h e a p p l i c a t i o n o f a t e n s i l e s t r e s s w i l l e v e n t u a l l y c a u s e f a i l u r e a c c o r d i n g t o t h e AE p r o b a b i l i t y f a c t o r , P <» e a / l k T ^ -p^e h i g h e r t h e l o a d a p p l i e d , the s m a l l e r AE, and h ence t h e s o l i d w i l l f a i l i n s h o r t e r t i m e s , The bond i s a t a l l t i m e s o s c i l l a t i n g a b o u t an e q u i l i b r i u m p o s i t i o n . The g r e a t e r t h e d i s t o r t e d i n t e r n u c l e a r d i s t a n c e t h e g r e a t e r w i l l be t h e f r e q u e n c y o f o s c i l l a t i o n . T h i s f r e q u e n c y a l s o c o n t r i b u t e s t o t h e p r o b a b i l i t y o f a c h i e v  i n g t h e p o t e n t i a l b a r r i e r and o f t h e s o l i d f a i l i n g . In t h e p r e s e n c e o f an e n v i r o n m e n t t h e c o u r s e o f e v e n t s w o u l d be as f o l l o w s . . P r i o r t o t h e a p p l i c a t i o n o f t h e l o a d , p h y s i c a l a d s o r p t i o n o f t h e a c t i v e s p e c i e s r e s u l t s i n a d e c r e a s e i n s u r f a c e t e n s i o n , T h i s r e d u c t i o n i n s u r f a c e t e n s i o n l e a d s t o a change i n t h e s u r f a c e s t r e s s , and t h e s t r a i n s i n d u c e d i n t h e s o l i d i n v a c u o a r e r e l i e v e d . The 156. s o l i d s w e l l s . The e x t e n t o f the s u r f a c e s t r e s s v a r i a t i o n , on s u r f a c e t e n s i o n r e d u c t i o n , w i l l be a f u n c t i o n o f the s l o o e of t h e Morse curve i n the r e g i o n A-P. For g l a s s , a r i g i d i o n i c s o l i d o f s t e e p s l o n e o v e r AP, t h e term AX w i l l be l a r g e s i n c e AE AE must be s m a l l . Thus the change i.n s u r f a c e s t r e s s w i l l be v e r y much d i f f e r e n t from the r e f l e c t e d change i n t h e s u r f a c e . t e n s i o n , ( A y ) . The s l o p e o f the cu r v e and t h e terms would AE t h e r e f o r e be a measure o f the a b i l i t y o f the s o l i d t o w i t h  s t a n d shear. I t i s t h i s v a r i a t i o n i n s u r f a c e s t r e s s r e s u l t  i n g from l a r g e v a l u e s o f A l which causes s i g n i f i c a n t volume AE c h a n g e s . i n r i g i d s o l i d s . The e f f e c t o f t h e i n c r e a s e i n s o l i d volume w i l l be to i n c r e a s e the t e n s i l e f o r c e a c r o s s t h e bond EQ-B-^, t h e r e b y extended t h e bond f u r t h e r than the e q u i l i b r i u m p o s i t i o n , a, i n the absence o f a d s o r b a t e . On a p p l i c a t i o n o f the l o a d the i n t e r n u c l e a r d i s t a n c e s w i l l be i n c r e a s e d s t i l l f u r t h e r . The a d s o r b a t e m o l e c u l e s , a l r e a d y a t t r a c t e d t o t h e s u r f a c e i n t h e absence o f t h e s t r e s s , w i l l now have a g r e a t e r a f f i n i t y f o r t h e s t r e s s e d r e g i o n due t o t h e l e s s e r s c r e e n i n g o f t h e i o n c o r e s , r e s u l t i n g from the i n c r e a s e d i n t e r n u c l e a r d i s t a n c e . The a d s o r b i n g s p e c i e s then s c r e e n t h e a t t r a c t i v e c o r e s t o a l a r g e r degree and the bond ext e n d s s t i l l f u r t h e r . The l o a d n e c e s s a r y . t o e x t e n d the bond beyond the b r e a k i n g p o i n t i s th e n a s s i s t e d by the c o n t r i b u t i n g f a c t o r s above and the s o l i d f a i l s a t a l o w e r a p p l i e d l o a d . However, s i n c e we are d e a l i n g w i t h a r i g i d i o n i c 157 body, l a r g e amounts o f energy are n e c e s s a r y t o e f f e c t a s m a l l e x t e n s i o n . The c o n t r i b u t i o n from th e a d s o r b i n g e f f e c t s may be s m a l l , w i t h t h e end r e s u l t t h a t t h e s o l i d may n o t be con s i d e r a b l y weakened. I f t h e a d s o r p t i o n e f f e c t s . , are c a p a b l e o f i n c r e a s i n g t h e i n t e r n u c l e a r d i s t a n c e beyond p o i n t P, t h e s o l i d w i l l f a i l s p o n t a n e o u s l y i n the absence o f a p p l i e d s t r e s s . S i n c e the e f f e c t o f a d s o r p t i o n i s a f u n c t i o n o f the s c r e e n i n g power o f the a d s o r b a t e , the g r e a t e r the s c r e e n i n g power, the g r e a t e r the e f f e c t . The s c r e e n i n g power may be measured by bond f r e q u e n c y s h i f t s and volume changes o f the s o l i d . The s t r e n g t h o f the a d s o r p t i o n bond w i l l not n e c e s s a  r i l y r e l a t e t o the s t r e n g t h o f s c r e e n i n g . I f the m o l e c u l a r s i z e o f t h e a d s o r b a t e i s l a r g e and b l o c k s a l a r g e number o f s i t e s , w h i l s t o n l y a t t a c h i n g a t one o r two p o i n t s , e f f e c t i v e s c r e e n i n g w i l l not be a c h i e v e d . T h e r e f o r e a c e r t a i n s e l e c t i  v i t y governs t h e c r a c k i n g system. Thus f o r r i g i d i o n i c s o l i d s the o n s e t o f c a t a s t r o p h i c f a i l u r e would be a c h i e v e d w i t h g r e a t d i f f i c u l t y , s i n c e a h i g h t e n s i l e s t r e s s i s n e c e s s a r y f o r i n c r e a s e d i n t e r n u c l e a r d i s t a n c e l e a d i n g to s t r e s s a c c e l e r a t e d a d s o r p t i o n . The more r i g i d t h e s o l i d the l e s s s u s c e p t i b l e i t would be t o s t r e s s s o r p t i o n f a i l u r e . F o r t h e s e m i - b r i t t l e c o v a l e n t a c r y l i c s the iMorse c u r v e would be as shown i n F i g , H6. E x t e n s i o n o f t h e s o l i d can be a c h i e v e d w i t h r e l a t i v e ease. The a b i l i t y o f the s o l i d t o s h e a r i s i n c l u d e d i n t h e slow r a t e i n c r e a s e o v e r the r e g i o n ^ . 153. A'-P'. L a c k o f r i g i d i t y does n o t n e c e s s a r i l y i m p l y d u c t i l i t y . R i g i d i t y i s a measure o f t h e e l a s t i c i t y o f t h e s o l i d w h i l s t d u c t i l i t y i s t h e a b i l i t y o f t h e n . a t e r i a l t o swap bonds and f l o w . The l e s s r i g i d s o l i d o f e q u i v a l e n t s t r e n g t h w i l l have a p o t e n t i a l b a r r i e r o f e q u a l h e i g h t t o s u r m o u n t , f o r f a i l u r e i n v a c u o . However, c o n s i d e r a b l e e x t e n s i o n can be a c h i e v e d w i t h o n l y s m a l l c h a n g e s i n e n e r g y , v i z , s m a l l a p p l i e d l o a d s would r e s u l t i n e x t e n s i v e s t r a i n . Due t o t h e i n c r e a s e d e l a s t i c i t y t h e s l o w c r a c k g r o w t h s t a g e o f f r a c t u r e w i l l become more p r o  n o u n c e d t h a n i n t h e f o r m e r c a s e f o r t h e r i g i d i o n i c s o l i d . An a d d i t i o n a l f o r c e would come i n t o p l a y i n t h i s c a s e w h i c h w o u l d n o t be e f f e c t i v e i n t h e f o r m e r c a s e . S i n c e low l o a d s c a u s e l a r g e r e x t e n s i o n o f t h e s o l i d , t h e bonds o f t h e t y p e B'-D', D'-E' i n F i g . 44, w i l l become o b l i q u e t o t h e t e n s i l e s t r e s s d i r e c t i o n . The g r e a t e r t h e ex t e n s i o n t h e g r e a t e r t h e c o n t r i b u t i o n o f t h e s e bonds t h r o u g h t h e i r component i n the d i r e c t i o n of. t h e t e n s i l e s t r e s s . The e n d r e s u l t i s f o r t h e bond 3-B' t o e x t e n d s t i l l ' f u r t h e r , t h u s i n c r e a s i n g t h e a d d i t i v e component, and t h e c r a c k can p r o p a g a t e s l o w l y u n d e r a v e r y low l o a d . I n t h e p r e s e n c e o f an a c t i v e e n v i r o n m e n t t h e same s i t u a t i o n w i l l e x i s t as f o r t h e r i g i d i o n i c s o l i d e x c e p t t h a t t h e e f f e c t s h o u l d be more p r o n o u n c e d i f t h e a d s o r p t i v e r e a c t i o n were i d e n t i c a l . However, t h e p o l y m e t h y l metha-159. F I G U R E 4 6 M O R S E C U R V E FOR T H E C O V A L E N T S O L I D I60o c r y l a t e has a low energy s u r f a c e and t h e Ay w i l l n o t be large-. Any change i n y w i l l r e s u l t i n a change i n t h e ex t e n s i o n , but w i l l be s m a l l s i n c e Ay i s s m a l l , and AE i s AE Ay l a r g e . E x t e n d i n g the case t o the s e m i - l i q u i d s t a t e - — . w i l l AE a lmost v a n i s h . Thus the s u r f a c e s t r e s s v a r i a t i o n w i l l be m a i n l y r e  f l e c t e d i n changes i n y, which w i l l be s m a l l , as the system c o u l d not be v e r y a d s o r p t i o n s e n s i t i v e , due t o t h e low s u r f a c e energy. A l s o s i n c e t h e a d s o r b i n g f o r c e s on p l a s t i c s w i t h o r g a n i c e n v i r o n m e n t s are l a r g e l y n o n - s p e c i f i c and the polymers are n o n - i o n i c , e f f e c t i v e s c r e e n i n g would not accompany an a d s o r p t i o n r e a c t i o n . As we e x t e n d t h e bond 3-B 1 towards i t s b r e a k i n g p o i n t , the bond i s o s c i l l a t i n g a t i n c r e a s i n g f r e q u e n c i e s . I f the f r e q u e n c y o f o s c i l l a t i o n can be made t o i n t e r a c t w i t h the f r e q u e n c y o f t h e r m a l v i b r a t i o n o f the e n v i r o n m e n t , s t r e n g t h r e d u c t i o n may be a c h i e v e d by a sudden decrease i n f r e e energy o f t h e s u r f a c e . C a t a s t r o p h i c f a i l u r e can ensue. Thus the p r o b a b i l i t y o f a system f a i l i n g under these c o n d i  t i o n s would be g r e a t e r , t h e c l o s e r the p h y s i c a l n a t u r e o f the t h e r m a l v i b r a t i o n s o f t h e s o l i d and t h e environment. The l i q u i d phase would be more co n d u c i v e t o c r a c k i n g than the gas. The c r a c k i n g o f p l a s t i c s i n hydrocarbons and c e r t a i n c a s e s o f l i q u i d m e t a l e m b r i t t l e m e n t c o u l d be e x p l a i n e d i n t h i s manner. ? 1 6 1 . That such a mechanism i s operative may be demonstrat ed by the rate at which a gas i s released from a super-saturated solution as a t o o l for studying adhesive f o r c e s ^ 1 1 9 \ Experi ments with C 0 2 from, supersaturated aqueous solutions re vealed that i n a clean glass vessel a high supersaturation could be retained, because of the strong adhesive forces between the glass and water. However, supersaturation was rapidly released in contact with l i q u i d p a r a f f i n . The l i q u i d p a r a f f i n o i l was not very e f f e c t i v e unless i t was smeared over a s o l i d surface such as a glass plate. Thus the van der Waal's forces are modified i f the adjacent phases- are s i m i l a r , so that they can adjust t h e i r thermal vibrations at the i n t e r  face. There should be l i t t l e difference between the surface energies of l i q u i d and s o l i d p a r a f f i n . During the thermal vibrations, the adhesive forces seem to fluctuate less at a water/liquid p a r a f f i n interface than at a water/solid p a r a f f i n i n t e r f a c e . Liquid p a r a f f i n smeared as a thin f i l m onto a glass surface has l o s t the a b i l i t y to follow the thermal vibrations of the aqueous system. Role of D u c t i l i t y P l a s t i c deformation r e s u l t s i n a loss of b r i t t l e n e s s of the s o l i d specimen. A certain amount of work must be ex pended i n the production of p l a s t i c flow in the v i c i n i t y of the crack t i p . The c r i t i c a l crack length in ductile materials would be several orders of magnitude larger than for b r i t t l e s o l i d s , i . e . the s t a b l e c r a c k p r o p a g a t i n g s t a g e i s a c c e n t u a t  ed. E x c e s s d u c t i l i t y r e s u l t s i n f l o w and the specimen w i l l n o t c r a c k s i n c e the work expended i n p l a s t i c d e f o r m a t i o n i s f a r g r e a t e r than t h a t needed to c r e a t e f r e s h s u r f a c e . How e v e r , a l i m i t e d amount o f p l a s t i c d e f o r m a t i o n would be bene-' f i c i a l t o the b r i t t l e f a i l u r e p r o c e s s . P l a s t i c f l o w r e s u l t s • i n t h e c r e a t i o n o f s m a l l a r e a s o f f r e s h s u r f a c e , o r p r e f e r e n  t i a l a d s o r p t i o n s i t e s . A d s o r p t i o n l o w e r s the s u r f a c e energy r e s u l t i n g i n an imbalance o f f o r c e s , and s l i p p roceeds at a f a s t e r r a t e than i n the absence o f a d s o r b a t e . Thus the c r i t i c a l c r a c k s i z e i s reached a t an a c c e l e r a t e d r a t e and the specimen f a i l s . ( I n an i d e a l l y b r i t t l e m a t e r i a l no such movement o c c u r s , w i t h the r e s u l t i n g s t r e n g t h d e c r e a s e ..being • o n l y the d e c rease o f i n i t i a l s u r f a c e f r e e energy due to the e n v i r o n m e n t . ) The r o l e o f an e m b r i t t l i n g s p e c i e s on a d u c t i l e s o l i d would be t o c r e a t e , t h r o u g h a new s u r f a c e compound, o r a d s o r p t i o n d i s l o c a t i o n l o c k i n g , a l i m i t e d amount o f d u c t i l i t y t h e r e b y a i d i n g b r i t t l e f a i l u r e . T h e r e f o r e the r o l e o f p l a s t i c f l o w o r s l i p d i s l o c a  t i o n s i n the s t a b l e c r a c k p r o p a g a t i o n s t a g e o f b r i t t l e f r a c t u r e i n c r y s t a l l i n e ' s e m i - b r i t t l e ' , s o l i d s s h o u l d not be " underemphasized. Si n c e i n a l l cases i t i s n e c e s s a r y f o r the e n v i r o n  ment to have an a f f i n i t y f o r the s o l i d and f o r the a d s o r b a t e e f f e c t s t o be f e l t i n t h e e x i s t i n g f l a w s , w e t t i n g i s a n e c e s s a r y a s p e c t i n s t r e s s - s o r p t i o n f a i l u r e . I t s h o u l d be emphasized t h a t not a l l a d s o r b i n g r e -actions w i l l r e s u l t in a.weakening of the specimen. If the change i n surface stress on adsorption i s compressive, strengthening e f f e c t s w i l l resul L.. This change w i l l be a function of the s o l i d surface and of the adsorbing species, i n d i c a t i n g a s e l e c t i v i t y i n the s t r c - s cracking system. The proposed variation i n the slope of the Morse curve i n the expansion regions of the r i g i d and semi-brittle s o l i d s can be emphasized by considering the energy released ( R 1 ) per unit area of crack surface. The Irwin r e l a t i o n s h i p f o r the c r i t i c a l energy released at the onset of unstable fracture propagation was given as • aJ- = C r i t i c a l Stress f o r F a i l u r e 2 CR GCR = 1 T°CR CCR' C„U = C r i t i c a l Crack Length CR G = Energy Released/Unit Crack Area CR The value of GQR has been found to be 0.03 i n - l b s . / i n c h ^ 1 2 0 ^ for glass at 2% r e l a t i v e humidity, and 4.0 i n - l b s . / Inch f o r polymethyl m e t h a c r y l a t e ^ 2 ^ . Since the breaking loads are of the same order of magnitude for the two s o l i d s , the difference arises from differences i n c r i t i c a l crack size Therefore for very r i g i d s o l i d s (glass), under a s t e a d i l y increasing load, the crack has only to extend very s l i g h t l y to reach the c r i t i c a l s i z e . It may be assumed there fore that, under these t e n s i l e test conditions, fracture i n i  t i a t i o n and strength f a i l u r e occur almost simultaneously. For the s e m i - b r i t t l e material, on the other hand, a period of stable crack propagation occurs during which strength f a i l u r e mechanisms due to environment can become operative. 16 Thus f o r t h e r i g i d i o n i c s o l i d the environment e s  s e n t i a l l y a f f e c t s t h e f r a c t u r e i n i t i a t i o n p r o c e s s . F o r t h e s e m i - b r i t t l e c o v a l e n t s o l i d the environment o p e r a t e s i n b o t h the f r a c t u r e i n i t i a t i o n and s t a b l e c r a c k p r o p a g a t i o n s t a g e s . 165. CHAPTER SIX • SUMMARY AND CONCLUSIONS A ^tudy o f s t r e s s - e n v i r o n m e n t a l c r a c k i n g o f two' t y p e s o f s i l i c a g l a s s e s and an a c r y l i c p l a s t i c has been eon- — 6 ducted i n a unique h i g h (10 mm rig) vacuum a p p a r a t u s . Ad s o r p t i o n i s o t h e r m s f o r a number o f gases and vapours c o n s t i  t u t i n g the environment o f s i l i c a g l a s s e s were de t e r m i n e d and c o r r e l a t e d w i t h f r a c t u r e d a t a o b t a i n e d under c o r r e s p o n d i n g c o n d i t i o n s . The r e s u l t s have l e d t o t h e - f o l l o w i n g major c o n c l u s i o n s : (a) Glasjs ~ (1) G l a s s does n o t f a i l c a t a s t r o p h i c a l l y i n c o n t a c t w i t h an aqueous environment t h a t may g i v e " c o r r o s i o n " - l i k e r e a c t i o n s . Due t o t h e r i g i d i o n i c s t r u c t u r e , f a i l u r e and f r a c t u r e i n i t i a t i o n o c c u r a l m o s t s i m u l  t a n e o u s l y , any a d s o r p t i o n e f f e c t s p r i m a r i l y a f f e c t the i n i t i a l s t age o f t h e f a i l u r e . (2) In comparison w i t h the c l e a n , vacuum f r a c t u r e d specimens, a l l environments t e s t e d r e s u l t e d i n a d e c r e a s e i n the t e n s i l e f r a c t u r e s t r e n g t h . Water vapour i s t h e c r i t i c a l a d s o r b a t e , even at coverages o f a p p r o x i m a t e l y 1/3 o f a condensed monolayer, the s t r e n g t h then f a l l i n g g r a d u a l l y w i t h i n c r e a s e i n vapour c o n c e n t r a t i o n . 166. (3) C o n t r a r y t o the f i n d i n g s o f o t h e r s , the t e n s i l e s t r e n g t h i s not a l i n e a r f u n c t i o n o f s u r f a c e t e n s i o n o f the w e t t i n g l i q u i d , i n f a c t , t h e y a r e . u n r e l a t e d , A g a i n m o i s t u r e c o n t a m i n a t i o n a f f e c t s t h e r e s u l t s d r a s t i c a l l y . (4) Any d i s s o l u t i o n p r o c e s s a t e x i s t i n g s u r f a c e f l a w s a c t s t o i n c r e a s e the s t r e n g t h by b l u n t i n g the c r a c k t i p . The e f f e c t i s most p r e v a l e n t i n the a c i d and a l k a l i n e r e g i o n s (pH < 5 and pH > 9 ) . (5) The measured " f r a c t u r e i s o t h e r m s " do not c o i n c i d e w i t h t h o s e c a l c u l a t e d from a d s o r p t i o n d a t a . T h i s does not i n v a l i d a t e t h e G r i f f i t h e q u a t i o n , s i n c e t h e a d s o r p t i o n data' r e f e r t o b u l k measurements and G r i f f i t h e q u a t i o n t o a l o c a l i z e d s t r e s s - s e n s i t i v e s i t e on the s u r f a c e o f the sample. (6) The magnitude o f the s u r f a c e bond (between the a d s o r b a t e and the s i t e ) i s not the d e c i s i v e p a rameter, but s t e r i c e f f e c t s a l s o p l a y " a n i m p o r t a n t r o l e , e.g., acetone i s bonded more s t r o n g l y than water (Av Acetone = 360 ems'. ; Av V/ater=280 cms.) but the e f f e c t o f w a t e r on f r a c t u r e i s g r e a t e r . (7) Dry g a s e s , N and CO^ , do not a f f e c t the t e n s i l e s t r e n g t h o f Vycor g l a s s . Po 1 yme t h y l Hethacryl_ate (1) S t r e s s - e n v i r o n m e n t a l f r a c t u r e does.not o c c u r i n the vapour phase. . S t r e s s i n g i n a l i q u i d o r g a n i c 1 6 7 s o l v e n t t h a t i s w e t t i n g t h e p l a s t i c s u r f a c e c a u s e s a d r a s t i c r e d u c t i o n i n t e n s i l e s t r e n g t h (2) ' T h o s e d i s s o l u t i o n p r o c e s s e s w h i c h o c c u r f a s t e r t h a n t h e c r a c k p r o p a g a t i o n a c t as a h e a l i n g mechanism and i n c r e a s e t h e s o . l i d ' s s t r e n g t h , (3) A non--wetting l i q u i d , w a t e r , has no e f f e c t on t h e t e n s i l e f r a c t u r e s t r e n g t h o f t h e p l a s t i c . ( lO The e x i s t e n c e o f a l a r g e s t a b l e c r a c k g r o w t h r e g i o n and a l a r g e c r i t i c a l c r a c k s i z e o f t h e c o - v a l e n t l y bonded s e m i - b r i t t l e m a t e r i a l r e s u l t s i n a c a t a s t r o p h i c f a i l u r e i n o r g a n i c s o l u t i o n s a t v e r y low a p p l i e d l o a d s . ' ( 1 ) F r a c t u r e o f s i l i c e o u s m a t e r i a l i s n o t f a c i l i t a t  e d by a d s o r p t i o n f r o m aqueous s o l u t i o n . Rock i n i t s n o r m a l w e a t h e r e d c o n d i t i o n w i l l a l r e a d y be i n a l o w e r e n e r g y s t a t e compared t o t h e c l e a n , a d s o r p t i o n - f r e e c o n d i t i o n . T h i s does n o t e x c l u d e t h e p o s s i b l e e f f e c t s o f a d s o r p t i o n f r o m a l e s s a c t i v e s o l u t i o n , o r t h e p o s s i b i l i t y o f s e p a r a t i o n o f m i n e r a l p a r t i c l e s a l o n g t h e i r b o u n d a r i e s w i t h s i l i c a . The main outcome o f t h e s t u d y was t o e x t e n d t h e p r e v i o u s l y c o n c e i v e d i d e a s f o r t h e s t r e s s - s o r p t i o n c r a c k i n g o f b r i t t l e s o l i d s ; a m o d i f i e d mechanism f o r s t r e s s - e n v i r o n  m e n t a l c r a c k i n g i s p r o p o s e d by t a k i n g i n t o a c c o u n t t h e n a t u r e o f t h e s o l i d s u r f a c e and t h e s p e c i f i c a c t i o n o f a c t i v e a d s o r b  i n g s p e c i e s on t h e s u r f a c e ( u n d e r t h e d e s c r i b e d t e s t i n g c o n d i t i o n 167(a) Changes i n s u r f a c e t e n s i o n w i t h a d s o r p t i o n may not be a s u f f i c i e n t c o n d i t i o n f o r c r a c k i n g to o c c u r . R e s u l t i n g s u r f a c e s t r e s s v a r i a t i o n can c o u n t e r a c t t h e d e c r e a s e i n y» t h e r e b y c a n c e l l i n g the weakening e f f e c t . 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S t r e s s C o r r o s i o n F r a c t u r e " , P i t t s b u r g h 1959, p. 1. 124.. U h l i g , H. and Sava, J . , Trans. Am. Soc. M e t a l s 56_, ( 1 9 6 3 ) , 361. . . . . ' A d d i t i o n a l p e r t i n e n t r e f e r e n c e s " T e n s i l e S t r e n g t h o f B r i t t l e M a t e r i a l s , " by R. S e d l a c e k , S t a n f o r d R e s e a r c h I n s t i t u t e , T e c h n i c a l Report AFML-TR-65-129, August 1965. " S t u d i e s o f the B r i t t l e B e h a v i o r o f Ceramic M a t e r i a l s , " T e c h n i c a l Documentary Report No. ASD-TR-61-628, P a r t I I , A p r i l 196 3. "Method f o r T e n s i l e T e s t i n g o f B r i t t l e M a t e r i a l s , " R u d o l f Sedlacek and Frank A. H a l d e n , Review o f S c i e n t i f i c I n s t r u m e n t s , V o l . 33, No. 3, pp. 298-300 , March 1962 . . ' •• " S u r f a c e s , S t r e s s - D e p e n d e n t S u r f a c e R e a c t i o n s and S t r e n g t h , " by W.3. H i l l i g and R.J. C h a r l e s , Chapter 17 i n HIGH STRENGTH MATERIALS, ed. V.F. Zackay, John W i l e y E Sons, I n c . , New York 1964, p. 682. 175 A p p e n d i x A D e s c r i p t i o n o f A p p a r a t u s Components L o a d M e a s u r i n g System ( a ) -Load C e l l - B a l d w i n , L i m a H a m i l t o n C o r p . (B.L.H.) SR-4, Model CXX, C a p a c i t y 50 ,000 l b s . (b) S t r a i n I n d i c a t o r - Budd, M o d e l P-350. ( i i ) High^Vacuum Pumping^ S y s t e m ( a ) R o t a r y Vacuum Pump - Welch Duo S e a l Model 139 7 3', 2 s t a g e 42 5 l i t r e s / r n i n f u l l a i r d i s p l a c e m e n t w i t h v e n t e d e x h a u s t . (b) R o t a r y Pump O i l - Welch Duo S e a l O i l . ( c ) O i l D i f f u s i o n Pump - C o n s o l i d a t e d Vacuum C o r p . M o d e l PAS-61 C 6 i n c h - 3 s t a g e f r a c t i o n a t i n g t y p e 300 l i t r e s / m i n pumping s p e e d . (d) D i f f u s i o n Pump O i l - S i l i c o n e DC-705 S.G., 1.095 F l a s h P t . , 4 7 0 ° F , B.P. 2 4 5 ° C a t .5 t o r r . ( e ) C o o l i n g c o i l s a f e t y s w i t c h - Ranco P r e s s u r e C o n t r o l Type "010", low and h i g h p r e s s u r e c u t - i n . ( f ) C o l d T r a p - C.V.C. M u l t i c o o l a n t B a f f l e , Type BCN C o o l a n t - L i q u i d N i t r o g e n . (g) H i g h Vacuum V a l v e s - C.V.C, r i g h t a n g l e vacuum v a l v e s t y p e VRA. 176 Gate V a l v e - Type VCS 61B.. (h) G a s k e t s , 0 r i n g s - Buna-N and Neoprene gaskets' and 0 - r i n g s . ( i ) Vacuum Gauges - C.V.C. Model GIC - 20 0 h ot f i l a m e n t gauge. Range l x l O " " 3 - 2 x l 0 ~ 1 2 mm Hg. C.V.C. Thermocouple gauge Model GTC - 004. Range 2.0 mm. l x l O " 3 mm Hg. C.V.C. GIC - 017.2 i o n tube. , ( j ) B e l l o f r a m R o l l i n g Diaphragm - 1Impervon' E l a s t o m e r . 177. Appendix B C a l i b r a t i o n o f Load C e l l The B.L.H. SR-4 l o a d c e l l ,.'as c a l i b r a t e d a g a i n s t a B a l d w i n T e s t i n g Machine by l o a d i n g i n i n c r e m e n t s o f 2,000 l b s . , then u n l o a d i n g i n decrements o f 5,000 l b s . A c a l i b r a t i o n c u r v e of l o a d , i n l b s , , v e r s u s s t r a i n , i n u - s t r a i n s , gave a l i n e a r p l o t o f s l o p e 12.5 l b s / u - s t r a i n . -1 7 8 . 179. Appendix C B.E.T. C a l i b r a t i o n s ( i ) Gas B u r r e t t e s The volume o f each b u l b was d e t e r m i n e d by we i g h i n g ' amounts, o f w a t e r run from t h e i n v e r t e d b u r r e t t e s between t h e e t c h marks. For w a t e r c a l i b r a t i o n the b u r r e t t e s are i n v e r t e d t o s i m u l a t e the mercury meniscus. D u r i n g the c a l i b r a t i o n the b u l b s were t h e r m o s t a t e d a t 30°C. R e s u l t s are g i v e n i n T a b l e 16. ( i i ) Free Volume (Va) The f r e e volume o f the a p p a r a t u s i s the volume from the ze r o e t c h marks on t h e gas b u r r e t t e s , i n c l u d i n g the manometers w i t h the mercury r a i s e d t o t h e c o n s t a n t volume marks, t o the sample v e s s e l s t o p c o c k s , i . e . t h e i n t e r n a l a p p a r a t u s volume e x c l u d i n g the volumes o f the sample v e s s e l s . The f r e e volume may be c a l c u l a t e d by a d m i t t i n g a dose o f He t o the a p p a r a t u s w i t h the sample v e s s e l s c l o s e d , and measuring the p r e s s u r e , w i t h a l l mercury l e v e l s a d j u s t e d to the c o n s t a n t volume marks. By r a i s i n g t h e mercury i n t h e gas b u r r e t t e s one b u l b a t a time a s e r i e s o f p r e s s u r e r e a d i n g s are o b t a i n e d . I f V i s t h e volume o f the empty b u l b s , and knowing the volumes o f the b u l b s , we have, P(V+Va) = K T i s c o n s t a n t PV+PVa = K PV = K-PVa 180. TABLE 16 Bulb C a l i b r a t i o n 5 B u r r e t t s Mo. 1 Temp. 30.2°C D e n s i t y o f H o0=.99561 Bulb No. Ave. Wt. H?0 1 98. 9319 2 29.5515 3 20.0473 4 10. 3923 B u r r e t t e No. 2 B u l b No. Ave. Wt^ H 20 Vo l (cos.) 1 145.2499 144.60 2 9 8.8351 9 8.39 3 30.0427 29.91 4 ' 9. 7 84 8 9. 74 181. A p l o t o f PV v e r s u s P has s l o p e - V a . ( i i i ) . Dead Space Vd The dead space i s the unoccupied volume o f the sample v e s s e l . T h i s i n c l u d e s t h e i n t e r n a l volume o f the specimen and s h o u l d t h e r e f o r e - b e d e t e r m i n e d b e f o r e each r u n . The method i s the same as f o r the f r e e volume c a l i b r a t i o n but w i t h the sample v e s s e l open t o the system. > The d i f f e r e n c e between t h e t o t a l volume o b t a i n e d and t h e f r e e volume y i e l d s the dead space. T y p i c a l r e s u l t s are g i v e n i n Table 17 and p l o t t e d i n F i g , 48. 182 Volume C a l i b r a t i o n TABLE (a) F r e e V o l . (b) Dead Space (1) (2) (3) P cms V c c s P x V V = = V o l O f empty b u l b s 7. 823 440. 841 3 44 8.59 9 10.813 296.245 3203.297 Temp = = 32.6°C 14 . 548 197.756 2876.983 22.376 99.368 2223.458 26.764 69.949 1872.115 33.217 40.041 1330.041 7.573 440. 841 3338.488 10. 2 84 296.245 3046.583 13.655 197. 758 2700.385 20.220 99.368 2009.220 23.667 6 9.949 16 55 . 982 13.666 197.758 2702.560 7. 313 440.841 3223.870 - 9.94 9 296.245 2947. 341 13.194 197.758 2609.219 19.641 99.368 1951.686 22.933 69. 949 16 04 . 14 0 13.220 197. 758 2614.360 7.104 440.841 3131.293 9.652 293.245] 2859.356 12.739 197.758 2512.239 19.141 99. 36 8 1902.002 22.443 6 9.94 9 1559.865 - 9.779 296.245 2896.979 Volume C a l i b r a t i o n C a l c u l a t i o n s ( a ) F r e e V o l . S l o p e o f c u r v e = i ~ = 84.1 c c s 1 8 3 (b) Dead Space Sample Vessel_JL Sample V e s s e l 2 Sample V e s s e l 3 1 8 4 . TABLE 17 (Cont'd) Slope = i l t i i l x 100 = 104 . 5 ccs 10 — — — V o l 1 = 20.4 ccs Slope = ±±LL = 102.2 ccs 10 — — — - — ' V o l 2 = 18.1 ccs Slope = 1 H £ = 102. 8 ccs 10 — — V o l 3 = 18.7 ccs 1 8 5 Appendix D B. E. T\_ Is_o^therm C ^ l ^ l a t i o n s (a) I s o t h e r m A p l o t o f R e l a t i v e P r e s s u r e v e r s u s Volume adsorbed i n ccs/gms a t STP i s c a l l e d the a d s o r p t i o n i s o t h e r m . I f P-^  i s the i n i t i a l p r e s s u r e o c c u p y i n g the f r e e volume Va and P 2 i s the p r e s s u r e a f t e r a d m i s s i o n to the sample v e s s e l , t h e n the amount o f gas adsorbed i s the i n i t i a l volume l e s s t h e f i n a l volume at the t e m p e r a t u r e o f t h e e x p e r i m e n t T. In ccs/gms at STP the volume adsorbed i s , Pj x V a - P 2 ( V a + Vd) 27 3 1 760 (273+T) m where m i s the specimen w e i g h t . For each a d d i t i o n a l dose s i n c e an amount at P 2 and Vd was a l r e a d y e n c l o s e d i n the sample v e s s e l the amount adsorbed w i l l be g i v e n by, P 3xVa+P 2Vd - P 4(Va+Vd) 760 x x — ccs/gm S.T.P. 273xT m The volume o f gas adsorbed at the e q u i l i b r i u m p r e s s u r e P i s then the sum o f the amounts adsorbed f o r the f i r s t and second doses. 1 8 6 . ' _ The example f o r H 20 i s g i v e n i n Table 18. (b) B.r..T. . L i n e a r P l o t The B.E.T. e q u a t i o n i s w r i t t e n i n t h e form V ( P o - 0 ) VmC + VmC * ° A p l o t o f — v e r s u s P/P w i l l g i v e a s t r a i g h t C 1 V ( V P ) n l i n e o f s l o p e « and i n t e r c e p t . VrnC VmCT Vm i s g i v e n by, 1 Slope + I n t e r c e p t T a b l e 18 and 19 g i v e d e t a i l s o f t h e da t a from which F i g . 22 i s c o n s t r u c t e d . Table 20 l i s t s the monolayer volumes f o r t h e f o u r systems measured. ( c ) S p e c i f i c S u r f a c e A r e a ^ C a l c u l a t i o n s In o r d e r t o determine the s u r f a c e a r e a o f the ad- s o r b a n t i t i s n e c e s s a r y to know t h e c r o s s - s e c t i o n o f t h e gas m o l e c u l e . T h i s a r e a i s g i v e n by 2/ 3 A = 4(0. 866) _ i i — 4 / 2ND where M i s the M o l e c u l a r weight o f the gas, d i t s d e n s i t y and N Avogadro's No. For n i t r o g e n at l i q u i d N 2 t e m p e r a t u r e s A i s e q u a l t o 16.2 A 0. Knowing Vm per gms. the s p e c i f i c s u r f a c e a r e a may be c a l c u l a t e d as f o l l o w s 1 8 7 . TABLE 18 A d s o r p t i o n I s o t h e r m Data on Vycor G l a s s V y c o r G l a s s A r e a = 225 m2/gms Temperature C o n s t a n t a t 2 5.2°C Water Vapour Vads p/p o (ccs/gm STP) 0.021 17.9 0.033 35. 0 0.088 62.4 0. 10 70.4 0.19 95.0 0.24 104. 8 0. 31 115.7 0.43 130.2 0.525 155.0 0.69 199.0 188 TABLE 19 B.E.T. L i n e a r P l o t s P mms P/P^ Vads ccs/gm P -P V(P -P) ° o o H 20 2.11 .088 62.4 21. 89 1365 . 9 .00154 2.40 . 1 70.4 21.60 1520.6 .00158 5. 76 .24 104. 8 18. 24 1911. 5 ' .00301 7. 44 . 31 116. 7 16. 56 1932 . 5 .00385 TABLE 20 Monolayer Volumes from B.E.T. L i n e a r P l o t s Slope I n t e r c e p t S l o p e + I n t e r c e p t V m =^7Y H 20 .010 .001 .011 90.9 n-Butylamine .046 -.0015 .0445 22.5 Acetone .026 .0015 .0275 36.4 Benzene .054 .005 .059 17.0 1 8 9 ' _ . Vm x 6.D23 x 1 0 2 3 x 15.2 S u r f a c e A r e a = — —--•< ~— — — — 22.4 x 1 0 3 x 1 0 2 0 square m e t r e s / g r a n . g i v e n by 0 =-JL The 'Vm s u r f a c e coverage 0 a t a volume o f gas V, i s * ^  S u r f a c e Free Energy Changes o n ^ A d s o r p t i o n I f Y o i s "the f r e e energy r e q u i r e d to c r e a t e 1 cms o f new s u r f a c e i n vacuo, and t h i s i s reduced to y i n the p r e s e n c e o f an a d s o r b a b l e gas, t h e n the decrease i n s u r f a c e f r e e energy i s = Y Q-Y . Tf = Y Q-Y i s a l s o c a l l e d the s p r e a d i n g p r e s s u r e , The-.Gibb's a d s o r p t i o n e q u a t i o n g i v e s , - dY = RT N d l n P where N i s t h e number o f moles ad- o s o r b e d p e r cms a t p r e s s u r e p. I n t e g r a t i n g Y - Y = RT N d l n P o RT MS f x : d l n P ' P / P o - 2.'..30.3 R T MS x d l o g P/P Q. X i s t h e number o f gms. a d s orbed per gm. o f s o l i d and S i s the s u r f a c e a r e a . 190 Thus by p l o t t i n g X v e r s u s l o g P/P Q and i n t e g r a t i n g g r a p h i c a l l y the decrease i n s u r f a c e f r e e energy an a d s o r p t i o n may be d e t e r m i n e d . The method i s n o r m a l l y a p p l i c a b l e t o r e v e r s i b l e p r o c e s s e s , i . e . where a d s o r p t i o n and d e s o r p t i o n are e q u a l . However i n t h i s a p p l i c a t i o n we a r e o n l y i n t e r e s t e d i n the s u r f a c e f r e e energy d e c r e a s e on a d s o r p t i o n and t h e h y s t e r e s i s on d e s o r p t i o n i s not t a k e n i n t o a c c o u n t . 191. 2.30 8 RT jf = Ay = — — — e MS P/P o Jo x d l o g P/P x = gms/gms adsorbed M = Mol. Wt. S = S u r f a c e A r e a u 2. 30 3 x l_»A8,J!L.L'..ii -3 ^- r e a 22 5 x 1 0 U X 1 0 M A 7 2 - 5.03 x 10 cals/cms M A r e a . . 0 . n .., , 2 — — — x 6.03 x 4.184 ergs/cms M A r e a ? ——-™- x 2 5.2 ergs/cms U n i t s = H^is- x x deg£i££ x M ± x _ A , degree moles gms ens e a l s , 'ergs. -—j- - 2 cms cms TABLE 21 Su r f a c e Energy P l o t s RT MS Vads d i n P/P, gft/giii o Vads P/P^ o - l o g P/P o mgms/g .021 + 1.6778 14. 4 .03 3 + 1.4 815 28. 3 .088 1.0555 50. 5 .10 1.0000 57.0 .19 . 7212 76.9 .24 .6198 84 . 8 . 31 . 50 86 94 . 5 .43 . 3565 105.4 .625 . 2041 125.5 .59 . 1612 161.1 193 Appendix E T e n s i l e F r a c t u r e . Strength_ C a l c u l a t i o n s " 1 m i c r o s t r a i n = 12.5 l b s l o a d . From B r a z i l i a n Test the t e n s i l e s t r e n g t h i s g i v e n as 2P TTDt where P i s the l o a d in. l b s D i s t h e specimen d i a m e t e r = .5" t i s the specimen t h i c k n e s s = .5" 6 = ^2.55 P An example f o r I^O^oh^K-imble g l a s s i s g i v e n i n T a b l e 23. TABLE 2 2 S u r f a c e Tension R e d u c t i o n s on A d s o r p t i o n . ( V y c o r G l a s s ) Area Area/M - l o g P/P o P/P o A Y A y l / 2 8 . 4 4 1 . 5 0 . 0 3 2 1 1 . 0 8 3 . 3 3 2 9 1 . 6 1 1 . 0 0 . 1 0 0 4 0 . 5 7 6 . 3 7 4 9 2 . 7 2 0 . 7 0 . 2 0 0 6 8 . 5 4 8 . 2 8 6 6 3 . 6 6 0 . 5 0 . 3 1 6 9 2 . 2 3 9 . 6 0 9 9 5 . 5 0 0 . 2 0 . 6 3 1 1 3 8 . 6 0 1 1 . 7 7 1 4 4 8 . 0 0 0 1 . 0 2 0 1 . 5 0 1 4 . 2 0 TABLE 2 3 F r a c t u r e Isotherms - H 20 on Kimble G l a s s P Q = 2 4 mms Hg T e n s i l e S t r e n g t h II1II Load d c y P mms P/P D 2 9 2 3 6 5 0 9 2 9 7 VAC 0 2 0 5 2 5 6 3 6 5 2 7 . 6 2 . 0 2 6 1 5 1 1 8 9 0 4 8 2 2 1 . 2 . 0 4 8 1 4 1 1 7 5 8 44 84 1 . 8 . 0 7 1 1 4 5 1 8 1 0 4 6 1 6 2 . 5 . 1 0 6 1 5 7 1 9 6 2 5 0 0 3 2 . 5 . 1 0 8 1 5 6 1 9 5 4 4 9 8 2 3 . 7 . 1 5 3 1 6 3 2 0 3 9 5 2 0 0 5 . 8 . 2 4 1 5 0 1 8 6 9 4 7 6 5 7 . 0 . 2 9 1 4 6 1 8 2 0 4 6 4 ] 9 . 1 . 3 8 1 5 1 1 8 9 0 4 8 2 2 1 1 . 3 . 4 7 1 4 4 1 8 0 0 4 5 84 1 4 . 2 . 5 9 1 4 8 1 8 4 7 4 7 1 1 1 8 . 2 . 76 1 4 1 1 8 5 6 4 2 2 2 2 0 . 4 . 8 5 1 5 1 1 8 9 0 4 8 2 2 . 2 1 . 4 . 8 9 1 3 5 1 6 85 4 2 9 8 2 2 . 8 . 9 5 

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