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Superplasticity in the cadmium-lead system Donaldson, Kenneth Cromwell 1971

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SUPERPLASTICITY IN THE CADMIUM-LEAD SYSTEM by KENNETH CROMWELL DONALDSON B . A . S c . U n i v e r s i t y of B r i t i s h Columbia , 1966 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY i n the Department of METALLURGY We accept . this t h e s i s as conforming to the r e q u i r e d s tandard THE UNIVERSITY OF BRITISH COLUMBIA February 1971 In presenting th i s thes is in pa r t i a l fu l f i lment o f the requirements fo r an advanced degree at the Un ivers i ty of B r i t i s h Columbia, I agree that the L ibrary sha l l make it f r ee l y ava i l ab le for reference and study. I fu r ther agree tha permission for extensive copying o f th is thes is for scho la r l y purposes may be granted by the Head of my Department or by his representat ives . It is understood that copying or pub l i ca t ion of th is thes is fo r f inanc ia l gain sha l l not be allowed without my wri t ten permiss ion. Department of M e t a l l u r g y  The Univers i ty of B r i t i s h Columbia Vancouver 8, Canada Date A p r i l 7, 1971 i . ABSTRACT S e v e r a l a p p r o p r i a t e l y t r e a t e d a l l o y s ( P b - 6 . 5 v o l . % C d , P b - 2 8 v o l . % C d , Cd-6vol .%Pb and Z n - l w t . % A l ) were i n v e s t i g a t e d f o r t h e i r s u p e r p l a s t i c p r o p e r t i e s , and documented i n terms of t h r e e - s t a g e s t r a i n r a t e s e n s i t i v i t y curves i n which stage I I , the r e g i o n of maximum s u p e r p l a s t i c i t y , was of prime i n t e r e s t . The i n v e s t i g a t i o n i n c l u d e d a n a l y s i s o f : creep and t e n s i l e t e s t d a t a , s u r f a c e de format ion m a r k i n g s , a c t i v a t i o n energy t e s t s and I n s t r o n i n f e r e n c e s of a " b a c k s t r e s s " . The r a t e c o n t r o l l i n g and prime s t r a i n - p r o d u c i n g process i n stage I I was i d e n t i f i e d to be d i f f u s i o n a l g r a i n boundary s l i d i n g w i t h s l i p accommodation at t r i p l e l i n e s . S e v e r a l i n t e r p r e t a t i o n s were f e a s i b l e f o r s tage I , a l l i n v o l v i n g processes concurrent w i t h , and dependent on , g r a i n boundary s l i d i n g . Stage I I I was i d e n t i f i e d as " n o r m a l " c o a r s e - g r a i n e d creep (adapted to permi t c o n s i d e r a b l e recovery i n the v i c i n i t y of g r a i n b o u n d a r i e s ) , o p e r a t i n g independent ly of s u p e r p l a s t i c p r o c e s s e s , and dominat ing at h i g h f l o w s t r e s s e s and s t r a i n r a t e s . ACKNOWLEDGEMENT S The author i s g r a t e f u l f o r the a d v i c e and a s s i s t a n c e g i v e n by D r . N . Risebrough and D r . T. A l d e n , and f o r the h e l p f u l d i s c u s s i o n s w i t h o ther f a c u l t y members and graduate s t u d e n t s . F i n a n c i a l a s s i s t a n c e was p r o v i d e d by the N a t i o n a l Research C o u n c i l . i i i . TABLE OF CONTENTS PAGE 1. INTRODUCTION * 1 2. LITERATURE SURVEY . 2 2 . 1 . I n t r o d u c t i o n 2 2 . 2 . S u p e r p l a s t i c phenomenology 4 2 . 2 . 1 . Evidence f o r d i s l o c a t i o n networks 4 2 . 2 . 2 . Evidence f o r s l i p 5 2 . 2 . 3 . Evidence f o r d i f f u s i o n a l s t r a i n 5 2 . 2 . 4 . Apparent a c t i v a t i o n energy 6 2 . 2 . 5 . G r a i n s i z e e f f e c t s 6 2 . 2 . 6 . Evidence f o r g r a i n boundary s l i d i n g . . . . 7 2 . 2 . 7 . E f f e c t of second phase 8 2 . 2 . 8 . G r a i n shape change and g r a i n growth . . . . 8 2 . 3 . S u p e r p l a s t i c mechanisms 9 2 . 3 . 1 . Genera l 9 2 . 3 . 2 . D i f f u s i o n a l processes 9 2 . 3 . 3 . G r a i n boundary s l i d i n g 11 2 . 3 . 4 . M i g r a t i o n and r e c r y s t a l l i z a t i o n 12 2 . 3 . 5 . D i s l o c a t i o n mechanisms 12 2 . 3 . 6 . Combined processes 13 2 .4 . O b j e c t i v e s of present i n v e s t i g a t i o n 14 3 . EXPERIMENTAL 15 3 . 1 . M a t e r i a l s cho ice 15 3 . 2 . Procedure • 16 i v . PAGE 3.2.1. A l l o y preparation 17 3.2.2. S t a b i l i z e d test structures 17 3.2.3. Preparation of specimens f or te s t i n g . . . . 23 3.2.4. Testing apparatus 23 3.2.5. Metallography . . . . . 23 4. RESULTS AND DISCUSSION 25 4.1. S t r a i n rate s e n s i t i v i t y 25 4.1.1. General 25 4.1.2. R e p r o d u c i b i l i t y 25 4.1.3. Mechanical equation of state f o r stages I, II . 34 4.1.4. Stage I I I . . . • 35 4.1.5. Secondary observations 36 4.2. Grain growth 37 4.2.1. General 37 4.2.2. Cd-3p* . 38 4.2.3. Eutectic-3y . . . 38 4.2.4. Zn-lu . 41 4.2.5. Conclusions 41 4.2.6. Discussion 41 4.2.7. Grain growth model 42 4.3. Grain shape 44 4.3.1. General 44 4.3.2. Experimental 44 4.3.3. Discussion 49 4.4. Surface observations 50 V . PAGE 4.4.1. Genera l 50 4.4.2. Modes of de format ion . . . . . . . . . 51 4.4.3. Surface o b s e r v a t i o n s of s l i p and t w i n n i n g . . 52 4.4.4. G r a i n boundary e f f e c t s 64 4.4.4.1. Shear ing and p e e l i n g 64 4.4.4.2. S t r i a t i o n s 66 4.4.4.3. M i g r a t i o n marks 68 4.5. Creep behaviour 71 4.5.1. G e n e r a l 71 4.5.2. Pb-5y and e u t e c t i c-3y 72 4.5.3. Cd-3u and Cd-8y 75 4.5.4. Z n - l u . . . . . . . . 82 4.6. A c t i v a t i o n energy 83 4.6.1. Genera l 83 4.6.2. E x p e r i m e n t a l . 87 4.6.3. R e s u l t s 89 4.6.4. D i s c u s s i o n 95 4.6.4.1. Stage I I 95 4.6.4.2. Stage I 97 4.6.4.3. Stage I I I 97 4.6.4.4. Combined processes 97 4.7. I n t e r n a l s t r e s s 99 4.7.1. Genera l 99 4.7.2. E x p e r i m e n t a l 104 v i . PAGE 4 . 7 . 3 . D i s c u s s i o n 104 4 . 7 . 3 . 1 . aQ i n normal creep 104 4 . 7 . 3 . 2 . aQ i n s u p e r p l a s t i c i t y 105 4 . 7 . 3 . 3 . E f f e c t of aQ on m stages I and I I . . 108 5 . MECHANISTIC INTERPRETATION 112 5 . 1 . Stage I I I 112 5 . 2 . Stages I and I I . . . . . . • 113 5 . 2 . 1 . Coble and H-N creep 113 5 . 2 . 2 . G r a i n boundary s l i d i n g 117 5 . 2 . 3 . G r a i n boundary m i g r a t i o n . . . . . . . 119 5 . 2 . 4 . D i s l o c a t i o n networks 119 5 . 2 . 5 . Stage I . . . . . . . 120 6. SUMMARY AND CONCLUSIONS 121 APPENDIX A . Low temperature de format ion 123 APPENDIX B . S u p e r p l a s t i c systems p r e v i o u s l y i n v e s t i g a t e d . . 136 APPENDIX C. Specimen c o n t r a c t i o n i n a " r e v e r s e r e l a x a t i o n t e s t " 137 BIBLIOGRAPHY 138 LIST OF FIGURES PAGE 2 . 1 . T y p i c a l m-curve f o r a s u p e r p l a s t i c m e t a l 3 2 . 2 . G r a i n s i z e e f f e c t i n s u p e r p l a s t i c a l l o y s 7 2 . 3 . D e s c r i p t i o n of m - c u r v e ' i n terms of combined p r o c e s s e s , assuming models proposed by A l d e n (1969) 2 are r e l e v a n t . 13 3 . 1 . Phase diagrams (Metals Handbook (1948)) . a . Lead-cadmium system. b . Aluminum-zinc system 16 3 . 2 . C d - 3 u . P o l i s h e d and e t c h e d . x2100 . 19 3 . 3 . C d - 8 u . P o l i s h e d and e t c h e d . x2100 . . 19 3 . 4 . E u t e c t i c - 3 ) j . P o l i s h e d . x2600 20 3 . 5 . E u t e c t i c - 8 y . P o l i s h e d . x2600 . . 20 3 . 6 . P b - 5 p . P o l i s h e d and deformed. x2600 21 3 . 7 . Z n - l v i . P o l i s h e d and e t c h e d . x3400 . 21 3 . 8 . Schematic diagram of constant s t r e s s creep apparatus . 24 4 . 1 . M-curves f o r Cd-3y 26 4 . 2 . M-curves . f o r Cd-8y 27 4 . 3 . M-curves f o r Pb-5y 28 4 . 4 . M-curves f o r e u t e c t i c - 3 u 29 4 . 5 . M-curves f o r e u t e c t i c - 8 u i . 30 4 . 6 . M-curves f o r Zn - lp . 31 4 . 7 . S e n s i t i v i t y of m-curve shape to thermal h i s t o r y . . . 32 4 . 8 . M - c u r v e d e t e r m i n a t i o n by two techniques (stage I and I I 32 4 . 9 . E f f e c t of g r a i n growth on m-curve f o r a h y p o t h e t i c a l a l l o y 33 4 .10 . T y p i c a l f l o w curves f o r s tage I I I 33 PAGE 4.11. Dependence of m on temperature (stage II) . . . . . 36 4.12. Structural stability of Cd-3y* as a consequence of strain in stage II (Instron test) 39 4.13. Structural instability of eutectic-3p as a consequence of strain, originally in stage II (Instron test) 40 4.14. Second phase coarsening produced by sliding. (a) Particle shear -(b) Short-range diffusion at interface of particle on sliding boundary, allowing particle to remain steady while grains slide 43 4.15. Cd-3u*. Near surface (^  20p). x2600. (a) Before test. L = 3.4, L / w = 1.14 (b) After 100% elongation (m = .5, e ^  lO'Vin" 1, 23°C) L = 5.0M, / w = 1.76 46 4.16. Cd-3y*. Interior. x2600 (a) Before test. L = 5.0, L / w = 1.57 (b) After 100% elongation (m = .5, e ^  10""3min_1, 23°C) L = 4.8p, L / w = 1.37 . . . . . . . . . . . 47 4.17. Cd~8u*. 16% Elongation. Stage III (e ^ IO - 3 min - 1, T = 23°C) . x4000 53 4.18. Cd-8p*. 16% Elongation. Stage III (e ~ 10" 3 min"1, T = 23°C). x4000 . . . . . . . 54 4.19. Cd-3p*. 15% Elongation. Stage II (e ^ 10" 3 min 1, T = 23°C). x8000 A - closely associated striations and migration marks B - sliding in vicinity of lead particle " C - partial migration of curved, peeling boundary . . 55 4.20. Cd-3p*. 15% Elongation. Stage II (E ^ 1 0 - 3 min"1, T = 23°C, m ^ .5). x8000 . . . . 56 4.21. Cd-3p*. 15% Elongation. Stage II (E ^ 1 0 - 3 min"1, T = 23°C, m ^ .5). xl0,000 . . . . 57 4.22. Cd-3u*. 250% Elongation. Stage II (e ^ 10~3. mxn-1, T = 23°C, m ^ .5). xl5,000 A - peeling boundary striations B - sliding boundary striations C - migration marks 58 i x . PAGE 4 . 2 3 . C d - 3 u * . 35% E l o n g a t i o n . Stage I I . (e ^ 5 x I O - 4 m i n " 1 , T = 23°C, m * .5) x30,000 A - s t r i a t i o n s a t peeled i n t e r p h a s e boundary . . . . 59 4 .24 . C d - 8 y * . 13% E l o n g a t i o n . Stage I I . . , (e <v I O - 3 m i n " 1 , T = 128°C, m ^ . 5 ) . x6000 . . . . , 60 4 .25 . P b - 5 y . 15% E l o n g a t i o n . Stage I I . (E ^ 5 x 10~k m i n " 1 , T = 23°C, m ^ . 3 5 ) . x4000 . . . 61 4 .26 . P b - 5 y . 15% E l o n g a t i o n . Stage I I . (e 5 x I0~k m i n - 1 , T = 23°C, m ^ . 3 5 ) . x4000 A - pee led boundaries 62 4 .27 . C.d-3y*. Deformed r a p i d l y w i t h p l i e r s (stage I I I ) . x6000 63 4 .28 . Shear ing and p e e l i n g a t the s u r f a c e 65 4 . 2 9 . P o s s i b l e o r i g i n of s l i d i n g s t r i a t i o n s 67 4 .30 . M i g r a t i o n of a bump o n . a s l i d i n g boundary to r e l i e v e normal s t r e s s e s 69 4 . 3 1 . P o s s i b l e e x p l a n a t i o n f o r s l i d i n g - m i g r a t i o n sequence observed at s u r f a c e 69 4 . 3 2 . Creep curves f o r Fb-5u (stages I I , I I I ) , 73 4 . 3 3 . Creep curves f o r e u t e c t i c - 3 y (stages I I , I I I ) , . . . . . 74 4 .34 . Creep curves f o r s tage I I de format ion 76 4 . 3 5 . Pr imary creep i n stages I , I I 77 4 .36 . Delayed y i e l d i n Cd-3p , Cd-8u (stage I I I ) 78 4 .37 . D i f f i c u l t y i n r e c o v e r i n g de layed y i e l d i n Cd-8u (stage I I I ) 79 4 .38 . E f f e c t of p r e s t r a i n i n g i n s tage I I on delayed y i e l d i n s tage I I I (Cd-8y) 80 4 .39 . Pr imary creep i n Z n - l y (stage I ) 80 4 .40 . D i f f e r e n t i a l creep t e s t i n which temperature changes " i n s t a n t l y " at e c 84 4 . 4 1 . Decremental temp, change creep t e s t i n Cd-3y at 500 p s i . (One specimen, each p o i n t corresponding to a S . S . creep r a t e . T o t a l s t r a i n < 20%.) Stages I and I I are both r e p r e s e n t e d . (See F i g u r e 4 . 1 . ) 90 ; X . PAGE 4.42. AH-plots from Figure 4.1. (Cd-3y; stages I and II. . 91 4.43. AHA vs. flow-stress in stages I and II for Z.n-ly ana Cd-3y (cf Figures 4.1., 6.) 92 4.44. AH^ vs. flow-stress i n stages II and III for Pb-5y and Cd-8y 93 4.45. AH^-plots for eutectic-3y, eutectic-8y. Stage II, 500 psi. (from Figures 4.4. and 4.5.) 94 4.46. Combined processes (AH^ a slope) 98 4.47. Reverse relaxation technique for determining 0 o . . 101 4.48. M-and mD-curves for two superplastic alloys . . . . 103 4.49. Diffusional accommodation model a. Zero strain b. Steady-state condition . . . . . . . . . 106 4.50. Slip accommodation model a. Start of generation cycle b. Bowing dislocation during cycle 106 4.51. Stage I-II, behaviour described in terms of Op, oQ and a* , . 109 4.51. Stage. I-II behaviour for the two backstress models proposed 110 A.1. Instron flow curves for Cd-3y*, assuming uniform reduction of cross-sectional area with strain . . . 125 A.2. Instron flow curves for Cd-8y*, assuming uniform reduction of cross-sectional area with strain . . . 126 A.3. Yield effects due to dislocation multiplication (from Hahn (1962)) . 127 A.4. Tensile flow stress as a function of temperature for various strains (from Figures A . l . and A.2.) . . 129 A.5. Twinning in Cd-3y*. - 140°C (petroleum ether), 3% e. x3500 131 A.6. Twinning i n Cd-8y*. - 140°C (petroleum ether), 3% E . x3500 ;. 131 Non-basal s l i p i n Cd-3u*. - 140°C (petroleum ether), 3%. xlO.OOO . . . . . . . Work-hardening rate (^—) as a function of temperature f o r various s t r a i n s (from Figures A . l . and A.2. LIST OF TABLES PAGE 2 . 1 . T y p i c a l s t r a i n r a t e s e n s i t i v i t i e s . . 2 3 . 1 . P o s t - e x t r u s i o n specimen treatments 18 4 . 1 . G r a i n e l o n g a t i o n i n Cd-3y* 48 4 . 2 . A c t i v a t i o n energy data r e l a t i v e to s u p e r p l a s t i c i t y . . 88 4 . 3 . E x p e r i m e n t a l v a l u e s of a Q / a p 100 5 . 1 . T h e o r e t i c a l creep r a t e s f o r Coble and H-N models versus exper imenta l creep r a t e s 114 1. 1. INTRODUCTION S u p e r p l a s t i c i t y i s the a b i l i t y of a m a t e r i a l to s u s t a i n abnormally l a r g e t e n s i l e elongations without f a i l u r e . During the 1940's and 1950's, the remarkable d u c t i l i t y of some metals at moderate temperatures was associated w i t h phase changes or a l l o t r o p i c transformations (Underwood (1962)). I n 1964, Backofen i d e n t i f i e d a d i s t i n c t l y d i f f e r e n t k i nd of s u p e r p l a s t i c i t y , i n v o l v i n g f i n e - g r a i n e d metals (£ lOu) at intermediate temperatures .5T M). The present work i n v e s t i g a t e s the l a t t e r phenomenon e x c l u s i v e l y . Although scant i n f o r m a t i o n i s a v a i l a b l e to date, f i n e - g r a i n e d s u p e r p l a s t i c i t y has f e a s i b l e i n d u s t r i a l a p p l i c a t i o n . P o t e n t i a l e x i s t s i n the realm of hot working where d u c t i l i t y and low s t r e s s e s are assets i n forming processes. Improved d u c t i l i t y i n s t r u c t u r a l m a t e r i a l s under normal creep conditions (^  .5T^), w i t h the s a c r i f i c e of some s t r e n g t h , has been reported (Weinstein (1969)). An extensive phenomenology has been developed to describe s u p e r p l a s t i c i t y , although there i s no u n i v e r s a l agreement concerning operative and r a t e - c o n t r o l l i n g mechanisms. Chapter 2. i s a l i t e r a t u r e survey of the fundamental experimental evidence and i t s current t h e o r e t i c a l i n t e r p r e t a t i o n . 2. 2 . LITERATURE SURVEY 2 . 1 . I n t r o d u c t i o n The degree to which a f i n e - g r a i n e d meta l i s s u p e r p l a s t i c depends p r i m a r i l y on m, i t s s t r a i n r a t e s e n s i t i v i t y . H a r t (1967)''' developed the f o l l o w i n g s t a b i l i t y c r i t e r i o n f o r n e c k - f r e e t e n s i l e d e f o r m a t i o n . m + y £ 1 » (2.1) where m = 9 In a ( s t r e s s ) 9 l h e ( s t r a i n r a t e ) e ( s t r a i n ) ' 9a 9e When m = 0 , E q u a t i o n (2.1) becomes y > 1, which i s e q u i v a l e n t to the w e l l -known Cons idere c r i t e r i o n f o r r a t e - i n s e n s i t i v e d e f o r m a t i o n . I n s u p e r p l a s t i c d e f o r m a t i o n , y - 0 , and m i s s u b s t a n t i a l , dominat ing E q u a t i o n ( 2 . 1 ) . However, s u p e r p l a s t i c deformat ion i s probably never s t a b l e as m i s never equal to 1. (See Table 2 . 1 . ) . TABLE 2 . 1 . T y p i c a l s t r a i n r a t e s e n s i t i v i t i e s Process m(> 0 , < 1) Low temperature deformat ion 0 ( R a t e - i n s e n s i t i v e ) " N o r m a l " creep (^ .5T^) a, .2 " S u p e r p l a s t i c " creep -5T^) .3 - .7 F l u i d g l a s s f l o w 1 (Newtonian v i s c o u s ) An important e x t e n s i o n of H a r t ' s s t a b i l i t y c r i t e r i o n i s that even i f m + y < 1, s u b s t a n t i a l d u c t i l i t y may o c c u r , as the r a t e of development of i n s t a b i l i t i e s ( i . e . "necks" ) decreases w i t h i n c r e a s i n g (m + y) . T h i s p r e d i c t i o n has been borne out e x p e r i m e n t a l l y . I n s t a b i l i t i e s may appear at the onset of s u p e r p l a s t i c f l o w , but develop s l o w l y ( M o r r i s o n (1968)^) . Moreover , s u p e r p l a s t i c d u c t i l i t y does i n c r e a s e w i t h i n c r e a s i n g m (Backofen e t a l (1964), Lee and Backofen (1967)) . E l o n g a t i o n s of 200% at m ^ .3 and 1200% at m ^ .7 appear to be c h a r a c t e r i s t i c (Lee and Backofen (1967) ) . F i g u r e 2 . 1 . d e f i n e s the regimes a s s o c i a t e d w i t h a s u p e r p l a s t i c metal on a c o n v e n t i o n a l s t r a i n - r a t e s e n s i t i v i t y p l o t (m - c u r v e ) . LOG STRAIN RATE FIGURE 2 . 1 . . . T y p i c a l m-curve f o r a s u p e r p l a s t i c m e t a l I f determined from, creep t e s t s at constant s t r e s s , s t r a i n r a t e s i n the m-curve are u s u a l l y "s teady s t a t e " creep r a t e s . I f determined by I n s t r o n t e s t s at constant e l o n g a t i o n r a t e , s t r e s s l e v e l s p l o t t e d are n o m i n a l l y the s t e a d y - s t a t e f l o w s t r e s s e s . The s tandard documentation technique f o r s u p e r p l a s t i c a l l o y s i n v o l v e s one specimen per m-curve on an I n s t r o n . By s t r a i n i n g f o r s m a l l increments 1 - 2%) a t v a r y i n g s t r a i n r a t e s , a corresponding s e r i e s of f l o w s t r e s s e s may be o b t a i n e d . For stages I and I I , at l e a s t , these s t r e s s e s are e f f e c t i v e l y s t e a d y - s t a t e s t r e s s e s . I t i s n a t u r a l to compare the de format ion p r o p e r t i e s of f i n e -gra ined metals w i t h those of c o a r s e - g r a i n e d meta ls a t the s t r e s s e s , s t r a i n r a t e s and temperatures a s s o c i a t e d w i t h s u p e r p l a s t i c i t y . The f o l l o w i n g e m p i r i c a l equat ion d e s c r i b e s both s u p e r p l a s t i c and normal c reep : AH /KT e = S . o . e , (2 .2) where S = a s t r u c t u r e f a c t o r , m = apparent s t r a i n r a t e s e n s i t i v i t y , and AH^ = apparent a c t i v a t i o n e n t h a l p y . For normal c reep , m - .2 and AH. AH^ . N . r ' A B (bulk d i f f u s i o n ) These v a l u e s are c o n s i d e r a b l y d i f f e r e n t from those observed i n s u p e r p l a s t i c c reep , as subsequent d i s c u s s i o n w i l l show. 2 . 2 . S u p e r p l a s t i c phenomenology 2 . 2 . 1 . Evidence f o r d i s l o c a t i o n networks T r a n s m i s s i o n e l e c t r o n microscopy has shown tha t d i s l o c a t i o n networks e x i s t i n stage I I I i n much the same way as i n normal creep (Hayden and Brophy (1968), Lee ( 1 9 6 9 ) 1 , B a l l and H u t c h i s o n (1969) ) . Extensive primary creep (Surges 1969) and evidence f o r s t r a i n hardening (Alden (1968)) confirm the development of d i s l o c a t i o n microstructures i n stage I I I . i D i s l o c a t i o n networks do not e x i s t i n stages I and I I , and the d i s l o c a t i o n density i s very low (Hayden and Brophy (1968), Lee (1969)*, 2 Morrison (1968) ). N e g l i g i b l e primary creep (Hayden and Brophy (1968), Surges (1969)), and evidence f o r n e g l i g i b l e s t r a i n hardening (Alden (1968)) i n stage II confirm that d i s l o c a t i o n d e n s i t i e s are small. 2.2.2. Evidence f o r s l i p S l i p l i n e s have been observed on occasion on specimen surfaces a f t e r stage II deformation (Cook (1968)). However these observations are i n s u f f i c i e n t to conclude that s l i p i s a s i g n i f i c a n t strain-producing mechanism. Indirect evidence (Packer et a l (1968)), based on the developed e l l i p t i c i t y i n textured Zn-Al eutectic t e n s i l e specimens, suggests that s l i p - s t r a i n may be s i g n i f i c a n t . 2.2.3. Evidence f o r d i f f u s i o n a l s t r a i n I n d irect evidence suggests that d i f f u s i o n a l s t r a i n may play an important r o l e i n su p e r p l a s t i c ! t y . D i f f u s i o n a l creep has been i d e n t i f i e d i n coarse-grained Mg - .5% Zr deformed at ^  *8T^, through the presence of "denuded" transverse grain boundaries (Squires et a l (1963), Harris and Jones (1963)). A s i m i l a r a l l o y , Mg - 6Zn - .5Zr, also ; displayed denuded zones during apparently superplastic deformation (grain s i z e L * 18y, T ^ .8T„, m ^ .6)(Karim et a l (1968)). M The l a t t e r a l l o y , when processed to produce a very f i n e g r a i n s i z e (< l u ) , displayed surface s t r i a t i o n s p a r a l l e l to the t e n s i l e axis when deformed at T ^ .5T , m ^ .02 (Backofen et a l (1968)). Backofen; concluded tha t the a l l o y was s u p e r p l a s t i c i n s p i t e of i t s low m, and that s t r i a t i o n s were a r e f l e c t i o n of a d i f f u s i o n a l creep process which had a l r e a d y been e s t a b l i s h e d under d i f f e r e n t c o n d i t i o n s f o r the same, and s i m i l a r , a l l o y s . S t r i a t i o n s have been observed i n o ther systems which were d e f i n i t e l y s u p e r p l a s t i c (Zehr and Backofen (1969), A l d e n (1967)), and s e v e r a l a u t h o r s , p a r t i c u l a r l y Backofen , Zehr and K a r i m , b e l i e v e t h a t t h i s c o n s t i t u t e s good evidence f o r d i f f u s i o n a l creep i n s u p e r p l a s t i c i t y . 2.2.4. Apparent a c t i v a t i o n energy Apparent a c t i v a t i o n energies (AH^) have o n l y been determined f o r s tage I I , and w i l l be d i s c u s s e d i n some d e t a i l i n Chapter 4.6.. I n g e n e r a l , AH < AK, . , and AH. ^ ^AH,, i s c h a r a c t e r i s t i c . A D A D 2.2.5. G r a i n s i z e e f f e c t s I n s tage I I I , the m-curves tend to approach the m-curve f o r normal c r e e p , i n d i c a t i n g tha t g r a i n s i z e has minor s i g n i f i c a n c e (Alden (1967), H o l t (1968)), as i s the case f o r normal c r e e p . (A H a l l - P e t c h r e l a t i o n s h i p presumably a p p l i e s a t very h i g h s t r a i n r a t e s . ) F i g u r e 2.2. i l l u s t r a t e s s e v e r a l techniques used to e v a l u a t e the s t r o n g g r a i n s i z e e f f e c t i n s tage I I . Technique (1) l eads to a r e l a t i o n s h i p : o.= KL^ 5 , where b ranges from about 1 to 3 (Zehr and Backofen (1968), H o l t and Backofen (1966), H o l t (1968)). Techniques (2) - (4) l e a d to a r e l a t i o n s h i p : i = KL where a depends r a t h e r s e n s i t i v e l y on the t e c h n i q u e . For example, A l d e n and Schadler (1968) determined a ^ 9 by technique (2) (— c o n s t a n t ) , and a ^ 4.5 by technique (3) (a c o n s t a n t ) , f o r the same se t of m-curves . Values of a ^ 2 have been r e p o r t e d f o r technique (4) i n s e v e r a l a l l o y s ( M a r t i n and Backofen (1967), H o l t and Backofen (1966), Avery and Backofen (1965)). 7. LOG STRAIN RATE FIGURE 2.2." G r a i n s i z e e f f e c t i n s u p e r p l a s t i c a l l o y s . N o t w i t h s t a n d i n g the a r b i t r a r i n e s s i n d e f i n i n g the g r a i n s i z e e f f e c t , one t h i n g i s c e r t a i n : s tage I I i s s h i f t e d s t r o n g l y to lower s t r a i n r a t e s w i t h i n c r e a s i n g g r a i n s i z e . G i f k i n s (1967) observed enhanced s t r a i n r a t e s e n s i t i v i t y i n c o a r s e - g r a i n e d l e a d (200-500y) at very low s t r a i n r a t e s , which may have been a r e f l e c t i o n of s tage I I b e h a v i o u r . L i t t l e i n f o r m a t i o n e x i s t s concerning stage I , a l though i t may be s a i d that w i t h respect to stage I I , b i s lowered w h i l e a i s r a i s e d (Lee ( 1 9 6 9 ) 1 , H o l t (1968)) . 2 . 2 . 6 . Evidence f o r g r a i n boundary s l i d i n g D i r e c t evidence f o r g r a i n boundary s l i d i n g l i e s i n the s u r f a c e o b s e r v a t i o n of r e l a t i v e g r a i n mot ion (Alden (1967), A l d e n and Schadler (1969), Lee ( 1 9 6 9 ) 1 , C l i n e and A l d e n (1967)) . Lee (1969) 1 c a l c u l a t e d £GB to be as much as 93% i n s tage I I by measuring o f f s e t s on an imposed ETOT s u r f a c e g r i d . The o f f s e t marker technique f o r measuring the s t r a i n c o n t r i b u t i o n of g r a i n boundary s l i d i n g i s w e l l - e s t a b l i s h e d i n normal c reep , a l though i t i s belaboured w i t h s t a t i s t i c a l d i f f i c u l t i e s and o b s c u r i n g f a c t o r s such as boundary m i g r a t i o n ( B e l l et a l (1967)) . The p o s s i b i l i t y of accommodation s l i d i n g f o r d i f f u s i o n a l p r o c e s s e s , i n which no net s l i d i n g s t r a i n o c c u r s , would p r e j u d i c e e v a l u a t i o n of on the h i g h \jD 1U1 s i d e ( G i f k i n s and Langdon (1970)) . Moreover , Langdon and G i f k i n s (1970) have p o i n t e d out mathemat ica l e r r o r s i n L e e ' s a n a l y s i s . Thus i t may be concluded t h a t no accura te e v a l u a t i o n of e x i s t s , a l t h o u g h q u a l i t a t i v e l y i t appears that z„^/z^nm i s l a r g e . b o 1U1 2 . 2 . 7 . E f f e c t of second phase The purpose of a second phase i s p r i m a r i l y to r e f i n e and s t a b i l i z e the g r a i n s i z e . As Appendix 1. s h o w s , v i r t u a l l y a l l s u p e r p l a s t i c r e s e a r c h has i n v o l v e d m u l t i p h a s e a l l o y s . E u t e c t i c s and e u t e c t o i d s are popular a l l o y s . P r o v i d e d tha t the second phase i s a t l e a s t as s o f t as the m a t r i x , s u p e r p l a s t i c i t y can g e n e r a l l y be a c h i e v e d ; however, i n t e r p r e t a t i o n can be obscured i f the second phase occupies a c o n s i d e r a b l e volume f r a c t i o n . A hard second phase ( e . g . o x i d e , i n t e r m e t a l l i c , r e l a t i v e l y h i g h m e l t i n g p o i n t phase) may tend to i n h i b i t g r a i n boundary s l i d i n g and promote i n t e r - g r a n u l a r c a v i t a t i o n (Risebrough and Lund (1968), Donaldson (1968) , Waldron (1970)) . 2 . 2 . 8 . G r a i n shape change and g r a i n growth A s p e c i a l s tage I I c h a r a c t e r i s t i c i s the r e t e n t i o n of an approximate ly equiaxed s t r u c t u r e a f t e r e x t e n s i v e d e f o r m a t i o n (Chaudhari (1967) A l d e n (1967), Zehr and Backofen (1968) , Hayden and Brophy (1968) ) . I n c o a r s e - g r a i n e d creep there may be a tendency to r e t a i n an equiaxed 9. s t r u c t u r e , a l though not to the extent observed i n s u p e r p l a s t i c i t y ( B e l l et a l (1967)) . Another s t r i k i n g f e a t u r e of s tage I I de format ion i s s t r a i n -induced g r a i n - g r o w t h and second phase c o a r s e n i n g . A r e l a t i o n s h i p of the form ^— « e may be approximate ly c o r r e c t f o r a t l e a s t 100% s t r a i n i n > some a l l o y s (Cook (1968), A l d e n and Schadler (1968)) . 2 . 3 . S u p e r p l a s t i c mechanisms 2 . 3 . 1 . Genera l S e v e r a l mechanisms have been proposed as important s u p e r p l a s t i c p r o c e s s e s . Developed p r i m a r i l y to account f o r s tage I I b e h a v i o u r , the mechanisms attempt to e x p l a i n the unique phenomenology o u t l i n e d p r e v i o u s l y . To be r a t e - c o n t r o l l i n g , any such mechanism must p r e d i c t a reasonable creep r a t e , a l a r g e s t r a i n r a t e s e n s i t i v i t y , a s t r o n g g r a i n s i z e e f f e c t , and a reduced a c t i v a t i o n energy (< AHg). 2 . 3 . 2 . D i f f u s i o n a l p r o c e s s e s . The d r i v i n g f o r c e f o r the Newtonian v i s c o u s d i f f u s i o n a l processes i s the vacancy g r a d i e n t e x i s t i n g between t e n s i l e and compressive r e g i o n s . The H e r r i n g - N a b a r r o (H-N) a n a l y s i s ( H e r r i n g (1950)) assumes that b u l k d i f f u s i o n occurs between t r a n s v e r s e boundar ies under t e n s i o n and l o n g i t u d i n a l boundaries under compress ion, and p r e d i c t s : 10. . a.v.Dg.a ' H" N = " l ? ^ T ~ ' where a - 10 (geometric constant), Dg = diffusion coefficient for bulk diffusion, v = atomic volume, L = mean intercept grain size. The H~N equation predicts creep rates which are orders of magnitude too slow for some alloys (e.g. Alden (1967)) , and an activation energy which is probably too high. The Coble analysis (Coble (1963)) assumes an identical driving force, with the grain boundaries being the diffusion path rather than the bulk, leading to: , • 3.v.w.D„._.a Go ^ L3.KT ' ( 2 ' 4 ) where 8 - 150 (geometric constant), w = grain boundary width ('v 10^) , D = diffusion coefficient for grain boundary diffusion. The Coble equation predicts a reasonable activation energy (AH-,,), and creep rates which are generally several orders of magnitude faster than 11. H-N c reep , a l though o f t e n c o n s i d e r a b l y s lower than observed r a t e s ( e . g . G i f k i n s (1967)) . Zehr and Backofen (1968) contend tha t Coble creep may reasonably account f o r s u p e r p l a s t i c behaviour i n s e v e r a l a l l o y s . An a d a p t a t i o n of the Coble model i s the d i f f u s i o n a l accommodation of g r a i n boundary s l i d i n g at t r i p l e l i n e s . C a l c u l a t i o n s by G i f k i n s (1967) suggest that t h i s may be a r a t e - c o n t r o l l i n g s t e p . 2 . 3 . 3 . G r a i n boundary s l i d i n g Al though gra in-boundary s l i d i n g appears to be a d i s t i n c t i v e s u p e r p l a s t i c p r o c e s s , i t s p r e c i s e r61e i s u n c e r t a i n . I t may ac t as an accommodation process f o r d i f f u s i o n a l processes (Gibbs (1965)) , or i t may act as a pr imary s t r a i n - p r o d u c i n g p r o c e s s , r e q u i r i n g accommodation by other processes to m a i n t a i n c o m p a t i b i l i t y . To dec ide whether s l i d i n g i s a l i k e l y r a t e - c o n t r o l l i n g process r e q u i r e s an unders tanding of the nature of b o u n d a r i e s . I f boundaries were smooth and f l a t , then boundary v i s c o s i t y would probably be l o w , and s l i d i n g would be easy ( i n which case , o ther processes would c o n t r o l ) . Boundar ies , however, are not smooth. F i e l d i o n microscopy has shown tha t " l e d g e s " of l e n g t h <v 100S e x i s t i n tungsten (Ryan and S u i t e r (1964)) . G i f k i n s (1968) proposed that s l i d i n g c o u l d be c o n t r o l l e d by d i f f u s i o n around the l a r g e s t l e d g e s . (The d r i v i n g f o r c e would then be analogous to tha t o c c u r r i n g i n H-N or Coble c r e e p . ) A s i m i l a r model , developed by A l d e n 2 (1969) , g i v e s the d e s i r e d s t r o n g g r a i n s i z e dependence by assuming that the " s c a l e of roughness" of the boundaries i n c r e a s e s w i t h g r a i n s i z e . G i f k i n s and Alden conclude that creep r a t e s r e s u l t i n g from t h e i r models could make s l i d i n g a c o n c e i v a b l e , Newtonian, r a t e - c o n t r o l l i n g p r o c e s s . G r a i n boundary s l i d i n g , accomplished by the d i r e c t a b s o r p t i o n 12. of d i s l o c a t i o n s has been suggested as a p o s s i b l e r a t e - c o n t r o l l i n g process 2 (Alden (1968, 1969 ) , I s h i d a and Brown (1967)) . Edge components would c l imb i n the v i c i n i t y of the boundaries w h i l e screw components would be absorbed by g l i d e . 2 . 3 . 4 . M i g r a t i o n and r e c r y s t a l l i z a t i o n I t has been suggested that cont inuous g r a i n boundary m i g r a t i o n or r e c r y s t a l l i z a t i o n occurs i n the v i c i n i t y of s l i d i n g boundaries where p l a s t i c s t r a i n energy may accumulate (Cook (1968), H o l t (1968), Packer et a l (1968), Packer and Sherby (1967)) . However, no d e t a i l e d or p r e d i c t i v e models have been p r e s e n t e d . Moreover , r e c r y s t a l l i z a t i o n ( i . e . the growth of new g r a i n s ) has not been demonstrated e x p e r i m e n t a l l y f o r s u p e r p l a s t i c i t y . The evidence suggests that r e c r y s t a l l i z a t i o n does not occur ( G i f k i n s (1967), A l d e n (1967)) . 2 . 3 . 5 . D i s l o c a t i o n mechanisms The models proposed f o r normal creep ( e . g . " j o g g e d - s c r e w " , " c l i m b " , and "network" ) are i m p l i c i t l y assumed to apply i n stage I I I i n the s u p e r p l a s t i c l i t e r a t u r e . A d a p t a t i o n s of these models , p a r t i c u l a r l y the c l imb models of Weertman (1955, 1957), have been made to account f o r stage I I behaviour (Hayden and Brophy (1968), B a l l and H u t c h i s o n (1969)) . A s i m p l i f i e d a r r a y of d i s l o c a t i o n s i s assumed (perhaps one per g r a i n ) and the c l imb b a r r i e r i s a s s o c i a t e d w i t h the " h e i g h t " of a g r a i n boundary r a t h e r than the " h e i g h t " of a L o m e r - C o t t r e l l (or analogous) o b s t a c l e . The adapted models purpor t to e x p l a i n the h i g h m - v a l u e , the g r a i n s i z e e f f e c t , and the decreased a c t i v a t i o n energy i n s u p e r p l a s t i c i t y . I n order to e x p l a i n the low s t r a i n r a t e s e n s i t i v i t y i n stage I •13. 2 Alden (1969) proposed a r a t e - c o n t r o l l i n g model involving the "viscous g l i d e " of d i s l o c a t i o n s within the bulk. While behaving i n d i v i d u a l l y with Newtonian v i s c o s i t y , t h e i r density would increase with stress according 2 to p m  x a , a r e l a t i o n s h i p which i s common i n normal creep. As a r e s u l t , the apparent s t r a i n - r a t e s e n s i t i v i t y would be r e l a t i v e l y low (^  .33). 2.3.6. Combined processes It has become fashionable to describe the three-stage m-curve i n terms of concurrent (independent) and consecutive(dependent) processes. 2 Hart (1967) developed a mechanical analogue, with no reference to atomic models, to show how a combination of Newtonian and non-Newtonian processes could produce three stage behaviour. Figure 2.3. i l l u s t r a t e s a recent 2 model of Alden's (1969) . Processes "1" and "2" are consecutive. Whichever requires the higher stress at any s t r a i n rate controls. Process "3" i s independent of "1" or "2" and i s i d e n t i f i e d with normal creep. The s t r a i n rate for "3" i s added to the appropriate s t r a i n rate for "1" or "2" at any given stress l e v e l . LOG STRAIN RATE FIGURE 2.3. Description of m-curve i n terms of combined processes, assuming models proposed by Alden (1969) 2 are relevant. 14. The model developed by Zehr and Backofen (1968) i s s i m i l a r to A l d e n ' s except that processes " 1 " and " 2 " r e l a t e to non-Newtonian v i s c o u s gra in-boundary s l i d i n g and Coble c reep , r e s p e c t i v e l y . The low apparent m-value f o r s l i d i n g i n stage I would r e s u l t from some i n t e r n a l s t r e s s which r e s i s t s s l i d i n g . The concept of a b a c k s t r e s s i n f l u e n c i n g apparent s t r a i n r a t e s e n s i t i v i t y has a r i s e n o n l y r e c e n t l y i n the s u p e r p l a s t i c l i t e r a t u r e (Backofen et a l (1968), Chaudhari (1967), Avery and S t u a r t (1967)) , and w i l l be d e a l t w i t h f u l l y i n Chapter 4 . 7 . . 2 . 4 . O b j e c t i v e s of present i n v e s t i g a t i o n The b a s i c o b j e c t i v e s are to i n v e s t i g a t e areas f o r which i n f o r m a t i o n i s n o n - e x i s t e n t , sparse or i n c o n c l u s i v e , to e s t a b l i s h or c o n f i r m t r e n d s , and to i n t e r p r e t s u p e r p l a s t i c i t y i n the l i g h t of present f i n d i n g s . S p e c i f i c a l l y , the exper imenta l o b j e c t i v e s a r e : ( i ) To p r o v i d e b a s i c m-curve documentation f o r a p p r o p r i a t e and h e r e t o f o r e undocumented systems. ( i i ) To i n v e s t i g a t e creep behaviour i n stages I , I I , and I I I . ( i i i ) To determine apparent a c t i v a t i o n energies f o r s tages . I , I I and I I I . ( i v ) To i n v e s t i g a t e g r a i n shape and s i z e change as a f u n c t i o n of s u p e r p l a s t i c s t r a i n . (v) To i n v e s t i g a t e the p o s s i b i l i t y of a b a c k s t r e s s . ( v i ) To observe s u r f a c e deformat ion markings i n at l e a s t one a l l o y chosen f o r good m i c r o s c o p i c r e s o l u t i o n . 3. EXPERIMENTAL 1 5 . 3 . 1 . M a t e r i a l s cho ice Three a l l o y s i n the lead-cadmium system (Pb-6 v o l . % C d , Pb-28 v o l . % C d , C d - 6 . 5 v o l . % Pb) and one a l l o y i n the z inc -a luminum system (Zn-1 wt.% A l ) were i n v e s t i g a t e d . H e r e a f t e r , the a l l o y s w i l l u s u a l l y be r e f e r r e d to as " P b - " , " e u t e c t i c - " , " C d - " or " Z n - " r e s p e c t i v e l y , f o l l o w e d by a g r a i n s i z e n o t a t i o n ( e . g . P b - 5 y ) . The lead-cadmium system has s e v e r a l a t t r a c t i o n s . The o n l y p r e v i o u s work has i n v o l v e d a Pb-5 wt.% Cd a l l o y (Alden (1968) ) . The cadmium-rich end has never been i n v e s t i g a t e d f o r i t s s u p e r p l a s t i c p r o p e r t i e s ; n o r , f o r that m a t t e r , has any cadmium-based a l l o y . Lead and cadmium have s i m i l a r m e l t i n g p o i n t s (making the homologous temperature m e a n i n g f u l ) , and roughly e q u i v a l e n t hardnesses (thus a v o i d i n g the d i f f i c u l t i e s mentioned i n Chapter 2 . 2 . 7 . ) . By choosing three a l l o y s i n the same system, the behaviour of the e u t e c t i c can be compared w i t h the behaviour of i t s i n d i v i d u a l phases , as Pb-6 v o l . % Cd and C d - 6 . 5 v o l . % Pb are e s s e n t i a l l y s i n g l e phase. The cadmium-based a l l o y has two a d d i t i o n a l f e a t u r e s . The s o l u b i l i t y of l e a d i n cadmium i s n e g l i g i b l e below the e u t e c t i c temperature ( F i g u r e 3 . 1 . ) . Thus the a n a l y s i s of m-curves as a f u n c t i o n of temperature , and the d e t e r m i n a t i o n of AH, are not compl ica ted by p u r i t y and a temperature-dependent s t r u c t u r e . Moreover , cadmium lends i t s e l f w e l l to h i g h - m a g n i f i c a t i o n s u r f a c e o b s e r v a t i o n by r e p l i c a e l e c t r o n m i c r o s c o p y . ,• The prime reason f o r i n v e s t i g a t i n g the z inc-a luminum a l l o y was i t s p r e v i o u s l y demonstrated stage I behaviour (Turner (1970)) . (Stage I i s not g e n e r a l l y easy to achieve a t moderate s t r a i n r a t e s and C Atomic Percentage Cadmium 10 20 30 40 50 60 70 80 90 350 300 P 250 ZOO 600 - 500 400 Pb 10 20 30 40 50 60 70 80 90 Cd Weight Percentage Cadmium °C 700 600 500 400 300 200 100 Atomic Percentage Zinc "F 10 20 30 40 50 60 70 80 90 660° 1 i 1 i i L 1 1 1 (X + L -a 4/9.5? -a + a' a' / 6 2 . S 95 275° 31.6 78 993 -1200 1000 800 600 400 Al 10 2 0 3 0 4 0 5 0 60 70 8 0 90 Zn Weight Percentage Zinc FIGURE 3 . 1 . Phase diagrams (Metals Handbook (1948)) a . Lead-cadmium system. b . Aluminum-zinc system. 17. temperatures . ) Moreover , the a l l o y p r o v i d e d a d d i t i o n a l r e s u l t s f o r comparison w i t h the lead-cadmium a l l o y s . 3 . 2 . Procedure 3 . 2 . 1 . A l l o y p r e p a r a t i o n The lead-cadmium a l l o y s (99.999% P b , 99.999% Cd) were melted and s t i r r e d m e c h a n i c a l l y f o r f i f t e e n minutes a t 360°C i n a g r a p h i t e c r u c i b l e . A p r o t e c t i v e N a C l - K C l s a l t was used to m i n i m i z e o x i d a t i o n . The a l l o y s were bottom-poured i n a i r i n t o l " - d i a m e t e r copper moulds where s o l i d i f i c a t i o n occurred w i t h i n seconds. The i n g o t s were machined to c l o s e t o l e r a n c e f o r a , 9 " - d i a m e t e r e x t r u s i o n b l o c k , and extruded to e i t h e r .083" -diameter r o d or . 1 5 " - d i a m e t e r r o d , depending on the in tended a p p l i c a t i o n . Carbowax 1500 was used as an e x t r u s i o n l u b r i c a n t . The z i n c a l l o y (99.99% Z n , 99.99% A l ) was s i m i l a r l y p r o c e s s e d , except that the m e l t i n g temperature was 700°C and the e x t r u s i o n temperature 60°C. I n a l l cases , the a l l o y s were h o t - e x t r u d e d and the r e s u l t a n t s t r u c t u r e s were f u l l y r e c r y s t a l l i z e d . 3 . 2 . 2 . S t a b i l i z e d t e s t s t r u c t u r e s Table 3 . 1 . i n d i c a t e s the heat treatments g i v e n to the extruded a l l o y s i n order to produce s t a b l e s t r u c t u r e s f o r t e s t i n g . F i g u r e s 3 . 2 . - 3 . 7 . i l l u s t r a t e the r e s u l t a n t s t r u c t u r e s . Nominal g r a i n s i z e s (± ^ .5u) were c a l c u l a t e d f o r a l l a l l o y s by the i n t e r c e p t method i n which random l i n e s were drawn on micrographs ( t o t a l i n t e r c e p t s >100). As no i n v e s t i g a t i o n of the g r a i n s i z e e f f e c t per se was c a r r i e d o u t , great p r e c i s i o n i n g r a i n s i z e d e t e r m i n a t i o n was TABLE 3 . 1 . P o s t - e x t r u s i o n specimen treatments Compos i t ion Heat Treatment P o l i s h E t c h : Nominal G r a i n S i z e Cd-6 vo l .%Pb 5 m i n . @ 180°C (chemical) 40 gm. Na^SOit 400 gm. C r 0 3 1000 c c . H 2 0 2 (chemical) 30% H C l i n H 2 0 3 y ( " C d - 3 y " ) 2 days @ 220°C 8 y ( " C d - 8 y " ) Pb-28 v o l . % Cd 5 m i n . @ 180°C (chemical) 25% H 2 0 2 75% G l a c i a l a c e t i c 3 y ( " e u t e c t i c - 3 y " ) 4 h r . @ 220°C . . . . #]u("eutect ic-8y") Pb-6 v o l . % Cd 3 h r . @' 95°C 5 y ( " P b - 5 y " ) Zn-1 wt.% A l 2 days @ 23°C ( e l e c t r o l y t i c ) 800 m l . E t h y l a l c o h o l 50 m l . B u t y l c e l l u s o l v e 60 m l . Sodium t h i o c y a n a t e 20 m l . D i s t i l l e d H 2 0 l y ( " Z n - l y " ) FIGURE 3 . 3 . Cd - 8 u . P o l i s h e d and e t c h e d . x2100. 20. FIGURE 3 .5 . E u t e c t i c -8y . P o l i s h e d . x2600. FIGURE 3 . 6 . P b - 5 p . P o l i s h e d and deformed. x2600. 22. not a t tempted. The d i f f e r e n c e between the eutect ic-3u and e u t e c t i c - 8 y appeared to be m a i n l y one of s c a l e . The r e l a t i v e g r a i n s i z e s were f a i r l y a c c u r a t e , but a b s o l u t e v a l u e s were d i f f i c u l t to a s s i g n due to the presence of i n t e r p h a s e b o u n d a r i e s . In terphase boundaries were c o n s i d e r e d e q u i v a l e n t to i n t e r c r y s t a l l i n e boundaries p r o v i d e d the r e s p e c t i v e second phase g r a i n s were approx imate ly the same s i z e as the m a t r i x g r a i n s . Otherwise they were ignored i n g r a i n s i z e c a l c u l a t i o n s . Cd-3y and Cd-8u d i f f e r e d more than i n s c a l e . W h i l e Cd-8u had a f a i r l y u n i f o r m g r a i n - s i z e and a s t r i n g e r l e s s s t r u c t u r e , Cd-3p had a c o n s i d e r a b l e spread of g r a i n s i z e s , and a s l i g h t r e t e n t i o n of the e x t r u s i o n - i n d u c e d s t r i n g e r i n g of l e a d . The cadmium a l l o y s s p e c i f i e d i n Table 3.1. were from .083" extruded r o d , and were used e x c l u s i v e l y f o r m-curve d e t e r m i n a t i o n , creep t e s t s and a c t i v a t i o n energy t e s t s . Two s p e c i a l cadmium a l l o y s from .150" extruded rod were used p r i m a r i l y f o r m e t a l l o g r a p h y . These a l l o y s , Cd-3y* and Cd-8y*, were sub jec ted to the same heat treatments as Cd-3y and Cd-8y, r e s p e c t i v e l y , but had s l i g h t l y g r e a t e r g r a i n s i z e s . The r e l a t i v e l y l a r g e cross s e c t i o n of Cd-3y* and Cd-8y* made them amenable to s e c t i o n i n g and r e p l i c a t i o n . Due to the a n i s o t r o p y and l i m i t e d number of easy s l i p systems i n cadmium, a f i b r e t e x t u r e could a f f e c t the observed mechanica l p r o p e r t i e s . Specimens of Cd-3y* and Cd-8y* were r o t a t e d on t h e i r t e n s i l e a x i s p e r p e n d i c u l a r to an i m p i n g i n g X - r a y beam. The r e s u l t a n t back r e f l e c t i o n r i n g s were u n i f o r m l y i n t e n s e , sugges t ing n e g l i g i b l e p r e - t e s t f i b r e t e x t u r e . ( S i m i l a r a n a l y s i s showed that t e x t u r e d i d not r e s u l t from e x t e n s i v e s u p e r p l a s t i c de format ion e i t h e r . ) 23. 3 . 2 . 3 . P r e p a r a t i o n of specimens f o r t e s t i n g Reduced gauge s e c t i o n s f o r t e n s i l e and creep specimens were achieved w i t h a chemica l p o l i s h t e c h n i q u e . The g r i p ends were lacquered w i t h " m i c r o s t o p " and the specimens were r o t a t e d i n s o l u t i o n (Table 3 . 1 . ) to assure u n i f o r m r e d u c t i o n of c r o s s - s e c t i o n . Some specimens (from .15" rod) were cold-machined i n a m i c r o l a t h e , and subsequent ly reduced by ^ .002" by the chemica l technique to remove s u r f a c e d i s t o r t i o n . No d e t e c t a b l e mechanica l or s t r u c t u r a l d i f f e r e n c e e x i s t e d between specimens prepared i n e i t h e r way. 3 . 2 . 4 . T e s t i n g apparatus T e n s i l e t e s t s were performed on a s tandard f l o o r model I n s t r o n . Screw- t ightened clamps g r i p s s i m i l a r to those i l l u s t r a t e d i n F i g u r e 3 . 8 . were used . Creep t e s t s were performed on an "Andrade" constant s t r e s s d e v i c e . Creep e l o n g a t i o n was p l o t t e d a u t o m a t i c a l l y on a H e a t h k i t r e c o r d e r , w i t h an extensometer s i t u a t e d some d i s t a n c e from the specimen to permit bath immers ion . Automat ic temperature c o n t r o l of ± .5°C was achieved f o r mazola o i l and water immersion b a t h s . The nominal s e n s i t i v i t y of the r e c o r d e r f o r a 5 cm. gauge l e n g t h was ^ .01% s t r a i n or ^ .05% s t r a i n , depending on the extensometer u s e d . 3 . 2 . 5 . M e t a l l o g r a p h y Sur face f e a t u r e s were observed by normal l i g h t m e t a l l o g r a p h y , and by e l e c t r o n microscopy (50 k v ) . Two-stage r e p l i c a t i o n was employed, the f i r s t r e p l i c a be ing c e l l u l o s e ace ta te and the second chromium-shadowed carbon . 24. COUNTERBALANCES TO HEATHKIT RECORDER TAPE(S.S.) THREADED CLAMP GRIPS (AL) FIGURE 3.8. Schematic diagram of constant s t r e s s creep a p p a r a t u s . 25. 4. RESULTS AND DISCUSSION 4 . 1 . S t r a i n r a t e s e n s i t i v i t y 4 . 4 . 1 . Genera l F i g u r e s 4 . 1 . - 4 . 6 . i l l u s t r a t e the regimes f o r the a l l o y s i n v e s t i g a t e d . Only two stages are e v i d e n t f o r each a l l o y , a l t h o u g h stages I , I I and I I I are each represented i n a t l e a s t three a l l o y s . As w e l l as p r o v i d i n g documentation f o r new a l l o y s (except f o r Pb-5p), F i g u r e s 4 . 1 . - 4 . 6 . form the b a s i s f o r work and d i s c u s s i o n throughout the t h e s i s . The m-curves were ob ta ined by the s t r a i n r a t e change technique on a I n s t r o n (Chapter 2 . 1 . ) . A f t e r approaching s t e a d y - s t a t e -4 -1 at a low s t r a i n r a t e (e < 2%, i ^ 5 x 10 min ) , specimens (one per e m-curve) were s t r a i n e d i n 1% increments ( — — = 2 or 2.5) to a t t a i n e n f l o w s t r e s s r e a d i n g s . Each f a m i l y of m-curves corresponds to one batch of specimens prepared a c c o r d i n g to Table 3 .1 . 4 . 2 . 1 . R e p r o d u c i b i l i t y The shape r e p r o d u c i b i l i t y of the m-curves was e x c e l l e n t , a l though a s l i g h t l a t e r a l s h i f t i n g (< 10%) o c c u r r e d from specimen to specimen. T h i s s h i f t i n g was a s c r i b e d to v a r i a t i o n s i n gauge l e n g t h , c r o s s - s e c t i o n or g r a i n s i z e . I n any case , a 10% s h i f t i s n e g l i g i b l e on a l o g - l o g p l o t . There was a marked s e n s i t i v i t y of m-curve shape to p r e - t e s t thermal t rea tment , making i t necessary to d e r i v e any g i v e n f a m i l y of m-curves from a batch of i d e n t i c a l l y t r e a t e d specimens. F i g u r e 4 . 7 . i l l u s t r a t e s how two a p p a r e n t l y s i m i l a r heat treatments changed the shape FIGURE 4 . 1 . M - c u r v e s f o r Cd-3y FLOW STRESS (PSI) o 1 I I ! Mill I *8Z. I 1 « " i | i i l I il ii] 1 I M I a II | s—s I I nn [ r STRAIN R A T E (MIN" 1) FIGURE 4.4. M-curves f o r eutectic-3u. FIGURE 4.5. M-curves f o r eutectic - 8 p . o FIGURE 4 . 6 . M-curves f o r Z n - l u . FIGURE 4 . 8 . M -curve d e t e r m i n a t i o n by two techniques (stages I and I I ) . 33. GO O o o AB - N O G R A I N G R O W T H . AB — G R A I N G R O W T H . LOG STRAIN RATE FIGURE 4 . 9 . E f f e c t of g r a i n growth on m-curve f o r a h y p o t h e t i c a l a l l o y I i—I—I—i—i—i—i—i—i—i—i—r 12 -" I I I I I I I I I I I I I •'> 2 4 6 8 • 10 12 STRAIN (%) FIGURE 4 . 1 0 . T y p i c a l f l o w curves f o r stage I I I . of an m-curve w i t h o u t caus ing any s i g n i f i c a n t s h i f t . T h i s behaviour was r e p r o d u c i b l e f o r s e v e r a l specimens and temperatures . Batches I and I I came from the same e x t r u s i o n and were t e s t e d a t the same t i m e . Batch I I ( F i g u r e 4 . 1 . ) was annealed w i t h i n one day of e x t r u s i o n and s t o r e d at -20°C u n t i l t e s t e d three months l a t e r . Batch I was s i m i l a r l y t r e a t e d except tha t the a n n e a l i n g treatment occurred one day b e f o r e t e s t i n g , the specimens be ing kept a t -20°C u n t i l that t i m e . 4 . 1 . 3 . M e c h a n i c a l e q u a t i o n of s t a t e f o r s tages I and I I A unique r e l a t i o n s h i p e x i s t e d between s t e a d y - s t a t e s t r e s s and creep r a t e f o r any g i v e n temperature , independent of s t r a i n h i s t o r y , s u b j e c t to two r e s t r i c t i o n s : ( i ) A l l p r i o r s t r a i n must have occurred i n stages I and I I . ( i i ) T o t a l p r i o r s t r a i n must have been r e l a t i v e l y s m a l l to a v o i d c o m p l i c a t i o n s due to necking and g r a i n growth . A t o t a l s t r a i n of < 10% was s u f f i c i e n t l y s m a l l to meet t h i s c r i t e r i o n f o r a l l a l l o y s . As s t e a d y - s t a t e was e s s e n t i a l l y reached at each 1% s t r a i n increment i n the I n s t r o n t e s t s , the m-curves r e f l e c t a " m e c h a n i c a l equat ion of s t a t e " of the f o r m : CTs.s. " f(gs.s.> T )' <4-x> • One p r e d i c t i o n of e q u a t i o n (4.1) i s that m-curves may be ob ta ined by i n c r e m e n t a l creep t e s t s , i n which s t r e s s i s v a r i e d and creep r a t e s are recorded a f t e r 1% s t r a i n . F i g u r e 4 . 8 . demonstrates the g e n e r a l 35. a p p l i c a b i l i t y of the e q u a t i o n . I t i s important to e s t a b l i s h whether a mechanica l equat ion of s t a t e e x i s t s . I t i s u s u a l l y assumed i n the l i t e r a t u r e tha t such a s t a t e e x i s t s , a l though e x p l i c i t statement of the f a c t i s r a r e (Alden and Schadler (1968)) . I f such a s t a t e does not e x i s t , an m-curve may depend s t r o n g l y on the t e s t used to d e f i n e i t . A c o n c e i v a b l e s i t u a t i o n w i l l now be c o n s i d e r e d . Assume that the accumulated s t r a i n to p o i n t s B or B ' ( F i g u r e 4 . 9 . ) to o b t a i n an m-curve by the i n c r e m e n t a l technique i s = 15% f o r a h y p o t h e t i c a l a l l o y , AL _ 3 and t h a t : — a e , e a L . Both of these r e l a t i o n s h i p s are reasonable and may have f a i r l y g e n e r a l a p p l i c a b i l i t y (Chapter 2 . 2 . 5 . , 8 . ) . The r e s u l t a n t m-curve , A B ' , i s c o n s i d e r a b l y d i f f e r e n t from what i t would be i n the absence of g r a i n growth , AB. P o i n t B ' occurs at a s t r a i n r a t e 35% lower than does B . I n t h i s case , s t r a i n h i s t o r y s i g n i f i c a n t l y a f f e c t s the d e f i n i t i o n of an m-curve and may l e a d to f a u l t y a n a l y s i s . 4 . 1 . 4 . Stage I I I S t r a i n r a t e s e n s i t i v i t y was an ambiguous parameter i n s tage I I I (and i n the I I - I I I t r a n s i t i o n zone, whose extent was hard to e s t a b l i s h ) . For P b - 5 u , s t e a d y - s t a t e was not reached i n 1% i n c r e m e n t s . For Cd-3u and Cd-8y , and to a l e s s e r e x t e n t , the e u t e c t i c s , y i e l d p o i n t s occurred (see F i g u r e 4 . 1 0 . ) . Coupled w i t h these o b s c u r i n g f a c t o r s was the p r o p e n s i t y f o r r a p i d n e c k i n g . Documenting s tage I I I by the i n c r e m e n t a l I n s t r o n technique served m a i n l y to d i f f e r e n t i a t e between stages I I and I I I , as m was d e f i n i t e l y lower i n s tage I I I . A fundamental i n v e s t i g a t i o n of s t r a i n r a t e s e n s i t i v i t y ( f o r comparison w i t h normal creep) would have to i n v o l v e a n a l y s i s of f u l l f l o w curves and , i f p o s s i b l e , ins tantaneous 36. s t r e s s - c h a n g e t e s t s . No such i n v e s t i g a t i o n has been attempted i n t h i s work. 4 . 1 . 5 . Secondary o b s e r v a t i o n s There was a p e r s i s t e n t i n c r e a s e i n m w i t h i n c r e a s i n g temperature i n s tage I I f o r C d - 8 u , Cd-3u and e u t e c t i c ~ 3 u ( F i g u r e 4 .11 . ) O 260 O 0 - C D „ 3 u (2000 PSI). A - CD-8p (1000 PSI). Q-EUTECTIC -3u ^ (looc psi) o J I L 300 340 380 TEMPERATURE (°C) 420 FIGURE 4 . 1 1 . Dependence of m on temperature (s tage I I ) S i m i l a r behaviour has been r e p o r t e d f o r o ther a l l o y s ( H o l t and Backofen (1966), Lee and Backofen (1967), Lee (1969)* ) . S t r a i n r a t e s e n s i t i v i t y has a l s o been observed to i n c r e a s e w i t h temperature under normal creep c o n d i t i o n s ( L i (1968)) . Pb-6% Cd appeared to be l e s s s u p e r p l a s t i c than Cd-6.5% P b , 37. w h i l e the e u t e c t i c was i n t e r m e d i a t e , r e f l e c t i n g , perhaps , behaviour which depends on the volume f r a c t i o n of each phase. An unambiguous d e f i n i t i o n of " r e l a t i v e " s u p e r p l a s t i c i t y i s d i f f i c u l t . Q u a l i t a t i v e l y , a m a t e r i a l i s more s u p e r p l a s t i c than another i f , f o r e q u i v a l e n t g r a i n s i z e and homologous temperature , s tage I I occurs a t a f a s t e r s t r a i n r a t e and m max. i s l a r g e r . For any g i v e n temperature , s tage I I i n Cd-3u p e r s i s t e d to a h i g h e r s t r e s s than i n C d - 8 p . From m-curves i n the l i t e r a t u r e ( e . g . A l d e n (1967), Lee (1969)^) t h i s appears to be a g e n e r a l y e t undiscussed o c c u r r e n c e . I n the a l l o y s where stage I was w e l l - d e f i n e d (Cd-3u , Z n - l u ) , m appeared to decrease c o n t i n u o u s l y w i t h d e c r e a s i n g s t r a i n r a t e , r e a c h i n g v a l u e s l e s s than .2 ( Z n - l y ) . Values l e s s than .16 have been r e p o r t e d by Lee (1969). A stage I asymptote cannot be c o n f i d e n t l y d e f i n e d f o r any of the a l l o y s i n v e s t i g a t e d here or e l sewhere . 4 . 2 . G r a i n growth 4 . 2 . 1 . Genera l Al though g r a i n growth d i d not i n f l u e n c e the m-curves s i g n i f i c a n t l y (Chapter 4 . 1 . 3 . ) , i t i s a c h a r a c t e r i s t i c of s u p e r p l a s t i c deformat ion which warrants i n v e s t i g a t i o n . Specimens of C d - 3 u * and e u t e c t i c - 3 u were e longated 120% (stage I I a t the s t a r t ) to o b t a i n t r u e s t r e s s - e l o n g a t i o n c u r v e s . F i g u r e s 4.15.. and 4 . 1 3 . were c l o s e l y reproduced i n d u p l i c a t e t e s t s . As s t r a i n r a t e decreased c o n t i n u o u s l y d u r i n g the t e s t s (constant c ross -head speed) , the f l o w curves were n o r m a l i z e d to the 38. p o s i t i o n s they would have taken had s t r a i n r a t e and m remained constant from the s t a r t . The n o r m a l i z e d f l o w curves were obta ined by r a i s i n g 7 e l o n a t i m the t r u e f l o w curves by the c o r r e c t i o n f a c t o r (1 + — j-g^ ) . 4 . 2 . 2 . Cd-3u* That m remained constant a t .51 throughout the t e s t showed that deformat ion was s t i l l o c c u r r i n g i n stage I I a f t e r 120% e l o n g a t i o n , and that the normal ized f l o w curve was q u i t e v a l i d . The g r a i n s i z e -1 8 dependence of f l o w s t r e s s was determined to be a a L by s l i d i n g the stage I I p o r t i o n s of F i g u r e s 4 . 1 . and 4 . 2 . i n t o c o i n c i d e n c e at constant s t r a i n r a t e , and o b s e r v i n g the r e l a t i v e s h i f t i n f l o w s t r e s s . A l t h o u g h the r e l a t i v e g r a i n s i z e s f o r the two f a m i l i e s are not known p r e c i s e l y (Chapter 3 . 2 . 2 . ) , the exponent 1.8 i s i n reasonable agreement w i t h repor ted v a l u e s (Chapter 2 . 2 . 5 . ) . Given t h i s r e l a t i o n s h i p , any g r a i n growth should be s e n s i t i v e l y r e f l e c t e d i n the normal ized f l o w c u r v e . As the normal ized f l o w curve remains l e v e l from about 5% e l o n g a t i o n o n , i t i s concluded that g r a i n growth was n e g l i g i b l e over t h i s range of s t r a i n . S l i g h t necking (^ 5% maximum r e d u c t i o n i n c r o s s - s e c t i o n ) was observed at the end of the t e s t . The s t r e s s i n the necked r e g i o n w o u l d , as a consequence, have been about 10% h igher than the t r u e f l o w curve i n d i c a t e s . However, t h i s r i s e i n l o c a l i z e d f l o w s t r e s s would r e s u l t a t l e a s t i n p a r t from the enhanced l o c a l i z e d s t r a i n r a t e , and not from g r a i n growth. 4 . 2 . 3 . ' E u t e c t i c - 3 y That m v a r i e d from .4 a t the s t a r t of the t e s t to .28 at the end i n d i c a t e d a t r a n s i t i o n to s tage I I I d u r i n g the t e s t . I I I I 1 1 1 I 1 1 I 1 I 1 I I I I I I I I I I I 1 0 20 30 40 50 60 70 80 90 100 110 120 ELONGATION (%) FIGURE .4.12. S t r u c t u r a l s t a b i l i t y .of CdV3y* as a consequence of s t r a i n i n stage I I ( I n s t r o n t e s t ) . 2.4 NORMALIZED FLOW CURVE (M=.4) 2.2 2.0 b X I . 8 to a. to1-6 to UJ o r i -t n i . 4 NORMALIZED FLOW CURVE (M=.28) TRUE FLOW CURVE 1.2 1.0 i I I i I i i i I i i i J I I I L_J L_J 1 1 1 1 10 20 30 40 50 60 70 80 90 100 110 120 ELONGATION (%) FIGURE 4 . 1 3 . S t r u c t u r a l i n s t a b i l i t y of e u t e c t i c - 3 y as a consequence of s t r a i n , o r i g i n a l l y i n stage I I ( I n s t r o n t e s t ) . o 41. The s t r e s s i n the necked reg ions (20% maximum r e d u c t i o n i n c r o s s - s e c t i o n ) was c o n s i d e r a b l y h igher than the n o r m a l i z e d f l o w s t r e s s at the end of the t e s t . The h i g h s t r e s s i n necked reg ions c o u l d r e s u l t p a r t i a l l y from l o c a l i z e d s t r a i n - r a t e h a r d e n i n g , but p r i m a r i l y from s t r u c t u r a l change ( g r a i n growth and normal s t r a i n - h a r d e n i n g ) . 4 . 2 . 4 . Z n - l u Turner (1970) has shown t h a t g r a i n growth occurs r e a d i l y as a consequence of s t r a i n f o r s tages I and I I . 4 . 2 . 5 . C o n c l u s i o n s ( i ) G r a i n growth can i n some i n s t a n c e s ( e u t e c t i c - 3 u and Z n - l u ) occur r e a d i l y as a consequence of s t r a i n i n stage I I , an o b s e r v a t i o n w i t h c o n s i d e r a b l e precedent (Chapter 2 . 2 . 5 . ) . ( i i ) G r a i n growth does not n e c e s s a r i l y occur as a consequence of s t r a i n ( C d - 3 u * ) . I n o ther words , g r a i n growth i s not an e s s e n t i a l p a r t of the s u p e r p l a s t i c p r o c e s s , and need not be c o n s i d e r e d i n any fundamental model . A l though i n f e r e n t i a l j t h e technique used to c o n f i r m t h i s o b s e r v a t i o n appeared to be s i m p l e r and more accurate than the obvious a l t e r n a t i v e - d i r e c t m i c r o s c o p i c a n a l y s i s . 4 . 2 . 6 . D i s c u s s i o n Two p r o p e r t i e s of s u p e r p l a s t i c a l l o y s i n s tage I I tend to promote g r a i n growth as a f u n c t i o n of s t r a i n . A t low g r a i n s i z e s , the d r i v i n g f o r c e f o r g r a i n boundary energy r e d u c t i o n i s h i g h (energy per u n i t volume a j-). Moreover , s l i d i n g g r a i n s tend to m i g r a t e (Chapter 4 . 4 . 4 . 3 . ) . However, the degree to which growth i s r e s i s t e d may depend on a number of f a c t o r s : ( i ) P r e - t e s t s t a b i l i z a t i o n t rea tment . From the p o i n t of v iew of mechanica l p r o p e r t i e s , a l l a l l o y s t e s t e d (wi th the p o s s i b l e e x c e p t i o n of Z n - l u @ 60°C) were t h e r m a l l y s t a b l e over the times r e q u i r e d f o r t e s t i n g . However, a s t r o n g e r p r e - t e s t treatment may be r e q u i r e d to produce s t a b i l i t y i n the presence of s t r a i n than i n i t s absence. ( i i ) Nature and d i s t r i b u t i o n of second phase. Al though the second phase i n h i b i t s g r a i n growth , the degree to which i t does so may depend on such th ings as p a r t i c l e s i z e and d i s t r i b u t i o n on b o u n d a r i e s , and r e l a t i v e energies of phase and c r y s t a l l i n e b o u n d a r i e s . ( i i i ) P r o p o r t i o n of second phase . I t has been shown that an i n c r e a s e d volume f r a c t i o n of second phase can sometimes i n h i b i t g r a i n growth ( C l i n e and A l d e n (1967)) . T h i s o b s e r v a t i o n i s c o n s i s t e n t w i t h the i n a b i l i t y of i n t e r p h a s e boundaries to m i g r a t e . 4 . 2 . 7 . G r a i n growth model A model which may p a r t i a l l y e x p l a i n coarsening and g r a i n growth i n two-phase a l l o y s i s i l l u s t r a t e d i n F i g u r e 4 . 1 4 . , Boundary p a r t i c l e s exper ience a shear s t r e s s which i s u s u a l l y much h i g h e r than the r e s o l v e d shear s t r e s s over the e n t i r e s l i d i n g boundary. The magnitude of the s t r e s s depends i n v e r s e l y on the area f r a c t i o n of the boundary occupied by the second phase (Gibbs (1965))-. P a r t i c l e s e i t h e r shear ( F i g u r e 4 . 1 4 . a . ) , or remain s t a t i o n a r y w h i l e the g r a i n s s l i d e 43. (Figure 4.14,b.). I n the l a t t e r case, the mechanism would be one of l o c a l i z e d d i f f u s i o n (cf H-ty or Coble d i f f u s i o n ) . I n e i t h e r case, second phase accumulates at t r i p l e l i n e s . FIGURE 4.14. Second phase coarsening produced by s l i d i n g . (a) P a r t i c l e shear (b) Shor t - range d i f f u s i o n a t i n t e r f a c e of p a r t i c l e on s l i d i n g boundary, a l l o w i n g p a r t i c l e to remain steady w h i l e g r a i n s s l i d e . The r e s u l t a n t coarsening leads to m a t r i x g r a i n growth through the "Zener" r e l a t i o n s h i p (Smith (1949)): where L = m a t r i x g r a i n s i z e , d = second-phase s i z e , V f = second-phase volume f r a c t i o n . Although the above a n a l y s i s a p p l i e s s p e c i f i c a l l y to a 44. second phase which can be i d e n t i f i e d as " p a r t i c u l a t e " , s l i g h t a d a p t i o n could make i t apply to a e u t e c t i c i n which the second phase p a r t i c l e s can be i d e n t i f i e d as " g r a n u l a r " ^ The s l i d i n g of g r a i n s i n e v i t a b l y b r i n g s g r a i n s of the same phase i n c o n t a c t . Coarsening r e s u l t s from the tendency of the i n d i v i d u a l phases to agglomerate once they come i n t o c o n t a c t . The d r i v i n g f o r c e f o r agg lomerat ion would be the r e d u c t i o n of i n t e r f a c i a l energy through m i n i m i z a t i o n of phase boundary a r e a . 4.3. G r a i n shape 4.3.1. G e n e r a l The o b s e r v a t i o n that g r a i n s remain equiaxed a f t e r s u p e r p l a s t i c de format ion (Chapter 2.2.8.) has important t h e o r e t i c a l i m p l i c a t i o n s . I n the absence of boundary m i g r a t i o n and g r a i n growth (which would mask g r a i n e l o n g a t i o n ) , a r e t a i n e d equiaxed s t r u c t u r e would suggest g r a i n boundary s l i d i n g to be the c h i e f s t r a i n - p r o d u c i n g p r o c e s s . Normal s l i p and d i f f u s i o n a l (H-N or Coble) processes would be e l i m i n a t e d as they p r e d i c t g r a i n e l o n g a t i o n . (Some complex process i n v o l v i n g both s l i p and s l i d i n g cou ld p o s s i b l y be imagined which would m a i n t a i n equiaxed g r a i n s . ) Except i n c e r t a i n cases ( e . g . C l i n e and A l d e n (1967)), the r e p o r t e d i n s t a n c e s of r e t a i n e d equiaxed g r a i n s have g e n e r a l l y i n v o l v e d s i g n i f i c a n t g r a i n growth , making any i n t e r p r e t a t i o n obscure . 4.3.2. E x p e r i m e n t a l Cd-3u* was w e l l - s u i t e d to an a n a l y s i s of g r a i n e l o n g a t i o n i n tha t g r a i n growth d i d not occur i n stage I I (Chapter 4.2.2.). Such an a n a l y s i s was at tempted, a l though w i t h l i m i t e d s u c c e s s . Specimens were 45. deformed 100% i n tension, and the structures observed by r e p l i c a electron microscopy. To bring out g r a i n boundaries, specimens were sectioned p a r a l l e l to the t e n s i l e axis by c o n t r o l l e d p o l i s h attack, and subsequently deformed ^ 5% to show s l i p l i n e s and/or s l i d i n g . This technique was tedious and i n some cases ambiguous (due to the int r o d u c t i o n of subboundaries and confusing migration marks), but necessary, as a s u i t a b l e etch was not developed. V i s u a l examination of micrographs (e.g. Figures 4.15., 16.) led to the following observations: (i) The large number of transverse grain boundaries disappeared with s t r a i n along with any lead " s t r i n g e r i n g " . ( i i ) No s i g n i f i c a n t p a r t i c l e coarsening occurred. ( i i i ) S i g n i f i c a n t g rain elongation was apparent f or deformation near (^  25y) the surface, although not apparent f o r i n t e r i o r deformation. Quantitative analysis suggests that the t h i r d observation may be correct, although with l i t t l e s t a t i s t i c a l confidence (Table 4.1.). An inte r c e p t technique ( s i m i l a r to that developed by Hensler and G i f k i n s (1963-4)) was used to determine ^ g | ^ h ( L^B) r a t i o s . A square g r i d , approximately equal to the g r a i n s i z e , was superimposed on micrographs such that g r i d l i n e s were both p a r a l l e l and perpendicular to the t e n s i l e a x is. V a l i d L / g r a t i o s could be obtained f o r i n d i v i d u a l micrographs; however the following factors made ge n e r a l i z a t i o n d i f f i c u l t : ( i ) Grain s i z e was quite v a r i a b l e from r e p l i c a to r e p l i c a 4 6 . 47. TABLE 4 . 1 . G r a i n e l o n g a t i o n i n C D - 3 u * . (m = . 5 , 25°C. e ^ .001 m i n " 1 . ) Average G r a i n S i z e L/W (>100 i n t e r c e p t s ) (>100 i n t e r c e p t s ) Undeformed 3.4 JU 1.14 3.4 1.42 (1.22) SURFACE 3.7 1.10 Deformed 3.22 4.96 1.43 1.76 (1.59) Undeformed 5.0 1.57 (1.57) INTERIOR Deformed 4 .8 1.37 5.0 1.5 (1.49) 5.4 1.59 t The t e n s i l e a x i s was determined by r o t a t i n g the g r i d on the micrographs u n t i l a maximum L/W r a t i o was o b t a i n e d ; i n some cases , the t e n s i l e a x i s was obvious from the s t r i n g e r e d l e a d p a r t i c l e s ( e . g . f i g u r e s 4 .15a and 4 . 1 6 a ) . and even w i t h i n r e p l i c a s . The g r a i n s i z e , moreover, appeared to be l a r g e r i n the i n t e r i o r than a t the s u r f a c e . I t i s q u i t e p o s s i b l e t h a t L/w depends on both g r a i n s i z e d i s t r i b u t i o n and average g r a i n s i z e . To a v o i d the problem of v a r i a b l e g r a i n s i z e , an attempt was made to perform the same a n a l y s i s on C d - 8 u * (100°C, m . 5 , i. ^ .001 m i n - * ) . However a t 100°C, the l e a d p a r t i c l e s coarsened s i g n i f i c a n t l y , making meta l lography i m p o s s i b l e . ( i i ) C o n s i d e r a b l e ^ s c a t t e r occurred f o r r e p l i c a s where the average g r a i n s i z e was c o n s t a n t . (This may have been due , i n p a r t , to the g r a i n s i z e d i s t r i b u t i o n ) . Many o b s e r v a t i o n s would be r e q u i r e d to g i v e s t a t i s t i c a l l y meaningfu l d a t a , c l e a r l y u n f e a s i b l e f o r Cd-3vi* . 4 . 3 . 3 . D i s c u s s i o n I t i s important to e s t a b l i s h whether s u r f a c e o b s e r v a t i o n s r e f l e c t i n t e r n a l b e h a v i o u r . I n h i s q u a n t i t a t i v e e v a l u a t i o n of \jD 1UI Lee (1969)* assumed s o . The present r e s u l t s f o r g r a i n e l o n g a t i o n a t the s u r f a c e and i n the i n t e r i o r suggest t h a t the assumption may not be v a l i d . There i s f a i r evidence that s u r f a c e measurements of s l i d i n g and s l i p c o n t r i b u t i o n s to s t r a i n are v a l i d f o r the i n t e r i o r i n some c o a r s e -g r a i n e d a l l o y s ( I s h i d a et a l (1965), Graeme-Barber (1967)) , a l though Rachinger (1952) observed equiaxed i n t e r i o r g r a i n s and e longated s u r f a c e g r a i n s i n c rept aluminum (as i n the present exper iment . ) A n a l y s i s of g r a i n e l o n g a t i o n i n Z n - l u (Turner (1970)) a l s o shows t h a t g r a i n e l o n g a t i o n occurs as a f u n c t i o n of s t r a i n p a r t i c u l a r l y at the s u r f a c e . Moreover , g r a i n e l o n g a t i o n may be more pronounced i n stage I than i n stage I I . U n f o r t u n a t e l y , Z n - l p tends to show g r a i n 50. growth as a f u n c t i o n of s t r a i n . An i d e a l a l l o y would be one w h i c h combines the un i form g r a i n s i z e and m e t a l l o g r a p h i c ease of Zn-lu w i t h , the s t a b i l i t y of Cd-3u*. The apparent l o s s of t r a n s v e r s e g r a i n boundaries ( F i g u r e s 4.15, 16) c o u l d be a r e s u l t of the f o l l o w i n g : ( i ) R e o r i e n t a t i o n of g r a i n s so tha t boundaries occur on planes of maximum shear . ( i i ) Random d i s p e r s a l of p a r t i c l e s due to s l i d i n g , r e s u l t i n g i n a r e o r i e n t a t i o n of g r a i n b o u n d a r i e s . ( i i i ) G r a i n e l o n g a t i o n . The apparent g r a i n shape cou ld r e f l e c t an i n c r e a s i n g 77 r a t i o . W 4.4. Surface o b s e r v a t i o n s 4.4.1. General Sharp d e t a i l was observed i n Cd-8u* and Cd-3u*, and most of the m i c r o s c o p i c a n a l y s i s i n v o l v e d these a l l o y s . The c he m i c a l p o l i s h imparted a " p e b b l y " f i n i s h to the s u r f a c e , which may have i n t e r f e r e d w i t h the r e s o l u t i o n of very f i n e s l i p , but which a l l o w e d ready i d e n t i f i c a t i o n of f r e s h s u r f a c e exposed by g r a i n boundary s l i d i n g . F r e s h l y exposed s u r f a c e was i n g e n e r a l e i t h e r smooth or s t r i a t e d , w h i l e the o r i g i n a l p o l i s h e d sur face remained " p e b b l y " , even a f t e r 250% specimen e l o n g a t i o n (F igure 4.22.). Chemical p o l i s h i n g was l e s s s u c c e s s f u l f o r Pb-5u, al though some p e r t i n e n t o b s e r v a t i o n s of de format ion f e a t u r e s were made. 51. 4 . 4 . 2 . Modes of deformat ion Before a n a l y s i n g deformat ion m a r k i n g s , the modes of deformat ion must be cons idered f o r t h e i r s u f f i c i e n c y i n m a i n t a i n i n g c o m p a t i b i l i t y between g r a i n s . The three common s l i p systems i n cadmium and z i n c are {0001} <1120>, of which o n l y two are independent . A c c o r d i n g to the "Von M i s e s " c r i t e r i o n (Honeycombe (1968)) , f i v e independent s t r a i n components are r e q u i r e d to a l l o w any d e s i r e d shape change of a body. For the g r a i n s of a p o l y c r y s t a l , f i v e independent s l i p systems are r e q u i r e d i n the absence of n o n - s l i p modes. To a t t a i n a p p r e c i a b l e (though not u n l i m i t e d ) d u c t i l i t y may r e q u i r e approx imate ly four s l i p modes (Kochs (1967)) . The most u s u a l n o n - b a s a l s l i p systems observed i n cadmium and z i n c are second order p y r a m i d a l {1122} <1123>, which i n themselves supply f i v e independent modes. ( F i r s t order p y r a m i d a l {10Tl} <1120> and p r i s m a t i c {10l0} <1120> are o c c a s i o n a l l y observed. ) Processes other than s l i p may reduce the r e q u i r e d number of s l i p systems. T w i n n i n g , f o r example, produces s t r a i n and a t the same time a l l o w s cont inued s l i p and/or r e t w i n n i n g i n r e o r i e n t e d elements of volume. I n cadmium and z i n c , {1012} <1011> t w i n n i n g i s commonly observed . Under s u p e r p l a s t i c c o n d i t i o n s , there are a d d i t i o n a l deformat ion modes a v a i l a b l e : g r a i n boundary shear (wi th m i g r a t i o n ) , b u l k vacancy d i f f u s i o n (H-N or Coble c r e e p ) , and d i s l o c a t i o n c l i m b . I n f a c t , i t i s l i k e l y tha t s l i d i n g , m i g r a t i o n and b u l k vacancy d i f f u s i o n can meet c o m p a t i b i l i t y requirements w i t h o u t the need f o r s l i p . I n the case of l e a d , normal {111} <110> s a t i s f i e s c o m p a t i b i l i t y requirements . As w i t h cadmium and z i n c , however, s l i p i t s e l f may not be 52. r e q u i r e d under s u p e r p l a s t i c c o n d i t i o n s . 4.4.3. Sur face o b s e r v a t i o n s of s l i p and t w i n n i n g F i g u r e s 4.17., 18. i l l u s t r a t e the e x t e n s i v e , c l e a r l y d e f i n e d , b a s a l s l i p i n Cd-8u* deformed i n s tage I I I . Twinning and n o n - b a s a l s l i p ^ are i n h i b i t e d , w h i l e some s l i d i n g and much m i g r a t i o n i s e v i d e n t . Both t w i n n i n g and n o n - b a s a l s l i p are common i n c o a r s e - g r a i n e d cadmium, where boundary e f f e c t s are n e g l i g i b l e . F i g u r e s 4.19.-24. i l l u s t r a t e the v i r t u a l absence of even b a s a l s l i p i n the stage I I de format ion of Cd-3u* and Cd-8u*. The s l i p bands which do occur ( e . g . F i g u r e 4.21.) are undoubtedly the r e s u l t of unusual concurrences of s t r e s s c o n c e n t r a t i o n and g r a i n o r i e n t a t i o n , and are r e s t r i c t e d to about 5% of the g r a i n s . No s l i p was observed i n Pb-5u (stage I I ) , a l though the r e l a t i v e l y poor s u r f a c e p o l i s h rendered t h i s o b s e r v a t i o n i n c o n c l u s i v e . S i m i l a r o b s e r v a t i o n s f o r a l l o y s c o n t a i n i n g l e a d as an important phase ( e . g . Zehr and Backofen (1968)) p r o b a b l y s u f f e r r e d from the same drawback. The apparent l a c k of s l i p i n stage I I may be due to s e v e r a l reasons : ( i ) S l i p i s unimportant i n s u p e r p l a s t i c f l o w f o r the reasons suggested i n the p r e v i o u s s e c t i o n . ( i i ) S l i p i s u s u a l l y too f i n e to r e s o l v e . I t i s p o s s i b l e that " l e d g e s " or " p r o t r u s i o n s " ( G i f k i n s and Snowden (1966)) are f i n e l y spaced sources which operate i n c o n j u n c t i o n w i t h s l i d i n g . The sources ^ N o n - b a s a l s l i p i s c h a r a c t e r i z e d by f i n e , wavy t r a c e s i n g r a i n s where more than one s l i p system o p e r a t e s . (See Appendix A . ) 53. FIGURE 4 .18 . C d - 8 u * . 16% E l o n g a t i o n . Stage I I I O 1 (e * 10 min , T = 2 3 ° C ) . x4000. 55. FIGURE 4 . 1 9 . C d - 3 u * . 15% E l o n g a t i o n . Stage I I Ce ^ 10" min , T = 23°C, m % . 5 ) . x8000. A - c l o s e l y a s s o c i a t e d s t r i a t i o n s and m i g r a t i o n marks B - s l i d i n g i n v i c i n i t y of l e a d p a r t i c l e C - p a r t i a l m i g r a t i o n of c u r v e d , p e e l i n g boundary. 56. 57. FIGURE 4 . 2 1 . C d - 3 y * . 15% E l o n g a t i o n . Stage I I O 1 (I % 10" m i n " , T = 23°C, m ^ . 5 ) . x l 0 , 0 0 0 . 58. FIGURE 4 .22 . C d - 3 u * . 250% E l o n g a t i o n . Stage I I O 1 (e ti 10" min , T = 23°C, m * . 5 ) . x l 5 , 0 0 0 . A - p e e l i n g boundary s t r i a t i o n s B - s l i d i n g boundary s t r i a t i o n s C - m i g r a t i o n marks. FIGURE 4 . 2 3 . C d - 3 y * . 35% E l o n g a t i o n . Stage I I . (e * 5 x I O - 4 m i n " 1 , T = 23°C, m ^ .5) x 30,000 A - s t r i a t i o n s a t pee led i n t e r p h a s e boundary. 60. FIGURE 4 . 2 5 . (Above) . P b - 5 y . 15% E l o n g a t i o n . Stage (i * 5 x 1 0 " 4 m i n " 1 , T = 23°C, m "V. .35) . x4000. 6 2 . FIGURE 4.26. Pb-5u. 15% El o n g a t i o n . Stage I I ( i * 5 x I f f min" , T = 23°C, m <v .35). x4000. A - peeled boundaries. 63. FIGURE 4.27. Cd-3y*. Deformed r a p i d l y w i t h p l i e r s (Stage I I I ) . x6000. themselves would move d u r i n g s l i d i n g , f u r t h e r c o n t r i b u t i n g to the f i n e - n e s s of observed s l i p . t ( i i i ) S l i p i s i n h i b i t e d by s u r f a c e e f f e c t s , w h i l e be ing e x t e n s i v e i n the b u l k . No p l a u s i b l e reason f o r t h i s behaviour can be v i s u a l i z e d . Due to exper imenta l d i f f i c u l t y , m i c r o s c o p i c a n a l y s i s was not attempted i n stage I . 4.4.4. G r a i n boundary e f f e c t s (stage I I ) 4.4.4.1. Shear ing and p e e l i n g One of the s t r i k i n g c h a r a c t e r i s t i c s of f i g u r e s 4.19.-26. i s the r e l a t i v e mot ion of g r a i n s . There appears to be l i t t l e a c t i v i t y along l o n g i t u d i n a l boundary t r a c e s , and a maximum along t r a n s v e r s e b o u n d a r i e s . Boundaries whose s u r f a c e t r a c e s are l o n g i t u d i n a l c o n t a i n the t e n s i l e a x i s , and as a r e s u l t exper ience l i t t l e shear or t e n s i l e s t r e s s (Mohr's c i r c l e a n a l y s i s f o r v a r i a t i o n of s t r e s s a t a p o i n t ) . Moreover, boundaries whose t races are t r a n s v e r s e tend to shear normal to the t r a c e , producing a maximum amount of f r e s h s u r f a c e . Boundaries whose t races are not t r a n s v e r s e have a shear component a long the t r a c e which would show up as an o f f s e t on a marker l i n e across the boundary, but not as f r e s h s u r f a c e . " P e e l i n g " i s e s p e c i a l l y apparent i n Cd-3u* ( F i g u r e s 4.19.-23.). P e e l i n g i s probably a s u r f a c e e f f e c t which occurs whenever a s i g n i f i c a n t t e n s i l e s t r e s s e x i s t s across a boundary. F i g u r e 4.28 i l l u s t r a t e s how + The l i m i t of r e s o l u t i o n i s about 200$ f o r the two stage r e p l i c a t e c h n i q u e . one boundary w i l l p e e l w h i l e the o ther w i l l s h e a r , a l t h o u g h each has i t s t r a c e normal to the t e n s i l e a x i s . Combined p e e l i n g and shear i s c o n c e i v a b l e , a l though not obvious from the m i c r o g r a p h s . SURFACE SHEAR BOUNDARY PEEL BOUNDARY TENSILE AXIS >. FIGURE 4 .28 . Shear ing and p e e l i n g a t the s u r f a c e . P e e l i n g c o u l d r e s u l t from vacancy d i f f u s i o n i n the v i c i n i t y of the boundary s u r f a c e t r i p l e l i n e . A vacancy g r a d i e n t might w e l l e x i s t between regions of t e n s i o n (B) and the s u r f a c e s i n k ( A ) . The d i f f u s i o n path l e n g t h , B-A would be s h o r t compared w i t h tha t r e q u i r e d f o r N-H or Coble c reep , B - C , and would hence r e f l e c t a f a s t e r p r o c e s s . Moreover , the s t r a i n a s s o c i a t e d w i t h observable p e e l i n g i s hard to d e f i n e . I t may w e l l be s m a l l compared w i t h b u l k s t r a i n . Thus, o b j e c t i o n s to the model , on the b a s i s that b u l k d i f f u s i o n processes are too slow to be i m p o r t a n t , can be e a s i l y c o u n t e r e d . Pee led boundaries have been h i t h e r t o u n i d e n t i f i e d , a f a c t which has s e v e r a l i m p l i c a t i o n s . Perhaps the phenomenon i s unique to cadmium (and other HCP m e t a l s ) . However, p e e l i n g i s ev ident to a l i m i t e d extent i n Pb-5p ( F i g u r e 4 . 2 6 . ) , l e a d i n g to the c o n c l u s i o n t h a t 66. the phenomenon i s g e n e r a l , and tha t i d e n t i f i c a t i o n has not p r e v i o u s l y been made s imply due to the r e l a t i v e l y poor s u r f a c e f i n i s h e s i n p u b l i s h e d m i c r o g r a p h s . I f p e e l i n g i s a g e n e r a l s u r f a c e phenomenon, any c a l c u l a t i o n of g r a i n boundary shear s t r a i n by the o f f s e t technique ( e . g . Lee (1969)*) w i l l be i n e r r o r i f the e f f e c t i s not taken i n t o account . 4 . 4 . 4 . 2 . S t r i a t i o n s The s t r i a t i o n s which appear a t s l i d i n g i n t e r p h a s e and i n t e r c r y s t a l l i n e boundaries both have been observed i n p u b l i s h e d micrographs (Chapter 2 . 2 . 3 . ) . The s t r i a t i o n s observed at pee led boundaries have no precedent , as peeled boundaries themselves have not been i d e n t i f i e d . Backofen and others (Chapter 2 . 2 . 3 . ) c l a i m that any s t r i a t i o n s observed i n s u p e r p l a s t i c de format ion r e f l e c t b u l k d i f f u s i o n a l c reep . However, i f a s s o c i a t e d w i t h p e e l i n g , s t r i a t i o n s may w e l l r e f l e c t d i f f u s i o n a l c reep , but probably as a s u r f a c e phenomenon. I f a s s o c i a t e d w i t h s l i d i n g , the s t r i a t i o n s need not r e f l e c t d i f f u s i o n a l creep a t a l l . Thus no i n f e r e n c e concerning s u p e r p l a s t i c mechanisms i s warranted on the b a s i s of s u r f a c e s t r i a t i o n s . A c r y s t a l l o g r a p h i c i n t e r p r e t a t i o n seems reasonable f o r both s l i d i n g and p e e l i n g s t r i a t i o n s . C o n s i d e r i n g s l i d i n g f i r s t , i t i s conce ivab le that s t r i a t i o n s r e s u l t from a p r e f e r r e d d i r e c t i o n of boundary m i g r a t i o n d u r i n g s l i d i n g . That g r a i n boundary m o b i l i t y o f t e n depends on the d i r e c t i o n of mot ion i s w e l l - e s t a b l i s h e d . For example, G l e i t e r (1969) has proposed a c r y s t a l l o g r a p h i c a l l y stepped boundary to e x p l a i n the dependence. F i g u r e 4.29 i l l u s t r a t e s the r e l a t i o n s h i p of s t r i a t i o n s w i t h m i g r a t i o n marks i n l i g h t of the concept of a p r e f e r r e d m i g r a t i o n d i r e c t i o n . 67. The s t r i a t i o n s on p e e l i n g boundaries may r e p r e s e n t c r y s t a l l o g r a p h i c channels f o r d i f f u s i o n . Such an i n t e r p r e t a t i o n i s u n l i k e l y , as p r e f e r r e d channels would be expected o n l y f o r low angle b o u n d a r i e s , and even then they 1 would be spaced too c l o s e l y ( ^ 2 0 8 ) f o r r e s o l u t i o n . I t i s p o s s i b l e that s t r i a t i o n s r e s u l t from a s m a l l amount of shear and m i g r a t i o n a s s o c i a t e d w i t h p e e l i n g . I n t h i s case , the d i s c u s s i o n devoted to s l i d i n g s t r i a t i o n s would a p p l y . The p o s s i b i l i t y tha t s t r i a t i o n s r e s u l t from a b r a s i o n by hard boundary p a r t i c l e s or by s u r f a c e ox ide f i l m s cannot be d i s c o u n t e d , a l though there are s e v e r a l o b j e c t i o n s to t h i s argument: ( i ) There i s no ev idence , or reason to b e l i e v e , that f i n e boundary p a r t i c l e s or a tough ox ide s u r f a c e e x i s t s f o r the wide range of 68. i n t e r c r y s t a l l i n e and interphase boundaries i n which s t r i a t i o n s have been observed. ( i i ) The uniform spacing of s t r i a t i o n s on some planes, and the absence of s t r i a t i o n s on others, i s i n d i c a t i v e of c r y s t a l l o g r a p h i c o r i g i n . ( i i i ) I f produced by abrasion by boundary p a r t i c l e s , s t r i a t i o n s would have v a r i a b l e lengths. However, s t r i a t i o n s are generally quite uniform i n length, extending the f u l l length of the exposed boundaries. (iv) S t r i a t i o n s produced by p a r t i c l e abrasion suggest the formation of grooves on one side of the p a r t i c l e s and the buildup of matter on the other side, an u n l i k e l y process. 4.4.4.3. Migration marks Grain boundary migration appears to be an e s s e n t i a l concomitant to grain boundary s l i d i n g i n normal creep (e.g. Walter and Cline (1968)). In Figures 4.19.-24.^ most s l i d i n g boundaries have c l o s e l y associated migration marks which appear as d i s c r e t e steps, generally le s s than . 5u apart. Migration steps i n published micrographs where coarse-grained s l i d i n g occurs are s i m i l a r i n form but larger i n s c a l e . Figure 4.21. aptly demonstrates the unique type of boundary migration induced by s l i d i n g . Migration and s l i d i n g occur i n d i s c r e t e steps along A-C with l i t t l e apparent a c t i v i t y on A-B. Eventually, the tension produced by the migrating A-C boundary causes a sudden and r e l a t i v e l y large jump by the A-B boundary. S l i d i n g may induce migration i n several ways: 69. ( i ) Boundaries are seldom f l a t ; they have long- range curvatures and s h o r t - r a n g e " l e d g e s " . Unless the bumps are sheared o f f oir d i f f u s e d around, they must migra te to m a i n t a i n c o m p a t i b i l i t y d u r i n g s l i d ' i n g ( F i g u r e 4 . 3 0 . ) . A p o s s i b l e e x p l a n a t i o n f o r the s l i d i n g - m i g r a t i o n sequence d e s c r i b e d above d e r i v e s from t h i s concept ( F i g u r e 4 . 3 1 . ) , t a k i n g i n t o account the tendency f o r boundaries to meet the s u r f a c e a t r i g h t angles ( e . g . S t r u t t et a l (1964)) . FIGURE 4 .30 . M i g r a t i o n of a bump on a s l i d i n g boundary to r e l i e v e normal s t r e s s e s . SUFFACE / / / J I A V / / * / / w /// / / A. B, c 0. FIGURE 4 . 3 1 . P o s s i b l e e x p l a n a t i o n f o r s l i d i n g -m i g r a t i o n sequence observed a t s u r f a c e . . 70. ( i i ) An alternate explanation, which applies to the surface and the i n t e r i o r a l i k e , involves the complex r e d i s t r i b u t i o n of i n t e r n a l stresses due to the s p a t i a l arrangement of the grains ( L i f s h i t z (1963)). In other words, s l i d i n g creates stresses which may best be r e l i e v e d by continued s l i d i n g on a boundary whose o r i e n t a t i o n i s s l i g h t l y a l t e r e d . ( i i i ) Boundaries d i s t o r t e d by s l i d i n g , p a r t i c u l a r l y at t r i p l e l i n e s (Lee (1969)), migrate on a l o c a l i z e d scale to reduce boundary energy. The d r i v i n g force f or t h i s process i s b a s i c a l l y the same as for g r a i n growth. However, although grain growth i s often observed to occur, i t does not appear to be an e s s e n t i a l concomitant to the superplastic process (Chapter 4.2.). There i s no evidence to suggest that the recovery process involving the sweeping of boundaries through regions of high d i s l o c a t i o n density applies to s u p e r p l a s t i c i t y , unless the d i s l o c a t i o n s e x i s t very close to the boundary ( <".ly). I f sources emit d i s l o c a t i o n s almost p a r a l l e l to the s l i d i n g boundary ( i . e . from bumps) or are s l i g h t l y bowed (thus creating s t r a i n energy), such a process could be envisaged from surface observations. Figure 4.27. i l l u s t r a t e s the meandering boundary migration which accompanies extensive d i s l o c a t i o n a c t i v i t y (stage I I I ) , and which probably represents the sweeping out of tangles or pileups. The d i s t i n c t i o n between t h i s type of migration and that shown i n Figures 4.19.-24. i s unmistakable. While second phase p a r t i c l e s s t a b i l i z e the g r a i n s i z e , they do not seem to i n h i b i t s l i d i n g and i t s corresponding migration, at l e a s t i n the case of Cd-3y* (e.g. Figure 4.19B.). 4 . 5 . Creep behaviour 4 . 5 . 1 . General I t has been shown tha t the creep r a t e i n s tage I I i s e s s e n t i a l l y s t e a d y - s t a t e , independent of s t r a i n ( e . g . Hayden et a l , (1967)) . T h i s o b s e r v a t i o n corresponds w i t h the q u i c k l y a t t a i n e d steady s t a t e f l o w s t r e s s which occurs i n I n s t r o n t e s t s . The o n l y e x t e n s i v e i n v e s t i g a t i o n of the creep behaviour of a s u p e r p l a s t i c a l l o y (Surges (1969)) produced the f o l l o w i n g r e s u l t s : ( i ) The creep r a t e decreased as a f u n c t i o n of s t r a i n i n s tage I . ( i i ) S t e a d y - s t a t e occurred from the s t a r t i n s tage I I . ( i i i ) The creep r a t e i n c r e a s e d as a f u n c t i o n of s t r a i n i n stage I I - I I I " t r a n s i t i o n " . ( i v ) " N o r m a l " creep occurred i n s tage I I I ( i . e . p r i m a r y , secondary and t e r t i a r y c r e e p ) . The present work i n c l u d e d an i n v e s t i g a t i o n of the creep p r o p e r t i e s i n stages I , I I and I I I f o r s e v e r a l a l l o y s under c o n d i t i o n s of constant s t r e s s and temperature (± . 2 ° C ) , u s i n g a nominal s t r a i n s e n s i t i v i t y of .05%. Measurements of ins tantaneous creep e x t e n s i o n (at " z e r o " time) were not made, due to the l i m i t a t i o n s of the apparatus Q u a l i t a t i v e l y , the ins tantaneous e x t e n s i o n i n s tages I and I I was very s m a l l (< 1%), compared w i t h normal creep o b s e r v a t i o n s at e q u i v a l e n t s t r e s s e s . 72. 4 . 5 . 2 . Pb-5u and e u t e c t i c - 3 u F i g u r e s 4 . 3 2 . , 33. demonstrate the s tage I I , I I I creep behaviour of Pb-5u and e u t e c t i c - 3 y . Pb-5y showed a decrease i n the degree of pr imary creep i n going from stage I I I to stage I I . However, a s i g n i f i c a n t pr imary creep s t r a i n occurred even a t the lowest s t r e s s t e s t e d ( F i g u r e 4 . 3 2 A . ) . E u t e c t i c - 3 y d i s p l a y e d marked pr imary creep i n s tage I I I (F igure 4 . 3 3 E . ) a n d v i r t u a l l y none i n w e l l - d e f i n e d stage I I ( F i g u r e 4 .33A, D . ) Very l i t t l e primary creep was ev ident i n the t r a n s i t i o n r e g i o n e i t h e r . I n n e i t h e r case was there evidence f o r the s p e c i a l " t r a n s i t i o n " behaviour observed by Surges . (The p o s s i b i l i t y of some g r a i n growth p a r t i a l l y masking the e f f e c t must not be d i s c o u n t e d e n t i r e l y , however.) The present behaviour seems to r e f l e c t s imply an "average" of stages I I and I I I ( i . e . p a r a l l e l processes) i n the t r a n s i t i o n r e g i o n . The presence of s i g n i f i c a n t pr imary creep i n curve A ( F i g u r e 4 .32 . ) p r o b a b l y r e f l e c t s the f a c t that stage I I was not complete ly a t t a i n e d e x p e r i m e n t a l l y (m ^ . 3 2 ) . (As noted e a r l i e r (Chapter 4 . 1 . ) , the d e f i n i t i o n of s t a g e s , p a r t i c u l a r l y stage I I I and the t r a n s i t i o n r e g i o n s , can be somewhat ambiguous.) The argument of Surges was that t e r t i a r y creep dominated from the s t a r t due to the r a p i d development of i n s t a b i l i t i e s i n the t r a n s i t i o n r e g i o n . By d i f f e r e n t i a t i n g the equat ion a = K e m , Chaudhari 2 (1967 ) obta ined the r e l a t i o n s h i p : de 1 /da dm , ' a N , . — = — ( l n —) . (4 .2) e m a m K I n the t r a n s i t i o n r e g i o n , — i s n e g a t i v e f o r an i n c r e a s i n g s t r e s s . Thus the term i n the r i g h t s i d e of E q u a t i o n (4.2) enhances i n s t a b i l i t y by de . , i n c r e a s i n g —r a t any p o i n t where necking d e v e l o p s . The present r e s u l t s suggest that t h i s e f f e c t i s n e g l i g i b l e . However, any attempt to r e l a t e t h i s e f f e c t to o v e r a l l creep r a t e must i n v o l v e : ( i ) q u a n t i t a t i v e o b s e r v a t i o n of neck development, ( i i ) comparison of neck l e n g t h w i t h o v e r a l l gauge l e n g t h , ( i i i ) c a r e f u l d e t e r m i n a t i o n of m(a) i n the t r a n s i t i o n r e g i o n to o b t a i n the magnitude of — l n — , m K ' ( i v ) c a l c u l a t i o n of p o s s i b l e s t a b i l i z a t i o n e f f e c t due to i n c r e a s i n g y (Equat ion (2.1)) as " n o r m a l " s t r a i n -hardening begins to be i m p o r t a n t . 4.5.3. Cd-3u and Cd-8y Creep behaviour f o r Cd-3u and Cd-8u was observed i n a l l s t a g e s . F i g u r e 4.34 i l l u s t r a t e s the q u i c k l y - a t t a i n e d s t e a d y - s t a t e creep r a t e which c h a r a c t e r i z e d stage I I b e h a v i o u r . Curves A and C are p a r t i c u l a r l y meaningful i n that the s t r a i n - h a r d e n i n g due to g r a i n growth was m i n i m a l (Chapter 4.2.). The shape of the curves f o r s tage I creep i n Cd-3u was very s i m i l a r to these c u r v e s , a l though stage I was not i n v e s t i g a t e d e x t e n s i v e l y (i.e.<C4% t o t a l s t r a i n f o r any t e s t ) . E x t r a p o l a t i o n of the creep curve from the nominal onset of s t e a d y - s t a t e (2% e) back to zero s t r a i n g i v e s an a r b i t r a r y measure of the amount of pr imary creep i n stages I and I I . For Cd-3u, Cd-8u, eutectic-3u and Z n - l u , the amount of pr imary s t r a i n ranged from .1% to . 3 % and was e a s i l y recovered (Figure 4 . 3 5 . ) . Although not shown, Stage I behaviour f o r Cd-3u appeared to be very s i m i l a r when a t t a i n e d i n s p e c i a l A H-tests (Chapter 4 . 6 . ) . (The p e c u l i a r stage I behaviour of Zn-lu w i l l be discussed i n Chapter 4 . 5 . 4 . ) The existence of a s l i g h t amount of primary creep i s to be expected. A r a p i d i n i t i a l creep r a t e could r e s u l t from: ( i ) a n e l a s t i c g r a i n boundary s l i d i n g (Chapter 4 . 7 . ) , ( i i ) "hardening" of easy sources, and exhaustion of p r e - e x i s t i n g mobile d i s l o c a t i o n s , ( i i i ) exhaustion of e a s y - s l i d e g r a i n o r i e n t a t i o n s . A delayed y i e l d e f f e c t appeared i n both Cd-3u and Cd-8p once stage I I I became evident. The phenomenon was not due to the r a p i d development of i n s t a b i l i t i e s (Chapter 4 . 5 . 2 . ) . Specimen A (Figure 4 . 3 6 ) , f o r example, was deformed to over 20% s t r a i n w i t h no apparent necking. Figure 4 . 3 7 . i l l u s t r a t e s the d i f f i c u l t y i n recovering the y i e l d e f f e c t . A f t e r strong intermediate anneals, only a s l i g h t r e d u c t i o n of creep r a t e occurred, and pa r t of t h i s r e d u c t i o n could be accounted f o r by g r a i n growth during the anneals. P r e s t r a i n i n g i n stage I I d i d not appear to a f f e c t the y i e l d behaviour i n subsequent deformation at higher s t r e s s e s (Figure 4 . 3 8 ) . In other words, stage I I deformation does not s i g n i f i c a n t l y a l t e r s t r u c t u r e , a c o n c l u s i o n reached by other means (Chapter 4 . 1 . 3 . ) . On the other hand, p r e s t r a i n i n g i n the " y i e l d " r e g i o n enhanced the creep r a t e i f anything i n subsequent stage I I deformation. There are s e v e r a l i m p l i c a t i o n s of the delayed y i e l d i n g 75. ob s erva t i ons: v ( i ) Delayed y i e l d i n g and y i e l d points (the Instron counterpart) undoubtedly r e l a t e to d i s l o c a t i o n m u l t i p l i c a t i o n and w i l l be discussed i n greater d e t a i l i n Appendix A. ( i i ) The phenomenon i s unique to f i n e grained material. I t has not been reported i n the creep or t e n s i l e test l i t e r a t u r e for coarse-grained cadmium. The present i n v e s t i g a t i o n i s the f i r s t one to deal with fine-grained cadmium. ( i i i ) Dislocations produced during the y i e l d process are d i f f i c u l t to anneal out, but do not hinder subsequent deformation i n stage I I . I f anything, they speed up the superplastic creep rate, probably by being attracted to and absorbed by s l i d i n g boundaries. 4.5.4. Zn-lu Steady-state was attained f a i r l y quickly i n stage II (Figure 4.34.), although unlike Cd-3u and Cd-8u, a slow decrease of the "steady-state" rate occurred with s t r a i n . This behaviour was probably due to the s l i g h t g rain growth e f f e c t established f o r Zn-lu (Chapter 4.2.4.). Unique creep behaviour was observed i n stage I (Figures 4.35., 39.). A considerable amount of reproducible and recoverable primary creep occurred. An asso c i a t i o n of th i s behaviour with stage I per se i s not obvious. There was nothing unique about stage I i n Cd-3u, and the stage I behaviour observed by Surges was a gradually decreasing creep rate with s t r a i n . (In the l a t t e r case, grain growth could have 76. FIGURE 4 . 3 2 . Creep curves for pb-5u (Stages II, III). FIGURE 4 . 3 3 . Creep curves f o r e u t e c t i c - 3 u (Stages I I , I I I ) . TEMP STRESS TIME UNIT cf A CD-8u 65°C 2000 PSI 10 MIN FIG.4.2. B ZN-lp 40°C 5000 PSI 5 SEC FIG.4.6. C CD-3y 50°C 1380 PSI 1 MIN FIG.4.1. J I I I I I I I I I I I I I I I I I I I I I I ll 4 8 12 16 20 24 28 32 36 40 44 T I M E FIGURE 4 .34 . Creep curves f o r s tage I I d e f o r m a t i o n . FIGURE 4.35. P r i m a r y creep i n stages I , I I . TIME FIGURE 4 . 3 6 . Delayed y i e l d i n C d - 3 y , Cd-8u (s tage I I I ) . TIME (SEC) FIGURE 4 . 3 7 . D i f f i c u l t y i n r e c o v e r i n g delayed y i e l d i n cd-.&i (stage I I I ) . 82. 10 8 H 6 z < ce. 4 CO 2 _ — CD-8p 65°C (cf FIGURE 4.2^  STAGE III — 5000 PSI TIME UNIT = 20 SEC — I CHANGE STRESS . STAGE II 2000 PSI TIME UNIT = 10 MIN . ^ 1 1 1 1 1 1 1 1 1 1 1 1 1 1 I 1 1 2 4 6 8 10 12 14 16 TIME FIGURE 4 . 3 8 . E f f e c t of p r e s t r a i n i n g i n stage I I on delayed y i e l d i n stage I I I ( C d - 8 u ) . 5 TIME (HR) FIGURE 4 . 3 9 . Pr imary creep i n Z n - l u (stage I ) . been r e s p o n s i b l e ) . Much work remains to be done i n a l l o y s where a s t a b l e , w e l l - d e f i n e d , s tage I e x i s t s b e f o r e any g e n e r a l i z a t i o n can be made. 4 . 6 . A c t i v a t i o n energy 4 . 6 . 1 . General An apparent a c t i v a t i o n energy may be obta ined by d i f f e r e n t i a t i n g E q u a t i o n ( 2 . 2 ) : AH. = A -K91ne 9 o , S ( s t r u c t u r e ) (4.3) E x p e r i m e n t a l l y , AH^  may be determined at any p o i n t i n a constant s t r e s s creep t e s t by r e c o r d i n g e b e f o r e and a f t e r an " i n s t a n t a n e o u s " temperature change. An a l t e r n a t e technique i s to compare the creep curves from d i f f e r e n t t e s t s : The v a l i d i t y of the technique has been demonstrated f o r many meta ls ( e . g . Dorn (1957)) , and a r i s e s from the apparent independence of s t r u c t u r e to temperature f o r any g i v e n s t r a i n and s t r e s s l e v e l . The technique has p a r t i c u l a r a p p l i c a t i o n a t h i g h temperatures where an " i n s t a n t a n e o u s " temperature change i s d i f f i c u l t . (Most AH - v a l u e s -K91ne (4.4) 3 ~\- a , e ( d i f f e r e n t t e s t s ) quoted i n Table 4 . 2 . were obta ined i n t h i s manner.) I n s p i t e of i t s common use the technique has a t l e a s t two d i s a d v a n t a g e s : ( i ) A l a r g e number of t e s t s must be performed to a t t a i n the s t a t i s t i c a l accuracy of the d i f f e r e n t i a l t e c h n i q u e . ( i i ) S t r u c t u r e i s not always independent of temperature , p a r t i c u l a r l y i n s o l i d s o l u t i o n s and two-phase a l l o y s (Rawson and Argent (1967)).. A temperature-dependent s o l u b i l i t y , f o r example, c o u l d be r e f l e c t e d by a t r a n s i e n t i n a d i f f e r e n t i a l t e s t ( F i g u r e 4 .40 . ) The " t r u e " AH^ c o u l d i n t h i s case be obta ined o n l y by-measuring instantaneous creep r a t e s a t e^. As s u p e r p l a s t i c i t y g e n e r a l l y i n v o l v e s m u l t i - p h a s e a l l o y s , there may be e r r o r i n d e t e r m i n i n g AH^ by any other t e c h n i q u e . T I M E FIGURE 4 .40 . D i f f e r e n t i a l creep t e s t i n which temperature changes " i n s t a n t l y " at e . Even i n a d i f f e r e n t i a l t e s t , there are some ins tantaneous " p s e u d o - s t r u c t u r a l " changes which may i n f l u e n c e AH : ( i ) The u n r e l a x e d e l a s t i c modulus decreases w i t h i n c r e a s i n g temperature , and g ives a p o s i t i v e e r r o r to A H ^ . F l i n n and Duren (1966) suggest that AH may be overes t imated by about 4 k c a l a t »75T^ i n c o a r s e -gra ined cadmium, f o r example. The modulus e f f e c t i s g r e a t e s t a t very h i g h temperatures and probably i s n e g l i g i b l e below »6TM ( B a r r e t t et a l (1964)) . The present e x p e r i m e n t a l work i n v o l v e s temperatures g e n e r a l l y below .6T,,,. M ( i i ) A c t i v a t i o n entropy may vary w i t h temperature , g i v i n g some e r r o r to AH^ . A l though l i t t l e e x p e r i m e n t a l evidence e x i s t s , the entropy e f f e c t i s cons idered n e g l i g i b l e . ( i i i ) The shape of the a c t i v a t i o n b a r r i e r i t s e l f may v a r y w i t h temperature , a l though the p o s s i b i l i t y i s u n l i k e l y . Assuming that the above e f f e c t s are together n e g l i g i b l e , AH^ may s t i l l be lower than the process enthalpy A H ^ , due to the s t r e s s - a s s i s t e d over-coming of the s h o r t - r a n g e b a r r i e r : AH = AH - T * b A * , (4.5) A p where T * = e f f e c t i v e shear s t r e s s (Chapter 4 .6) A * = a c t i v a t i o n area ^ bA* i s o f t e n c a l l e d an " a c t i v a t i o n vo lume" , a l though V * should o n l y be a s s o c i a t e d w i t h h y d r o s t a t i c s t r e s s e s ( i . e . p * V * ) . Moreover , the concept of an " a c t i v a t i o n a r e a " has more p h y s i c a l r e l e v a n c e to a shear s t r e s s than has a volume term. The a c t i v a t i o n area i s r e l a t e d to the fundamental s t r a i n r a t e s e n s i t i v i t y m* through the f o l l o w i n g r e l a t i o n s h i p s : m * = 3 1 m * 31ne S,T * A * = "KI 31n£ b 8 T * S,T ' .'. x *bA* KT m* (4.6) A v a l u e f o r T * b A * may be obta ined w i t h o u t e v a l u a t i n g T * or A * , p r o v i d e d m* i s known. The apparent v a l u e f o r m i n normal creep i s about . 2 , a l though i t probably i n c o r p o r a t e s s t r u c t u r a l e f f e c t s ( e . g . Weertman (1955), B a r r e t t and N i x (1965)) ; m* i s probably c l o s e r to 1 ( e . g . Cuddy (1970)) , the v a l u e f o r a t r u l y Newtonian v i s c o u s p r o c e s s . I f m* = 1, then x*bA* = KT. For T < 1000°K, KT < 1 k c a l / m o l e , a v a l u e which i s s m a l l compared w i t h AH^ . Moreover , the p o s s i b i l i t y of backjumps i s very r e a l when x*bA* £ KT. E q u a t i o n (4.5) d e r i v e s f rom: -AH x *bA* - T * b A * . KT / KT KT « / / -7 \ e a e (e - e ) , (4 .7) - x * b A * KT and h o l d s o n l y when e can be ignored ( i . e . when x * b A * >> K T ) . The e f f e c t of the backjump term i s to reduce the a l r e a d y s m a l l e f f e c t of s t r e s s on AH.. The f o l l o w i n g e x p e r i m e n t a l o b s e r v a t i o n s c o n f i r m that the s t r e s s - a s s i s t a n c e term i s i n s i g n i f i c a n t ( G a r o f a l o (1965)): ( i ) AH^ i s at most a weak f u n c t i o n of s t r e s s i n normal c r e e p . ( i i ) AH ~ AH,, f o r a wide range of m a t e r i a l s , i n d i c a t i n g that vacancy d i f f u s i o n i s r a t e - c o n t r o l l i n g and t h a t , i n t u r n , the s t r e s s a s s i s t a n c e term oi 0. (Other experiments c o n f i r m that vacancy d i f f u s i o n i s r a t e - c o n t r o l l i n g , c o u n t e r i n g any c l a i m tha t the argument i s s y l l o g i s t i c . ) S u p e r p l a s t i c i t y occurs a t normal creep temperatures and s t r a i n r a t e s , and the above d i s c u s s i o n undoubtedly a p p l i e s . There i s no reason to b e l i e v e that a s t r e s s - a s s i s t a n c e term a f f e c t s AH^ to any s i g n i f i c a n t e x t e n t . 4.6.2. E x p e r i m e n t a l Instantaneous temperature-change t e s t s were performed on Cd-3y, Cd-8u, Pb-5y and Z n - l u i n a l l s tages where i t was e x p e r i m e n t a l l y convenient . There was no c o m p l i c a t i o n i n t r o d u c e d by t r a n s i e n t s except f o r one i n s t a n c e , which s h a l l be d i s c u s s e d l a t e r . Temperature s t a b i l i z a t i o n a f t e r changes up to 35°C was achieved w i t h i n 30 seconds , always i n v o l v i n g a s t a b i l i z a t i o n s t r a i n of l e s s than .1%, and u s u a l l y l e s s than .01%. Creep r a t e s a f t e r temperature change were recorded a t .1% s t r a i n a f t e r s t a b i l i z a t i o n , a l though the creep r a t e was e s s e n t i a l l y constant f o r .3% s t r a i n a f t e r s t a b i l i z a t i o n , except f o r the one i n s t a n c e . TABLE 4 . 2 . A c t i v a t i o n energy data r e l a t i v e to s u p e r p l a s t i c i t y . M a t e r i a l Stage AH, ( k c a l / m o l e ) Refer -ence M a t e r i a l A H B ( k c a l / m o l e ) A H G B (kca l /mole ) ^^Normal Creep ( k c a l / m o l e ) Pb 24-28 15-16 19-28 Pb-5%Cd - - 20 Cd 18.5 13 21 Sn 23-26 9.6 21-26 Zn 23 14 21 A l 33 - 35 Fe 64-74 40 70-73 Cr 52-73 46 -N i 63-67 26 66 Pb-5%Cd P b - C d ( e u t . ) P b - S n ( e u t . ) Cd-5%Pb Zn-1%A1 Zn-.2%A1 Z n - A l ( e u t . ) F e - C r - N i 2 9 . 6 f 1 2 ^12* • 2 3 ^13* 2 2 ^14f 2 2 11T 3 1 >13*=t= 2 2 ^ l O * * 2 3 ^ 1 1 * 2 1 >14* 2 2 ^10* 2 2 101 4 2 14 .5 t 5 2 21( 175°C) f 6 2 35( 175°C)+ 6 2 60+ 7 FROM: G a r o f a l o (1965) A l d e n (1969) 2 Wajda et a l (1955) S m i t h e l l s (1967) * Ins tantaneous temperature change. 4= Comparison of s t e a d y - s t a t e creep r a t e s a t d i f f e r e n t temperatures . REFERENCES: 1. A l d e n (1968) 5 . B a l l and H u t c h i s o n (1969) 2. P r e s e n t work. 6. Chaudhari (1967) 3 . C l i n e and A l d e n (1966) 7. Hayden et a l (1967) 4. Cook (1968) 4 . 6 . 3 . R e s u l t s ( i ) T r a n s i e n t s were not observed i n stage I I f o r Z n - l u , Cd-3y or C d - 8 u , a l l o w i n g meaningful comparison of AH - v a l u e s determined from m-curve f a m i l i e s w i t h those determined from ins tantaneous t e s t s (F igures 4 . 4 1 . - 4 4 . ) . ( i i ) There was no apparent dependence of AH^ on s t r a i n w i t h i n the exper imenta l s t r a i n l i m i t (<20%). The " i n s t a n t a n e o u s " p o i n t s p l o t t e d i n F i g u r e s 4 . 4 3 . - 4 4 . are are g e n e r a l l y the mean v a l u e s f o r three d i f f e r e n t s t r a i n s f o r any one specimen, and can be cons idered a c c u r a t e to ± 10%, e a s i l y , w i t h a conf idence of 95%. ( i i i ) There was no obvious change of AH over the range of temperatures i n v e s t i g a t e d . F i g u r e 4 . 4 1 . i l l u s t r a t e s the apparent constancy of AH over a range where stages I and I I were both i n v o l v e d and m v a r i e d c o n s i d e r a b l y . ( i v ) A s l i g h t but s i g n i f i c a n t p o s i t i v e t r a n s i e n t was observed at very low m i n stage I (0°C, 1500 p s i ) i n Z n - l u ( F i g u r e 4 . 4 3 ) . As a r e s u l t AH • ^ was about 85% AH_ , _ ^ . The p o s i t i v e Instantaneous S t e a d y - s t a t e t r a n s i e n t probably r e l a t e d to the r e l a t i v e l y l a r g e primary creep observed i n Z n - l y at 0°C (Chapter 4 . 5 . 4 . ) . (v) N o t w i t h s t a n d i n g the l a s t o b s e r v a t i o n , AH^ i n c r e a s e d s l i g h t l y w i t h d e c r e a s i n g s t r e s s i n s tage I I ( e . g . F i g u r e 4 . 4 2 . ) , and i n c r e a s e d at a s teeper r a t e at low s t r e s s e s where stage I became dominant (F igure 4 . 4 3 . ) , i n both Z n - l y and C d - 3 y . ( v i ) AH^ d i d not appear to i n c r e a s e i n s tage I I I f o r e i t h e r Cd-8y or P b - 5 y . Stage I I I was d i s t i n c t l y ev ident at the h i g h e r s t r e s s e s FIGURE 4 . 4 1 . Decremental temp, change creep t e s t i n Cd-3u a t 500 p S i , . (One specimen, each p o i n t corresponding to a S . S . creep r a t e . T o t a l s t r a i n < 20%.) Stages I and I I are both r e p r e s e n t e d . (See F i g u r e 4 . 1 . ) . 91. FIGURE 4 . 4 2 . AH^-plots from F i g u r e 4 . 1 . (Cd-3u; stages I , I I ) . 8.1 1 1 1 1 I I I • • • • • 1 1 1 0 2000 4000 6QQ0 F L O W S T R E S S ( P S I ) FIGURE 4.43. AIL^vs. f l o w - s t r e s s i n s tages I and I I f o r Z n - l y and Cd-3y (c f F i g u r e s 4.1., 4.6.). jS A PB-5u INSTANT. CREEP TEST * O CD-8y INSTANT. CREEP TEST * • CD-8u FROM FIGURE 4 . 3 . * 0.03% NOMINAL STABILIZATION STRAIN STAGE I I I STAGE I I O 1 1 1 1 1 I I I ' I I ' I I « I | ° 2 0 0 0 4000 6000 8000 FLOW S T R E S S ( P S I ) FIGURE 4 . 4 4 . AH v s . f l o w - s t r e s s i n s tages I I and I I I f o r Pb-5y and FIGURE 4.45. A H ^ - p l o t s f o r E u t e c t i c-3u, E u t e c t i c-8y. . Stage I I , 500 p s i . (from F i g u r e s 4.4. and 4.5.). i n Figure 4.44. At the lower s t r e s s e s stage I I was d i s t i n c t i n Cd-8u, and at l e a s t p a r t i a l l y a t t a i n e d i n Pb-5u. ( v i i ) AH A was determined to be approximately 14.5 k c a l a t 500 p s i (stage I I ) i n both e u t e c t i c - 3 u and e u t e c t i c - 8 y (Figure 4.45.). (No instantaneous t e s t s were performed.) The r e l a t i v e i n s e n s i t i v i t y of AH^ to g r a i n s i z e (at constant s t r e s s ) was a l s o apparent i n Cd-3u and Cd-8u i n stage I I . AH^ f o r the e u t e c t i c a l l o y s was somewhat higher than 4 f o r e i t h e r Pb-5y or Cd-3y at 500 p s i , although AH approached 14 k c a l i n Cd-3y at 500 p s i . 4.6.4. D i s c u s s i o n 4.6.4.1. Stage I I AH^ i n the present i n v e s t i g a t i o n corresponds w e l l w i t h the general observation that AH. ^ %AH n i n stage I I (Table 4.2.). As A D AH < AH (y JgAH ), i t i s n a t u r a l to consider g r a i n boundary d i f f u s i o n ou B B as a l i k e l y r a t e - c o n t r o l l i n g step. This idea i s e x p l i c i t i n most models discussed i n Chapter 2.3.. The s l i d i n g and Coble models p r e d i c t AH^ = AH^g, w h i l e the d i s l o c a t i o n climb models may p r e d i c t AH > AH.,,, as climb i s assumed to occur " i n the v i c i n i t y " of boundaries, p - G B ' 3 The same s u p e r p l a s t i c mechanisms which occur a t g r a i n -boundaries can probably occur at interphase boundaries (with the exception of boundary migration.) The a c t i v a t i o n energy f o r interphase boundary d i f f u s i o n i s intermediate between that of the parent phases and the apparent a c t i v a t i o n energy of a two-phase a l l o y i s reasonably represented by an expression of the f o l l o w i n g form: A H A = N l A H G B l + N 2 A H G B 2 • where N^, ^ are volume f r a c t i o n s . U n f o r t u n a t e l y , AH data f o r even pure metals are both scarce and c o n t r o v e r s i a l . There i s no c o n s i s t e n t c o r r e l a t i o n between A H G B AH and A H f i , as r e p o r t e d v a l u e s of — — range from .2 (S tark and Upthegrove (1966)) to .9 ( G i f k i n s (1968)) . Thus each a l l o y must be cons idered i n d i v i d u a l l y . AH can even be i n c o n s i d e r a b l e d i s p u t e f o r a g iven m e t a l . For example, AH f o r l e a d has been r e p o r t e d to be 5 k c a l by S tark and Upthegrove (1966), and 16 k c a l by Okkerse (1954). (The present work has e s t a b l i s h e d AH^ - 12 k c a l f o r stage I I i n P b - 5 u . ) Any p r e c i s e c o r r e l a t i o n of s u p e r p l a s t i c a c t i v a t i o n energies w i t h AH GB r e q u i r e s more accurate c o n f i r m a t i o n of the l a t t e r . Al though i n most cases (Table 4 . 2 . ) AH^ f o r stage I I c o u l d r e l a t e to boundary d i f f u s i o n ( sub jec t to the above-mentioned a m b i g u i t i e s ) , some d e f i n i t e anomalies do e x i s t . The a c t i v a t i o n energy observed by Hayden and Brophy (1968) compares w i t h AH^ f o r the major c o n s t i t u e n t s i n t h e i r a l l o y ( F e - C r - N i ) . A l d e n (1969) has suggested tha t Hayden and Brophy were observ ing stage I r a t h e r than stage I I . Another p o s s i b i l i t y i s that the AH observed by Hayden and Brophy (60 k c a l / m o l e ) was i n e r r o r , as the technique used to e s t a b l i s h AH^ p r e c l u d e d the o b s e r v a t i o n of t r a n s i e n t s . A negat ive t r a n s i e n t i n an ins tantaneous t e s t , f o r example, would produce a lower but more accurate v a l u e . Moreover , AH^„, AH„ or AIL, ., have not been e s t a b l i s h e d f o r the GB B Normal creep compl ica ted i r o n - b a s e d a l l o y i n v e s t i g a t e d . Perhaps these v a l u e s are h igher than the v a l u e s of the i n d i v i d u a l components might sugges t . 4 . 6 . 4 . 2 . Stage I Al though s tage I has not been i n v e s t i g a t e d p r e v i o u s l y , the c o n s i s t e n t i n c r e a s e i n AH^ w i t h d e c r e a s i n g s t r e s s i n both Z n - l y and Cd-3u suggests that the behaviour i s g e n e r a l . A c c o r d i n g to Chapter 4 . 6 . 4 . 1 . i t i s u n l i k e l y tha t the i n c r e a s i n g AH^ i s a r e s u l t of s t r e s s per s e . I t i s more l i k e l y tha t a new process of h i g h e r a c t i v a t i o n energy becomes important a t low s t r e s s e s . Al though tempting to a s s o c i a t e the i n c r e a s i n g AH^ w i t h d e c r e a s i n g m i n stage I , the a s s o c i a t i o n i s perhaps unwarranted as the l i m i t e d evidence suggests that AH^ ^ f(m) f o r a g i v e n f l o w s t r e s s ( F i g u r e 4 . 4 1 . ) . 4 . 6 . 4 . 3 . Stage I I I Al though u n i n v e s t i g a t e d , AH^ has been assumed i m p l i c i t l y to be equal to AHg i n the l i t e r a t u r e . The present r e s u l t s f o r two d i s s i m i l a r a l l o y s (Cd-8u and Pb-5y) i n d i c a t e tha t t h i s assumption i s wrong. The r a t e - c o n t r o l l i n g s tep i n stage I I I has an a c t i v a t i o n energy s i m i l a r to that found i n Stage I I , approximate ly ^ A H ^ . Thus stages I I and I I I cannot be d i f f e r e n t i a t e d on the b a s i s of apparent a c t i v a t i o n energy, even though the process may be d i f f e r e n t . For example, d i s l o c a t i o n c l imb i n the v i c i n i t y of g r a i n boundaries c o u l d occur i n stage I I I w h i l e g r a i n boundary s l i d i n g might predominate i n stage I I . 4 . 6 . 4 . 4 . Combined processes I t i s p o s s i b l e to o b t a i n s t a t i s t i c a l l y s i g n i f i c a n t v a l u e s f o r AH which are ambiguous from a m e c h a n i s t i c p o i n t of v iew ( G i f k i n s (1970)) . A The ambigui ty a r i s e s through the o p e r a t i o n of more than one process 98. (Chapter 2.3.6.) . F i g u r e 4.46. i l l u s t r a t e s tha t AH (a s lope) depends on how the processes i n t e r a c t . T E M P " 1 FIGURE 4 .46 . Combined processes (AH a s l o p e ) . Processes may operate i n p a r a l l e l (s imultaneous and independent ) , i n s e r i e s (dependent and c o n s e c u t i v e ) , or i n some more compl ica ted manner. For example, processes A and B may operate i n a " p a r a l l e l - p r o p o r t i o n e d " f a s h i o n where: ,, /. v . /100 - Ys -e = -rfr; (e . ) + ( — , n n J ) eT 100 v A' v 100 B I t i s apparent t h a t , except f o r the s e r i e s case , AH. w i l l be ambiguous i f i t i s c a l c u l a t e d anywhere i n the v i c i n i t y of 0 or 0'. The " v i c i n i t y " of 0 or 0' may extend to many degrees c e n t i g r a d e , depending f o r one t h i n g on the s t a t i s t i c a l conf idence a s s o c i a t e d w i t h the p l o t t e d v a l u e s . I t i s l i k e l y that a combined process a n a l y s i s i s warranted f o r the present d a t a , i n v iew of the m u l t i - s t a g e nature of the m-curves . 4.7. I n t e r n a l s t r e s s 4.7.1. General That an i n t e r n a l s t r e s s O q e x i s t s i n low temperature deformat ion i s a w e l l e s t a b l i s h e d concept . A s s o c i a t e d w i t h long-range athermal d i s l o c a t i o n i n t e r a c t i o n s , 0"q supposedly reduces the e f f e c t i v e s t r e s s a* f e l t by mobi le d i s l o c a t i o n s to a v a l u e lower than the a p p l i e d s t r e s s a , a cc or d i ng t o : r a* = a _ a . (4.8) F o Only r e c e n t l y has t h i s concept been a p p l i e d to h i g h temperature creep ( e . g . Cuddy (1969), N i x and B a r r e t t (1968), Jonas (1969)). S e m i - q u a n t i t a t i v e e v a l u a t i o n s of OQ /Q^ have been made, a l though the va lues vary g r e a t l y (Table 4./.). The v a r i a t i o n depends p a r t l y on the exper imenta l t e c h n i q u e s , and p a r t l y on the t e s t c o n d i t i o n s ( e . g . s t r a i n r a t e ) . 100. TABLE 4 . | . E x p e r i m e n t a l v a l u e s of a /a M a t e r i a l a o / o F Reference F e - S i S t a i n l e s s S t e e l Mg (e > 1 0 " 4 S e c . " 1 ) (e < I O - 4 S e c . " 1 ) Cd-6% Pb .7 - .9 .1 - .25 ^ .25 ^ . 8 v a r i a b l e N i x and B a r r e t t (1968) Cuddy (1970) Gibbs (1966) { it II Present work . F i g u r e 4 .47 . i l l u s t r a t e s the " r e v e r s e r e l a x a t i o n technique" commonly used to determine aQ i n I n s t r o n t e s t s . A g e n e r a l e q u a t i o n f o r s t r e s s r e l a x a t i o n may be w r i t t e n , assuming no recovery of aQ i t s e l f : - H ( a ) , -H(a) "I* . _!l= i = A ( e K T - e K T ) (4 .9) E dt p combined e l a s t i c modulus of specimen and machine, a p p l i e d s t r e s s , p l a s t i c specimen s t r a i n , ca*bA* , j. c j . \ H —— ( a c t i v a t i o n energy f o r forward jumps) p KT co*bA* ( a c t i v a t i o n energy f o r backward jumps) , H p + ~ K T ~ ~ a c t i v a t i o n energy of deformat ion p r o c e s s , f a c t o r r e l a t i n g o* to the a c t i v a t i o n shear s t r e s s T * (^h), assuming a d i s l o c a t i o n p r o c e s s , a c t i v a t i o n a r e a . where E * = e P H ( a ) f H ( a ) b H P c = A* = 101. in u or o ORIGINAL I — ORIGINAL FLOW CURVE 2~ QUICK UNLOADING 3 — POSITIVE STRESS RELAXATION 4— NEGATIVE STRESS RELAXATION TIME FIGURE 4.47. Reverse r e l a x a t i o n technique f o r determining a Q . 102, Equation (4.9) may be r e w r i t t e n as: —H , _p_ co*bA* -co*bA* -1 . 0 F . . KT. . KT KT . E* d T = £ P = A ( e ) ( e " e > a*bA* = A' s i h h 2_£A (4.10) When a F > a , a * i s p o s i t i v e and p o s i t i v e s t r e s s r e l a x a t i o n d°F occurs ( i . e . i s p o s i t i v e and -^r— i s n e g a t i v e ) . When a < a , a* i s negative and negative s t r e s s r e l a x a t i o n r O , d 0 F occurs ( i . e . £^ i s negative and i s p o s i t i v e ) . This s i t u a t i o n occurs only when an a p p l i e d s t r e s s l e s s than O q i s imposed on the specimen by re v e r s i n g the cross-head d i r e c t i o n . Then upon stopping the cross-head, the a p p l i e d s t r e s s r i s e s w i t h time due to specimen c o n t r a c t i o n . When o_ = a , o* i s zero, and no s t r e s s r e l a x a t i o n occurs. F o ' (The s t r e s s l e v e l aQ i s the assymtote approached i n a l l r e l a x a t i o n t e s t s . ) A value f o r aQ may be obtained from the m u l t i s t e p t e s t i l l u s t r a t e d i n Figure 4.47., although there are f a c t o r s which make the value ambiguous. Guiu (1969) has pointed out that " a r t i f i c i a l " negative s t r e s s r e l a x a t i o n may occur i n s o f t specimens due to machine c o n t r a c t i o n s . (He has conceded i n p r i v a t e communication that machine e f f e c t s are u n l i k e l y to account f o r the gross e f f e c t s observed i n the present work, and that a r e a l specimen e f f e c t i s being observed.) Another problem i n determining aQ at high temperatures i s that aQ i t s e l f recovers with both time and specimen c o n t r a c t i o n , making estimates of aQ g e n e r a l l y low. 103 . 4- 7 .2 . E x p e r i m e n t a l F i g u r e 4 .48 . i l l u s t r a t e s the m-curves f o r Cd-3u (0°C) and Z n - l u ( 2 1 ° C ) , w i t h t h e i r corresponding n ^ - c u r v e s determined by the " r e v e r s e r e l a x a t i o n t e c h n i q u e " . (M-curves r e l a t e to o^; m Q -curves to oQ.) • An i n t e r n a l s t r e s s oQ of some magnitude i s e v i d e n t i n s tages I , I I and I I I . S i m i l a r r e s u l t s were obta ined f o r Cd-3u ( 2 1 ° C ) , Cd-8y ( 2 9 ° C ) , Pb-5u (21°C) and e u t e c t i c - 3 u ( 2 1 ° C ) . I t was e s t a b l i s h e d that aQ r e l a x e d q u i c k l y enough to i n t e r f e r e w i t h readings unless the t e s t ( F i g u r e 4 .47 . ) was performed very q u i c k l y ( w i t h i n seconds) . The r a t e of r e l a x a t i o n of oQ i n c r e a s e d w i t h i n c r e a s i n g i n i t i a l f l o w s t r e s s or s t r a i n r a t e f o r any g i v e n m-curve . As a r e s u l t the es t imate of O q f o r any g i v e n Op becomes i n c r e a s i n g l y low from l e f t to r i g h t a long the m-curve . Al though i m p o s s i b l e to determine the p r e c i s e r e l a t i o n s h i p between OQ and Op, m a i n l y due to the recovery of aQi i t may be s a i d w i t h f a i r conf idence that the m Q -curves i n F i g u r e 4 .48 . represent minimum va lues of a Q . 4 . 7 . 3 . D i s c u s s i o n 4 . 7 . 3 . 1 . a Q i n normal creep The s i g n i f i c a n c e of a measured oQ i n normal creep (and stage I I I i n the present work) i s not c l e a r . I f equat ion (4.8) a p p l i e s , then a* should be used i n the s t r a i n r a t e e q u a t i o n s , r a t h e r than Op. Except i n i s o l a t e d recent work ( e . g . Cuddy (1970), Jonas (1969)) , s t r a i n r a t e equations have been w r i t t e n i n terms of Op. A c c o r d i n g to N i x and B a r r e t t S T R A I N R A T E (MIN"') K 4.48. m-and m 0-curves f o r two s u p e r p l a s t i c a l l o y s . (1968), both the e x i s t e n c e of an i n t e r n a l s t r e s s and the use of a„ i n F the equat ions may be r a t i o n a l i z e d . However, the matter i s u n r e s o l v e d and remains one of the important cha l lenges i n creep t h e o r y . 4 . 7 . 3 . 2 . O q i n s u p e r p l a s t i c i t y Assuming tha t d i s l o c a t i o n i n t e r a c t i o n s p l a y no r o l e i n c r e a t i n g a b a c k s t r e s s ( reasonable i n view of the observed l a c k of networks and low d e n s i t y ) , i t i s p o s s i b l e to c o n s t r u c t p h y s i c a l models i n which a o c c u r s i n s u p e r p l a s t i c i t y and i n which o* (= a_ - a ) i s o r r j F o a p p r o p r i a t e i n the r a t e e q u a t i o n s . S p e c i f i c a l l y , two models i n v o l v i n g g r a i n boundary s l i d i n g as a r a t e - c o n t r o l l i n g s tep w i l l be c o n s i d e r e d . The b a c k s t r e s s r e s i s t i n g s l i d i n g o r i g i n a t e s a t the t r i p l e l i n e s where accommodation must o c c u r . The two models i n v o l v e the two l i k e l y accommodation mechanisms of d i f f u s i o n and s l i p , r e s p e c t i v e l y . ( i ) D i f f u s i o n a l accommodation: F i g u r e 4 . 4 9 . i l l u s t r a t e s how g r a i n boundary s l i d i n g may be accommodated by l o c a l i z e d d i f f u s i o n ( G i f k i n s (1967)) . I n i t i a l l y , the shear s t r e s s x * on boundary A-B i s r e l a t e d to the t e n s i l e f l o w s t r e s s a ( e . g . i f 6 = 4 5 ° , then x* = . 5 c O . r F Once s l i d i n g b e g i n s , reg ions of t e n s i l e and compressive s t r e s s a r i s e a t boundaries B-C and A - C , r e s p e c t i v e l y . The r e s u l t i n g vacancy g r a d i e n t produces the necessary accommodation. The magnitude of a (& - a^) depends on the r e l a t i v e k i n e t i c s of the s l i d i n g and accommodation mechanisms, w i l l be s m a l l i f d i f f u s i o n a long the s t r e s s g r a d i e n t i s f a s t , and v i c e v e r s a . ^ The b a c k s t r e s s g(a ) r e s u l t i n g from accommodation t I t i s i m p l i c i t i n the model tha t accommodation i s always f a s t e r than s l i d i n g . O t h e r w i s e , the accommodation process i t s e l f w i l l be r a t e -c o n t r o l l i n g , as o r i g i n a l l y suggested by G i f k i n s (1967). r* = f O F l - %^yf MATERIAL T ~ \ ( FLUX / b . FIGURE 4.49. D i f f u s i o n a l accommodation model . a . Zero s t r a i n b . S t e a d y - s t a t e c o n d i t i o n . T* = f(ov) ~ ^ g ( T R ) / FIGURE 4.50. S l i p accommodation model . a . S t a r t of g e n e r a t i o n c y c l e b . Bowing d i s l o c a t i o n d u r i n g c y c l e Tg = bowing s t r e s s T F . R * T B ^ ° . 107. i s probably l i n e a r l y r e l a t e d to a . A sudden r e d u c t i o n of ap to zero by r e v e r s i n g the I n s t r o n cross-head q u i c k l y w i l l now reduce T * to - g ( o c ) i n s t a n t l y . The g r a i n s w i l l exper ience r e v e r s e shear which produces specimen c o n t r a c t i o n ; a t the same time a d r i v i n g f o r c e f o r cont inued, forward creep by t r i p l e l i n e d i f f u s i o n w i l l e x i s t . As the l a t t e r process i s the f a s t e r of the two, i t should predominate , and no net c o n t r a c t i o n should o c c u r . Thus the model does not p r e d i c t the r e f l e c t i o n of a b a c k s t r e s s i n a " r e v e r s e r e l a x a t i o n t e s t " . Analogous d i f f u s i o n a l models c o u l d be developed f o r o t h e r p o s s i b l e r a t e c o n t r o l l i n g mechanisms. ( e . g . Coble creep w i t h s l i d i n g accommodation). As i n the present model the b a c k s t r e s s would be l i n e a r l y r e l a t e d to the f l o w s t r e s s and would not show up on a " r e v e r s e r e l a x a t i o n t e s t . " ( i i ) S l i p Accommodation: I t w i l l now be assumed that s l i p r a t h e r than d i f f u s i o n a l accommodation o c c u r s . A c r i t i c a l s t r e s s must be reached at the t r i p l e l i n e be fore a d i s l o c a t i o n can be generated from a Frank-Read s o u r c e . The s i z e of the source cannot g r e a t l y exceed l u as t h i s i s the order of the g r a i n s i z e . (Thus the source s t r e n g t h 3 T may be f a i r l y l a r g e , i n the order of 10 p s i . ) From F i g u r e 4 . 5 0 . , i t i s apparent that T * w i l l not reach a steady s t a t e v a l u e as i n the d i f f u s i o n a l case , due to the d i s c o n t i n u o u s nature of the s l i p accommodation. A t zero s t r a i n or immediate ly a f t e r d i s l o c a t i o n g e n e r a t i o n , T * = f ( a „ ) . r A t any other i n s t a n t , however^ i * w i l l depend on how f a r the d i s l o c a t i o n has bowed o u t : T * = f ( G f ) - g ( T g ) • When T F I reaches T f _ r > , the d i s l o c a t i o n escapes and a new c y c l e b e g i n s . For a complete c y c l e an average b a c k s t r e s s 2(1,,) may be v i s u a l i z e d i n F i g u r e 4 . 5 0 . . The v a l u e of a il o determined by r e v e r s e r e l a x a t i o n would be p r o p o r t i o n a l to g ( T ) . Now, g (T ) i s a c o n s t a n t , independent of a , so i t s s i g n i f i c a n c e w i l l i n c r e a s e w i t h decreas ing a „ . ( I t should be noted tha t g ( x _ ) , and hence a „ , r is o depend on T and i n c r e a s e w i t h d e c r e a s i n g g r a i n s i z e . ) r . K . Appendix C shows that the a n e l a s t i c s t r a i n a s s o c i a t e d w i t h the d i s l o c a t i o n model can produce s u f f i c i e n t specimen c o n t r a c t i o n to a l l o w the d e t e r m i n a t i o n of aQ i n a " r e v e r s e " r e l a x a t i o n t e s t " . I f the I n s t r o n l i n k a g e had an i n f i n i t e e l a s t i c modulus, oQ would be observed w i t h i n f i n i t e s i m a l specimen c o n t r a c t i o n . I n f a c t , the l i n k a g e " g i v e s " as the specimen c o n t r a c t s , and a c a l c u l a b l e amount of s t r a i n i s r e q u i r e d to accommodate the " g i v e " . 4.7.3.3. E f f e c t of aQ on m i n stages I and I I The presence of a b a c k s t r e s s may w e l l i n f l u e n c e apparent s t r a i n r a t e s e n s i t i v i t y and l e a d to erroneous c o n c l u s i o n s . For example, the appearance of two stages (I and I I ) suggests two processes i n which the stage I process cannot be Newtonian v i s c o u s due to i t s low m. F i g u r e 4.51. shows how a s i n g l e p r o c e s s , fundamenta l ly Newtonian v i s c o u s , can account f o r both s t a g e s , when a s u i t a b l e r e l a t i o n s h i p e x i s t s between a* and aQ. F i g u r e 4 . 5 2 . i l l u s t r a t e s how a F v a r i e s w i t h s t r a i n r a t e f o r the two b a c k s t r e s s models a n a l y s e d . For the d i f f u s i o n a l m o d e l , a * i s probably p r o p o r t i o n a l of a , meaning t h a t m = 1 at a l l t imes and two F stages w i l l not e x i s t . C l e a r l y , t h i s model , by i t s e l f , cannot d e s c r i b e 109. the observed b e h a v i o u r . The d i s l o c a t i o n mechanism i s more f e a s i b l e , as i t p r e d i c t s a constant a Q f o r any g i v e n g r a i n s i z e . As a r e s u l t , Of -> oQ i n stage I , l e a d i n g to low s t r a i n r a t e s e n s i t i v i t y . I t i s l i f t e l y that both accommodation mechanisms would operate i n p a r a l l e l to some e x t e n t , w i t h the d i f f u s i o n a l process becoming more important w i t h decreas ing s t r e s s . FIGURE 4 . 5 1 . Stage I - I I behaviour d e s c r i b e d i n terms of a , a 0 and o * . The i d e a of a b a c k s t r e s s i n f l u e n c i n g m i n s u p e r p l a s t i c i t y i s not new (Chapter 2 . 3 . 6 . ) . However, no exper imenta l c o n f i r m a t i o n or * L O G S T R A I N R A T E FIGURE 4.52. Stage I - I I behaviour f o r the two ba c k s t r e s s models proposed. 111. d e t a i l e d p h y s i c a l r a t i o n a l e f o r the e x i s t e n c e of oQ has been p r e v i o u s l y r e p o r t e d . The present d i s l o c a t i o n model appears to be a reasonable one-process i n t e r p r e t a t i o n of s tage I - I I behaviour where g r a i n boundary s l i d i n g i s r a t e - c o n t r o l l i n g . No e l a b o r a t e i n t e r p r e t a t i o n of the data i n F i g u r e 4.48 i s w a r r a n t e d . I t c o u l d be s a i d tha t the stage I Z n - l u r e s u l t s support the model w h i l e the stage I I Cd-3u r e s u l t s do n o t . (Presumably, oQ i n s tage I I I i s r e l a t e d to d i s l o c a t i o n i n t e r a c t i o n s and does not r e l a t e to the present models . ) Whether a b a c k s t r e s s i n t e r p r e t a t i o n of stages I and I I i s reasonable i n v iew of o ther evidence w i l l be d i s c u s s e d i n Chapter 5 . 5. MECHANISTIC INTERPRETATION 5.1. Stage I I I A creep process independent of s u p e r p l a s t i c mechanisms i s a p p r o p r i a t e f o r stage I I I . Wi th s l i g h t a d a p t a t i o n the process c o u l d be d e s c r i b e d by the models g e n e r a l l y a p p l i c a b l e to normal c r e e p ; the s p e c i a l i z e d case of recovery at the head of a d i s l o c a t i o n p i l e u p ( e . g . Weertman (1955)) w i l l be assumed i n the present d i s c u s s i o n . The low a c t i v a t i o n energies observed i n Cd-8u and Pb-5u (Chapter 4.6.4.3.) s t r o n g l y suggest that r e c o v e r y occurs i n the v i c i n i t y of g r a i n b o u n d a r i e s , by enhanced c l imb r a t e s around " n o r m a l " o b s t a c l e s ( e . g . L o m e r - C o t t r e l l b a r r i e r s ) or by a more d i r e c t d i s l o c a t i o n -boundary i n t e r a c t i o n . Wi th r e g a r d to the l a t t e r p o s s i b i l i t y , the o b s t a c l e h e i g h t c o u l d be a s s o c i a t e d w i t h the g r a i n s i z e , the maximum d i s t a n c e an edge d i s l o c a t i o n would have to c l imb to a l l o w the r e l e a s e of a new d i s l o c a t i o n i n t o the p i l e u p . Other i n t e r a c t i o n s at the boundary could be v i s u a l i z e d , e s p e c i a l l y i n v o l v i n g d i s l o c a t i o n a b s o r p t i o n by s l i d i n g . Models i n v o l v i n g p i l e u p s and subsequent boundary i n t e r a c t i o n s have been proposed (Hayden and Brophy (1968), B a l l and H u t c h i s o n (1968)) to account f o r s tage I I b e h a v i o u r , a l though they seem more r e l e v a n t to stage I I I . The f l e x i b i l i t y of these models i s s u f f i c i e n t to accommodate the s t r a i n r a t e s e n s i t i v i t i e s or g r a i n s i z e e f f e c t s observed i n e i t h e r s t a g e . The t r a n s i t i o n from stage I I to stage I I I i s an ambiguous r e g i o n , not o n l y because s u p e r p l a s t i c and normal creep processes are independent " p a r a l l e l " mechanisms, but a l s o because a " y i e l d i n g " may be a s s o c i a t e d w i t h the onset of s tage I I I . The t r a n s i t i o n to s tage I I I 113. occurs at lower s t r e s s e s the f i n e r the g r a i n s i z e f o r a g i v e n a l l o y (Chapter 4 . 1 5 . ) . I f the m-curve approaches a g r a i n - s i z e independent assymptote i n stage I I I (Chapter 2 . 2 . 5 . ) , ther? the t r a n s i t i o n should be more abrupt the f i n e r and more u n i f o r m the g r a i n s i z e . 5 . 2 . Stages I and I I 5 . 2 . 1 . Coble and H-N creep The importance of Coble and/or H-N creep w i l l f i r s t be cons idered i n terms of p r e d i c t e d versus exper imenta l creep r a t e s . Table 5 . 1 . l i s t s the r e l e v a n t data f o r the present work (at 40°C f o r convenience) , and f o r other work from which meaningfu l c a l c u l a t i o n s can be made. ( In a l l cases the second phase volume percentage i s s m a l l . ) The s t r e s s l e v e l s are chosen to correspond w i t h the stage I I i n f l e c t i o n p o i n t s i n the exper imenta l m-curves . I t i s a p p r o p r i a t e to i n v e s t i g a t e the p r e d i c t e d versus e x p e r i m e n t a l r a t e s f o r two reasons : ( i ) The Coble model has been accepted by some ( e . g . Z e h r , Backofen) as be ing the r a t e - c o n t r o l l i n g process i n stage I I . ( i i ) Both the Coble and H-N models are d e r i v e d r i g i d l y from b a s i c p r i n c i p l e s and lend themselves w e l l to r a t e - a n a l y s i s . From Table 5 . 1 . , e „ , , >> eTT „ f o r a l l cases , meaning Coble H-N that H-N creep can g e n e r a l l y be i g n o r e d , a l though i t s r e l a t i v e importance i n c r e a s e s w i t h i n c r e a s i n g temperature and g r a i n s i z e . I n most cases , the p r e d i c t e d Coble r a t e s are too s m a l l to be important at the s tage I I i n f l e c t i o n . I g n o r i n g p o s s i b l e e r r o r i n TABLE 5 . 1 . T h e o r e t i c a l creep r a t e s f o r Coble and H-N models versus e x p e r i m e n t a l creep r a t e s . 5 2 D (cm /sec ) Temp. (°K) T/T M S t r e s s ( p s i ) £„, (min l ) Theor . e C o b l e TC ^ E x p e r . A l l o y GB D B Coble H-N Pb-5y 1 -4930 t . i n - 4 RT 1.25x10 e -26 ,060 i / RT 1,4e 313 .52 1000 I O " 3 5 x 1 0 " 1 ^ 5 x l 0 ~ 4 2. -15 ,700 * . 8e 2 . 5 x l 0 ~7 .0005 Cd-3u 1 -13 ,000 RT . 7e -18 ,700 .075e R T 313 .53 2000 1 . 5 x l 0 ~ 4 3 x l 0 " 6 ^ 5 x l 0 - 3 .03 Cd-8u 1 1000 1 . 7 x l 0 " 6 6 x l 0 " 7 %10"4 .017 Z n - l y 1 -14 ,400 Q RT . 3e -22 ,500 RT . 16e 313 .45 10,000 I O " 3 3 x l 0 ~ 6 ^ 2 x l 0 - 1 .005 Sn- l%Bi(5u) 2 -9550 9 T?T -23 ,300 i / R T 1. 4e 295 .58 ' 1500 3 x l 0 ~ 4 3 x 1 0 " 1 1 o , 2 x l 0 " 3 .06 S n - 5 % B i ( 3 . 5 u ) d 6.4x10 e 9x10-4 6 x 1 0 " 1 1 ^3x10-^ .3 F e ( " l o w a l l o y : ^2p) 4 -39 ,000 c RT • 5e -57 ,000 0 RT 2e 1073 .59 'WOOO 5 x l 0 ~ 2 i o " 1 1 ^ 5 x 1 0 " 3 10 1 Present work 2 A l d e n (1966) : ! A l d e n (1967) 4 M o r r i s o n (1968) 1 5 from S m i t h e l l (1968) f S t a r k and Upthegrove (1966) + Okkerse (1955) * E corresponds to s tage I I i n f l e c t i o n rixper a ( i . e . maximum m) . B 2 v w D G B a ' C 0 b l e L? KT ' H " N ~ L?KT ' where B, v s w 10 150 o i n " 2 3 3 2 x 10 cm 10" 7 cm. D f o r the moment, there are two f a c t o r s which would make the p r e d i c t e d creep r a t e s even l o w e r : ( i ) L has been c a l c u l a t e d by the i n t e r c e p t method i n a l l cases , whereas the " t r u e " g r a i n s i z e i s l a r g e r by a f a c t o r of about 1 .5 , as the i n t e r c e p t method i n v o l v e s a c r o s s - s e c t i o n a l cut i n which the g r a i n s are not cut h e m i s p h e r i c a l l y , but a t some " a p p a r e n t " g r a i n s i z e ranging from zero to the t r u e d i a m e t e r . The e f f e c t on the p r e d i c t e d 3 creep r a t e i s to reduce i t by a f a c t o r of (1.5) ^ 3 (Equat ion ( 2 . 4 ) ) . ( i i ) The a p p l i e d s t r e s s has been assumed e q u a l to the e f f e c t i v e s t r e s s . I f a b a c k s t r e s s e x i s t s , then the p r e d i c t e d creep r a t e w i l l be reduced a c c o r d i n g l y . A l t h o u g h l i t t l e e r r o r i s expected i n the v a l u e s ass igned to D ^ , v and w, there i s c o n s i d e r a b l e doubt concerning the e x p e r i m e n t a l va lues f o r D ^ . I n the case of P b - 5 u , a c c e p t i n g S t a r k and Upthegrove ' s GU v a l u e of D_„ f o r l e a d produces a reasonable creep r a t e , s e v e r a l orders Go of magnitude f a s t e r than tha t obta ined by u s i n g O k k e r s e ' s v a l u e . Al though the former v a l u e appears to be the more e x p e r i m e n t a l l y v a l i d of the two, i t has gained l i t t l e acceptance i n the l i t e r a t u r e . (The AH^ obta ined f o r Pb-5u i n the present work does not support e i t h e r v a l u e . ) Given the u n c e r t a i n t y i n D ( e s p e c i a l l y f o r l e a d ) , i t i s G D g e n e r a l l y u n l i k e l y that Coble creep has much r e l e v a n c e to s tage I I from the p o i n t of v iew of r a t e a n a l y s i s . Whether the Coble model f a i l s to s a t i s f y other c r i t e r i a w i l l now be d i s c u s s e d : ( i ) Coble creep p r e d i c t s g r a i n e l o n g a t i o n as a f u n c t i o n of s t r a i n , c o n t r a r y to g e n e r a l o b s e r v a t i o n . However, the present r e s u l t s 116. suggest that some e l o n g a t i o n may occur i n Cd-3u (Chapter 4 . 3 . 2 . ) ; i n any case , g r a i n boundary m i g r a t i o n may w e l l obscure the o b s e r v a t i o n of e l o n g a t i o n , p a r t i c u l a r l y when i t produces g r a i n growth . ( i i ) The model p r e d i c t s the s t r o n g g r a i n s i z e e f f e c t g e n e r a l l y observed i n stage I I . The ambigui ty i n d e f i n i n g the exper imenta l r e l a t i o n s h i p between s t r e s s and g r a i n s i z e (Chapter 2 . 2 . 5 . ) , a long w i t h the p o s s i b i l i t y of a b a c k s t r e s s , p r o h i b i t s c l e a r c o r r e l a t i o n of theory w i t h exper iment . ( i i i ) The model r e q u i r e s g r a i n boundary s l i d i n g to occur as an accommodation p r o c e s s . Backofen (1968) suggested tha t a b a c k s t r e s s could be somehow a s s o c i a t e d w i t h t h i s s l i d i n g which c o u l d l e a d to a low apparent s t r a i n - r a t e s e n s i t i v i t y (stage I , presumably) . Zehr and Backofen (1968) suggested tha t s l i d i n g c o u l d become r a t e - c o n t r o l l i n g i n stage I i f the process has an i n h e r e n t l y low s t r a i n r a t e s e n s i t i v i t y . N e i t h e r e x p l a n a t i o n i s l i k e l y , as d i f f u s i o n a l s l i d i n g i s p o s s i b l e a t a f a s t e r r a t e than the Coble process (see next s e c t i o n ) . Thus the accommodation process would never c o n t r o l , and any b a c k s t r e s s r e s u l t i n g from s l i d i n g would probably be l i n e a r l y r e l a t e d to the f l o w s t r e s s and thereby i n c a p a b l e of e x p l a i n i n g s tage I (see Chapter 4 . 7 . 3 . 2 . ) . ( i v ) The observed a c t i v a t i o n energy i n s tage I I i s c o n s i s t e n t w i t h Coble c reep , a l though observed v a l u e s do not correspond p r e c i s e l y w i t h g r a i n boundary d i f f u s i o n v a l u e s . The i n c r e a s e d a c t i v a t i o n energy as stage I i s approached from stage I I i s i n c o n s i s t e n t w i t h e i t h e r Coble creep or i t s accommodation p r o c e s s , s l i d i n g . I t i s not l i k e l y that the i n c r e a s e i s due to a s t r e s s - a s s i s t a n c e term (Chapter 4 . 6 . 4 . 4 . ) , a l though the p o s s i b i l i t y that i t r e l a t e s to a 117. d i f f e r e n t process a l t o g e t h e r w i l l be d i s c u s s e d l a t e r . 5 . 2 . 2 . G r a i n boundary s l i d i n g G r a i n boundary s l i d i n g may depend on the d i f f u s i o n of vacanc ies around boundary p r o t r u s i o n s , i n which case the d i f f u s i o n path would r e l a t e to the p r o t r u s i o n s i z e r a t h e r than the g r a i n s i z e (Chapter 2 . 3 . 3 . ) . The model developed by G i f k i n s (1968) p r e d i c t s creep r a t e s which are orders of magnitude f a s t e r than the Coble model , e s p e c i a l l y i f a l l the g r a i n s s l i d e a l l the t i m e . ( In f a c t i t i s l i k e l y that some g r a i n s would pause some of the t ime , r e d u c i n g the p r e d i c t e d r a t e , but s t i l l l e a v i n g i t f a s t e r than Coble c r e e p . ) The 2 model developed by A l d e n (1969) does not assume the p r o t r u s i o n s i z e to be as s m a l l as i n the G i f k i n s model . However, i t more r e a l i s t i c a l l y assumes that the normal s t r e s s e s on the p r o t r u s i o n s may be v e r y h i g h , depending on the nature and d i s t r i b u t i o n of p r o t r u s i o n s . A g a i n , the p r e d i c t e d creep r a t e i s c o n s i d e r a b l y f a s t e r than i n the Coble model , e s p e c i a l l y i f the l a r g e r p r o t r u s i o n s tend to be e l i m i n a t e d by m i g r a t i o n (Chapter 4 . 4 . 4 . 3 . ) . Thus, g r a i n boundary s l i d i n g i s more l i k e l y than Coble creep from r a t e a n a l y s i s . Whether the process s a t i s f i e s other c r i t e r i a w i l l now be c o n s i d e r e d : ( i ) S l i d i n g p r e d i c t s no g r a i n e l o n g a t i o n as a f u n c t i o n of s t r a i n , which i s g e n e r a l l y c o n s i s t e n t w i t h o b s e r v a t i o n (a l though see Chapter 5 . 2 . 1 . ) . 2 ( i i ) The G i f k i n s model p r e d i c t s e a L , w h i l e the A l d e n 3 E^'Ael j , r t ' l l c t fe a r a t h e r s t r o n g e r dependence (perhaps 'z s L ) . Both models are c o n s i s t e n t w i t h o b s e r v a t i o n f o r s tage I I . ( i i i ) The model r e q u i r e s t r i p l e l i n e accommodation, e i t h e r by d i f f u s i o n or s l i p . The former process appears to be about as f a s t as Coble creep (from G i f k i n s (1968)), and thereby too s low to be s i g n i f i c a n t . The r a t e - i n s e n s i t i v e d i s l o c a t i o n process developed i n Chapter 4 . 7 . 3 . 2 . seems a p p r o p r i a t e , e s p e c i a l l y as i t accounts f o r s tage I . However, the i n c r e a s e i n AH^ i n s tage I i s the major o b s t a c l e to t h i s t h e o r y . I t i s p o s s i b l e , a l though hard to v i s u a l i z e , that the i n c r e a s e i n AH^ i s a s p u r i o u s e f f e c t , due to a temperature dependent b a c k s t r e s s . (Such an i n t e r p r e t a t i o n would e x p l a i n the anomalous r e s u l t i l l u s t r a t e d i n F i g u r e 4 . 4 1 ) . I f the d i s l o c a t i o n s emit ted i n the above model are not q u i c k l y d i s p e r s e d , t h e i r movement away from the sources through the b u l k cou ld be r a t e - c o n t r o l l i n g w i t h an a c t i v a t i o n energy equal to tha t f o r b u l k d i f f u s i o n . The model proposed by A l d e n (1969) i n v o l v e s the " v i s c o u s g l i d e " of d i s l o c a t i o n s (unusual concept I ) , i n which the low s t r a i n r a t e s e n s i t i v i t y of the process a r i s e s through a s t r e s s dependence of mobi le d i s l o c a t i o n d e n s i t y . However, a dependence of at l e a s t p m a would be r e q u i r e d to e x p l a i n the v e r y low v a l u e s of m observed f o r stage I i n some cases ( e . g . m ^ .15m Lee (1969)* ) . There i s no exper imenta l evidence to suggest such a r e l a t i o n s h i p i n any deformat ion p r o c e s s , l e t a lone t h i s i n s t a n c e . On the o ther hand, such a r e l a t i o n s h i p cou ld occur i f the number of sources e m i t t i n g d i s l o c a t i o n s were to decrease w i t h d e c r e a s i n g s t r e s s , due to an i n c r e a s i n g i n a b i l i t y of s l i d i n g g r a i n s to produce s t r e s s c o n c e n t r a t i o n s s u f f i c i e n t to cause y i e l d . 119. 5.2.3. G r a i n boundary m i g r a t i o n That boundary m i g r a t i o n may be a r a t e - c o n t r o l l i n g process i n s tage I should not be i g n o r e d . The a c t i v a t i o n energy i s expected to be l a r g e r than that f o r boundary d i f f u s i o n , c o n s i s t e n t w i t h the observed b e h a v i o u r . M i g r a t i o n i n v o l v e s b u l k d i f f u s i o n to or away from b o u n d a r i e s ; moreover, the s o l u t e spec ies may c o n t r o l i f t h e i r d i f f u s i o n k i n e t i c s are slow w i t h respec t to the m a t r i x (Honeycombe (1968)) . M i g r a t i o n may always accompany s l i d i n g i n s u p e r p l a s t i c i t y : i t appears i n e v i t a b l e a t t r i p l e l i n e s and very l i k e l y at bumps on s l i d i n g boundaries (Chapter 4.4.4.3.). To be the s tage I p r o c e s s , m i g r a t i o n would have to have an inherent s t r a i n r a t e s e n s i t i v i t y l e s s than tha t of the stage I I process ( s l i d i n g ) , a l though the apparent s e n s i t i v i t y cou ld be reduced by a decrease i n a c t i v e sources w i t h decreas ing f l o w s t r e s s , as d i s c u s s e d i n the p r e v i o u s s e c t i o n . No t h e o r e t i c a l or exper imenta l i n f o r m a t i o n e x i s t s f o r the s t r a i n r a t e s e n s i t i v i t y of m i g r a t i o n . 5.2.4. D i s l o c a t i o n networks The s tage I I d i s l o c a t i o n models of Hayden and Brophy (1968) and B a l l and H u t c h i s o n (1968) cannot be reasonably sub jec ted to r a t e a n a l y s i s , as they are b a s i c a l l y ad hoc d e s c r i p t i o n s w i t h h i g h l y f l e x i b l e . parameters . Moreover , the nature of the networks , the g e n e r a t i o n of d i s l o c a t i o n , and the manner i n which the d i s l o c a t i o n s i n t e r a c t w i t h boundaries to produce s l i d i n g have been i n a d e q u a t e l y d e s c r i b e d ; nor has any e x p l a n a t i o n f o r stage I been proposed. The absence of pr imary creep (Chapter 4.5.) argues a g a i n s t the e x i s t e n c e of networks ( p i l e u p s 120. or o t h e r w i s e ) . Furthermore , i t i s i m p l i c i t i n the d i s l o c a t i o n models that e x t e n s i v e s l i p s t r a i n o c c u r s , whereas v e r y l i t t l e i s e v i d e n t from t the s u r f a c e o b s e r v a t i o n s of Chapter 4.4.3.. I n g e n e r a l , i t i s not expected tha t the above models have much r e l e v a n c e to s u p e r p l a s t i c i t y . 5 . 2 . 5 . Stage I U l t i m a t e l y , i t i s expected tha t m should i n c r e a s e w i t h d e c r e a s i n g s t r a i n - r a t e i n s tage I , as d i f f u s i o n a l processes of Newtonian v i s c o s i t y dominate„(e .g . d i f f u s i o n a l accommodation f o r s l i d i n g ) . T h i s p r e d i c t i o n has not y e t been demonstrated, presumably because of the extremely low s t r a i n - r a t e s a t which i t h o l d s t r u e . I t i s not expected that the s t r a i n i n v o l v e d i n the s l i p accommodation f o r s l i d i n g need by l a r g e compared w i t h the net s l i d i n g s t r a i n , e x p l a i n i n g the i n f r e q u e n t o b s e r v a t i o n of s l i p . (Other p o s s i b l e reasons f o r s l i p absence have been o u t l i n e d i n Chapter 4.4.3.). 121. 6. SUMMARY AND CONCLUSIONS S t r a i n r a t e s e n s i t i v i t y curves were determined over a range of temperatures f o r s e v e r a l a l l o y s : P b - 6 v o l . % C d , Pb-28vol .%Cd (two g r a i n s i z e s ) , Cd-6 .5vol .%Pb (two g r a i n s i z e s ) , and Z n - l w t . % A l . A l i m i t e d mechanica l equat ion of s t a t e was e s t a b l i s h e d f o r s tages I and I I , a l though the shape of the m-curves i n s tage I I I depended s e n s i t i v e l y on the t e s t d e f i n i t i o n . I n g e n e r a l , pr imary creep was n e g l i g i b l e i n stages I and I I . For the lead-based a l l o y s , the amount of pr imary creep i n c r e a s e d the more stage I I I became apparent i n any g i v e n m-curve . For the cadmium-based a l l o y s , s tage I I I was c h a r a c t e r i z e d by "de layed y i e l d i n g " which corresponded w i t h a y i e l d drop i n I n s t r o n t e s t s . Al though g r a i n growth occurred as a f u n c t i o n of s t r a i n i n eutect ic-3y and Z n - l u , i t c l e a r l y d i d not i n C d - 3 u * (120% e l o n g a t i o n ) , i n d i c a t i n g that g r a i n growth i s not a necessary f e a t u r e of s u p e r p l a s t i c i t y (stage I I ) . The i n v e s t i g a t i o n of g r a i n e l o n g a t i o n i n C d - 3 u * (stage I I ) was i n c o n c l u s i v e , a l though the technique has been o u t l i n e d . A s t r o n g s h i f t i n g of the m-curves as a f u n c t i o n of g r a i n s i z e was observed i n Cd-6 .5vol .%Pb and P b - 2 8 v o l . % C d , c o n s i s t e n t w i t h prev ious o b s e r v a t i o n . From the l i m i t e d experiments i n v o l v i n g the e u t e c t i c a l l o y s (m-curve f a m i l i e s , a c t i v a t i o n energy a n a l y s i s creep i n v e s t i g a t i o n ) , e u t e c t i c behaviour was probably best d e s c r i b e d i n terms of a weighted average of the volume f r a c t i o n s of the two phases . The presence of a, l a r g e s p e c i f i c area of i n t e r p h a s e boundary had no unusual e f f e c t . 122. Surface i n d i c a t i o n s of s l i p s t r a i n were n e g l i g i b l e i n stage I I f o r Cd-3u* and Cd-8u*, c o n s i s t e n t w i t h o ther i n v e s t i g a t i o n s . The e x t e n s i v e s l i d i n g which o c c u r r e d had c l o s e l y a s s o c i a t e d m i g r a t i o n marks and s t r i a t i o n s on the s l i d i n g b o u n d a r i e s . " P e e l i n g " (observed i n Pb-5u as w e l l ) was i n t e r p r e t e d as a s u r f a c e e f f e c t . B a s a l s l i p was s t r o n g l y apparent i n stage I I i n Cd-8u*, the absence of t w i n n i n g and n o n - b a s a l s l i p due to the p a r t i a l presence of s l i d i n g . A b a c k s t r e s s was i n f e r r e d from " r e v e r s e r e l a x a t i o n t e s t s " , a p l a u s i b l e reason f o r i t s e x i s t e n c e i n s u p e r p l a s t i c i t y i n v o l v i n g the s l i p accommodation f o r s l i d i n g . The a c t i v a t i o n energy i n stage I I I was a s s o c i a t e d w i t h g r a i n boundary d i f f u s i o n . A p i l e u p model i n which recovery occurs a t or near the boundaries was adopted f o r s tage I I I , the process a c t i n g independent ly of s u p e r p l a s t i c processes ( i . e . " p a r a l l e l " p r o c e s s e s . ) The a c t i v a t i o n energy i n stage I I was a s s o c i a t e d w i t h g r a i n boundary d i f f u s i o n . D i f f u s i o n a l g r a i n boundary s l i d i n g w i t h s l i p accommodation at t r i p l e l i n e s was adopted as the most l i k e l y r a t e -c o n t r o l l i n g process i n stage I I . The model c o u l d apply to s tages I and I I , the low s t r a i n r a t e s e n s i t i v i t y i n stage I r e s u l t i n g from the b a c k s t r e s s i n v o l v e d i n s l i p accommodation. I f the i n c r e a s e d a c t i v a t i o n energy observed i n s tage I i n Cd-3u and Z n - l u r e f l e c t s a d i f f e r e n t r a t e - c o n t r o l l i n g s tep i n s tage I , the l i k e l y processes i n v o l v e boundary m i g r a t i o n or d i s l o c a t i o n mot ion through the b u l k . I n e i t h e r case , the process i n v o l v e s the b a s i c s l i d i n g mechanism (wi th s l i p accommodation) as a dependent or " s e r i e s " p r o c e s s . 123. APPENDIX A Low temperature deformat ion General The deformat ion c h a r a c t e r i s t i c s of f i n e - g r a i n e d cadmium have not p r e v i o u s l y been r e c o r d e d , as s t a b l e g r a i n - s i z e s l e s s than about 25u are not f e a s i b l e i n pure cadmium. I n order to p r o v i d e b a s i c d a t a and to open areas f o r f u t u r e i n v e s t i g a t i o n , C d - 3 u * and C d - 8 u * have been deformed over a wide range of temperature . Due to the s o f t n e s s and s m a l l volume f r a c t i o n of the second phase p a r t i c l e s and the v i r t u a l i n s o l u b i l i t y of l e a d i n cadmium, the f l o w p r o p e r t i e s of the a l l o y s are assumed to be e s s e n t i a l l y those of pure cadmium. Y i e l d behaviour At h i g h e r temperatures u n i f o r m y i e l d i n g occurs (stage I I I ) , the y i e l d drop d i s a p p e a r i n g w i t h the onset of s u p e r p l a s t i c i t y (stage I I ) . Al though d i s c u s s e d i n the t e x t (Chapter 4 . 1 . ) , the phenomenon i s r e l e v a n t to the present d i s c u s s i o n , and s e v e r a l h i g h temperature f l o w curves have been i n c l u d e d i n F i g u r e s A . l . and A . 2 . . At lower temperatures non-uni form y i e l d i n g occurs presumably by Luders band p r o p a g a t i o n . (However, Luders bands have not been confirmed by m i c r o s c o p i c a n a l y s i s f o r C d - 3 u * and C d - 8 u * ) . The o c c a s i o n a l j o g observed at the end of the non-cont inuous y i e l d regime ( e . g . F i g u r e A . l . , -140°C) has c o n s i d e r a b l e precedent , and probably r e f l e c t s the approach and mutual a n n i h i l a t i o n of two Luders f r o n t s . P e c u l i a r l y , non-cont inuous y i e l d i n g i s absent i n C d - 8 u * a t I ^ - 1 4 0 ° C , 124. w h i l e i t i s very pronounced i n C d - 3 u * . As non-cont inuous y i e l d i n g i s unprecedented i n c o a r s e - g r a i n e d cadmium, the phenomenon appears to be r e l a t e d to the f i n e g r a i n s i z e per s e . To t e s t the h y p o t h e s i s , Z n - l u was deformed at -96°C (.25 T w ) . M A s i m i l a r l y unprecedented Liiders y i e l d occurred ( f o l l o w e d by b r i t t l e f r a c t u r e ) , c o n s i s t e n t w i t h the r e s u l t s f o r C d - 3 u * at .25 T w . I t would M be i n t e r e s t i n g to see whether the phenomenon, common to z i n c and cadmium, a p p l i e s g e n e r a l l y to f i n e - g r a i n e d H . C . P . m e t a l s . Y i e l d theory I g n o r i n g f o r the moment the anomalous y i e l d behaviour of Cd-8u* at T < - 1 4 0 ° C , a model i n v o l v i n g d i s l o c a t i o n m u l t i p l i c a t i o n seems a p p r o p r i a t e f o r both uni form and non-uni form y i e l d i n g . The argument d e r i v e s from the g e n e r a l e m p i r i c a l r e l a t i o n s h i p ? p = p + f ( e ) , ( A . l ) m o p ' mobi le d i s l o c a t i o n d e n s i t y a f t e r macroscopic y i e l d , mobi le d i s l o c a t i o n d e n s i t y a t the p o i n t of macroscopic y i e l d , an i n c r e a s i n g f u n c t i o n of p l a s t i c s t r a i n (approximate ly l i n e a r i n B . C . C . metals^Hahn (1962)) . Unless P q = 0, a p r e r e q u i s i t e f o r a y i e l d drop i s tha t the d i s l o c a t i o n v e l o c i t y be s t r e s s - s e n s i t i v e . The lower the s t r e s s - s e n s i t i v i t y exponent n(= ^ ) , the more pronounced the y i e l d c h a r a c t e r i s t i c s . N has not been determined f o r the present a l l o y s at low temperatures . where p = m P o = f ( e ) = P 125. 0 4 8 12 16 20 24 S T R A I N (%) FIGURE A . l . I n s t r o n f l o w curves f o r Cd-3y* , assuming u n i f o r m r e d u c t i o n of c r o s s - s e c t i o n a l area w i t h s t r a i n . 12 6.. S T R A I N (%) ^FIGURE A.2. I n s t r o n flow curves f o r Cd-Su*, assuming uniform r e d u c t i o n of c r o s s - s e c t i o n a l area w i t h s t r a i n . . Ignor ing e l a s t i c e f f e c t s , a g e n e r a l i z e d e q u a t i o n may be d e r i v e d from the work of Hahn (1962) and C o t t r e l l (1963): J. - *<EP> + HIT) > (A. 2) m where a = f l o w s t r e s s , g(e ) = work hardening f u n c t i o n (zero when e = 0) P P E q u a t i o n (A.2) p r e d i c t s u n i f o r m y i e l d i n g ( F i g u r e A . 3 a . ) , s i m i l a r to s tage I I I behaviour i n the present work ( e . g . F i g u r e A . l . , + 65°rj) . Hahn suggests that non-uni form y i e l d i n g ( F i g u r e A . 3 b . ) i s an a l t e r n a t e form of d e f o r m a t i o n , which occurs i f the d e f o r m a t i o n o u t s i d e the Luders band spreads s l o w l y . I n e i t h e r case , the upper y i e l d and the lower y i e l d o' T V are dynamical p r o p e r t i e s u n r e l a t e d to normal y i e l d Li JL mechanisms. CO CO LU or h-co a. UNIFORM YIELDING b . NON-UNIFORM YIELDING STRAIN FIGURE A . 3 . Y i e l d e f f e c t s due to d i s l o c a t i o n m u l t i p l i c a t i o n (from Hahn (1962) ) . 128. C o t t r e l l accepts the dynamical approach i n the case of s i n g l e c r y s t a l de format ion where d i s l o c a t i o n u n p i n n i n g or m u l t i p l i c a t i o n i s u n i f o r m along the gauge l e n g t h . However, i n the case of p o l y c r y s t a l l i n e non-uni form d e f o r m a t i o n , he r e l a t e s a e x p l i c i t l y to Li 1 the " u n l o c k i n g " s t r e s s f o r the p r o p a g a t i o n of y i e l d from one g r a i n to the n e x t . Whatever the p r e c i s e i n t e r p r e t a t i o n of the y i e l d drop and subsequent f l o w c h a r a c t e r i s t i c s , the phenomenon i s g e n e r a l l y a s s o c i a t e d w i t h metals and non-metals where p Q i s v e r y s m a l l . I t occurs i n 6—8 — non-metals l i k e L i F where p = 102 c m - 2 (p =10 cm 2 i n most o o annealed m e t a l s ) , i n " w h i s k e r s " , and i n B . C . C . meta ls where mobi le d i s l o c a t i o n s can be e f f e c t i v e l y pinned by i n t e r s t i t i a l s e g r e g a t i o n . I t i s p o s s i b l e , as w e l l , that P q i s r e l a t i v e l y low i n Cd-3u* and Cd-8u*, due to g r a i n boundary p i n n i n g . Assuming the t o t a l d i s l o c a t i o n d e n s i t y to be independent of g r a i n s i z e i n annealed cadmium, the f r a c t i o n whose ends are pinned by boundaries would be expected to i n c r e a s e w i t h decreas ing g r a i n s i z e . (The boundary area per u n i t volume v a r i e s i n v e r s e l y as the g r a i n s i z e . ) When the lower y i e l d s t r e s s e x i s t s below -60°C i t i s v i r t u a l l y temperature i n s e n s i t i v e ( F i g u r e A .4.), c o n s i s t e n t w i t h the concept of athermal y i e l d . The o p e r a t i o n of Frank-Read sources ( i . e . d i s l o c a t i o n s pinned by boundar ies ) i s a p l a u s i b l e mechanism. The lower y i e l d p o i n t f o r Cd-3u* i s c o n s i d e r a b l y h i g h e r than t h a t f o r Cd-8u*, a l though a P e t c h - t y p e r e l a t i o n s h i p can not be e s t a b l i s h e d on the b a s i s of two g r a i n s i z e s . . The lower y i e l d s t r e s s decreases q u i t e s t r o n g l y w i t h i n c r e a s i n g temperature above -100°C f o r Cd-3u* and above -60°C f o r Cd-8u*. 36 H . 1 3 T , A h 4 * t .22T t . 2 9 T , I M .36T\ J I I I ! I 1 I I I I I I I I I - 2 0 0 - 1 5 0 - 1 0 0 T E M P E R A T U R E (°c) - 5 0 FIGURE A.4. T e n s i l e flow s t r e s s as a f u n c t i o n of temperature f o r v a r ious s t r a i n s (from Figures A . l . and A. 2 . ) . 13 Any i n t e r p r e t a t i o n of the i n t e r m e d i a t e r e g i o n , between the low temperature regime and the s u p e r p l a s t i c reg ime, i s ambiguous i n v iew of the l i m i t e d d a t a . The area does , however, correspond w i t h the b e g i n n i n g of boundary m o b i l i t y and s l i d i n g (Risebrough (1965)), and w i t h the disappearance of twinning and n o n - b a s a l s l i p . F i g u r e s A .5.-7. i l l u s t r a t e the e x i s t e n c e of twinning and n o n - b a s a l s l i p at -140°C, whereas n e i t h e r mode i s ev ident i n the s u p e r p l a s t i c r e g i o n (Chapter 4.4.3.). I t i s p o s s i b l e tha t boundary m o b i l i t y and s l i d i n g r e l a x the Von Mises requirements and the disappearance of two r e l a t i v e l y " h a r d " modes c o n t r i b u t e s to the drop i n f l o w s t r e s s . An e x t e n s i v e m i c r o s c o p i c a n a l y s i s of de format ion modes over the " i n t e r m e d i a t e " temperature range would be very u s e f u l i n extending t h i s i n t e r p r e t a t i o n . T e n t a t i v e l y , i t i s proposed t h a t the l a c k of d i s c o n t i n u o u s y i e l d i n g i n Cd-8u* a t T < -140°C r e s u l t s from an enhanced p r o p e n s i t y f o r twinning which masks or e l i m i n a t e s s l i p y i e l d i n g by Luders p r o p a g a t i o n . The l i m i t e d evidence suggests that t w i n n i n g frequency i n c r e a s e s w i t h decreas ing temperature ( R e e d - H i l l (1963)), and f o r d e c r e a s i n g g r a i n s i z e (Risebrough (1965)), c o n s i s t e n t w i t h the present o b s e r v a t i o n s . To t e s t the h y p o t h e s i s , Cd-8u* and Cd-3u* were deformed 3% at -140°C, and the s u r f a c e markings a n a l y s e d . The absence of twins i n Cd-3u* and the presence of twins i n Cd-8u* would have l e n t support to the argument. The r e s u l t s , however, were i n c o n c l u s i v e i n tha t t w i n n i n g occurred i n both cases ( F i g u r e A .5.6.), a l though not e x t e n s i v e l y . I t i s q u i t e p o s s i b l e tha t twinning occurs l e s s f r e q u e n t l y i n Cd-3u* than i n Cd-8u*, and t h a t when i t does occur i n Cd-3u* i t i s r e s t r i c t e d to the l a r g e s t g r a i n s . To c l a r i f y the i s s u e would r e q u i r e a s t a t i s t i c a l i n t e r p r e t a t i o n of numerous micrographs over a range of temperatures , 131. FIGURE A . 5 . T w i n n i n g i n C d - 3 u * . - 140°C (petroleum ether), 3% e, x3500. FIGURE A . 6 . T w i n n i n g i n C d - 8 u * . _ 140°C (petroleum ether), 3% e. x3500. 132. FIGURE A . 7 . Non b a s a l s l i p i n C d . 3 y * . - 140°C (petroleum e t h e r ) , 3%6. X10,000 . s t r a i n s and g r a i n s i z e s . An unexplored p o s s i b i l i t y i s that p l a s t i c de format ion i s induced by p r e - t e s t thermal c y c l i n g . A n i s o t r o p i c thermal c o n t r a c t i o n s i n cadmium can be a potent source of s t r e s s c o n c e n t r a t i o n (Evans (1966)) , and the e f f e c t should be most pronounced i n c o a r s e - g r a i n e d cadmium deformed at very low temperature . . Dynamic recovery F i g u r e A . 8 . shows how the macroscopic work-hardening r a t e decreases w i t h i n c r e a s i n g temperature above -196°C , f o r s t r a i n s beyond 2% i n C d - 8 u * and 4% i n C d - 3 u * . (At lower s t r a i n s the y i e l d e f f e c t obscures i n t e r p r e t a t i o n . ) The i m p l i c a t i o n i s tha t dynamic recovery occurs even at very low temperatures . Moreover , the work-hardening r a t e i s c o n s i s t e n t l y lower i n C d - 3 u * than i n C d - 8 u * , sugges t ing tha t the recovery process i s enhanced by the presence of g r a i n boundaries^". Broadly s p e a k i n g , dynamic recovery may occur as the r e s u l t of c r o s s - s l i p or d i f f u s i o n . C r o s s - s l i p i s f e a s i b l e w i t h i n the second order p y r a m i d a l f a m i l y , and between b a s a l , p r i s m a t i c and f i r s t order p y r a m i d a l systems s h a r i n g a common b u r g e r s ' v e c t o r < 1 1 2 0 > . A l though c r o s s - s l i p has not been unambiguously i d e n t i f i e d i n cadmium or z i n c , there i s good evidence f o r i t s e x i s t e n c e . For example, P r i c e (1963) I n f a c t , at -100 C i n C d - 3 u * , dynamic recovery i s f a s t enouth to prevent hardening past the L u d e r s ' e x t e n s i o n . A t - 6 0 ° C , immediate L u d e r s ' f a i l u r e o c c u r s . The i n s t a b i l i t y which occurs a t 'v -60°C i n C d - 3 u * , i s a s t r i k i n g m a n i f e s t a t i o n of H a r t s ' p r i n c i p l e (Chapter 1 . 1 . ) . At low temperatures the Cons id^re parameter y i s w e l l - s a t i s f i e d , a l l o w i n g s t a b l e d e f o r m a t i o n . A t h i g h temperatures , the s t r a i n r a t e s e n s i t i v i t y m i s h i g h , a l l o w i n g a s low development of i n s t a b i l i t i e s . A t i n t e r m e d i a t e . t e m p e r a t u r e s , bo th m and y are s m a l l , making m = y << 1, and l e a d i n g to the observed gross i n s t a b i l i t y . 134. o L _ J — I I I I I I I i i i i i i i -200 -150 -100 - 5 0 TEMERATURE (°C) FIGURE A.8. Work-hardening r a t e (•—) as a f u n c t i o n of temperature .for v a rious s t r a i n s (from Figures A . l . and A.2.). 135. associated the production of elongated basal loops with the c r o s s - s l i p of {1122} <1123> screw d i s l o c a t i o n s . Whether c r o s s - s l i p can act as an ef f e c t i v e recovery process i n cadmium or zinc has not yet been resolved. However, i t i s u n l i k e l y that c r o s s - s l i p could account for the more rapid recovery i n Cd -3u* than i n Cd-8u*. A conceivable d i f f u s i o n a l recovery process involves the conservative climb of s e s s i l e d i s l o c a t i o n loops produced either by cr o s s - s l i p or by vacancy condensation (Price (1963)) . Climb occurs through "pipe" d i f f u s i o n around the loops. I t i s not expected that grain boundaries should a f f e c t t h i s process. However, grain boundaries could absorb loops by acting as vacancy sink/sources f o r the loop half-planes. Such a recovery process i s consistent with the observed g r a i n s i z e dependence of the work-hardening r a t e . A s i m i l a r recovery process invloves the boundary absorption of excess vacancies produced by the non-conservative motion of jogged screw d i s l o c a t i o n s . Recovery at »2T^ i n cadmium has been interpreted i n terms of vacancy migration ( P e i f f e r and Stevenson (1963)) , and i s a legitimate p o s s i b i l i t y i n the present context. A p o s s i b i l i t y which has been ignored i n the previous discussion i s that the work-hardening rate may be influenced by twinning. What has, been assumed to r e f l e c t dynamic recovery may i n fa c t p a r t i a l l y r e f l e c t a dependence of twinning on temperature and grain s i z e . APPENDIX B . S u p e r p l a s t i c systems p r e v i o u s l y i n v e s t i g a t e d 136. A l - C u ( e u t e c t i c ) A l - M g ( e u t e c t i c ) B i - S n (Sn - 1% B i ) (Sn - 5% B i ) Cd-Pb (Pb - 5 W / Q Cd) A l - Z n ( e u t e c t o i d ) ( e u t e c t i c ) (Zn . 5% A l ) ; Low a l l o y s t e e l s T i tan ium and z i r c o n i u m a l l o y s N i c k e l (pure) F e - N i - C r a l l o y s Pb-Sn ( e u t e c t i c ) (Pb - 19% Sn, Sn - 2% Pb) ( e l e c t r o p l a t e d composites) P b - T l (Pb - ( 0 . 5 - 7.9) % TI) H o l t and Backofen (1966) Lee (1969) 1 A l d e n (1966) A l d e n (1967) A l d e n (1968) B a l l and H u t c h i s o n (1969), H o l t (1968), A l d e n and Schadler (1968), Chaudhari (1967) , Kossowski (1966) , Backofen et a l (1965). Packer et a l (1968) Cook (1968) 1 2 M o r r i s o n (1968) ' Lee and Backofen (1967) F l o r e e n (1968) Hayden e t a l (1967), Hayden and Brophy (1968) Zehr and Backofen (1968) M o r r i s o n (1968) 1 , 2 , C l i n e and A l d e n (1967) C l i n e and A l d e n (1967) M a r t i n and Backofen (1967) G i f k i n s (1967) APPENDIX C. 137. Specimen c o n t r a c t i o n i n a " r e v e r s e r e l a x a t i o n t e s t " I f the d i s l o c a t i o n model proposed i n Chapter 4.7. i s v a l i d , i t must p r o v i d e the a n e l a s t i c s t r a i n a s s o c i a t e d w i t h specimen c o n t r a c t i o n . The amount of c o n t r a c t i o n A2. may be c a l c u l a t e d a c c o r d i n g t o : AO P .L . ,.—6. A& = -:-=• 10 m . A . E where P = observed c o n t r a c t i o n l o a d ( c h a r a c t e r i s t i c a l l y , ^ 1 l b ) , L = I n s t r o n l i n k a g e l e n g t h 20 i n ) , 2 A = I n s t r o n l i n k a g e c r o s s - s e c t i o n a l area .5 i n ) , E = e l a s t i c modulus of l i n k a g e (> 3 x 10 7 p s i ) . With the specimen gauge l e n g t h I <v 1 i n . , the minimum —6 a n e l a s t i c s t r a i n r e q u i r e d of the model i s ^ 10 . Now assume one d i s l o c a t i o n source of l e n g t h ^ l u per g r a i n , which on the average i s ^ 2 F . R . bowed to h a l f i t s "breakaway" area ( i . e . %( ") - .2u z). Aysuming L ^ 3u and w i t h b ^ 2 x 10 S, the s t r a i n per g r a i n i s (2 x 10 ^p) -^~-y3 = 2 x I O - 5 . The e q u i v a l e n t s t o r e d specimen s t r a i n w i l l be s l i g h t l y l e s s than 2 x 10 - 6, but a t l e a s t as l a r g e as the r e q u i r e d 10 6 . Although the above c a l c u l a t i o n i s o n l y an order of magnitude e s t i m a t e , i t shows that the model cannot be d i s m i s s e d o u t - o f -hand on the b a s i s of i n s u f f i c i e n t s t o r e d s t r a i n . 138. BIBLIOGRAPHY Alden, T.H. Trans. AIME 236 (1966) 1633. Acta Met. _15 (1967) 469. Trans.ASM 61_ (1968) 559. Acta Met. _17 (1969) 1 1435. J'. Aust. Inst. Met. 14 (1969) 2 207. Alden, T.H. and Schadler, H.W. Trans. AIME 242 (1968) 825. Avery, D.H. and Backofen, W.A. Trans. ASM _51_ (1965) 551. Avery, D.H. and Stuart, J.M. Fourteenth Sagamore Army Materials Research Conf. (1967). Backofen, W.A. et a l . Trans. ASM 57 (1964) 980. Trans. AIME 242 (1968) 329. B a l l , A. and Hutchison, M.M. Metal Science J . _3 (1969) 1. Barrett, CR. et a l . Trans. AIME 230 (1964) 200. Barrett, CR. and.Nix, W.D. Acta Met. 1_3 (1965) 1247. B e l l , R.L. et a l . . Trans. AIME 239 (1967) 1821. Chaudhari, P. Acta Met. _15 (1967) 1 1777. IBM Research Report RC 1946 (1967) 2. 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Ph.D. Thesis, U.B.C. (1965). Risebrough, N.R. and Lund, J.A. Trans. ASM £1 (1968) 723 Ryan, H.F. and Suiter, J.W. P h i l . Mag. K) (1964) 729, Smith, G.S. Trans. AIME 175 (1948) 15. Smithells, C.J. "Metals Reference Book", Butterworths (1967). Squires, R.L. et a l . J . Nucl. Met. 8 (1963) 77. Stark, J.P. and Upthegrove, W.R. Trans. ASM 59 (1966) 486. Str u t t , P.R. et a l . J . Inst. Met. 93 (1964) 71. Surges, A.K. M.A.Sc. Thesis, U.B.C. (1969). Turner, D. Private Communication (1970). Underwood, E.E. J . Metals U (1962) 914. Wajda, E.S. et a l . Acta Met. 3 (1955) 39. Walter, J.L. and Cli n e , H.E. Trans. AIME 242 (1968) 1823. Waldron, R.J. Ph.D. Thesis, U.B.C. (1969). Weertman, J . J . App. Phys. 26 (1955) 1213. J . App. Phys. 28 (1957) 362. Trans. ASM 61 (1968) 681. Weinstein, D. Trans. AIME 245 (1969) 2041. Zehr, S.W. and Backofen, W.A. Trans. ASM 61 (1968) 300. 

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