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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.Sc.  U n i v e r s i t y of B r i t i s h C o l u m b i a ,  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 . t h i s t h e s i s as conforming required  to  standard  THE UNIVERSITY OF BRITISH COLUMBIA February  1971  the  In p r e s e n t i n g t h i s  thesis  an advanced degree at the L i b r a r y I  the U n i v e r s i t y  s h a l l make i t  f u r t h e r agree tha  in p a r t i a l  freely  f u l f i l m e n t o f the of B r i t i s h  available  for  requirements f o r  Columbia, I agree  that  reference and study.  p e r m i s s i o n f o r e x t e n s i v e copying o f t h i s  thesis  f o r s c h o l a r l y purposes may be granted by the Head o f my Department o r by h i s of  this  representatives.  It  thesis for financial  i s understood that copying o r p u b l i c a t i o n gain s h a l l  written permission.  Department o f  Metallurgy  The U n i v e r s i t y o f B r i t i s h Columbia Vancouver 8, Canada  Date  A p r i l 7,  1971  not be allowed without my  i.  ABSTRACT  Several appropriately treated  alloys  (Pb-6.5vol.%Cd,  P b - 2 8 v o l . % C d , C d - 6 v o l . % P b and Z n - l w t . % A l ) were i n v e s t i g a t e d superplastic properties,  their  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 , 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 . analysis of:  for  creep and t e n s i l e  the r e g i o n of maximum  The i n v e s t i g a t i o n i n c l u d e d  t e s t data, surface deformation markings,  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 p r o c e s s i n s t a g e 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 a t t r i p l e l i n e s . feasible  for stage I ,  Several interpretations  were  a l l i n v o l v i n g p r o c e s s e s c o n c u r r e n t w i t h , and  dependent o n , g r a i n boundary s l i d i n g . "normal" coarse-grained  Stage I I I  was i d e n t i f i e d as  creep (adapted to p e r m i t c o n s i d e r a b l e  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 ) ,  operating independently  recovery of  s u p e r p l a s t i c p r o c e s s e s , and d o m i n a t i n g at h i g h f l o w s t r e s s e s and s t r a i n rates.  ACKNOWLEDGEMENT S  The a u t h o r 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 . R i s e b r o u g h and D r . T. A l d e n , and f o r t h e h e l p f u l d i s c u s s i o n s w i t h o t h e r f a c u l t y members and g r a d u a t e  students.  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  Council.  iii. TABLE OF CONTENTS PAGE 1.  INTRODUCTION  *  2.  LITERATURE SURVEY  .  2  2.1.  Introduction  2  2.2.  S u p e r p l a s t i c phenomenology  4  2 . 2 . 1 . E v i d e n c e 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. Grain size effects  6  2 . 2 . 6 . E v i d e n c e f o r g r a i n boundary s l i d i n g 2.2.7. Effect  2.3.  2.4.  .  .  .  .  7  of second phase  2 . 2 . 8 . G r a i n shape change and g r a i n growth  3.  1  8 .  .  .  .  8  S u p e r p l a s t i c mechanisms  9  2 . 3 . 1 . General  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 p r o c e s s e s  13  Objectives  14  of p r e s e n t  investigation  EXPERIMENTAL  15  3.1.  M a t e r i a l s choice  15  3.2.  Procedure  •  16  iv.  PAGE 3.2.1. A l l o y p r e p a r a t i o n  17  3.2.2. S t a b i l i z e d  17  test structures  3.2.3. P r e p a r a t i o n o f specimens f o r t e s t i n g  .  .  .  .  23  3.2.4. T e s t i n g apparatus  23  3.2.5. M e t a l l o g r a p h y 4.  .  .  .  .  .  23  RESULTS AND DISCUSSION  25  4.1. S t r a i n r a t e s e n s i t i v i t y  25  4.1.1. G e n e r a l  25  4.1.2. R e p r o d u c i b i l i t y  25  4.1.3. M e c h a n i c a l  34  e q u a t i o n o f s t a t e f o r stages I, I I .  4.1.4. Stage I I I . . .  •  35  4.1.5. Secondary o b s e r v a t i o n s  36  4.2. G r a i n growth  37  4.2.1. G e n e r a l  37  4.2.2. Cd-3p* .  38  4.2.3. E u t e c t i c - 3 y  . . .  4.2.4. Zn-lu  38 .  41  4.2.5. C o n c l u s i o n s  41  4.2.6. D i s c u s s i o n  41  4.2.7. G r a i n growth model  42  4.3. G r a i n shape  44  4.3.1. G e n e r a l  44  4.3.2. E x p e r i m e n t a l  44  4.3.3. D i s c u s s i o n  49  4.4. S u r f a c e o b s e r v a t i o n s  50  V.  PAGE 4.4.1. G e n e r a l  50  4.4.2. Modes of d e f o r m a t i o n . 4.4.3. S u r f a c e 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 .  4.4.4. G r a i n boundary e f f e c t s  51 .  52 64  4.4.4.1. S h e a r i n g 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 b e h a v i o u r  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 - 3 y  72  4.5.3. Cd-3u and Cd-8y  75  4.5.4. Z n - l u  .  4.6. A c t i v a t i o n energy  .  .  .  .  .  .  82 83  4.6.1. G e n e r a l 4.6.2. E x p e r i m e n t a l  .  83 .  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. S t a g e I  97  4.6.4.3. Stage I I I  97  4.6.4.4. Combined p r o c e s s e s  97  4.7. I n t e r n a l s t r e s s 4.7.1. G e n e r a l 4.7.2. E x p e r i m e n t a l  99 99 104  vi. PAGE 4.7.3. Discussion  104  4.7.3.1. a  i n normal creep  104  4.7.3.2. a  i n superplasticity  105  Q  Q  4 . 7 . 3 . 3 . E f f e c t of a  Q  5.  on m s t a g e s I and I I .  .  MECHANISTIC INTERPRETATION  112  5.1.  Stage I I I  112  5.2.  Stages I and I I  . . . . . .  •  113  5 . 2 . 1 . C o b l e 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 5 . 2 . 5 . Stage I 6.  108  .  .  .  .  .  119 .  .  120  SUMMARY AND CONCLUSIONS  121  APPENDIX A .  Low temperature d e f o r m a t i o n  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  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 "  BIBLIOGRAPHY  123 .  .  136 137 138  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.  Grain size effect i n superplastic alloys  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 ( 1 9 6 9 ) are r e l e v a n t .  13  Phase diagrams ( M e t a l s Handbook ( 1 9 4 8 ) ) . a. Lead-cadmium s y s t e m . b. A l u m i n u m - z i n c system  16  3.2.  Cd-3u.  P o l i s h e d and e t c h e d .  x2100  .  19  3.3.  Cd-8u.  P o l i s h e d and e t c h e d .  x2100  ..  19  3.4.  Eutectic-3)j.  P o l i s h e d . x2600  3.5.  Eutectic-8y.  P o l i s h e d . x2600 .  3.6.  Pb-5p.  P o l i s h e d and deformed. x2600  3.7.  Zn-lvi.  P o l i s h e d and e t c h e d .  3.8.  Schematic  4.1.  M - c u r v e s f o r Cd-3y  26  4.2.  M - c u r v e s . f o r Cd-8y  27  4.3.  M - c u r v e s f o r Pb-5y  28  4.4.  M-curves f o r eutectic-3u  29  4.5.  M-curves f o r eutectic-8u  4.6.  M-curves f o r Zn-lp  4.7.  S e n s i t i v i t y of m-curve shape to t h e r m a l h i s t o r y  4.8.  M - c u r v e d e t e r m i n a t i o n by two t e c h n i q u e s  4.9.  Effect  2  3.1.  4.10.  20 .  x3400  20 21 .  21  diagram of c o n s t a n t s t r e s s creep a p p a r a t u s  .  .  .  24  i .  30  .  31  .  ( s t a g e I and I I  32 32  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  alloy  33  T y p i c a l f l o w curves f o r s t a g e 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  Structural instability of eutectic-3p as a consequence of strain, originally i n stage II (Instron test)  40  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  4.13.  4.14.  4.15.  Cd-3u*. Near surface (^ 20p).  x2600.  (a) Before test. L = 3.4, / = 1.14 (b) After 100% elongation (m = .5, e ^ l O ' V i n " , 23°C) L  w  1  L = 5.0M,  4.16.  Cd-3y*.  /  w  Interior.  = 1.76  46  x2600  (a) Before test. L = 5.0, / = 1.57 (b) After 100% elongation (m = .5, e ^ 10"" min , 23°C) L  w  3  L = 4.8p,  4.17.  Cd~8u*. (e ^ IO  4.18.  /  w  = 1.37  16% Elongation. -3  Cd-8p*. 3  Cd-3p*. 3  .  .  .  .  .  .  .  .  .  .  min" , T = 23°C). x4000 1  53  Stage III  1  min  .  .  .  .  .  .  .  Cd-3p*. (E  4.21.  - 3  Cd-3p*. (E  4.22.  ^ 10  ^ 10  - 3  x8000  15% Elongation. Stage II min" , T = 23°C, m ^ .5). x8000 1  56  15% Elongation. Stage II min" , T = 23°C, m ^ . 5 ) . xl0,000 . . . .  57  1  .  .  .  55  .  Cd-3u*. 250% Elongation. Stage II (e ^ 10~ . mxn- , T = 23°C, m ^ . 5 ) . xl5,000 A - peeling boundary striations B - sliding boundary striations C - migration marks 3  54  Stage II  , T = 23°C).  A - closely associated striations and migration marks B - sliding in vicinity of lead particle " C - partial migration of curved, peeling boundary . . 4.20.  47  Stage III  min , T = 23°C) . x4000  15% Elongation.  (e ^ 10"  .  -1  16% Elongation.  (e ~ 10" 4.19.  L  _1  1  58  ix.  PAGE 4.23.  C d - 3 u * . 35% E l o n g a t i o n . Stage I I . (e ^ 5 x I O m i n " , T = 23°C, m * .5) x30,000 A - s t r i a t i o n s a t p e e l e d i n t e r p h a s e boundary . .  .  .  59  Cd-8y*. (e <v I O  .  .  ,60  . . .  61  - 4  4.24. 4.25.  - 3  1  13% E l o n g a t i o n . Stage I I . . , m i n " , T = 128°C, m ^ . 5 ) . x6000 1  Pb-5y. 15% E l o n g a t i o n . Stage I I . (E ^ 5 x 10~ m i n " , T = 23°C, m ^ . 3 5 ) . k  4.26.  1  Pb-5y. 15% E l o n g a t i o n . Stage I I . (e 5 x I0~ m i n , T = 23°C, m ^ . 3 5 ) . A - peeled boundaries k  - 1  Deformed r a p i d l y w i t h p l i e r s  .  .  x4000 x4000  62  4.27.  C.d-3y*.  (stage I I I ) .  x6000  4.28.  S h e a r i n g and p e e l i n g a t the s u r f a c e  65  4.29.  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  relieve  normal s t r e s s e s 4.31.  69  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  69  4.32.  Creep curves f o r Fb-5u ( s t a g e s I I ,  4.33.  Creep curves f o r e u t e c t i c - 3 y  4.34.  Creep curves f o r s t a g e I I  4.35.  P r i m a r y creep i n s t a g e s I ,  4.36.  Delayed y i e l d i n C d - 3 p , Cd-8u ( s t a g e I I I )  4.37.  D i f f i c u l t y i n recovering delayed y i e l d i n Cd-8u  4.38.  (stage I I I ) E f f e c t of p r e s t r a i n i n g i n s t a g e I I i n s t a g e I I I (Cd-8y)  4.39.  P r i m a r y creep i n Z n - l y  4.40.  D i f f e r e n t i a l creep t e s t i n w h i c h temperature " i n s t a n t l y " at e  III),  (stages I I ,  73 III),..  . . .  deformation  74 76  II  77 78  on d e l a y e d y i e l d  (stage I)  79 80 80  changes  c  4.41.  63  Decremental temp, change creep t e s t i n Cd-3y a t 500 p s i . (One specimen, each p o i n t c o r r e s p o n d i n g to a S . S . creep rate. T o t a l s t r a i n < 20%.) Stages I and I I are b o t h represented. (See F i g u r e 4 . 1 . )  84  90  ;  PAGE 4.42.  AH-plots from Figure 4.1.  4.43.  AH vs. flow-stress i n stages I and II for Z.n-ly ana Cd-3y (cf Figures 4.1., 6.)  92  AH^ vs. flow-stress i n stages II and III f o r Pb-5y and Cd-8y  93  4.44. 4.45.  (Cd-3y; stages I and I I .  .  A  AH^-plots for eutectic-3y, eutectic-8y. Stage I I , 500 p s i .  (from Figures 4.4. and 4.5.)  94  4.46.  Combined processes (AH^ a slope)  4.47.  Reverse relaxation technique for determining 0  4.48.  M-and m -curves for two superplastic alloys . . . .  4.49.  D i f f u s i o n a l accommodation model a. Zero s t r a i n b. Steady-state condition . . . S l i p accommodation model a. Start of generation cycle b. Bowing d i s l o c a t i o n during cycle  4.50.  4.51. 4.51. A.1. A.2. A.3. A.4. A.5.  A.6.  91  98 .  o  .  103  D  .  .  .  Stage I-II, behaviour described i n terms of Op, and a *  .  .  101  .  106  106 o  Q  ,.  109  Stage. I-II behaviour for the two backstress models proposed  110  Instron flow curves for Cd-3y*, assuming uniform reduction of cross-sectional area with s t r a i n . . .  125  Instron flow curves for Cd-8y*, assuming uniform reduction of cross-sectional area with s t r a i n . . .  126  Y i e l d effects 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)) Tensile flow stress as a function of temperature for various strains (from Figures A . l . and A.2.)  .  .  127  .  129  Twinning i n Cd-3y*. - 140°C (petroleum ether), 3% e. x3500  131  Twinning i n Cd-8y*. - 140°C (petroleum ether), 3% E . x3500 ;.  131  X.  Non-basal s l i p i n Cd-3u*. - 140°C (petroleum e t h e r ) , 3%. xlO.OOO . . . . . . . Work-hardening r a t e  (^—) as a f u n c t i o n o f  temperature f o r v a r i o u s and A.2.  s t r a i n s (from F i g u r e s A . l .  LIST OF TABLES PAGE 2.1.  Typical s t r a i n rate s e n s i t i v i t i e s  3.1.  P o s t - e x t r u s i o n specimen t r e a t m e n t s  18  4.1.  Grain elongation i n Cd-3y*  48  4.2.  A c t i v a t i o n energy d a t a r e l a t i v e to s u p e r p l a s t i c i t y  4.3.  E x p e r i m e n t a l v a l u e s of a / a p  5.1.  T h e o r e t i c a l creep r a t e s f o r C o b l e and H - N models  Q  v e r s u s e x p e r i m e n t a l creep r a t e s  .  .  .  .  2  88 100  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  large t e n s i l e elongations without f a i l u r e .  and 1950's, the remarkable d u c t i l i t y o f some m e t a l s was a s s o c i a t e d w i t h phase changes o r a l l o t r o p i c (Underwood ( 1 9 6 2 ) ) .  D u r i n g t h e 1940's  a t moderate temperatures  transformations  I n 1964, B a c k o f e n i d e n t i f i e d a d i s t i n c t l y  kind 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 i n t e r m e d i a t e temperatures  .5T ). M  different  (£ lOu) a t  The p r e s e n t work i n v e s t i g a t e s t h e  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 .  Potential exists i n  the realm o f h o t w o r k i n g where d u c t i l i t y and low s t r e s s e s a r e a s s e t s i n forming p r o c e s s e s .  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 c o n d i t i o n s (^ .5T^), w i t h t h e s a c r i f i c e o f some s t r e n g t h , has been r e p o r t e d ( W e i n s t e i n  (1969)).  An e x t e n s i v e phenomenology has been developed s u p e r p l a s t i c i t y , although  t h e r e i s no u n i v e r s a l agreement  o p e r a t i v e and r a t e - c o n t r o l l i n g mechanisms.  to describe concerning  Chapter 2. i s a l i t e r a t u r e  survey o f the fundamental e x p e r i m e n t a l evidence and i t s c u r r e n t t h e o r e t i c a l interpretation.  2. 2 . LITERATURE SURVEY  2.1.  Introduction The degree to w h i c h a f i n e - g r a i n e d m e t a l i s  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 .  superplastic  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  (2.1)  m + y £ 1 »  where  9 In a (stress) = 9 l h e (strain rate)  m  When m = 0 , E q u a t i o n (2.1)  e  9a 9e  (strain)'  becomes y > 1, w h i c h i s e q u i v a l e n t to the  known C o n s i d e r e 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 deformation, y - 0,  deformation.  and m i s s u b s t a n t i a l ,  deformation.  In  dominating Equation  superplastic  (2.1).  However, s u p e r p l a s t i c d e f o r m a t i o n i s p r o b a b l y never s t a b l e as m i s e q u a l to 1.  (See T a b l e  TABLE 2 . 1 .  2.1.).  Typical s t r a i n rate  sensitivities  Process Low temperature  deformation  " N o r m a l " creep (^ "Superplastic"  m(> 0 ,  F l u i d glass flow  (Rate-insensitive)  a, .2  .5T^)  creep  0  < 1)  -5T^)  .3 -  .7  1 (Newtonian v i s c o u s )  well-  never  An i m p o r t a n t e x t e n s i o n o f 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 (m + y) .  ( i . e . "necks") decreases w i t h  increasing  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 .  Instabilities  may appear a t the onset of s u p e r p l a s t i c f l o w , b u t develop s l o w l y ( M o r r i s o n (1968)^).  M o r e o v e r , 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  m (Backofen e t a l ( 1 9 6 4 ) , Lee and Backofen  (1967)).  E l o n g a t i o n s o f 200%  a t m ^ . 3 and 1200% a t m ^ .7 appear to be c h a r a c t e r i s t i c Backofen  increasing  (Lee and  (1967)). Figure 2 . 1 . defines  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  m e t a l 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 -  curve).  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 a t c o n s t a n t m-curve a r e u s u a l l y " s t e a d y 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  s t a t e " creep r a t e s .  elongation rate,  I f determined by I n s t r o n  stress l e v e l s p l o t t e d are nominally  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 t a n d a r d 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 i n c r e m e n t s  1 - 2%) a t v a r y i n g s t r a i n r a t e s ,  c o r r e s p o n d i n g 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 . II,  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  It  For s t a g e s I and  steady-state stresses.  i s n a t u r a l to compare the d e f o r m a t i o n p r o p e r t i e s of  g r a i n e d m e t a l s w i t h those of c o a r s e - g r a i n e d m e t a l s a t the s t r a i n r a t e s and temperatures  e  where  The  b o t h s u p e r p l a s t i c and normal c r e e p :  AH /KT  = S.o.e  S = a structure  fine-  stresses,  associated with s u p e r p l a s t i c i t y .  following e m p i r i c a l equation describes  a  ,  (2.2)  factor,  m = apparent s t r a i n r a t e s e n s i t i v i t y , and  A H ^ = apparent a c t i v a t i o n e n t h a l p y .  F o r normal c r e e p , m ' r  .2 and AH. A  AH^ . . B (bulk d i f f u s i o n ) N  These v a l u e s a r e 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 superplastic creep, 2.2.  Superplastic  as subsequent  d i s c u s s i o n w i l l show.  phenomenology  2 . 2 . 1 . E v i d e n c e 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 m i c r o s c o p y has shown t h a t networks e x i s t  i n stage I I I  dislocation  i n much the same way as i n normal creep  (Hayden and Brophy ( 1 9 6 8 ) , Lee ( 1 9 6 9 ) , B a l l and H u t c h i s o n ( 1 9 6 9 ) ) . 1  Extensive primary creep  (Surges  1969)  and evidence f o r s t r a i n  hardening  (Alden (1968)) c o n f i r m the development o f d i s l o c a t i o n m i c r o s t r u c t u r e s i  i n stage I I I .  D i s l o c a t i o n networks do n o t 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 d e n s i t y i s v e r y low (Hayden and Brophy (1968), Lee (1969)*, 2 M o r r i s o n (1968) ) . Surges  N e g l i g i b l e primary  creep  (Hayden and Brophy  (1969)), and evidence f o r n e g l i g i b l e s t r a i n hardening  (1968),  (Alden (1968))  i n stage I I confirm that d i s l o c a t i o n d e n s i t i e s are s m a l l . 2.2.2. Evidence f o r s l i p S l i p l i n e s have been observed on o c c a s i o n on specimen s u r f a c e s a f t e r stage I I deformation insufficient mechanism. developed  (Cook (1968)).  to conclude t h a t s l i p I n d i r e c t evidence  However these o b s e r v a t i o n s a r e  i s a significant strain-producing  (Packer e t a l (1968)), based  on the  e l l i p t i c i t y i n t e x t u r e d Zn-Al e u t e c t i c t e n s i l e specimens,  suggests  t h a t 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  strain  I n d i r e c t e v i d e n c e suggests an important r o l e i n s u p e r p l a s t i c ! t y .  t h a t d i f f u s i o n a l s t r a i n may p l a 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 c o a r s e - g r a i n e d Mg - .5% Zr the presence  deformed a t ^ *8T^, through  o f "denuded" t r a n s v e r s e g r a i n boundaries  H a r r i s and Jones  (1963)).  ( S q u i r e s e t a l (1963),  A s i m i l a r a l l o y , Mg - 6Zn - .5Zr, a l s o  ;  d i s p l a y e d denuded zones d u r i n g a p p a r e n t l y s u p e r p l a s t i c d e f o r m a t i o n  (grain  L * 18y, T ^ .8T„, m ^ .6)(Karim e t a l (1968)).  M The size  l a t t e r a l l o y , when p r o c e s s e d t o produce  a very f i n e  (< l u ) , d i s p l a y e d s u r f a c e 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  when deformed a t T ^ .5T  , m ^ .02 (Backofen e t a l (1968)).  grain  axis  Backofen;  size  concluded t h a 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 t h a t 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 c r e e p p r o c e s s had  already  which  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  and s i m i l a r , a l l o y s .  same,  S t r i a t i o n s have been observed i n o t h e r 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 B a c k o f e n , Zehr and K a r i m , b e l i e v e this constitutes  that  good e v i d e n c e 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. A p p a r e n t a c t i v a t i o n energy Apparent a c t i v a t i o n e n e r g i e s for stage 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..  g e n e r a l , AH < A K , . , and A H . ^ ^AH,, i s A  (AH^) have o n l y been determined  D  A  D  In  characteristic.  2.2.5. G r a i n s i z e e f f e c t s In stage I I I , normal c r e e p ,  the m-curves tend to approach the m-curve f o r  i n d i c a t i n g t h a t g r a i n s i z e has minor s i g n i f i c a n c e  (1967), H o l t (1968)), as i s the case f o r normal c r e e p .  (Alden  (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 v e r y 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 t e c h n i q u e s used to 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 t a g e I I . relationship:  Technique (1) l e a d s to a  o.= K L ^ , where b ranges from about 1 to 3 (Zehr and 5  Backofen (1968), H o l t and Backofen (1966), H o l t (1968)). (2) - (4) l e a d to a r e l a t i o n s h i p : s e n s i t i v e l y on the t e c h n i q u e . determined a ^ 9 by t e c h n i q u e (3) (a c o n s t a n t ) ,  evaluate  i = KL  where a depends  rather  For example, A l d e n and S c h a d l e r (1968) (2) (— c o n s t a n t ) ,  f o r the same s e t of m - c u r v e s .  been r e p o r t e d f o r t e c h n i q u e  Techniques  and a ^ 4.5 by  technique  V a l u e s of a ^ 2 have  (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 B a c k o f e n (1966), Avery and B a c k o f e n (1965)).  7.  LOG STRAIN FIGURE 2.2."  RATE  Grain size effect i n superplastic  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 e f f e c t , one t h i n g i s c e r t a i n :  stage II  alloys.  i n d e f i n i n g the g r a i n s i z e  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 rates with increasing grain s i z e .  G i f k i n s (1967)  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  observed  l e a d (200-500y) a t v e r y  low s t r a i n r a t e s , w h i c h may have been a r e f l e c t i o n of s t a g e I I L i t t l e information exists be s a i d t h a t w i t h r e s p e c t to s t a g e I I , (Lee ( 1 9 6 9 ) , H o l t  concerning stage I ,  behaviour.  a l t h o u g h i t may  b i s lowered w h i l e a i s  raised  (1968)).  1  2 . 2 . 6 . E v i d e n c e f o r g r a i n boundary s l i d i n g D i r e c t e v i d e n c e f o r g r a i n boundary s l i d i n g l i e s i n the  surface  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 m o t i o n ( A l d e n ( 1 9 6 7 ) , A l d e n and S c h a d l e r ( 1 9 6 9 ) , Lee ( 1 9 6 9 ) , C l i n e and A l d e n ( 1 9 6 7 ) ) . 1  £  GB  E  TOT  Lee ( 1 9 6 9 )  1  calculated  to be as much as 93% i n s t a g e I I by measuring o f f s e t s on an imposed  surface g r i d .  The o f f s e t marker t e c h n i q u e f o r measuring t h e 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 r e e p , a l t h o u g h i t i s b e l a b o u r e d 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 factors  such as boundary m i g r a t i o n ( B e l l e t a l ( 1 9 6 7 ) ) .  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 w h i c h no n e t 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  s i d e ( G i f k i n s and Langdon ( 1 9 7 0 ) ) .  M o r e o v e r , Langdon and G i f k i n s (1970)  have p o i n t e d out m a t h e m a t i c a l e r r o r s i n L e e ' s  analysis.  concluded t h a t no a c c u r a t e e v a l u a t i o n of q u a l i t a t i v e l y i t appears  t h a t z„^/z^  nm  bo  2 . 2 . 7 . E f f e c t o f second  1U1  is  exists,  Thus i t may be although  large.  1U1  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 . popular a l l o y s .  Eutectics  and e u t e c t o i d s  are  P r o v i d e d t h a t t h e 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,  interpretation  can be obscured i f t h e second phase o c c u p i e s a c o n s i d e r a b l e volume f r a c t i o n . A h a r d second phase  (e.g. oxide, i n t e r m e t a l l i c , r e l a t i v e l y high melting  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 ( R i s e b r o u g h and Lund ( 1 9 6 8 ) , Donaldson ( 1 9 6 8 ) , 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 stage 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  a p p r o x i m a t e l y 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 ( 1 9 6 7 ) , Zehr and B a c k o f e n ( 1 9 6 8 ) , Hayden and Brophy In coarse-grained  (1968)).  creep t h e r e may be a tendency to r e t a i n an equiaxed  9. structure, et a l  a l t h o u g h not to the e x t e n t observed i n s u p e r p l a s t i c i t y  (1967)). Another s t r i k i n g f e a t u r e  of s t a g e I I  i n d u c e d g r a i n - g r o w t h and second phase c o a r s e n i n g . form ^— « e may be a p p r o x i m a t e l y c o r r e c t  Superplastic  2.3.1.  deformation i s  A r e l a t i o n s h i p of  the >  (1968)).  mechanisms  General S e v e r a l mechanisms have been proposed as i m p o r t a n t  processes.  superplastic  Developed p r i m a r i l y to account f o r s t a g e I I b e h a v i o u r ,  mechanisms attempt  the  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 rate,  strain-  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 ( 1 9 6 8 ) , A l d e n and S c h a d l e r  2.3.  (Bell  a  reasonable  creep  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  (< A H g ) .  2.3.2. D i f f u s i o n a l processes. 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 p r o c e s s e s 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 regions.  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  b u l k d i f f u s i o n o c c u r s between t r a n s v e r s e b o u n d a r i e s under t e n s i o n and l o n g i t u d i n a l b o u n d a r i e s under c o m p r e s s i o n , and p r e d i c t s :  that  10.  . a.v.Dg.a ' " H  N  =  "l?^T~  '  a - 10 (geometric constant),  where  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 ( 1 9 6 7 ) ) , 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  ^  L .KT 3  '  ( 2  '  4 )  8 - 150 (geometric constant),  where  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  creep,  (e.g.  a l t h o u g h o f t e n c o n s i d e r a b l y s l o w e r than observed r a t e s  G i f k i n s (1967)).  Zehr and Backofen (1968) contend t h a t Coble creep  may r e a s o n a b l y account f o r s u p e r p l a s t i c b e h a v i o u r i n s e v e r a l  alloys.  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 a t t r i p l e l i n e s . Gifkins  (1967) suggest t h a t  2 . 3 . 3 . G r a i n boundary  Calculations  t h i s may be a r a t e - c o n t r o l l i n g  by  step.  sliding  A l t h o u g h g r a i n - b o u n d a r y s l i d i n g appears  to be a d i s t i n c t i v e  superplastic process,  i t s p r e c i s e r61e i s u n c e r t a i n .  accommodation p r o c e s s  f o r d i f f u s i o n a l p r o c e s s e s (Gibbs  a c t as a p r i m a r y s t r a i n - p r o d u c i n g p r o c e s s ,  I t may a c t as an ( 1 9 6 5 ) ) , o r i t may  r e q u i r i n g accommodation by  o t h e r p r o c e s s e s to m a i n t a i n c o m p a t i b i l i t y . To d e c i d e 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 r e q u i r e s an u n d e r s t a n d i n g of the n a t u r e of b o u n d a r i e s . smooth and f l a t ,  I f b o u n d a r i e s were  then boundary v i s c o s i t y would p r o b a b l y be l o w , and  s l i d i n g would be easy ( i n which c a s e , o t h e r p r o c e s s e s would B o u n d a r i e s , however, a r e not smooth. " l e d g e s " of l e n g t h <v 100S e x i s t Gifkins  process  control).  F i e l d i o n m i c r o s c o p y has shown t h a t  i n tungsten  (Ryan and S u i t e r  (1964)).  (1968) proposed t h a t 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  ledges.  occurring i n  (The d r i v i n g f o r c e would then be analogous  H - N o r Coble c r e e p . )  to t h a t  A s i m i l a r m o d e l , developed by A l d e n  2 (1969)  , g i v e s t h e 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 t h e b o u n d a r i e s 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 A l d e n conclude t h a t creep r a t e s r e s u l t i n g from t h e i r models c o u l d 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  G r a i n boundary s l i d i n g , a c c o m p l i s h e d by the d i r e c t  process. absorption  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 ( 1 9 6 7 ) ) .  Edge components would  c l i m b i n the v i c i n i t y of the b o u n d a r i e s 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  t h a t c o n t i n u o u s g r a i n boundary m i g r a t i o n  o r r e c r y s t a l l i z a t i o n o c c u r s i n the v i c i n i t y of s l i d i n g b o u n d a r i e s where p l a s t i c s t r a i n energy may accumulate al  ( 1 9 6 8 ) , Packer and Sherby  models have been p r e s e n t e d .  (1967)).  (Cook ( 1 9 6 8 ) , H o l t ( 1 9 6 8 ) , P a c k e r  et  However, no d e t a i l e d o r p r e d i c t i v e  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  superplasticity.  The e v i d e n c e suggests t h a t r e c r y s t a l l i z a t i o n does not o c c u r  ( G i f k i n s (1967),  Alden  (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 .  "jogged-screw",  " c l i m b " , and " n e t w o r k " ) are i m p l i c i t l y assumed to a p p l y i n s t a g e I I I superplastic literature.  i n the  A d a p t a t i o n s of t h e s e m o d e l s , p a r t i c u l a r l y the  c l i m b models of Weertman (1955, 1957), have been made to account  for  s t a g e I I b e h a v i o u r (Hayden and Brophy ( 1 9 6 8 ) , B a l l and H u t c h i s o n ( 1 9 6 9 ) ) . 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 i m b 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)  obstacle.  adapted models p u r p o r 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 and the decreased  The effect,  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 o r d e r 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 s t a g e I  Alden  (1969)  2  •13. proposed  a r a t e - c o n t r o l l i n g model i n v o l v i n g t h e " v i s c o u s  g l i d e " o f d i s l o c a t i o n s w i t h i n the b u l k . Newtonian v i s c o s i t y ,  While behaving  i n d i v i d u a l l y with  t h e i r d e n s i t y would i n c r e a s e w i t h s t r e s s a c c o r d i n g  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 c r e e p .  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  2.3.6. Combined  As a r e s u l t ,  low (^ .33).  processes  I t has become f a s h i o n a b l e to d e s c r i b e the t h r e e - s t a g e m-curve i n terms o f c o n c u r r e n t  (independent)  and c o n s e c u t i v e ( d e p e n d e n t )  processes.  2 Hart  (1967)  developed  a mechanical  models, to show how a combination  (1969) .  w i t h no r e f e r e n c e to atomic  o f Newtonian and non-Newtonian p r o c e s s e s  could produce t h r e e stage b e h a v i o u r . 2 model o f Alden's  analogue,  F i g u r e 2.3. i l l u s t r a t e s a r e c e n t  P r o c e s s e s "1" and "2" a r e c o n s e c u t i v e .  Whichever r e q u i r e s the h i g h e r s t r e s s a t any s t r a i n r a t e c o n t r o l s . "3" i s independent  Process  o f "1" or "2" and i s i d e n t i f i e d w i t h normal c r e e p .  The  s t r a i n r a t e f o r "3" i s added t o the a p p r o p r i a t e s t r a i n r a t e f o r "1" o r "2" a t any g i v e n s t r e s s  level.  LOG FIGURE 2.3.  STRAIN  RATE  D e s c r i p t i o n o f m-curve i n terms o f combined p r o c e s s e s , assuming models proposed by A l d e n ( 1 9 6 9 ) a r e r e l e v a n t . 2  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 t h a t p r o c e s s e s " 1 " and " 2 " r e l a t e to non-Newtonian v i s c o u s g r a i n - b o u n d a r y s l i d i n g and C o b l e c r e e p ,  respectively.  The low  apparent m - v a l u e f o r s l i d i n g i n s t a g e 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  sliding.  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 superplastic literature and S t u a r t  2.4.  (Backofen et a l ( 1 9 6 8 ) , C h a u d h a r i ( 1 9 6 7 ) , A v e r y  ( 1 9 6 7 ) ) , and w i l l be d e a l t w i t h f u l l y i n Chapter  Objectives  of p r e s e n t  4.7..  investigation  The b a s i c o b j e c t i v e s a r e information i s non-existent,  to i n v e s t i g a t e areas f o r w h i c h  s p a r s e o r i n c o n c l u s i v e , to e s t a b l i s h  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 findings.  S p e c i f i c a l l y , the e x p e r i m e n t a l o b j e c t i v e s (i)  (ii) (iii)  and h e r e t o f o r e  undocumented  To i n v e s t i g a t e  creep b e h a v i o u r i n s t a g e s I ,  I, (iv)  I I and  (vi)  appropriate  systems.  apparent a c t i v a t i o n e n e r g i e s  II, for  and  III.  stages.  III.  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  (v)  present  are:  To p r o v i d e b a s i c m-curve documentation f o r  To determine  or  To i n v e s t i g a t e  strain. the p o s s i b i l i t y of a  backstress.  To observe s u r f a c e d e f o r m a t i o n markings i n a t 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 .  15.  3 . EXPERIMENTAL  3.1.  Materials  choice  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 i n c - a l u m i n u m system (Zn-1 wt.% A l ) were i n v e s t i g a t e d .  Hereafter,  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 ,  by a g r a i n s i z e n o t a t i o n ( e . g .  the a l l o y s w i l l u s u a l l y be followed  Pb-5y).  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 P b - 5 wt.% Cd a l l o y ( A l d e n ( 1 9 6 8 ) ) . cadmium-rich end has never been i n v e s t i g a t e d f o r i t s properties;  nor, for that matter,  (making the homologous  m e a n i n g f u l ) , and r o u g h l y e q u i v a l e n t hardnesses d i f f i c u l t i e s mentioned i n Chapter 2 . 2 . 7 . ) .  b e h a v i o u r of i t s i n d i v i d u a l p h a s e s ,  Lead and  temperature  (thus a v o i d i n g the  By c h o o s i n g t h r e e a l l o y s i n  the same s y s t e m , the b e h a v i o u r of the e u t e c t i c  single  superplastic  has any cadmium-based a l l o y .  cadmium have s i m i l a r m e l t i n g p o i n t s  are e s s e n t i a l l y  The  can be compared w i t h  the  as Pb-6 v o l . % Cd and C d - 6 . 5 v o l . % Pb  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  (Figure 3 . 1 . ) .  temperature,  Thus the a n a l y s i s of m-curves as a f u n c t i o n o f  and the d e t e r m i n a t i o n of A H , a r e not c o m p l i c a t e d by p u r i t y and a temperature-dependent  structure.  M o r e o v e r , cadmium l e n d s i t s e l f w e l l  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 r e a s o n f o r i n v e s t i g a t i n g the z i n c - a l u m i n u m a l l o y  was i t s p r e v i o u s l y demonstrated s t a g e I b e h a v i o u r (Turner  (1970)).  (Stage I i s not g e n e r a l l y easy to a c h i e v e a t moderate s t r a i n r a t e s and  to  C  Atomic 10 20  350  30  40  Percentage 50  Cadmium  60  70  80  90 600  P  300  -  250  ZOO  Pb  10  20  30  Weight  °C 700  40  60  Percentage  Atomic  660°  50  70  20 i  90  Cd  30 1  Zinc 40  "F  50 i  60 i  70 80 90 1 1 1  L  1200  600  - 1000  (X + L  500  400  Cadmium  Percentage  10 1  80  500  4/9.5? -  a  800  400 300  31.6  a + a'  275°  a'  /62.S  95 600 993  78  400  200  -  100 Al  10  20  30  Weight  FIGURE 3 . 1 .  40  50  60  Percentage  Phase diagrams  70  80  90  Zn  Zinc  (Metals Handbook (1948))  a.  Lead-cadmium s y s t e m .  b.  Aluminum-zinc system.  17. temperatures.)  M o r e o v e r , 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  for  comparison w i t h the lead-cadmium a l l o y s .  3.2.  Procedure  3.2.1. Alloy preparation The lead-cadmium a l l o y s (99.999% P b , 99.999% Cd) were m e l t e d 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 crucible.  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 o c c u r r e d w i t h i n s e c o n d s . to c l o s e t o l e r a n c e either  for a ,9"-diameter  e x t r u s i o n b l o c k , and e x t r u d e d to  .083"-diameter rod or .15"-diameter  intended a p p l i c a t i o n .  The i n g o t s were machined  r o d , depending on the  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 , that 60°C.  the m e l t i n g temperature was 700°C and the e x t r u s i o n I n a l l c a s e s , the a l l o y s were h o t - e x t r u d e d and the  except  temperature resultant  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. Stabilized test Table 3 . 1 .  structures indicates  the heat t r e a t m e n t s g i v e n to  e x t r u d e d a l l o y s i n o r d e r to produce s t a b l e s t r u c t u r e s Figures 3.2.  - 3.7.  i l l u s t r a t e the r e s u l t a n t  Nominal g r a i n s i z e s  for  the  testing.  structures.  (± ^ .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 m i c r o g r a p h s (total intercepts  >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  effect  per se was c a r r i e d o u t , g r e a t 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 .  Composition  Cd-6 v o l . % P b  P o s t - e x t r u s i o n specimen t r e a t m e n t s  Heat Treatment  5 m i n . @ 180°C  Polish  Etch  (chemical)  (chemical)  40 gm. Na^SOit 400 gm. C r 0 1000 c c . H 0  30% H C l in H 0  3  2 days @ 220°C  2  :  2  2  Nominal G r a i n S i z e  3y("Cd-3y") 8y("Cd-8y")  (chemical) Pb-28 v o l . % Cd  5 m i n . @ 180°C 4 hr.  25% H 0 2  @ 220°C  75% G l a c i a l  3y("eutectic-3y")  2  acetic  #]u("eutectic-8y") . . . .  P b - 6 v o l . % Cd  3 hr.  @' 95°C  5y("Pb-5y") (electrolytic)  Zn-1 wt.% A l  2 days @ 23°C  800 50 60 20  ml. ml. ml. ml.  Ethyl alcohol Butylcellusolve Sodium t h i o c y a n a t e Distilled H 0 2  ly("Zn-ly")  FIGURE 3 . 3 .  Cd-8u.  P o l i s h e d and e t c h e d .  x2100.  20.  FIGURE 3 . 5 .  Eutectic-8y.  P o l i s h e d . x2600.  FIGURE 3 . 6 .  Pb-5p.  P o l i s h e d and deformed.  x2600.  22. not  attempted. The d i f f e r e n c e between the e u t e c t i c - 3 u  appeared to be m a i n l y one of s c a l e . accurate,  and  eutectic-8y  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  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  presence of i n t e r p h a s e b o u n d a r i e s .  the  I n t e r p h a s e b o u n d a r i e s 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 b o u n d a r i e s 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 a p p r o x i m a t e l y the same s i z e as the m a t r i x g r a i n s . O t h e r w i s e they were i g n o r e d i n g r a i n s i z e  calculations.  Cd-3y and Cd-8u d i f f e r e d more than i n s c a l e . 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 a c o n s i d e r a b l e s p r e a d of g r a i n s i z e s ,  W h i l e Cd-8u  structure,  Cd-3p had  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 T a b l e 3.1. were from .083" e x t r u d e d 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 , 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" e x t r u d e d 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 . Cd-3y* and Cd-8y*, were s u b j e c t e d and Cd-8y, r e s p e c t i v e l y ,  creep  These a l l o y s ,  to the same heat t r e a t m e n t s as Cd-3y  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 c r o s s 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  properties.  Specimens  c o u l d a f f e c t the observed m e c h a n i c a l  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. 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 , pre-test fibre texture.  suggesting  The  resultant  negligible  ( S i m i l a r a n a l y s i s showed t h a t t e x t u r e  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 d e f o r m a t i o n  either.)  d i d not  3 . 2 . 3 . P r e p a r a t i o n of specimens  for  Reduced gauge s e c t i o n s  23.  testing f o r t e n s i l e and creep specimens  achieved w i t h a chemical p o l i s h technique.  The g r i p ends were  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 to a s s u r e 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  3.1.)  (from  .15"  rod) were c o l d - m a c h i n e d i n a m i c r o l a t h e , and s u b s e q u e n t l y reduced by ^ .002"  by the c h e m i c a l t e c h n i q u e to remove s u r f a c e d i s t o r t i o n .  detectable mechanical 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  No specimens  p r e p a r e d i n e i t h e r way.  3.2.4. Testing  apparatus  T e n s i l e t e s t s were performed on a s t a n d a r d f l o o r model Instron.  Screw-tightened  Figure 3.8. constant  were u s e d .  stress device.  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  Creep t e s t s were performed on an " A n d r a d 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 the specimen to p e r m i t b a t h i m m e r s i o n .  A u t o m a t i c temperature  from  control  of ± .5°C was a c h i e v e d f o r mazola o i l and w a t e r 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 o r ^ .05% s t r a i n , depending on the extensometer u s e d .  3 . 2 . 5 . Metallography S u r f a c e 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 m i c r o s c o p y (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 b e i n g c e l l u l o s e a c e t a t e and the second chromium-shadowed carbon.  24.  COUNTERBALANCES  TO HEATHKIT RECORDER TAPE(S.S.)  THREADED CLAMP GRIPS (AL)  FIGURE 3.8.  Schematic diagram o f c o n s t a n t s t r e s s  creep a p p a r a t u s .  25. 4. RESULTS AND DISCUSSION  4.1. Strain rate sensitivity  4.4.1.  General 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  investigated. stages I ,  alloys  Only two s t a g e s a r e e v i d e n t f o r each a l l o y , a l t h o u g h  I I and I I I  a r e each r e p r e s e n t e d  i n at 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 ( e x c e p t f o r P b - 5 p ) , 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  The m-curves were o b t a i n e d by the s t r a i n r a t e t e c h n i q u e on a I n s t r o n  (Chapter 2 . 1 . ) .  -4  flow stress readings.  change  A f t e r approaching s t e a d y - s t a t e  at a low s t r a i n r a t e (e < 2%, i ^ 5 x 10 m-curve) were s t r a i n e d i n 1% i n c r e m e n t s  thesis.  e  min  (—— e n  -1 ),  specimens  (one  = 2 or 2.5) to  Each f a m i l y of m-curves corresponds  per  attain  to one b a t c h  of specimens p r e p a r e d a c c o r d i n g to T a b l e 3 . 1 . 4.2.1. Reproducibility The shape r e p r o d u c i b i l i t y of the m-curves was  excellent,  a l t h o u g h 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 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  cross-section  or g r a i n s i z e .  to  length,  I n any c a s e , a 10% s h i f t i s n e g l i g i b l e on  a log-log plot. 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 treatment,  making i t n e c e s s a r y to d e r i v e any g i v e n f a m i l y of  m-curves from a b a t c h of i d e n t i c a l l y t r e a t e d s p e c i m e n s .  Figure 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 h e a t t r e a t m e n t s changed the  shape  FIGURE 4 . 1 .  M-curves  for  Cd-3y  STRESS (PSI)  FLOW  o  1  I I ! Mill  I  *8Z.  I « "i| 1  i i l I il ii]  IM I a  1  STRAIN  FIGURE 4.4.  RATE  s—s  II |  (MIN" ) 1  M-curves f o r e u t e c t i c - 3 u .  II  nn[  r  FIGURE 4.5.  M-curves f o r e u t e c t i c - 8 p .  o  FIGURE 4 . 6 .  M-curves f o r Z n - l u .  FIGURE 4 . 8 . M - c u r v e d e t e r m i n a t i o n by two t e c h n i q u e s  ( s t a g e s I and  II).  33.  GO  O  o o  AB  NO GRAIN  -  AB  —  GRAIN  GROWTH.  GROWTH.  LOG STRAIN RATE FIGURE 4 . 9 .  E f f e c t o f 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  12  I i—I—I—i—i—i—i—i—i—i—i—r -  "I •'>  I  I  2  FIGURE 4 . 1 0 .  I  I  4  I  I  6  I  I  8 •  I  I  10  I  I  12  STRAIN (%)  T y p i c a l f l o w curves  f o r stage I I I .  alloy  of an m-curve w i t h o u t c a u s i n g any s i g n i f i c a n t s h i f t . was r e p r o d u c i b l e f o r s e v e r a l specimens  This behaviour  and t e m p e r a t u r e s .  Batches I and  II  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 .  II  (Figure 4.1.)  Batch  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  -20°C u n t i l t e s t e d  t h r e e months l a t e r .  except t h a t the a n n e a l i n g treatment  at  Batch I was s i m i l a r l y t r e a t e d  o c c u r r e d one day b e f o r e t e s t i n g ,  specimens b e i n g k e p t a t - 2 0 ° C u n t i l t h a t  the  time.  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 t a g e s I and I I A u n i q u e 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 t e m p e r a t u r e , s u b j e c t to two (i) (ii)  independent of s t r a i n h i s t o r y ,  restrictions: A l l p r i o r s t r a i n must have o c c u r r e d i n s t a g e s I and  II.  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 n e c k i n g and g r a i n g r o w t h . 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 this c r i t e r i o n for a l l alloys.  As s t e a d y - s t a t e was e s s e n t i a l l y increment i n the I n s t r o n t e s t s ,  reached a t each 1% s t r a i n  the m-curves r e f l e c t  a "mechanical  e q u a t i o n of s t a t e " of the f o r m :  s.s. " s.s.> '  CT  f(g  One p r e d i c t i o n of e q u a t i o n (4.1)  <-> •  T)  4  x  i s t h a t m-curves may be o b t a i n e d 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 r e c o r d e d a f t e r 1% s t r a i n .  Figure 4.8.  demonstrates  the  general  are  35. a p p l i c a b i l i t y of the It  i s i m p o r t a n t to e s t a b l i s h whether a m e c h a n i c a l  of s t a t e e x i s t s . state exists, and S c h a d l e r  equation.  It  i s u s u a l l y assumed i n the l i t e r a t u r e  equation  t h a t such a  a l t h o u g h e x p l i c i t statement of the f a c t i s r a r e (1968)).  If  such a s t a t e does not e x i s t ,  depend s t r o n g l y on the t e s t used to d e f i n e  (Alden  an m-curve may  it.  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 . t h a t the accumulated s t r a i n to p o i n t s B o r B '  Assume  (Figure 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 t e c h n i q u e 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 and t h a t :  —  _ 3  a e,e a L  .  Both of t h e s e r e l a t i o n s h i p s a r e  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 - c u r v e , 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 g r o w t h , A B . 35% lower than does B .  P o i n t B ' occurs at a s t r a i n r a t e  In this 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 4 . 1 . 4 . Stage  analysis.  III 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  (and i n the I I - I I I  t r a n s i t i o n zone, whose e x t e n t was h a r d to  i n stage  III  establish).  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  C d - 8 y , 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 ,  occurred  (see F i g u r e 4 . 1 0 . ) .  y i e l d points  Coupled w i t h these o b s c u r i n g f a c t o r s was  propensity for rapid necking.  Documenting s t a g e I I I  by the  the  incremental  I n s t r o n t e c h n i q u e s e r v e d m a i n l y to d i f f e r e n t i a t e between s t a g e s I I and as m was d e f i n i t e l y lower i n s t a g e I I I .  III,  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 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 a n d , i f p o s s i b l e ,  instantaneous  to  36. stress-change  tests.  No such i n v e s t i g a t i o n has been a t t e m p t e d 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 stage I I  O  f o r C d - 8 u , Cd-3u and e u t e c t i c ~ 3 u  (Figure 4.11.)  O  0 - C D „ 3 u (2000 PSI). A - CD-8p (1000 PSI). Q-EUTECTIC -3u  ^  (looc psi)  o  260  300  340  J 380  I L  TEMPERATURE (°C) FIGURE 4 . 1 1 .  420  Dependence of m on temperature ( s t a g e  II)  S i m i l a r b e h a v i o u r has been r e p o r t e d f o r o t h e r a l l o y s ( H o l t and B a c k o f e n ( 1 9 6 6 ) , Lee and Backofen ( 1 9 6 7 ) , Lee ( 1 9 6 9 ) * ) .  Strain rate s e n s i t i v i t y  has a l s o been observed t o i n c r e a s e w i t h temperature under normal creep conditions  ( 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 , p e r h a p s , b e h a v i o u r w h i c h depends on the volume f r a c t i o n of each p h a s e . 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 . i s more s u p e r p l a s t i c than another homologous t e m p e r a t u r e ,  if,  An unambiguous d e f i n i t i o n Qualitatively, a material  f o r e q u i v a l e n t g r a i n s i z e and  s t a g e I I o c c u r s a t a f a s t e r s t r a i n r a t e and m max.  is  larger. For any g i v e n t e m p e r a t u r e ,  h i g h e r s t r e s s than i n C d - 8 p .  stage I I  i n Cd-3u p e r s i s t e d to a  From m-curves i n the l i t e r a t u r e  ( 1 9 6 7 ) , Lee (1969)^) t h i s appears to be a g e n e r a l  (e.g.  Alden  yet undiscussed  occurrence. I n the a l l o y s where s t a g e I was w e l l - d e f i n e d ( C d - 3 u , Z n - l u ) , m appeared to d e c r e a s e 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 , v a l u e s l e s s than .2 ( Z n - l y ) . by Lee ( 1 9 6 9 ) .  V a l u e s l e s s than .16 have been r e p o r t e d  A s t a g e 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 h e r e or 4.2.  reaching  elsewhere.  G r a i n growth  4.2.1.  General A l t h o u g h g r a i n growth d i d n o t 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 d e f o r m a t i o n which w a r r a n t s i n v e s t i g a t i o n .  of  Specimens of C d - 3 u * and  e u t e c t i c - 3 u were e l o n g a t e d 120% ( s t a g e I I a t the s t a r t ) stress-elongation  curves.  superplastic  F i g u r e s 4.15.. and 4 . 1 3 .  to o b t a i n t r u e  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 (constant  cross-head speed),  tests  the f l o w c u r v e s 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 t a k e n had s t r a i n r a t e and m remained from the s t a r t .  The n o r m a l i z e d f l o w curves were o b t a i n e d by r a i s i n g  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  4.2.2.  7 elon a t i (1 + — j-g^  m  ) .  Cd-3u* That m remained c o n s t a n t  at  .51  throughout the t e s t showed  t h a t d e f o r m a t i o n was s t i l l o c c u r r i n g i n s t a g e I I and  constant  that  a f t e r 120%  the n o r m a l i z e d f l o w curve was q u i t e v a l i d .  elongation,  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 s t a g e I I p o r t i o n s of F i g u r e s 4 . 1 . strain rate,  and 4 . 2 .  by s l i d i n g  i n t o coincidence at  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 .  the  constant Although  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 a r e not known p r e c i s e l y (Chapter 3 . 2 . 2 . ) , reported values  the exponent  1.8  (Chapter 2 . 2 . 5 . ) .  i s i n reasonable  agreement w i t h  G i v e n t h i s r e l a t i o n s h i p , any g r a i n  growth s h o u l d be s e n s i t i v e l y r e f l e c t e d  i n the n o r m a l i z e d f l o w c u r v e .  the n o r m a l i z e d 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 s concluded t h a t g r a i n growth was n e g l i g i b l e over t h i s range of  As it  strain.  S l i g h t n e c k i n g (^ 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 . consequence, indicates.  The s t r e s s i n the necked r e g i o n w o u l d , as a  have been about 10% h i g h e r than t h e t r u e f l o w curve 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  least i n part  from the enhanced l o c a l i z e d s t r a i n r a t e ,  at  and not from  g r a i n growth. 4.2.3. ' Eutectic-3y 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 a t the end i n d i c a t e d a t r a n s i t i o n to s t a g e I I I  d u r i n g the  test.  I  I 1 0  I  I 20  1 1 1 30  FIGURE .4.12.  I 40  1 1 50  I  1 60  ELONGATION  1  I  (%)  70  I  I 80  I  I  I  90  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  (Instron  test).  I 100  I  I 110  I  I 120  I  2.4  NORMALIZED FLOW CURVE (M=.4) 2.2  2.0  NORMALIZED FLOW CURVE (M=.28)  b X I . 8  to a.  to to 1  TRUE FLOW CURVE  6  UJ or i -  tni.4  1.2  1.0  i  I  10  I  i  20  I  i  30  i  i  I  40  i  50  i  i  60  ELONGATION FIGURE 4 . 1 3 .  J  I  70  I  I  80  L_J  90  L_J  100  1111 110  120  (%)  S t r u c t u r a l i n s t a b i l i t y o f 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  (Instron t e s t ) . o  41. The s t r e s s i n the necked r e g i o n s  (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 i g h e r than the n o r m a l i z e d f l o w s t r e s s a t the end of the t e s t .  The h i g h s t r e s s i n necked r e g i o n s c o u l d r e s u l t p a r t i a l l y from  localized strain-rate  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.  Zn-lu T u r n e r (1970) has shown t h a t g r a i n growth o c c u r s r e a d i l y as  a consequence of s t r a i n f o r s t a g e s I and  II.  4 . 2 . 5 . Conclusions (i)  G r a i n growth can i n some i n s t a n c e s  (eutectic-3u  Z n - l u ) o c c u r r e a d i l y as a consequence of s t r a i n i n s t a g e I I , 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 (ii)  (Chapter  G r a i n growth does not n e c e s s a r i l y  of s t r a i n ( C d - 3 u * ) .  fundamental m o d e l .  an  2.2.5.). occur as a consequence  I n o t h e r w o r d s , g r a i n growth i s not an  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  essential  and need not be c o n s i d e r e d i n any  Although i n f e r e n t i a l j t h e  t e c h n i q u e 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 a c c u r a t e than the o b v i o u s alternative - direct microscopic  analysis.  4.2.6. Discussion 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 t a g e I I promote g r a i n growth as a f u n c t i o n of s t r a i n .  tend to  A t low g r a i n s i z e s ,  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 u n i t volume a j-). 4.4.4.3.).  M o r e o v e r , s l i d i n g g r a i n s tend to m i g r a t e  the per  (Chapter  However, the degree to w h i c h growth i s r e s i s t e d may  depend on a number of (i)  factors:  Pre-test stabilization  treatment.  From the p o i n t of v i e w of m e c h a n i c a l p r o p e r t i e s ,  a l l alloys  tested  ( w i t h 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 p r e s e n c e of s t r a i n than i n i t s absence. (ii)  N a t u r e and d i s t r i b u t i o n o f second  phase.  A l t h o u g h the second phase i n h i b i t s g r a i n g r o w t h , the degree to w h i c h i t does so may depend on such t h i n g s 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 e n e r g i e s (iii)  of phase and c r y s t a l l i n e  P r o p o r t i o n of second  boundaries.  phase.  I t has been shown t h a t an i n c r e a s e d volume f r a c t i o n of second phase 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 ( 1 9 6 7 ) ) .  observation i s consistent  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  can  This boundaries  to m i g r a t e .  4 . 2 . 7 . G r a i n growth model A model w h i c h may p a r t i a l l y e x p l a i n c o a r s e n i n g 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 . , particles  experience  Boundary  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  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 b o u n d a r y .  The  magnitude of the s t r e s s depends i n v e r s e l y on the a r e a f r a c t i o n of boundary o c c u p i e d by the second phase (Gibbs (1965))-.  Particles  shear ( F i g u r e 4 . 1 4 . a . ) , o r r e m a i n s t a t i o n a r y w h i l e the g r a i n s  than  the either  slide  43. ( F i g u r e 4.14,b.). of l o c a l i z e d  I n t h e l a t t e r c a s e , t h e mechanism would be one  diffusion  ( c f H-ty o r C o b l e d i f f u s i o n ) .  second phase accumulates a t t r i p l e  lines.  Second phase c o a r s e n i n g produced by s l i d i n g .  FIGURE 4.14. (a) (b)  The r e s u l t a n t  I n e i t h e r case,  P a r t i c l e shear Short-range d i f f u s i o n at 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 while grains s l i d e .  coarsening  leads  to m a t r i x g r a i n growth through  "Zener" r e l a t i o n s h i p  (Smith  where  L = matrix grain s i z e ,  the  (1949)):  d = second-phase s i z e , V  f  = second-phase volume f r a c t i o n .  A l t h o u g h t h e 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 t o 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 adaption  c o u l d make i t a p p l y to a e u t e c t i c  i n w h i c h the second phase  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  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 .  inevitably  Coarsening r e s u l t s  the tendency of the i n d i v i d u a l phases to agglomerate contact.  particles  from  once they come i n t o  The d r i v i n g f o r c e f o r a g g l o m e r a t i o n 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 t h a t g r a i n s r e m a i n equiaxed a f t e r  superplastic  d e f o r m a t i o n (Chapter 2.2.8.) has i m p o r t a n t t h e o r e t i c a l i m p l i c a t i o n s .  In  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 elongation),  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 o r Coble) p r o c e s s e s would be e l i m i n a t e d as they p r e d i c t grain elongation.  (Some complex p r o c e s s  c o u l d p o s s i b l y be imagined i n c e r t a i n cases ( e . g .  i n v o l v i n g b o t h s l i p and s l i d i n g  w h i c h would m a i n t a i n equiaxed g r a i n s . )  Except  C l i n e and A l d e n ( 1 9 6 7 ) ) , 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 g r o w t h , 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 t h a t g r a i n growth d i d not occur i n s t a g e I I a n a l y s i s was a t t e m p t e d ,  (Chapter 4.2.2.).  although with l i m i t e d success.  Such an  Specimens  were  45. deformed 100% i n t e n s i o n , and the s t r u c t u r e s observed by r e p l i c a microscopy.  electron  To b r i n g out g r a i n b o u n d a r i e s , specimens were s e c t i o n e d  p a r a l l e l to the t e n s i l e a x i s by c o n t r o l l e d p o l i s h a t t a c k , and s u b s e q u e n t l y deformed ^ 5% t o show s l i p tedious  l i n e s and/or s l i d i n g .  T h i s t e c h n i q u e was  and i n some cases ambiguous (due to the i n t r o d u c t i o n of  subboundaries  and c o n f u s i n g m i g r a t i o n marks),  but n e c e s s a r y , as a s u i t a b l e  etch was n o t developed. V i s u a l examination o f micrographs led  (e.g. F i g u r e s 4.15., 16.)  to the f o l l o w i n g o b s e r v a t i o n s :  (i)  The l a r g e number o f t r a n s v e r s e g r a i n  d i s a p p e a r e d w i t h s t r a i n a l o n g w i t h any l e a d  (ii)  (iii) d e f o r m a t i o n near  boundaries  "stringering".  No s i g n i f i c a n t p a r t i c l e c o a r s e n i n g o c c u r r e d .  S i g n i f i c a n t g r a i n e l o n g a t i o n was apparent f o r (^ 25y) the s u r f a c e , a l t h o u g h n o t apparent  for interior  deformation.  Q u a n t i t a t i v e a n a l y s i s suggests may be c o r r e c t , although w i t h l i t t l e An i n t e r c e p t technique (1963-4)) was used approximately  t h a t the t h i r d o b s e r v a t i o n  statistical  confidence (Table 4.1.).  ( s i m i l a r to t h a t developed by H e n s l e r and G i f k i n s  to determine ^ g | ^  ( ^B) r a t i o s . L  h  A square  equal to the g r a i n s i z e , was superimposed  on  grid,  micrographs  such t h a t g r i d l i n e s were both p a r a l l e l and p e r p e n d i c u l a r t o the t e n s i l e axis.  V a l i d / g r a t i o s c o u l d be o b t a i n e d f o r i n d i v i d u a l L  however the f o l l o w i n g f a c t o r s made g e n e r a l i z a t i o n  (i)  micrographs;  difficult:  G r a i n s i z e was q u i t e v a r i a b l e from r e p l i c a t o r e p l i c a  4 6 .  47.  TABLE 4 . 1 .  Grain elongation i n CD-3u*. (m = . 5 , 25°C. e ^ .001 m i n " . ) 1  L/W  Average G r a i n S i z e (>100  1.14  3.4  1.42  3.7  1.10  3.22  1.43  4.96  1.76  Undeformed  5.0  1.57  Deformed  4.8  1.37  5.0  1.5  5.4  1.59  SURFACE Deformed  t  (>100  3 . 4 JU  Undeformed  INTERIOR  intercepts)  intercepts)  (1.22)  (1.59)  (1.57)  (1.49)  The t e n s i l e a x i s was d e t e r m i n e d by r o t a t i n g the g r i d on the m i c r o g r a p h s 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 c a s e s , the t e n s i l e a x i s was o b v i o u s 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 . 1 5 a 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 t h e i n t e r i o r than a t t h e s u r f a c e .  I t i s quite possible  that  /w depends on b o t h 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  L  a v o i d t h e problem of v a r i a b l e g r a i n s i z e , an attempt was made t o p e r f o r m the same a n a l y s i s on C d - 8 u * ( 1 0 0 ° C , m  . 5 , i.  ^ .001 m i n * ) . -  However a t 100°C, t h e 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 metallography impossible. (ii)  C o n s i d e r a b l e ^ s c a t t e r o c c u r r e d f o r r e p l i c a s where t h e  average g r a i n s i z e was c o n s t a n t . the g r a i n s i z e d i s t r i b u t i o n ) .  ( T h i s may have been due , i n p a r t ,  to  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 meaningful 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. Discussion I t i s i m p o r t a n t to e s t a b l i s h whether s u r f a c e reflect  i n t e r n a l behaviour.  observations  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 1UI  \jD  Lee (1969)* assumed s o .  The p r e s e n t r e s u l t s  for grain elongation at  the s u r f a c e and i n the i n t e r i o r s u g g e s t t h a t the assumption may n o t be valid.  There i s f a i r e v i d e n c e t h a t 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 a r e v a l i d f o r t h e 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 ( 1 9 6 5 ) , Graeme-Barber  (1967)),  although  R a c h i n g e r (1952) observed e q u i a x e d i n t e r i o r g r a i n s and e l o n g a t e d g r a i n s i n c r e p t aluminum (as i n t h e p r e s e n t  surface  experiment.)  A n a l y s i s of g r a i n elongation i n Zn-lu  (Turner (1970))  also  shows t h a t g r a i n e l o n g a t i o n o c c u r s 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 a t the s u r f a c e .  M o r e o v e r , g r a i n e l o n g a t i o n may be more pronounced i n  s t a g e I than i n s t a g e 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 u n i f o r m 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 o f 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 b o u n d a r i e s 4.15, 16) c o u l d be a r e s u l t of the (i)  (Figures  following:  R e o r i e n t a t i o n of g r a i n s so t h a t b o u n d a r i e s o c c u r on  p l a n e s of maximum s h e a r . (ii)  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 ,  resulting  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 . (iii)  Grain elongation.  The apparent g r a i n shape c o u l d 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. S u r f a c e  observations  4.4.1. G e n e r a l 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 t h e s e a l l o y s . i m p a r t e d a " p e b b l y " f i n i s h to t h e s u r f a c e , the r e s o l u t i o n of  The c h e m i c a l p o l i s h  w h i c h may have i n t e r f e r e d w i t h  v e r y f i n e s l i p , but w h i c h 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 . s u r f a c e was  i n general  F r e s h l y exposed  e i t h e r smooth or s t r i a t e d , w h i l e t h e o r i g i n a l  p o l i s h e d s u r f a c e 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 i g u r e 4.22.).  C h e m i c a l 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,  a l t h o u g h some p e r t i n e n t o b s e r v a t i o n s of d e f o r m a t i o n f e a t u r e s were made.  51. 4 . 4 . 2 . Modes o f d e f o r m a t i o n B e f o r e a n a l y s i n g d e f o r m a t i o n m a r k i n g s , t h e modes o f d e f o r m a t i o n must be c o n s i d e r e d 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 t h r e e common s l i p systems i n  cadmium and z i n c a r e {0001} <1120>, o f w h i c h o n l y two a r e i n d e p e n d e n t . According to the "Von M i s e s " c r i t e r i o n  (Honeycombe ( 1 9 6 8 ) ) ,  five  independent s t r a i n components a r e r e q u i r e d t o a l l o w any d e s i r e d change of a body.  F o r the g r a i n s o f a p o l y c r y s t a l , f i v e independent s l i p  systems a r e r e q u i r e d i n the absence of n o n - s l i p modes. appreciable  shape  To a t t a i n  (though n o t 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 a p p r o x i m a t e l y  f o u r s l i p modes (Kochs ( 1 9 6 7 ) ) .  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 a r e second o r d e r p y r a m i d a l {1122} <1123>, which i n themselves  s u p p l y f i v e independent modes.  p y r a m i d a l {10Tl} <1120>  (First  order  and p r i s m a t i c {10l0} <1120> a r e o c c a s i o n a l l y  observed.) P r o c e s s e s o t h e r than s l i p may reduce t h e r e q u i r e d number o f 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 c o n t i n u e d s l i p a n d / o r r e t w i n n i n g i n r e o r i e n t e d elements o f volume.  I n cadmium and z i n c , {1012} <1011> t w i n n i n g i s commonly o b s e r v 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 , t h e r e a r e a d d i t i o n a l  d e f o r m a t i o n modes a v a i l a b l e :  g r a i n boundary s h e a r ( w i t h 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 o r C o b l e c r e e p ) ,  and d i s l o c a t i o n c l i m b .  In  f a c t , i t i s l i k e l y t h a 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 t h e need f o r s l i p . I n t h e case of l e a d , normal {111} <110> s a t i s f i e s requirements.  compatibility  As w i t h cadmium and z i n c , however, s l i p i t s e l f may n o t be  52.  r e q u i r e d under s u p e r p l a s t i c  conditions.  4.4.3. S u r f a c e  of s l i p and t w i n n i n g  observations  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 , b a s a l s l i p i n Cd-8u* deformed i n s t a g e I I I .  clearly defined,  T w i n n i n g and n o n - b a s a l  a r e 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 . t w i n n i n g and n o n - b a s a l s l i p a r e common i n c o a r s e - g r a i n e d boundary e f f e c t s a r e  Both  cadmium, where  negligible.  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 s t a g e I I  d e f o r m a t i o n o f Cd-3u* and Cd-8u*.  bands w h i c h do o c c u r ( e . g .  F i g u r e 4.21.) a r e u n d o u b t e d l y the r e s u l t  unusual concurrences are r e s t r i c t e d (stage I I ) ,  slip^  The s l i p  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 ,  t o about 5% of the g r a i n s .  of and  No s l i p was observed i n Pb-5u  a l t h o u g h the r e l a t i v e l y poor s u r f a c e  observation inconclusive.  S i m i l a r observations  l e a d as an i m p o r t a n t phase  (e.g.  p o l i s h rendered for alloys  this  containing  Zehr and B a c k o f e n (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 s t a g e I I may be due t o  several  reasons: (i) reasons suggested (ii) that "ledges"  S l i p i s unimportant i n s u p e r p l a s t i c flow f o r i n the p r e v i o u s  section.  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 .  It  is  possible  or " p r o t r u s i o n s " ( G i f k i n s and Snowden (1966)) a r e  spaced s o u r c e s w h i c h o p e r a t e 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  The  finely 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 A p p e n d i x A . )  53.  FIGURE 4 . 1 8 .  Cd-8u*.  16% E l o n g a t i o n .  III  1  O  (e * 10  Stage  min  , T = 23°C).  x4000.  55.  FIGURE 4 . 1 9 .  Cd-3u*. Ce ^ 10"  15% E l o n g a t i o n . min  Stage I I  , T = 23°C, m % . 5 ) .  A - closely associated s t r i a t i o n s B - s l i d i n g i n v i c i n i t y of l e a d  x8000.  and m i g r a t i o n marks particle  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 .  Cd-3y*.  15% E l o n g a t i o n . O  (I % 10"  1  Stage I I  m i n " , T = 23°C, m ^ . 5 ) .  xl0,000.  58.  FIGURE 4 . 2 2 .  Cd-3u*.  250% E l o n g a t i o n .  1  O  (e ti 10"  min  Stage I I  , T = 23°C, m *  A - p e e l i n g boundary  striations  B - s l i d i n g boundary  striations  C - m i g r a t i o n marks.  .5).  xl5,000.  FIGURE 4 . 2 3 .  Cd-3y*.  35% E l o n g a t i o n .  (e * 5 x I O A -  - 4  Stage  II.  m i n " , T = 23°C, m ^ .5) 1  x 30,000  s t r i a t i o n s at peeled interphase boundary.  60.  FIGURE 4 . 2 5 . Pb-5y.  (Above).  15% E l o n g a t i o n .  (i * 5 x 1 0 " m "V. .35) .  4  Stage  m i n " , T = 23°C,  x4000.  1  62.  FIGURE 4.26.  Pb-5u.  15% E l o n g a t i o n .  Stage I I  ( i * 5 x I f f m i n " , T = 23°C, m <v . 3 5 ) . 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 , fine-ness  f u r t h e r c o n t r i b u t i n g to  the  of observed s l i p . t (iii)  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 b e i n g  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 r e a s o n f o r t h i s b e h a v i o u r can be  visualized. Due to e x p e r i m e n t a 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 s t a g e I .  4.4.4. G r a i n boundary e f f e c t s ( s t a g e I I )  4.4.4.1. S h e a r i n g 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 i s the r e l a t i v e m o t i o n of g r a i n s .  o f f i g u r e s 4.19.-26.  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 a l o n g boundaries.  transverse  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 e x p e r i e n c e  l i t t l e shear o r  tensile  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, b o u n d a r i e s whose t r a c e s a r e t r a n s v e r s e to the t r a c e ,  tend to shear n o r m a l  p r o d u c i n g a maximum amount of f r e s h s u r f a c e .  Boundaries  whose t r a c e s are not t r a n s v e r s e have a shear component a l o n g the which would show up as an o f f s e t but not as f r e s h  on a marker l i n e a c r o s s  trace  the b o u n d a r y ,  surface.  " 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 p r o b a b l y a s u r f a c e e f f e c t which o c c u r s whenever a s i g n i f i c a n t tensile stress exists +  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 s t a g e r e p l i c a technique.  one boundary w i l l p e e l w h i l e the o t h e r w i l l s h e a r , a l t h o u g h each has t r a c e normal to the t e n s i l e conceivable,  axis.  Combined p e e l i n g and shear  a l t h o u g h n o t obvious from the  its  is  micrographs.  SURFACE  SHEAR BOUNDARY  PEEL BOUNDARY  TENSILE AXIS  FIGURE 4 . 2 8 .  S h e a r i n g and p e e l i n g a t the  Peeling could r e s u l t  of t e n s i o n  (B)  path l e n g t h , B-A would be s h o r t  surface.  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 . between r e g i o n s  >.  A vacancy g r a d i e n t might w e l l e x i s t  and the s u r f a c e s i n k ( A ) .  The d i f f u s i o n  compared w i t h t h a t r e q u i r e d f o r N - H or  Coble c r e e p , 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 o b s e r v a b l e p e e l i n g i s h a r d to d e f i n e . 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 m o d e l ,  on the b a s i s t h a t b u l k d i f f u s i o n p r o c e s s e s a r e too slow to be can be e a s i l y  I t may  important,  countered.  P e e l e d b o u n d a r i e s 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  implications.  cadmium (and o t h e r HCP m e t a l s ) . l i m i t e d e x t e n t i n Pb-5p  Perhaps  the phenomenon i s unique  to  However, p e e l i n g i s e v i d e n t to a  ( 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  that  66. the phenomenon i s g e n e r a l , and t h a 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 i m p l y 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 published micrographs.  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 t a k e n i n t o account.  4.4.4.2.  Striations 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 b o u n d a r i e s b o t h have been observed i n p u b l i s h e d micrographs (Chapter 2 . 2 . 3 . ) . b o u n d a r i e s have no p r e c e d e n t , been i d e n t i f i e d .  The s t r i a t i o n s observed a t p e e l e d as p e e l e d b o u n d a r i e s themselves have not  Backofen and o t h e r s  (Chapter 2 . 2 . 3 . ) c l a i m t h a t 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 d e f o r m a t i o n r e f l e c t b u l k d i f f u s i o n a l creep.  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  d i f f u s i o n a l c r e e p , but p r o b a b l y as a s u r f a c e phenomenon. with 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  If  reflect  associated  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 c o n c e r n i n g s u p e r p l a s t i c mechanisms i s w a r r a n t e d on the b a s i s of s u r f a c e  striations.  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 r e a s o n a b l e 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 .  Considering s l i d i n g f i r s t ,  it  f o r both is  c o n c e i v a b l e t h a t 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 migration during 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 m o t i o n i s w e l l - e s t a b l i s h e d . F o r 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  with  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 b o u n d a r i e s 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 a n g l e b o u n d a r i e s , and even then they would be spaced too c l o s e l y 1  resolution.  (^208)  for  I t i s p o s s i b l e t h a t 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 .  In this 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 t h a 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 h a r d boundary p a r t i c l e s or by s u r f a c e o x i d e f i l m s cannot be d i s c o u n t e d , a l t h o u g h t h e r e are s e v e r a l o b j e c t i o n s (i)  to t h i s  argument:  There i s no e v i d e n c e , or r e a s o n to b e l i e v e ,  boundary p a r t i c l e s o r a tough o x i d e s u r f a c e e x i s t s  that  fine  f o r the w i d e range of  68. i n t e r c r y s t a l l i n e and been  i n t e r p h a s e boundaries  i n which s t r i a t i o n s have  observed.  (ii)  The  uniform s p a c i n g of s t r i a t i o n s on some p l a n e s ,  the absence of s t r i a t i o n s on o t h e r s , i s i n d i c a t i v e of  and  crystallographic  origin.  (iii)  I f produced by a b r a s i o n by boundary p a r t i c l e s ,  would have v a r i a b l e l e n g t h s . uniform  However, s t r i a t i o n s are g e n e r a l l y  i n l e n g t h , extending  (iv)  striations  the f u l l  l e n g t h of the exposed  quite  boundaries.  S t r i a t i o n s produced by p a r t i c l e a b r a s i o n suggest  f o r m a t i o n of grooves on one  s i d e of the p a r t i c l e s and  on the other s i d e , an u n l i k e l y  the  the b u i l d u p of m a t t e r  process.  4.4.4.3. M i g r a t i o n marks  concomitant Cline  G r a i n boundary m i g r a t i o n appears to be an  essential  to g r a i n boundary s l i d i n g i n normal creep  (e.g. Walter  (1968)).  In Figures  4.19.-24.^ most s l i d i n g boundaries  and  have 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 which appear as d i s c r e t e s t e p s , g e n e r a l l y l e s s than  . 5u a p a r t .  M i g r a t i o n steps i n p u b l i s h e d micrographs where c o a r s e -  g r a i n e d s l i d i n g occurs a r e s i m i l a r i n form but l a r g e r i n s c a l e . F i g u r e 4.21.  a p t l y demonstrates the unique type of boundary  m i g r a t i o n induced by s l i d i n g . steps along A-C  w i t h l i t t l e apparent  t e n s i o n produced by relatively  M i g r a t i o n and  large  the m i g r a t i n g A-C  jump by the A-B  S l i d i n g may  s l i d i n g occur i n d i s c r e t e  a c t i v i t y on A-B.  E v e n t u a l l y , the  boundary causes a sudden and  boundary.  induce m i g r a t i o n i n s e v e r a l ways:  69. (i)  B o u n d a r i e s a r e seldom f l a t ;  c u r v a t u r e s and s h o r t - r a n g e " l e d g e s " .  they have  long-range  U n l e s s the bumps a r e sheared  off  oir d i f f u s e d a r o u n d , they must m i g r a t e 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 slid'ing (Figure 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  (Figure  4.31.),  t a k i n g i n t o account the tendency f o r b o u n d a r i e s to meet the s u r f a c e r i g h t angles  (e.g.  S t r u t t et a l  FIGURE 4 . 3 0 .  /  SUFFACE  A.  (1964)).  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 .  J B,  FIGURE 4 . 3 1 .  w  /  /  I A  V  //* // c  ///  //  0.  Possible explanation for 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 . .  at  70. (ii)  An a l t e r n a t e e x p l a n a t i o n , which a p p l i e s to the s u r f a c e  and the i n t e r i o r a l i k e , i n v o l v e s the complex r e d i s t r i b u t i o n of s t r e s s e s due  to the s p a t i a l arrangement o f the g r a i n s ( L i f s h i t z  I n o t h e r words, s l i d i n g  c r e a t e s s t r e s s e s which may  (iii)  Boundaries  (1963)).  b e s t be r e l i e v e d  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  lines  internal  by  altered.  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 a t  triple  (Lee (1969)), m i g r a t e on a l o c a l i z e d s c a l e to reduce boundary  The d r i v i n g f o r c e f o r t h i s process i s b a s i c a l l y growth.  (Chapter  the same as f o r g r a i n  However, although g r a i n growth i s o f t e n observed  does not appear to be an e s s e n t i a l concomitant  energy.  to o c c u r , i t  to the s u p e r p l a s t i c p r o c e s s  4.2.).  There i s no evidence to suggest t h a t the r e c o v e r y p r o c e s s i n v o l v i n g the sweeping of boundaries  through r e g i o n s o f h i g h  dislocation  d e n s i t y a p p l i e s to s u p e r p l a s t i c i t y , u n l e s s the d i s l o c a t i o n s e x i s t v e r y c l o s e 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 a r e s l i g h t l y bowed (thus c r e a t i n g s t r a i n energy), such a process c o u l d be envisaged surface observations.  F i g u r e 4.27.  illustrates  from  the meandering boundary  m i g r a t i o n which accompanies e x t e n s i v e 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 r e p r e s e n t s the sweeping out of t a n g l e s or p i l e u p s . d i s t i n c t i o n between t h i s type of m i g r a t i o n and  The  t h a t shown i n F i g u r e s  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 c o r r e s p o n d i n g m i g r a t i o n , a t l e a s t i n the case of Cd-3y* (e.g. F i g u r e 4.19B.).  4.5.  Creep b e h a v i o u r  4 . 5 . 1 . General I t has been shown t h a t the creep r a t e i n s t a g e I I essentially steady-state, (1967)).  independent of s t r a i n ( e . g .  is  Hayden et a l ,  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  s t a t e f l o w s t r e s s which o c c u r s i n I n s t r o n t e s t s .  The o n l y  extensive  i n v e s t i g a t i o n of the creep b e h a v i o u r of a s u p e r p l a s t i c a l l o y (1969)) produced the f o l l o w i n g (i)  (iii)  (Surges  results:  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 stage  (ii)  steady  I.  Steady-state  o c c u r r e d from the s t a r t  i n stage  II.  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 " .  (iv)  " N o r m a l " creep o c c u r r e d i n s t a g e I I I secondary and t e r t i a r y  ( i . e . primary,  creep).  The p r e s e n t 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 p r o p e r t i e s i n stages I ,  I I and I I I  of c o n s t a n t s t r e s s and temperature s e n s i t i v i t y of  .05%.  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 (± . 2 ° C ) , u s i n g a n o m i n a l s t r a i n  Measurements of i n s t a n t a n e o u s  creep  extension  (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 Q u a l i t a t i v e l y , the i n s t a n t a n e o u s s m a l l (< stresses.  1%),  creep  apparatus  e x t e n s i o n i n s t a g e s I and I I was v e r y  compared w i t h n o r m a l creep o b s e r v a t i o n s  at  equivalent  72. 4 . 5 . 2 . Pb-5u and  eutectic-3u  F i g u r e s 4 . 3 2 . , 33. demonstrate b e h a v i o u r of Pb-5u and e u t e c t i c - 3 y .  the s t a g e I I ,  III  creep  Pb-5y showed a d e c r e a s e i n the  degree of p r i m a r y creep i n g o i n g from s t a g e I I I  to s t a g e I I .  However, a  s i g n i f i c a n t p r i m a r y creep s t r a i n o c c u r r e d even a t the l o w e s t s t r e s s (Figure  4.32A.). Eutectic-3y  d i s p l a y e d marked p r i m a r y creep i n s t a g e  ( F i g u r e 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 s t a g e I I  In neither  "transition"  (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 , The p r e s e n t b e h a v i o u r seems to r e f l e c t s i m p l y an " a v e r a g e " (i.e.  however.)  of s t a g e s  p a r a l l e l p r o c e s s e s ) i n the t r a n s i t i o n r e g i o n .  the f a c t t h a t s t a g e I I was not c o m p l e t e l y a t t a i n e d  stage I I I  (Chapter 4 . 1 . ) ,  and the t r a n s i t i o n r e g i o n s ,  can be somewhat  The argument of Surges was t h a t t e r t i a r y  By d i f f e r e n t i a t i n g  (m ^  particularly  creep dominated from i n the  the e q u a t i o n a = K e , C h a u d h a r i m  2 (1967  ) o b t a i n e d the  relationship:  de 1 /da — = — ( e m a  dm , ' a l n —) . 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  N  .32).  ambiguous.)  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 transition region.  reflects  experimentally  the d e f i n i t i o n of s t a g e s ,  II  The p r e s e n c e  of s i g n i f i c a n t p r i m a r y creep i n curve A ( F i g u r e 4 . 3 2 . ) p r o b a b l y  (As noted e a r l i e r  D.)  either.  case was t h e r e evidence f o r the s p e c i a l  b e h a v i o u r observed by S u r g e s .  III  (Figure 4.33A,  Very l i t t l e p r i m a r y creep was e v i d e n t i n the t r a n s i t i o n r e g i o n  and I I I  tested  ,. (4.2)  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 n e c k i n g The p r e s e n t r e s u l t s However, any attempt  develops.  suggest t h a t t h i s e f f e c t i s  negligible.  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  involve: (i) (ii) (iii)  quantitative  o b s e r v a t i o n of neck development,  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 , c a r e f u l d e t e r m i n a t i o n of m(a) to o b t a i n the magnitude of  (iv)  i n the t r a n s i t i o n r e g i o n  — ln — , m K '  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 ( E q u a t i o n (2.1)) as " n o r m a l " s t r a i n hardening begins  to be  important.  4.5.3. Cd-3u and Cd-8y Creep b e h a v i o u r 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 characterized  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 w h i c h  stage I I behaviour.  Curves A and C a r e p a r t i c u l a r l y  m e a n i n g f u l i n t h a t 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 t a g e I creep i n Cd-3u was  v e r y s i m i l a r to t h e s e c u r v e s , extensively  a l t h o u g h s t a g e I was not  (i.e.<C4% t o t a l s t r a i n f o r any  investigated  test).  E x t r a p o l a t i o n of the creep curve from the n o m i n a l 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 p r i m a r y creep i n s t a g e s I and I I . e u t e c t i c - 3 u and Z n - l u ,  For Cd-3u, Cd-8u,  the amount of p r i m a r y s t r a i n ranged from .1% to  .3%  (Figure 4 . 3 5 . ) .  and was e a s i l y r e c o v e r e d  b e h a v i o u r f o r Cd-3u appeared A H - t e s t s (Chapter 4 . 6 . ) .  A l t h o u g h n o t shown, Stage I  t o be v e r y 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  (The p e c u l i a r s t a g e I b e h a v i o u r o f Z n - l u w i l l  be d i s c u s s e d i n Chapter 4 . 5 . 4 . ) p r i m a r y creep i s t o be e x p e c t e d .  The e x i s t e n c e o f a s l i g h t amount o f A r a p i d i n i t i a l creep r a t e c o u l d r e s u l t  from:  (i)  (ii)  a n e l a s t i c g r a i n boundary s l i d i n g  4.7.),  " h a r d e n i n g " o f easy s o u r c e s , and e x h a u s t i o n o f p r e - e x i s t i n g mobile  (iii)  (Chapter  dislocations,  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 d e l a y e d y i e l d e f f e c t appeared once s t a g e I I I became e v i d e n t . development o f i n s t a b i l i t i e s  i n b o t h Cd-3u and Cd-8p  The phenomenon was not due t o the r a p i d  (Chapter 4 . 5 . 2 . ) .  Specimen A ( F i g u r e 4 . 3 6 ) ,  f o r example, was deformed t o over 2 0 % s t r a i n w i t h no apparent n e c k i n g . 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 yield effect.  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 o c c u r r e d , and p a r t o f t h i s r e d u c t i o n c o u l d be accounted f o r by g r a i n growth d u r i n g t h e a n n e a l s . P r e s t r a i n i n g i n s t a g e I I d i d n o t appear b e h a v i o u r i n subsequent  to a f f e c t the y i e l d  deformation a t higher stresses (Figure 4 . 3 8 ) .  I n o t h e r words, s t a g e I I d e f o r m a t i o n does n o t s i g n i f i c a n t l y a l t e r a c o n c l u s i o n reached by o t h e r means (Chapter 4 . 1 . 3 . ) .  On t h e o t h e r hand,  p r e s t r a i n i n g i n t h e " y i e l d " r e g i o n enhanced t h e creep r a t e i n subsequent  structure,  i f anything  stage I I deformation.  There a r e s e v e r a l i m p l i c a t i o n s o f t h e d e l a y e d y i e l d i n g  75. ob s erva t i ons:  (i)  v  Delayed y i e l d i n g and y i e l d p o i n t s (the I n s t r o n  c o u n t e r p a r t ) 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 d i s c u s s e d i n g r e a t e r d e t a i l i n Appendix A.  (ii)  The phenomenon i s unique t o f i n e g r a i n e d m a t e r i a l .  It  has not been r e p o r t e d i n the creep or t e n s i l e t e s t l i t e r a t u r e f o r c o a r s e g r a i n e d cadmium.  The p r e s e n t i n v e s t i g a t i o n i s the f i r s t one t o d e a l w i t h  f i n e - g r a i n e d cadmium.  (iii) difficult stage I I .  D i s l o c a t i o n s produced  d u r i n g the y i e l d p r o c e s s a r e  to anneal out, b u t do n o t h i n d e r subsequent d e f o r m a t i o n i n I f a n y t h i n g , they speed up the s u p e r p l a s t i c creep r a t e , probably  by being a t t r a c t e d t o and absorbed by s l i d i n g  boundaries.  4.5.4. Zn-lu S t e a d y - s t a t e was a t t a i n e d f a i r l y q u i c k l y i n s t a g e I I ( F i g u r e 4.34.), a l t h o u g h u n l i k e Cd-3u and Cd-8u, a slow decrease o f t h e "steady-state" rate occurred with s t r a i n . due  T h i s behaviour was p r o b a b l y  to the s l i g h t g r a i n growth e f f e c t e s t a b l i s h e d f o r Z n - l u  (Chapter 4.2.4.). Unique creep behaviour was observed i n stage I ( F i g u r e s 4.35., 39.). A c o n s i d e r a b l e amount o f r e p r o d u c i b l e and r e c o v e r a b l e primary creep o c c u r r e d . per s e i s not obvious.  An a s s o c i a t i o n o f t h i s behaviour w i t h s t a g e I There was n o t h i n g unique about s t a g e I i n Cd-3u,  and the stage I behaviour observed by Surges was a g r a d u a l l y d e c r e a s i n g creep r a t e w i t h s t r a i n .  ( I n t h e l a t t e r case, g r a i n growth c o u l d have  76.  FIGURE 4 . 3 2 .  Creep curves for pb-5u (Stages II, III).  FIGURE 4 . 3 3 .  Creep c u r v e s f o r e u t e c t i c - 3 u (Stages I I ,  III).  J  I 4  I  I 8  I  I 12  I  I 16  I  I 20  I  TEMP  STRESS  TIME UNIT  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.  I 24  I  I 28  I  I 32  I  I 36  TIME  FIGURE 4 . 3 4 .  Creep c u r v e s f o r s t a g e I I d e f o r m a t i o n .  I  cf  I 40  I  I 44  I  ll  FIGURE 4.35. P r i m a r y c r e e p i n s t a g e s I ,  II.  TIME FIGURE 4 . 3 6 .  D e l a y e d y i e l d i n C d - 3 y , Cd-8u ( s t a g e  III).  TIME (SEC) FIGURE 4 . 3 7 .  Difficulty  i n recovering delayed y i e l d  i n cd-.&i ( s t a g e I I I ) .  82.  10  _ 8—  H  CD-8p 65°C (cfFIGURE 4.2^  STAGE III  6  5000 PSI TIME UNIT = 20 SEC  —  z <  ce.  4  CO  —  I CHANGE STRESS .  2  STAGE II 2000 PSI TIME UNIT = 10 MIN .  ^ 1  1 2  1  1 4  1 1  6  1  1  8  1  1 1  10  1  1  12  1  I  14  1 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 s t a g e I I on d e l a y e d y i e l d i n s t a g e I I I  (Cd-8u).  5  TIME (HR) FIGURE 4 . 3 9 .  P r i m a r y creep i n Z n - l u ( s t a g e I ) .  1  been r e s p o n s i b l e ) .  Much work remains t o 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 t a g e 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 o b t a i n e d by d i f f e r e n t i a t i n g Equation (2.2):  AH. = -K91ne A  9  o,  (4.3)  S(structure)  E x p e r i m e n t a l l y , AH^ may be determined a t any p o i n t i n a c o n s t a n t  stress  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  from d i f f e r e n t  t e c h n i q u e i s to compare the creep c u r v e s  tests:  -K91ne 3 ~\- a , e ( d i f f e r e n t  tests)  (4.4)  The v a l i d i t y of the t e c h n i q u e has been demonstrated f o r many m e t a l s ( e . g . Dorn ( 1 9 5 7 ) ) , and a r i s e s from t h e 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  t e c h n i q u e 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 "instantaneous"  temperature change i s d i f f i c u l t .  (Most AH  - values  quoted i n T a b l e 4 . 2 .  were o b t a i n e d i n t h i s manner.)  of i t s common  the t e c h n i q u e has a t l e a s t two d i s a d v a n t a g e s :  use  (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 a c c u r a c y of the d i f f e r e n t i a l (ii)  In spite  technique.  S t r u c t u r e i s n o t 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 A r g e n t (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 . 4 0 . ) The " t r u e " AH^ c o u l d i n t h i s case be o b t a i n e d o n l y b y - m e a s u r i n g 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 , t h e r e may be e r r o r i n d e t e r m i n i n g AH^ by any o t h e r technique.  TIME FIGURE 4 . 4 0 .  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 " a t e .  Even i n a d i f f e r e n t i a l t e s t , "pseudo-structural" (i) temperature,  instantaneous  changes w h i c h may i n f l u e n c e AH :  The u n r e l a x e d e l a s t i c  modulus d e c r e a s e s w i t h  increasing  and g i v e s 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 t h a t AH may be o v e r e s t i m a t e d g r a i n e d cadmium, f o r example. h i g h temperatures (1964)).  t h e r e a r e some  by about 4 k c a l a t  »75T^ i n c o a r s e -  The modulus e f f e c t i s g r e a t e s t a t v e r y  and p r o b a b l y i s n e g l i g i b l e below »6T  ( B a r r e t t et  M  The p r e s e n t e x p e r i m e n t a l work i n v o l v e s temperatures  al  generally  below .6T,,,. M (ii)  A c t i v a t i o n e n t r o p y may v a r y w i t h t e m p e r a t u r e ,  giving  some e r r o r to A H ^ . A l t h o u g h l i t t l e e x p e r i m e n t a l e v i d e n c e e x i s t s , entropy e f f e c t i s c o n s i d e r e d (iii) w i t h temperature,  negligible.  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 a l t h o u g h the p o s s i b i l i t y i s u n l i k e l y .  Assuming t h a t the above e f f e c t s a r e t o g e t h e r  negligible,  AH^ may s t i l l be lower than the p r o c e s s e n t h a l p y A H ^ , due t o s t r e s s - a s s i s t e d o v e r - c o m i n g of the s h o r t - r a n g e  AH = AH A p  where  the  T * = effective  barrier:  T*bA*,  shear s t r e s s  (Chapter  the  (4.5)  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 v o l u m e " , a l t h o u g h V * s h o u l d 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 * ) . M o r e o v e r , 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 a r e a i s r e l a t e d  to the fundamental  strain  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 :  * = 31m* m 31ne  .'.  x*bA*  S,T  A  *  *  =  "KI 31n£ b 8T*  S,T  '  KT m*  (4.6)  A v a l u e f o r T * b A * may be o b t a i n e d w i t h o u t e v a l u a t i n g T * o r A * , p r o v i d e d m* i s known. .2,  The apparent v a l u e f o r m i n normal creep i s  although i t probably incorporates  (1955), B a r r e t t  and N i x ( 1 9 6 5 ) ) ;  structural effects  m* i s p r o b a b l y c l o s e r  (e.g.  F o r T < 1000°K, KT < 1 k c a l / m o l e ,  s m a l l compared w i t h  I f m* =  1,  a v a l u e which i s  AH^.  M o r e o v e r , the p o s s i b i l i t y of backjumps x*bA* £ KT.  Weertman  to 1 ( e . g . Cuddy  ( 1 9 7 0 ) ) , 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 . then x * b A * = K T .  about  E q u a t i o n (4.5)  derives  -AH . KT / e a e (e  i s v e r y r e a l when  from:  x*bA* KT  -T*bA* KT « - e ),  / / -7 \ (4.7)  -x*bA* KT and h o l d s o n l y when  e  can be i g n o r e d ( i . e .  The e f f e c t of the backjump term i s s t r e s s on  AH..  when x * b A * >> K T ) .  to reduce the a l r e a d y s m a l l e f f e c t  of  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 t h a t stress-assistance (i) (ii)  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)): AH^ i s a t most a weak f u n c t i o n of s t r e s s  AH  ~ AH,, f o r a wide range o f m a t e r i a l s ,  t h a t 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 , assistance  the  term oi 0.  i n normal c r e e p . indicating  i n turn,  the  stress  (Other e x p e r i m e n t s c o n f i r m t h a t 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 t h a t the argument i s syllogistic.) S u p e r p l a s t i c i t y o c c u r s a t normal creep temperatures and strain rates,  and the above d i s c u s s i o n u n d o u b t e d l y a p p l i e s .  no r e a s o n to b e l i e v e t h a t a s t r e s s - a s s i s t a n c e significant  term a f f e c t s  There  is  AH^ to any  extent.  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 t a g e s 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  f o r one i n s t a n c e , w h i c h s h a l l be d i s c u s s e d l a t e r . stabilization after  than .01%.  Temperature  changes up to 35°C was a c h i e v e d w i t h i n 30 s e c o n d s ,  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 less  except  Creep r a t e s  after  than .1%, and u s u a l l y  temperature change were r e c o r d e d 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 t h o u g h the c r e e p r a t e was e s s e n t i a l l y c o n s t a n t 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 . Material  Stage  A c t i v a t i o n energy d a t a r e l a t i v e  AH,  (kcal/mole) Pb-5%Cd Pb-Cd(eut.) Pb-Sn(eut.) Cd-5%Pb Zn-1%A1 Zn-.2%A1 Zn-Al(eut.) Fe-Cr-Ni  2 2 3 2 2 1 2 3 1 2 2 2 2 2 2  REFERENCES:  9.6f ^12* • ^13* ^14f 11T >13* ^lO** ^11* >14* ^10* 101 14.5t 21( 1 7 5 ° C ) f 35( 175°C)+ 60+ =t=  Reference  Material  1 2 2 2 3 2 2 2 2 2 4 5 6 6 7  Pb Pb-5%Cd Cd Sn Zn Al Fe Cr Ni  to  superplasticity.  B (kcal/mole) AH  GB (kcal/mole) AH  24-28  15-16  18.5 23-26 23 33 64-74 52-73 63-67  13 9.6 14  -  FROM:  -  40 46 26  -  G a r o f a l o (1965) Alden (1969) Wajda e t a l (1955) S m i t h e l l s (1967) 2  * 4=  I n s t a n t a n e o u s t e m p e r a t u r e change. 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  1. 2. 3. 4.  A l d e n (1968) P r e s e n t work. C l i n e and A l d e n (1966) Cook (1968)  temperatures.  5 . B a l l and H u t c h i s o n (1969) 6. C h a u d h a r i (1967) 7. Hayden e t a l (1967)  ^ ^ N o r m a l Creep (kcal/mole) 19-28 20 21 21-26 21 35 70-73 66  -  4.6.3.  Results (i)  T r a n s i e n t s were n o t observed i n s t a g e I I  for Zn-lu,  Cd-3y o r C d - 8 u , a l l o w i n g m e a n i n g f u l comparison of AH - v a l u e s d e t e r m i n e d from m-curve f a m i l i e s w i t h those determined from i n s t a n t a n e o u s (Figures  tests  4.41.-44.). (ii)  There was no apparent dependence of A H ^ on s t r a i n  w i t h i n the e x p e r i m e n t a 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 "  points  p l o t t e d i n F i g u r e s 4 . 4 3 . - 4 4 . a r e 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 c o n s i d e r e d a c c u r a t e ± 10%, e a s i l y , w i t h a c o n f i d e n c e of (iii) temperatures  to  95%.  There was no o b v i o u s change of AH over the range of  investigated.  Figure 4.41.  i l l u s t r a t e s the  apparent  constancy of AH over a range where s t a g e s I and I I were b o t h 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 . (iv)  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 o b s e r v e d  a t v e r y low m i n s t a g e I ( 0 ° C , r e s u l t AH • ^ Instantaneous  1500 p s i ) i n Z n - l u  (Figure 4.43).  was about 85% A H _ , _ ^ . Steady-state  As a  The p o s i t i v e  t r a n s i e n t p r o b a b l y r e l a t e d to the r e l a t i v e l y l a r g e p r i m a r y creep observed i n Z n - l y a t 0°C (Chapter (v)  4.5.4.).  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 , A H ^ i n c r e a s e d  s l i g h t l y w i t h decreasing s t r e s s i n stage I I  (e.g.  F i g u r e 4 . 4 2 . ) , and  i n c r e a s e d a t a s t e e p e r r a t e a t low s t r e s s e s where s t a g e I became dominant ( F i g u r e 4 . 4 3 . ) , i n b o t h Z n - l y and C d - 3 y . (vi) Cd-8y or P b - 5 y .  A H ^ d i d not appear to i n c r e a s e Stage I I I  i n stage I I I  for  either  was d i s t i n c t l y e v i d e n t a t 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 C d - 3 u a t 500 p i , . (One specimen, each p o i n t c o r r e s p o n d i n g 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 a r e b o t h r e p r e s e n t e d . (See F i g u r e 4 . 1 . ) . S  91.  FIGURE 4 . 4 2 .  AH^-plots from F i g u r e 4 . 1 .  (Cd-3u; stages I ,  II).  8.1 0  1  1  1  1  I  I  2000  I  •  •  4000  FLOW  •  •  •  1  1  1  6QQ0  STRESS (PSI)  FIGURE 4.43. AIL^vs. f l o w - s t r e s s i n s t a g e s 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  O  STAGE I I  1  1  °  1  1  1  I  I  '  I  I  4000  2 0 0 0  FLOW  FIGURE 4 . 4 4 .  I  STRESS (PSI)  AH v s . f l o w - s t r e s s i n s t a g e s I I and I I I f o r P b - 5 y and  ' 6000  I  I  «  I 8000  |  FIGURE 4.45. .  AH^-plots for Eutectic-3u, Stage I I ,  500 p s i .  Eutectic-8y.  (from F i g u r e s 4.4. and 4.5.).  i n F i g u r e 4.44.  A t t h e lower s t r e s s e s s t a g e I I was d i s t i n c t i n Cd-8u,  and a t 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.  (vii)  AH  A  was determined t o be a p p r o x i m a t e l y  14.5 k c a l a t  500 p s i ( s t a g e 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 ( F i g u r e 4.45.). (No i n s t a n t a n e o u s  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 o f  AH^ t o g r a i n s i z e ( a t c o n s t a n t s t r e s s ) was a l s o apparent i n Cd-3u and Cd-8u i n s t a g e I I .  AH^ f o r t h e e u t e c t i c a l l o y s was somewhat h i g h e r  than 4  f o r e i t h e r Pb-5y o r Cd-3y a t 500 p s i , a l t h o u g h AH  approached 14 k c a l i n  Cd-3y a t 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 t h e p r e s e n t i n v e s t i g a t i o n corresponds g e n e r a l o b s e r v a t i o n t h a t AH. ^ % A H A  AH  ou  < AH  B  w e l l w i t h the  i n s t a g e I I (Table 4.2.).  n  As  D  (y JgAH ) , i t i s n a t u r a l t o c o n s i d e r g r a i n boundary d i f f u s i o n B  as a l i k e l y r a t e - c o n t r o l l i n g s t e p .  T h i s i d e a i s e x p l i c i t i n most  models d i s c u s s e d 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 t h e d i s l o c a t i o n c l i m b models may p r e d i c t AH  > AH.,,, as c l i m b i s assumed t o occur " i n t h e v i c i n i t y " o f b o u n d a r i e s , p GB' 3  The boundaries  same s u p e r p l a s t i c mechanisms w h i c h o c c u r a t g r a i n -  can p r o b a b l y occur  a t interphase boundaries  e x c e p t i o n o f boundary m i g r a t i o n . )  ( w i t h the  The a c t i v a t i o n energy f o r i n t e r p h a s e  boundary d i f f u s i o n i s i n t e r m e d i a t e between t h a t o f t h e p a r e n t phases and the apparent a c t i v a t i o n energy o f a two-phase a l l o y i s r e a s o n a b l y r e p r e s e n t e d by an e x p r e s s i o n o f the f o l l o w i n g form:  A H  where N^, ^  A =  N  l  A H  G  +  B l  N  A H  GB  2  •  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 s c a r c e and c o n t r o v e r s i a l .  d a t a f o r even pure m e t a l s a r e both  There i s no c o n s i s t e n t AH  AH  2  GB  and A H , as r e p o r t e d v a l u e s of — — fi  Upthegrove (1966)) t o .9  ( G i f k i n s (1968)).  considered i n d i v i d u a l l y . a given metal.  AH  c o r r e l a t i o n between  range from .2 ( S t a r k and Thus each a l l o y must be  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  F o r 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 t a r k and Upthegrove ( 1 9 6 6 ) , and 16 k c a l by Okkerse ( 1 9 5 4 ) . p r e s e n t work has e s t a b l i s h e d AH^ - 12 k c a l f o r s t a g e I I  (The  i n Pb-5u.)  Any  p r e c i s e c o r r e l a t i o n o f s u p e r p l a s t i c a c t i v a t i o n e n e r g i e s w i t h AH GB r e q u i r e s more a c c u r a t e  c o n f i r m a t i o n o f the  latter.  A l t h o u g h i n most cases (Table 4 . 2 . ) relate  AH^ f o r s t a g e I I  t o boundary d i f f u s i o n ( s u b j e c t t o the above-mentioned  some d e f i n i t e anomalies do e x i s t .  ambiguities),  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 in their alloy (Fe-Cr-Ni).  could  constituents  A l d e n (1969) has suggested t h a t Hayden and  Brophy were o b s e r v i n g s t a g e I r a t h e r  than s t a g e I I .  Another p o s s i b i l i t y  i s t h a t 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 t e c h n i q u e used t o 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 negative transient  i n an i n s t a n t a n e o u s  example, would produce a lower but more a c c u r a t e value. AH^„, AH„ o r AIL, ., have not been e s t a b l i s h e d f o r GB B Normal creep complicated iron-based a l l o y i n v e s t i g a t e d .  test,  for  Moreover, the  Perhaps these v a l u e s  h i g h e r than the v a l u e s of the i n d i v i d u a l components might  are  suggest.  4 . 6 . 4 . 2 . Stage I A l t h o u g h s t a g e 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  increase  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 b o t h Z n - l y  and Cd-3u s u g g e s t s t h a t the b e h a v i o u r i s g e n e r a l .  i t i s u n l i k e l y t h a t the i n c r e a s i n g A H ^ i s a r e s u l t  to Chapter 4 . 6 . 4 . 1 . of s t r e s s per s e .  According  It  i s more l i k e l y t h a t a new p r o c e s s  a c t i v a t i o n energy becomes i m p o r t a n t a t low s t r e s s e s .  of  higher  Although 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 s t a g e I , a s s o c i a t i o n i s perhaps unwarranted as the l i m i t e d e v i d e n c e t h a t A H ^ ^ f(m)  for a given flow stress  4 . 6 . 4 . 3 . Stage  III  (Figure  the  suggests  4.41.).  A l t h o u g h u n i n v e s t i g a t e d , A H ^ has been assumed i m p l i c i t l y be e q u a l to AHg i n the l i t e r a t u r e .  The p r e s e n t r e s u l t s  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 t h a 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 t e p i n s t a g e I I I  s i m i l a r to t h a t found i n Stage I I ,  f o r two  has an a c t i v a t i o n  approximately ^AH^.  to  energy  Thus s t a g e s  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  energy,  even though the p r o c e s s may be d i f f e r e n t .  II  activation  For example,  d i s l o c a t i o n c l i m b 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 c o u l d o c c u r i n s t a g e 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 s t a g e  II.  4 . 6 . 4 . 4 . Combined p r o c e s s e s It AH  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  for  w h i c h are ambiguous from a m e c h a n i s t i c p o i n t of v i e w ( G i f k i n s ( 1 9 7 0 ) ) .  A  The a m b i g u i t y 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 t h a t AH  on how the p r o c e s s e s  (a s l o p e )  depends  interact.  TEMP" FIGURE 4 . 4 6 .  1  Combined p r o c e s s e s  (AH a s l o p e ) .  P r o c e s s e s may o p e r a t e i n p a r a l l e l ( s i m u l t a n e o u s and i n d e p e n d e n t ) , i n series  (dependent and c o n s e c u t i v e ) , o r i n some more c o m p l i c a t e d manner.  For example, p r o c e s s e s A and B may o p e r a t e 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 J  ,,  e = -rfr; ( e . ) 100 A' v  I t i s apparent t h a t ,  + (—, 100 v  n n  except f o r the s e r i e s  )  -  e B  T  c a s e , AH. w i l l be ambiguous  if  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 o r 0'.  of 0 o r 0' may extend to many degrees c e n t i g r a d e ,  The " v i c i n i t y "  depending f o r one  t h i n g on the s t a t i s t i c a l c o n f i d e n c e 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 t h a t a combined p r o c e s s a n a l y s i s i s w a r r a n t e d f o r the p r e s e n t d a t a , i n v i e w of the m u l t i - s t a g e n a t u r e of the m - c u r v e s .  4.7.  Internal  stress  4.7.1. G e n e r a l 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  deformation i s a w e l l e s t a b l i s h e d concept. athermal d i s l o c a t i o n i n t e r a c t i o n s ,  Associated with  0" s u p p o s e d l y reduces q  the  long-range effective  s t r e s s a* f e l t by m o b i l e 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 stress a , according to: r  a* =  _  a  F  .  a  (4.8)  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  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 O values vary greatly  (Table 4 . / . ) .  experimental techniques, rate).  Q  (1968), Jonas ( 1 9 6 9 ) ) .  /Q^ have been made, a l t h o u g h the The v a r i a t i o n depends p a r t l y on the  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 .  strain  100.  TABLE 4 . | .  E x p e r i m e n t a l v a l u e s of a / a  Material Fe-Si Stainless  Steel  Mg (e > 1 0 " (e < I O  o  a  / o  .7 -  .9  N i x and B a r r e t t  .1 -  .25  Cuddy (1970)  4  Sec." )  ^.25  - 4  Sec." )  ^.8  1  1  Cd-6% Pb  Reference  F  Gibbs  (1968)  (1966)  { it  variable  II  Present work.  Figure 4.47. i l l u s t r a t e s commonly used t o determine a  the " r e v e r s e r e l a x a t i o n  i n Instron tests.  Q  A general equation 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 r e c o v e r y o f a  -H(a),  "I* . _!l= i E  where  dt  = (e A  technique"  Q  itself:  -H(a) - e  K T  K T  )  (4.9)  p  E * = combined e l a s t i c modulus of specimen and m a c h i n e , applied stress, p l a s t i c specimen  e  P H(a) f  H(a) H  H  b H  strain,  ca*bA* , j. j . \ —— ( a c t i v a t i o n energy f o r f o r w a r d jumps) KT co*bA* ( a c t i v a t i o n energy f o r backward j u m p s ) , ~KT~~ c  p  p  +  a c t i v a t i o n energy of d e f o r m a t i o n p r o c e s s , P c = f a c t o r r e l a t i n g o* t o the a c t i v a t i o n shear s t r e s s T * assuming a d i s l o c a t i o n  A* =  activation  area.  process,  (^h),  101.  ORIGINAL I —  ORIGINAL FLOW CURVE  2~  QUICK UNLOADING  3—  POSITIVE STRESS RELAXATION  4—  NEGATIVE STRESS RELAXATION  in u or  o  TIME FIGURE 4.47.  Reverse r e l a x a t i o n technique f o r determining a . Q  102, E q u a t i o n (4.9) may be r e w r i t t e n a s :  -1  , . F  .  0  dT  E*  —H _p_ . KT. .  =  £  P  =  A  (  e  co*bA* KT  "  ) ( e  -co*bA* KT .  >  e  a*bA* = A' s i h h 2_£A  When a  (4.10)  > 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  F  °F i s p o s i t i v e and -^r— i s n e g a t i v e ) . d  occurs  (i.e.  When a  < a , a* i s n e g a t i v e and n e g a t i v e s t r e s s r e l a x a t i o n  r  O  ,  d 0  occurs  F  ( i . e . £^ i s n e g a t i v e and  i spositive).  o n l y when an a p p l i e d s t r e s s l e s s than O r e v e r s i n g t h e cross-head d i r e c t i o n .  q  This s i t u a t i o n  occurs  i s imposed on t h e specimen by  Then upon s t o p p i n g t h e c r o s s - h e a d ,  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 t o specimen c o n t r a c t i o n . When o_ = a , o* i s z e r o , and no s t r e s s r e l a x a t i o n o c c u r s . F o ' (The s t r e s s l e v e l a  Q  i s t h e assymtote approached i n a l l r e l a x a t i o n t e s t s . )  A value for a  Q  may be o b t a i n e d from t h e 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 F i g u r e 4.47., a l t h o u g h t h e r e a r e f a c t o r s w h i c h make the v a l u e ambiguous.  Guiu  (1969) has p o i n t e d o u t t h a t " a r t i f i c i a l "  n e g a t i v e s t r e s s r e l a x a t i o n may o c c u r i n s o f t specimens due t o machine contractions.  (He has conceded i n p r i v a t e communication t h a t machine  e f f e c t s a r e u n l i k e l y t o account  f o r t h e g r o s s e f f e c t s observed  i n the  p r e s e n t work, and t h a t a r e a l specimen e f f e c t i s b e i n g observed.) problem i n d e t e r m i n i n g a  Q  a t h i g h temperatures  i s that a  Q  itself  w i t h both time and specimen c o n t r a c t i o n , making e s t i m a t e s o f a  Q  low.  Another  recovers generally  103 . 4- 7 . 2 .  Experimental Figure 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 c o r r e s p o n d i n g n ^ - c u r v e s d e t e r m i n e d by the "reverse relaxation technique". An i n t e r n a l s t r e s s o  Q  III.  (M-curves r e l a t e  to o^; m - c u r v e s to o .) Q  •  Q  of some magnitude i s e v i d e n t i n s t a g e s I ,  II  and  S i m i l a r r e s u l t s were o b t a i n e d 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  (21°C).  I t was e s t a b l i s h e d t h a t a  Q  r e l a x e d q u i c k l y enough to  interfere  w i t h r e a d i n g s u n l e s s the t e s t ( F i g u r e 4 . 4 7 . ) was performed v e r y q u i c k l y (within seconds).  The r a t e of r e l a x a t i o n of o  Q  increased with increasing  i n i t i a l f l o w s t r e s s o r s t r a i n r a t e f o r any g i v e n m - c u r v e . the e s t i m a t e of O  q  As a r e s u l t  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 l o n g the m - c u r v e . A l t h o u g h i m p o s s i b l e to determine the p r e c i s e between O  and Op, m a i n l y due to the r e c o v e r y of a  Q  Qi  i t may be s a i d  w i t h f a i r c o n f i d e n c e t h a t the m - c u r v e s i n F i g u r e 4 . 4 8 . Q  relationship  represent  minimum v a l u e s of a . Q  4.7.3. Discussion  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 o  i n the p r e s e n t work) i s not c l e a r .  If  r e c e n t work ( e . g .  i n normal creep  e q u a t i o n (4.8)  s h o u l d be used i n the s t r a i n r a t e e q u a t i o n s , isolated  Q  rather  (and s t a g e  a p p l i e s , then a* than Op.  Except i n  Cuddy ( 1 9 7 0 ) , Jonas ( 1 9 6 9 ) ) , s t r a i n r a t e  e q u a t i o n s 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  III  STRAIN  RATE  (MIN"')  K 4.48. m-and m - c u r v e s f o r two s u p e r p l a s t i c 0  alloys.  ( 1 9 6 8 ) , b o t h 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 t h e use o f a „ i n F the e q u a t i o n s may be r a t i o n a l i z e d .  However, the m a t t e r i s u n r e s o l v e d  and remains one o f t h e i m p o r t a n t c h a l l e n g e s  i n creep  theory.  4.7.3.2. O i n superplasticity q  Assuming t h a t d i s l o c a t i o n i n t e r a c t i o n s creating a backstress (reasonable  p l a y no r o l e i n  i n v i e w of the observed l a c k o f  networks and low d e n s i t y ) , i t i s p o s s i b l e t o c o n s t r u c t p h y s i c a l models i n which a o o c c u r s i  n  s u rp e rrp l a s t i c i t yj and i n w h i c h o * (= a_ F - ao ) i s  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  involving  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 t e p 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 accommodation must o c c u r .  a t the t r i p l e l i n e s where  The two models i n v o l v e t h e two l i k e l y  accommodation mechanisms of d i f f u s i o n and s l i p , (i)  D i f f u s i o n a l accommodation:  respectively.  Figure 4.49.  illustrates  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 (Gifkins  (1967)).  I n i t i a l l y , t h e 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 = 45°, r  Once s l i d i n g b e g i n s ,  then x * = . 5 c O . F  r e g i o n s of t e n s i l e and c o m p r e s s i v e s t r e s s a r i s e  b o u n d a r i e s 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  produces the n e c e s s a r y accommodation.  The magnitude of a  at  gradient  (& -  a^)  depends on the r e l a t i v e k i n e t i c s o f 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 l o n g the s t r e s s g r a d i e n t  f a s t , and v i c e v e r s a . ^  t  is  The b a c k s t r e s s g ( a ) r e s u l t i n g from accommodation  I t i s i m p l i c i t i n the model t h a t accommodation i s always f a s t e r than sliding. O t h e r w i s e , t h e accommodation p r o c e s s 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 ( 1 9 6 7 ) .  r*  =  fOFlT  %^yf ~ \  (  / b. FIGURE 4.49.  D i f f u s i o n a l accommodation model.  a.  Zero  strain  b.  Steady-state condition.  T * = f(o ) v  ~^g(T ) R  / FIGURE 4.50.  S l i p accommodation m o d e l .  a.  S t a r t of g e n e r a t i o n  b.  Bowing d i s l o c a t i o n d u r i n g Tg = bowing s t r e s s  T  F.R *  T  B^°  cycle cycle  MATERIAL FLUX  . 107.  is  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 t o zero by r e v e r s i n g the c r o s s - h e a d q u i c k l y w i l l now reduce T * t o - g ( o ) i n s t a n t l y .  Instron  The g r a i n s  c  w i l l e x p e r i e n c e r e v e r s e shear w h i c h produces specimen c o n t r a c t i o n ;  at  the same time a d r i v i n g f o r c e f o r c o n t i n u e d , f o r w a r d creep by t r i p l e line diffusion w i l l exist. two,  As the l a t t e r p r o c e s s  i s the f a s t e r of  i t s h o u l d p r e d o m i n a t e , and no net c o n t r a c t i o n s h o u l d o c c u r .  the model does not p r e d i c t the r e f l e c t i o n o f a b a c k s t r e s s relaxation  in a  Thus "reverse  test". Analogous d i f f u s i o n a l models c o u l d be developed f o 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. accommodation).  (e.g.  C o b l e creep w i t h  As i n the p r e s e n t model the b a c k s t r e s s  would be "reverse  test." (ii)  S l i p Accommodation:  r a t h e r than d i f f u s i o n a l  I t w i l l now be assumed t h a t  accommodation o c c u r s .  from a Frank-Read s o u r c e .  generated  The s i z e o f the s o u r c e cannot g r e a t l y  as t h i s i s the o r d e r of the g r a i n s i z e .  slip  A c r i t i c a l s t r e s s must  be reached a t the t r i p l e l i n e b e f o r e a d i s l o c a t i o n can be  lu  other  sliding  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 n o t show up on a relaxation  the  (Thus t h e s o u r c e  exceed  strength  3 T it  may be f a i r l y l a r g e , i n the o r d e r of 10  psi.)  From F i g u r e 4 . 5 0 . ,  i s apparent t h a t T * w i l l not r e a c h 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 c a s e , due to the d i s c o n t i n u o u s n a t u r e of the s l i p At zero s t r a i n or immediately a f t e r  d i s l o c a t i o n generation,  accommodation.  T * = f(a„). r  A t any o t h e r i n s t a n t , has bowed o u t :  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  * = f ( ) Gf  - g( g)• T  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 . backstress  F o r a complete c y c l e an average  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 . . il  The v a l u e of a  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  increase  ) i s a constant,  independent of a , so i t s s i g n i f i c a n c e w i l l  with decreasing a „ . r depend on T  r .K.  (It  s h o u l d be noted t h a t g ( x _ ) , is  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  Appendix C shows t h a t the a n e l a s t i c  and hence a „ , o size.)  s t r a i n associated  with  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 a  Q  i n a "reverse" relaxation t e s t " .  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 m o d u l u s , o  Q  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 . as the specimen c o n t r a c t s ,  In f a c t ,  If  the  would be observed the l i n k a g e " g i v e 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 a  Q  on m i n s t a g e s 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  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 . the appearance of two s t a g e s (I and I I ) the s t a g e I p r o c e s s  suggests  apparent F o r example,  two p r o c e s s e s  i n which  cannot be Newtonian v i s c o u s due t o 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 , can account f o r b o t h s t a g e s , when  fundamentally Newtonian v i s c o u s ,  a suitable relationship exists  between  a* and a . Q  Figure 4.52. the two b a c k s t r e s s  i l l u s t r a t e s how a  models a n a l y s e d .  F  varies with s t r a i n rate for  For t h e d i f f u s i o n a l m o d e l , a *  is  p r o b a b l y p r o p o r t i o n a l of a , meaning t h a t m = 1 a t a l l times and two F s t a g e s w i l l not e x i s t . C l e a r l y , t h i s m o d e l , 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 . i t p r e d i c t s a constant a Of -> o  Q  i n stage I ,  The d i s l o c a t i o n mechanism i s more f e a s i b l e , Q  f o r any g i v e n g r a i n s i z e .  as  As a r e s u l t ,  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 .  It  is  l i f t e l y t h a t b o t h accommodation mechanisms would o p e r a t e 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 p r o c e s s becoming more i m p o r t a n t w i t h decreasing  FIGURE 4 . 5 1 .  stress.  Stage I - I I  b e h a v i o u r 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 e x p e r i m e n t a l c o n f i r m a t i o n o r  *  LOG FIGURE 4.52.  STRAIN  RATE  Stage I - I I b e h a v i o u r f o r t h e two b a 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 o  Q  reported. one-process  The p r e s e n t  d i s l o c a t i o n model appears  i n t e r p r e t a t i o n of s t a g e I - I I  No e l a b o r a t e  i n F i g u r e 4.48  It  results  Q  i n stage I I I  c o u l d be s a i d t h a t the s t a g e I  i s reasonable  d i s c u s s e d i n Chapter  5.  Cd-3u r e s u l t s  Zn-lu  do n o t .  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  does not r e l a t e to the p r e s e n t m o d e l s . ) of stages I and I I  reasonable  i n t e r p r e t a t i o n of the d a t a  s u p p o r t the model w h i l e the s t a g e I I  (Presumably, o  to be a  b e h a v i o u r where g r a i n boundary  sliding is rate-controlling. i s warranted.  has been p r e v i o u s l y  Whether a b a c k s t r e s s  and  interpretation  i n v i e w of o t h e r e v i d e n c e w i l l  be  5. MECHANISTIC INTERPRETATION  5.1. Stage  III A creep p r o c e s s  appropriate f o r stage I I I .  independent of s u p e r p l a s t i c mechanisms W i t h s l i g h t a d a p t a t i o n the p r o c e s s  is  could  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 r e c o v e r y a t 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 p r e s e n t The low a c t i v a t i o n e n e r g i e s  (Chapter 4.6.4.3.) s t r o n g l y suggest  discussion.  observed i n Cd-8u and Pb-5u  t h a t r e c o v e r y o c c u r s 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 i m b r a t e s around " n o r m a l " obstacles (e.g.  Lomer-Cottrell barriers)  boundary i n t e r a c t i o n .  or by a more d i r e c t d i s l o c a t i o n -  W i t h 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 ,  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  t h e 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 i m b 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  a t the boundary  c o u l d 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 sliding.  Models i n v o l v i n g p i l e u p s and subsequent boundary  interactions  have been proposed (Hayden and Brophy (1968), B a l l and H u t c h i s o n (1968)) to account stage I I I .  f o r s t a g e I I b e h a v i o u r , a l t h o u g h they seem more r e l e v a n t The f l e x i b i l i t y of t h e s e models i s s u f f i c i e n t  the s t r a i n r a t e s e n s i t i v i t i e s  to  to  accommodate  or g r a i n s i z e e f f e c t s observed i n  either  stage. The t r a n s i t i o n from s t a g e I I  to s t a g e 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 p r o c e s s e s independent " p a r a l l e l " mechanisms,  are  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 t a g e I I I .  The t r a n s i t i o n to s t a g e  III  113. o c c u r s a t 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 . ) .  If  the m-curve approaches a g r a i n - s i z e independent  assymptote i n s t a g e I I I  (Chapter 2 . 2 . 5 . ) , ther? the t r a n s i t i o n s h o u l d  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 . C o b l e and H-N creep The importance of C o b l e a n d / o r H - N creep w i l l f i r s t c o n s i d e r e d i n terms of p r e d i c t e d v e r s u s e x p e r i m e n t a l creep Table 5 . 1 .  lists  be  rates.  the r e l e v a n t d a t a f o r the p r e s e n t work (at 40°C f o r  convenience),  and f o r o t h e r work from w h i c h m e a n i n g f u l c a l c u l a t i o n s  can be made.  ( I n a l l cases the second phase volume p e r c e n t a g e  small.)  is  The s t r e s s l e v e l s a r e chosen to c o r r e s p o n d w i t h the s t a g e  i n f l e c t i o n p o i n t s i n the e x p e r i m e n t a l m - c u r v e s .  It  II  i s appropriate to  i n v e s t i g a t e the p r e d i c t e d v e r s u s e x p e r i m e n t a l r a t e s f o r two r e a s o n s : (i) Backofen)  The C o b l e model has been a c c e p t e d by some ( e . g .  as b e i n g the r a t e - c o n t r o l l i n g p r o c e s s (ii)  i n stage  II.  Both the C o b l e and H - N models a r e 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 l e n d themselves w e l l to From T a b l e 5 . 1 . ,  rate-analysis.  e „ , , >> e „ f o r a l l c a s e s , meaning Coble H-N TT  t h a t H-N creep can g e n e r a l l y be i g n o r e d , a l t h o u g h i t s r e l a t i v e increases  Zehr,  importance  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 c a s e s , the p r e d i c t e d Coble r a t e s a r e too s m a l l to  be i m p o r t a n t at the s t a g e I I  inflection.  Ignoring possible error 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 C o b l e and H - N models v e r s u s e x p e r i m e n t a l creep 5  Temp. (°K)  2  D (cm / s e c ) Alloy  GB  D  -4930 t . -4 RT 1.25x10 e i n  Pb-5y  1  -15,700 *  T/T M  Stress (psi)  -26,060 i / RT 1,4e  313  .52  1  Cd-8u  1  Zn-ly  1  -13,000 RT . 7e -14,400 RT . 3e  R T  Q  Sn-l%Bi(5u)  2  Sn-5%Bi(3.5u)  6.4x10  d  Fe("low a l l o y : ^2p) 4  5e c  9  -9550  e  T?T  -39,000 RT •  1  P r e s e n t work  2  Alden  (1966)  :!  Alden  (1967)  4  Morrison  5  from S m i t h e l l (1968)  f  S t a r k and Upthegrove (1966)  +  Okkerse (1955)  *  E rixper  a  .075e -22,500 RT . 16e -23,300 i1. /4e  313  .53  R T  2e 0  -57,000 RT  313  .45  295  .58  1073  .59  ^Exper. 2.  1000  5x10"  ^5xl0~  1  .0005  1.5xl0~  4  3xl0"  6  ^5xl0  1000  1.7xl0"  6  6xl0"  7  %10"4  6  ^2xl0  .03  - 3  .017 .005  IO"  3  3xl0~  3xl0~  4  3x10"  1 1  o,2xl0"  6x10"  1 1  ^3x10-^  .3  ^5x10"  10  10,000  'WOOO  4  7  2000  ' 1500  Coble  TC  H-N  3  2.5xl0~ -18,700  e  l  IO"  . 8e Cd-3u  £„, (min ) Theor. Coble  B  rates.  9x10-4 5xl0~  io"  2  1 1  - 1  .06  3  3  B vwD a 2  (1968)  1  '  L ? KT  C 0 b l e  v  (i.e.  w  '  H  10  where B,  corresponds to stage I I i n f l e c t i o n maximum m ) .  GB  s  150 o in" 2 x 10 10" cm. 7  2 3  cm  3  "  N  ~  L?KT  '  D  f o r the moment, t h e r e a r e two f a c t o r s w h i c h 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  c a s e s , 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 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  1.5,  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 r a n g i n g 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  creep r a t e i s to reduce i t by a f a c t o r of (ii) effective  stress.  (1.5)  3  ^ 3 (Equation  The a p p l i e d s t r e s s has been assumed e q u a l to If a backstress  exists,  (2.4)). the  t h e n 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 a s s i g n e d D^,  v and w, t h e r e i s c o n s i d e r a b l e doubt c o n c e r n i n g the  values f o r D ^ . GU  to  experimental  I n the case of P b - 5 u , a c c e p t i n g S t a r k and U p t h e g r o v e ' s  v a l u e of D_„ f o r l e a d produces a r e a s o n a b l e Go  creep r a t e ,  several  orders  of magnitude f a s t e r than t h a t o b t a i n e d by u s i n g O k k e r s e ' s v a l u e . A l t h o u g h 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 g a i n e d l i t t l e a c c e p t a n c e i n the l i t e r a t u r e . AH^ o b t a i n e d f o r Pb-5u i n the p r e s e n t work does not s u p p o r t  (The  either  value.) Given the u n c e r t a i n t y i n D  (especially for lead),  it  is  GD  g e n e r a l l y u n l i k e l y t h a t Coble creep has much r e l e v a n c e the p o i n t of v i e w of r a t e a n a l y s i s .  to s t a g e I I  Whether the C o b l e model f a i l s  from to  s a t i s f y o t h e r c r i t e r i a w i l l now be d i s c u s s e d : (i) strain,  C o b l e 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  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 p r e s e n t  results  116. suggest t h a t some e l o n g a t i o n may o c c u r i n Cd-3u (Chapter 4 . 3 . 2 . ) ; any c a s e , g r a i n boundary m i g r a t i o n may w e l l o b s c u r e the  in  observation  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 g r o w t h . (ii)  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  g e n e r a l l y observed i n s t a g e I I .  effect  The a m b i g u i t y i n d e f i n i n g the  e x p e r i m e n t a 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 a l o n g 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 , of t h e o r y w i t h (iii)  prohibits clear  2.2.5.),  correlation  experiment. The model r e q u i r e s g r a i n boundary s l i d i n g to o c c u r  an accommodation p r o c e s s .  Backofen (1968) suggested  as  that a backstress  c o u l d 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 w h i c h c o u l d l e a d to a low apparent s t r a i n - r a t e Backofen  (1968) suggested  s e n s i t i v i t y (stage I ,  presumably).  Zehr and  t h a 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  s t a g e I i f the p r o c e s s 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 . Neither explanation 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  f a s t e r r a t e than the Coble p r o c e s s  (see next s e c t i o n ) .  Thus  a  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 p r o b a b l y 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 t a g e I (iv)  (see  Chapter 4 . 7 . 3 . 2 . ) .  The observed a c t i v a t i o n energy i n  c o n s i s t e n t w i t h Coble creep,  stage I I  a l t h o u g h observed v a l u e s do not  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  not l i k e l y t h a t the i n c r e a s e  correspond  increased  a c t i v a t i o n energy as s t a g e I i s approached from s t a g e I I i s w i t h e i t h e r C o b l e creep o r i t s accommodation p r o c e s s ,  is  inconsistent  sliding.  It  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 t h o u g h the p o s s i b i l i t y t h a t i t r e l a t e s to a  is  117. d i f f e r e n t process  altogether  w i l l be d i s c u s s e d  later.  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 vacancies  around boundary p r o t r u s i o n s , i n w h i c h case the d i f f u s i o n  p a t h 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 (Chapter 2 . 3 . 3 . ) .  t h a n the g r a i n s i z e  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 w h i c h a r e o r d e r s of magnitude f a s t e r than the C o b l e m o d e l , 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  is  l i k e l y t h a t some g r a i n s would pause some of the t i m e , r e d u c i n g predicted rate,  but s t i l l  the  l e a v i n g i t f a s t e r than C o b l e 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 m o d e l . assumes t h a t  However, i t more r e a l i s t i c a l l y  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 n a t u r e and d i s t r i b u t i o n o f p r o t r u s i o n s .  Again,  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 C o b l e m o d e l , 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 C o b l e c r e e p  from r a t e a n a l y s i s . now be  Whether the p r o c e s s  other c r i t e r i a  will  considered: (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 Chapter  satisfies  with observation (although  see  5.2.1.). 2 (ii)  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 f e a r a t h e r s t r o n g e r dependence  (perhaps  'z s L  ).  Both  models a r e c o n s i s t e n t (iii)  with observation for stage  II.  The model r e q u i r e s t r i p l e l i n e accommodation,  by d i f f u s i o n or s l i p .  appears  to be about as  as C o b l e creep (from G i f k i n s ( 1 9 6 8 ) ) , and thereby  too s l o w to be  significant.  The former p r o c e s s  either  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 p r o c e s s 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 stage I .  However, the i n c r e a s e  to t h i s t h e o r y . increase  It  for  i n AH^ i n s t a g e I i s the major  obstacle  i s p o s s i b l e , a l t h o u g h h a r d to v i s u a l i z e , t h a t  i n AH^ i s a s p u r i o u s e f f e c t , due to a temperature  backstress.  fast  (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  the  dependent  anomalous  result i l l u s t r a t e d i n Figure 4.41). If  the d i s l o c a t i o n s e m i t t e d i n the above model are  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  not  t h r o u g h the  b u l k c o u l d 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 e q u a l to  that  for  the  bulk 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  " 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  ( u n u s u a l concept I ) , i n w h i c h 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 p r o c e s s a r i s e s dependence of m o b i l e d i s l o c a t i o n d e n s i t y . at l e a s t p  m  a  through a s t r e s s  However, a dependence  of  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  m observed f o r s t a g e I i n some cases ( e . g .  m ^ .15m Lee ( 1 9 6 9 ) * ) .  of There  i s no e x p e r i m e n t a l e v i d e n c e to suggest such a r e l a t i o n s h i p i n any deformation process,  l e t alone t h i s i n s t a n c e .  On the o t h e r h a n d , such  a r e l a t i o n s h i p c o u l d occur i f the number of sources  emitting  dislocations  were to d e c r e a s e 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 yield.  sufficient  to cause  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 i n s t a g e I s h o u l d not be i g n o r e d .  The a c t i v a t i o n energy i s expected  be l a r g e r than t h a t f o r boundary d i f f u s i o n , c o n s i s t e n t behaviour. moreover,  process  w i t h the  to  observed  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 o r away from b o u n d a r i e s ; the s o l u t e s p e c i e s 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  slow w i t h r e s p e c t t o the m a t r i x (Honeycombe  are  (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 v e r y l i k e l y a t bumps on s l i d i n g boundaries  (Chapter 4.4.4.3.).  To be the s t a g e I  process,  m i g r a t i o n would have to have an i n h e r e n t s t r a i n r a t e s e n s i t i v i t y than t h a t of the s t a g e I I p r o c e s s  ( s l i d i n g ) , a l t h o u g h the  apparent  s e n s i t i v i t y c o u l d be reduced by a d e c r e a s e i n a c t i v e sources d e c r e a s i n g 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 . t h e o r e t i c a l or e x p e r i m e n t a l i n f o r m a t i o n e x i s t s  less  with No  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 t a g e 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 r e a s o n a b l y s u b j e c t e d  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.  M o r e o v e r , the n a t u r e of the n e t w o r k s , the g e n e r a t i o n  d i s l o c a t i o n , and the manner i n w h i c h the d i s l o c a t i o n s i n t e r a c t  of  with  b o u n d a r i e s 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 s t a g e I been p r o p o s e d . creep (Chapter 4.5.) argues a g a i n s t  The absence of p r i m a r y  the e x i s t e n c e of networks  (pileups  120. or o t h e r w i s e ) .  F u r t h e r m o r e , 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  t h a t 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..  In general, i t i s  expected t h a t the above models have much r e l e v a n c e  not  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 t h a t m s h o u l d i n c r e a s e decreasing s t r a i n - r a t e  i n stage I ,  Newtonian v i s c o s i t y d o m i n a t e „ ( e . g . sliding).  as d i f f u s i o n a l p r o c e s s e s  with  of  d i f f u s i o n a l accommodation f o r  T h i s p r e d i c t i o n has not y e t been d e m o n s t r a t e d , presumably  because of the e x t r e m e l y 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 t h a t 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 c u r v e s were d e t e r m i n e d over a range of temperatures (two g r a i n s i z e s ) ,  for several a l l o y s :  Pb-6vol.%Cd, Pb-28vol.%Cd  C d - 6 . 5 v o l . % P b (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 m e c h a n i c a l e q u a t i o n of s t a t e was e s t a b l i s h e d and I I ,  f o r stages I  a l t h o u g h the shape of the m-curves i n s t a g e 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 , p r i m a r y creep was n e g l i g i b l e i n s t a g e s I and II.  For the l e a d - b a s e d a l l o y s , the amount of p r i m a r y creep  the more s t a g e I I I  became apparent i n any g i v e n m - c u r v e .  cadmium-based a l l o y s , s t a g e I I I  increased  For  was c h a r a c t e r i z e d by " d e l a y e d 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  tests.  A l t h o u g h g r a i n growth o c c u r r e d as a f u n c t i o n of i n eutectic-3y  strain  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%  i n d i c a t i n g t h a t g r a i n growth i s not a n e c e s s a r y f e a t u r e of (stage  the  elongation),  superplasticity  II). 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 * ( s t a g e  II)  was i n c o n c l u s i v e , a l t h o u g h the t e c h n i q u e 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 C d - 6 . 5 v o l . % P b and P b - 2 8 v o l . % C d , c o n s i s t e n t previous  observation. 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  (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 c r e e p eutectic  with  alloys  investigation),  b e h a v i o u r was p r o b a b l y b e s t d e s c r i b e d i n terms of a w e i g h t e d  average of the volume f r a c t i o n s  of the two p h a s e s .  The p r e s e n c e of  l a r g e s p e c i f i c a r e a of i n t e r p h a s e boundary had no u n u s u a l e f f e c t .  a,  122.  Surface stage I I  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  f o r Cd-3u* and Cd-8u*, c o n s i s t e n t  The e x t e n s i v e  w i t h other  investigations.  s l i d i n g w h i c h 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  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 .  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  migration  " P e e l i n g " (observed  in  effect.  B a s a l s l i p was s t r o n g l y apparent i n s t a g e I I  i n Cd-8u*,  the  absence o f t w i n n i n g and n o n - b a s a l s l i p due t o the p a r t i a l p r e s e n c e of sliding. 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 p l a u s i b l e reason f o r i t s s l i p accommodation f o r  existence i n superplasticity involving  the  was a s s o c i a t e d w i t h g r a i n  A p i l e u p model i n w h i c h r e c o v e r y o c c u r s a t o r near  the b o u n d a r i e s was adopted f o r s t a g e I I I , of s u p e r p l a s t i c processes ( i . e .  the p r o c e s s  acting  independently  " p a r a l l e l " processes.)  The a c t i v a t i o n energy i n s t a g e 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 a t t r i p l e l i n e s was adopted as the most l i k e l y c o n t r o l l i n g process II,  i n stage I I .  rate-  The model c o u l d a p p l y t o s t a g e s I and  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 s t a g e 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. If  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 t a g e 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 step i n stage  I,  the l i k e l y p r o c e s s e s i n v o l v e boundary m i g r a t i o n o r d i s l o c a t i o n m o t i o n through the b u l k .  In either  c a s e , the p r o c e s s i n v o l v e s the  s l i d i n g mechanism ( w i t h s l i p accommodation) process.  a  sliding.  The a c t i v a t i o n energy i n s t a g e I I I boundary d i f f u s i o n .  relaxation tests",  basic  as a dependent o r  "series"  123. APPENDIX A  Low temperature  deformation  General The d e f o r m a t i o n 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 25u are not f e a s i b l e  i n pure cadmium.  l e s s than about  I n o r d e r to p r o v i d e b a s i c  data  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 w i d e range of t e m p e r a t u r e .  Due t o 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 essentially  those of pure cadmium.  Y i e l d behaviour At h i g h e r temperatures  uniform y i e l d i n g occurs  (stage  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 A l t h o u g h d i s c u s s e d i n the t e x t (Chapter 4 . 1 . ) ,  III),  (stage  II).  the phenomenon i s  r e l e v a n t to the p r e s e n t d i s c u s s i o n , and s e v e r a l h i g h temperature  flow  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 by L u d e r s band p r o p a g a t i o n .  non-uniform y i e l d i n g occurs  presumably  (However, L u d e r s bands have n o t been  c o n f i r m e d 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 a t the end of the n o n - c o n t i n u o u s y i e l d regime (e.g.  Figure A . l . ,  reflects  -140°C)  has c o n s i d e r a b l e p r e c e d e n t ,  and p r o b a b l y  the approach and m u t u a l a n n i h i l a t i o n of two Luders  fronts.  P e c u l i a r l y , n o n - c o n t i n u o u s y i e l d i n g i s absent i n C d - 8 u * a t I ^  -140°C,  124. w h i l e i t i s v e r y pronounced i n C d - 3 u * . As n o n - c o n t i n u o u s y i e l d i n g i s unprecedented i n  coarse-grained  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 a t - 9 6 ° C  (.25  T ). w  M A s i m i l a r l y unprecedented Liiders y i e l d o c c u r r e d ( f o l l o w e d by b r i t t l e fracture),  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 * a t  .25 T . M w  I t would  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 . Yield  metals.  theory I g n o r i n g f o r the moment the anomalous y i e l d b e h a v i o u r of  Cd-8u* at T < -140°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 b o t h u n i f o r m and n o n - u n i f o r m 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  where  m  = p  o  + f(e ), p '  (A.l)  p = mobile d i s l o c a t i o n density a f t e r macroscopic m P  o  =  yield,  m o b i l e 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 m a c r o s c o p i c yield,  f(e  Unless P  q  P  ) = an i n c r e a s i n g f u n c t i o n o f p l a s t i c s t r a i n  (approximately  l i n e a r i n B . C . C . metals^Hahn ( 1 9 6 2 ) ) .  = 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 t h a 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 . exponent n(= ^ ) ,  The lower the  stress-sensitivity  the more pronounced the y i e l d c h a r a c t e r i s t i c s .  not been determined f o r the p r e s e n t a l l o y s a t low t e m p e r a t u r e s .  N has  125.  0  4  8  12  STRAIN  FIGURE A . l .  I n s t r o n flow curves f o r  16  20  24  (%)  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  S T R A I N (%)  ^FIGURE A.2.  I n s t r o n f l o w curves f o r C d - S u * , assuming r e d u c t i o n of c r o s s - s e c t i o n a l a r e a w i t h  uniform  strain.  6..  .Ignoring e l a s t i c e f f e c t s , a generalized d e r i v e d from the work of Hahn (1962) and C o t t r e l l  e q u a t i o n may be (1963):  J. - *< > E  +  P  where  m  ( A . 2)  >  a = flow s t r e s s , g(e  P  ) = work h a r d e n i n g f u n c t i o n ( z e r o when e  E q u a t i o n (A.2) p r e d i c t s stage I I I  HIT)  P  uniform y i e l d i n g (Figure A . 3 a . ) ,  b e h a v i o u r i n the p r e s e n t work ( e . g .  form of d e f o r m a t i o n , w h i c h o c c u r s i f  lower y i e l d o'  TV  + 65°rj) .  the d e f o r m a t i o n o u t s i d e  are d y n a m i c a l p r o p e r t i e s  and  the L u d e r s the  u n r e l a t e d t o normal y i e l d  Li JL  mechanisms.  CO CO LU  or hco  a. UNIFORM YIELDING  to  i s an a l t e r n a t e  I n e i t h e r c a s e , the upper y i e l d  b . NON-UNIFORM YIELDING  STRAIN FIGURE A . 3 .  similar  Figure A . l . ,  Hahn s u g g e s t s t h a t n o n - u n i f o r m y i e l d i n g ( F i g u r e A . 3 b . )  band spreads s l o w l y .  = 0)  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 ( 1 9 6 2 ) ) .  128. C o t t r e l l a c c e p t s the d y n a m i c a l approach i n the case of s i n g l e c r y s t a l d e f o r m a t i o n where d i s l o c a t i o n u n p i n n i n g o r m u l t i p l i c a t i o n i s u n i f o r m a l o n g 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 n o n - u n i f o r m 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  next. 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  flow 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  w i t h m e t a l s and non-metals where p non-metals  l i k e L i F where p  annealed m e t a l s ) ,  o  = 10  2  Q  i s very s m a l l . I t occurs i n 6—8 — cm (p =10 cm i n most o - 2  2  i n " w h i s k e r s " , and i n B . C . C . m e t a l s where m o b i l e  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 p i n n e d by i n t e r s t i t i a l It is possible,  associated  as w e l l ,  due to g r a i n boundary  that P  q  pinning.  segregation.  i s r e l a t i v e l y low i n Cd-3u* and Cd-8u*, 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 ends are pinned by b o u n d a r i e s would be expected decreasing g r a i n s i z e . i n v e r s e l y as the g r a i n  to i n c r e a s e  with  (The boundary a r e a p e r u n i t volume v a r i e s size.)  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 v i r t u a l l y temperature i n s e n s i t i v e concept of a t h e r m a l y i e l d . (i.e.  (Figure A.4.), consistent  The o p e r a t i o n of Frank-Read  d i s l o c a t i o n s p i n n e d by b o u n d a r i e s )  is with  the  sources  i s a p l a u s i b l e mechanism.  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  The  for  Cd-8u*, a l t h o u g h 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 the b a s i s  whose  of two g r a i n s i z e s .  on .  The lower y i e l d s t r e s s d e c r e a s e s 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  t  A  h4 * -200  J  t  .22T  .13T,  I I I ! I -150  I  1  I I I I  I  - 1 0 0  TEMPERATURE  FIGURE A.4.  .36T\  .29T,M  I  I  I -50  (°c)  T e n s i l e f l o w s t r e s s as a f u n c t i o n o f temperature f o r v a r i o u s s t r a i n s (from F i g u r e s A . l . and A . 2 . ) .  I  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 r e g i m e , i s ambiguous i n v i e w of the l i m i t e d d a t a .  The a r e a d o e s , however, c o r r e s p o n d 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  d i s a p p e a r a n c e of t w i n n i n g and n o n - b a s a l s l i p .  (1965)), and w i t h  the  Figures A.5.-7. i l l u s t r a t e  the e x i s t e n c e of t w i n n i n g and n o n - b a s a l s l i p a t -140°C, whereas mode i s e v i d e n t 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.).  neither  It  is  p o s s i b l e t h a 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 M i s e s requirements contributes  and the d i s a p p e a r a n c e  of two r e l a t i v e l y " h a r d " modes  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  a n a l y s i s of d e f o r m a t i o n modes over the " i n t e r m e d i a t e " would be v e r y u s e f u l i n e x t e n d i n g t h i s Tentatively,  microscopic temperature  range  interpretation.  i t i s proposed t h a t  y i e l d i n g i n Cd-8u* a t T < -140°C r e s u l t s  the l a c k of  discontinuous  from an enhanced p r o p e n s i t y  for  t w i n n i n g 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 L u d e r s p r o p a g a t i o n .  The l i m i t e d e v i d e n c e s u g g e s t s t h a t  twinning frequency i n c r e a s e s w i t h  decreasing  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  ( R i s e b r o u g h (1965)), c o n s i s t e n t  w i t h the p r e s e n t  To t e s t the h y p o t h e s i s ,  observations.  Cd-8u* and Cd-3u* were deformed 3%  a t -140°C, and the s u r f a c e markings a n a l y s e d .  The absence of t w i n s  i n Cd-3u* and the p r e s e n c e o f t w i n s i n Cd-8u* would have l e n t s u p p o r t 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 t h a t  twinning  o c c u r r e d i n b o t h cases ( F i g u r e A . 5 . 6 . ) , a l t h o u g h not e x t e n s i v e l y . i s quite possible that  twinning occurs  grains.  It  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 the l a r g e s t  To c l a r i f y the i s s u e would r e q u i r e a  i n t e r p r e t a t i o n of numerous m i c r o g r a p h s over a range of  to  to  statistical  temperatures,  131.  FIGURE A . 5 .  Twinning i n Cd-3u*. -  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 ( p e t r o l e u m e t h e r ) , 3%6. X 1 0 , 0 0 0 .  s t r a i n s and g r a i n s i z e s . An u n e x p l o r e d p o s s i b i l i t y i s t h a t p l a s t i c d e f o r m a t i o n 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 contractions  i n cadmium can be a p o t e n t s o u r c e o f 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 s h o u l d be most pronounced i n c o a r s e - g r a i n e d cadmium deformed a t v e r y low t e m p e r a t u r e .  . Dynamic r e c o v e r y F i g u r e A . 8 . shows how the m a c r o s c o p i c w o r k - h a r d e n i n g r a t e d e c r e a s e s w i t h i n c r e a s i n g temperature above - 1 9 6 ° C beyond 2% i n C d - 8 u * and 4% i n C d - 3 u * . obscures i n t e r p r e t a t i o n . )  , for  strains  (At l o w e r s t r a i n s the y i e l d  effect  The i m p l i c a t i o n i s t h a t dynamic r e c o v e r y  occurs even at v e r y low t e m p e r a t u r e s .  M o r e o v e r , the w o r k - h a r d e n i n g 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 * , s u g g e s t i n g t h a t  the  r e c o v e r y p r o c e s s i s enhanced by the presence of g r a i n boundaries^". B r o a d l y s p e a k i n g , dynamic r e c o v e r y may o c c u r 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  o r d e r 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 o r d e r 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  <  1120 . >  Although  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 o r t h e r e i s good e v i d e n c e f o r i t s e x i s t e n c e .  zinc,  F o r example, P r i c e (1963)  I n f a c t , a t -100 C i n C d - 3 u * , dynamic r e c o v e r y i s f a s t enouth t o p r e v e n t h a r d e n i n g p a s t the L u d e r s ' e x t e n s i o n . A t - 6 0 ° C , immediate Luders' f a i l u r e occurs. The i n s t a b i l i t y w h i c h o c c u r s a t 'v - 6 0 ° 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 C o n s i d ^ r e 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 t e m p e r a t u r e s , 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 l o w 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 , b o t h m and y a r e s m a l l , making = y << 1, and l e a d i n g to the observed g r o s s i n s t a b i l i t y . m  134.  oL_J—II  -200  I  I  I  I  I  -150  i  i  i  i  i  i  -100  i -50  TEMERATURE (°C)  FIGURE A.8.  Work-hardening .for various  r a t e (•—)  as a f u n c t i o n o f temperature  s t r a i n s (from F i g u r e s A . l . and A . 2 . ) .  135. a s s o c i a t e d t h e p r o d u c t i o n o f elongated b a s a l loops w i t h t h e 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 a c t as an  e f f e c t i v e r e c o v e r y process i n cadmium o r z i n c has not y e t been r e s o l v e d . However, i t i s u n l i k e l y t h a t c r o s s - s l i p c o u l d account  f o r the more r a p i d  r e c o v e r y i n C d - 3 u * than i n Cd-8u*. A c o n c e i v a b l e d i f f u s i o n a l r e c o v e r y process i n v o l v e s t h e c o n s e r v a t i v e climb o f s e s s i l e d i s l o c a t i o n loops produced c r o s s - s l i p o r by vacancy  condensation  " p i p e " d i f f u s i o n around the l o o p s . boundaries absorb  (Price  I t i s not expected  should a f f e c t t h i s p r o c e s s .  loops by a c t i n g as vacancy  (1963)).  e i t h e r by  Climb  occurs  through  that grain  However, g r a i n boundaries  could  s i n k / s o u r c e s f o r the loop h a l f - p l a n e s .  Such a r e c o v e r y process i s c o n s i s t e n t w i t h t h e observed g r a i n s i z e dependence o f the work-hardening  rate.  A s i m i l a r recovery  process  i n v l o v e s the boundary a b s o r p t i o n o f excess v a c a n c i e s produced n o n - c o n s e r v a t i v e motion o f jogged screw d i s l o c a t i o n s .  Recovery a t »2T^  i n cadmium has been i n t e r p r e t e d i n terms o f vacancy m i g r a t i o n and Stevenson  ( 1 9 6 3 ) ) , and i s a l e g i t i m a t e p o s s i b i l i t y  by t h e  (Peiffer  i n the present  context. A p o s s i b i l i t y which has been i g n o r e d i n the p r e v i o u s d i s c u s s i o n i s t h a t the work-hardening r a t e may be i n f l u e n c e d by t w i n n i n g . What has, been assumed t o r e f l e c t dynamic r e c o v e r y may i n f a c t r e f l e c t a dependence o f twinning on temperature  and g r a i n  partially  size.  136.  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  Al-Cu  (eutectic)  H o l t and Backofen (1966)  Al-Mg  (eutectic)  Lee ( 1 9 6 9 )  1  B i - S n (Sn - 1% B i ) (Sn - 5% B i )  Alden Alden  (1966) (1967)  Cd-Pb (Pb - 5  Alden  (1968)  Al-Zn  W  /  Q  Cd)  (eutectoid)  B a l l and H u t c h i s o n ( 1 9 6 9 ) , H o l t ( 1 9 6 8 ) , A l d e n and S c h a d l e r ( 1 9 6 8 ) , C h a u d h a r i (1967) , K o s s o w s k i ( 1 9 6 6 ) , B a c k o f e n e t a l (1965).  (eutectic) (Zn  . 5% A l )  P a c k e r e t a l (1968) Cook (1968)  ;  12  Low a l l o y s t e e l s T i t a n i u m and z i r c o n i u m a l l o y s Nickel  '  Lee and Backofen (1967)  (pure)  F l o r e e n (1968) Hayden e t a l ( 1 9 6 7 ) , Hayden and Brophy (1968)  Fe-Ni-Cr alloys Pb-Sn  M o r r i s o n (1968)  (eutectic)  Zehr and B a c k o f e n (1968) M o r r i s o n (1968) , , C l i n e and A l d e n 1  (Pb - 19% S n , Sn - 2% Pb) (electroplated  composites)  P b - T l (Pb - ( 0 . 5 - 7.9) % T I )  2  C l i n e and A l d e n (1967) M a r t i n and B a c k o f e n (1967) Gifkins  (1967)  (1967)  137.  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 " If  the d i s l o c a t i o n model proposed i n Chapter 4.7. i s  valid,  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 :  P .L A& = -:-=• A.E  . ,.—6. 10 m.  AO  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 = Instron linkage length  20 i n ) , 2  A = Instron linkage cross-sectional  area  .5 i n  E = e l a s t i c modulus of l i n k a g e (> 3 x 1 0  7  ),  psi).  With the specimen gauge l e n g t h I <v 1 i n . , the minimum anelastic  —6  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 s o u r c e of l e n g t h ^ l u per g r a i n , w h i c h on the average  is  ^ F.R. 2  bowed to h a l f i t s "breakaway" a r e a Aysuming L ^ 3u  (i.e.  and w i t h b ^ 2 x 10 S,  (2 x 10 ^p) ^-~-y3 = 2 x I O . - 5  %(  ") -  .2u ). z  the s t r a i n per g r a i n i s  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 1 0 , b u t a t l e a s t as l a r g e as - 6  the  r e q u i r e d 10 . 6  A l t h o u g h the above c a l c u l a t i o n i s o n l y an o r d e r of magnitude e s t i m a t e ,  i t shows t h a t 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.  T r a n s . AIME 236 (1966) 1633. A c t a Met. _15 (1967) 469. Trans.ASM 61_ (1968) 559. A c t a Met. _17 ( 1 9 6 9 )  1435.  1  J'. A u s t . I n s t . Met. 14 ( 1 9 6 9 ) A l d e n , T.H. and S c h a d l e r , H.W.  Backofen, W.A.  et a l .  207.  T r a n s . AIME 242 (1968) 825.  Avery, D.H. and Backofen, W.A. Avery, D.H. and S t u a r t , J.M.  2  T r a n s . ASM _51_ (1965) 551. F o u r t e e n t h Sagamore Army M a t e r i a l s Conf. (1967).  Research  T r a n s . ASM 57 (1964) 980. T r a n s . AIME 242 (1968) 329.  B a l l , A. and H u t c h i s o n , M.M. Barrett, CR.  et a l .  T r a n s . AIME 230 (1964) 200.  B a r r e t t , C R . and.Nix, W.D. B e l l , R.L. e t a l . . Chaudhari, P.  M e t a l S c i e n c e J . _3 (1969) 1.  A c t a Met. 1_3 (1965) 1247.  T r a n s . AIME 239 (1967) 1821.  A c t a Met. _15 ( 1 9 6 7 )  1  1777.  IBM Research Report RC 1946 C l i n e , H.E. and A l d e n , T.H.  J . App. Phys. 34 (1963) 1679.  Cuddy, L . J .  Met. T r a n s . 1 (1970) 395.  K.C  Dorn, J . E . Evans, D.  Unpublished Work (Cu-5%Fe) 1968.  "Creep  and Recovery",  Ph.D. T h e s i s , U.B.C.  F l i n n , J . E . and Duran, S.A. G a r o f a l o , F.  2  T r a n s . AIME 239 (1967) 710.  Coble, R.L.  Donaldson,  (1967) .  ASM (1957) 255. (1964).  T r a n s . AIME 236 (1966) 1056.  "Fundamentals o f Creep and Creep-Rupture i n M e t a l s " , M a c M i l l a n (1965).  139.  Gibbs, G.B..  P h i l . Mag. L3 (1966) 317. Memoires S c i e n t i f i q u e s  G i f k i n s , R.C.  Rev. Met. L X I I No. 10 (1965).  J . I n s t . Met. 95 (1967) 373. J . Amer. Ceramic  Soc. _51_ (1968) 69.  J . Mat. S c i . _5 (1970) 156. G i f k i n s , R.C. and Langdon, T.G.  S c r i p t a Met. 4 (1970) 563.  G i f k i n s , R.C. and Snowden, K.U.  Nature 21_1 (1966) 916. T r a n s . AIME 239 (1967) 910.  G l e i t e r , H.  A c t a Met. _17 (1969) 565.  Graeme-Barber, Guiu, F.  C.  Ph.D. T h e s i s , U n i v . London  (1967).  S c r i p t a Met. 3 (1969) 753.  Hahn, G.T.  A c t a Met. 10 (1962) 727..  Harris, J.E. H a r t , E.W.  J . N u c l . Mat. _10 (1963) 360. A c t a Met. _15 ( 1 9 6 7 ) A c t a Met. 15 ( 1 9 6 7 )  Hayden, H.W.  and Brophy, J.H.  Hayden, H.W.  et a l .  351.  2  1545.  T r a n s . ASM 61^ (1968) 542.  T r a n s . ASM ^0 (1967) 3.  H e n s l e r , J.H. and G i f k i n s , R.C. H e r r i n g , C.  1  J . I n s t . Met. 92 (1963-64) 340.  J . App. Phys. 21 (1950) 437. T r a n s . AIME 2A2 (1968) 25.  Holt,  D.L.  Holt,  D.L. and Backofen, W.A.  T r a n s . ASM _59 (1966) 755.  Honeycombe, R.W.K.  "The P l a s t i c Deformation o f M e t a l s " A r n o l d  Ishida,  Y. et a l .  T r a n s . AIME 233 (1965) 204.  Ishida,  Y. and Brown, M.H.  Johnston, W.G.  A c t a Met. _13 (1967) 875.  and Gilman, J . J .  J . App. Phys. _30 (1959) 129.  (1968).  Jonas, J . J . Karim, A.  A c t a Met. _17 (1969) 397. S c r i p t a Met. _3 (1969) 887.  Karim, A. e t a l . Kochs, U.F. Kossowski,  T r a n s . AIME 245 (1969) 1131.  T r a n s . AIME 239 (1967) 1107.  R.  T r a n s . AIME 242 (1968) 716.  Langdon, T.G. and G i f k i n s , R.C. Lee, D.  S c r i p t a Met. 4- (1970) 337.  T r a n s . AIME 239 (1967) 1034. A c t a Met. JL7 (1969)  1057.  1  S c r i p t a Met. 2 ( 1 9 6 9 ) Lee, D. and Backofen, W.A. L i , J.C.M.  893.  2  T r a n s . AIME 59 (1966) 755.  " D i s l o c a t i o n Dynamics", McGraw-Hill  L i f s h i t z , M.  Phys. J.E.T.P. l]_ (1963) 909.  Soviet  MacEwan, S.R. et a l .  S c r i p t a Met. 3_ (1969) 441.  M a r t i n , P.J. and Backofen, W.A. McLean, D.  T r a n s . ASM _60 (1967) 352.  T r a n s . AIME 242 ( 1 9 6 8 )  "Metals Handbook" M o r r i s o n , W.B.  ASM  1  1193.  (1948).  T r a n s . ASM 61 (1968)  1  423,  T r a n s . AIME 242 ( 1 9 6 8 ) Nix, W.D.  and B a r r e t t ,  Okkerse, B.  CR.  2  2221.  T r a n s . ASM _61 (1968) 695.  A c t a Met. 2 (1954) 551.  Packer, C M .  and Sherby, O.D.  Packer, C M .  et a l .  T r a n s . ASM 60 (1967) 23.  T r a n s . AIME _242 (1968) 2485.  P e i f f e r , H.R. and.Stevenson, F.R. P r i c e , P.B.  (1967) 87.  J . App. Phys. 34 (1963) 2804.  " E l e c t r o n Microscopy and S t r e n g t h o f C r y s t a l s " , I n t e r s c i e n c e (1963) 41.  Rachinger, W.A. Rawson and Argent  J . I n s t . Met. jtt (1952) 33.^ J . I n s t . Met. j)5 (1967) 212.  Risebrough, N.R.  Ph.D. T h e s i s , U.B.C.  Risebrough, N.R. and Lund, J.A. Ryan, H.F. and S u i t e r , J.W. Smith, G.S.  T r a n s . ASM £ 1 (1968) 723  P h i l . Mag. K) (1964) 729,  T r a n s . AIME 175 (1948) 15.  S m i t h e l l s , C.J.  "Metals R e f e r e n c e Book", B u t t e r w o r t h s  S q u i r e s , R.L. e t a l .  S t r u t t , P.R. e t a l . Surges, A.K.  T r a n s . ASM 59 (1966) 486.  J . I n s t . Met. 93 (1964) 71.  M.A.Sc. T h e s i s , U.B.C. P r i v a t e Communication  Underwood, E.E.  J . Metals U  Wajda, E.S. e t a l .  Weertman, J .  (1969).  (1970).  (1962) 914.  A c t a Met. 3 (1955) 39.  W a l t e r , J . L . and C l i n e , H.E. Waldron, R.J.  (1967).  J . N u c l . Met. 8 (1963) 77.  S t a r k , J.P. and Upthegrove, W.R.  T u r n e r , D.  (1965).  T r a n s . AIME 242 (1968) 1823.  Ph.D. T h e s i s , U.B.C.  (1969).  J . App. Phys. 26 (1955) 1213. J . App. Phys. 28 (1957) 362. T r a n s . ASM 61 (1968) 681.  W e i n s t e i n , D. T r a n s . AIME 245 (1969) 2041. Zehr, S.W.  and Backofen, W.A.  T r a n s . ASM 61 (1968) 300.  

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