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Superplastic creep in the lead tin eutectic Surges, Albert Keith 1969

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SUPERPLASTIC CREEP IN THE LEAD TIN EUTECTIC  by  ALBERT KEITH SURGES B.A. S c . , U n i v e r s i t y of B r i t i s h Columbia,  1967  A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED SCIENCE  i n the Department of METALLURGY  We a c c e p t t h i s t h e s i s as conforming to t h e required standard  THE UNIVERSITY OF BRITISH COLUMBIA A u g u s t , 1969  In  presenting  this  .an a d v a n c e d d e g r e e the L i b r a r y I  further  for  of  this  written  at  agree  tha  for  of  October  gain  Metallurgy  2 7 . 1970  of  Columbia,  British  by  for  Columbia  shall  the  requirements  reference copying of  I agree and this  that  not  copying  or  for  that  study. thesis  t h e Head o f my D e p a r t m e n t  is understood  financial  The U n i v e r s i t y o f B r i t i s h V a n c o u v e r 8 , Canada  of  for extensive  p u r p o s e s may be g r a n t e d It  fulfilment  available  permission.  Department  Date  freely  permission  representatives. thesis  in p a r t i a l  the U n i v e r s i t y  s h a l l make i t  scholarly  by h i s  thesis  or  publication  be a l l o w e d w i t h o u t  my  i  Abstract  An e x t e n s i v e creep study o f a s u p e r p l a s t i c m a t e r i a l has n o t p r e v i o u s l y been made. The p r e s e n t study was c a r r i e d out to determine i f t h e r e a r e any b a s i c d i f f e r e n c e s between the creep o f c o a r s e g r a i n e d m a t e r i a l s and f i n e g r a i n e d s u p e r p l a s t i c m a t e r i a l s . The r e s u l t s g i v e i n f o r m a t i o n about t h e m e c h a n i c a l 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 and a r e r e l e v e n t to an u n d e r s t a n d i n g o f t h e mechanics o f superplasticiy. A t h i g h s t r a i n r a t e s the s u p e r p l a s t i c l e a d - t i n e u t e c t i c deforms by r e c o v e r y creep and a 3-stage creep c u r v e i s o b s e r v e d , s i m i l a r t o t h a t found f o r c o a r s e g r a i n e d m a t e r i a l s . As the s t r a i n r a t e i s d e c r e a s e d , the i n i t i a l  transient  (primary creep) d i s a p p e a r s and the creep curve i s l i n e a r u n t i l n e c k i n g o c c u r s and t e r t i a r y creep ends i n f a i l u r e . I n the p r i n c i p a l s u p e r p l a s t i c range, a t medium s t r a i n r a t e s , creep c u r v e s a r e l i n e a r to a t l e a s t 50 % s t r a i n . The r e c o v e r y r a t e i s i m m e d i a t e l y e q u a l t o t h e s t r a i n h a r d e n i n g r a t e and t h e r e i s no p r i m a r y c r e e p . A t low s t r a i n r a t e s the creep c u r v e i s s l i g h t l y convex as the creep r a t e d e c r e a s e s w i t h time. T h i s may be due t o t h e s e l f e x t i n g u i s h i n g n a t u r e o f d i f f u s i o n a l creep or p o s s i b l y s t r a i n i n d u c e d g r a i n growth. These r e s u l t s a r e c o n s i s t e n t w i t h the g r a i n boundary s l i d i n g  theories  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 e t a i l s o f t h e accommodation p r o c e s s e s a r e n o t known. A t the l o w e s t s t r a i n r a t e s , d i f f u s i o n a l creep may o p e r a t e .  ii  ACKNOWLEDGMENT  The a u t h o r i s g r a t e f u l f o r t h e a d v i c e o f and h e l p f u l d i s c u s s i o n w i t h h i s r e s e a r c h d i r e c t o r , Dr. T.H. A l d e n . Thanks a r e a l s o extended t o R.C. Cook and K.C. Donaldson f o r t h e i r d i s c u s s i o n s and s u g g e s t i o n s . C.B. Sullivan's assistance with draghting i s also  appreciated.  f o r the p r e s e n t a t i o n of t h i s t h e s i s  Iii  TABLE OF CONTENTS  1.  INTRODUCTION  1  1.1  Stage I I ( S u p e r p l a s t i c Stage)  3  1.1.1 Review o f Experiment  3  1.1.2 T h e o r e t i c a l D i s c u s s i o n  5  1.2  Stage I I I  6  1.3  Stage I  6  1.4  P r e v i o u s Creep S t u d i e s on Lead and T i n Systems ... 8  2.  EXPERIMENTAL  2.1 2.2  M a t e r i a l and Specimen P r e p a r a t i o n Creep T e s t s  9 10  3.  RESULTS  13  3.1  Calculations  13  .3.2  Log S t r e s s v e r s u s Log S t r a i n Ra±e Curves  13  3.3  Creep Curves  16  9  3.3.1 Stage I I Creep Curves  16  3.3.2 Stage I Creep Curves  17  3.3.3 Stage I I - Stage I I I T r a n s i t i o n Creep Curves .... 17 3.3.4 Stage I I I Creep Curves  23  3.4  I n c r e m e n t a l Loading and Unloading  23  3.5  Strain After-Effects  29  4.  DISCUSSION  30  4.1  Stage I I I  30  4.2  Stage I I I - Stage I I T r a n s i t i o n  35  4.3  Stage I I I  37  4.4  Stage I  5.  SUMMARY AND CONCLUSIONS  44  6.  SUGGESTIONS FOR FUTURE WORK  46  7. 7.1  APPENDICES Computer Programme  47 47  7.2  A d d i t i o n a l Creep Curves  52  •  • 40  iv  7.3  8.  C a l c u l a t i o n of T h e o r e t i c a l Creep Curves f o r Pure N a b a r r o - H e r r i n g Creep and Pure Coble Creep  53  BIBLIOGRAPHY  64  V  LIST OF FIGURES  No.  Page  1.  C h a r a c t e r i s t i c l o g s t r e s s versus l o g s t r a i n rate curve.  1  2.  Specimen i n g r i p s .  10  3.  Constant s t r e s s creep machine.  12  4.  Log s t r e s s v e r s u s l o g s t r a i n r a t e c u r v e . (SGS, 2 m i c r o n s ) .  14  5.  Log s t r e s s v e r s u s l o g s t r a i n c u r v e . (LGS, 8 m i c r o n s ) .  15  6.  Comparison of the S-curve d a t a o f the p r e s e n t and p r e v i o u s work.  16  7.  Stage I I creep c u r v e (SGS), 429 p s i .  18  8.  Stage I I creep c u r v e (SGS), 1716 p s i .  9.  Stage I I creep c u r v e (SGS), 715 p s i .  20  10.  Stage I I creep c u r v e (LGS), 814 p s i .  21  11.  Stage I creep c u r v e (SGS), 97 p s i .  22  12.  Creep c u r v e i n s t a g e I I - s t a g e  I I t r a n s i t i o n (SGS, 3432 p s i .  24  13.  Creep c u r v e i n s t a g e I I - s t a g e  I I I t r a n s i t i o n (LGS), 3582 p s i .  25  , 19  14.. Stage I I I creep c u r v e (5212 p s i ) .  26  15.  Stage I I I creep c u r v e (5535 p s i ) .  26  16.  Stage I I I creep c u r v e (6512 p s i ) .  28  17.  Strain required  27  18.  Incremental loading duringsuperplastic  19.  R e t u r n o f an i n i t i a l t r a n s i e n t w i t h i n c r e m e n t a l l o a d i n g  20.  T r a n s i t i o n to s t e a d y s t a t e w i t h u n l o a d i n g i n s t a g e I I I .  31  21.  S t r a i n r e l a x a t i o n study i n s t a g e I I  32  22.  Reloading a f t e r recovery i n stage I I I  32  23.  Log s t r e s s v e r s u s l o g s t r a i n r a t e r e l a t i o n s h i p f o r Pb-2.45 wt%.  to r e a c h steady s t a t e v e r s u s creep s t r e s s . creep.  18 i n stage III31  vi  24.  Log s t r e s s v e r s u s l o g s t r a i n r a t e r e l a t i o n s h i p f o r Pb-2.45 wt% t h a l l i u m (100 u ) .  25.  E x p e r i m e n t a l , t h e o r e t i c a l N-H and t h e o r e t i c a l Coble creep c u r v e s (97 p s i ) .  Appendix I I I a.  Stage I I (SGS) 572 p s i .  b.  Stage I I (SGS), 858 p s i .  c.  Stage I I (SGS), 1144 p s i .  d.  Stage I I LGS), 407 p s i .  e.  Stage I I (LGS), 1221 p s i .  f.  Stage I (SGS), 120 p s i .  g.  Stage I (SGS), 143 p s i .  h. Stage I (SGS), 286 p s i . i.  T r a n s i t i o n (SGS), 2574 p s i .  j.  T r a n s i t i o n (SGS), 2860 P s i .  k. T r a n s i t i o n (LGS), 1954 p s i . 1. T r a n s i t i o n (LGS), 2280 p s i . m. T r a n s i t i o n (LGS), 2606 p s i . n. T r a n s i t i o n (LGS), 2932 p s i . o. T r a n s i t i o n (LGS), 32580 p s i . p. T r a n s i t i o n (LGS), 3908 p s i . q. T r a n s i t i o n (LGS), 4234 p s i . r . T r a n s i t i o n (LGS), 4560 p s i . s. T r a n s i t i o n (LGS), 4886 p s i . t . Stage I I I , 2931 p s i . u. Stage I I I , 7326 p s i . v. Stage I I i n c r e m e n t a l l o a d i n g , w. Stage I I I u n l o a d i n g  -1-  I.  Introduction  S u p e r p l a s t i c b e h a v i o u r has been found i n many m e t a l systems.  Alloys  of l e a d and z i n c have been i n v e s t i g a t e d most f r e q u e n t l y , b u t systems c o n t a i n i n g n i c k e l , i r o n , aluminium,  t i n , cadmium, magnesium, and copper have a l s o e x h i b i t e d  s u p e r p l a s t i c p r o p e r t i e s . S t u d i e s have a l s o been made t o determine  deformation  mechanisms which a r e c o n s i s t e n t w i t h experiment. R e s u l t s o f these s t u d i e s may a l s o be i m p o r t a n t i n the development o f new m e t a l - f o r m i n g t e c h n i q u e s . Stress versus s t r a i n been p l o t t e d  r a t e r e s u l t s from t e n s i l e and creep t e s t s have  as l o g s t r e s s ( l o g a) v e r s u s l o g s t r a i n r a t e ( l o g e) t o produce  a c h a r a c t e r i s t i c t h r e e s t a g e S-shaped c u r v e . I n the s u p e r p l a s t i c range, I I , the s t r a i n r a t e (e) i s i n s e n s i t i v e t o t h e a p p l i e d s t r e s s ( C T ) .  LOG  STRAIN  RATE  F i g u r e 1. C h a r a c t e r i s t i c l o g s t r e s s - l o g s t r a i n r a t e c u r v e .  stage  -2-  Each s t a g e of the S-curve may a  =  be d e s c r i b e d by the e q u a t i o n (1)  Ke  where K i s a c o n s t a n t and m i s c a l l e d the s t r a i n r a t e s e n s i t i v i t y parameter. T y p i c a l v a l u e s of m v a r y from l e s s than .1 f o r most m e t a l s up to 1.0 polymers and g l a s s e s . S u p e r p l a s t i c m e t a l s have been observed v a l u e s as h i g h as •SS''", .but a r e t y p i c a l l y about 0.5.  f o r hot  to e x h i b i t m  I n s t a g e I I , where m i s  high, p r o p a g a t i o n of a neck i s prevented by a l o c a l h a r d e n i n g r e s u l t i n g from an i n c r e a s e d s t r a i n r a t e , and thus d e f o r m a t i o n w i l l proceed  i n a softer portion  of the m a t e r i a l . A c c o r d i n g l y , a h i g h v a l u e of m i s a s s o c i a t e d w i t h l a r g e e l o n g a 2 t i o n s , r e p o r t e d l y as h i g h as 2000 % . M a t h e m a t i c a l l y , the r e l a t i o n s h i p between m and e l o n g a t i o n can be' shown more e x p l i c i t l y by f i r s t d i f f e r e n t i a t i n g e q u a t i o n  (1) to o b t a i n (2)  I t can be seen t h a t the l a r g e r the v a l u e of m,  the more i n s e n s i t i v e  r a t e becomes to a change i n s t r e s s . A l s o , over a c e r t a i n s t r a i n r a t e  strain range  in superplastic materials, m increases s l i g h t l y with increasing s t r a i n rate. The p o s i t i v e v a r i a t i o n of m i n s u p e r p l a s t i c m a t e r i a l s w i l l cause the f a c t o r i n b r a c k e t s i n e q u a t i o n (2) to be reduced, and w i l l f u r t h e r reduce s e n s i t i v i t y to  necking. F u r t h e r d e s c r i p t i o n of e x p e r i m e n t a l and t h e o r e t i c a l s t u d i e s on  super-  p l a s t i c i t y i s most c o n v e n i e n t l y done by c o n s i d e r i n g the s t a g e s of the l o g o l o g e curve s e p a r a t e l y . Of t h e s e , the most i m p o r t a n t and i n t e n s i v e l y s t u d i e d i s stage I I .  -3-  1.1.  Stage I I ( S u p e r p l a s t i c Stage)  1.1.1. Review of Experiment A f i n e g r a i n s i z e has been shown to be the most i m p o r t a n t 3-11 a l requirement f o r s u p e r p l a s t i c i t y .  Providing  microstructur-  the phases are of comparable  h a r d n e s s , the c o m p o s i t i o n and means by w h i c h g r a i n r e f i n e m e n t i s a c h i e v e d  are  6 9 of secondary importance. ' p e r m i t the f o r m a t i o n  of a f i n e g r a i n s i z e , w h i l e phase b o u n d a r i e s i n h i b i t  growth. Thus e x t e n s i v e and  I n two phase systems, a hot or c o l d w o r k i n g s t e p  a l s o e x h i b i t e d s u p e r p l a s t i c i t y . The  ^  inherent  a n  d  pure metal  systems,have  For a g i v e n time and  tem-  grain size i s larger i n dilute alloys. L a r g e e l o n g a t i o n s d u r i n g s t a g e I I have been c o n s i s t e n t l y r e p o r t e d .  largest elongations 16 values  % Al  problem w i t h these systems i s to  produce and m a i n t a i n a f i n e l y - d i v i d e d m i c r o s t r u c t u r e . perature,  grain  s t u d i e s have been made on the e u t e c t o i d Zn - 22 wt.  the Pb-Sn systems. D i l u t e a l l o y ^  will  The  occur a t s t r a i n r a t e s near t h a t a s s o c i a t e d w i t h peak m  18 '  . Maximum e l o n g a t i o n may  o b s c u r r e d by  the d e c r e a s i n g  o c c u r p r e c i s e l y a t peak m but  the r e s u l t i s  s t r a i n r a t e d u r i n g a t e n s i l e t e s t on a c o n s t a n t  head r a t e machine such as an I n s t r o n .  cross-  i  T e n s i l e t e s t s i n v o l v i n g s e v e r a l g r a i n s i z e s show t h a t the e f f e c t of g r a i n c o a r s e n i n g i s to s h i f t the s t r a i n r a t e a t c o n s t a n t s t r e s s to l o w e r T h i s s h i f t i s e x p r e s s e d by i s u s u a l l y between 2 and  the r e l a t i o n s h i p k ^ 1/L 1 3 5 7 8 1 2 1 3  A ' ' ' ' '  '  values.  ( f o r c o n s t a n t m) where a  and L i s the s p a c i n g  between g r a i n or  phase b o u n d a r i e s . Temperature  a l s o has  an e f f e c t on the S-curve. The  each temperature drops w i t h d e c r e a s i n g  temperature''". The  i n g to peak m a l s o d e c r e a s e s w i t h d e c r e a s i n g  maximum m f o r  s t r a i n r a t e correspond-  t e m p e r a t u r e ; An i n c r e a s e  i n tempera-  _4-  t u r e s h i f t s the c u r v e to h i g h e r s t r a i n r a t e s and to s l i g h t l y lower s t r e s s e s . G r a i n boundary s l i d i n g i s observed and i t s c o n t r i b u t i o n to t o t a l s t r a i n i n c r e a s e s as the s t r a i n r a t e i s lowered from s t a g e I I I i n t o s t a g e 11^' . lL  E x p e r i m e n t a l l y , the c o n t r i b u t i o n of GBS  by measuring  to t o t a l s t r a i n i s determined  the o f f s e t o f g r i d l i n e s i n s c r i b e d a c r o s s g r a i n b o u n d a r i e s  prior  to d e f o r m a t i o n . S u p e r p l a s t i c d e f o r m a t i o n does not cause the b u i l d up of a d i s l o c a t i o n s u b s t r u c t u r e . An Mg-Al alloy''" has been water quenched from 400°C d u r i n g s u p e r p l a s t i c d e f o r m a t i o n and t r a n s m i s s i o n e l e c t r o n m i c r o s c o p y showed no d i s l o c a t i o n t r a c e s . D i s l o c a t i o n s are present a f t e r deformation i n stage I I I . The low temperature y i e l d s t r e s s remains unchanged, r e l a t i v e to t h a t of the 13 undeformed m a t e r i a l , a f t e r s t a g e I I d e f o r m a t i o n  . Pb-5% Cd specimens were  deformed 2 % a t a s e l e c t e d t e m p e r a t u r e , s t r a i n r a t e and g r a i n s i z e and immediately  quenched to -90°C. The  .2% y i e l d s t r e s s was  then d e t e r m i n e d .  Specimens  deformed i n the s u p e r p l a s t i c range showed no i n c r e a s e i n y i e l d s t r e s s w h i l e those deformed i n s t a g e I I I showed an i n c r e a s e i n y i e l d  stress.  G r a i n shape remains equiaxed a f t e r as much as 1000- % e l o n g a t i o n ^ . G r a i n growth o c c u r s ^ ' ^ arid may may  be i m p o r t a n t i n the d e f o r m a t i o n p r o c e s s or  mask o t h e r r e l a t i o n s h i p s . 13 Recovery  r a t e s are f a s t i n s u p e r p l a s t i c m a t e r i a l s  and  decrease  w i t h i n c r e a s i n g g r a i n s i z e . Pb-5% Cd specimens were deformed 2% a t -90°C, annealed f o r v a r i o u s times a t 50°C then deformed a g a i n a t -90°C. The amount o f r e c o v e r y , R, was  determined by R = (aH - aR)/(aH  - aY) , where aH i s  determined a f t e r 2% s t r a i n , oR a f t e r r e c o v e r y and aY on the annealed There was  40% r e c o v e r y f o r a 4.1p  took 100 minutes  material.  g r a i n s i z e a f t e r o n l y .2 minutes w h i l e i t  to o b t a i n 30 % r e c o v e r y i n a 15y  specimen.  -5-  Although  t h e r e i s g e n e r a l agreement i n t h e e x p e r i m e n t a l  observations  made on s u p e r p l a s t i c m a t e r i a l s , disagreement on t h e r e l a t i v e importance o r i n t e r p r e t a t i o n o f i n d i v i d u a l o b e s e r v a t i o n has l e a d t o a wide range o f suggested  mechanisms.  1.1.2. T h e o r e t i c a l D i s c u s s i o n Work on t h e Al^-33 wt. % Cu e u t e c t i c ^ and t h e Zn-Al eutectic*"'" l e a d to s i m i l a r p r o p o s a l s t h a t t h e h i g h s t r a i n r a t e s e n s i t i v i t y w h i c h c h a r a c t e r i z e s s u p e r p l a s t i c i t y i s t h e r e s u l t o f boundary s h e a r i n g and m i g r a t i o n . G r a i n boundary shear was suggested  t o be r a t e c o n t r o l l i n g , and m e c h a n i c a l  obstruct-  i o n s t o s l i d i n g were removed by s t r a i n r a t e enhanced boundary 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 . A t t h i s intermediate s t r a i n r a t e , boundaries smoother and s t r e s s i s determined  6 on the Pb-Sn  become  by v i s c o u s drag a l o n g t h e b o u n d a r i e s .  Work  5 and S n - B i  systems a l s o l e a d t o t h e p r o p o s a l t h a t g r a i n boundary  s l i d i n g was t h e r a t e c o n t r o l l i n g mechanism. E x p e r i m e n t a l r e s u l t s showed^ t h a t the g r e a t e s t c o n t r i b u t i o n o f g r a i n boundary s l i d i n g o c c u r r e d when t h e s t r a i n r a t e s e n s i t i v i t y parameter, m, reached mechanism f o r d e f o r m a t i o n s l i d i n g and d i f f u s i o n a l  i t s peak v a l u e . A n o t h e r  suggested  o f Pb-Sn*^ i n c o r p o r a t e s non-Newtonian g r a i n boundary  (Newtonian) creep a c t i n g t o g e t h e r i n p a r a l l e l , and  then i n s e r i e s w i t h non-Newtonian s l i p c r e e p . C l o s e r e p r o d u c t i o n o f an exp e r i m e n t a l l o g a - l o g ! c u r v e , o b t a i n e d by u s i n g new and p r e v i o u s l y p l o t t e d p o i n t s , c o u l d be made u s i n g s e m i - e m p i r i c a l p r o c e d u r e s  based on the model.  G r a i n boundary s l i d i n g was proposed t o e x p l a i n the s u p e r p l a s t i c b e h a v i o u r o f t h e Mg-Al e u t e c t i c by Lee*. GBS i s accompanied by g r a i n and r e c o v e r y . These c o o p e r a t i v e p r o c e s s e s  deformation  are necessary, e s p e c i a l l y i n regions  near the boundary, t o p e r m i t e x t e n s i v e p l a s t i c d e f o r m a t i o n . No d i s l o c a t i o n s  -6-  were seen a f t e r s u p e r p l a s t i c d e f o r m a t i o n . T h i s i s p o s s i b l e because the g r a i n s i z e p e r m i t s a l l d i s l o c a t i o n s , even i n the b u l k of a g r a i n ,  to  fine  be  20 21 a t t r a c t e d to ' and r e a c h a b o u n d a r y w h i c h i s s l i d i n g by d i s l o c a t i o n 22 13 2A movement ' or d i f f u s i o n a l processes , and b e a n n i h i l a t e d . I t i s s u g g e s t e d t h a t t h i s m o d e l m i g h t e x p l a i n t h e l o w a m o u n t s o f GBS 25 '  thus l i m i t i n g  where the e f f e c t i v e g r a i n s i z e recovery to r e g i o n s near 3  Another  motion.  model  , based  d i f f u s i o n , was 1.2.  suggested  boundary.  (N-H)  c r e e p , and  m o d e l i s d o m i n a n t and  of t h i s model, i n v o l v i n g  i s based  flow i s strongly  the Coble v a r i a n t of  the  to b e t t e r account  f o r the observed  strain  rates.  Stage I I I  plastic.  Low  m values are t y p i c a l .  from photomicrographs  of the S-curve  T h e r e seems t o b e  t h e mode o f d e f o r m a t i o n p r e s e n t . S l i p  little  probably  i s not  and e l e c t r o n m i c r o g r a p h s  which  super-  controversy as  i s the deformation process show s l i p  l o c a t i o n s t r u c t u r e s r e m a i n i n g a f t e r d e f o r m a t i o n . The  to  indicated  lines  and  dis-  c o n t r o l l i n g process i s  r e c o v e r y by d i s l o c a t i o n c l i m b .  Stage  I  Stage at  dislocation  on g r a i n b o u n d a r y d i f f u s i o n r a t h e r t h a n v o l u m e  T h i s r e g i o n a t t h e h i g h s t r a i n r a t e end  1.3.  infinite,  o n e x p e r i m e n t a l w o r k o n P b - S n , i n v o l v e s two  I n t h e h i g h m r e g i o n , t h e N-H 27  a n a l y s i s which  i s more o r l e s s  the g r a i n  p r o c e s s e s . These are N a b a r r o - H e r r i n g  viscous. A modification N-H  sliding  26  experiments  competing  during b i c r y s t a l  •  ,.  .  _ , . . 7,28 . . 10 . . j 29 I shows g r a m e l o n g a t i o n , striations o r denuded zones  t r a n s v e r s e b o u n d a r i e s , and  b e e n some q u e s t i o n a s  reduced  to whether t h i s  g r a i n boundarty  sliding^'  1 1  .  There  has  stage i s r e p r e s e n t a t i v e of a separate  -7-  mechanism o r i s a t l e a s t p a r t i a l l y a c o n t i n u a t i o n of s t a g e I I . F u r t h e r  study  over a w i d e r range o f v a r i a b l e s may e x p l a i n the t r u e r e l a t i o n s h i p . Study of d e f o r m a t i o n i n t h i s r e g i o n o f t e n r e q u i r e s l o n g term creep t e s t s because o f t h e low s t r a i n r a t e s  involved. 30  Chaudhari and  proposes t h a t i n s t a g e I t h e d i s l o c a t i o n d e n s i t y i s s m a l l  the d i s l o c a t i o n s reaching  t h e g r a i n boundary can be absorbed a t t h e  boundary by e i t h e r s l i d i n g or m i g r a t i o n and l o c a l d i s l o c a t i o n c l i m b . As £he stress i s increased,  t h e f l u x o f d i s l o c a t i o n s a p p r o a c h i n g a g r a i n boundary  i n c r e a s e s more r a p i d l y than does t h e a b i l i t y of the g r a i n boundary t o absorb them. T h i s r e s u l t s i n a d i s l o c a t i o n b u i l d u p , an i n t e r n a l s t r e s s which  increases  w i t h s t r a i n r a t e and f i n a l l y s t a g e I I where s t r e s s i n c r e a s e s r a p i d l y w i t h  strain  rate. D e f o r m a t i o n o f the Mg-Al e u t e c t i c a t a low s t r a i n r a t e was s t u d i e d by Lee*. He found d e f o r m a t i o n t o be a combined e f f e c t o f g r a i n d e f o r m a t i o n and d e f o r m a t i o n a c r o s s  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 . The l a t t e r made up 1/3  of the d e f o r m a t i o n and o c c u r r e d  by GBS and p o s s i b l y some d i f f u s i o n a l c r e e p .  31 Alden  has r e c e n t l y proposed t h a t s l i p a t t r i p l e l i n e s i n response  to s l i d i n g i s r a t e c o n t r o l l i n g . The model i n v o l v e s the 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 between a s o u r c e ( t h e t r i p l e l i n e ) and a p e r f e c t s i n k ( t h e o p p o s i t e g r a i n boundary) and p r e d i c t s an m v a l u e between .33 and .5 and an a c t i v a t i o n energy o f b u l k d i f f u s i o n . He s u g g e s t s t h a t s u p e r p l a s t i c creep of F e - N i - C r may be of t h i s type. F e - N i - C r and Z n - A l (40.6 a t . % A l e u t e c t o i d )  show o n l y  2-stage l o g a c u r v e s . A l d e n suggests t h a t s t a g e I I i s n o t e n e r g e t i c a l l y f a v o r a b l e and o n l y s t a g e s I and I I I a r e seen i n these systems.  -8-  Constant l o a d creep t e s t s on the 2-stage  Zn-Al e u t e c t i c  lead  32 Chaudhari  to the c o n c l u s i o n t h a t a d i s l o c a t i o n model was  temperatures  above 200°C. The model i n v o l v e d the motion  i n an i n t e r n a l s t r e s s f i e l d periment  involved at  of d i s l o c a t i o n s  generated by n e i g h b o u r i n g d i s l o c a t i o n s .  Ex-  showed t h a t above 200°C the s t r a i n r a t e i s c o n t r o l l e d by a t h e r m a l l y  a c t i v a t e d p r o c e s s w i t h an a c t i v a t i o n energy  of 35.3  k cal./g-atom:  175°C, by a t h e r m a l l y a c t i v a t e d p r o c e s s w i t h an a c t i v a t i o n energy  below of  21k-calv/  g-atom. These v a l u e s a r e c l o s e to those a s s o c i a t e d w i t h b u l k d i f f u s i o n i n A l and Zn  respectively.  Zehr and B a c k o f e n ^  r e p r e s e n t stage I by a non-Newtonian  dashpot  model. They a s s i g n an m v a l u e .33 and p l o t a l i n e on the logo - l o g E curve but s t a t e t h a t i t s r a t i o n a l e i s no more than  1.4  P r e v i o u s Creep  speculative.  S t u d i e s on Lead and T i n Systems  The p r e s e n t work was  c a r r i e d out on the e u t e c t i c Pb-Sn a l l o y of  f i n e g r a i n s i z e . Constant s t r e s s creep t e s t i n g was t h i s method would show any  chosen  to determine i f  d i f f e r e n c e between the creep o f s u p e r p l a s t i c  and n o n - s u p e r p l a s t i c m a t e r i a l s . A l l r e p o r t e d creep work on l e a d , t i n and l e a d - t i n has  i n v o l v e d l a r g e g r a i n s i z e m a t e r i a l s . In l e a d  a t the i n i t i a t i o n of creep and a time ation  34  law was  o c c u r r e d . A t h r e e stage creep curve was  e u t e c t i c , and on pure I t was  1/3  suggested  33  obeyed u n t i l  found. Work  t i n and l e a d , always showed a 3-stage  t h a t primary  slip  35  occurred  recrystallizon the Pb-Sn  creep  curve.  creep must always o c c u r . 36  Creep p s i and 22 and  s t u d i e s on l a r g e g r a i n e d t i n  a t s t r e s s e s between 629  224.5°C always r e s u l t e d i n 3-stage  creep c u r v e s .  and  1394  -9-  I f a m a t e r i a l i s t o t a l l y unloaded a f t e r d e f o r m a t i o n , changes w i t h time beyond an i n i t i a l p r e d o m i n a n t l y  i t s shape  e l a s t i c r e c o v e r y and  to approach i t s i n i t i a l shape. T h i s i s known as the " a n e l a s t i c a f t e r T h i s e f f e c t i s shown by G a r o f a l o f o r l e a d ^ formation i s  7  tends  effect".  a t 25°C where 25 % of the  de-  recovered.  Most r e p o r t e d s t r e s s v e r s u s s t r a i n r a t e d a t a has been o b t a i n e d u s i n g a t e n s i l e t e s t i n g machine. T h i s r e s u l t s i n s t r a i n r a t e  decreasing  and s t r e s s changing w i t h time. The r e s u l t s of these t e s t s are not u s u a l l y r e p o r t e d w i t h a statement i n d i c a t i n g whether c o r r e c t i o n s were made f o r these e f f e c t s i n h e r e n t i n the t e n s i l e t e s t i n g machine. I t i s a l s o d i f f i c u l t to determine a "steady a v o i d these  2.  s a t e " w i t h the t e n s i l e machine. A creep t e s t s h o u l d  difficulties.  EXPERIMENTAL .  2.1.  i  M a t e r i a l and Specimen P r e p a r a t i o n I n g o t s of the Pb-Sn e u t e c t i c (61.9  % Sn) were c a s t i n g r a p h i t e molds  under argon. M a t e r i a l s of 99.99 % p u r i t y or b e t t e r were used. Ingot were 5/8  i n c h d i a m e t e r and 5 i n c h e s The  extruded  dimensions  long.  s u r f a c e of the c a s t b i l l e t s was  machined and  a t room temperature i n t o rods of.099 and  .083  the m a t e r i a l was  i n c h diameter.  f i r s t and l a s t 18 i n c h e s of the e x t r u s i o n s were d i s c a r d e d . The  r o d was  •  The then  c u t i n t o 3% i n c h l e n g t h s . Samples of .099  i n c h d i a m e t e r rods were roughened  a t each end w i t h emery paper and epoxied  i n t o b r a s s g r i p s (Fig.2) w i t h Epon  828  epoxy r e s i n . The  and  the h o l e was  g r i p s were d r i l l e d  one  i n c h deep w i t h a .113  inch d r i l l  tapped to improve the epoxy bond. These specimens were aged  -10-  7 days a t room temperature and then s t o r e d i n l i q u i d n i t r o g e n . The l e n g t h of time of t e s t i n g was  g e n e r a l l y s m a l l compared to the t o t a l time a t room  temperature so t h a t g r a i n growth d u r i n g  t e s t i n g a t room temperature  was  m i n i m i z e d . Rods o f .083 i n c h diameter were s e a l e d i n evacuated g l a s s  tubes  and were annealed a t 165 ± 2°C f o r 30 d a y s ' i n an o i l b a t h to produce growth. These rods were a l s o e p o x i e d i n t o b r a s s g r i p s w i t h a .1015 tapped h o l e . These specimens were s t o r e d a t room Comparison  grain  inch  temperature.  of l o g s t r e s s v e r s u s l o g s t r a i n r a t e c u r v e s p r e v i o u s l y  presented f o r t h i s m a t e r i a l  w i t h those r e s u l t i n g from t h i s study shows  the s m a l l g r a i n s i z e m a t e r i a l (SGS) t o have a g r a i n s i z e of 2 microns  while  the l a r g e g r a i n s i z e m a t e r i a l (LGS) has a g r a i n s i z e o f 8 m i c r o n s .  F i g u r e 2. Specimen i n g i p s  2.2.  Creep T e s t s Creep t e s t s were performed on a c o n s t a n t s t r e s s machine ( F i g u r e 3 ) .  The cam d e s i g n has a m e c h a n i c a l advantage i s twice t h a t i n t h e  w e  such t h a t the l o a d on the  specimen  i h t b u c k e t . The c o n s t a n t s t r e s s cam i s d e s i g n e d f o r  a specimen guage length  g  of 25 mm.  The a p p l i e d l o a d was  t r a n s m i t t e d to the  -11-  specimen by a chromel tape w h i c h f o l l o w e d t h e c o n t o u r o f t h e cam e x a c t l y r a t h e r than t e n d i n g t o bow as round w i r e s were found t o do. The maximum e l o n g a t i o n p o s s i b l e w i t h t h i s creep machine corresponded t o 50 p e r c e n t t r u e s t r a i n . L o a d i n g and u n l o a d i n g o p e r a t i o n s were c a r r i e d o u t by l o w e r i n g and r a i s i n g a s c i s s o r j a c k under t h e w e i g h t b u c k e t . A l l t e s t s were done a t room temperature  (22±1°C).  E l o n g a t i o n measurements were made w i t h b o t h a t r a v e l l i n g  optical  m i c r o s c o p e and an extensometer w h i c h was connected t o a m o d i f i e d H e a t h k i t r e c o r d e r and a t t a c h e d t o the sample w i t h k n i f e edges. HiElongations c o u l d be measured t o ± .001 cm w i t h t h e m i c r o s c o p e and t o w i t h i n .0002 i n c h e s w i t h the extensometer and r e c o r d e r . The m i c r o s c o p e was used t o f o l l o w t h e e l o n g a t i o n o f specimens deforming under low s t r e s s e s . Measurement was made o f the d i s p l a c e m e n t o f a s i n g l e mark i n s c r i b e d on t h e specimen g r i p w i t h a r a z o r b l a d e . Experiment showed t h a t t h e r e was no s l i p p a g e i n the g r i p s and t h a t i t was n o t n e c e s s a r y to observe t h e t r a v e l o f two marks on t h e specimen i t s e l f .  .'  The extensometer was used a t h i g h e r s t r e s s e s and s t r a i n r a t e s where a u t o m a t i c c o n t i n u o u s r e c o r d i n g was e s s e n t i a l . No s i g n i f i c a n t  extensometer  k n i f e edge i n d e n t a t i o n o c c u r r e d a t t h e s e s t r a i n r a t e s . The l o a d was i n c r e a s e d o r d e c r e a s e d d u r i n g some t e s t s t o d e t e r m i n e the e f f e c t o f s t r e s s changes on the r e s u l t i n g c r e e p c u r v e s . A t h i g h s t r e s s e s , i n v o l v i n g t h e l a r g e g r a i n s i z e m a t e r i a l , changes i n s t r e s s were made d u r i n g the i n i t i a l t r a n s i e n t o f th© creep c u r v e s . Specimens were a l s o suddenly unloaded and the guage l e n g t h was r e c o r d e d w i t h t h e extensometer t o d e t e r m i n e i f u n l o a d i n g t r a n s i e n t s e x i s t e d over any s t r e s s range.  -12-  F i g u r e 3.  Constant s t r e s s c r e e p machine.  3.  RESULTS  3.1.  Calculations All  c a l c u l a t i o n s were done on an IBM  360  shown i n Appendix I . Keypunched d a t a i n c l u d e d elongations  to i n c h e s . The  recorder,  programme i s  i n i t i a l guage l e n g t h ,  a t a s e r i e s of times ( h o u r s ) . A s c a l e f a c t o r was  c o n v e r t d e f l e c t i o n s on the H e a t h k i t  used w h i t h the  and  included  s t r a i n rateversus  time. A l s o i n c l u d e d was  l i s t i n g each t r u e s t r a i n , s t r a i n r a t e and  to  extensometer,  computer o u t p u t i n c l u d e d a s c a l e d creep c u r v e p l o t of  s t r a i n v e r s u s time and table  computer. The  true  a printed  time p o i n t p l o t t e d .  I n i t i a l l y , high s t r a i n r a t e values which f a l l o f f very q u i c k l y be due  may  to s t r a i g h t e n i n g of the specimen. T h i s e f f e c t s h o u l d be maximum when  a l a r g e quage l e n g t h i s used as was  done w i t h t e s t s u s i n g the  travelling  m i c r o s c o p e . E l a s t i c s t r a i n would a l s o c o n t r i b u t e to t h i s r e s u l t . These e f f e c t s c o u l d not be i s o l a t e d and  remain i n the computer o u t p u t .  P l o t s of s t r a i n r a t e are determined from the s t r a i n r a t e between two  successive  p o i n t s . T h i s r e s u l t s i n a j a g g e d s t r a i n r a t e c u r v e . The  r a t e s c a l e i s o f t e n expanded and  strain  t h i s a l s o tends to make the r e s u l t i n g c u r v e  jagged.  3.2.  Log  S t r e s s v e r s u s Log  S t r a i n Rate Curves  S t r a i n r a t e data obtained  from creep t e s t s were used to o b t a i n  s t r e s s v e r s u s l o g s t r a i n r a t e p l o t s f o r each g r a i n s i z e . These p l o t s shown i n F i g u r e s  4 and  r a t e i n s t a g e s I and  5. S t r a i n r a t e v a l u e s used were the i n i t i a l  I I and  log  are  strain  the s t e a d y s t a t e creep r a t e i n s t a g e I I I .  4Y Log s t r e s s v e r s u s l o g s t r a i n curve (SGS, 2 m i c r o n s ) .  F i g u r e 5. Log s t r e s s v e r s u s l o g s t r a i n r a t e curve  (LGS,  8 microns).  - 16 The p l o t f o r the 2 m i c r o n g r a i n s i z e i s s i m i l a r t o t h a t determined by Zehr and Backofen*^. is  .33.  The s l o p e , o r m v a l u e , i n Stage I  Stage I I shows a s l o p e o f ;5 g e n e r a l l y w i t h a peak v a l u e  of about .6.  The s l o p e decreases  i n c r e a s e s and approaches  a f t e r peak m as s t r a i n r a t e  .10 i n s t a g e I I I .  The c u r v e determined by  Zehr and B a c k o f e n , and a l s o u s i n g C l i n e and Alden's d a t a , i s shown i n F i g u r e 6. Other p o i n t s a r e those determined i n the p r e s e n t work. Even i f the two s e t s o f d a t a were brought more c l o s e l y  into  c o i n c i d e n c e by moving one s e t o f d a t a t o a s l i g h t l y d i f f e r e n t  strain  r a t e , the p r e s e n t work shows h i g h e r s t r e s s v a l u e s i n s t a g e I I and lower v a l u e s i n s t a g e I I I .  to 10  '  1  10"  :  10"  7  6  I  I  •  10" 10" 10~ STRAIN RATE ( S E C . ) 5  • 1  ; 1  4  3  10"  2  1 10"'  - 1  F i g u r e 6:  Comparison of the S-curve d a t a of the p r e s e n t and p r e v i o u s work.  The p l o t f o r the 8 m i c r o n g r a i n s i z e shows o n l y s t a g e s I I and I I I . Stage I I shows an m v a l u e o f .5 which f a l l s o f f t o a s t a g e I I I v a l u e o f .10. A s t a g e I I - s t a g e t r a n s i t i o n might be p r e s e n t but lower s t r a i n r a t e d a t a would be, r e q u i r e d b e f o r e i t c o u l d be s t a t e d t h a t s t a g e I has been reached. 3.3. 3.3.1.  Creep  Curves  Stage I I Creep  Curves  F o r specimens of b o t h g r a i n s i z e s the t r u e s t r a i n v e r s u s time curves were s t r a i g h t l i n e s .  No p r i m a r y creep was  observed.  Steady s t a t e creep was  -17-  observed  from the s t a r t of each  t i o n . For SGS  specimens,  t e s t . No n e c k i n g  w i t h a s t r a i n r a t e of 5 x 10  s t r e s s range. Another  hr  , to 2400 p s i which i s approximately 8 show curves near  the extremes of  the  this  curve i s shown i n F i g u r e 9. Above t h i s s t r e s s range approached.  Below 300 p s i , stage I behaviour  found. More curves t y p i c a l o f stage I I are shown i n  to determine  from near 300 p s i  -1  F i g u r e s 7 and  decreased as stage I I I was  Creep  p r e s e n t d u r i n g deforma-  l i n e a r creep curves were observed -2  s t r e s s a t maximum m.  was  t e s t s on LGS  specimens d i d not extend  m  was  Appendix I I , F i g u r e s a to c. to low enough s t r a i n r a t e s  a t r a n s i t i o n s t r e s s and s t r a i n r a t e between stages I and I I .  S t r a i g h t l i n e creep curves were e v i d e n t up  to a s t r e s s of 1500  p s i where m  began to decrease. Examples are shown i n F i g u r e 10 and Appendix I I , F i g u r e s d and  e.  3.3.2.  Stage I Creep Creep  Curves  t e s t s c a r r i e d out i n the s t r e s s range  a s s o c i a t e d w i t h stage I  showed a creep curve w i t h ever d e c r e a s i n g s t r a i n r a t e . A t a s t r e s s of 97 p s i , a SGS  specimen was  extended  to a t r u e s t r a i n of .446  11 shows t h i s creep curve. LGS  a f t e r 696.5 h o u r s . F i g u r e  creep t e s t s a t low s t r e s s e s were o n l y taken to  a few p e r c e n t e l o n g a t i o n and o n l y the creep r a t e r a t h e r than the creep shape was  determined.  F i g u r e s f , g , and h i n Appendix I I show more SGS  curve creep  curves f o r stage I .  3.3.3.  Stage I I -Stage  I I I T r a n s i t i o n Creep  Curves  As s t r a i n r a t e i s i n c r e a s e d above t h a t a s s o c i a t e d w i t h peak m, creep curves change from the s t r a i g h t l i n e s o f stage I I . Creep t r a n s i t i o n range a l l had an i n i t i a l  the  curves i n t h i s  l i n e a r r e g i o n but the curve i n c r e a s e d i n  s l o p e , as i n t e r t i a r y c r e e p , a f t e r a s t r a i n of a few p e r c e n t . A l l specimens,  -19-  o  F i g u r e 11. Stage I creep curve (SGS), 97 p s i .  -23-  i n t h i s r e g i o n o f d e c r e a s i n g m, e x h i b i t e d neck f o r m a t i o n and f a i l u r e o c c u r r e d a t l e s s than .50 t r u e s t r a i n . The t r a n s i t i o n r e g i o n c o n t i n u e d t o 5000 p s i , i n the LGS, where m approached vented  a c o n s t a n t v a l u e o f .10. High s t r a i n r a t e s p r e -  the d e t e r m i n a t i o n of the end o f the s t a g e I I - stage I I I t r a n s i t i o n .  F i g u r e s 12 and 13 show creep curves f o r the s t a g e I I - stage I I t r a n s i t i o n f o r both g r a i n s i z e s . More p l o t s a r e shown i n F i g u r e s i to s i n Appendix I I .  3.3.4. Stage I I I Creep  Curves  Creep p l o t s i n t h i s s t r e s s range was an i n i t i a l  t r a n s i e n t . Primary  showed 3-stage  creep c u r v e s .  There  creep was f o l l o w e d by steady s t a t e or second-  ary creep as s t r a i n i n c r e a s e d . F r a c t u r e g e n e r a l l y o c c u r r e d a t lower and lower s t r a i n s as the creep s t r e s s was i n c r e a s e d . Creep  curves were o b t a i n e d o n l y  f o r LGS specimens because the v e r y h i g h s t r a i n r a t e s i n v o l v e d to a t t a i n  stage  I I I behaviour i n the SGS m a t e r i a l made r e c o r d i n g o f the d e f o r m a t i o n i m p o s s i b l e w i t h the e x p e r i m e n t a l equipment used. F i g u r e s 14,15 and 16 demonstrate c u r v e s , o b t a i n e d from LGS specimens,  creep  over a range o f s t r e s s . Two more curves  are shown i n F i g u r e s t and u i n Appendix I I . F i g u r e 17 i s a p l o t o f the s t r a i n a t which steady s t a t e creep appears v e r s u s the t e s t i n g s t r e s s for. the LGS m a t e r i a l . The b e g i n n i n g o f s t a g e I I I i s thus near 2500 p s i . ii  3.4. Incremental Loading and U n l o a d i n g Incremental l o a d i n g and u n l o a d i n g t e s t s were made d u r i n g creep  tests  on specimens o f both g r a i n s i z e s i n stage I I and I I I . I n stage I I , where creep curves a r e l i n e a r , i n c r e a s i n g and d e c r e a s i n g the load r e s u l t s i n an abrupt t r a n s i t i o n to l i n e a r curves o f i n c r e a s i n g o r d e c r e a s i n g s l o p e . F i g u r e 18 i s an example o f i n c r e m e n t a l l o a d i n g o f a SGS specimen. The s h o r t s t r a i n r a t e peak,  F i g u r e 12. Creep curve i n s t a g e IT - stage I I t r a n s i t i o n (SGS), 3432 p s i .  F i g u r e 13. Creep curve i n stage I I - stage I I I t r a n s i t i o n (LGS), 3582 p s i .  -26-  T 0.0  I 0.0B  :  T 0.16  "I 0.24  1 — 0.32  1 . 0.4  1 0.48  TIME HOUR  F i g u r e 1A.  .-CS  i 3.0  1 O.OB  1 0.56  1 0.64  1 0.72  Tc D.8  1 0.64  1 0 72  -|"--; OS  mo ) -1  Stage I I I creep c u r v e (5212 p s i )  '_=6803  GM S - 5 5 3 5  1 • 0.16  1 0.24  PSI  O=.0B3  1 • 0.32  TIME  IN.  EXT..  1 0.4  HOUR  1 0.4B  1X10"  1  )  1 0.56  F i g u r e 15. Stage I I I creep c u r v e (5535 p s i )  STRAIN  TO  STEADY  STATE  -28-  F i g u r e 18. Incremental  l o a d i n g d u r i n g s u p e r p l a s t i c creep.  -29-  when t h e s t r e s s reaches 832 p s i , i s due t o an e r r o r i n one r e a d i n g e x a c t l y at  t r a n s i t i o n . Another i n c r e m e n t a l l o a d i n g example i s shown i n F i g u r e v  Appendix  I I . Curves have the same s l o p e a t a l l s t r e s s e s i n s t a g e I I , d u r i n g  i n c r e m e n t a l l o a d i n g , as when they a r e i n i t i a l l y loaded t o t h a t s t r e s s . r a t e i s independent  Strain  of p r i o r h i s t o r y i n stage I I .  I n c r e m e n t a l l o a d i n g d u r i n g p r i m a r y creep i n s t a g e I I I r e s u l t s i n a change i n t h e i n i t i a l  t r a n s i e n t . The s l o p e o f t h e curve i s i n s t a n t l y i n -  c r e a s e d and a t r a n s i e n t remains at  t o a h i g h e r s t r a i n than would have o c c u r r e d  t h e lower s t r e s s . F i g u r e 19 shows t h e r e s u l t o f i n c r e a s i n g the l o a d d u r i n g s t e a d y  s t a t e creep i n s t a g e I I I .  Here, a t r a n s i e n t r e a p p e a r s . F i g u r e 20 shows t h e  immediate t r a n s i t i o n t o steady s t a t e creep when the l o a d i s decreased d u r i n g p r i m a r y creep. T h i s r e s u l t i s a l s o shown i n F i g u r e w, Appendix I I . The purpose o f t h e s e t e s t s was t o compare the b e h a v i o u r o f a s u p e r p l a s t i c m a t e r i a l , d u r i n g l o a d i n g and u n l o a d i n g , t o t h e b e h a v i o u r o f i c n - s u p e r p l a s t i c m a t e r i a l s under s i m i l a r t e s t i n g  3.5.  conditions.  Strain After-Effects Specimens deforming i n s t a g e I I and s t a g e I I I were unloaded.  specimens were then c o n t i n u o u s l y measured w i t h an extensometer  These  to look f o r  s t r a i n r e l a x a t i o n . A t no time was t h e r e any s i g n o f c o n t r a c t i o n d u r i n g s t a g e I I . An example o f t h i s r e s u l t i s shown i n F i g u r e 21. R e u s I t s o f t e s t s on LGS samples i n s t a g e I I I were n o t c o n c l u s i v e b u t always suggested some s t r a i n r e l a x a t i o n . R e l a x a t i o n s o f .003 t o .004 i n c h e s were found on a guage l e n g t h of  .500 i n c h e s a f t e r times o f 45 minutes  t o 60 minutes a f t e r s t r a i n s ^ o f .10  ^30-  to .30. The r e t u r n of primary  creep a f t e r r e c o v e r y was  looked f o r . Once a g a i n  the e f f e c t i s s m a l l as shown by F i g u r e 22 a f t e r 5 minutes r e c o v e r y time. I t may  be  that r e c o v e r y r a t e s are too slow a t room temperature.  temperatures  f o r c e d the removal  o f the extensometer  Recovery  at higher  and specimen d i s t o r t i o n  o c c u r r e d . These problems once a g a i n l e a d to i n c o n c l u s i v e r e s u l t s . .  4.  DISCUSSION Creep  s t u d i e s of s u p e r p l a s t i c m a t e r i a l s have seldom been made. P r e -  v i o u s work on l e a d , t i n and  the l e a d - t i n  eutectic  s t r e s s e s , s t r a i n r a t e s and g r a i n s i z e s necessary  33-35  has not i n v o l v e d  to o b t a i n s u p e r p l a s t i c  be-  38 h a v i o u r . Packer, Johnson and Sherby  used  c o n s t a n t s t r e s s creep t e s t s i n  t h e i r study of e u t e c t i c Zn-Al and s t a t e t h a t they found n e g l i g i b l e hardening d u r i n g s u p e r p l a s t i c creep and under c o n s t a n t s t r e s s and  temperature.  t h a t the creep r a t e remained Zehr and Backofen*^  to o b t a i n a low s t r a i n r a t e v a l u e on an S-curve  constant  used a creep 32  f o r Pb-Sn. Chaudhari  a l s o done some creep work. The p r e s e n t study has been the o n l y one designed  strain  has  specifically  to g a i n more i n s i g h t i n t o the s u p e r p l a s t i c phenomena through  of creep curve d e t a i l s over a wide s t r e s s range. D i s c u s s i o n w i l l  test  the study  cover mainly  the m e r i t s of r e c e n t l y suggested mechanisms of s u p e r p l a s t i c i t y , c o n s i d e r e d i n view o f new 4.1.  creep r e s u l t s and o t h e r c o n s i s t e n t l y r e p o r t e d o b s e r v a t i o n s .  Stage I I I Deformation  i n stage I I I i s not s u p e r p l a s t i c . I t i s s i m i l a r  to the  creep o f c o a r s e g r a i n e d m a t e r i a l s where d e f o r m a t i o n i s by r e c o v e r y c r e e p . T h i s c o n c l u s i o n f o l l o w s from the c u r r e n t o b s e r v a t i o n s of primary c r e e p , a  -31-  F i g u r e 20.  T r a n s i t i o n to s t e a d y s t a t e w i t h u n l o a d i n g i n s t a g e I I I .  -32-  F i g u r e 22.  Reloading a f t e r recovery i n stage I I I .  -33-  3 - s t a g e c r e e p c u r v e and is  a low m v a l u e near  a l s o present a f t e r stage I I I creep  .10. A d i s l o c a t i o n s u b s t r u c t u r e  1>6,7,39^  ^  a g  n  t  ^  e  c  r  e  e  p  Q  f  c  o  a  r  s  e  37 grained materials initial  . R e s u l t s ( F i g u r e 21)  a l s o seem t o show t h e r e t u r n o f  t r a n s i e n t a f t e r r e c o v e r y . However, s i g n i f i c a n t l y  larger  transients  were not seen a t l a r g e r r e c o v e r y t i m e s . A s t r a i n a f t e r - e f f e c t , whereby s p e c i m e n s s h o r t e n e d s l i g h t l y when t h e l o a d was  removed a f t e r  an  the  e l o n g a t i o n , has  37 a l s o been observed results was  i n coarse grained m a t e r i a l s  seem t o show t h a t t h i s d i d o c c u r a f t e r s t a g e I I I d e f o r m a t i o n .  associated with tertiary Recovery  strain  a f t e r recovery creep.  creep  Present Necking  creep.  t h e o r i e s i n v o l v e a general equation f o r steady  state  rate, E  =  r/h  (3)  w h e r e r i s t h e r e c o v e r y r a t e , d a / d t , and h i s s t r a i n h a r d e n i n g S t r a i n hardening  i s a s s o c i a t e d w i t h an i n c r e a s e i n d i s l o c a t i o n d e n s i t y  w h i l e r e c o v e r y r e p r e s e n t s a decrease,.  Primary  creep r e s u l t s  r e c o v e r y r a t e i s s m a l l e r t h a n t h e h a r d e n i n g r a t e . The annealed  dh/de.  specimen i s c l o s e to z e r o . Steady  b e t w e e n h a r d e n i n g and  occurs during primary  initial  v a l u e o f r i n an 1  s t a t e creep represents a  r e c o v e r y . Such a b a l a n c e i s expected  increase i n dislocation density, relative  i f the  (p)  to the annealed  balance  only after condition,  some which  creep. 40  A modern t h e o r y f o r s t a g e I I I i s t h a t o f McLean temperatures  i n v o l v e s the behaviour  of a three-dimensional d i s l o c a t i o n  work. Three i m p o r t a n t a s p e c t s of t h i s b e h a v i o u r itivity  . Deformation  are the temperature  corresponds  to a decrease  i n p and  net-  insens-  of the f l o w s t r e s s of a g i v e n network, the network's tendency  c o a r s e n on h e a t i n g w h i c h  at high  to  i t s refinement  -34-  on s t r a i n i n g w h i c h corresponds to an i c r e a s e . McLean shows t h a t the r e c o v e r y r a t e , r , v a r i e s w i t h s t r e s s by 3 r a a  (4)  The r e c o v e r y p r o c e s s i n v o l v e s d i f f u s i o n c o n t r o l l e d d i s l o c a t i o n c l i m b and m i g r a t i o n of j o g s i n screws. T h e r e f o r e , i f D i s the d i f f u s i o n  coefficient  3 r a a  D  P l a s t i c d e f o r m a t i o n r e f i n e s the d i s l o c a t i o n network.  (5) During deformation,  moving d i s l o c a t i o n s a r e h e l d up a t p o i n t s where the network i s f i n e bow  and  out to i n c r e a s e the average d i s l o c a t i o n d e n s i t y . M u l t i p l e s l i p p e r m i t s  network geometry to remain c o n s t a n t as the meshes become s m a l l e r . The  strain  h a r d e n i n g c o e f f i c i e n t h = 8c/3e i s a measure o f the r e f i n i n g a c t i o n . I f -3/2 e x p r e s s i o n f o r r from eqn.(5) and h from the e m p i r i c a l r e l a t i o n s h i p are used i n eqn(3) the r e s u l t i s e = BDa or i f  K =  (VBD)  1 7 4  '  4-5  haa  (6)  5  .22  ,  (7)  a = Ke  w h i c h i s the same as e q u a t i o n (1) w i t h m = .22. T h i s v a l u e of m i s not q u i t e as low as t h a t found e x p e r i m e n t a l l y . T h e o r i e s o f t h i s type a r e , of c o u r s e r a t h e r s p e c u l a t i v e and e v i d e n t l y approximate /  i n n a t u r e . I t i s not  known to what e x t e n t the p h y s i c a l model of McLean corresponds to the det a i l e d d e f o r m a t i o n and r e c o v e r y p r o c e s s e s i n s t a g e I I I .  -  4.2.  35 -  Stage I I - S t a g e I I I T r a n s i t i o n In  t h e s t a g e I I - s t a g e I I I t r a n s i t i o n , on i n c r e a s i n g s t r a i n  r a t e , m f a l l s from a maximum t o a s m a l l e s s e n t i a l l y  constant  v a l u e a s s o c i a t e d w i t h s t a g e I I I . The t r a n s i t i o n s t r a i n r a t e range was from 2 x 1 0 s i z e and above 2.5 h r  1  9  - z  hr.  -1  to 2 hr.  -1  f o r the 8 micron g r a i n  f o r the 2 micron g r a i n s i z e .  s t r a i n r a t e s i n v o l v e d prevented  The h i g h  d i f f e r e n t i a t i o n between t h e end  of t h e t r a n s i t i o n range and t h e s t a r t o f s t a g e I I I i n t h e s m a l l g r a i n s i z e specimens.  Creep curves i n t h e t r a n s i t i o n r e g i o n  are convex upward ( t e r t i a r y creep) i s no p r i m a r y creep.  ( F i g u r e s 12 and 13).  F a i l u r e occurs at s t r a i n s of l e s s  There than  41  .50 and f a i l u r e o c c u r s a t a neck. t h i s r e s u l t mathematically.  Chaudhari  may have e x p l a i n e d  D i f f e r e n t i a t i o n o f e q u a t i o n (1)  leads t o dt  ^  1 j-da - l o g ^ dm j m a K m  ^)  The e f f e c t of a l a r g e m v a l u e i s t o decrease a neck t o grow.  t h e tendency f o r  C o n v e r s e l y , an i n c r e a s e i n t h e b r a c k e t e d  increases the s e n s i t i v i t y t o necking.  term  I f m i s decreasing with  i n c r e a s i n g s t r a i n r a t e , as i t i s i n t h e t r a n s i t i o n range, dm i s n e g a t i v e and t h e second term w i l l be added t o t h e f i r s t . The b r a c k e t e d term becomes l a r g e r and s e n s i t i v i t y t o n e c k i n g i s more pronounced.  Observations  o f neck f o r m a t i o n and growth  a f t e r o n l y a few p e r c e n t s t r a i n were made d u r i n g t h e p r e s e n t 16  work ( F i g u r e s 12 and 13).  Previous observations  of l a r g e  superplastic elongations using i n i t i a l s t r a i n rates i n t h i s r e g i o n were made w i t h I n s t r o n t e n s i l e machines.  These machines  have a constant c r o s s head" speed and t h e s t r a i n r a t e imposed on a specimen i s c o n t i n u o u s l y d e c r e a s i n g .  The e f f e c t o f a  -36-  d e c r e a s i n g s t r a i n r a t e i n the t r a n s i t i o n range i s t o g i v e a r i s i n g m v a l u e as t e s t i n g proceeds. A convex upward creep curve has p r e v i o u s l y been r e p o r t e d , i n the l i t e r 36 ature  b u t no comment o r e x p l a n a t i o n was a t t e m p t e d . C o n s t a n t s t r e s s creep t e s t s  were performed on a number o f pure t i n specimens. Four d i f f e r e n t g r a i n s i z e s were used b u t o n l y the f i n e s t , 37 m i c r o n s , primary  e x h i b i t e d t h i s behaviour.  Others showed  creep. F i g u r e 23 shows a l o g a r i t h m i c p l o t o f s t r e s s v e r s u s s t r a i n r a t e  u s i n g Breen and Weertman's creep r a t e d a t a f o r t h e s m a l l e s t g r a i n s i z e . curve i s somewhat comparable t o t h a t of A l d e n  This  and d i f f e r e n c e s may be due to  g r a i n growth and t h e f a c t t h a t A l d e n ' s curve was o b t a i n e d u s i n g an  Instron tensile  machine, m v a r i e s from .3 to .12. The i n c r e a s e i n ui w i t h d e c r e a s i n g i n sub-grain s i z e v i t h decreasing  s t r a i n . r = t e i s due to a slow i n c r e a s e  s t r a i n r a t e ' . Stage I I i s reached when s u b - g r a i n -  1 13 • s i z e has reached the g r a i n s i z e ' . As t h i s c o n d i t i o n i s approached, accommodation for  GBS by s l i p becomes e a s i e r and m i n c r e a s e s to i t s maximum v a l u e . The stage I I I -  stage I I t r a n s i t i o n i s a s s o c i a t e d w i t h i n c r e a s e d amounts o f GBS"\ S u p e r p l a s t i c i t y may a c t u a l l y be p o s s i b l e i n l a r g e r g r a i n e d m a t e r i a l s i f , a t low enough s t r a i n r a t e s , the sub g r a i n s i z e approaches t h e g r a i n s i z e . Creep 43 t e s t s by G i f k i n s wt%  may be i n d i c a t i v e o f t h i s . The g r a i n s i z e o f extruded  t h a l l i u m was 100 m i c r o n s .  Pb-2.45  S t r e s s e s o f 300,500,1000,1500, and 2000 p s i were  used on creep specimens. These creep r e s u l t s a r e p l o t t e d i n F i g u r e 24. The m v a l u e from .15 to .45. M i c r o s t r u e t u r a l o b s e r v a t i o n s r e g u l a r and" more w i d e l y spread s t r a i n rates deformation  increases  showed t h a t s l i p l i n e s became l e s s  as the s t r e s s was d e c r e a s e d and a t the l o w e s t  proceeded by "boundary m i c r o - f l o w " and g r a i n s were unde-  formed. A t 500 p s i e l o n g a t i o n t o f a i l u r e was 208 %. S i m i l a r o b s e r v a t i o n s weremade  -37-  by Wood e t a l  on aluminum w i t h a g r a i n s i z e o f 100 t o 200 m i c r o n s . S l i p was  prominent d u r i n g d e f o r m a t i o n a t lower temperatures and h i g h e r r a t e s o f s t r a i n . As the temperature was i n c r e a s e d o r the s t r a i n r a t e d e c r e a s e d , s l i p l i n e s g r a d u a l l y v a n i s h e d and t h e elements o f the a s s o c i a t e d s u b s t r u c t u r e showed an i n c r e a s e i n s i z e . T h i s l e f t a c o a r s e s u b s t r u c t u r e which i n c r e a s e d i n s i z e w i t h a f u r t h e r i n c r e a s e i n temperature o r d e c r e a s e i n s t r a i n r a t e u n t i l i t was t h e s i z e o f t h e g r a i n i t s e l f . T h i s c o i n c i d e d w i t h t h e onset o f prominent  "boundary m i c r o f l o w "  or GBS. They found t h a t l a t t i c e s t r u c t u r e was unchanged and no s t r a i n h a r d e n i n g occurred during deformation. The o b s e r v a t i o n s o f Wood e t a l and G i f k i n s seem t o be v e r y s i m i l a r to t h e o b s e r v a t i o n s made on f i n e g r a i n e d s u p e r p l a s t i c m a t e r i a l s where GBS becomes 13  more dominant as the s t r a i n r a t e i s decreased from t h a t o f s t a g e I I I  4.3.  Stage I I The new o b s e r v a t i o n s a s s o c i a t e d w i t h s t a g e I I a r e t h a t t h e creep c u r v e s  a r e l i n e a r and t h a t t h e r e a r e no u n l o a d i n g t r a n s i e n t s . The l i n e a r creep c u r v e s a r e shown i n F i g u r e s 8,11. There a r e no s i g n s o f p r i m a r y o r t e r t i a r y c r e e p , o n l y s t e a d y s t a t e . The r e s u l t s o f u n l o a d i n g t e s t s a r e shown i n F i g u r e 21. No c o n t r a c t i o n s due to r e c o v e r y has o c c u r r e d . These r e s u l t s show t h a t r e c o v e r y t h e o r i e s , which may be v a l i d f o r normal c r e e p , and s t a g e I I I . a r e u n s a t i s f a c t o r y f o r s u p e r 45 p l a s t i c creep. Alden  has demonstrated  t h a t many proposed models f o r super-  p l a s t i c i t y a r e r e a l l y models based on r e c o v e r y creep and a r e thus u n a c c e p t a b l e . An 32 i n t e r n a l s t r e s s model  which i n c o r p o r a t e s an a c c u m u l a t i o n o f d i s l o c a t i o n s  near  the g r a i n boundary seems t o be u n a c c e p t a b l e because d i s l o c a t i o n s a r e n o t seen d u r i n g s u p e r p l a s t i c d e f o r m a t i o n even when specimens a r e quenched under l o a d * .  F i g u r e 23. Log s t r e s s v e r s u s l o g s t r a i n r a t e r e l a t i o n s h i p f o r pure  tin,(37u) i  OJ CO  I  _1000 _  10-2 STRAIN RATE F i g u r e 24.  10" I ( DAY" ) 1  Log s t r e s s v e r s u s l o g s t r a i n - r a t e r e l a t i o n s h i p f o r Pb-2.45 wt.% t h a l l i u m (lOOy).  -39-  A l s o , the low temperature  y i e l d s t r e s s is unchanged a f t e r s t a g e I I d e f o r m a t i o n  I f d i s l o c a t i o n s a r e accumulated d u r i n g c r e e p , t h i s y i e l d s t r e s s s h o u l d i n c r e a s e . Mechanisms and accommodation p r o c e s s e s which would show no t r a n s i e n t s a r e those which do n o t i n v o l v e a s t r u c t u r a l change accommodation p r o c e s s e s , N a b a r r o - H e r r i n g  G r a i n boundary s l i d i n g w i t h  some s p e c i a l  o r Coble creep and g r a i n boundary m i g r a t i o n  are examples. G r a i n boundary m i g r a t i o n , i n a s s o c i a t i o n w i t h GBS, has been  observed  46 47 in superplastic materials  '  . Opposition to the idea that m i g r a t i o n i s r a t e -  c o n t r o l l i n g i s based on doubt t h a t m i g r a t i o n can be e f f e c t i v e when many phase boundaries  a r e p r e s e n t i n two phase systems. A t t h e same t i m e , i t must be con-  s i d e r e d t h a t i f t h e r e a r e e q u a l amounts o f two p h a s e s , each phase might s t i l l be i n c o n t a c t w i t h 50 % o f t h e l i k e phase. Thus t h e r e i s a r e a s o n a b l e chance f o r m i g r a t i o n t o be an e f f e c t i v e means o f accommodation f o r GBS i n a s u p e r p l a s t i c m a t e r i a l . With o n l y one phase p r e s e n t , d i l u t e a l l o y systems do n o t , o f c o u r s e , p r e s e n t t h i s problem. G r a i n e l o n g a t i o n s h o u l d r e s u l t d u r i n g d i f f u s i o n a l c r e e p . T h i s i s not observed  i n s t a g e 11*^ b u t Zehr and Bachofen's e x p l a n a t i o n i s t h a t e l o n g a t e d  g r a i n s w i l l e x p e r i e n c e a shape r e l a x a t i o n d u r i n g s t r a i n i n g through d i r e c t t i o n and r e c r y s t a l l i z a t i o n . They c l a i m t h a t t h e presence  o f s t r i a t e d bands on a  2 m i c r o n Pb-Sn e u t e c t i c specimen p u l l e d a t 3.3 x 10 ^ sec. * s u p p o r t s  diffusional  creep. T h i s s t r a i n r a t e i s v e r y near the t r a n s i t i o n t o s t a g e I . S i m i l a r 47 have been oserved i n Cd-5 % Pb  migra-  striations  over s t r a i n r a t e s a s s o c i a t e d w i t h s t a g e s I and I I .  47 Donaldson  suggests  t h a t s t r i a t i o n s may i n d i c a t e t h a t boundary s l i d i n g o c c u r s on  p r e f e r r e d c r y s t a l l o g r a p h i c p l a n e s . The t e s t o f t h i s i s t o c o r r e l a t e g r a i n o r i e n t a t i o n and t h e p l a n a r o r i e n t a t i o n o f the s l i p p e d b o u n d a r i e s  with s t r i a t i o n spacing.  -40-  Narrow s t r i a t i o n s p a c i n g would i n d i c a t e l a r g e m i s - o r i e n t a t i o n . The absence of s t r i a t i o n s would i n d i c a t e t h a t t h e s l i d i n g p l a n e i s a p r e f e r r e d  plane.  I n a Mg-Al a l l o y , t h e s t r a i n c o n t r i b u t i o n o f g r a i n boundary s l i d i n g i n s t a g e I I reached 65 %*. A l d e n s u g g e s t s t h a t the g r a i n b o u n d a r i e s may a c t as " p e r f e c t " s i n k s and t h a t s l i d i n g i s r a t e - c o n t r o l l e d  by d i f f u s i o n . T h i s model  demands t h a t t h e a b s o r p t i o n r a t e by b o u n d a r i e s of d i s l o c a t i o n s generated a t triple  l i n e s be so h i g h t h a t i t i s n o t r a t e c o n t r o l l i n g . F a s t r e c o v e r y  rates i n  13 superplastic materials t h i s becomes a r e c o v e r y a t t r a c t i o n f o r c e between  s u p p o r t t h i s b u t l i t t l e o r no c l i m b can be i n v o l v e d o r creep model. A b s o r p t i o n  may be enhanced by GBS by t h e  s l i d i n g b o u n d a r i e s and d i s l o c a t i o n s * . The r a t e o f  s l i d i n g i s determined by the e f f e c t i v e v i s c o s i t y o f t h e boundary. The b o u n d a r i e s are rough and the s l i d i n g r a t e i s determined by d i f f u s i o n around these rough areas.  The s c a l e o f roughness w i l l u s u a l l y i n c r e a s e w i t h g r a i n s i z e . The model  predicts  the s t r a i n r a t e semi q u a n t i t a t i v e l y i n agreement w i t h observed e f f e c t s  of s t r e s s , g r a i n s i z e , and temperature. 4.4.  Stage I Stage I , as shown i n F i g u r e  11, i s s i m i l a r t o s t a g e I I i n t h a t  there  a r e no t r a n s i e n t s s i m i l a r t o those found i n s t a g e I I I . The creep c u r v e i s n o t l i n e a r , however. There i s a d e f i n i t e d e c r e a s e i n s t r a i n r a t e w i t h time. decreasing  This  s t r a i n r a t e i s n o t b e l i e v e d t o be i n any way r e p r e s e n t a t i v e o f a r e -  covery creep model where a d e c r e a s i n g Stage I may r e p r e s e n t  creep r a t e i s found d u r i n g p r i m a r y c r e e p .  a change i n the r a t e c o n t r o l l i n g p r o c e s s f o r  GBS from d i f f u s i o n around bumps on b o u n d a r i e s t o s l i p a t t r i p l e t i o n s are emitted  lines. I f disloca-  from a s o u r c e , proceed through a m a t e r i a l w i t h o u t b a r r i e r s and  are then absorbed a t a " p e r f e c t " s i n k , no s t r a i n h a r d e n i n g w i l l r e s u l t . ' I f t h e  -41-  s o u r c e s o f d i s l o c a t i o n s a r e t h e edges o f s l i d i n g g r a i n s , and t h e s i n k s a r e g r a i n 30 boundaries, Alden  suggests t h a t s t r a i n r a t e w i l l depend on s t r e s s t o t h e power  2 t o 3. The s l o p e depends on whether accommodation d i s l o c a t i o n s  move on a few  s l i p p l a n e s o r throughout t h e g r a i n volume. A l i n e a r a r r a y i s expected i n a l l o y s w i t h a low s t a c k i n g f a u l t energy such as F e - N i - C r and m s h o u l d be .5. M o t i o n to  t h e s l i p p l a n e i s e a s i e r through c r o s s s l i p i n h i g h s t a c k i n g f a u l t energy  normal material:  and t h e s l o p e s h o u l d be .33 as was observed. Lee* found t h e b e h a v i o u r i n s t a g e I t o be a combined e f f e c t o f g r a i n d e f o r m a t i o n and d e f o r m a t i o n a c r o s s 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 , a c c o u n t i n g r o u g h l y for  1/3 and 2/3 o f t h e t o t a l d e f o r m a t i o n , r e s p e c t i v e l y . The l a t t e r c o n s i s t e d , a t  l e a s t i n p a r t , o f GBS b u t whether t h e r e m a i n i n g f r a c t i o n was due t o GBS or Coble creep c o u l d n o t be determined. S e v e r a l e x p e r i m e n t a l o b s e r v a t i o n s suggest t h a t d i f f u s i o n a l creep may 7 28 10 c o n t r i b u t e t o d e f o r m a t i o n i n s t a g e I . These a r e g r a i n e l o n g a t i o n ' , s t r i a t i o n s 29 and denunded zones , and creep curves o f d e c r e a s i n g s l o p e . Creep curves o f d e c r e a s i n g s l o p e c o u l d o c c u r by t h e s e l f - e x t i n g u i s h i n g n a t u r e o f d i f f u s i o n a l c r e e p . A t h e o r e t i c a l a n a l y s i s o f N-H and Coble creep has been made and d e t a i l s a r e shown i n Appendix  I I I . F i g u r e 25 shows t h e shape o f creep  curves expected f o r pure N-H and Coble c r e e p . A s t a g e I e x p e r i m e n t a l c u r v e i s a l s o shown and a l l a r e p u t on a time s c a l e r e p r e s e n t i n g t h e f r a c t i o n o f t o t a l time t o leach .40 t r u e s t r a i n . Times i n v o l v e d f o r .40 s t r a i n a r e .87 h r s . f o r Coble creep and 5.39 x 10^ h r s . f o r N-H c r e e p . The e x p e r i m e n t a l curve r e p r e s e n t s 700 hours and c o u l d  be p a r t i a l l y r e p r e s e n t a t i v e o f some c o m b i n a t i o n o f N-H and Coble c r e e p . I t has been r e p o r t e d t h a t t h e r e i s no g r a i n e l o n g a t i o n i n t h e Pb-Sn  e u t e c t i c * ^ i n s t a g e I ; There i s g r a i n growth d u r i n g d e f o r m a t i o n * ^ and a l s o g r a i n 16 s t r a i n . G r a i n r o t a t i o n has been observed  . Lack o f g r a i n e l o n g a t i o n might n o t  -42-  e x c l u d e d i f f u s i o n a l creep as an i m p o r t a n t p a r t o f t h e d e f o r m a t i o n mechanism o f s t a g e I . A g r a i n may e l o n g a t e , by d i f f u s i o n , p a r a l l e l t o t h e t e n s i l e a x i s . G r a i n boundary m i g r a t i o n c o u l d account f o r t h e r e t u r n o f an equiaxed shape and an i n c r e a s e d g r a i n s i z e . G r a i n r o t a t i o n would change t h e t e n s i l e a x i s and p e r m i t e l o n g a t i o n i n a l l directions.  I f g r a i n growth does n o t i n v o l v e d i f f u s i o n a l c r e e p , g r a i n s t r a i n  would n o t be expected.Lee* measured t h e t r a v e l o f two marker w h o l l y w i t h i n a g r a i n . I n s t a g e I I I no movement was found. I n s t a g e I I t h i s was e q u a l t o .21 o f t h e t o t a l s t r a i n and i n s t a g e I t h i s i n c r e a s e d t o .30. Growth o f one g r a i n a t t h e expense of another would n o t c o n t r i b u t e t o an i n t e r n a l t r a v e l o f markers b u t o n l y t o t h e g r a i n volume. G r a i n growth by any means, however, c o u l d r e s u l t i n a creep curve o f d e c r e a s i n g s l o p e because t h e s t r a i n r a t e does d e c r e a s e w i t h i n c r e a s i n g g r a i n s i z e . Stage I d e f o r m a t i o n i n v o l v e s GBS and p r o b a b l y some c o m b i n a t i o n o f N-H and Coble c r e e p .  4>  FRACTION OF TIME TO REACH -40  STRAIN  F i g u r e 25. E x p e r i m e n t a l , t h e o r e t i c a l N-H and t h e o r e t i c a l Coble creep c u r v e s (97 p s i ) .  -4A-  5. SUMMARY AND  CONCLUSIONS  I n the s u p e r p l a s t i c range, m a t e r i a l s d i s p l a y u n u s u a l creep p r o p e r t i e s . S t r a i n r a t e i s dependent on g r a i n s i z e and i n s e n s i t i v e to s t r e s s . Creep c u r v e s are l i n e a r w i t h no i n i t i a l o r f i n a l t r a n s i e n t s . A m a t e r i a l i s c o n s i d e r e d " s u p e r p l a s t i c " i f s u p e r p l a s t i c p r o p e r t i e s a r e observed a t e x p e r i m e n t a l l y a b l e s t r a i n r a t e s . There i s e v i d e n c e t h a t s u p e r p l a s t i c p r o p e r t i e s may  reason-  occur  a t low enough s t r a i n r a t e s i n "normal" m a t e r i a l s . C o n v e r s e l y , a " s u p e r p l a s t i c " m a t e r i a l may  d i s p l a y normal creep p r o p e r t i e s a t s u f f i c i e n t l y h i g h s t r a i n r a t e s .  I n s t a g e I T , a l i n e a r creep c u r v e suggests t h a t the d e f o r m a t i o n mechanism a c c o u n t i n g f o r s u p e r p l a s t i c b e h a v i o u r must be one which i n v o l v e s  no  s i g n i f i c a n t s t r u c t u r a l change. Creep c u r v e s i n s t a g e I I show no t r a n s i e n t s , a f t e r l o a d i n g or u n l o a d i n g and the s t r a i n r a t e , a t any s t r e s s i n the s u p e r p l a s t i c range, i s independent of p r i o r s u p e r p l a s t i c d e f o r m a t i o n h i s t o r y . P r i o r e v i d e n c e i n d i c a t e s t h a t most of the d e f o r m a t i o n i n s t a g e I I i s a c c o m p l i s h e d by  grain  boundary s l i d i n g . There must be accommodation f o r g r a i n boundary s l i d i n g to operate.Accommodation c o u l d i n v o l v e one or more of g r a i n boundary  migration,  d i f f u s i o n , or s l i p a t t r i p l e p o i n t s . The m v a l u e f o r s t a g e I I i n the- l e a d - t i n e u t e c t i c i s near .5 and has a maximum v a l u e near  .6.  A t low s t r a i n r a t e s creep c u r v e s show an ever d e c r e a s i n g s l o p e , t h i s c o u l d be due to d i f f u s i o n or g r a i n growth. GBS  o c c u r s i n s t a g e I, but  i s not as d o m i n a t i n g as i n s t a g e I I . G r a i n s t r a i n i n c r e a s e s  i n s t a g e I and  i s n o t a b l y i n d i c a t i v e of a d i f f u s i o n a l p r o c e s s . Some c o m b i n a t i o n of N-H  and  Coble d i f f u s i o n a l creep i s l i k e l y s i n c e the e x p e r i m e n t a l creep r a t e s ; a r e much f a s t e r than those expected f o r N-H  creep and much s l o w e r than c o u l d  be  -45-  a t t r i b u t e d t o Coble c r e e p . The r a t e c o n t r o l l i n g p r o c e s s i s n o t known. G r a i n growth, g r a i n r o t a t i o n , g r a i n boundary m i g r a t i o n , and s l i p and t r i p l e  lines  may a l l have some e f f e c t on d e f o r m a t i o n and t h e r e s u l t i n g creep c u r v e . The m v a l u e f o r s t a g e I i s .33 and i s c o n s t a n t over the s t r e s s range s t u d i e d . In  the s t a g e I I - s t a g e I I t r a n s i t i o n r e g i o n , s u p e r p l a s t i c p r o p e r t i e s  depend on the t e s t i n g method. I n a c o n s t a n t s t r e s s creep t e s t t e r t i a r y  creep  b e g i n s , as necks propagate and grow, a f t e r o n l y a few p e r c e n t s t r a i n and f a i l u r e o c c u r s a t l e s s than.50 t r u e s t r a i n i n t h e l e a d - t i n e u t e c t i c . T e s t i n g under c o n d i t i o n s where the s t r a i n r a t e d e c r e a s e s as the t e s t proceeds the tendency  to neck and e l o n g a t i o n t o f a i l u r e i s much g r e a t e r .  reduces  -46-  SUGGESTIONS FOR FUTURE WORK  There a r e s e v e r a l l i n e s o f i n v e s t i g a t i o n which c o u l d extend from the p r e s e n t work. These i n c l u d e : (1) A d e t e r m i n a t i o n of creep c u r v e s and creep r a t e s over a wide s t r e s s range i n stage I f o r s e v e r a l g r a i n s i z e s . (2) A m i c r o g r a p h i c study of the v a r i a t i o n of the 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 and g r a i n s t r a i n w i t h s t r e s s over s t a g e I . A study of g r a i n e l o n g a t i o n , g r a i n boundary m i g r a t i o n and g r a i n r o t a t i o n might prove h e l p f u l a t low s t r e s s e s . (3) A s t u d y of a c t i v a t i o n energy i n s t a g e I over a wide s t r e s s and  temperature  range and a l s o i n t o s t a g e I I . (4) An e v a l u a t i o n of f a c t o r s , such as time temperature and e l o n g a t i o n , c o n t r i b u t i n g to g r a i n growth d u r i n g s t a g e I I d e f o r m a t i o n . (5) An i n v e s t i g a t i o n of e l o n g a t i o n a t v a r i o u s c o n s t a n t s t r e s s e s over the s t a g e I I s t a g e I I I t r a n s i t i o n to determine i f t h e r e i s a r e l a t i o n s h i p to f a i l u r e and  between'elongation  m.  (6) A more c a r e f u l study of the r e l a t i o n s h i p between s t r a i n r a t e and g r a i n s i z e . 1 2 R e l a t i o n s h i p s between /L and 1/4^ 5 have been r e p o r t e d i n the l i t e r a t u r e 1,3,10,13,20^ j-^ggg i t i o n s i p s to be v a l i d , each v a l u e t a k e n must be r e  a  i n s t a g e I I . Some r e l a t i o n s h i p s i n the l i t e r a t u r e have i n v o l v e d a' s t r e s s which i s i n two s t a g e s of the S-curve and a r e t h e r e f o r e i n v a l i d . The p r e s e n t work 1 3 shows a /L dependence a l t h o u g h t h e r e i s some doubt i n the g r a i n s i z e s . A 13 1 ••• 3 p l o t o f v a l i d p o i n t s f o r Pb-5 %Cd and e u t e c t i c Pb-Sn shows a /L relation3 1  s h i p . The r e l a t i o n s h i p s show s c a t t e r between -2.2 and -3 f o r a Mg-Al a l l o y .  and -3.9  f o r Pb-Sn  and  -2  -47-  APPENDIX I  Computer Programme  •--•i-T!.•/<•; i n r, C v n i L ^ r  r s  />  '»0 0 ? Tim 00 4  q  i  0014 0 015 001*1  0017  coin 0010 00 ?0 00 21 00?? 00? 3 00?4 0025 00?f> 0027 O0?3 0079 00 30 0031 0032 _ 0033 0034 0035 0036 0037 003S 003O 0040 C041 004? 004 3 0044 0045 004 6 004? 0048 004  s.  0  Q^-17-6<1  1Ai?lt04  PAGE 0001  AM/ll.vcjc; r T H F CRFFP TEST CUPVFS P l M c . M s i r i M T [Tl c ( 14) , INOI20.20 ), TIMFf?0,?0),GP.AD(20,?0), l S T " A l N ( ? ' . - 0 ) , TTMry(200),RATF(200),INI 200),DIAL(20,20),XC(5),YC(5) RFAOf, NFxrr.i.! FC'P^ATI 15X.I3) 'IV f-0 1. = 1 , NFXFCU RFAOfS, D T 1 T L F FriPM&T('14A4) PrAO(5,4) SCAFAC»MSHIFT,ELNOT riRMATI FI 0 . 5 , 5X.I 3,Fa.3) K =0 n  ooo^  000 7 '.' ? C " r.ro 001 0 001 1 001 ?  MAIM  4  PHB004 PHB005 PH8006 PHB007 PHB008 PHB009 PHB010  PHB014 PHB015 PHB016 su«sm = 0 . ., •. -.. PHB017 OP 10 I = l.NSHIFT PHB018 R F A O ( 5 , 5 ) SHIFT, NMEASW -V'. PHB0L9 rpRMAT(F10.5,5X, 13) '" ' PHB020 SUMSHI = SUMSHI • SHIFT • ... 0 T MF NS I ON COMNTSI 9,50,7) , IMPORT (20 ,50 )', T IHEXHt 9 i 5 0 )t STRA IH (9 ,50).PHB021 IMTRANS(O),CRISIS! 20,20,7) PHB022 OP 20 J = 1, NMFASU PHB023 PFAO (5,ft) T I M F ( l , j ) , G R A D ( I , J ) , 0 I A L t t i a i * t l » P 0 R T ( I , J J , ( C R I S I S < I , J , P H B 0 2 4 PHB025 1 I J ) , IJ = 1,7) rt • FPRMAT(F9.2,1X,F5.1,3X,F8.5,2X,I2,7A4) , , PHB027 K = K + 1 . \ PHB028 IN(K) = K y i^^'i^M^'Vy^:.):['."' :'. PHB029 IF ( O T A L t l . J ) .GT.O.) GO TO 1? «OFITAL = SCAFAC * GRAO(I.J) * SUM'HI r , PHB030 GH TO 11 PHB031 ^ DFLTAL = 0 1 A L ( I , J ) " PHB032 12 On TP 11 PHB033 TSTRAI = ALOG ( 1. • DEL TAL / ELNOT) ** / , 11., C PHB035 SFLECTION P.F COMMENTS ' v/Vt'Si'.^'^fey'' ^^i^fi^.^.,;:-^,.' ' PHB036 IF ( IMPORT (I , J) . GT.O ) GO TO 13 . ' * _' GO TO 14 • "' - •' " PHB037 13 PHB038 , M = M + i . / • .. . • . .• .•.'•:v.v , j v ^ ; ^ \ : v : i ; K ^ ^ PHB039 00 120 I J = 1,7 PH8040 120. . CPMNTS(L,M,I J)..- C R I S t S . U , J t I J > I»P0RT(L,M) = IMP0RT(1,J) , ' PHB041 TIMEXMIL,M) : = TIKE(I.J) PHB042 STRAIM(L.M) = TSTRAI PHB043 MTRANSID = M , PHB044 14 STRAIN(K) • . = TSTRAI , PHB045 .'. TIMEX <K)....=. TIME! I,.jl . . , . PH8046 ?0 CONTINUE , PHB047 . 10 CONTINUE . ^ PHB048 H = K — 1 • . '" • • •' ' ' •S'-'-- .v :i -.'' : PHB049 DO 30 I = 2, K • PHB050 IFII.FO.K1 GO TO 32 PHB051 RATE(I) = (STRA IN(I +1) - STRATN(I-l) ) / ( TIMEXU + l ) - T I HEX ( T -1)IPHB052 PHB053 GO TO 30 • , i.rv:. . 32 RATF(I)=( S T R A I N ( I ) - S T R A I N ( I - l ) ) / ( T I M E X ( I ) —TI HEX ( I —11 ) • PHB054 30 CONTINUE ' PH8055 RATE (I ) = RATEI2) ... PHB056 C • PHB057 TRYING TO GFT A OFCFNT OUTPUT V; N U M F R o =o ........ ' ... ., . . <" •. , PHB058 . /  f = o  ..  •'.v..:• •. '  r  t  r  t  :  r  i  :  -48-  n r-? o  !V T, f p ' - " l l i '  T r, -i  "j . 1 0 0 «. 7  " F J M 1 S  r  I-.  '"ATM  11  , NSTART •IPACF  fAOF f>002 PHH059  = 4 0  PHB06 0  PHB061 P H B .16.2  K / 4 0+ 1  =  NPAOTF  ]i:4'):l".  03-G7-6O  = 1  K  =  (.H'PAGF  -  -  1  )  *  t,n  IT ( N P A O ! F . l - ' O . O ) O P T O 41  ,, r,c 0 0^6  on  PH306 3  PHB064 PHn065 "0^7 . .PH8066 / NUMFRO = 'NIIM R0 + 1 • "'• ' ' ' PHfl067 ons a PHB068 • WRITFI6,?) NUMFRO , T I T L E '.V ? "060 FORMAT(lOX,33HANA|.YSI.S PF THE C R F F P T F S T CURVES. 1 2/. 5HPAGE ,!?.4X,PHR069 1 IHS/66X, 1H*/1X, 1 4 A 4 . 2 ! /66X.1H* 1/7H NI.IMRFR , 10X.4HTIME,10X.6HSTRAIM ,PHB070 H O U R *i * , - 12 x, i H * i . ; .PHB071 . J' 2 9 X , UHSTRAIN R A T F ,9X , 1H*/16X , 5HH0URS , 2 3 X , 10H 0 06 1 '.'..''. ' • " "PH3072" , : ; .... G O TO 46 p .' ,-.• ; T O ,43^-.'I?I4J. . V ' . ~SV' . 0062 PHB07 3 ••'' jr;$ e~' ,• '• "• PHR074 0 0 6 3 43 ' ' N F I N I S = 'K'" ' 'v«i^;>' ' •'' .-'Or.' •..''•' 0 0 6 4 46 ., . 00.130 I = NSTART ,NFINI$/: . PHB075 ' . ••.•.•',..; ;,r^"; •>',..,;,• 0065 PHB076 V . N S P A = INf-T) - ( !VU »/10n»:-l6 v'='':.;':^ . :i,V \ : PHB077 • .0066 h. I F ( N S P A . E Q . l ) GO T O 44' '-'-'^^^C •?> \v ?.' "• \vA;•/,=''.'; •:•' ...... ..... 0 0 6 7 ' PHB078 ..' GO-TO 45 ;:• •' ; ; ' ' - . ^ ^ ^ ^ ^ ^ f ^ ^ ^ Y ^ .'' .; ':' . ' PH8079' • • 44 .•• WRITER,7).M; . ' . ' , . . ' • , •'• ' , ; 5 S S 3 ^ 0 063 • 0 0 6 9 7 . ••'•• FORMAT { 66X> l.H*')'•'•'• '•'••' "'''>'• PHP080 0 0 7 0 45 PHB081 .; WRITE!*,3).-IMUt.. TI,MEX!iI;,lSST,«A,lfH M , RATE (11 • 0 0 7 1 • .• 3 •''" •'• FORMAT ( 3 X , 1.3 , 6X , F 9 . 3 ,7xV'EiiQ'^3.'»^feiE,tO . 3 ,'.11 X^TH*!-'*!'-if. i 'V ' PIIB082 ... . 1 3 0 . PHB08 3 0072 >|"'i.', • ' . . ' • "PHB084" "•' ~'"-"o07 3 .:f ..NSTART .= ",' NSTART ; * - . * O j ; < i ! ^ P p g ^ S ^ ^ ^ % l , i r - I V f 0 074 5 '••\")>"}i~'' •• ',PHB08 • i / 'NFINIS = j.NF IN! S' +j ^ O W ^ 0 l ^ m ^ ^ ^ ^ r < P . 0075 ••• W R I T E t 6 , 9 ) -r; 'rtji.v-i '•.'' • PHBC86 0076 9 PHB 0(3 7 .-, • . FORMAT! 1H11 . ' -1i":^^l^|^Mfe ;^ • v- 0077 . •.'•V"r.40^'; >:vCONTINUE^,:^f X^^^^S^^^M^^^^^ ^v'X" '.C:'.- "-PHB088 CH^::y"V'." J"' '' , 1.PHB0S9 :.l.'i.'.C_.'J; A TR ANSF'E R^/tQi^THEPL'OTT-NGi^'OU^ " •' ooV<i '"' ^"'ot'MENS'lON'ftR^^^ 1 ,KTPANS(9) '. PHB090 • 0 0 7 9 ' . • PHB091 e> no' 70 i ^ K : ^ : * i i a ^ W w € l ^ '• 00«0 T i M t t . n .,= T t M F x m . / . l?:':^'/'' • • '• ''-PHB092 '^ . . 00«l PHB093 RAT!L,.IK.i»:j..RATEm.;;.'^ )rt,'i/:-;^'v'. . t\- . • . 008? • .PHB094 ;.*~ ' iv^.'jv/-''' v}-.^; ; . STOAd.Il = S T R A I N m ? © ^ « P ^ # § S ^ . PHB095. :'±Y 0O83._ ,'...•; I.kti/7P4=;!i.C.ONTTNllfi^B-vi^ .'PHB096 . CS-'«'^'-\ , 0 0 / 8 4 •' 0O;,10d'. Xtfyktr-lt-ff&'Wti^ J'!,- ••'-;'^''7^.V^ 'V.'.'t"'' >i |;PHB097 • '.';V- 0 0 8 5 . . . V T I T (I..T1U: TITLE (,i:)?'\V'< -'ti;VffMf»?€?^ ' • 100 ' CONT INUE.VM" 00P6 '..'r'-vtV'"' ' ' i''-:<^' 'PHB098 • '•'' '•'•kCij/feSHli&Sv »'-^S'^%te Ki W'*' .':. . . . •; 0 0 8 7 KTRANS(L) = K > > , •'t , , 1 PHB099 ',. 0088' • • • ' " 6 0 ' / ..V.'CONTINUF PHB100 ,» ' •, i , , ' ", * 0089 P H B 1 0 1 . 7' .i^c.,yc. v;5,; .i!...5,.i.^ ./,..'-.';::•. . .... ... .- .. PHB 102 ''^jCiyV* • "V""... "c'".' PLOTTING ROUTINE ^ * ' » ;,PHB103 •.'•" -'''fit r\r-f^V-'.-j'':- "'•'.•''V ' ,r ; .; :-'i: :C.'.>'"..''' •'' P H B 1 0 4 ''"c ''A • ; 0090 C A I L PLOTS , > ..i;',.-^..j.,-..... PHB105. :. . 0 0 9 1 :-"i:^A"; •" '" - P H B 1 0 6 • :;> n ao L - i,NEXECir io K. = KTP.ANS!L) . PHB 10 7 i::'^ 0 0 9 ? ' . . ... 0 0 9 3 PHB108 •' " ..on'90 I = i , K . . ' - • -'.-"i>-7 .V.. O094 TIMEX! I ) = . : T I M ( L ' , 11 ' .i..v!''-„..; /-'''.;c'.'. r -.^'''' P H B 1 0 9 •• . ' ;.v'"' ' •.. •• P H B 1 1 0 • '•0095 R A T F ( I 1 = RAT 1 1 . , t ) -•".•:V''-.-"':'' ;' -.V •• ' -:^"'V' ., ..... 0096 •PHB112 ... S T P A ! \ ( I) - S T R A ( 1 , I) .., ..• .•;••/< ..... . ' : 0097 9 0 " :•• C O N T ' T N M F : ' - ' - . - . ' - . ' : . - ' V . ! ' ' : •'' •:'.• • ' • ' '.V • ; e .'': "'' '' -PHB113 • . : 009s PHB114 ;.. on up. i... f i ' » ' . 4 . .... . .' ','••. • ' i ' . . ' " ' . • v ;)  TO  4 ?  .  . 41 .NPAGP ;=. NPAOF. - 1 42 • ' " D O 40 J = 1,N»AGF  ,  C  ;  :  I F ( K > L T > N  I N  ;  S )  R  0  :  ;  :i  1  i  :  V;  :  x  ;  =  v  V  ;  ;  i  l V  ;  :  :  V  l  1  1  ;  ::  :  %  j  :  1  5:  J  J  1  NA  ;  A  5  1  !  :  :  J  ;  ;  >  :  :  v  1  :  ; v  :'  -49-  0 pnqn 0 100  0 to 1 010? 010' 0 104 0 105  in of.  0107 CIO" oioo Oil:) 0111 0112 0111  0114 0 11 = 011ft -.0117 CUR Olio 0120 0121 0 122  . "12 3  012'. • 0125 012ft .. ' 0127 012B 0129 0130 0131 013? 0 133 0134 0 135 01.36 0137 0138 0139 • 0140 0141 014? ... 0143 0144 0145 014ft 01 47 014 8 014 0 .'  W P I I F P  MAIN  18:31:0 4  03-17-C9  PAC.P 0003  TITLF ( 1 ) = TIT(Ltl) PHBI lb CONTIVUF PHB116 CALL 1 IMF (XC.,YC,5,l) PHB117 WRITF(ft.lOOO) X C . Y C 1 000 FORMAT(12F6.2) CALL PLOT ( l.,0.,-3) PHB118 CALL SC AL F (TIMFX,K,10.,XMIN, DX , I) PHB119 CALL SCAtE (STRAIN,K,7.,YMIN,DY,1) PHB120 CALL SCALE <RATE,K,7.,ZMIN,07,1> PHB121 nn 50 I = 1,K PH8122 RATE (I) = RATE(I) f I. PHB123 STRAIN! I) = STRAIN!! 1 + 1 . PHB124 l-IR?TF<6,1000) TIMEX( I ), STRAIN (I I.RATFd ) 50 CONTINUE PHB125 CALL AXIS (0..I..18H TIME HOUR,-18,10.,0 .,XMIN ,DX) PHB126 Y) CALL AXIS (0..1..12H STRAIN , 1 2, 7. , 90. , YMI DN, PHB127 CALL IINF (TIMEX,STRAIN,K,l) PHB128 XO = TIMFX(K) - .4 , PHB129 ;' ' • " • ..YO =. STRAIN (K) .1. • : ... PHB130 CALL SYMBOL (XO,Y0,.07,6HSTRAIN,0.,ft) PHB131 CALL AXIS (10.,1.,25H STRAIN RATE 1/HOUR,-25,7.,90.,7MIN ,DZ)PHB132 CALL LINE ( TTMEX.P.ATE.K, tl • PHB133 ZP = RATF(K) • .5 ...... PHB134 . CALL SYMBOL 1X0,Z0, .07, UHSTRATN RATE.O. , 111 ' • PHB135 CALL. SYMROL tl. , 8. , . 1 4, T I TLF , 0. , 80 ), .«.sj •***.> PH8136 PHB137 "c :• PHB138 . c PRINTING.(IF COMMENTS .. ,•'•',)["li/' "?S'0i'idM:., PHB139 c ' M = MTRANS(L) . . ,•,:•;:..:'.-••,..'. PHB140 ,YE(2) ,C0M1I4).C0MPHB141 DT MENS T ON TI MM<50),STRAM(501.XFf6),YF(6)i XE(2) 1213),LfAP(50) . PHB142 00 9999 t = l,6 ' • "i. • •', • . XF(1)=0. 1 (' , 9909 YFII) = 0. • > * 110  X E ( 1 ) = O . :v  ...  . .-i. : ......  v  , -  «  • .  XE(2)=0. YE(1)=0. YE(2)=0. SPACIN = 0. ALTITU - 0. 01 STAN = 1. • .. ... .T.-.•.••:. . J ' -'•.>:.. . KOUNT=0 '. •'''^•^•''^'s'ti'^'V'?" WRITF(ft,1002) KOUNT 'S^til 1002 FORMAT(16) < 1 I'-; -V'v on ' 140 J - 1, M ., VTIMM(J) = (TTMEXM(L.J) - XHIN) / DX ' STR AM ( J ) .'= (STRAIM(L.J) - YMIN >/ OY • .1 ^ • XF(1) •= TTMM(J) XF(2) - XF(1) + .0? XF(3) = XF( 1 ) XF(4) = XF( 1 ) • - .02 XF(5) = X F ( 1 ) '. XF(6) = XF(1) LOGICAL MIDDLE, PLACE,CLFAR .MIDDLE. =. STR AM (J) .GT.5. •• ' :  :k  PHB143 PHB144 PHB 150 ••"••J"i.  : PHB151 PHB152 PHB153 .-.< . PHB154 PHB155 PHB156 PHB157 PHB158 PHB159 PHB160 PHB161  -50-  rp(} (; ••, rv i; rr'MM i.  "A IN  T  0 1  so  0 1  S1 7  0 1 <  R  143  1s4 1 4 4  0 1 5 ~ R  I F ( PISTAM . L T . . 2 ) xrni = TIM«IJI  0156  IF  (  X F ( 1)  0 15 7  IF  {  xtrm  XF(2)  0 15 8  r> i '.T  "Iff ^161  xm  =  X02  =  =  .LT.  .1)  1  . T I M M I J )  9.35 i TTMMU) . G T .  *  16? 0170 0171 017? 0173  T  GO  0  1.46  0174  Ot7S 0176  147  0175 0179 0 180  0181 01"? 0183 0184 0185 0186 • 0187 0188 0189 0190 019? 0193 0194 0195 01O6 0 1 9 7  0198 0199 0?00 0?0? 0704  =  9.85  •  147 = 3.7 Y F ( 2 ) = 3.5 Y01 = 2.06 YM1) = S T R AM IJ 1 - .08 Y F ( 6 ) = STBAMUI - . 2 5 . Y P 2 = Y01 ANGLF = 9 0 . TO  *'  ...  : •• .  . ' '•'''','  ',' ... , •  - 0  PHB179 PHB180 PHB181 PHB182 PHB183 PHB184 PHB185 PHB186 PHB187  KOUNT=KCUNT+l  WITE(6,I002) K O U N T I F ( OISTAN .LT. . 2 ... AND. PL AC E ) GO TO 142 G O T O 148 ..... .,.,.''•••.•• :, • I F I PLACE I G O T O ,141 d ' I F ( TIMMIJ) . G T . .72 ) GO T O 151 X01 = .1 ' , '. . ;j  ' PHB188 •PHB189 145 PHB190 ' '•' ' PHB191 PHB192 GO T O 1 5 2 ' •'•.'-• • , / ]•'• , " ••: • PHB194 '' . . 151 ..I F (..TIMMIJ) . G T . 9.27 ). GO.TO 153 ;.'•'"_.-.. . .• '• ,-.'. •' '.. . ''. .. PHB195 X01 = TIMMIJ) - .72 .". .• ;•.«;.'» PHB196 G O T O 152 .". . PHB198 153 xm =8.55 ' PHB 199 152 X02 = X01 . •.. •• PHB201 XE(1) = TIMMIJ) . "'•"'•;' •..'•''.' ~ • PHB202 PHB203 . X E ( 2 I =. TIMMIJ) .... •.'".'. . ,.1 •• ROOM = TIMMIJ) - SPACIN . ' •". ',. PHB204 .'•'' '• '•" ' CLEAR '= ROOM . G T . 1.44 . O R . VCLEAR . G T . .2 . PHB205 VCl.FAR = STRAM(J) - A L T I T U ' PHB206 SPACIN = TIMMIJ) PHB207 ALTITU = STRAMI J) ' . "• PHB208 ;  ••'.'••'  r  1  :  ?  KOUNT=KOUNT+I  0701 0 7 0 3  .1  KOUNT  YF( 1)  LFAP(J)  0177  =  .1  W?I F(6,190?)  6 5  "'  X F ( ? I X F I ? )  016 8  "  01 6 6  0191  PHB162 PHB163 PHB164 PHB165 PHB166 PHB167 PHB168 PHB169 PH8170 PHB171 PHB172 PHB173 PHB174 PHB175 PHB176 PHB17 7 PH8178  V  T I M M I J I  0167  141  " 1 6 4  CI  PAGF 0Q04  -->  GO TO 1 4 !  .  IF ( MIPPLF) GO TO 146 YF( 1) = 5 . P YF(?) = 6. YP1 = YE ( ? ) V F ( T'l = STRAM(J) •' .08 v r ( 6 ) = STRAMI J I + .?5 K0UNT=K0UNT+1  0 16? " 1 6 3  ...  PLAC.F = IMPORTU.J) .LT.? I ( J.GT.l) G O Tp 1 V 3 G O T'l 1 4 4 0 1ST AN = TIMM(J) - TIMOUT  18:31:04  F  0 1 5 3 0  0 3-17-6')''  156 159  .  .  . ' : . : ...  ..,.;•'.'.''..•'•.:•'.  WRITEI6,10021 KOUNT ' I F ( MIOOLF) G O T O 154 I F ( .NOT. CLEAR ) G O T O 157 I F ( I F A P ( J - l ) . F O . 1 ) G O T O 15R Y F ( 1 ) = STRAMIJ) + .08 LFAPt J 1 = 1  PHB209 PHB210 PHB211 PHB212 PHB213 J  -51-  r  tf'L'I'-'A'  II " c  I 1/ [  1 54 157 153  n  c  155  149 160 170  r  0?4"< 0?',4 P?45 0246 0 74 7  1P:31:04  c  r? \ i  0 71 1 07I r:7?o <~??1 07?? i??t 0 ? 7 /, 0?7 0??6 0??7 0?7o 0??° "O?30 o ? 31 0 71? r, ? 3 3 0 7 3/, 0?? i n?3f. 0737 ^7 3? 0?3i 0?40 o?4i 0?47  03-17-69  YF(6)'= STRAM(J) + .75 YF( 1 > - YFIM + .? Y>-(?) = YC(6I * .4 vni = YF(?) + .1 vn? = YF(?) KPU'NT-KOIINT + 1 WPITF(6,1007) K flUNT 00 TO 155 IF ( .MOT. CLEAR ) GO TO 156 IF ( LEAP(J-l) .EQ. ? ) GO T O 159 YF(l) = STRAM(J) - .OB L A°(j) = ? YF ( 6 ) = S TR AM t J I .- .75 YF( 1 ) = VF(6) - .2 ••. , YE(?) = YF(6) - .4 ' \ .. YD 1 = YF(7) - .1 ANGI. F = 0. YP2 = YEI?) - .? • ' ., KOUNT=KOUNT*l WRITE (6,100?) KOUNT DO 160 1 = 1,4 CPM1(I) = COMNTSIL,J, I) in 170 I = 5,7 IA = I - 4 -. • . ' . • •• ' , CPM?(IA) = COMNTSIL, J, I ) . •.. CALL LINF ( XE«YE,2,1) ; . , WRITF(6,1000) XE,YE CALL SYMBOL ( X01 ,Y01 , .07 ,C0M1 , ANGLE,24) CALL SYMpnt (X02,YD2,.07,COM2,ANGLE,18) WPITF(6,1000) X01,X02,YDl,Y02 , V: TTMOUT = TIMM(J) YF(?) =.YF(1) YF(3) = STRAM(J) YFI4) = YF ( 11 • • ' •'• YF(5) = YFf 1) .. ... CALL LINE (XF, Y F , 6,1) WRITEI6.1000) . X F . Y F ; CONTINUE ., THE END O F COMMENTS' CALL PLOT (12.,0..-3) CONTINUE ... , , ... CALL P L O T N O . ,>.'  7 0 (• "70 7 0  071 C>1 I 071 ? o?l < 0 714 0715 0?1  MAPI  14?  1 40  c  no ..  STOP  _  END  •• , '. •.  •  V  ' -  . ' ...  °*GF 0005 PHB214 PHB215 PHB216 PHB217 PHB218  ;  PHB220 PHB221 PHB222 PHR223 PHB224 PHB225 PHB226 PHB227 PHB228 PHB230 , PHB231 PHB232 PHB233 PH8234 PHB235 PHB236 PHB237 PHB238 PHB239 PHB240 PHB241 PHB242 PHB243 PHB244 PHB245 PHB251 PHB252 PH8253 PHB256 PHB257 PHB258 PHB259  -52-  APPENDIX I I A d d i t i o n a l Creep Curves  F i g u r e a. Stage I I (SGS), 572 p s i .  F i g u r e b. Stage I I (SGS), 858 p s i .  F i g u r e e. Stage I I (LGS), 1221 p s i  F i g u r e f . Stage I (SGS),  120 p s i .  Figure i .  T r a n s i t i o n (SGS), 2574 p s i .  F i g u r e k. T r a n s i t i o n (LGS). 1954 p s i .  F i g u r e 1. T r a n s i t i o n (LGS), 2280 p s i .  F i g u r e m. T r a n s i t i o n (LGS),.2606 p s i .  F i g u r e n. T r a n s i t i o n (LGS,), 2932 p s i .  F i g u r e o. T r a n s i t i o n (LGS), 3258 p s i .  F i g u r e p. T r a n s i t i o n (LGS), 3908 p s i .  F i g u r e r . T r a n s i t i o n (LGS), 4560 p s i .  F i g u r e s. T r a n s i t i o n  (LGS), 4886 p s i .  F i g u r e u. Stage I I I , 7326 p s i  F i g u r e v. Stage I I i n c r e m e n t a l l o a d i n g .  -58-  F i g u r e w.  Stage I I I u n l o a d i n g .  -59-  APPENDIX I I I  C a l c u l a t i o n o f T h e o r e t i c a l Creep Curves f o r Pure N a b a r r o - H e r r i n g and  Pure Coble  Creep  Creep.  N-H. Assume t h a t a g r a i n d e f o r m s o n l y b y N-H d i f f u s i o n a l Initial  length  = lo  I n i t i a l widths  = w6  creep.  Increases i n length = A l Increase i n width  = Aw  Final  = lo + o l  length 1  Final width w  = wo + Aw  Engineering s t r a i n  =  T r u e s t r a i n de  = dl/1;e = l n^ = In lo F, + 1 = e or E = e  = E  e  For constant  1  £  +  -  ^  1  = I n (1 4- E ) lo .  volume  + £g = 0  e. +  Assume E £ = £ 3 = -  l n ( l  Hz\ w i t h a  f , . -  +  1. (  ( 1 Assume i n i t i a l  %  l „ ( l  - i „ +  E ) T  =  (  Poissons r a t i o of % f o r p l a s t i c  +  ( 1  1 +% ) ~  h  L  g r a i n dimensions  After engineering s t r a i n E  | i ,  L o , Wo  deformation.  -60-  L = Lo(1 + E ) = L o e  E  J_i _\,  W = Wo(l + E )  2  2  = Woe  D e f i n e g r a i n s i z e L where L If  2  _  G  / 9  '  2 2 2 2c 2 = ^ ( L rw ) = %Lo e + ^ Wo e  - E  t h e g r a i n i s i n i t i a l l y equiaxed -2 ! 2 j. 2e , _£-, L = %Lo {e + e }  From Zehr and B a c k o f e n ^  e  «VDL  "  a i s a g e o m e t r i c a l c o n s t a n t - 10  where  -23 3 v i s t h e a t o m i c volume (1.43 x 10 cm f o r Sn) D  i s the c o e f f i c i e n t f o r l a t t i c e  L  diffusion — 16  k i s Boltzman's c o n s t a n t = 1.38 x 10  o erg/ K  T i s the a b s o l u t e temperature (°K) Pure N-H creep i s much s l o w e r than t h a t found e x p e r i m e n t a l l y . V a l u e s o f D f o r Sn w i l l g i v e t h e f a s t e s t r a t e . I f t h e g r a i n s i z e i s 2 m i c r o n s and T = 26°C. J{  N-H = 2.74 x 1 0 de =  1 7  d  y  I crn^  n e S  = 3.96 x 1 0  s e c  1 2  lb-sec/in  2  dt  71m  1** T2  ,  f  v craD  -f  kT  L  e  mvD J • , 2 a\ L) t = h Lo kT T  t  =  ZLN^ 4s  dt  (e  T  { e  2e _  2 e  o -e  2 e  2 2e + e ) d e - \ Lo { ^ - + e e  £  + Jg}  -61-  a = 97 p s i  71 N-H  = 3.96 x 1 0  v  1 2  ,9  _ 1-1 x 10 • , 2e * ""4 x 97 " { e  t = 2.85 x 1 0 { e 5  N-H  x  ^ 5 f £ "  * 3600 sec r  =  1.1 x 1 0  9  in  o -e , 2 e  +  1 }  - 2 e " + 1} h r s  2 e  e  Creep  True S t r a i n  F r a c t i o n o f time t o r e a c h .40 s t r a i n  Time ( h r s )  0  0  0  .01  1.14 x 1 0  4  .02  2.28 x 1 0  4  4.2  .05  5.70 x 1 0  4  10.6  1.16 x 1 0  5  21.5  .20  2.42 x 1 0  5  45.0  .30  3.82 x 1 0  5  71.0  .40  5.39 x 1 0  5  100.0  .10  .  Coble The a n a l y s i s  i s s i m i l a r to t h a t f o r N-H creep.  G r a i n s i z e i s i d e n t i f i e d as L  3  = h ( L o + Wo ) 3  = h Lo e  3  3  f o r e q u i a x e d g r a i n s Lo = Wo 7 3 _ , _ 3 , _ 3 e , _ .3. - /2 L = %Lo (e"" + e '") J  T  J  a  I  rn =  7 l c  E >  J  L kT 3  ° ~~ BvwF  u  gb  3 £  + %Wo e 3  3 / 2 e  2.1  -62-  where  D ^ i s the g r a i n boundary d i f f u s i o n  coefficient  i s a c o n s t a n t - 150 w  i s g r a i n boundary w i d t h  T  i s 26° C  L  i s 2 microns  a  i s 97 p s i  77 co =  3.88 x 1 0 ^ dynes sec/cm  =  than the e x p e r i m e n t a l r a t e and 7 ^  3  kT  3 Lo 2  t =  t =  f  2  dt  , 3e . - /2e, , ,aBvwD„>. , (e + e )de = (____££ )  J  kT  Lo\t 3vwDgk Lo kT 3vwD gb  r  v  6a  e  3e  . - /2 . . 1 - 2e + 1J 3  • /2e + l ] 3  f^)Le  3e  - 2e  , f 3e „ - / 2 e . .1 t = . 271 e - 2e Ihrs. 3  7  s i n c e c o b l e creep i s much f a s t e r  g i v e s a slower r a t e of creep than7?Sn.  agvwD  L de  T  ,-7 10 cm)  -63-  Coble Creep  True S t r a i n  F r a c t i o n o f time to r e a c h .40 s t r a i n  Time ( h r s )  0  0  0  .01  1.62 x 1 0 ~  2  •02  3.24'x 1 0 "  2  .05  8.4  x 10~  2  .096  .10  1.7  x 10"  1  .196  .20  ,. 3.6  - 1  .415  .30  5.9  x 10"  1  8.7  x IO"  1  .40  •  *  x 10  .0187 ,  .0374  '  .680 1.00  -64-  BIBLIOGRAPHY  1. D. Lee, G.E. Res. and Dev. Center Report #69-C-005. 2. C.E. Pearson, J . I n s t . M e t a l s , 54 3. D.H.  Avery and W.A.  4. D. Lee and W.A.  (1934).  Backofen, ASM T r a n . Quart., 58 (1965) 551.  Backofen, T r a n s . AIME, 239  (1967) 1034.  5. T.H. A l d e n , A c t a . Met., 15 (1967) 469. 6. H.E. C l i n e and T.H. A l d e n , T r a n s . AIME., 239 7. D.L. H o l t and W.A.  Backofen, ASM T r a n s . Quart., 59 (1966) 755.  8. T.H. A l d e n and H.W.  S c h a d l e r , Trans. AIME., 242  9. P.J. M a r t i n and W.A. 10. S.W.  Zehr and W.A.  (19°?) 710.  (1968) 825.  Backofen, ASM T r a n s . Quart., 60(1967) 352.  Backofen, ASM T r a n s . Quart.  11. D.L. H o l t , T r a n s . AIME, 242  , 6(1968) 300.  (1968) 25.  12. H.W. Hayden, R.C. Gibson, H.F. M e r r i c k and J.H. Brophy, ASM T r a n s . Quart., 60, 3 (1967). 13. T.H. A l d e n , ASM T r a n s . Quart., 61 (1968) 559. 14. T.H. A l d e n , T r a n s . AIME, 236  (1966) 1633..  15. R.C. G r i f k i n s , J.. I n s t . M e t a l s , 95 (1967) 373.. 16. R.C. Cook, M.A.Sc. T h e s i s , U n i v e r s i t y of B r i t i s h  Columbia.  17. S. F l o r e e n , S c r i p t a M e t . , 1 (1967) 19. 18. W.A.  Backofen,  I..R. Turner, and D.H.  Avery, ASM T r a n s . Quart., 57 (1964) 980.  19. P r i v a t e communication w i t h T.H. A l d e n . 20. A.K. Head, P h i l . Mag.,  44, (1953) 92.  21., A.K. Head, P r o c . Phys. Soc. (London), 22. Y. I s h i d a and M.H.  1366  (1953) 793.  Brown, A c t a Met., 15 (1967) 857.  .13. H. G l e i t e r , E. Hornbogen and G. Baro, A c t a Met.  , 16 (1968) 1053.  -65-  24. R.G. G i f k i n s and K.V. Snowden, T r a n s . AIME, 239 (1967) 105. 25. S.K. Tung and R. Maddin, T r a n s . AIME, 109 (1967) 905. 26. P.R. S t r u t t , A.M. Lewis and R.C. G i f k i n s , J . I n s t . M e t a l s , 93 (1964) 71. 27. R.B. Jones and R.H. J o h n s o n , D i s c u s s i o n , ASM. T r a n s . Quart., 59 (1966) 356. 28. W.A. Backofen e t a l i n D u c t i l i t y , ASM, M e t a l s Park,  (1968) 279.  29. A. Karim, D.L. H o l t and W.A. Backofen, Trans AIME, 245 (1969) 1131. 30. P. Chaudhari, IBM Research Report, RC 1946. 31. T.H. A l d e n , " I n t e r a c t i o n o f D i s l o c a t i o n s and G r a i n Boundaries D u r i n g Superp l a s t i c c r e e p " , I n t e r n a t i o n a l Conference, " I n t e r f a c e s " , Melbourne, A u s t r a l i a , August, 1969. 32. P. Chaudhari, A c t a Met. , 15 (1967) 1777. 33. E.N. Andrade and K.H. J o l i f f e , P r o c . Roy. Soc. (London) A 254 (1960) 291. 34. R.C. G i f k i n s , Trans AIME, 215 (1969) 1015. 35. S. B h a t t a c h a r y a , W.K.A. Congreve and F.C. Thompson, J . I n s t . M e t a l s , 81 (1952) 83. 36. J . E . Breen and J . Weertman, J . M e t a l s , 7 (1955) 1230. 37. F . G a r o f a l o , Fundamentals (1965).  o f Creep and Creep-Rupture  i n M e t a l s , N.Y. M c M i l l a n  38. C M . Packer, R.H. Sohnsen and O.D. Sherby, Trans AIME., 242 (1968), 2485. 39. R. Kossowsky and S.H. B e c h t o l d , Trans AIME, 242 (1968) 716. 40. D. McLean, Trans AIME, 242 (1968) 1193. 41. P. Chaudhari, S c i e n c e and Technology, Sept. 1968, P.42. 42. H.J. McQueen, W.A.. Wong, and J . J . J o n e s , Can. J . Phys.,  45 (1967) 1225.  43. R.C. G i f k i n s , J . I n s t . M e t a l s , 79 (1951) 233. 44. W.A. Wood, G.R. Wilms and W.A. RachinRer, J . I n s t . M e t a l s , 79 (1951) 159. 45. T.H. A l d e n , " D i s l o c a t i o n Climb. T h e o r i e s o f Creep and S u p e r p l a s t i c i t y " , (1969). 46. C.M. P a r k e r and O.D. Sherby, ASM T r a n s . Quart., 60 (1967) 21. 47. P r i v a t e communication  with K.C  Donaldson.  

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