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The deformation characteristics of zinc and cadmium Risebrough, Neil Reesor 1965

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THE DEFORMATION  CHARACTERISTICS  OF ZINC AND CADMIUM  by  NEIL REESOR RISEBROUGH B.A.Sc.,.University of Toronto,.i960 M.A.Sc, U n i v e r s i t y o f T o r o n t o , 196I  A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY  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, t o t h e required standard  THE UNIVERSITY OF BRITISH COLUMBIA  December,  I965  In the  requirements  British  mission  for  Columbia, I  available  for  for  an  reference  be  without  of my  Department  this  of  advanced  and  the  study.  by  for  the  Library I  this  Head  financial  permission,.  Metallurgy  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 Date  that  F e b r u a r y 15th,  Columbia,  1966  in partial  degree at  the  thesis  fulfilment  University  shall  further  o f my  I t i s understood  thesis  written  thesis  copying of  granted  representatives.  cation  this  agree  extensive  p u r p o s e s may his  presenting  make i t  agree for  that  Department  shall  not  of freely per-  scholarly or  that, c o p y i n g or  gain  of  be  by publi-  allowed  The  University  of B r i t i s h  FACULTY OF GRADUATE  Columbia  STUDIES  PROGRAMME OF THE F I N A L ORAL EXAMINATION FOR THE DEGREE OF DOCTOR OF PHILOSOPHY  of  N E I L REESOR RISEBROUGH  B.A.SCc, U n i v e r s i t y  o f T o r o n t o , 1960  M.A.Sc.p U n i v e r s i t y  o f T o r o n t o , 1961  TUESDAY, FEBRUARY 1 5 , 1966 AT 2:30 P.M. I N ROOM 210 METALLURGY BUILDING COMMITTEE I N CHARGE Chairman:  J . Ross MacKay  W. M. A r m s t r o n g J . A. L u n d C, A, B r o c k l e y E. T e g h t s o o n i a n L . G. H a r r i s o n D. T r o m a n s D. L. W i l l i a m s E x t e r n a l Examiner: Professor  J , E, D o r n  of Materials  Science  Lawrence R a d i a t i o n L a b o r a t o r y Berkeley,  California.  THE  DEFORMATION CHARACTERISTICS OF  ZINC AND  CADMIUM  ABSTRACT T h i s w o r k was u n d e r t a k e n t o s t u d y t h e n a t u r e o f the d e f o r m a t i o n mechanisms i n p o l y c r y s t a l l i n e z i n c a n d cadmium o v e r a t e m p e r a t u r e r a n g e f r o m 77°K t o 300°K. I t has been o b s e r v e d t h a t the s l i p system which i s observed under microscopy i s that of second o r d e r <1123>. A t t e m p e r a t u r e s a b o v e T = H  o n l y non b a s a l normal l i g h t _ p y r a m i d a l £ll22j T = , 4 t h e amount T M o f n o n b a s a l s l i p i s g r e a t e r i n z i n c t h a n i n cadmium. The amount o f t w i n n i n g , s u b s t r u c t u r e f o r m a t i o n a n d g r a i n boundary m i g r a t i o n i s comparable i n b o t h systems. N e g a t i v e w o r k h a r d e n i n g b e y o n d t h e U.T-. S. a t t e m p e r a t u r e s a b o v e T = .4 i s a s s o c i a t e d w i t h r e i i . . H crystallization. In  both systems  at temperatures  }  below T  = ,26 a H r e g i o n o f t e m p e r a t u r e and s t r a i n r a t e i n d e p e n d e n t l i n e a r w o r k h a r d e n i n g o c c u r s . The e x t e n t o f l i n e a r h a r d e n i n g i n c r e a s e s w i t h d e c r e a s i n g temperature below T = .26. Above T = .26 p o l y c r y s t a l l i n e h a r d e n i n g i n .H H b o t h s y s t e m s i s p a r a b o l i c f r o m y i e l d on a n d t h e r a t e o f hardening at a g i v e n value of s t r a i n decreases w i t h increasing temperature. Cadmium s i n g l e c r y s t a l s showed a s i m i l a r t r e n t i n t h a t b e l o w .26 b o t h 0^. a n d 0^.^ s  r e m a i n e d c o n s t a n t . H o w e v e r , a b o v e .26 t h e r e was decrease i n the shear hardening r a t e s . I t was o b s e r v e d t h a t obeyed o n l y i n the l i n e a r p o l y c r y s t a l s and i n Stage b e l o w .26. When d y n a m i c with increasing strain.  a steady  the C o t t r e l l - S t o k e s law i s hardening regions of I I hardening of s i n g l e c r y s t a l s recovery occurs A C T increases °~  I t h a s b e e n o b s e r v e d t h a t b e l o w .26 t h e l i n e a r h a r d e n i n g r a t e i n cadmium d e c r e a s e d w i t h i n c r e a s i n g g r a i n s i z e ( c o n s t a n t s p e c i m e n d i m e n s i o n s ) so t h a t  e =  0  O  +  kd  The v a l u e o f 8 was shown t o c o r r e s p o n d t o t h e t e n s i l e hardening r a t e d u r i n g Stage I I s i n g l e c r y s t a l deformation. T h e t e n s i l e h a r d e n i n g r a t e was u s e d b e c a u s e o f t h e e x t e n s i v e t w i n n i n g f o u n d t o be a s s o c i a t e d w i t h Stage I I hardening. The g r a i n s i z e dependence o f 8 has been i n t e r p r e t e d i n terms o f a g r a i n s i z e dependence o f t h e e x t e n t o f {1122} <1123> , s l i p . 0  I t was f o u n d t h a t d u r i n g l i n e a r h a r d e n i n g i n b o t h z i n c a n d cadmium t h e d i f f e r e n c e i n f l o w s t r e s s a t t w o d i f f e r e n t temperatures i s a r e v e r s i b l e d i f f e r e n c e implying that the d i s l o c a t i o n c o n f i g u r a t i o n s produced w i t h i n c r e a s i n g s t r a i n do n o t v a r y i n n a t u r e o r e x t e n t w i t h temperature. Under such c o n d i t i o n s i t i s p o s s i b l e to formulate a mechanical equation of state. E x t e n s i v e r a t e t h e o r y m e a s u r e m e n t s h a v e b e e n made i n b o t h s y s t e m s i n o r d e r t o a t t e m p t a n e v a l u a t i o n o f the, r a t e c o n t r o l l i n g mechanisms b o t h d u r i n g l i n e a r h a r d e n i n g and d u r i n g d y n a m i c r e c o v e r y . The f o r m e r h a s t e n t a t i v e l y been a s s o c i a t e d w i t h i n t e r s e c t i o n . Dynamic r e c o v e r y on the o t h e r hand has been l i n k e d t o t h e l o o p a n n e a l i n g observations of Price. GRADUATE STUDIES Field  o f Study:  Metallurgy  M e t a l l u r g i c a l Thermodynamics  C. S. S a m i s  Metallurgical Kinetics  E. P e t e r s  Hydrometallurgy  E. P e t e r s  Structure of Metals Topics  III  i n Physical Metallurgy  E.  Teghtsoonian J . A. L u n d  Related  Studies;  S t a t i s t i c a l Mechanics E l e m e n t a r y Quantum M e c h a n i c s Computer Programming  R. F. F. W„ C.  Snider Dalby Froese  Chairman:  D r . E . Teghtsoonian  ^  ABSTRACT  T h i s work was undertaken t o study t h e n a t u r e o f t h e d e f o r m a t i o n mechanisms i n p o l y c r y s t a l l i n e z i n c and cadmium over a temperature  range  from  77°K t o 300°K.  I t has been observed t h a t t h e o n l y non b a s a l s l i p system which i s observed under normal  l i g h t microscopy  [ l l 2 2 ] <(ll23>. A t temperature  slip  above  i s t h a t o f second o r d e r p y r a m i d a l  T = T = .k, H <V  t h e amount o f non b a s a l  i s g r e a t e r i n z i n c than i n cadmium. The amount o f t w i n n i n g , s u b s t r u c t u r e  f o r m a t i o n and g r a i n boundary m i g r a t i o n i s comparable i n b o t h systems. Nega t i v e work h a r d e n i n g beyond t h e U.T.S. a t temperatures associated with  recrystallization.  and s t r a i n r a t e independent  below  e x t e n t o f l i n e a r h a r d e n i n g i n c r e a s e s w i t h d e c r e a s i n g temperature T  H  = .26 . Above  is  T = .26 a r e g i o n o f H l i n e a r work h a r d e n i n g o c c u r s . The  In b o t h systems a t temperatures temperature  T = .k H  above  below  .. =  T = .26 , p o l y c r y s t a l l i n e h a r d e n i n g i n b o t h systems i s n n  p a r a b o l i c from y i e l d on and t h e r a t e o f h a r d e n i n g a t a g i v e n v a l u e o f s t r a i n decreases w i t h • i n c r e a s i n g temperature. Cadmium s i n g l e c r y s t a l s showed a s i m i l a r t r e n d i n t h a t below above  .26 b o t h  0^ and •  remained  c o n s t a n t . However  .26 t h e r e was a s t e a d y decrease i n t h e shear h a r d e n i n g  rates.  I t was observed t h a t t h e C o t t r e l l - S t o k e s law i s obeyed o n l y i n t h e l i n e a r h a r d e n i n g r e g i o n s o f p o l y c r y s t a l s and i n Stage I I h a r d e n i n g o f s i n g l e c r y s t a l s below  .26 ..When dynamic r e c o v e r y o c c u r s  A°~  increases  cr with increasing  strain.  I t has been observed t h a t below  .26  the l i n e a r hardening  rate  ii i n cadmium decreased w i t h i n c r e a s i n g g r a i n s i z e  ( constant specimen dimen-  s i o n s ) so t h a t  1 -2 0 The v a l u e o f Stage  =  Qo  +  kd  0 was shown t o correspond t o t h e t e n s i l e h a r d e n i n g o  I I s i n g l e c r y s t a l d e f o r m a t i o n . The t e n s i l e hardening  rate during  r a t e was  used  because o f t h e e x t e n s i v e t w i n n i n g found t o be a s s o c i a t e d w i t h Stage I I h a r d e n i n g . The g r a i n s i z e dependence o f  0  has been i n t e r p r e t e d , ih.iterms o f a  g r a i n s i z e dependence o f t h e e x t e n t o f £ll2*2]^1123^ s l i p . I t was  found t h a t d u r i n g l i n e a r h a r d e n i n g  i n b o t h z i n c and  cadmium t h e d i f f e r e n c e i n flow s t r e s s a t two d i f f e r e n t temperatures  is a  r e v e r s i b l e d i f f e r e n c e i m p l y i n g t h a t the d i s l o c a t i o n c o n f i g u r a t i o n s produced with i n c r e a s i n g s t r a i n do not v a r y i n n a t u r e or e x t e n t w i t h  temperature.  Under such c o n d i t i o n s i t i s .possible t o f o r m u l a t e ai.mechanical e q u a t i o n o f state.  . E x t e n s i v e r a t e t h e o r y measurements have been made i n b o t h systems i n order t o attempt  an e v a l u a t i o n o f the r a t e c o n t r o l l i n g  b o t h d u r i n g l i n e a r h a r d e n i n g and.during  mechanisms  dynamic recovery.. The former  has  t e n t a t i v e l y been a s s o c i a t e d w i t h i n t e r s e c t i o n . . Dynamic r e c o v e r y on the o t h e r hand has been l i n k e d t o the l o o p a n n e a l i n g o b s e r v a t i o n s o f P r i c e .  ACKNOWLEDGEMENT  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 and encouragement by h i s r e s e a r c h d i r e c t o r , . D r . . E . • T e g h t s o o n i a n ,  given  and f o r h e l p f u l d i s c u s s i o n s  w i t h f e l l o w graduate s t u d e n t s . F i n a n c i a l a s s i s t a n c e was r e c e i v e d i n t h e form o f an I n t e r n a t i o n a l N i c k e l Company o f Canada L i m i t e d F e l l o w s h i p .  iv  :  TABLE OF CONTENTS ., Page 1.  • DEFORMATION CHARACTERISTICS' OF ZINC AND CADMIUM  1.1.  INTRODUCTION  1.2.  EXPERIMENTAL PROCEDURE  1  1 3  ,  1.2.1.  M a t e r i a l s and S p e c i m e n - P r e p a r a t i o n  3  1.2.2.  T e s t i n g Procedure  6  1.3.  .STRESS-STRAIN RELATIONSHIPS  7  •  1.3-1.  Nature o f t h e S t r e s s - S t r a i n Curves  1.3.2.  Ductility  7 14  .  a) Cadmium  •  b> Z i n c  1416  :•  1.3.. 3 .  G r a i n Boundary E f f e c t s  16  1.3-4.  .Recrystallization  25  1.3-5-  .Maximum S t r e s s V a r i a t i o n w i t h Temperature and 27  S t r a i n Rate. 1.4. 1.4.1.  DEFORMATION MODES IN ZINC AND CADMIUM  30 -50  Slip  -. . 3 1  a) Z i n c b) Cadmium  •  37  1.4.2.  Twinning  1.4.3.  The Formation o f Low Angle Boundaries during' D e f o r m a t i o n . 46  1.5.  4l  YIELD STRESS AND WORK HARDENING  I.5..I.  The Temperature  I..5.2.  Temperature  Dependence o f Y i e l d  S e n s i t i v i t y o f t h e Flow. S t r e s s  50 53 55  a) Cadmium b) Z i n c  50  '  57  TABLE OF CONTENTS  (continued) Page  - 5 -. 3 -  o f t h e Flow S t r e s s  6l  I.5A.  The Deformation o f Cadmium S i n g l e C r y s t a l s  66  1.5.5.  Temperature  1.5.6.  The G r a i n S i z e Dependence o f Hardening a t -196°C  1  Strain Rate'Sensitivity  Dependence o f Work Hardening  2.  MECHANISMS - OF HARDENING IN ZINC AND CADMIUM  2.1.  INTRODUCTION  2.2.  TEMPERATURE  7 1 71  78  78 85  CHANGE TESTS  2.2.1.  Procedure  85  2.2.2.  Cottre11-Stokes Tests  85  2.2.3.  The M e c h a n i c a l E q u a t i o n o f S t a t e  88 90  a) Cadmium  90  b) . Z i n c 2.2.4.  2.5.  Equivalent  S t a t e s above T = .26 H  Procedure  2.3.2.  Cottrell-Stokes  2.4.  99 B e h a v i o u r i n Cadmium a t -196°C  99  b) . P o l y c r y s t a l s  101  The E f f e c t  o f Temperature  on C o t t r e l l - S t o k e s  Behaviour ..103  HARDENING AT -196°C IN CADMIUM - A c t i v a t i o n Volume  2.4.2.  • A c t i v a t i o n Energy  2.5.I.  99  a) . S i n g l e C r y s t a l s  2.4.1.  2.5.  9^  98  STRAIN RATE CHANGE TESTS  2.5.1.  2.3.3.  •  HARDENING ABOVE -196°C IN ZINC AND CADMIUM . Y i e l d Behaviour i n Cadmium  107 107 '  HI 112 112  VI  TABLE OF CONTENTS  (continued) Page  2.5.2.  The V a r i a t i o n o f AH with£Strain i n 25u Cadmium  2.5.3.  Y i e l d behaviour i n Zinc  '. 118 119  3 .  DISCUSSION  123  3.1.  LOOP FORMATION AND ANNEALING  123  3.2.  DYNAMIC RECOVERY  128  3.2.2.  Cross s l i p  129  3.2.3.  D i f f u s i o n C o n t r o l l e d Processes  131  3.3.  THE MECHANICAL EQUATION OF STATE  135  3.4.  THE COTTRELL-STOKES LAW  136  3-4.1. 3.4.2. 3.5. 3.5.1. 3.5.2. 3.5.3. 3.5.4.  137  • Obeyance  138  Dynamic Recovery . RATE CONTROLLING PROCESSES 'BELOW T  = .26  138 138  .Peierls Stress Cross S l i p  .'  .The Non C o n s e r v a t i v e - M o t i o n o f Jogs  139 140 l4l  Intersection  4.  - SUMMARY AND CONCLUSIONS  143  5.  - SUGGESTIONS FOR FUTURE WORK  146  6.  APPENDICES  147  6.1.  RATE THEORY  147  6.2.  UNLOADING YIELD POINTS IN CADMIUM  6.3.  THE DETERMINATION OF  A C T FROM- STRAIN RATE CHANGE TESTS  . . 154 160  vii TABLE OF CONTENTS  (continued)  Page  BIBLIOGRAPHY  164  viii LIST OF FIGURES  No.  1. 2.  Page  8  P o l y c r y s t a l l i n e specimen  8  . P o l y c r y s t a l t e s t i n g apparatus  9  J.  Single  c r y s t a l t e s t i n g apparatus  4.  Stress-strain  curves f o r 25u cadmium  5.  Stress-strain  curves f o r 400u cadmium..  11  6.  Stress-strain  curves f o r 2 0 u z i n c  12  7.  Stress-strain  curves f or .400u z i n c  8.  The e f f e c t o f temperature on t h e d u c t i l i t y o f 25u cadmium .... 15  9.  The e f f e c t o f temperature on t h e d u c t i l i t y o f 400u cadmium ... 15  . .•  .10-  13  "  10.  The e f f e c t o f g r a i n  17.  11.  The e f f e c t o f temperature on t h e d u c t i l i t y o f 20u z i n c  12.  G r a i n b o u n d a r i e s i n 25u cadmium b e f o r e and a f t e r  s i z e on t h e d u c t i l i t y o f z i n c  ....... 18  7$ d e f o r m a t i o n a t 20°C  20  13.  G r a i n boundary motion i n 400u z i n c and cadmium  1.4.  G r a i n boundary shear i n 400u z i n c and cadmium a t +20°C  22  15.  R e c r y s t a l l i z a t i o n i n 25u cadmium deformed 20$ a t +20°C  26  16.  The temperature dependence o f t h e maximum s t r e s s  i n cadmium .. 28  17.  The temperature dependence o f t h e maximum s t r e s s  i n zinc  18.  The e f f e c t o f s t r a i n r a t e i n 25u cadmium  on t h e maximum  . 21  .. ...  28  stress 29  . ~  19.  The e f f e c t o f s t r a i n r a t e . on t h e maximum stress;:.in': 20u.-,zinc , . . 29  20.  P y r a m i d a l g l i d e systems i n z i n c and cadmium ( a f t e r P r i c e )  21.  {ll22l  <112~3>  22.  {ll22]  23.  [ll22]  24.  M i c r o s t r u c t u r e o f 400u cadmium deformed 7/0 a t +20°C  ..... 32  s l i p i n 400u z i n c a t v a r i o u s s t r a i n s  35  <H23>  s l i p i n 400u z i n c a t -196°C  39'  <1123>  traces  o n . 4 0 0 u cadmium deformed 7$ a t -196°C..  40 42  LIST OF FIGURES  (continued)  ...No.  Page  25.  M i c r o s t r u c t u r e of 400u cadmium deformed 7$ a t -196"C  26.  Lack o f t w i n n i n g i n the presence  27.  Twin b a s a l s l i p and t w i n n u c l e a t i o n  28.  Low angle boundaries  29.  The f o r m a t i o n o f non c r y s t a l l o g r a p h i c boundaries, i n  Kj>  o f boundary m i g r a t i o n  45"  i n cadmium deformed 7$ * a  48  -J0 C o  48  cadmium.due t o u n d e r l y i n g s m a l l g r a i n s 30.  Crystallographic  boundary f o r m a t i o n i n 400u z i n c and cadmium . 49  .31.  Flow s t r e s s - t e m p e r a t u r e r e l a t i o n s h i p s f o r 0.020 i n c h  32.  g r a i n diameter cadmium as found by S t o l o f f Temperature dependence o f the y i e l d s t r e s s i n p o l y c r y s t a l l i n e z i n c and cadmium  33-  45"" "  51 52  The temperature'dependence o f the s t r a i n hardening parameter i n p o l y c r y s t a l l i n e copper as found by R u s s e l l  54  34.  Flow s t r e s s - t e m p e r a t u r e r e l a t i o n s h i p s f o r 25)i cadmium  55"""  35-  Flow s t r e s s - t e m p e r a t u r e r e l a t i o n s h i p s f o r 400u cadmium  56  .36.  The v a r i a t i o n w i t h temperature  o f the work hardening  37-  •parameter i n 25u cadmium The v a r i a t i o n w i t h temperature  o f the work hardening  38.  58  parameter i n 400u cadmium  59  Flow s t r e s s - t e m p e r a t u r e r e l a t i o n s h i p s f o r 20u z i n c  60  39•  The v a r i a t i o n w i t h temperature  40.  parameter i n 20u z i n c L i n e a r hardening o f p o l y c r y s t a l l i n e z i n c and cadmium below T = .26  of the work h a r d e n i n g 60 62  11  41.  The e f f e c t of s t r a i n r a t e on the flow s t r e s s of 20u z i n c 63  at +20°C 42.  The v a r i a t i o n o f the s t r a i n r a t e parameter temperature  43.  with  and s t r a i n i n 25>i cadmium  The v a r i a t i o n o f the s t r a i n r a t e parameter temperature  Ao~  and s t r a i n i n 20u z i n c  .>':• 64  Ao~  with 65  •LIST OF FIGURES  x  (continued)  . No. 44. 45.  Page • Single  c r y s t a l stress  Stress-strain  s t r a i n curve f o r cadmium a t +20°C  curves f o r cadmium s i n g l e  68  crystals  a t v a r i o u s temperatures  69  4 6 .  The temperature dependence o f S t a g e - I h a r d e n i n g i n cadmium ...  74  47.  The temperature dependence o f Stage I I h a r d e n i n g i n cadmium ..  74  4 8 .  Temperature  49.  d u r i n g Stage I d e f o r m a t i o n S t r e s s - s t r a i n curves f o r cadmium o f v a r i o u s g r a i n a t -196°C  50.  51.  dependence o f the r a t e  The e f f e c t o f g r a i n a t -196°C  o f work h a r d e n i n g  s i z e on the r a t e  75 sizes 76  of l i n e a r hardening 77  •The temperature dependence o f y i e l d i n terms o f the components •  stress 79  52.  The components o f t h e . t o t a l flow s t r e s s  i n f.c.c. crystals  ...  53.  Components, o f the d i f f e r e n c e i n flow s t r e s s when two i d e n t i c a l specimens a r e deformed a t d i f f e r e n t temperatures  ...  54.  55.  The r e l a t i o n s h i p , between the change i n f l o w s t r e s s p e r °K and the r e s u l t a n t s t r e s s a t -196°C o b t a i n e d d u r i n g the temperature c y c l i n g o f cadmium The e f f e c t o f e l e v a t e d . temperature p r e s t a i n i n g on the s t r e s s s t r a i n curve o f p o l y c r y s t a l l i n e copper a t 77°K  56.  Temperature  57.  The e f f e c t o f p r e s t r a i n i n g a t -95°C on the subsequent d e f o r m a t i o n b e h a v i o u r a t -120°C i n 20u z i n c  58.  c y c l i n g o f 25u cadmium between - l 4 0 ° C  and  o  u  81  87 '• 89  -196°C  .  91 !>..,.-.a  ... . 92  The e f f e c t o f p r e s t r a i n i n g a t -70°C on the subsequent d e f o r m a t i o n b e h a v i o u r a t -120°C i n 20u z i n c  93  59.  Equivalent states  95  60.  R e v e r s i b l e temperature change t e s t s a t e q u i v a l e n t i n p o l y c r y s t a l l i n e copper  61.  at d i f f e r e n t strains  The c o r r e l a t i o n o f s t r a i n s a t d i f f e r e n t i n 20u z i n c  states 96  temperatures 97  xi LIST OF. FIGURES  (continued)  No. 62.  Page The v a r i a t i o n p f the C o t t r e l l - S t o k e s the  63.  c r y s t a l s a t -196°C  d e f o r m a t i o n o f cadmium s i n g l e  The g r a i n  A°~  s i z e dependence o f  parameter d u r i n g  a t -196°C  100 102  cr  64.  The v a r i a t i o n w i t h s t r e s s  A°~  of  o b t a i n e d from 25u  cr  104  cadmium a t d i f f e r e n t temperatures 65. 66. 67.  68. 69.  The s t r e s s  Ao~  dependence o f  cr  (400u cadmium) law a t -50°G  The f a i l u r e o f the C o t t r e l l - S t o k e s • The v a r i a t i o n w i t h s t r e s s  o f the C o t t r e l l - S t o k e s  o b t a i n e d from s t r a i n r a t e  change t e s t s on 20u z i n c  The s t r e s s  105 105 parameter  dependence o f the a c t i v a t i o n volume (cadmium) ..... 108 115  • F o r c e - d i s t a n c e curves  70.  The v a r i a t i o n o f /\G w i t h temperature f o r - 2 5 u cadmium  71.  The v a r i a t i o n o f AH w i t h s t r a i n and temperature i n 25u cadmium  The v a r i a t i o n o f AG w i t h , temperature f o r 20u z i n c  73..  The f o r m a t i o n o f a p r i s m a t i c  75.  76.  Dislocations  122  d i s l o c a t i o n l o o p by an edge  d i s l o c a t i o n which i s h e l d up a t an o b s t a c l e The e f f e c t o f jogs of v a r i o u s h e i g h t s on screw d i s l o c a t i o n motion Stages i n the f o r m a t i o n o f an e l o n g a t e d l o o p on the b a s a l p l a n e by the c r o s s g l i d e o f a  116  120  •  72.  74.  106  £ l l 2 2 | 0-123,) screw d i s l o c a t i o n  i n hexagonal c l o s e packed c r y s t a l s  .123 124  . 126 127  77'  The c o n s e r v a t i v e climb o f a b a s a l d i s l o c a t i o n l o o p  132  78.  Typical force-distance deformation process  153  curve f o r a t h e r m a l l y  activated  79.  Unloading y i e l d point  i n p o l y c r y s t a l l i n e cadmium  154  80.  Unloading y i e l d point  terminology  156  81.  .The v a r i a t i o n o f  <J\Jc^  w i t h s t r a i n a t -196°C  158  xii LIST OF FIGURES  (continued) Page  No. 82.  83.  The decrease i n flow s t r e s s due t o s t a t i c r e c o v e r y d u r i n g i n t e r r u p t e d t e s t i n g o f 25u cadmium a t -95°C The nature o f t h e flow s t r e s s o b t a i n e d d u r i n g r a t e change t e s t s i n p o l y c r y s t a l s  strain ,  159  l6l  xiii LIST OF TABLES  No.  P  a  §  e  1.  P h y s i c a l p r o p e r t i e s o f hexagonal metals  2.  Non b a s a l s l i p  systems observed i n z i n c  33  3.  Non b a s a l s l i p  systems observed i n cadmium  $k  .k. 5.  6.  7.  S l i p systems i n hexagonal metals  38  Upper temperature l i m i t s f o r l i n e a r h a r d e n i n g i n p o l y c r y s t a l l i n e z i n c and cadmium  6l  S t r e s s r e q u i r e d f o r t w i n f o r m a t i o n i n cadmium s i n g l e crystals  70  I n c u b a t i o n s t r a i n r e q u i r e d i n p o l y c r y s t a l l i n e copper p r i o r t o the appearance o f an i r r e v e r s i b l e component o f the d i f f e r e n c e i n flow s t r e s s  89  8.  G r a i n s i z e dependence  of C o t t r e l l - S t o k e s behaviour  9.  G r a i n s i z e dependence i n cadmium a t -196°C  o f the a c t i v a t i o n volume a t y i e l d  10.  Energy v a l u e s a t y i e l d f o r cadmium deformed a t -196°C  11.  Energy v a l u e s a t y i e l d f o r 2^yi cadmium  12. 13.  k  .Rate parameters a t y i e l d i n 20u z i n c Loop f o r m a t i o n i n z i n c and cadmium  101  109 m 113 121 127  -1-  PART I  1.  DEFORMATION CHARACTERISTICS OF ZINC AND  1.1  INTRODUCTION  In  CADMIUM  the p a s t , the major emphasis i n the f i e l d  has been p l a c e d on f a c e c e n t e r e d c u b i c m e t a l s .  of p l a s t i c  deformation  Much o f t h i s work has been  r e s t r i c t e d t o the use o f s i n g l e c r y s t a l s i n an attempt  t o determine  d i s l o c a t i o n mechanisms which c o n t r o l the work h a r d e n i n g p r o c e s s e s .  the The  o f a v o i d i n g the d i f f i c u l t  study  of  s i n g l e c r y s t a l b e h a v i o u r has the advantage  of  d e a l i n g w i t h the c o n s t r a i n i n g c o n d i t i o n s imposed by g r a i n boundaries d u r i n g  the d e f o r m a t i o n o f p o l y c r y s t a l l i n e a g g r e g a t e s . one t o o b t a i n a better.knowledge  problem .  T h i s s i m p l i c i t y , which enables  o f shear s t r e s s c o n d i t i o n s on p a r t i c u l a r  slip  p l a n e s has d i s a d v a n t a g e s due t o the poor r e p r o d u c i b i l i t y o f flow s t r e s s v a l u e s of  different  factors  s i n g l e c r y s t a l s because  changes i n such  a s s u b s t r u c t u r e , i m p u r i t y c o n c e n t r a t i o n , o r i e n t a t i o n and  dislocation density. for  o f the e f f e c t s o f s l i g h t  The  initial  c o r r e l a t i o n o f s i n g l e c r y s t a l and p o l y c r y s t a l l i n e  f a c e c e n t r e d metals i s a t o p i c o f some c u r r e n t i n t e r e s t " 1  5  data  and s h o u l d i n  the f u t u r e p r o v i d e a groundwork f o r the u n d e r s t a n d i n g o f macroscopic  deformation  characteristics.  I n the p a s t few y e a r s the study o f body c e n t r e d cubic-metals,,' n o t a b l y , i r o n ; , h a s been i n t e n s i f i e d . o t h e r s h a v e attempted r a n g e o f temperaturei specimens.  t o determine  Conrad  6 - 1 0  ,  Gregory , 11  Basinski  1 2  and  the r a t e c o n t r o l l i n g mechanism over a wide  Much o f t h i s work i n v o l v e d the use o f p o l y c r y s t a l l i n e  -  2  -  The f i e l d of hexagonal m e t a l d e f o r m a t i o n has "been somewhat i g n o r e d due  i n most p a r t t o the a n i s o t r o p i c nature of the hexagonal  resultant d i f f i c u l t i e s  encountered  i n mechanical working  system and  and e n g i n e e r i n g use.  With p o s s i b l y the e x c e p t i o n of z i n c and cadmium, the more prominent metals i n c l u d i n g T i , Be, Mg, m e t a l l u r g i c a l procedures  the  Co, and Z r are a s s o c i a t e d w i t h  hexagonal  difficult  d u r i n g e x t r a c t i o n and r e f i n i n g which tend t o make  them, expensive and hence u n d e s i r a b l e as e n g i n e e r i n g m a t e r i a l s except i n a p p l i c a t i o n s where d e f i n i t e advantages  occur.  Of a l l . the hexagonal m e t a l s , t i t a n i u m and-magnesium have been s t u d i e d i n the g r e a t e s t d e t a i l because o f t h e i r f a v o u r a b l e s t r e n g t h t o weight Because of gaseous  embrittlement and d i f f i c u l t i e s  encountered  d u r i n g mechanical  f o r m i n g , t i t a n i u m has not become as w i d e l y used as once p r e d i c t e d . i s d i f f i c u l t t o produce T h e r e f o r e the problem  i n wrought form due t o embrittlement  ratio. .  Magnesium  during cold  working.  of d e t e r m i n i n g the d e f o r m a t i o n mechanisms which c o n t r o l  flow i n magnesium has been a s u b j e c t of c o n s i d e r a b l e i n t e r e s t .  On the o t h e r hand v e r y l i t t l e work has been done on z i n c  and 23  cadmium s i n c e the c l a s s i c works of  Scamid and Boas- i n the e a r l y 1 9 3 0 ' s .  R e c e n t l y c o n s i d e r a b l e i n t e r e s t has been shown i n the development o f new  wrought  z i n c a l l o y s t o compete commercially w i t h some aluminum and copper a l l o y s .  Poor  creep p r o p e r t i e s due t o i t s h i g h e f f e c t i v e temperature  and  at" room temperature  reduced d u c t i l i t y because of cleavage f r a c t u r e a t reduced temperatures far of  l i m i t e d i t s use.  have so  I t i s n e c e s s a r y t h e r e f o r e t o have a more d e t a i l e d knowledge  the d e f o r m a t i o n mechanisms t o p r o v i d e a ground work f o r f u t u r e a l l o y - d e v e l o p -  ment.  Most i n v e s t i g a t i o n s t o date have been concerned w i t h e i t h e r t h e h a r d e n i n g  mechanisms d u r i n g b a s a l g l i d e Very l i t t l e  or the nature o f eleavage f r a c t u r e .  2 4 - 2 5  work has been done w i t h p o l y c r y s t a l l i n e z i n c t o determine  f a c t o r s as the s t r a i n r a t e and temperature mode and degree of  o f non b a s a l s l i p ,  2 6  2  7  such  s e n s i t i v i t y o f the f l o w s t r e s s , the  the n a t u r e of dynamic recovery,, the r e l e v a n c e  g r a i n boundary e f f e c t s e t c .  A l t h o u g h s i m i l a r i t i e s e x i s t between z i n c and cadmium as shown i n Table I , the apparent d e f o r m a t i o n c h a r a c t e r i s t i c s d i f f e r i n t h a t cadmium does not f a i l by cleavage f r a c t u r e and m a i n t a i n s s u b s t a n t i a l d u c t i l i t y down t o 4 . 2 ° K „ However a q u a s i d u c t i l e - - b r i t t l e t r a n s i t i o n i n v o l v i n g a change i n f r a c t u r e mode from d u c t i l e shear t o i n t e r g r a n u l a r f r a c t u r e has been r e p o r t e d by S t o l o f f  2 8  and M a g n u s s e n .  25  . T h e r e f o r e by comparing  s t a n d a r d c o n d i t i o n s o f p u r i t y , g r a i n s i z e , temperature, specimen  geometry i t may  z i n c and cadmium under s t r a i n rate  and  be p o s s i b l e t o o b t a i n a more d e t a i l e d knowledge o f  the f l o w and f r a c t u r e mechanisms.  The f i r s t p a r t o f t h i s t h e s i s i s concerned w i t h the more macroscopic  flow parameters whereas p a r t two  d e s c r i b e s attempts  t o determine  the r a t e c o n t r o l l i n g mechanisms by the use o f r a t e t h e o r y .  1.2  1.2  EXPERIMENTAL PROCEDURE  .1  M a t e r i a l s and Specimen P r e p a r a t i o n  The  z i n c and cadmium used i n the course o f t h i s work was  of  99.999% p u r i t y and was s u p p l i e d i n the form o f o n e - h a l f i n c h rods by the C o n s o l i d a t e d M i n i n g and S m e l t i n g Company, T r a i l ,  B.C.  These rods were r e m e l t e d i n a i r and c a s t i n t o g r a p h i t e moulds t o g i v e i n g o t s w i t h dimensions  5"  x 2^"  x  .  These were then r o l l e d  into  TABLE  I  P h y s i c a l P r o p e r t i e s o f Hexagonal Metals  Zn  Cd  Mg  Be  M e l t i n g Temperature °C  420  320  65O  1277  Density  7.14  8.65  1.74  I.856  1.886  Stacking Fault Energy*  medium  P e r i o d i c Group No.  11B  Element  c  /a  gms/c.c.  ratio  Stacking Fault Energies  Co  Ti  Zr  1495  1668  1852  I.85  8.9  4.51  6.49  1.624  I.586  1.623  1.588  1.590  medium  high  high  low  high  high  11B  11A  11A  VIII  IVB.--  IVB  Low - under 25 ergs/cm Medium - 2 5 - 1 0 0 ergs/em High - > 100 ergs/cm 2  2  2  sheet.  The i n i t i a l r o l l i n g  order t o avoid cracking. hot r o l l i n g  passes f o r z i n c were c a r r i e d out a t 150°C i n  The g r a i n refinement  which o c c u r r e d d u r i n g  this  o p e r a t i o n was such as t o a l l o w f u r t h e r r e d u c t i o n s t o be  c a r r i e d out a t room temperature.  R e c r y s t a l l i z a t i o n during r o l l l i n g  readily  o c c u r r e d a t room temperature because o f the s m a l l g r a i n s i z e .  Cadmium was r o l l e d a t room temperature throughout process. .150  the-reduction  . I n b o t h cases r e d u c t i o n was c a r r i e d out i n .010 i n c h s t e p s  inches t o the f i n a l sheet  produced a . v e r y u n i f o r m  s i z e o f .031 i n c h e s .  from  T h i s treatment  and f i n e g r a i n e d r e c r y s t a l l i z e d sheet w i t h a g r a i n  s i z e o f 20u f o r z i n c and 25u f o r cadmium.  The  g r a i n s i z e c o u l d be v a r i e d s i g n i f i c a n t l y by changing the  amount o f r e d u c t i o n i n the f i n a l r o l l p a s s .  For instance a f i n a l  s i z e o f 50;i i n s t e a d o f 25u c o u l d be o b t a i n e d  i n cadmium by u s i n g a  r e d u c t i o n o f 5 / i n s t e a d o f 25%. 1  0  from the same sheet  F o r t h i s reason  grain final  a l l specimens were c u t  i n order to e l i m i n a t e small d i f f e r e n c e s i n g r a i n s i z e  and p r e f e r r e d o r i e n t a t i o n .  T e n s i l e specimens were punched t o g i v e a reduced gauge l e n g t h of  . 8 inches w i t h c r o s s s e c t i o n a l dimensions o f . 2 0 0 " x . 0 3 1 "  S i n c e t h i s procedure, caused s l i g h t d e f o r m a t i o n i t was n e c e s s a r y Approximately of  around the specimen edges  t o c h e m i c a l l y p o l i s h the s u r f a c e p r i o r t o t e s t i n g .  .0015  .0280 i n c h e s .  (Fig.l).  inches were removed t o g i v e a f i n a l specimen t h i c k n e s s  The p o l i s h i n g s o l u t i o n used f o r b o t h z i n c and cadmium was  as f o l l o w s -  320 20 1000 This represents  gms  Cr0  gms mis  Na  2  H 0  3  S0  4  2  , . 30 a s l i g h t m o d i f i c a t i o n o f G i l m a n s s o l u t i o n 1. -  Besides  - 6 - . p o l i s h i n g the s u r f a c e , t h i s treatment  caused g r a i n boundaries  s l i g h t l y grooved t h e r e b y f a c i l i t a t i n g m e t a l l o g r a p h i c  t o become  examination  after  testing.  Large g r a i n e d specimens were o b t a i n e d by a n n e a l i n g punched specimens i n a i r . under the f o l l o w i n g c o n d i t i o n s :  Cadmium - 2 h r s at 230°C Zinc - 2 h r s at.l80°C  The  specimens were then furnace  1 hour.  The  c o o l e d from temperature over a p e r i o d o f 400u- - 25u.  r e s u l t a n t g r a i n s i z e i n each case was  This  produced specimens w i t h o n l y 1 t o 2 g r a i n s a c r o s s the specimen t h i c k n e s s . Because o f t h i s , the s c a t t e r i n f l o w s t r e s s v a l u e s was than f o r f i n e g r a i n e d specimens. was  to f a c i l i t a t e metallographic  somewhat g r e a t e r  The purpose o f p r o d u c i n g  o b s e r v a t i o n s and t o p r o v i d e an  t e s t specimen between the normal f i n e g r a i n e d m a t e r i a l and  The technique  such specimens  single crystals.  s i n g l e c r y s t a l s used were grown by a m o d i f i e d  i n evacuated  $mm  diameter p y r e x g l a s s tubes.  l e n g t h s o f cadmium were p l a c e d i n the tubes which were  Bridgman  Extruded  .100  inch  subsequently  lowered a t the r a t e of 1" p e r hour through a. 12" v e r t i c a l tube C r y s t a l s up t o 18  intermediate  furnace.  inches i n l e n g t h c o u l d be grown p r o v i d i n g numerous  samples of the same o r i e n t a t i o n .  1.2.2  T e s t i n g Procedure  Specimens were deformed on a F l o o r Model I n s t r o n u s i n g r a t e s t h a t v a r i e d from 4.0  x 10 s e c 3  1  t o 4.0  included l i q u i d nitrogen^cooled petroleum water (+20  t o + 100°C) and  x 10 s e c 5  e t h e r (-140  s i l i c o n e o i l ( a b o v e 100°C).  *.  strain  T e s t i n g media  t o +20°C), The bath  hot  temperature  - 7 i n each case c o u l d be c o n t r o l l e d t o i 2°C.  S p l i t jaw g r i p s which  a v e r y r i g i d t e s t i n g apparatus were used f o r the p o l y c r y s t a l l i n e  produced specimens.  (Fig.2).  • S i n g l e c r y s t a l s were mounted i n s o l d e r i n aluminum g r i p s and were deformed rotation  i n a t e s t i n g r i g which a l l o w e d complete freedom o f  (Fig.3).  The d i s t a n c e between g r i p s was between 30 and 35  g i v i n g a l e n g t h t o diameter r a t i o o f 10/1.  . I n o r d e r t o f a c i l i t a t e comparison w i t h p r e v i o u s work a l l d a t a on p o l y c r y s t a l s i s expressed i n terms pounds p e r square i n c h  (p.s.i.)  whereas s i n g l e c r y s t a l r e s u l t s a r e g i v e n i n terms o f c.g.s. u n i t s .  1..3  STRESS ^-STRAIN RELATIONSHIPS  1.3-1  Nature o f the S t r e s s S t r a i n Curves  True s t r e s s - t r u e • s t r a i n curves f o r b o t h g r a i n s i z e s i n z i n c and cadmium a t a few s e l e c t e d temperatures a r e shown i n F i g u r e s k,, 5 , and 7>  6  The cadmium curves a r e q u a l i t a t i v e l y t h e same as those observed by  S t o l o f f and G e n s a m e r  28  f o r .020 i n c h g r a i n s i z e m a t e r i a l .  -Specifically,  work h a r d e n i n g i n the e a r l y r e g i o n s o f s t r a i n i s p a r a b o l i c a t h i g h e f f e c t i v e temperatures and tends t o become m o r e • l i n e a r w i t h d e c r e a s i n g temperature.  ( E f f e c t i v e temperature  i s g i v e n b y Tg .=  T_ T  where T^ i s  M  the m e l t i n g p o i n t ) .  A t temperatures above a p p r o x i m a t e l y  T^  =  .kO  t h e r e i s a l a r g e amount o f s t r a i n beyond the p o i n t o f maximum s t r e s s which was not observed t o be a s s o c i a t e d w i t h n e c k i n g .  I t was a l s o observed t h a t  t h i s e f f e c t i s g r e a t l y reduced i n t h e UOOu m a t e r i a l .  - 8  Fig. 2  P o l y c r y s t a l t e s t i n g apparatus.  -  - 9  Fig. 3  Single crystal testing  apparatus.  -  Fig. 5  .Stress-strain  curves f o r k00u cadmium.  - ST  Fig.7  .Stress - s t r a i n curves f o r kOOn z i n c  1.3-2  •Ductility  -  D u c t i l i t y w i l l be g i v e n o n l y i n terms, o f p e r c e n t  ^  elongation  or true s t r a i n as i t was n o t p r a c t i c a l t o o b t a i n r e d u c t i o n i n a r e a  values  because o f t h e specimen dimensions. .As an a i d t o i n t e r p r e t a t i o n , d u c t i l i t y i s g i v e n not o n l y as the t r u e s t r a i n t o f r a c t u r e b u t a l s o :in terms o f the t r u e s t r a i n t o maximum s t r e s s c o n d i t i o n s . when c o n s i d e r i n g d e f o r m a t i o n a t h i g h values  o f T^ because o f the l a r g e  amounts o f d e f o r m a t i o n a s s o c i a t e d w i t h n e g a t i v e  1.3.2  work h a r d e n i n g .  a) Cadmium  The  e f f e c t o f temperature on t h e d u c t i l i t y o f 25p and 400u  cadmium i s shown i n F i g u r e s increase  T h i s i s important  8 and 9-  I t i s observed t h a t t h e r e  i s an  i n t h e s t r a i n t o f r a c t u r e as the temperature d e c r e a s e s t o -120°C.  T h i s i n c r e a s e i s more pronounced w i t h an i n c r e a s e i n g r a i n s i z e .  At  -120°C b o t h g r a i n s i z e s have a p p r o x i m a t e l y the same s t r a i n t o f r a c t u r e o f about kO$>. Below -120°C t h e r e  i s a steady decrease i n d u c t i l i t y  independent o f g r a i n s i z e , i n agreement w i t h t h e r e s u l t s o f S t o l o f f and Gensamer.  T h i s decrease corresponds t o a change i n t h e f r a c t u r e mode from  d u c t i l e shear t o i n t e r g r a n u l a r . f r a c t u r e .  From F i g u r e s 8 and 9±t ,1.)  i s a l s o observed, t h a t above  -120°C  7  the t r u e s t r a i n t o maximum s t r e s s i s g r e a t e r f o r kOOp. than f o r 25u cadmium  2)  t h e percentage o f the t o t a l d u c t i l i t y which i s a s s o c i a t e d w i t h  negative  h a r d e n i n g a f t e r maximum s t r e s s c o n d i t i o n s have been r e a l i z e d i s g r e a t e r f o r t h e 25u cadmium.  I  I  I  -160  I  I  -120  I  I  -80  I  I  -40  I  0  L  I  +40  1  1 +80  Temperature °C Fig.9  The e f f e c t  o f temperature on the d u c t i l i t y o f 4 0 0 j j cadmium.  - 16 •1.3.2  -  b). Z i n c  The r e s u l t s f o r z i n c are q u a l i t a t i v e l y the same as those f o r cadmium except f o r the occurrence o f a d i s t i n c t d u c t i l e t o b r i t t l e t r a n s i t i o n due t o cleavage  From F i g u r e 10  fracture.  i t i s observed t h a t t h i s t r a n s i t i o n i s s h i f t e d  about 50°C as the g r a i n s i z e i s i n c r e a s e d from 25u t r a n s i t i o n temperature  t o 400u.  Above the  i t i s observed t h a t b o t h the t o t a l s t r a i n t o  f r a c t u r e and the t r u e s t r a i n t o maximum s t r e s s decrease w i t h temperature  i n a manner s i m i l a r t o cadmium.  increasing  L i k e w i s e the percentage  of  the t o t a l d u c t i l i t y a t f r a c t u r e which i s a s s o c i a t e d w i t h n e g a t i v e work h a r d e n i n g i s g r e a t e r f o r 20u z i n c than f o r 4 0 0 u ' z i n c .  A l s o the t r u e s t r a i n  t o maximum s t r e s s i s g r e a t e r a t the same temperature, f o r hOOu z i n c than f o r 20u z i n c .  T h i s i s i n agreement w i t h o b s e r v a t i o n s (1)  and  (2)  o f the  p r e v i o u s s e c t i o n on cadmium.  The e f f e c t o f s t r a i n r a t e on the d u c t i l e t o b r i t t l e i s shown i n F i g u r e 11.  . Changing the s t r a i n r a t e by a f a c t o r o f 10  the t r a n s i t i o n f o r 20u z i n c by about  1.3.3  transition shifted  25°C.  G r a i n Boundary E f f e c t s  The o b s e r v a t i o n s o f the p r e v i o u s s e c t i o n w i t h r e g a r d t o g r a i n s i z e e f f e c t s i n d i c a t e t h a t some form o f r e c o v e r y and r e c r y s t a l l i z a t i o n are o p e r a t i v e d u r i n g d e f o r m a t i o n a t e l e v a t e d temperatures.  These p r o c e s s e s .  a r e expected because o f the h i g h p u r i t y and h i g h e f f e c t i v e However 20°C .  temperatures.  S t o l o f f found no evidence o f r e c r y s t a l l i z a t i o n d u r i n g t e s t i n g a t  - 17  Fig. 10  The  effect  of g r a i n  size  on the  d u c t i l i t y of  zinc.  -  -18  . Temperature F i g . 11  The e f f e c t  • °C  o f temperature on the d u c t i l i t y o f 20u, z i n c .  -  -.19  -  F i g u r e 12 shows t h e r e l a t i v e g r a i n boundary s t r u c t u r e s i n 25u cadmium b e f o r e and a f t e r 7$ d e f o r m a t i o n at room temperature. have become v e r y jagged i n appearance  The boundaries  indicating considerable grain  boundary m i g r a t i o n d u r i n g d e f o r m a t i o n .  F i g u r e 13 shows o t h e r examples o f boundary motion and cadmium.  With d e c r e a s i n g temperature  i n kOOp z i n c  the m i g r a t i n g boundaries show  a more continuous type o f m i g r a t i o n a l o n g the boundary (Fig.13b) t o the c o r r u g a t e d type observed a t room, temperature At a g i v e n temperature  and above  opposed  (Fig.13d).  t h e s e boundary e f f e c t s were much more prominent i n  fine grained material.  F i g u r e 13(b)-shows a "stepped" type o f boundary m i g r a t i o n s i m i l a r t o t h a t observed by Chang and' G r a n t aluminum a t e l e v a t e d temperatures.  3 1  d u r i n g creep o f p o l y c r y s t a l l i n e  They i n t e r p r e t e d such o b s e r v a t i o n s i n  terms o f a l t e r n a t e p r o c e s s e s o f shear and m i g r a t i o n .  I n o r d e r t o o b t a i n a q u a t i t a t i v e assessment shear as a d e f o r m a t i o n p r o c e s s , p o l i s h e d kOOp specimens  o f t h e importance .of were f i n e l y marked  by means o f a s o f t b r u s h and then deformed. . As shown i n F i g u r e lk, shear was  observed i n b o t h systems  associated with migration.  a t room temperature.  I t was n o t n e c e s s a r i l y  Only a few boundaries showed, v i s i b l e  offsets  and such o f f s e t s c o u l d o n l y be seen a t r a t h e r .high m a g n i f i c a t i o n s .  The e f f e c t o f boundary m i g r a t i o n and shear p r o c e s s e s on t h e s t r e s s s t r a i n curve i s n o t f u l l y understood.  Shear i s b a s i c a l l y a work  h a r d e n i n g p r o c e s s and i n v o l v e s t h e d e f o r m a t i o n and subsequent areas a d j a c e n t t o the b o u n d a r i e s .  hardening o f  On the o t h e r hand m i g r a t i o n occurs  /  - 20 -  X 2k0 (a)  undeformed  X (b) Fig.12  deformed and immediately  240  repolished  G r a i n boundaries i n 25u cadmium b e f o r e and a f t e r 7% d e f o r m a t i o n  at +20°C.  f  *  21 -  (a) corrugated g r a i n boundary i n cadmium deformed 7$ a t +20°C and r e p o l i s h e d .  Fig.1$  G r a i n boundary motion i n kOOu  X  2k0  X  2k0  z i n c and cadmium.  - 22 -  x 700 (a) cadmium a t 10$  strain.  X 700 (b) z i n c a t 7$  Fig.l4  strain.  G r a i n boundary shear i n kOOy z i n c and cadmium a t +20°C.  - 23- because  o f a net d i f f e r e n c e i n f r e e energy a c r o s s the boundary caused by  d i f f e r e n c e s i n t h e d i s l o c a t i o n c o n f i g u r a t i o n s a s s o c i a t e d w i t h the work hardened it  s t a t e s on each s i d e o f the boundary.. I f when a boundary moves  l e a v e s b e h i n d a s t r a i n f r e e r e g i o n i n t o which d e f o r m a t i o n can t h e n  proceed, t h e m i g r a t i o n i s e s s e n t i a l l y a r e c o v e r y p r o c e s s a c t i n g as a p r e l u d e t o r e c r y s t a l l i z a t i o n . . T h e r e f o r e any c o - o p e r a t i v e p r o c e s s o f shear and m i g r a t i o n r e p r e s e n t s a h a r d e n i n g and r e c o v e r y c y c l e . Very s m a l l amounts of m i g r a t i o n and shear were observed i n cadmium a t -95°C  (^V. = . 3 0 ) , where  m i g r a t i o n was observed more as a s l i g h t g r a i n boundary c o r r u g a t i o n and d i d not i n v o l v e g r o s s boundary movement. More d e t a i l e d s t u d i e s w i l l have t o be made t o a c c u r a t e l y determine the temperature processes..Dorn  22  dependence o f these  observed s u b s t a n t i a l shear i n p o l y c r y s t a l l i n e magnesium  a t +20°C (T = . 3 2 ) . The p o s s i b i l i t y e x i s t s t h e r e f o r e t h a t t h e d u c t i l i t y H t r a n s i t i o n i n cadmium a t -120°C i s a s s o c i a t e d w i t h the c e s s a t i o n o f g r a i n boundary recovery.. I f d u c t i l e shear as opposed t o i n t e r g r a n u l a r f r a c t u r e occurs because  o f boundary r e c o v e r y then i t i s n e c e s s a r y t h a t  the a c t i v a t i o n energy a s s o c i a t e d w i t h m i g r a t i o n be a v a i l a b l e down, t o T  R  = .26 .  The a c t i v a t i o n energy c o n t r o l l i n g boundary m o b i l i t y i s not  95 known. However Winegard  has shown t h a t the a c t i v a t i o n energy  associated  w i t h g r a i n growth i n u l t r a pure metals can be r e l a t e d t o the l i q u i d d i f f u s i o n energy. T h i s i s u s u a l l y i n the range from  self  .1 e.v. t o .k e.v.  A l t h o u g h the d r i v i n g f o r c e i s somewhat d i f f e r e n t i n each case i t i s not expected t h a t the a c t u a l r a t e c o n t r o l l i n g mechanism d u r i n g boundary m i g r a t i o n w i l l be d i f f e r e n t than t h a t a s s o c i a t e d w i t h g r a i n growth. There:f o r e i t i s probable t h a t the energy r e q u i r e d f o r boundary m i g r a t i o n w i l l be  s u f f i c i e n t l y low t h a t some boundary i n s t a b i l i t y can o c c u r i n cadmium  .- 2k down t o -120  a t temperatures  o C.  Boundary m i g r a t i o n i n p o l y c r y s t a l l i n e z i n c poses a d i f f i c u l t problem f o r the development of s u c c e s s f u l z i n c a l l o y s w i t h good  creep  r e s i s t a n c e . I t i s d e s i r a b l e t o o b t a i n as f i n e a g r a i n s i z e as p o s s i b l e i n o r d e r t o improve s t r e n g t h and m e c h a n i c a l  working c h a r a c t e r i s t i c s . With  such a s t r u c t u r e however i t i s then n e c e s s a r y by  t o s t a b i l i z e the  boundaries  a s u i t a b l e a l l o y i n g technique. • o  S i n c e climb i s known t o occur a t temperatures it  i s probable  -30  above  C,  t h a t the d u c t i l e - b r i t t l e t r a n s i t i o n i s r e l a t e d t o the ease  w i t h which climb the c i r c u m v e n t i o n  can o c c u r as a dynamic r e c o v e r y mechanism t o a l l o w f o r of p o i n t s of s t r e s s c o n c e n t r a t i o n . T h i s  interpretation  however does not e x p l a i n the known g r a i n s i z e dependence of the  transition  temperature. T h i s dependence on g r a i n s i z e may  be e x p l a i n e d i n terms of  e a s i e r c r a c k p r o p a g a t i o n i n l a r g e g r a i n e d r m a t e r i a l . I t may  a l s o be  explained  i n terms of the r e l a t i v e amount o f m a t e r i a l b e i n g r e c o v e r e d b y the a c t i o n of boundary m i g r a t i o n boundaries,  . Cleavage c r a c k s are u s u a l l y n u c l e a t e d a t g r a i n  t w i n i n t e r s e c t i o n s e t c . where s t r e s s concentration o c c u r s . I f  t h e s e p o i n t s o f s t r e s s c o n c e n t r a t i o n can be removed by boundary m i g r a t i o n then cleavage ormation  f r a c t u r e should not o c c u r .  I f i t i s assumed t h a t the  p r o c e s s e s do not change s i g n i f i c a n t l y w i t h g r a i n s i z e , then  i n c r e a s e d d u c t i l i t y of z i n c w i t h d e c r e a s i n g g r a i n s i z e a t low may  be  defthe  temperatures  r e l a t e d t o the i n c r e a s e d importance of g r a i n boundary m i g r a t i o n  as a r e c o v e r y mechanism. A t any  g i v e n v a l u e o f s t r a i n and boundary m i g r a t i o n  r a t e , the amount o f r e c o v e r e d m a t e r i a l w i l l : . i n c r e a s e as the g r a i n s i z e decreases.  - 25 1.3,k  Recrystallization  G r a i n boundary m i g r a t i o n always preceded the i n t r o d u c t i o n of new r e c r y s t a l l i z e d g r a i n s which had t h e i r o r i g i n on t h e . g r a i n boundaries.  A r e c r y s t a l l i z e d g r a i n which s u b s e q u e n t l y deformed i s  shown growing from the boundary  i n Fibure 15(b).  The growth o f t h e new  g r a i n appears t o have been stepped s i m i l a r t o t h e m i g r a t i o n o f e x i s t i n g boundaries.  F i g . 15(a) i l l u s t r a t e s the movement o f t w i n boundaries i n t o  the p a r e n t g r a i n by a d i f f u s i o n p r o c e s s . s t r e s s dependent t w i n which formed  This process i s d i s t i n c t  t w i n growth which i s a shear t r a n s f o r m a t i o n . i s s t i l l v i s i b l e due t o s u r f a c e  from  The o r i g i n a l  distortion.  R e c r y s t a l l i z e d g r a i n s were never observed b e f o r e maximum s t r e s s c o n d i t i o n s , b u t were a s s o c i a t e d w i t h t h e n e g a t i v e work h a r d e n i n g s l o p e o b t a i n e d a t e l e v a t e d temperatures above T^ = .kO'.  A t a l l temperatures  s t u d i e d , r e c r y s t a l l i z a t i o n never went t o c o m p l e t i o n d u r i n g t e s t i n g except i n t h e f i n a l necked a r e a .  A t room temperature  i n 20u z i n c a b o u t 50$ of ?  the specimen volume remained u n r e c r y s t a l l i z e d a f t e r 60% d e f o r m a t i o n . R e c r y s t a l l i z e d g r a i n s were r a r e l y observed i n 400u specimens a t any temperature.  T h i s i s r e f l e c t e d by the s m a l l e r amount o f d u c t i l i t y from  maximum s t r e s s t o f a i l u r e  ( F i g u r e 9)•  The lower d u c t i l i t y t o maximum  s t r e s s f o r 20n Zn and 25u Cd a t h i g h temperatures as opposed t o t h a t f o r 400u m a t e r i a l i s merely a r e f l e c t i o n o f more pronounced boundary m i g r a t i o n and the e a r l i e r i n t r o d u c t i o n o f r e c r y s t a l l i z a t i o n i n the f i n e material.  grained  - 27 1.3-5  Maximum S t r e s s - V a r i a t i o n ' w i t h  S t o l o f f using t e n s i l e strength are  500u cadmium found a p l a t e a u  below about - l 6 0 ° C .  shown i n F i g u r e  Temperature and S t r a i n Rate  i n ultimate  -The r e s u l t s o f the p r e s e n t work  16 and i n d i c a t e t h a t the occurrence- o f t h i s  i s g r a i n s i z e dependent.  .Continuously i n c r e a s i n g  strength  plateau  v a l u e s can be  o b t a i n e d t o lower temperatures w i t h a f i n e g r a i n s i z e .  S i m i l a r r e l a t i o n s h i p s are observed f o r z i n c a t h i g h temperatures (Fig.17).  However w i t h the onset o f cleavage f r a c t u r e t h a t  accompanies  d e c r e a s i n g temperature, t h e r e i s a g r a d u a l decrease i n maximum.stress which l e v e l s • o f f a t a more o r l e s s c o n s t a n t v a l u e when d u c t i l i t y becomes l e s s than 1 $ ,  i n d i c a t i n g a temperature independent f r a c t u r e p r o c e s s .  e f f e c t o f s t r a i n r a t e on f r a c t u r e s t r e s s i s shown i n F i g u r e s I t i s seen from F i g u r e  19 t h a t  The  18 and 19.  i n z i n c when f r a c t u r e occurs by cleavage  as opposed t o d u c t i l e shear, the macroscopic f r a c t u r e -stress i s s t r a i n r a t e independent over the range of s t r a i n r a t e s  With cadmium ( F i g . 18) s t r e s s v a r i e s only  used.  the s t r a i n r a t e dependence of maximum  s l i g h t l y above 77°K. .At 77°K where f r a c t u r e i s c o m p l e t e l y  i n t e r c r y s t a l l i n e , t h e r e i s v i r t u a l l y no s t r a i n r a t e dependence o f maximum s t r e s s .  - 28 -  J  1  I  -160  I  I  I  -120  I  -80  I  I  -hO  Temperature Fig.l6  I  0  I  I  I  I  O L  +80  +k0  °C  The temperature dependence o f t h e maximum s t r e s s i n cadmium.  o  -k  6 = 4 . 0 x 10  X  "I sec.  •H  •  20M'Zn.  O  k00n Zn.  ft ra ra <u u  t 20 -p  S.10  I J  L  J  -16 o F i g . 1.7  -120  J  L  L  -8o  -ho •Temperature  J  o  +ko  L  J  +8o  °C  The temperature dependence o f t h e maximum s t r e s s i n z i n c .  L  -29 -  •o  -1 10" _4 «_j_ x 10_^ s e c . ^ 4.0.x 10 s e c . ~  4.0 4.0  40  H  x  ;  s e c  ft 30 CQ CQ  0) rl  -P CQ V  20  U  -P  a  •H  10  X  -160  -200  -120  -80 Temperature  F i g . 18  +40  -4o °C  The e f f e c t o f s t r a i n r a t e on t h e maximum s t r e s s i n 25w cadmium.  O - €'= 4.0 x 10_| sec."1  4.0 4.0  30  x x  10 10"  sec. sec.  _j_  D u c t i l e shear f r a c t u r e Cleavage  ft  fracture  CQ CQ  <u u -p  20  CQ  cu pi u -p  1.0  -160  -120  -80  -40  0  -+4o  Temperature • °C. Fig.19  The e f f e c t o f s t r a i n r a t e on t h e maximum s t r e s s i n 20p z i n c .  +80  - 30 1.4  DEFORMATION MODES IN.ZINC AND  In I 9 2 8 Von independent s l i p  Mises  showed t h a t i t was  3 2  systems t o be  CADMIUM  necessary  for five  operative before a p o l y c r y s t a l l i n e m a t e r i a l  can undergo a g e n e r a l homogeneous s t r a i n by s l i p .  In many systems  however o t h e r mechanisms such as twinning bending and. k i n k i n g may 7  thereby  r e d u c i n g the number of d i s t i n c t  1.4.1  slip  occur  systems r e q u i r e d .  Slip  The  predominant s l i p ^l^oy  system (0001)  .  cadmium i s the  basal  I t has been a p o p u l a r b e l i e f t h a t i f and when  non b a s a l s l i p does occur have °/a  system i n z i n c and  i t w i l l do so much more r e a d i l y i n systems which  r a t i o s e q u a l t o or l e s s t h a n i d e a l .  T h i s argument f o l l o w s from 33  r e l a t i v e close packing i n a d d i t i o n t o the / a c  considerations. r a t i o , the  i n f l u e n c e , on d e f o r m a t i o n process.  S t o l o f f and  Seeger  has  s t a c k i n g f a u l t energy w i l l have a  modes i n as much as i t c o n t r o l s the c r o s s  Davies  3 4  c  The Tables  2 and  basal s l i p  p o s s i b l e pyramidal  slip  c h a r a c t e r i s t i c s o f z i n c and  out u s i n g s i n g l e c r y s t a l s .  investigation.  r a t i o i s not the  as b e i n g o p e r a t i v e  only  systems are i n d i c a t e d i n F i g u r e  Oilman  4 3  i n v e s t i g a t i o n s i n t o the  non  observed p r i s m a t i c s l i p ^ l O l O ^ O-120/"-  o n l y non b a s a l system t h a t has been r e l i a b l y i n z i n c i s the  20.  cadmium. . A l l s t u d i e s were c a r r i e d  o n l y a t h i g h e r temperatures t h a n those used i n the The  slip  slip.  3 show the r e s u l t s of p r e v i o u s  i n cadmium, but  strong  u s i n g hexagonal c l o s e packed Zn-Ag a l l o y s  of s l i g h t l y v a r y i n g a x i a l r a t i o s showed t h a t the / a c r i t e r i o n . f o r non b a s a l  suggested however t h a t  second o r d e r p y r a m i d a l  present reported  £ l l 2 2 j <^112~3^ .  - 31 However b o t h p y r a m i d a l  systems [ l O l l j < 1120/" and £ l l 2 2 J <C 1123/> have  been observed i n cadmium by P r i c e u s i n g d i s l o c a t i o n f r e e p l a t e l e t s . T h i s i s i n t e r e s t i n g i n t h a t the f i r s t s l i p plane.  .Alden  ease o f c r o s s s l i p  4  1  i s a p o s s i b l e cross .  u s i n g z i n c and cadmium, s i n g l e c r y s t a l s found t h a t  z i n c has a. much h i g h e r n e t hardening tension-compression  order pyramidal  4 0  tests.  r a t e than cadmium d u r i n g a l t e r n a t i n g  T h i s he i n t e r p r e t e d t o be due t o the g r e a t e r  i n cadmium. . However  the 1st- o r d e r p y r a m i d a l  has never been observed d u r i n g the deformation  system  o f bulk c r y s t a l s .  On the  other hand P r i c e f a i l e d t o observe any c r o s s s l i p from b a s a l t o p y r a m i d a l planes.  His pyramidal  d i s l o c a t i o n s were a l l n u c l e a t e d  on the p y r a m i d a l  planes.  . Metallographic slip  s t u d i e s f o r - t h i s work i n d i c a t e d t h a t non b a s a l  i s a common o c c u r r e n c e .  A l l o b s e r v a t i o n s were-made u s i n g 400u m a t e r i a l  because o f the d i f f i c u l t y i n r e s o l v i n g t r a c e s - o n f i n e g r a i n e d Q u a l i t a t i v e l y i t appeared t h a t t h e occurrence i n frequency  with decreasing  w i l l have t o w a i t  1.4.1  surfaces.  o f non b a s a l s l i p  increased  g r a i n s i z e . .However any q u a n t i t a t i v e . r e s u l t s  an e x t e n s i v e e l e c t r o n microscopy r e p l i c a  study.  a) Z i n c  Non b a s a l t r a c e s were much more p r e v a l e n t a t +20°C i n z i n c than i n cadmium a t an e q u i v a l e n t temperature.  F i g u r e 21 shows s l i p  line  t r a c e s i n z i n c over a s e r i e s o f s t r a i n s a t +20°C. . Approximately•50$ o f the g r a i n s i n z i n c showed non b a s a l t r a c e s a t f r a c t u r e . were u s u a l l y wavy and d i s c o n t i n u o u s completely and  traverse a grain.  g r a d u a l l y progress  i n nature  These t r a c e s  a t +20°C and d i d not  They would s t a r t near g r a i n b o u n d a r i e s  a c r o s s the g r a i n ( G r a i n A, F i g . . 21).  showed two d i f f e r e n t t r a c e s and a few t h r e e  (Grain B).  Many g r a i n s  - 32 -  (a) First-order pyramidal glide occurs when_dislocations with a $[1210] Burgers vector move on (lOTl) planes, (b) Secondorder pyramidal glide occurs when dislocations_with a Burgers vector J[ll23] = c+a move on (1122) planes.  (b)  F i g . 20  P y r a m i d a l g l i d e systems i n z i n c and cadmium ( a f t e r P r i c e ' ).  TABLE 2 Non B a s a l S l i p Systems Observed i n Z i n c Temperature  Author Rosenbaum  35  36  B e l l and Cahn  Price  3 7  '  3 8  '  4 2  Predvoditelev  Oilman  S t o f e l , Wood 4 4 and C l a r k  Non B a s a l System  Remarks  +20°C  Bending  {ll22} < 1 1 2 J >  +20°C  T e n s i o n 11 t o b a s a l planes  [ l l 2 2 j <^1125/'  Tension  {ll22]<1123>  dislocation free platelets  Compression 11 t o c a x i s  (1122} <1123>  etch p i t studies  Compression 11 t o b a s a l planes  {ll22}<1123> [1010]<1120>  Prismatic only a t e l e v a t e d temperatures  T e n s i o n and Compression 11 to c a x i s  {1122] < i i 2 3 y  r a t e o f work h a r d e n i n g = 7.5 x. 1 0 5 psi.. decreases w i t h d e c r e a s i n g temperature  +20°C-^-150°C  3 9  Loading  +20°C  +20°C-^ +150°C  25°C and ^78°C  e t c h p i t t i n g on b a s a l planes  s l i g h t d e p a r t u r e from { l l 2 2 } - s l i p p l a n e may be i r r a t i o n a l  TABLE  3  Non B a s a l S l i p Systems Observed i n Cadmium  Author'  Temperature  Loading  Non B a s a l System  Remarks  S t o l o f f and Gensamer  +20°C -*- -196°C  bending and compression  £ll22j < 1 1 2 3 >  Price  +20°C -*- -150°C  tension  (1122] <1123> [ l O l l ] <11207  tension  {lOlo} <1120>  Only a t e l e v a t e d temperatures  compression  £1122} <1123>  etch p i t studies  47  ~ '  4 0  Gilman  4 1  +150°C -»-275 C 0  4 8  Wernick and Thomas 9 4  +25°C — - -150°C  S i n g l e c r y s t a l s used  Dislocation free p l a t e l e t s [ l O l l j predominates a t e l e v a t e d temperatures  (b) 4.7  $  strain  (c) 7 • ! io s t r a i n F i g . 21  £l_122] ^ 1 1 2 3 ^ s l i p i n 400u z i n c a t v a r i o u s Temperature = +20°C  strains. M a g n i f i c a t i o n X kQO  - 37 By a t r a c e a n a l y s i s t e c h n i q u e s i m i l a r t o t h a t d e s c r i b e d R e e d - H i l l and  Baldwin,  o r i g i n a t i n g from at  a l l non  6 5  £ll22^  <C 1123  l e a s t 3 t w i n t r a c e s and  by an a p p r o p r i a t e  b a s a l t r a c e s were i d e n t i f i e d  slip.  The  p o s s i b l e s o l u t i o n f o r the non  basal traces.  o f the o r i e n t a t i o n f o r two  basal traces. pyramidal  In b o t h cases, the two  observed.  Because- o f the  slight  checked a g a i n s t X-Ray  s e l e c t e d g r a i n s showing  techniques  i n d i c a t e d 2nd  non  order  slip.  P r i c e observed t h a t screw d i s l o c a t i o n s w i t h a Burgers 3  Then  i t i s possible to a r r i v e at a  ambiguity a s s o c i a t e d w i t h t h i s p r o c e d u r e , i t was determination  as  t e c h n i q u e can o n l y be used i f  the b a s a l s l i p t r a c e s can be  measurement o f a n g l e s  by  {^11233  c r o s s g l i d e d f r e q u e n t l y between p l a n e s  direction.  vector  c o n t a i n i n g the ^1123^]  T h i s c o u l d e x p l a i n the wavy n a t u r e of the t r a c e s a t room  temperature.  With decreasing s t r a i g h t e r and  temperature the non  tended t o c o n c e n t r a t e  p r e v i o u s l y by S t o l o f f  4 7  r e a d i l y i n t e r s e c t one  1.4.1.  i n t o bands, an o b s e r v a t i o n made  i n cadmium and  e a s i l y be mistaken f o r f i n e t w i n s . a n o t h e r and  b a s a l t r a c e s became  Gilman  4 3  in zinc.  These bands  However as seen i n F i g u r e 22  may  they  were, removed by p o l i s h i n g .  b) Cadmium  At 30°C and  above non  than i n z i n c . -With d e c r e a s i n g shown i n F i g . 23.  b a s a l s l i p was  l e s s extensive  i n cadmium  temperature i t became more p r e v a l e n t  These low. temperature markings were v e r y  those observed i n z i n c a t e q u i v a l e n t  temperatures.  As  as  s i m i l a r to  i n zinc-trace  - 38 a n a l y s i s showed them t o o r i g i n a t e from first  { 1 1 2 2 } ^ 1 1 2 3 s l i p . I n no case was  o r d e r p y r a m i d a l observed. The o b s e r v a t i o n o f e x t e n s i v e  {1122} 0-123^  slip  i n z i n c and  86  cadmium i s not unexpected.•As reviewed by Dorn  , this  system i s t h e o n l y  one which can promote e x t e n s i v e d e f o r m a t i o n p a r a l l e l t o the c - a x i s . The c o n t r i b u t i o n t h a t t w i n n i n g can make i s not s i g n i f i c a n t total can  strain.  No combination o f  provide the f i v e  £000l]<1120>, £l010}<1120>, and{l01l}<1120>  independent systems r e q u i r e d f o r homogeneous d e f o r m a t i o n .  However the o p e r a t i o n o f £L122^<1123> i s s u f f i c i e n t the  i n terms of the  number o f r e q u i r e d systems. Table  4  systems f o r each o f the prominent s l i p  by i t s e l f i n p r o v i d i n g  shows the number o f independent  systems .  TABLE 4 S l i p Systems  No.  Slip  System  i n Hexagonal M e t a l s  Burgers V e c t o r  Number o f Independent Systems  1  (000l]O.120>  a  2  2  [1010] CL120?  a  2  3  £l011^ <1120>  a  4  4  [1122] <1123>  c + a  5  5  1 + 2+3  a  4 ( a f t e r Dorn  ).  39 -  twins  cleavage  X (a)  Non  b a s a l t r a c e s near f r a c t u r e  240  surface.  twins  X (b)  Fig.  22  As  above a f t e r  240  polishing.  £ll22] ^ 1 1 2 3 > s l i p i n 400ju z i n c a t -196°C  crack  F i g . 23  ^1122J<1123> t r a c e s on UOOJJ cadmium deformed 7$ a t - 1 9 6 ° C .  -.41 1.4.2  Twinning  In i n the  b o t h z i n c and cadmium t w i n n i n g occurs on t h e  <1011^  directions.  £l012^  planes  However s l i g h t d i f f e r e n c e s occur i n t h e two  systems i n t h e frequency o f t w i n n i n g .  In of  the absence o f g e n e r a l g r a i n boundary m i g r a t i o n t h e amount  t w i n n i n g d i d not v a r y a p p r e c i a b l y w i t h temperature.  As the temperature  decreased t h e twins became f i n e r i n d i c a t i n g r e s t r i c t e d t w i n growth w i t h d e c r e a s i n g temperature.  A comparison  o f t h e d e f o r m a t i o n markings a f t e r  7$  s t r a i n a t +20°C and -196°C in-400 u cadmium i s shown i n F i g u r e s 24 and 25.  The temperature  amount o f t w i n n i n g under e q u i v a l e n t c o n d i t i o n s o f  and s t r a i n was s l i g h t l y l e s s i n z i n c than i n cadmium.  However  P r i c e observed t h a t i n d i s l o c a t i o n f r e e p l a t e l e t s , twins formed more r e a d i l y and grew t o l a r g e r s i z e s i n z i n c t h a n t h e y d i d i n cadmium.  T h i s he  e x p l a i n e d i n terms o f the g r e a t e r shear a s s o c i a t e d w i t h t w i n n i n g i n cadmium ( .171) as opposed t o z i n c ( .139) difficult argue  a n c i  "the p o s s i b i l i t y t h e r e f o r e o f a more  p r o c e s s o f t w i n n u c l e a t i o n i n cadmium.  However one c o u l d e a s i l y  t h a t twins s h o u l d n u c l e a t e and grow more r e a d i l y i n cadmium because  t h e y r e p r e s e n t a more e f f e c t i v e d e f o r m a t i o n mechanism.  The lower f r e q u e n c y o f t w i n n i n g i n z i n c may a l s o be due t o t h e f a c t t h a t second  order pyramidal s l i p  occurs more r e a d i l y i n p o l y c r y s t a l l i n e  z i n c than i n cadmium and t h e amount o f t w i n n i n g needed t o meet Von M i s e s ' requirements  i s t h e r e f o r e reduced.  F i g . 2k  M i c r o s t r u c t u r e o f 400JJ cadmium deformed 7$ a t +20°C.  - 43 -  X 100  F i g . 25  Micro-structure  o f 400/4 cadmium deformed 7$ a t -196°C  -.kh The  amount o f t w i n n i n g i n b o t h systems was always.governed by  the r e l a t i v e temperature  and s t r a i n . . I n the r e g i o n o f room  temperature  w i t h i n c r e a s i n g boundary m i g r a t i o n accompanying i n c r e a s i n g ' s t r a i n , f o r m a t i o n became much l e s s f r e q u e n t . t w i n f o r m a t i o n was not observed.  twin  Once d i s t i n c t r e c r y s t a l l i z a t i o n  started  T h e r e f o r e cadmium which had f r a c t u r e d a t  20$ s t r a i n a t -196°C always showed more t w i n n i n g than cadmium deformed t o 20$ s t r a i n a t +20°C s i n c e a t the l a t t e r temperature  migration i s occurring.  M i g r a t i o n a f f e c t s t w i n n i n g due t o i t s r e c o v e r y e f f e c t on areas o f s t r e s s concentration r e q u i r e d f o r twin n u c l e a t i o n .  T h e r e f o r e t r u e comparisons o f  r e l a t i v e t w i n n i n g c o u l d o n l y be made e i t h e r a t low v a l u e s o f s t r a i n b e f o r e e x t e n s i v e m i g r a t i o n had s t a r t e d , o r a t low  On t h i s b a s i s o f comparison tendency  temperatures.  and keeping  i n mind the g r e a t e r  f o r 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 w i t h d e c r e a s i n g g r a i n  i t was observed t h a t the amount o f t w i n n i n g d i d not v a r y  size  significantly  w i t h ' g r a i n i .size .•  . A t temperatures very l i t t l e  above +20°C where e x t e n s i v e m i g r a t i o n occurs7  t w i n n i n g o c c u r r e d as shown i n F i g . 26.  S t o l o f f observed l e s s b a s a l s l i p decrease  i n temperature.  i n twinned  T h i s was not observed as i n d i c a t e d i n F i g u r e 27  which shows e x t e n s i v e t w i n b a s a l s l i p a t -196°C. t r a c e s a t low temperatures  regions with a  The f i n e r nature o f b a s a l  makes them more d i f f i c u l t  to resolve.  When t w i n n i n g on one p a r t i c u l a r t w i n plane was stopped by a t w i n on another p l a n e as shown i n F i g u r e 27, e x t e n s i v e s l i p would occur i n b a s a l p l a n e s o f the l a t t e r and e v e n t u a l l y cause t w i n n u c l e a t i o n on the o p p o s i t e s i d e o f the t w i n . .This p r o c e s s o f t w i n n u c l e a t i o n was a common occurrence e s p e c i a l l y i n cadmium.  - +5 -  X 260 F i g . 26  Lack o f t w i n n i n g  i n the presence o f boundary  ( 25ji cadmium deformed 10$ a t +60°C.)  X 120 Fig.27  Twin b a s a l s l i p and t w i n  nucleation.  ( 400jj cadmium deformed 7$ a t +20°C )  migration.  -.46 1.4.3  The  Formation  Low deformation  confused  deformation  angle boundaries  during  have been observed  Deformation  t o form d u r i n g the  have been r e f e r r e d t o by a . v a r i e t y o f nomenclatures which  t h e i r nature  of f o r m a t i o n and. t h e i r importance as a  process.  The first  Angle Boundaries  of b o t h s i n g l e c r y s t a l s and p o l y c r y s t a l s i n many m a t e r i a l s .  Such b o u n d a r i e s has  o f Low  -  observed  f o r m a t i o n o f " k i n k s " i n s i n g l e c r y s t a l s o f cadmium and d i s c u s s e d by O r o w a n . 54  and Washburn and P a r k e r ' ' 5 -  5 3  Hess and  s t u d i e d the nature  5 2  , Gilman  of k i n k i n g i n z i n c  c r y s t a l s . .Gilman d i s t i n g u i s h e d between compression p o s t u l a t i n g t h a t the l a t t e r form o n l y due  Barrett  was  to c r y s t a l  k i n k s and  been e x t e n s i v e l y deformed).  5  6  single  tension kinks,  inhomogeneities.  Compression k i n k s were f u r t h e r s u b d i v i d e d i n t o " o r t h o " (formed, under s t r e s s c o n d i t i o n s ) and"para" (formed  5 5  low  a t h i g h s t r e s s e s i n c r y s t a l s which have  Compression o r t h o k i n k s were observed  by  Gilman i n w h i c h the k i n k p l a n e s were always p e r p e n d i c u l a r t o s u r f a c e basal, traces.  They were observed  i n d i c a t i n g t h a t the p r o c e s s  t o form i n z i n c a t temperatures  down t o -196°C  of t h e i r f o r m a t i o n i s more l i k e l y  induced d i s l o c a t i o n rearrangement on the b a s a l p l a n e s - t h a n  one  one  of s t r e s s  of  d i s l o c a t i o n climb which i s t h e r m a l l y a c t i v a t e d .  Boundary f o r m a t i o n i n p o l y c r y s t a l s i s more c o m p l i c a t e d of the nature  of the s t r e s s e s .  v a r i e t y of terms such as mosaic g r a p h i c boundary f o r m a t i o n . d u r i n g the d e f o r m a t i o n  I t has  t h e r e f o r e been r e f e r r e d t o by  w a l l s , c e l l f o r m a t i o n and non  Gifkins  5 0  temperature independent "non  a  crystallo-  r e p o r t e d the f o r m a t i o n of  of p o l y c r y s t a l l i n e z i n c above 200°C.  s t u d y i n g magnesium observed  because  Dorn  "cells" 2 1  2  2  crystallographic"  -A7 boundary f o r m a t i o n which i n many cases c r o s s e d g r a i n b o u n d a r i e s . p o s t u l a t e d t h a t t h e s e boundaries formed because  He  o f the bending o f the  l a t t i c e a s s o c i a t e d w i t h t h e non homogeneous d e f o r m a t i o n o f u n d e r l y i n g grains.  The  o b s e r v a t i o n s o f t h e p r e s e n t work i n d i c a t e t h a t the  f o r m a t i o n o f b o u n d a r i e s . i s s i m i l a r i n degree and type i n b o t h z i n c and cadmium.  "Non c r y s t a l l o g r a p h i c " b o u n d a r i e s  Dorn a r e shown i n F i g u r e 28 and 29.  s i m i l a r . t o those observed by  From F i g u r e 28 i t i s a l s o  observed  t h a t t h e s e b o u n d a r i e s can c r o s s g r a i n b o u n d a r i e s .  On c l o s e examination o f F i g u r e 28 i t i s observed t h a t some boundaries  seem t o be " c r y s t a l l o g r a p h i c " i n t h a t t h e y a r e p e r p e n d i c u l a r t o  the b a s a l s l i p t r a c e s .  S i m i l a r b o u n d a r i e s a r e shown i n F i g u r e 30.  b o u n d a r i e s a r e s i m i l a r t o t h e o r t h o k i n k p l a n e s o f Gilman. d i s t i n g u i s h e d by t h r e e d i s t i n c t 1)  They were  features:  The m i s o r i e n t a t i o n o f the b a s a l t r a c e s was always the c r y s t a l l o g r a p h i c  These  greater across  " k i n k s " than a c r o s s non c r y s t a l l o g r a p h i c  boundaries. 2)  C r y s t a l l o g r a p h i c b o u n d a r i e s formed most prominent  3)  i n those g r a i n s which had t h e  b a s a l t r a c e s and f e w . i f any  twins.  The b o u n d a r i e s were sometimes observed t o be composed o f two o r more s m a l l e r b o u n d a r i e s . ( F i g u r e 30) s i m i l a r t o those o f Washburn and  Parker.  I t would appear t h a t the " c r y s t a l l o g r a p h i c k i n k s " from o n l y under f a i r l y simple s t r e s s c o n d i t i o n s such as ..bending or compression basal planes.  o f the  The b o u n d a r i e s become non c r y s t a l l o g r a p h i c however where  crystallographic non "  x4oo F i g . 28  Low angle boundaries i n cadmium deformed 7% " t -30°C a  X F i g . 29  1.20  The f o r m a t i o n o f non c r y s t a l l o g r a p h i c boundaries i n cadmium due t o u n d e r l y i n g s m a l l g r a i n s . ( deformed 15$ a t +20°C.)  - k  9  X240 (a) cadmium deformed 15$ a t  +20°C.  X240 (b) z i n c deformed 7$ a t +20°C. Fig.30  C r y s t a l l o g r a p h i c boundary f o r m a t i o n i n 400p Zn and Cd.  -  -50 boundary r e s t r a i n t s on a g i v e n g r a i n become more c o m p l i c a t e d . non  c r y s t a l l o g r a p h i c boundary f o r m a t i o n o f F i g u r e 29 i s due t o t h e r e s t r a i n t s  imposed by t h e u n d e r l y i n g . f i n e g r a i n  structure.  1.5  YIELD STRESS AND WORK HARDENING  1.5-1  The Temperature Dependence o f Y i e l d  The  flow stress-temperature  shown i n F i g u r e 31temperature  r e l a t i o n s h i p s found by S t o l o f f a r e  He found t h a t the y i e l d s t r e s s was independent  below about -80°C and t h a t t h e work h a r d e n i n g  over an i n c r e a s i n g s t r a i n r e g i o n as t h e temperature at  The e x t e n s i v e  of  r a t e was c o n s t a n t  decreased.  . The. r e s u l t s  k.2°K a r e somewhat i n doubt due t o the d i f f e r e n t specimen geometry.  The  d e f i n i t i o n o f y i e l d i n p o l y c r y s t a l l i n e z i n c and cadmium i s  d i f f i c u l t because o f the g r a d u a l n a t u r e o f the. y i e l d process".  Therefore the  yield  s t r e s s f o r the purpose o f t h i s work was d e f i n e d by an o f f s e t  using  .Yfo s t r a i n as the y i e l d s t r a i n .  . In o r d e r t o compare the  technique  temperature  dependence o f y i e l d i n z i n c and cadmium, the y i e l d s t r e s s e s were n o r m a l i z e d i n each case by d i v i d i n g by the shear modulus G;. -Shear'modulus, v a l u e s were "57  o b t a i n e d from the t a b l e s o f Koster  .  The y i e l d  stress-effective  temperature  r e l a t i o n s h i p s a r e shown i n F i g u r e 32. It  i s seen t h a t below t h e c r i t i c a l temperature  c o m p l e t e l y t h e r m a l l y a c t i v a t e d the y i e l d w i t h d e c r e a s i n g temperature.  s t r e s s appears  The temperature  t o increase l i n e a r l y  dependence o f y i e l d f o r b o t h  g r a i n s i z e s i s s l i g h t l y g r e a t e r f o r z i n c t h a n f o r cadmium. yield  s t r e s s i s a l s o somewhat h i g h e r f o r z i n c .  where y i e l d i s  The n o r m a l i z e d  .In 400u m a t e r i a l the  - 51 -  28  r  24 -  -250  - 200  -150  -100  - 50  0  50  TEMPERATURE,°C  Fig.51  Flow s t r e s s - t e m p e r a t u r e r e l a t i o n s h i p s f o r 0 . 0 2 0 i n c h g r a i n diameter cadmium as found by S t o l o f f .  O  Fig.32  .Temperature dependence  zinc  o f the y i e l d s t r e s s i n p o l y c r y s t a l l i n e z i n c and cadmium  - 53 c r i t i c a l temperature  (Tc) i s a p p r o x i m a t e l y the same f o r b o t h z i n c  cadmium(Tjj = .520).  T e s t s c o u l d not be done on f i n e g r a i n e d  and  material  above about Tg = .5 due t o g r a i n growth a t t h e s e temperatures.  I.5.2  Temperature  Bullen  5 8  S e n s i t i v i t y o f the Flow  6  0  Stress  u s i n g p o l y c r y s t a l l i n e copper.found a l i n e a r  r e l a t i o n s h i p between the f l o w s t r e s s  ( a t c o n s t a n t s t r a i n ) , and  over a range o f temperature from h.2°K t o q-50°K.  temperature  He p o s t u l a t e d t h a t the  h a r d e n i n g mechanism i n copper remained the same over the temperature  range  s t u d i e d but t h a t the lower f l o w s t r e s s v a l u e s o b t a i n e d w i t h i n c r e a s i n g temperatures were due t o e i t h e r a. d i f f e r e n t r a t e o f o b s t a c l e f o r m a t i o n w i t h s t r a i n , or t o a temperature dependent tended t o remove o b s t a c l e s once formed.  dynamic r e c o v e r y p r o c e s s which  On the o t h e r hand R u s s e l l , a g a i n 4  u s i n g p o l y c r y s t a l l i n e copper found t h a t the work h a r d e n i n g r a t e was  linear,-  and temperature i n s e n s i t i v e below a c e r t a i n c r i t i c a l temperature.  The  amount o f s t r a i n i n v o l v e d w i t h t h i s c o n s t a n t l i n e a r h a r d e n i n g was  also a  f u n c t i o n o f temperature, and i n c r e a s e d w i t h d e c r e a s i n g temperature. H i s r e s u l t s are shown i n F i g u r e 33-  Stoloff  ( F i g u r e 31) a l s o i n d i c a t e d a l i n e a r  and temperature i n s e n s i t i v e work h a r d e n i n g r a t e f o r cadmium a t low temperatures where the flow s t r e s s i t s e l f was  I.5.2  not a f u n c t i o n o f temperature.  a) Cadmium  Flow s t r e s s - t e m p e r a t u r e r e l a t i o n s f o r 25^. and hOOyx cadmium o b t a i n e d d u r i n g t h i s study are shown i n F i g u r e s 3^  a n o  -  35-  - 5+ -  Fig-33  The temperature dependence of the s t r a i n h a r d e n i n g parameter of p o l y c r y s t a l l i n e copper as found by R u s s e l l " .  F i g . $4  .Flow s t r e s s - t e m p e r a t u r e  relationships  f o r 25p  cadmium.  - 56 -  . "jo s t r a i n  -200  -160  -120  •  -80  -40  Temperature Fig.  35  0  +k0  for  400p cadmium.  °C  .Flow s t r e s s - t e m p e r a t u r e r e l a t i o n s h i p s  +80  - 57 I t i s seen t h a t as•opposed  t o S t o l o f f ' s r e s u l t s , t h e flow s t r e s s  c o n t i n u e s t o i n c r e a s e w i t h d e c r e a s i n g temperature down t o -1^6°C. U n t i l t e s t s can be performed below -196°C i t i s not known whether t h i s  trend  continues.  In o r d e r t o o b t a i n a more d i r e c t comparison o f t h e s t r e s s  strain  r e l a t i o n s h i p s , the y i e l d s t r e s s was s u b t r a c t e d from t h e flow-' s t r e s s f o r each p o i n t g i v i n g p l o t s o f the work h a r d e n i n g parameter vs.temperature."  strain)  These a r e shown i n F i g u r e s 36 and 37- . I t I s seen t h a t i n  b o t h c a s e s , a .region o f temperature independent below -120°C  ( °"flow ~ ^ . 1 $  similar  work h a r d e n i n g develops  t o t h a t observed by R u s s e l l . .With  temperature the amount o f s t r a i n i n v o l v e d d e c r e a s e s .  increasing  The temperature  independent work h a r d e n i n g r e g i o n covers, t h e same temperature range f o r both grain sizes. temperature  However l a r g e r amounts o f s t r a i n i n hOOyx m a t e r i a l show independent work h a r d e n i n g than t h a t found, f o r 25u ( i . e . l4fo  s t r a i n a t -196°C f o r 400u and 7$ f o r 25u).  1.5.2  b). Z i n c  Because o f the l i m i t e d d u c t i l i t y e v a l u a t i o n c o u l d be made.  o f ,400u z i n c , no s i m i l a r  However the r e s u l t s o b t a i n e d f o r 20u z i n c a r e  shown i n F i g u r e s 38 and 39-  Temperature independent work h a r d e n i n g i s  observed below a p p r o x i m a t e l y -95°C•  T a b l e k shows a comparison between  z i n c and cadmium o f the maximum temperature f o r t h i s r e g i o n a t the a r b i t r a r y v a l u e o f 1$ s t r a i n .  . I t i s seen t h a t temperature independent work  h a r d e n i n g occurs below a common e q u i v a l e n t temperature o f Tg = .26 systems.  i n both  - 58 -  F i g . 56  The v a r i a t i o n w i t h temperature o f t h e work h a r d e n i n g parameter i n 25/j cadmium.  - 59 -  F i g . 3 7 The v a r i a t i o n w i t h temperature o f t h e work h a r d e n i n g parameter i n  k-00[l  cadmium.  - 60 20  •  A H  x  ^A \ A.  16  cK  A  "\  'v  X  ID  ft w to <D SH -P w  "  12  symbol H  ^  \  10  •  5 ,3  A  A O  \Q A » \ ^ \ ^  A  ° \  A  ^--o ^^o_  ..2 1  •  -A  o \  $ strain  V  \  _ C = 4 . 0 x 10' s e c . k  x  >.(.5) I  -160  I  I  I  .... -120 .  I  I  -80  I  I  -4o  ...  Temperature F i g . 38  I o  I .  I  I  L_  +4o : :,  +8o  °C  Flow s t r e s s - t e m p e r a t u r e r e l a t i o n s h i p s  f o r 20j_l z i n c .  16  ^  12  1I  i ft  —A—A—A  8  $> s t r a i n  -m • b  1  -A  4h  A • -O  8 H  -160  -120  -80  -40 .Temperature  Fig.39  0  +40  7 5 3 2 1 .5 +80  °C  The v a r i a t i o n w i t h temperature o f the work hardening i n 20jj z i n c .  parameter  - 61 The  comparison o f the work hardening  b e h a v i o u r o f z i n c and  cadmium.in the temperature i n s e n s i t i v e hardening' r e g i o n i s shown i n F i g u r e 40.  Taking  i n t o account the shear•modulus o f each system, i t i s  seen t h a t the work hardening  o f f i n e g r a i n e d z i n c and cadmium i s i d e n t i c a l .  Except f o r a p a r a b o l i c r e g i o n below 1% s t r a i n , the hardening  i s also linear.  TABLE 5 Upper temperature l i m i t s for, l i n e a r hardening i n p o l y c r y s t a l l i n e z i n c and cadmium  . Maximum Temperature f o r ' l i n e a r . hardening  Maximum E q u i v a l e n t T  1.5-3  Zinc  Cadmium  -95°C  -120°C  .26 ..  .26  Temperature  S t r a i n Rate S e n s i t i v i t y o f t h e Flow S t r e s s  The  e f f e c t o f s t r a i n r a t e on the flow s t r e s s was . i n v e s t i g a t e d  f o r 20u Zn and 25u Cd over the temperature.range from - I 9 6 t o +20°C.'  Tests  were n o t done w i t h 400u m a t e r i a l because o f the p o o r e r r e p r o d u c i b i l i t y o f flow s t r e s s v a l u e s . 4.0 x 10  5  sec  1  F i v e s t r a i n r a t e s between 4.0 x 10  were used.  t e s t c o n d i t i o n s between flow  3  sec  1  L i n e a r r e l a t i o n s h i p s were o b t a i n e d s t r e s s a t constant  and for a l l  s t r a i n , and the n a t u r a l  l o g a r i t h m o f the s t r a i n r a t e as i l l u s t r a t e d f o r 20u z i n c i n F i g u r e 4 l . ACT Aln£*  was chosen as a s t r a i n r a t e parameter and v a l u e s  obtained  as a  f u n c t i o n o f s t r a i n a r e shown i n F i g u r e s 42 and 4 j f o r cadmium and z i n c respectively.  - 62 -  1  i  2  3 '  F i g . hO  +  5  6  °jo s t r a i n  Linear hardening of p o l y c r y s t a l l i n e  below T =.26'  1  TJ  z i n c and cadmium  - 6k -  k  8  •%  Fig-42  .The v a r i a t i o n  .12  16  strain  o f the s t r a i n r a t e parameter  temperature and s t r a i n i n 25p cadmium.  AO" Aln£"  with  i6oo  - 65 -  •  o . . .. -120°C • .... -105°C A . . .. -95°C • • ' . • -6o°c • . . .. -30°c • • . ... +20°C  12 $ Fig.^3  The v a r i a t i o n  16  20  strain  o f t h e s t r a i n r a t e parameter  w i t h temperature and s t r a i n i n 20(j z i n c .  ACT Alng'  - 66 From F i g u r e 42 f o r 25u i s an almost  cadmium i t i s seen t h a t a t -]_96°C t h e r e  s t r a i n above which t h e . s e n s i t i v i t y  increases.  insensitive  i n t h i s region.  at  f$.  c o n s t a n t v a l u e of s t r a i n r a t e s e n s i t i v i t y up t o about  r a t e o f work hardening  -196°C i s a p p r o x i m a t e l y  of the hardening  This implies a s t r a i n rate T h i s r e g i o n of  the same t h a t showed temperature  insensitivity  rate.  Between -95°C and  -196°C t h e r e i s a c o n t i n u a l i n c r e a s e of  s e n s i t i v i t y w i t h i n c r e a s i n g temperature and  strain.  A t about -60°C  above however i t i s seen t h a t , a t h i g h v a l u e s o f s t r a i n the s e n s i t i v i t y with strain  i s much l e s s .  results  increase i n  degree.  f o r z i n c are q u a l i t a t i v e l y the same ( F i g . 45).  Below -95°C "the s t r a i n r a t e s e n s i t i v i t y does not v a r y w i t h s t r a i n . a g a i n i s the same temperature r e g i o n which g i v e s a temperature work h a r d e n i n g  1.5.4  The  and  It i s i n this region that grain  boundary m i g r a t i o n i s known t o occur t o a s i g n i f i c a n t  The  strain  This  independent  rate.  Deformation  o f Cadmium S i n g l e C r y s t a l s  R u s s e l l has proposed t h a t the d e v i a t i o n s which occur from hardening are due  a t h i g h v a l u e s of s t r a i n or w i t h i n c r e a s e d temperature i n copper  t o a dynamic r e c o v e r y mechanism i n v o l v i n g c r o s s s l i p .  a s s o c i a t e d the stage  linear  i n i t i a l l i n e a r hardening  s i n g l e c r y s t a l hardening.  understanding  of the d e f o r m a t i o n  He  has  region of p o l y c r y s t a l s with  Therefore  i n o r d e r t o have a b e t t e r  behaviour  of. cadmium i t was  undertake some study of s i n g l e c r y s t a l  behaviour.  decided  second  to  - 67 - • Resolved  shear s t r e s s - s h e a r s t r a i n curves f o r cadmium  single  c r y s t a l s o f i d e n t i c a l o r i e n t a t i o n s a r e shown i n F i g s , hk and h^. The o r i e n t a t i o n used was as shown i n F i g . hh w i t h t h e angle between t e n s i l e a x i s and s l i p plane and t e n s i l e a x i s and s l i p d i r e c t i o n b e i n g 3 6 r e s p e c t i v e l y . A t +20°C a t h r e e stage h a r d e n i n g i n which t h e i n i t i a l  and 38°  0  curve was o b t a i n e d  (Fig.U5)  stage i s s u b d i v i d e d i n t o two r e g i o n s s i m i l a r t o t h a t  observed b y S e e g e r ^ i n z i n c a t room temperature.  He a l s o p o s t u l a t e d t h a t t h e  t r a n s i t i o n from Stage I t o Stage I I h a r d e n i n g i s due t o t h e e s t a b l i s h m e n t o f a c r i t i c a l , d e n s i t y o f immobile d i s l o c a t i o n l o o p s due t o vacancy  At different  condensation.  -50°C and below t h e n a t u r e o f t h e curves i s somewhat  ( F i g . kk\. Stage I was l i n e a r a t a l l temperatures  and d i d n o t show t h e "S" "type o f h a r d e n i n g  observed  down t o -196°C  i n magnesium^. Of about  20 c r y s t a l s t e s t e d a l l showed e x t e n s i v e t w i n n i n g d u r i n g Stage I I . A l l p o s s i b l e care was t a k e n i n o r d e r t o a v o i d c r y s t a l damage p r i o r t o t e s t i n g and no o b s e r v a b l e twins were p r e s e n t . T h e r e f o r e a t low temperatures  i t must  89 be  concluded t h a t t w i n n i n g i s a g e n e r a l f e a t u r e o f Stage I I h a r d e n i n g .  Lally  has reached a s i m i l a r .conclusion w i t h r e s p e c t t o magnesium. An i n t e r e s t i n g o b s e r v a t i o n i s t h a t t h e r e s o l v e d shear on t h e b a s a l p l a n e a s s o c i a t e d w i t h i n i t i a l t w i n f o r m a t i o n was independent  o f temperature  w i t h i n c r e a s i n g temperature  stress  virtually  as shown i n T a b l e 6. The shear s t r a i n i n c r e a s e d due t o t h e lower r a t e o f work  hardening.  A l t h o u g h t h e maximum r a t e o f h a r d e n i n g d u r i n g Stage I I i s a f u n c t i o n o f t h e nature- and e x t e n t o f t w i n n i n g , t h e t r a n s i t i o n from Stage I to  Stage I I cannot be a s s o c i a t e d w i t h t w i n n i n g . T h i s f o l l o w s from t h e  experimental o b s e r v a t i o n t h a t a c o n s i d e r a b l e p r o p o r t i o n o f the c r y s t a l remains untwinned i n t h e t r a n s i t i o n r e g i o n . The f l o w s t r e s s i s d e r i v e d  - 70 t h e r e f o r e o n l y from t h e n a t u r e  o f t h e d i s l o c a t i o n c o n f i g u r a t i o n i n untwinned  regions.  Due t o t h e above r e a s o n i n g . i t i s more a c c u r a t e t o say t h a t i t i s t h e s t r e s s a s s o c i a t e d w i t h t h e end o f Stage I ffb.iffih.lis,. independeht'npf, temperature  .Twinning  t h e r e f o r e i s an  " a f t e r the fact" consideration ; 1  10U Somewhat s i m i l a r o b s e r v a t i o n s were made by Lucke .eit. al.i;v during the deformation  o f z i n c s i n g l e c r y s t a l s . They found t h a t t h e s t r e s s  a s s o c i a t e d w i t h t h e end o f Stage I h a r d e n i n g a t +20°C. The r e l a t e d  i s independent  of s t r a i n rate  shear s t r a i n i n c r e a s e d w i t h decreased  strain  fates.  TABLE 6 B a s a l shear s t r e s s r e q u i r e d f o r i n i t i a l twin formation.  Temperature  Shear s t r e s s on b a s a l plane gm/mm  Shear  strain  2  +20°C  260  550  -50°C  280  2^0  -78°C  280 .  190  -120°C  285  1^5  -196°C  300  130  Wo attempt  was made t o c a l c u l a t e t h e macroscopic  the t w i n n i n g system.. I t i s k n o w n t h a t a r e a t l e a s t an  39  s t r e s s on  t h a t such c a l c u l a t i o n s produce v a l u e s  o r d e r o f magnitude lower t h a n the s t r e s s  t o be r e q u i r e d f o r t w i n n u c l e a t i o n . l i t  thought  i s i m p o s s i b l e t o e s t i m a t e w i t h any degree  of a c c u r a c y t h e s t r e s s a t p o i n t s o f s t r e s s c o n c e n t r a t i o n which i s r e q u i r e d  -.71 for twin nucleation i n bulk c r y s t a l s .  .However i f one assumes a .constant  r e l a t i o n s h i p between macroscopic shear s t r e s s and the v a l u e of s t r e s s a t p o i n t s o f s t r e s s c o n c e n t r a t i o n i t i s t h e n p o s s i b l e t o p r e d i c t a temperature independent t w i n n i n g s t r e s s .  1.5.5  Temperature  Dependence o f Work Hardening  The temperature dependence o f the r a t e o f work' h a r d e n i n g i n Stage I (&xj and Stage I I ^Qgjj i s shown i n F i g u r e s 4 6 and 4 7 t h a t below -120°C the work h a r d e n i n g r a t e s are c o n s t a n t .  I t i s seen  Above t h i s  temperature f o r b o t h h a r d e n i n g r e g i o n s the r a t e o f h a r d e n i n g d e c r e a s e s . F a h r e n h o r s t and S c h m i d , and Seeger and T r a u b l e 6 2  r e l a t i o n s h i p s f o r Stage I . h a r d e n i n g o f z i n c . n o r m a l i z i n g f o r shear modulus changes t h i s study o f cadmium i n F i g u r e 4 8 .  2 5  have found  similar  The d a t a o f Seeger  after  i s compared w i t h t h a t o b t a i n e d d u r i n g I t i s seen t h a t the drop i n the  h a r d e n i n g r a t e s o c c u r s a t t h e same e q u i v a l e n t temperature o f Tg =. .26 i n bo£h systems.  T h i s i s the same temperature below which temperature  and  s t r a i n r a t e i n s e n s i t i v e h a r d e n i n g began i n p o l y c r y s t a l l i n e z i n c and cadmium. I f t h i s decrease i n hardening' r a t e i s a s s o c i a t e d w i t h some dynamic r e c o v e r y mechanism i t would appear t h a t such a mechanism, i s s i m i l a r i n b o t h p o l y c r y s t a l s and s i n g l e c r y s t a l s .  •  From F i g u r e 4 8 i t i s a l s o noted t h a t t h i s work h a r d e n i n g t r a n s i t i o n r e g i o n has an upper temperature l i m i t  o f about Tg = - . 4 0  i n both  systems.  1.5.6  The G r a i n S i z e Dependence.of Hardening a t -196°C  2 Clarebrcugh and Hargreaves have attempted an a n a l y s i s o f the s i m i l a r i t i e s o f Stage I I h a r d e n i n g o f .f.c.c. s i n g l e c r y s t a l s and the deformation c h a r a c t e r i s t i c s of p o l y c r y s t a l s .  T h i s was  initial  based t o a l a r g e  extent on the r e s u l t s of Feltham and Meakih  3  - 72 who  observed a l i n e a r  hardening  r e g i o n d u r i n g the e a r l y r e g i o n s o f s t r a i n a s s o c i a t e d w i t h the d e f o r m a t i o n of p o l y c r y s t a l l i n e copper.  They a l s o observed t h a t the magnitude o f the  p o l y c r y s t a l l i n e l i n e a r hardening r a t e was hardening.  There was  comparable t o t h a t of Stage I I  t h e r e f o r e no a p p r e c i a b l e e f f e c t of g r a i n s i z e on the  k work h a r d e n i n g r a t e .  S i m i l a r c o n c l u s i o n s , were reached by R u s s e l l who  also  c o r r e l a t e d the stress, a t the end of p o l y c r y s t a l l i n e hardening t o t h a t a t the end of Stage I I s i n g l e c r y s t a l hardening. to  P a r a b o l i c , hardening as opposed  l i n e a r h a r d e n i n g , occurs i n f . c . c . p o l y c r y s t a l s  a c t i o n of c r o s s s l i p i n a s i m i l a r manner t o s i n g l e In  crystals.  o r d e r t o t e s t t h i s concept, cadmium of 5 g r a i n s i z e s  t e s t e d a t -196°C. thought  t h e r e f o r e , due t o the  was  S i n c e the specimen dimensions were h e l d c o n s t a n t i t was  t h a t any c o n s i s t e n t t r e n d towards s i n g l e c r y s t a l data.might  be  observed.  Due  t o the e x t e n s i v e t w i n n i n g d u r i n g 2nd  stage s i n g l e  crystal  d e f o r m a t i o n a t -196°C the meaning of the r e s o l v e d shear stress- on the b a s a l planes i s clouded. i t was  T h e r e f o r e f o r comparison  with p o l y c r y s t a l l i n e material  d e c i d e d t o merely r e p o r t the s i n g l e c r y s t a l Stage I I h a r d e n i n g i n  terms of the t e n s i l e hardening r a t e . a s s o c i a t e d w i t h a s s i g n i n g some average  T h i s a l s o a v o i d s the  difficulty  shear s t r e s s v a l u e f o r p o l y c r y s t a l s .  The p o l y c r y s t a l l i n e s t r e s s s t r a i n curves o b t a i n e d are shown i n F i g u r e ^9-  I t i s seen t h a t w i t h i n c r e a s i n g g r a i n s i z e a two  curve g r a d u a l l y appears.  S i n c e i t was  stage. hardening  d e s i r e d t o compare the 2nd•stage  h a r d e n i n g , the maximum h a r d e n i n g . r a t e was  used  i n a l l cases as shown.  With  d e c r e a s i n g g r a i n s i z e the r e g i o n of l i n e a r hardening decreased t o s m a l l e r  - 73 values of s t r a i n .  The comparison  o f h a r d e n i n g r a t e s i s made by a d ~  2  p l o t as shown _JL  i n F i g . 50- I t i s s e e n . t h a t the r a t e o f h a r d e n i n g v a r i e s l i n e a r l y w i t h d and e x t r a p o l a t e s t o the s i n g l e c r y s t a l v a l u e a t d = 2  0. There  2  i s an i n c r e a s e  by a f a c t o r o f about J i n the h a r d e n i n g r a t e from the s i n g l e c r y s t a l v a l u e t o 25u m a t e r i a l . - S i n c e a l l c r y s t a l s a r e twinned t o about the same degree, i n c r e a s e r e f l e c t s t h e n a t u r e o f the h a r d e n i n g change w i t h i n c r e a s i n g  this  grain  boundary a r e a p e r u n i t volume and d e c r e a s i n g p r o p o r t i o n o f g r a i n s w i t h a f r e e s u r f a c e . S i n c e no p y r a m i d a l s l i p was observed i n s i n g l e crystals;, and an i n c r e a s i n g amount o c c u r s i n p o l y c r y s t a l s as t h e g r a i n s i z e d e c r e a s e s , t h e i n c r e a s e d h a r d e n i n g r a t e can be e x p l a i n e d i n terms o f a g r a d u a l change (  i n t h e n a t u r e and e x t e n t o f the d e f o r m a t i o n mechanisms. However s i n g l e c r y s t a l and p o l y c r y s t a l h a r d e n i n g r a t e s can be compared because  the d e f o r m a t i o n mechanisms do not change w i t h g r a i n  i n copper directly  size.  Temperature g. ^7  fC  The temperature dependence o f stage I I h a r d e n i n g i n cadmium.  - 75 -  F i g . 48  Temperature dependence o f the r a t e o f work h a r d e n i n g d u r i n g Stage I d e f o r m a t i o n  F i g . 5°  The e f f e c t o f g r a i n s i z e on t h e r a t e o f l i n e a r h a r d e n i n g o f cadmium a t -196°C.  - 78 PART  II  2.  MECHANISMS O F HARDENING IM ZINC AND CADMIUM  2.1  INTRODUCTION  Many t e c h n i q u e s have been used i n r e c e n t y e a r s _in a n - e f f o r t t o  /  e v a l u a t e t h e hardening mechanisms t h a t c o n t r o l d e f o r m a t i o n . Some o f the more prominent i n c l u d e t h e use o f t r a n s m i s s i o n e l e c t r o n microscopy,.the  study o f  C o t t r e l l - S t o k e s Law obeyance, and. t h e a p p l i c a t i o n o f r a t e t h e o r y t o determine the r a t e c o n t r o l l i n g mechanisms. A l l have t h e i r l i m i t a t i o n s depending upon e x p e r i m e n t a l procedures  and t h e o r e t i c a l  assumptions.  •Although t r a n s m i s s i o n microscopy  t e c h n i q u e s have proven t o be  v a l u a b l e i n o b s e r v i n g d i s l o c a t i o n motion and b e h a v i o u r , i s encountered  considerable  i n p r e p a r i n g specimens which t r u l y r e p r e s e n t b u l k  difficulty  samples  S e v e r a l authors have made d e t a i l e d studies, o f the C o t t r e l l Stokes • L a w ' 6  1 1  1 3 ;  '  6 8  7  2  , However t h e r e i s c o n s i d e r a b l e c o n t r o v e r s y as- t o t h e  exact meaning o f C o t t r e l l - S t o k e s . o b e y a n c e . The  a p p l i c a t i o n o f r a t e t h e o r y t o d e f o r m a t i o n p r o c e s s e s .has been 1 1 9 73~* 7 8  plagued  by a m u l t i t u d e  of formulations  a l l o f which . r e q u i r e  certain  s i m p l i f y i n g assumptions t o a r r i v e a t mathematical e x p r e s s i o n s which may be. e a s i l y used t o i n t e r p r e t e x p e r i m e n t a l  data.  79  Seeger  o r i g i n a l l y p o s t u l a t e d . t h a t t h e a p p l i e d s t r e s s c o u l d be  c o n s i d e r e d as t h e sum o f two components such t h a t  r  a  where  "X  =  r  G  +  r*  .................(D  i s a s s o c i a t e d w i t h s h o r t range o b s t a c l e s which can be  -  79  -  overcome w i t h the a i d o f t h e r m a l energy ( f o r e s t d i s l o c a t i o n s ) . . T h e r e f o r e i t m a y b e r e f e r r e d t o as the t h e r m a l component o f the a p p l i e d s t r e s s . and  i s the a t h e r m a l component o f s t r e s s w h i c h a r i s e s due -to l o n g range e l a s t i c i n t e r a c t i o n s such as those between p a r a l l e l g l i d e d i s l o c a t i o n s a t d i s t a n c e s l a r g e compared w i t h "b". Such o b s t a c l e s cannot be overcome w i t h the a i d of t h e r m a l energy.  .The temperature  dependence o f y i e l d as p o s t u l a t e d by Seeger when  the mechanism o f y i e l d does not change w i t h temperature, The i n t e r n a l s t r e s s T shear modulus. The  n  v a r i e s w i t h temperature  increase i n T  a  i s shown i n F i g . 51  o n l y through a change i n the  below the c r i t i c a l temperature  r e f l e c t s the  decrease i n the amount o f t h e r m a l energy a v a i l a b l e and s u b s e q u e n t l y the increased e f f e c t i v e stress necessary f o r activation.-  Yield stress  7*  1 k  c  Temperature  F i g . 51  The temperature  dependence of y i e l d i n terms o f the components ( a f t e r S e e g e r ) .  stress  Much o f the work i n d e f o r m a t i o n i n r e c e n t y e a r s has been w i t h o b t a i n i n g a b e t t e r knowledge o f the n a t u r e and o r i g i n o f the components i n v a r i o u s systems.  concerned  stress  -.80 Basinski  17  postulated  c e r t a i n f . c . c . metals,, the  two  t h a t because of., C o t t r e l l - S t o k e s  components ^  and  -  obeyance i n  J*~ a r i s e from a  single 66  source ( the  i n t e r a c t i o n o f g l i d e and  forest dislocations  s i n c e m o d i f i e d h i s o r i g i n a l d e f i n i t i o n of 7G  to include  ). Seeger  a s h o r t range  i n t e r a c t i o n term . However he m a i n t a i n s t h a t a major p o r t i o n stress of single c r y s t a l s i s s t i l l derived between p a r a l l e l d i s l o c a t i o n s  from longe range  o f the  elastic  flow  interactions  ).  (Fig.52  Shear s t r a i n  F i g . 52  has  J  The components of the t o t a l flow s t r e s s i n . f . c . c . c r y s t a l s . 3g = c o n t r i b u t i o n o f the l o n g range i n t e r n a l s t r e s s Tc/^= e l a s t i c i n t e r a c t i o n between g l i d e and f o r e s t d i s l o c a t i o n s T * = t h e r m a l component of the s t r e s s ( e f f e c t i v e s t r e s s ) ; l,  In the  only consistent  a i d of r a t e t h e o r y s e p a r a t e d the  s t u d y t o date, M i t r a and two 5)  aluminum and stresses  the  components of the a t h e r m a l s t r e s s i n BO  copper s i n g l e c r y s t a l s . .It would appear, t h a t  as proposed by B a s i n s k i  Dorn have w i t h  account .for,a 'greater ;  short  range e l a s t i c  proportion  of  the  - 81 -  t o t a l f l o w s t r e s s than has been i n d i c a t e d by Seeger.  In 195^ C o t t r e l l and Stokes u s i n g aluminum s i n g l e c r y s t a l s found t h a t t h e r e v e r s i b l e change i n f l o w s t r e s s t e s t was d i r e c t l y p r o p o r t i o n a l AO"* 7  w  a s n o t o n l y independent  ( A T )  d u r i n g a. temperature  change  t o t h e t o t a l flow s t r e s s and t h a t t h e v a l u e o f o f s t r a i n b u t a l s o o f t h e p r i o r t h e r m a l and  mechanical h i s t o r y . C o t t r e l l - S t o k e s  obeyance occurs t h e r e f o r e when w i t h  increasing s t r a i n AT  =  *  QTJ ~ OTI.  =  %,  1 -  3T>  =  a constant  (2)  Tfr,  C o t t r e l l a l s o r e c o g n i z e d t h a t when two i d e n t i c a l specimens a r e deformed  t o t h e same s t r a i n a t d i f f e r e n t temperatures, t h e t o t a l f l o w s t r e s s  difference  i s made up o f a r e v e r s i b l e component due t o t h e d i f f e r e n t amount  of t h e r m a l energy a v a i l a b l e and an i r r e v e r s i b l e component due t o t h e d i f f e r e n t dislocation configurations  produced a t t h e d i f f e r e n t temperatures  ( F i g . 53  ).  Strain  Components o f t h e d i f f e r e n c e i n f l o w s t r e s s when two i d e n t i c a l specimens a r e deformed a t d i f f e r e n t t e m p e r a t u r e s .  - 82 C o t t r e l l - S t o k e s obeyance has  69  been i n t e r p r e t e d .  type o f d i s l o c a t i o n c o n f i g u r a t i o n must remain constant w i t h o n l y the a constant  s c a l e changing. Obeyance has  t o mean t h a t  during  and  *J  during  a constant  temperature by p e r i o d i c a l l y v a r y i n g the  such .tests might be more a c c u r a t e difficulties stopping  to y i e l d point .The  o r i g i n of 0"  the t h e r m a l component may  been used i n an attempt t o e s t a b l i s h the systems.- S i n c e 7 *  i s the  s t r a i n r a t e and  the d i f f i c u l t y  that  the  in defining  of flow  effects•).  p r o c e s s e s a l l of which can be t h e r m a l l y  of the  some of  a s s o c i a t e d w i t h temperature change t e s t s ( the n e c e s s i t y  the t e s t t o change temperature and  s t r e s s due  carried., out  s t r a i n r a t e and  i n that they eliminate  that  deformation.  B a s i n s k i showed t h a t a C o t t r e l l - S t o k e s t e s t c o u l d be at  the  deformation  a l s o been shown t o r e q u i r e  p r o p o r t i o n a l i t y e x i s t s between T/Q T8  -  be  due  a c t i v a t e d . Therefore  t o a number of rate theory  rate c o n t r o l l i n g process f o r  has  various  s t r e s s associated with thermal a c t i v a t i o n , studies  temperature dependence o f  can be  c a r r i e d out  in  o r d e r t o determine such r a t e parameters as a c t i v a t i o n energy, a c t i v a t i o n volume and  a c t i v a t i o n d i s t a n c e . By  theoretically predicted,  comparing e x p e r i m e n t a l v a l u e s w i t h those  i t i s sometimespossible t o postulate  c o n t r o l l i n g mechanism. Mechanisms t h a t can be t h e r m a l l y f o r e r a t e c o n t r o l l i n g i n c l u d e the •1)  cross  the  rate  a c t i v a t e d and  following:  slip  2)  forest intersection  3)  the non  conservative  motion o f jogs  k)  climb  5)  overcoming of the. E e i e r l s s t r e s s  i n screw, d i s l o c a t i o n s  there-  -  I f a s i n g l e a c t i v a t i o n process i s rate c e r t a i n temperature may  be e x p r e s s e d  range  83  c o n t r o l l i n g over a  then the s t r a i n r a t e a s s o c i a t e d  with deformation  as •  w  -AG/kT  6 = uc,e  (3)  -AG/kT j[ = NAb V e  (4)  where N = number o f s i t e s p e r u n i t volume where a c t i v a t i o n o c c u r s A = a r e a swept out p e r s u c c e s s f u l  a c t i v a t i o n event  b = Burgers v e c t o r V = f r e q u e n c y w i t h which b a r r i e r i s attempted G = Gibbs f r e e energy The  of a c t i v a t i o n  development o f e q u a t i o n 5 t o g i v e u s e f u l  expressions i s outlined  i n Appendix I..The r e l a t i o n s h i p s  t h e p r e s e n t work i n c l u d e  . A c t i v a t i o n volume  v  the  = bdl  I£  *-2kT  - k^  (5)  j/L  In  / A In 6 / g  l AH =  t o be used i n  following:  = kT  A c t i v a t i o n enthalpy  mathematical  ! t/j  a* 7  (6)  (7)  \  0  ACT* / (j I n  \  0  T  \  I  c)"J*  h  I  6T  \  (8)  /ty.o  - 8k Thermal component of the  a c t i v a t i o n energy-  AG  AH - T A s  =  A  =  H  (10)  -4  - L *  +  .Tv ..(11).  Apparent a c t i v a t i o n energy  =  AG  =  AG  +  (12)  v  where d =  activation  1  d i s l o c a t i o n length involved  =  distance i n thermal a c t i v a t i o n  •  J( =  tensile strain  T  shear  =  rate  stress  CT =  . t e n s i l e .. s t r e s s  u  ..shear modulus  I t has  w i l l not  rate  <5 =  AS  approximated by  shear s t r a i n  = =  been assumed t h a t  taking  a f f e c t the  e n t r o p y change d u r i n g t h e r m a l  the  o n e - h a l f of the  calculated  shear s t r e s s  activation  in polycrystals  t e n s i l e s t r e s s . .Such an  values of  AH,  AG,  • or  can  :  AG  be  approximation since  the  O  c o n v e r s i o n must be a f f e c t the  made i n b o t h numerator and  v a l u e s of the  denominator. I t w i l l however  a c t i v a t i o n volume i n t h a t  denominator of e x p r e s s i o n .6  . T h i s w i l l be  ^f*  appears in. the  d i s c u s s e d i n more d e t a i l l a t e r .  -85 2.2,  -  .TEMPERATURE CHANGS TESTS  Temperature change t e s t s were undertaken n o t o n l y t o check t h e v a l i d i t y o f t h e C o t t r e l l - S t o k e s law but a l s o , t o o b t a i n a better, knowledge o f the e f f e c t o f p r e s t r a i n a t elevated, temperatures on t h e subsequent d e f ormation b e h a v i o u r a t low.temperatures.  2.2.1.  Procedure  In cadmium -196°C was used as a base temperature w h i l e . t h e upper c y c l i n g temperature v a r i e d from - l 4 0 ° C t o -30°C . - S t r a i n increments between 1.5$ and .2.O/0 were used a t each temperature. A f t e r d e f o r m a t i o n a t t h e upper temperature, t h e specimens were c o o l e d t o -196°C as r a p i d l y as p o s s i b l e i n o r d e r t o minimize r e c o v e r y e f f e c t s . T h i s c o o l i n g c o u l d u s u a l l y be accomp l i s h e d w i t h i n 30 seconds. D u r i n g t h e temperature change o p e r a t i o n , the l o a d was m a i n t a i n e d a t about 20% o f t h e f l o w s t r e s s . S i n c e s t a t i c r e c o v e r y i s n e g l i g i b l e a t -196°C, t h e specimens were h e l d f o r 15 minutes p r i o r t o resumption o f t e s t i n g i n o r d e r t o e q u i l i b r a t e t h e t e s t i n g d e v i c e .  A.O" v a l u e s  c o u l d n o t be o b t a i n e d d u r i n g an i n c r e a s e i n temperature due t o r e c o v e r y d u r i n g the time n e c e s s a r y . f o r temperature  equilibration.  Because o f the l i m i t e d d u c t i l i t y o f z i n c , t h e C o t t r e l l - S t o k e s law f o r temperature change t e s t s c o u l d not be i n v e s t i g a t e d . T h e r e f o r e t e s t s were l i m i t e d t o p r e s t r a i n i n g 20u z i n c t o a g i v e n v a l u e o f s t r a i n a t some e l e v a t e d temperature between +20°C and -95°C and s u b s e q u e n t l y deforming t h e specimen t o f r a c t u r e a t -120°C.  2.2.2.  C o t t r e l l - S t o k e s Tests  F o r t h e v a r i o u s temperature change t e s t s on 25u and kOOp cadmium, the  Ac"* v a l u e s o b t a i n e d were c o r r e c t e d t o take i n t o account the change i n  - 86 ACT  due t o the temperature dependence o f the shear modulus Shear modulus k  v a l u e s were o b t a i n e d from the work of K o s t e r  The A,cr  57  Ao~  v a l u e s were t h e n n o r m a l i z e d t o  i n order, t o g i v e  A T  v a l u e s o f the r e v e r s i b l e change i n flow s t r e s s p e r °K..When.these are exami n e d .in terms of the flow s t r e s s a t the s t a n d a r d temperature o f -196°C, C o t t r e l l - S t o k e s p l o t s as shown i n F i g . 5^4 I t i s observed  obtained.  a r e  from F i g . 54 t h a t the C o t t r e l l - S t o k e s law i s not  s t r i c t l y obeyed f o r temperature change t e s t s . .  Ao~*  cr s l i g h t l y d u r i n g . t h e e a r l y stages of d e f o r m a t i o n v a l u e s of  77  and  values  decrease  A^T i n c r e a s e a g a i n a t higher-  Oyy. T h i s i s t r u e f o r b o t h g r a i n s i z e s . The  dotted l i n e s  indicate  i d e a l C o t t r e l l - S t o k e s , obeyance. From F i g . 54 i t i s a l s o noted t h a t the e x p e r i m e n t a l v a l u e A_o~*  A  at a g i v e n v a l u e o f flow s t r e s s at -196°C i s independent-  of  of the  T  upper c y c l i n g temperature. v a l u e s of  A "* 0  CT  77  The  a  A  r  e  This i s true f o r both g r a i n sizes although  the  c o n s i d e r a b l y lower f o r ,40Qu m a t e r i a l .  T  r e s u l t s o f the temperature change -tests are t h e r e f o r e v e r y  s i m i l a r t o those r e p o r t e d by B u l l e n e t a l f o r p o l y c r y s t a l l i n e copper deformed between 173°K and 373°K and  subsequently, deformed a t Y ^ K ^  They noted a d e v i a t i o n f r o m . i d e a l C o t t r e l l . - S t o k e s b e h a v i o u r of  5  8  '  5  9  '  6  0  ^  at high values  Ao~* . They a l s o found v a l u e s o> A T which a t a g i v e n v a l u e of s t r e s s a t 77°K were independent of the  s t r e s s which gave i n c r e a s e d v a l u e s of  7  of  ACT AT  upper c y c l i n g temperature between 173 °K and 37-5 °K. They t h e r e f o r e t h a t the same sequence o f o b s t a c l e " f o r m a t i o n occurs d u r i n g  concluded  deformation  independent of the temperature but t h a t the r a t e of o b s t a c l e p r o d u c t i o n w i t h i n c r e a s i n g s t r a i n may  be temperature dependent due  to, the removal of o b s t a c l e s  by some p r o c e s s o f dynamic r e c o v e r y . They made no attempt t o i d e n t i f y  the  Symbol  O • D A A £  Temp, c y c l e °C  (-140..-196) (-120..-196) (-95-..-196) (-60. ..-196) (-30...-196)  o /•  -k -1 = k.O x 10 s e c . 2514 cadmium  Broken l i n e s i n d i c a t e C o t t r e l l - S t o k e s obeyance.  400^1 cadmium  1.0  2.0 .True s t r e s s a t -196°C  2i  k  3.0  p . s . i . x 10  The r e l a t i o n s h i p between t h e change i n f l o w s t r e s s p e r °K and t h e r e s u l t a n t s t r e s s a t -196°C o b t a i n e d d u r i n g the temperature c y c l i n g of. cadmium. 1  00 ^1  '  "obstacles" but postulated  thaf'recovery  "  "  8 8  -  -  was a s s o c i a t e d w i t h the a n n i h i l a t i o n  and.rearrangement o f d i s l o c a t i o n s by the a c t i o n o f p o i n t  defects.  A o~* GT  , only  AT  a r a t h e r narrow range o f g r a i n s i z e s was used. I t a l s o appeared t h a t  there  was no e f f e c t o f p r e f e r r e d o r i e n t a t i o n . 2,2.3.  The M e c h a n i c a l E q u a t i o n o f S t a t e  I f t h e sequence o f events o c c u r r i n g d u r i n g  d e f o r m a t i o n i s the same  at any two temperatures, then one would expect t h a t t h e i r r e v e r s i b l e ent  o f the f l o w  erence i n flow  compon-  s t r e s s d i f f e r e n c e as shown i n F i g . 53- would be z e r o . The d i f f stress at a given  s t r a i n a t two d i f f e r e n t temperatures i s  t h e r e f o r e due o n l y t o a d i f f e r e n c e i n o~ .. Under such c o n d i t i o n s  i t i s ex-  p e c t e d t h a t a m e c h a n i c a l equation- o f s t a t e might be v a l i d . The f l o w  stress  can t h e n be e x p r e s s e d as a unique f u n c t i o n o f t h e i n s t a n t a n e o u s v a l u e  o f the  s t r a i n , s t r a i n r a t e and temperature and i s independent o f t h e p r i o r s t r a i n 81  history  . Therefore  cr =  a(6,6 ) T  B u l l e n i n f a c t d i d observe t h a t d u r i n g temperature c y c l i n g below a p p r o x i m a t e l y 300°K t h e r e was always an 'Incubation irreversible  component o f t h e flow  zero. H i s r e s u l t s f o r various incubation  s t r a i n " d u r i n g which t h e  s t r e s s d i f f e r e n c e as shown i n F i g . 53 was  temperature c y c l e s a r e shown i n Fig.55- The  s t r a i n s t a k e n from h i s r e s u l t s a r e shown i n T a b l e  observed t h a t t h e magnitude o f t h e i n c u b a t i o n  7  s t r a i n increased  . Iti s as t h e upper "  c y c l i n g temperature d e c r e a s e d . I n t h i s r e g i o n o f s t r a i n t h e r e f o r e , t h e d i s l o c a t i o n c o n f i g u r a t i o n at a given value  o f s t r a i n i s independent o f temper-  a t u r e which l e a d s t o temperature i n s e n s i t i v e work h a r d e n i n g and the obeyance  - 89 -  PRE-STRAIN  F i g . 55  20 1%  30  The e f f e c t o f e l e v a t e d temperature p r e s t r a i n i n g on the s t r e s s s t r a i n curve o f p o l y c r y s t a l l i n e copper a t 7 7 ° K ( a f t e r B u l l e n ) . 5 8  TABLE  7  I n c u b a t i o n s t r a i n required- i n p o l y c r y s t a l l i n e - copper p r i o r t o the appearance o f an i r r e v e r s i b l e component o f the d i f f e r e n c e i n flow s t r e s s  Lower c y c l i n g temperature  Upper c y c l i n g temperature  Incubation strain  77°K  173°K  9$  77°K  233 °K  5%  77°K  293 °K  It  - 90 of"the  m e c h a n i c a l e q u a t i o n of s t a t e . The  t o temperature and a t u r e are  the  increase  i n s e n s i t i v i t y of the h a r d e n i n g  in,..incubation  rate  s t r a i n witbJdecre.asingi,temper-  i n q u a l i t a t i v e agreement w i t h jthe' r e s u l t s , of R u s s e l l a l t h o u g h  the  temperature range of i n s e n s i t i v i t y as found by R u s s e l l extended t o somewhat h i g h e r temperatures than those found by  2.2.J.  a  )  Bullen.  Cadmium  Fig.  56  i l l u s t r a t e s the  cadmium i s deformed a l t e r n a t e l y at  - l 4 0 ° C and  normal s t r e s s - s t r a i n curves a t the  two  i s seen t h a t  i n the  o b t a i n e d on r e l o a d i n g  As the  at  can be  difference  -196°C are due  erature  was  i n o~  t o t a l flow s t r e s s  . The  t o an u n l o a d i n g e f f e c t as  d e f o r m a t i o n proceeded i n t o the  region  c o u l d not  points described  of dynamic r e c o v e r y ,  account f o r t h e ' t o t a l  s t r e s s a t a g i v e n v a l u e o f s t r a i n . As  increased  slight yield  diff-  ignored.  r e v e r s i b l e flow stress d i f f e r e n c e  erence i n the  n  temperatures are a l s o i n d i c a t e d . I t  temperatures involved,, the  e n t i r e l y t o the  i n Appendix I I and  -196°C. F o r comparison the  e a r l y r e g i o n s of s t r a i n where dynamic r e c o v e r y does not  occur at e i t h e r of the erence i s due  25u  flow s t r e s s c y c l i n g o b t a i n e d when  diff-  the upper c y c l i n g temp-  above -120°C, i r r e v e r s i b l e components of the  flow  s t r e s s d i f f e r e n c e were e v i d e n t immediately a f t e r y i e l d i n g .  2.2.3  .  "b)  Zinc  r e s u l t s o f the p r e s t r a i n t e s t s on 20u  The F i g s . 57  and 58.  Fig. %  a t -95°C , was  shown i n  i l l u s t r a t e s the e f f e c t of p r e s t r a i n i n g a t  f i v e d i f f e r e n t s t r a i n s on the i s observed t h a t  z i n c are  subsequent d e f o r m a t i o n b e h a v i o u r a t i:120°C. I t  i n a l l cases the  flow s t r e s s a t  -120°C a f t e r p r e s t r a i n i n g  e x a c t l y t h a t found, on s t r a i n i n g e x c l u s i v e l y a t  p a r t i c u l a r value of s t r a i n .  -95°C t o  -120°C t o  that  - 91 -  F i g . 56  Temperature c y c l i n g of 25)J cadmium between -lkO°C  and -196°C.  - 9 3  I  .5  1_ 1.0  '.  I 1.5  I 2.0  L _  2.5  $ strain  F i g . 58  The e f f e c t o f p r e s t r a i n i n g a t -70°C on.the subsequent d e f o r m a t i o n b e h a v i o u r a t -120°C o f 2 0 L l z i n c .  -  -  k  9  The  r e s u l t s are t h e r e f o r e s i m i l a r t o cadmium i n . t h a t the  s t r e s s a t a p a r t i c u l a r v a l u e o f s t r a i n a t temperatures  below.T^. =  flow  .26  a r i s e s due t o a common d i s l o c a t i o n c o n f i g u r a t i o n and the change i n s t r e s s w i t h temperature cr*~  merely  r e f l e c t s a change i n the t h e r m a l component of s t r e s s  . However i n t h i s temperature  irreversible effect  range f o r z i n c , f r a c t u r e occurs b e f o r e an  i s o b t a i n e d w i t h i n c r e a s i n g s t r a i n as i s observed  with  cadmium.  =  . P r e s t r a i n i n g above  .26 as shown i n F i g . §>S, produced  an  i r r e v e r s i b l e component of the flow s t r e s s d i f f e r e n c e a t a l l v a l u e s of s t r a i n .  I t would t h e r e f o r e appear t h a t i n the r e g i o n s of s t r a i n below T^ =  .26 where l i n e a r h a r d e n i n g  occurs i n b o t h z i n c and  cadmium,,that"equi-  v a l e n t s t a t e s " are o b t a i n e d a t e q u a l s t r a i n s . . In t h i s r e g i o n t h e r e f o r e i t i s probable t h a t a mechanical mechanical  e q u a t i o n of s t a t e c o u l d be f o r m u l a t e d . A  e q u a t i o n of s t a t e f o r metals, i s r a r e l y v a l i d except  Stage I and Stage I I h a r d e n i n g  during  of f . c . c . s i n g l e c r y s t a l s a t low  temperatures.  Once p a r a b o l i c h a r d e n i n g a s s o c i a t e d w i t h dynamic r e c o v e r y b e g i n s , the mecha n i c a l e q u a t i o n o f s t a t e becomes  invalid.  •5  M i t r a and Dorn ;  have s t a t e d t h a t e q u i v a l e n t s t a t e s are  i n p o l y c r y s t a l s o n l y when O g and  "1" (the average  d i s l o c a t i o n length being  t h e r m a l l y a c t i v a t e d ) are c o n s t a n t . S i n c e the r e s u l t s below :T  =  .26  t h a t the flow s t r e s s d i f f e r e n c e i s j u s t due t o a d i f f e r e n c e i n cr* O~Q  Hp  must be  c o n s t a n t independent  obtained  of temperature  indicate , then  a t a g i v e n v a l u e of  s t r a i n . T e s t s were not comprehensive enough t o e s t a b l i s h the constancy  2.2.4.  E q u i v a l e n t S t a t e s above T =.26 H  I t may  be as suggested  by B u l l e n t h a t i n a g i v e n system the  o f "1'  - 95 sequence o f events occuringo. d u r i n g  d e f o r m a t i o n does not change w i t h temper-  a t u r e b u t the r a t e a t which the sequence proceeds, might be temperature dependent .. Under such a d e f i n i t i o n , t h e r e s u l t s . o f t h e p r e v i o u s s e c t i o n would be  i n t e r p r e t e d i n terms o f a c o n s t a n t r a t e o f obstacle, p r o d u c t i o n  below  T  = .26 i n t h e temperature i n s e n s i t i v e h a r d e n i n g r e g i o n . However above  T^. = .2.6 where dynamic r e c o v e r y occurs a t a l l v a l u e s o f s t r a i n , i t i s n e c e s s a r y t o equate s t a t e s a t d i f f e r e n t v a l u e s o f s t r a i n a t any two temperaturesi n order t o . s a t i s f y B u l l e n  s postulate.  This.condition  i s illustrated i n  F i g . 5.9...  Stress  Strain  F i g . 59  The  Equivalent  states at d i f f e r e n t strains.  i r r e v e r s i b l e d i f f e r e n c e i n f l o w s t r e s s t h e n develops because  of a d i f f e r e n t r a t e o f o b s t a c l e  production  s t a t e o f t h e c r y s t a l a t "E" deformed a t T a t "A" when deformed a t Tj_. ,CE r e p r e s e n t s  a t d i f f e r e n t temperatures.•The 2  i s t h e same as.the s t a t e  obtained  the d i f f e r e n c e i n t h e t h e r m a l com-;  ponent o f s t r e s s and CD can be r e l a t e d d i r e c t l y t o AB. The e q u i v a l e n t  strain  - 96 values  at T  x  and T  2  a r e then g i v e n by <g  and  (5m  respectively.  U s i n g t h i s above method o f a n a l y s i s , t h e amount o f p r e s t r a i n a t v a r i o u s e l e v a t e d temperatures was r e l a t e d t o an e q u i v a l e n t v a l u e o f s t r a i n a t -120°C i n 20u z i n c . The r e s u l t s a r e shown i n F i g . 61.. W i t h i n c r e a s i n g temperature o f prestrain,an,:.increasing amount o f s t r a i n i s r e q u i r e d t o g i v e a c e r t a i n e q u i v a l e n t s t r a i n a t -120°C. .When t h e s e c t i o n s CD and AB were superimposed, t h e h a r d e n i n g  r a t e s i n a l l cases were t h e same. T i e t z and Dorn  u s i n g aluminum found t h a t t h e hardening  r a t e CD was s l i g h t l y greater, t h a n AB  83  On t h e o t h e r hand S y l w e s t r o w i c z  u s i n g p o l y c r y s t a l l i n e copper and aluminum  was a b l e t o q u a l i t a t i v e l y show, t h a t t h e A c r v a l u e  ( A A ) obtained- on d e c r e a s -  i n g t h e t e s t temperature from 300°K t o 77°K was i d e n t i c a l t o t h e her v a l u e (BB) o b t a i n e d on i n c r e a s i n g t h e temperature a t a s t r e s s c o r r e s p o n d i n g t o A  ( F i g . 60). T h i s suggests e q u i v a l e n c e  ol 0  o f s t a t e s a t A and B.  1  I  I  !  5  10  15  20  25%  STRAIN  —Stress -strain curves of copper specimens, strained at different temperatures. Curve No. 1-at 300°K; Curve No. 3 — at 76° K; Curve RN — at 300° K after pre-strainingat 76* K; Curve NR —at 76° K after presenting at 300° K. F i g . 60  R e v e r s i b l e temperature change t e s t s a t e q u i v a l e n t s t a t e s i n p o l y c r y s t a l l i n e copper. OO  ( a f t e r Sylwestrowicz  \  ).  F i g . 6l  The  c o r r e l a t i o n o f s t r a i n s , at d i f f e r e n t i n 2Cu z i n c .  temperatures  Although  such an a n a l y s i s might appear unwarranted a t t h i s  p o i n t because o f t h e l a c k o f d e t a i l e d e x p e r i m e n t a l d a t a , i t i s thought  that  t h e r e i s some m e r i t i n t h e i d e a o f e q u i v a l e n t s t a t e s a t v a r i o u s s t r a i n s a t d i f f e r e n t temperatures  i n z i n c and cadmium above T .= .26.-This i s n o t t o H  be c o n s t r u e d as a p p l y i n g t o a l l metal systems where dynamic r e c o v e r y can a f f e c t t h e nature o f t h e hardening.-Much would depend on t h e e x a c t n a t u r e of the r e c o v e r y p r o c e s s . I f i t i n v o l v e d a p r o c e s s which caused a d i s t i n c t i v e change i n t h e n a t u r e and c h a r a c t e r o f  o^  then i t i s d o u b t f u l i f such an  a n a l y s i s can be made. However i f r e c o v e r y i s l i n k e d t o t h e o b s e r v a t i o n s o f 39 P r i c e c o n c e r n i n g t h e rearrangement and g r a d u a l disappearance  o f d e b r i s then  the above i d e a s may have some m e r i t . P r i c e observed t h a t b a s a l d i s l o c a t i o n s and d e b r i s i n t e r a c t  s t r o n g l y . Because o f t h e rearrangement and removal  of d e b r i s i n a temperature  region o f recovery, l a r g e r values of s t r a i n are  t h e r e f o r e r e q u i r e d t o a r r i v e a t an e q u i v a l e n t o b s t a c l e density- t o t h a t produced  a t a g i v e n v a l u e o f s t r a i n when r e c o v e r y does n o t occur. S i n c e t h e  r a t e o f rearrangement o f d e b r i s as observed by P r i c e i n c r e a s e d w i t h temperature,  i t i s expected t h a t t h e " e q u i v a l e n t s t r a i n " as observed  will, increase w i t h increasing 2.3.  increasing in Fig.6l  temperature.  -STRAIN PATE CHANGE TESTS  The a c c u r a t e d e t e r m i n a t i o n o f the r e v e r s i b l e change i n f l o w s t r e s s a c c o m p a n y i n g a change i n s t r a i n r a t e i s o f prime importance  since the  e x p e r i m e n t a l v a l u e o f /\cr a s : used not o n l y i n d e t e r m i n i n g the, v a l i d i t y o f the  C o t t r e l l - S t o k e s law but a l s o t o determine  the experimental values of  a c t i v a t i o n v o l u m e and a c t i v a t i o n energy.-A d i s c u s s i o n o f t h e d i f f i c u l t i e s e n c o u n t e r e d i n c o r r e c t l y determining  Acr* i s g i v e n i n Appendix I I I .  2.3.1.  - 99 -  Procedure  7 y  Acr*"was o b t a i n e d d u r i n g an  F o r the purpose o f t h i s work,  i n c r e a s e i n s t r a i n r a t e . F o r p o l y c r y s t a l l i n e z i n c and cadmium t h e s t r a i n  -5 r a t e was c y c l e d between t o a crosshead  speed  4.0 x 10  change from  -h and  4.0 x 10"  -1 sec.  • -3 and 3-8 x 10 sec. n  2.3.2.  speeds o f .02 and .2 inches p e r x  10  1  Single crystals (  corresponding  shear s t r a i n r a t e s o f a p p r o x i m a t e l y 3-8  C o t t r e l l - S t o k e s Behaviour  different grain sizes  sec  .002 t o .02 i n c h e s p e r minute. Cadmium  s i n g l e c r y s t a l s were c y c l e d u s i n g crosshead minute c o r r e s p o n d i n g t o i n i t i a l  -1  i n Cadmium a t -196°C.  (#o= 36°, Ao  38°) and p o l y c r y s t a l s o f t h r e e  =  25u., 400u 1250u ) were t e s t e d f o r C o t t r e l l - S t o k e s  b e h a v i o u r a t -196°C.  2.3.2.  a) S i n g l e C r y s t a l s  Three s i n g l e c r y s t a l s o f i d e n t i c a l o r i e n t a t i o n were t e s t e d and a l l showed s i m i l a r b e h a v i o u r d u r i n g b a s a l g l i d e i n Stage I, AX  t o t h a t shown i n F i g . 62-. ..It i s seen t h a t  t h e r e i s a g r a d u a l decrease  i n the value of  w i t h i n c r e a s i n g s t r a i n . However i n Stage I I the- C o t t r e l l - S t o k e s law  y  6 i  i s obeyed c o n f i r m i n g t h e r e s u l t s o f Davis  . W i t h the b e g i n n i n g o f Stage I I I  i t would appear t h a t t h e r e i s a s l i g h t but c o n s i s t e n t i n c r e a s e i n Although  i t may be argued t h a t t h i s apparent  o f the e x p e r i m e n t a l e r r o r i n d e t e r m i n i n g  AT  AT  i n c r e a s e c o u l d j u s t be a r e s u l t > i t w i l l be shown i n t h e  ensuing r e s u l t s f o r p o l y c r y s t a l s t h a t dynamic r e c o v e r y f o l l o w i n g l i n e a r hardening  •  i s associated with c o n t i n u a l l y increasing values of  AQ~  o~  016  Ql4 r-  \ O O \  b o  012  o ?-° Q  010  Stage I I  Stage I  008 Temperature •= -196°C Cadmium s i n g l e c r y s t a l Ko= 36°  006  Ao= 38°  _L  400  800 R e s o l v e d shear s t r e s s  Fig.62  1600  1200 T  2000  gm/mm.  The v a r i a t i o n o f the C o t t r e l l - S t o k e s parameter d u r i n g the deformation of a cadmium s i n g l e c r y s t a l a t -196°C.  H  o o  - 101 2.3.2.  b)  Polycrystals  The t h r e e stage b e h a v i o u r d u r i n g the d e f o r m a t i o n o f p o l y c r y s t a l s r e g i o n o f s t r a i n i n the f i r s t  f o r single crystals i s also  observed  ( F i g . 63). I n a l l cases t h e r e i s a  few p e r c e n t o f d e f o r m a t i o n d u r i n g which  A o~  cr d e c r e a s e s . The e x t e n t o f t h i s i n i t i a l r e g i o n i n c r e a s e s w i t h i n c r e a s i n g s i z e and a t 1250n corresponds s l o p e s observed  grain  r a t h e r w e l l t o the change i n work hardening  i n F i g . . 4 9 . T h i s i n i t i a l r e g i o n i n p o l y c r y s t a l s may t h e r e f o r e  be r e l a t e d i n some manner t o the b a s a l g l i d e r e g i o n o f s i n g l e c r y s t a l deformation. From F i g . 63 i t ' i s seen t h a t the C o t t r e l l - S t o k e s law i s obeyed in  i n t e r m e d i a t e s t r a i n r e g i o n s s i m i l a r - t o t h a t observed  f o r Stage I I of  s i n g l e c r y s t a l s . T h i s r e g i o n o f obeyance ends w i t h a g r a d u a l i n c r e a s e i n the v a l u e of  A Q~ cr  • The s t r e s s and s t r a i n v a l u e s a t which t h i s occurs f o r each  g r a i n s i z e a r e summarized i n Table b e g i n n i n g o f p a r a b o l i c hardening  8  . They correspond v e r y w e l l t o t h e  observed  in Fig..49.  I t would t h e r e f o r e  a p p e a r . t h a t the i n i t i a t i o n o f dynamic r e c o v e r y a t -196°C i n s i n g l e  crystals  and p o l y c r y s t a l s i s a s s o c i a t e d w i t h i n c r e a s i n g v a l u e s o f the C o t t r e l l - S t o k e s ratio. . TABLE 8 G r a i n s i z e dependence o f C o t t r e l l - s t o k e s b e h a v i o u r (cadmium a t -I96 Strain at Strain at Stress at Constant Grain Size beginning of beginning of beginning of Cottrell-Stokes C .S.. obeyance r e c o v e r y ratio recovery  25u  2.5$  7$  19,000  .0195  p. s . i .  400u  4.5$  13$  14,500  .0180  125 Qu  10$  20$  11,000  •0155  Single crystal  130$  shear  100$ t e n s i l e l 8 0 $ shear  5,500 p . s . i . 1,100 gm/mm. (shear)  .0115  .023  O n  O-ff  O  O  O  .021  .019 O . . . 25y Cd  ACT  A . . • kOOu Cd .017  Q . .. 1250p Cd  ,015  Numbers a t arrows i n d i c a t e % s t r a i n £, = 4.0 x 10 sec._^ C = 4.0 x 10" s e c . z  .013  Stage I I s i n g l e c r y s t a l (from f i g . 62  .011 -  L 1.0 F i g . 63  The g r a i n s i z e dependence o f  2.0  jj_  True s t r e s s p . s . i . x 10 ACT a t -196°C.(cadmium)  3-0  4.0 O  ro  2.3.3.  The E f f e c t  o f Temperature on C o t t r e l l - S t o k e s Behaviour  "  _  The r e s u l t s of s t r a i n r a t e changes on p o l y c r y s t a l s above -196°C shown i n F i g s . 64 and 65 f o r 25u  are  l e s s o f the temperature initial  and 400u cadmium r e s p e c t i v e l y .  Regard-  or g r a i n s i z e t h e r e i s a decrease i n  ACT i n the cr r e g i o n s o f d e f o r m a t i o n p r e v i o u s l y r e l a t e d t o Stage I d e f o r m a t i o n o f  s i n g l e c r y s t a l s . F i g . 66 shows t h a t  ACT  decreases during'Stage I  deform-  cr  a t i o n o f a s i n g l e c r y s t a l deformed a t -50°C where r e c o v e r y i s known t o a f f e c t h a r d e n i n g . . T h e r e f o r e whether dynamic r e c o v e r y occurs or n o t , the C o t t r e l l Stokes r a t i o decreases d u r i n g Stage I d e f o r m a t i o n . As the temperature  i n c r e a s e s above -196°C,.there i s a d e c r e a s e '  i n the. amount o f s t r a i n showing C o t t r e l l - S t o k e s , obeyance u n t i l above -120°C (T„  =  .26), t h i s r e g i o n d i s a p p e a r s c o m p l e t e l y . Above T  = .26 f o r cadmium H  r e g a r d l e s s o f the g r a i n s i z e , the v a l u e s o f  ACT  i n c r e a s e Immediately  cr a f t e r the i n i t i a l and temperature  r e g i o n a s s o c i a t e d w i t h Stage I . T h e r e f o r e the s t r a i n  i n s e n s i t i v e h a r d e n i n g regions.below Tg = ,26 d e s c r i b e d i n :  P a r t I would seem t o be a s s o c i a t e d w i t h C o t t r e l l - S t o k e s law  obeyance.  S e v e r a l s t r a i n r a t e change t e s t s were performed•on at  rate  temperatures between -70°C and  20u  zinc  -120°C. The r e l a t i o n s h i p s shorn i n F i g •  i n d i c a t e t h a t the r e s u l t s are q u a l i t a t i v e l y the same as those f o r cadmium. However a t -95°C  a n  d . -120°C  general increase i n At  -70°C t h e r e was  A cr  cr a slight  (below Tg = .26)  f r a c t u r e occurs b e f o r e any  i n d i c a t i n g the absence increase i n  d u r i n g dynamic r e c o v e r y above Tv, =  o f dynamic r e c o v e r y .  Acr s i m i l a r to that cr .26 i n cadmium.  observed  67  £,= 4.0 x 10" s e c .  -95°c  .05  5  £,= 4.0 x 10  1  sec.  Numbers a t arrows i n d i c a t e % s t r a i n  .04  -120°C  .03 5>P ACT  x  .02  5o  -196°C  .01  1.0 Fig.64  The v a r i a t i o n w i t h s t r e s s of  ^  2-0 Ao~  True s t r e s s  p . s . i . x 10  o b t a i n e d from  25JJ  3-0  cadmium a t d i f f e r e n t temperatures.  4.0  105 400JJ cadmium  6.= 4.0 x 10  -5  sec.  -4  - .06  -1 -1  -95 °C  -  .04  \Q  rCT  L  -i4o°c  Acr cr  -196°C  .02  4.0  8.0 •True s t r e s s  F i g . 65  16.0  12.0  The s t r e s s dependence o f  20.0  p . s . i . x 10 ACT  (400JJ cadmium)  .04  .05 S i n g l e c r y s t a l cadmium Oo= 36°  .02  Ao= 38°  Temperature = -50°C  A T  7 .01 End o f stage I  _L  200  400  600  R e s o l v e d shear s t r e s s F i g . 66  800  1000 2  gm/mm.  The f a i l u r e o f t h e C o t t r e l l - S t o k e s  law a t -50°C,  - .106 -  .06  g  a—•—•—a  a  -  •  -70°  .05  .04 o  ACT  o— °  o—  o-  -95°C  CT  .05 -120°C  .02 -5  ,01  £,= 4.0 x 10  sec,  £,= 4.0 x 10  sec,  1.5  1.0 True  stress  p.s.i. x  2.0 k 10  F i g . 67 The v a r i a t i o n w i t h s t r e s s o f the. C o t t r e l l - S t o k e s parameter A C T o b t a i n e d from s t r a i n r a t e change t e s t s O" on 20p z i n c .  2.k.  .HARDENING AT -196°C IN CADMIUM  S i n c e l i n e a r hardening  "  i n p o l y c r y s t a l s a t -196°C  by dynamic r e c o v e r y , the e x p e r i m e n t a l  0  "  7  i s not a f f e c t e d  d e t e r m i n a t i o n o f a c t i v a t i o n volume and  a c t i v a t i o n energy i s s i m p l i f i e d and more a c c u r a t e than a t h i g h e r  2.4.1.  1  temperatures.  A c t i v a t i o n Volume In o r d e r t o c a l c u l a t e t h e a c t i v a t i o n volume i t i s assumed  that  the shear s t r e s s i n p o l y c r y s t a l s i s e q u a l t o o n e - h a l f o f the t e n s i l e s t r e s s y  =  o~  . The c o r r e c t f a c t o r f o r the c o n v e r s i o n i s c o n t r o l l e d by the degree  2  84  of p r e f e r r e d  o r i e n t a t i o n and t h e r e f o r e can v a r y w i t h g r a i n s i z e  . However i t  85  w i l l have a v a l u e somewhere between 1/2 and l/k volume i s e x p e r i m e n t a l l y determined  . S i n c e the a c t i v a t i o n  from t h e e x p r e s s i o n  v = kT /_Aln5/eo)  \  AT*  IT  the v a l u e s o f "v" o b t a i n e d r e p r e s e n t t h e lowest p o s s i b l e v a l u e s i f t h e conversion  f a c t o r o f 1/2 i s used.  The manner i n which the a c t i v a t i o n volume v a r i e s w i t h t h e a p p l i e d s t r e s s f o r p o l y c r y s t a l s i s shown i n F i g . 66J. T O a f i r s t a p p r o x i m a t i o n , is a function increasing  o f t h e s t r e s s , d e c r e a s i n g i n an almost  e x p o n e n t i a l manner w i t h  s t r e s s . A t any c o n s t a n t v a l u e o f s t r e s s , v i n c r e a s e s w i t h  i n g g r a i n s i z e , an o b s e r v a t i o n expected  v  increas-  due t o t h e d e c r e a s i n g v a l u e s o f  A Q" cr  with.an i n c r e a s e i n g r a i n s i z e ( F i g . 63 -).  .The g r a i n s i z e ( s t r e s s ) dependence o f t h e a c t i v a t i o n volume a t yield  i s shown i n Table  9  . I f a simple assumption i s now made t h a t t h e  a c t i v a t i o n d i s t a n c e "d" can be approximated by t h e B u r g e r s v =lb  2  v e c t o r b, then  TABLE 9 Grain size  Grain Size  dependence o f the a c t i v a t i o n volume a t y i e l d i n cadmium a t -196°C.  Activation volume a t y i e l d  3  (cm. ) 3  kOOp.  125 Ou  Single  (* )  .30 x 1 0 "  25u  crystal  2 0  -20 1.20 x 10  -20 . 2.70 x 10  -20 • 30.0 x 10  Activation volume a t y i e l d  Forest density at y i e l d  2  lines/cm.  10  110  9.0 x 10  450  5.5 x 10  IgOO  1.1 x 10  11,000  1.0 x 10  Average a c t i v a t e d l e n g t h "1" a t yield (cm.)  3-3 x 10"  7  3  -20  6  .20 x 10  -20  -5  9  9  Activation volume a t s t a r t of dyn. r e c o v e r y (cm. )  .26 x 10  1.3 x 10  3.0 x 10  5  3-3 x 10 *  _20 .38 x 10  -20 1.75 x 10  *o= 36°, \>= 38° o VO  - 110 From t h i s an e s t i m a t e o f some smeared average  -  of d i s l o c a t i o n  l e n g t h b e i n g a c t i v a t e d p e r event a t y i e l d can be o b t a i n e d . These v a l u e s a l o n g w i t h s i n g l e c r y s t a l d a t a are shown i n T a b l e 9 is a consistent increase i n  1  from 3.J x 10  the g r a i n s i z e i n c r e a s e s from 25u  If is  one  to single c r y s t a l  t o 3-3  x.10  cm.  as  dimensions.  i t i s f u r t h e r assumed t h a t the r a t e c o n t r o l l i n g mechanism  o f f o r e s t i n t e r s e c t i o n , t h e n an e s t i m a t e o f the f o r e s t d e n s i t y a t  y i e l d may  be o b t a i n e d s i n c e  d e n s i t y . From T a b l e 9  p  1  = ~  i s a good a p p r o x i m a t i o n o f the  ^  i t i s seen t h a t p  v a r i e s from  7  for  cm.  . I t i s seen t h a t t h e r e  25u  cadmium t o a p p r o x i m a t e l y 10  9-0 x 10  1 0  forest 2  lines/cm .  2  lines/cm. f o r single c r y s t a l s .  These  v a l u e s are r e a l i s t i c f o r the i n i t i a l f o r e s t d e n s i t y . M i t r a and Dorn found t h a t i n t e r s e c t i o n i s the r a t e c o n t r o l l i n g p r o c e s s d u r i n g the d e f o r m a t i o n of  aluminum and copper s i n g l e c r y s t a l s a t J J°K. F o r c r y s t a l s r  initially  r  o r i e n t e d f o r easy g l i d e , t h e y c a l c u l a t e d a f o r e s t d e n s i t y a t y i e l d o f the 9  o r d e r of 10  2  5  l i n e s / c m . F o r aluminum p o l y c r y s t a l s t h e y found an  d e n s i t y of about  10  initial  2  1 0  lines/cm.  The a c t i v a t i o n volume a t the end o f Stage I d e f o r m a t i o n i n ~ 2 0  cadmium was  found t o be 5 . 0  x 10  3  cm.  On the b a s i s o f the  previous.assump8  t i o n s t h i s would i n d i c a t e a f o r e s t d e n s i t y o f a p p r o x i m a t e l y  3 x 10  lines  2  p e r cm. of  T h i s r e p r e s e n t s an i n c r e a s e i n the f o r e s t d e n s i t y d u r i n g Stage I.  s l i g h t l y more than an o r d e r of magnitude. By assuming an a c t i v a t i o n d i s t a n c e o f  c a l c u l a t e d f o r cadmium may  be s l i g h t l y low i n t h a t  d=  b the d e n s i t y v a l u e s  "d"" may  be somewhat  l a r g e r . P r i c e found t h a t the s t a c k i n g f a u l t energy f o r cadmium i s p r o b a b l y 2  between 15  and 30 ergs/cm. • T h i s i s c o n s i d e r a b l y lower than p r e v i o u s l y b e l i e v -  ed. T h e r e f o r e b e f o r e i n t e r s e c t i o n can o c c u r t h e r e must be a r e c o m b i n a t i o n o f the b a s a l p a r t i a l s . T h i s tends t o g i v e a more g r a d u a l s l o p e t o the  force-  - I l ld i s t a n c e curve than would be expected i f the s t a c k i n g f a u l t energy was  high.  T h i s i n t u r n e f f e c t i v e l y i n c r e a s e s the p o s s i b l e a c t i v a t i o n distance.•Howe v e r a t 77°K, a s i g n i f i c a n t p r o p o r t i o n of the energy r e q u i r e d f o r i n t e r s e c t i o n i s s u p p l i e d by the e f f e c t i v e s t r e s s s i n c e the t h e r m a l component of the a c t i v a t i o n energy value  /\G  s h o u l d be q u i t e s m a l l . T h i s t h e r e f o r e l i m i t s  o f the a c t i v a t i o n d i s t a n c e d u r i n g t h e r m a l a c t i v a t i o n and  t i o n that  d = b i s not  I t has  the  the assump-  unrealistic.  been assumed up t o t h i s p o i n t t h a t i n t e r s e c t i o n i s the  rate c o n t r o l l i n g process  g o v e r n i n g y i e l d and  l i n e a r hardening at  T h i s w i l l be d i s c u s s e d more f u l l y i n subsequent s e c t i o n s w i t h  -196°C.  regard  to  p o s s i b l e a l t e r n a t i v e mechanisms.  2.4.2.  • A c t i v a t i o n Energy  With the known v a l u e s i b l e t o c a l c u l a t e a value f o r 25u and  o f the apparent a c t i v a t i o n ' e n e r g y  400u cadmium. The  were o b t a i n e d  o f the a c t i v a t i o n volume i t i s now  Ao~* AT  values  AG  D  poss-  at  yield  r e q u i r e d f o r the c a l c u l a t i o n  from the y i e l d s t r e s s - t e m p e r a t u r e  r e l a t i o n s h i p s of F i g . , 3 2 .  They agreed v e r y w e l l w i t h the e x t r a p o l a t e d v a l u e s a t y i e l d of  A o~  AT obtained  from C o t t r e l l - S t o k e s temperature change t e s t s .  The v a l u e s i n Table 10  obtained  f o r the v a r i o u s r a t e parameters are shown  and were c a l c u l a t e d u s i n g e q u a t i o n s TABLE Energy v a l u e s  Grain size  AH  9,\1 .and  10  a t y i e l d f o r cadmium deformed at  e.v.  12 .  AG  e.v.  vT*  e.v.  -196°C.  AG  o  25u  .10  .08  .28  • 36  400u  .08  .06  • 33  • 39 •  e.v.  - 112 The v a l u e s shown i n T a b l e 10 can be c o n s i d e r e d - a c c u r a t e t o at b e s t ± 10$. W i t h i n e x p e r i m e n t a l e r r o r the apparent AGo  appears  t o be independent  activation  energy  of g r a i n s i z e . . T h i s suggests t h a t the  force-  d i s t a n c e curve does not change s i g n i f i c a n t l y w i t h g r a i n s i z e and t h e r e f o r e t h a t the mechanism, of y i e l d i s independent  of g r a i n s i z e . . T h e change i n  a c t i v a t i o n volume w i t h g r a i n s i z e t h e r e f o r e merely of  the f o r e s t  r e f l e c t s the  s p a c i n g "1" as p r e v i o u s l y assumed. The  variation AG  s i g n i f i c a n c e of  o  w i l l be d i s c u s s e d later..However AG  v j  i s much s m a l l e r than, the  d e c r e a s i n g temperature  i t i s noted, t h a t the t h e r m a l  component  term. T h i s i s t o be expected  an i n c r e a s i n g p r o p o r t i o n of the energy  since with  AG  will  o be a s s o c i a t e d w i t h the work done by the e f f e c t i v e  2.5.  HARDENING ABOVE -196°C IN ZINC AND. CADMIUM  2.5.I.  Y i e l d Behaviour  i n Cadmium  The v a l u e s of v, at two  stress.  temperatures significant  A , H  AG,  AG  D  and v T  a t y i e l d i n 25u  cadmium  above -196°C are shown i n T a b l e 11. Values, are quoted f i g u r e s which i s u n j u s t i f i e d because o f  l i m i t a t i o n s . T h i s procedure  was  to  experimental  f o l l o w e d only, t o p r o v i d e a method of  comparison between v a l u e s c a l c u l a t e d i n the same manner u s i n g c o n s i s t e n t techniques  of a n a l y s i n g e x p e r i m e n t a l It  and  data.  i s seen, t h a t below -120°C t h e r e i s a steady i n c r e a s e i n  vX w i t h i n c r e a s i n g temperature.  energy b a r r i e r as shown i n F i g . 69a  AGo  T h i s i n c r e a s e i s c o n s i s t e n t w i t h an i n which t h e r e i s a f a i r l y g r a d u a l s l o p e  of the f o r c e d i s t a n c e r e l a t i o n s h i p . • W i t h t h i s type of b a r r i e r i t i s expected that both  AG  0  and  vTwill  i n c r e a s e w i t h i n c r e a s i n g temperature  as  indicated  TABLE 11 Energy v a l u e s a t y i e l d i n 25u cadmium.  Temperature  (°c)  AH (e.v.)  AG  vT  (e.v.)  A G  (e.v.)  (e.v.)  Activation volume g (cm.)  -20  -196  .10  .08  .28  • 36  .30 x 10  -lUO  .ko  • 35  .h2  • 77  .60 x 1 0 °  -120  M  .Ul  M  .82  .70 x 10  -95  M  •57  .26  • 63  .55 x 1 0 ~  -60  •50  M  .20  .63  .55 x 10  -50  •57  .50  .12  .62  .50 x 10  _2  -20  2 0  -20  -20  by. the two random temperatures T  x  and  T . 2  Under such c o n d i t i o n s i t i s t h e r e f o r e i m p o s s i b l e t o p r e d i c t a .. r a t e c o n t r o l l i n g mechanism s t r i c t l y from the v a l u e s o f A G  . . I t was  for this  o reason that  AG  was  l a b e l l e d " a p p a r e n t " . . I t does not i n c l u d e the work done  o by.the e f f e c t i v e AG,  s t r e s s b e f o r e t h e r m a l a c t i v a t i o n . In o r d e r t o c a l c u l a t e  the t o t a l a c t i v a t i o n energy, i t i s n e c e s s a r y t o know the  0  temperature T  c  where T = 0. Under such c o n d i t i o n s  AG A  Alternatively  critical  = AG  d  = AGo*  *  AG  O  may  be c a l c u l a t e d simply, by knowing the s t r a i n r a t e  de-  86  pendence of the c r i t i c a l temperature AG  0  . T h e r e f o r e a l l t h a t can be s a i d  below -120°C i s t h a t i t i s something  about  i n excess o f .8e.v.. (the v a l u e o f  AGo a t -120°C) . Above -120°C  AG  0  tends t o remain c o n s t a n t a t a p p r o x i m a t e l y  .6 e . v . . T h i s temperature independence might  suggest a r a t e c o n t r o l l i n g p r o -  cess above -120°C which i s a s s o c i a t e d w i t h an energy b a r r i e r as shown i n F i g . 69-b f o r which n e i t h e r  A G  AG*  may  Under such c o n d i t i o n s equal to  q  nor  d  changes a p p r e c i a b l y w i t h temperature.  be approximated by AG  o  and.is therefore  .6 e.v. + .1 e.v. T h i s proposed change i n the r a t e c o n t r o l l i n g mechanism a t -120°C  i n 25u cadmium i s i l l u s t r a t e d q u i t e c l e a r l y by the dependence o f A G  at y i e l d  on temperature as shown i n F i g . 7/Q. B e f o r e such a proposed i n t e r p r e t a t i o n can become a c c e p t a b l e two major i n c o n s i s t e n c i e s w i t h t h e o r y must be  First  explained.  o f a l l the r a t e t h e o r y r e s u l t s i n d i c a t e a change i n the  r a t e c o n t r o l l i n g mechanism o f y i e l d a t a .temperature o f -120°C. However the  AG = bcdb abdea c  \ /  AG = abcdea / 0  Force  / \ 1\ /  1  1  1 a  \  AG = b'cd'b'  }  vT* = ab'dea  )  AGo = ab'cde'a' / sd  1  e  Distance  AG = bcdb vT*= abdea  AG = abcdea 0  Force  Distance  F i g . 69  Force-Distance  curves  - 116 -  ho  80  120  Temperature g. 7°  .200  160  2ko  °K  The v a r i a t i o n o f A G w i t h temperature f o r 25/j cadmium.  280  - 117 y i e l d s t r e s s has been found t o v a r y • l i n e a r l y w i t h temperature  (Fig..32).  T h i s l i n e a r i t y suggests a common mechanism c o n t r o l l i n g y i e l d . I t may  be  however t h a t the change a t -120°C causes  yield  o n l y a s l i g h t change i n the  s t r e s s - t e m p e r a t u r e s l o p e which f a l l s w i t h i n the e x p e r i m e n t a l s c a t t e r of the l i n e a r r e l a t i o n s h i p shown i n F i g . . 3 2 . F u r t h e r t e s t s below -196°C s h o u l d p r o v i d e a more complete  u n d e r s t a n d i n g of the temperature  dependence of y i e l d .  S t o l o f f a c t u a l l y d i d observe a change i n s l o p e a t a p p r o x i m a t e l y h i s e x p e r i m e n t a l s c a t t e r was  -120°C but  too g r e a t t o a c c u r a t e l y e s t a b l i s h the change  Ao~* . AT  in  The dependence o f AG  second  i n c o n s i s t e n c y concerns the n a t u r e of the  below -120°C..From the  AG = -kT. I n  temperature  relationship  _t_ to  if  $  0  i s not a . f u n c t i o n of temperature,.then  AG  should vary i n a l i n e a r  manner w i t h temperature.I.However from F i g . 72 i t i s seen t h a t a l i n e a r a t i o n s h i p does not e x i s t below -120°C. E i t h e r d e f o r m a t i o n i s not  rel-  controlled  by a s i n g l e mechanism which would p l a c e i n doubt any c a l c u l a t i o n based  on  r a t e t h e o r y or the nature o f the f o r c e -distance curve changes w i t h tempera t u r e . T h i s l a t t e r p o s s i b i l i t y c o u l d occur w i t h o u t a change i n the b a s i c r a t e p r o c e s s i f f o r i n s t a n c e t h s s t a c k i n g f a u l t energy changes w i t h temperis ature  . A t t h i s p o i n t t h e r e i s c o n s i d e r a b l e doubt as t o the magnitude of  the s t a c k i n g f a u l t energy  i n cadmium l e t alone any p o s s i b l e  temperature  dependence. 68  Thornton and. H i r s c h tance w i l l v a r y w i t h temperature  have proposed t h a t the a c t i v a t i o n  due t o a change i n the s t a c k i n g f a u l t  disenergy.  T h i s would a l t e r the shape o f the f o r c e - d i s t a n c e curve w i t h o u t a f f e c t i n g the b a s i c r a t e mechanism.  - 118 14  Conrad c r y s t a l s has  15  '  u s i n g an i n t e r s e c t i o n model f o r magnesium s i n g l e  shown t h a t the nature of the f o r c e - d i s t a n c e curve may  vary  s l i g h t l y w i t h temperature, ( s t r e s s ) due t o the i n f l u e n c e o f s t r e s s on the amount g l i d i n g d i s l o c a t i o n s how effective forest  out i n the s l i p p l a n e t h e r e b y  changing-the  s p a c i n g "1".  • Another p o s s i b i l i t y i s t h a t the pre-^exponential t e r m v a r i e s w i t h temperature. ions,  Xo  m u s  "t  i  However i n the development o f r a t e t h e o r y e x p r e s s -  he assumed temperature  f u l mathematical  J(= NAby  independent  expressions. I f i n fact  i n o r d e r t o a r r i v e at use-  )( does v a r y t h e n the d e r i v e d form0  ?  u l a t i o n s must be m o d i f i e d .  At t h i s time riot enough e x p e r i m e n t a l d a t a are a v a i l a b l e because of the l i m i t e d t e s t temperatures  a v a i l a b l e below -120°C i n order-  t o d i s t i n g u i s h between the above p o s s i b l e causes. A l i q u i d h e l i u m i s now  . i..  crydstat  n e a r i n g c o m p l e t i o n which w i l l a l l o w f o r a more e x t e n s i v e t e s t i n g  program.  At t h i s p o i n t no attempt  has been made t o d i s c u s s the  i f i c a n c e o f the e x p e r i m e n t a l v a l u e o f A G above T  H  = .26.  D  =  sign-  .6 + .1 e.v. at. temperatures  T h i s d i s c u s s i o n w i l l f o l l o w i n s e c t i o n 3.2.  which i n c l u d e s  a. comprehensive survey o f the p o s s i b l e mechanisms o f dynamic r e c o v e r y .  2.5.2.  The V a r i a t i o n o f  AH w i t h S t r a i n i n 2^u Cadmium.  The manner i n which temperatures  AH  v a r i e s with s t r a i n at d i f f e r e n t  i s shown i n F i g . 71- Because o f the unknown v a r i a t i o n o f  w i t h s t r a i n the v a l u e s of s t r a i n dependence o f  AG  AG  and  AGo  cannot be o b t a i n e d . However the  w i l l be s i m i l a r t o t h a t o f  e n t r o p y f a c t o r i s not expected t o lower AH  AH  i n that  by more than about  the  20%.  T  - 119 From F i g . 71 i t i s observed  t h a t the l i n e a r hardening  below -120°C a r e a s s o c i a t e d w i t h s t r a i n independent i s as expected when t h e C o t t r e l l - S t o k e s occurs  AH  2.5.3.  decreases  regions  v a l u e s o f AH. T h i s  law i s obeyed. When dynamic r e c o v e r y  substantially.  Y i e l d Behavior i n Z i n c .  The  e x p e r i m e n t a l v a l u e s of- t h e v a r i o u s components o f the  a c t i v a t i o n energy a t y i e l d i n 20u z i n c a r e g i v e n i n T a b l e 12..It  i s observed  t h a t t h e r e s u l t s f o r z i n c a r e s i m i l a r t o those f o r cadmium. Both  indicate  a temperature range above  independent T  H  = .26.  value of A G  o  o f about  .6 e.v. i n t h e r e c o v e r y  The v a l u e s o f A G f o r z i n c a r e s l i g h t l y lower  those f o r cadmium but do show a s i m i l a r temperature i n F i g . 72. The break at T  H  i n the A G  - temperature  than  r e l a t i o n s h i p as shown  relationship f o r zinc  = .26 i s not as obvious because o f the l i m i t e d data below, t h i s  temperature.. The a c t i v a t i o n volume v a l u e s f o r z i n c a r e comparable t o those of cadmium w i t h the z i n c values, beingaabout..25% s m a l l e r .  - 120  Linear  hardening  Dynamic r e c o v e r y  k  8  12  16  20  .2k  "jo s t r a i n 71  The v a r i a t i o n  of  AH  with strain.and i n 25/j cadmium.  temperature  • TABLE 12 Rate parameters a t y i e l d i n 20u  Temperature  T  H  °C  AH  *  A G  e.v.  e.v.  vT e.v.  zinc.  AG  0  V  3  e.v.  cm.  -120  .26  .21  • 17  .40  •57  -20 .36 x 10  -105  .28  .27  • 23  .42  .65  -20 .41 x 10  -95  •30  .29  .24  .40  .64  -20 .43 x 10  -70  • 34  • 33  .27  .34  .61  .40 x  -30  .41  .42  • 36  .24  .60  -20 10  -20 .40 x  10  - 122 -  .26 CD  •5  <  .0 •3  25JJ  .2  cadmium  20p  /  zinc  .1 40  80  J_ 120 Temperature  Fig.  72  .The v a r i a t i o n o f  160 .  200  2k0  °K  AG w i t h temperature for' 20p. z i n c .  -123 3-  DISCUSSION  B e f o r e any d i s c u s s i o n of the p r e s e n t r e s u l t s i s attempted, i t i s d e s i r a b l e t o review the e l e c t r o n t r a n s m i s s i o n o b s e r v a t i o n s of P r i c e on d i s l o c a t i o n s t r u c t u r e and motion i n p l a t e l e t s o f z i n c and cadmium. S i n c e the f l o w s t r e s s i s g e n e r a l l y thought and  s h o r t range  1  elastic  t o a r i s e from some combination  of l o n g  i n t e r a c t i o n s between d i s l o c a t i o n s and fromaa s h o r t  range t h e r m a l component of s t r e s s , P r i c e ' s o b s e r v a t i o n s on t,he f o r m a t i o n  i and b e h a v i o u r  o f d i s l o c a t i o n l o o p s and t h e i r subsequent i n t e r a c t i o n w i t h  d i s l o c a t i o n s are thought  t o be  of h a r d e n i n g i n z i n c and  cadmium.  3.1  Loop Formation  and  s i g n i f i c a n t w i t h r e g a r d t o the mechanisms  Annealing  D i s l o c a t i o n l o o p s can form on s p e c i f i c atomic  p l a n e s by  a  v a r i e t y of p r o c e s s e s .  (i)  P r i c e observed t h a t p r i s m a t i c l o o p s can form b e h i n d moving b a s a l  edge d i s l o c a t i o n s by  Fig.  73  a process i l l u s t a t e d i n F i g .  73  The f o r m a t i o n of a p r i s m a t i c d i s l o c a t i o n l o o p by an edge d i s l o c a t i o n which i s h e l d up a t an o b s t a c l e .  - 124 T h i s l o o p f o r m a t i o n i s thought  t o be a s s o c i a t e d w i t h t h e c r o s s  g l i d e o f t h e screw components ( c ) and t h e subsequent a n n i h i l a t i o n of t h e s e components b y g l i d e on a p a r a l l e l g l i d e p l a n e . T h i s t y p e - o f • l o o p w i l l be s e s s i l e b e c a u s e o f i t s edge components on non b a s a l p l a n e s . The k i n k s the o r i g i n a l d i s l o c a t i o n (d) a r e expected Loops thought by L a l l y 8 9 (ii)  t o r e t a r d . i t s f u r t h e r motion.  t o b e formed b y t h i s type o f mechanism have been  d u r i n g t h e Stage I d e f o r m a t i o n  P r i c e a l s o observed  t i o n s . A j o g on a screw  on  observed  o f magnesium a t 20°C.  l o o p f o r m a t i o n b e h i n d moving b a s a l screwvrdisloca-  may a f f e c t the-motion  o f t h e screw depending on  the s i z e o f t h e j o g as shown i n F i g . 7U  (c)  Fig.  7^  The e f f e c t o f jogs o f v a r i o u s h e i g h t s on screw d i s l o c a t i o n motion.  S m a l l jogs ( l b - 2 b ) can move non c o n s e r v a t i v e l y a l o n g w i t h t h e d i s l o c a t i o n l e a v i n g a row o f p o i n t d e f e c t s b e h i n d  ( a ) . T h i s p r o c e s s may be  t h e r m a l l y a c t i v a t e d and t h e r e f o r e r a t e , c o n t r o l l i n g . Very l a r g e jogs do n o t move and can a c t as p i n n i n g p o i n t s f o r s i n g l e ended Frank-Read s o u r c e s . ( b ) . Intermediate  jogs (3b-300b) however can l e a d t o t h e f o r m a t i o n o f an edge  -125 d i s l o c a t i o n d i p o l e ( c ) and a f t e r p i n c h i n g off:,, t o the f o r m a t i o n of an e l o n g a t e d l o o p on a non b a s a l p l a n e . Such d i p o l e s and l o o p s have been observed  i n a v a r i e t y of m e t a l  (iii)  systems.  S e s s i l e d i s l o c a t i o n l o o p s which c o n t a i n a s t a c k i n g f a u l t and  a Burgers  vector  \ c + p , may  d i s c s as p o s t u l a t e d by  Seeger  be  2 5  have  produced by the c o l l a p s e of vacancy  . Berghezan  has observed  6 3  such  loops o  on b a s a l p l a n e s i n z i n c f o i l s which were h e a v i l y deformed a t +20 S i m i l a r l o o p s were observed e l e c t r o n microscope.  The  C.  t o form by P r i c c f d u e t o i o n damage i n the 3  temperature range s t u d i e d by P r i c e extended down  o  to  -100  C. Whether such l o o p s w i l l c o n t r i b u t e t o work h a r d e n i n g  will  depend on the r a t e of l o o p p r o d u c t i o n compared t o the s t r a i n r a t e imposed on the system. The  r a t e of l o o p p r o d u c t i o n i n t u r n w i l l depend on  the  super s a t u r a t i o n of v a c a n c i e s i n a g i v e n a r e a and the t h e r m a l energya v a i l a b l e f o r vacancy m i g r a t i o n . (iv)  A f o u r t h type of l o o p f o r m a t i o n was  by P r i c e . E l o n g a t e d observed  <^1123^  observed  s e s s i l e l o o p s w i t h B'urgers  i n considerable d e t a i l  vectors  c + a  were  t o form on the b a s a l p l a n e s by the m u l t i p l e c r o s s g l i d e of £ll22^ d i s l o c a t i o n s . The  i l l u s t r a t e d i n F i g . 75  stages i n the f o r m a t i o n o f t h e s e  • I t was  observed  loops  t h a t the l o o p s a c t e d as  are  strong  b a r r i e r s t o the motion o f b a s a l d i s l o c a t i o n s on the same g l i d e plane  and  a l s o produced a s t r o n g e l a s t i c i n t e r a c t i o n w i t h o t h e r b a s a l d i s l o c a t i o n s on p a r r a l e l g l i d e p l a n e s as l o n g as the d i s t a n c e between the plane d i s l o c a t i o n and  the l o o p p l a n e was  not g r e a t e r than the l o o p  o f the  width.  A summary of the v a r i o u s types of l o o p s i s g i v e n i n T a b l e The  13  d i f f e r e n t types of d i s l o c a t i o n s p o s s i b l e i n the hexagonal system are  i l l u s t r a t e d f o r c l a r i t y i n F i g . 76  -126 -  (b)  (c)  F i g . 75  Stages i n the f o r m a t i o n of an e l o n g a t e d l o o p on the b a s a l plane by the c r o s s g l i d e of a £ll22? <1123^ screw d i s l o c a t i o n  The  v a r i o u s types  of l o o p f o r m a t i o n  d e t a i l because i t i s thought t h a t t h i s d e b r i s may o b s t a c l e s l e a d i n g t o hardening strong Cottrell-Lomer  due  of  £ll22^ \1123"^  the a n n e a l i n g b e h a v i o u r of  have o n l y been c a r r i e d out f o r those d i s l o c a t i o n motion. P r i c e has  c o n c l u s i o n s r e g a r d i n g the b e h a v i o r  and  a p r i n c i p a l source  barriers.  loops d u r i n g d e f o r m a t i o n  (i)  be  t o the l a c k i n the hexagonal system of  Comprehensive s t u d i e s c o n c e r n i n g  r e s u l t of  have been d e s c r i b e d i n  A t temperatures below  T  of these  =  .27,  formed as  a  come t o the f o l l o w i n g  l o o p s i n z i n c and  cadmium.  the loops are completely  can a c t as s t r o n g b a r r i e r s t o the motion of b a s a l d i s l o c a t i o n s .  stable  TABLE 13  Method o f F o r m a t i o n  Plane of Loop  .,. v ^  Behind moving b a s a l edges as i n F i g . 7 3  Non b a s a l  /..\, v /  Cross g l i d e of b a s a l screws  Non  1  1 1  ,  (111)  -  Loop f o r m a t i o n i n z i n c and cadmium.  . Condensation o f vacancies  .. . Cross g l i d e of ( I v J £1122} <1123> screws  127  Burgers V e c t o r  a  basal  Basal  Basal  -ic + p  c + a can decompose t o c  or  -§c + p  -  - 128 (ii)''  A t temperatures  between  T  = .27 and T  H  = A O the e l o n g a t e d  loops  H  break up i n t o rows o f c i r c u l a r l o o p s by a p r o c e s s o f p i p e d i f f u s i o n . The d r i v i n g f o r c e f o r s p l i t t i n g i s s u p p l i e d by t h e p o t e n t i a l decrease  i n line  energy.. The a r e a w i t h i n t h e e l o n g a t e d l o o p s i s conserved, d u r i n g t h e s p l i t t i n g o p e r a t i o n and t h e r a t e a t w h i c h s p l i t t i n g occurs i n c r e a s e s w i t h temperature.  P r i c e envisaged t h a t t h e a c t i v a t i o n energy  f o r such a p r o c e s s  w i l l be e q u a l t o  U  f o r m a t i o n and U a?  i s t h e p i p e d i f f u s i o n e n e r g y . . I m p l i c i t i n t h e concept o f  j  + U  increasing  P  where U. i s a s s o c i a t e d w i t h t h e r e q u i r e d j o g J  l o o p s p l i t t i n g as opposed t o l o o p shrinkage than t h e s e l f d i f f u s i o n energy (iii)  A t temperatures  i s that  U •+  must be l e s s  U  above T  = A,0. the c i r c u l a r l o o p s g r a d u a l l y d i s -  H  appeared  by a p r o c e s s o f c l i m b . The measured a c t i v a t i o n energy  f o r the  shrinkage o f l o o p s was found t o be e q u a l t o t h e s e l f d i f f u s i o n  energy.  The  observations of Price are of p a r t i c u l a r s i g n i f i c a n c e  r e g a r d t o t h e p r e s e n t work i n t h a t the temperature splitting  occurs  r e g i o n above which l o o p  (.27), i s s i m i l a r t o t h a t above which temperature  s t r a i n r a t e independent  l i n e a r work h a r d e n i n g  and  disappear i n p o l y c r y s t a l l i n e  z i n c and cadmium and above which t h e r e i s a decrease a s s o c i a t e d w i t h b o t h Stage I and Stage I I d e f o r m a t i o n  3.2.  with  i n the hardening of single  rate  crystals.  DYNAMIC RECOVERY  In a v e r y broad  sense dynamic r e c o v e r y may be r e l a t e d t o e i t h e r  of t h e f o l l o w i n g p r o c e s s e s : i ) cross ii)  slip  diffusion controlled  processes  ; 3.2.1.  Cross  - 129 -  Slip  Cross  slip  i s known t o be a dynamic r e c o v e r y mechanism i n  f . c c . metals.. In hexagonal m e t a l s ,  c r o s s s l i p must be l o o k e d a t from a  s l i g h t l y d i f f e r e n t p o i n t o f v i e w . . I t may  be a . r e q u i r e d mechanism t o permit  b a s a l d i s l o c a t i o n s t o move r e a d i l y onto non b a s a l p l a n e s and t h e r e b y for  the o p e r a t i o n o f a d d i t i o n a l s l i p  allow  systems. On the o t h e r hand i t may  operate as an a d j u n c t t o the o p e r a t i n g systems i n o r d e r t o a l l o w  dislocations  t o move around b a r r i e r s and t h e r e f o r e r e l i e v e p o i n t s of s t r e s s c o n c e n t r a t i o n . Only under, the l a t t e r c o n d i t i o n would c r o s s s l i p be  c l a s s i f i e d as a dynamic  recovery process.  Cross  s l i p has not been observed  under normal l i g h t  i n e i t h e r z i n c cadmium o r magnesium. However L a l l y it  d u r i n g the stage I d e f o r m a t i o n  microscopy  u s i n g r e p l i c a s has  o f magnesium at +20°C. T h e r e f o r e  s t u d i e s on p o l y c r y s t a l l i n e z i n c and  observed  replica  cadmium a r e c u r r e n t l y i n p r o g r e s s  to  e s t a b l i s h whether c r o s s - s l i p occurs t o a s i g n i f i c a n t degree. I t must  occur  on a l i m i t e d s c a l e i n o r d e r t o account  moving  f o r the l o o p f o r m a t i o n b e h i n d  b a s a l d i s l o c a t i o n s d e s c r i b e d i n the p r e v i o u s s e c t i o n . However such i n s t a n c e s are not expected  t o m a t e r i a l l y a f f e c t the flow s t r e s s . - A l t h o u g h i t  i s t r u e t h a t such c r o s s s l i p does a l l o w f o r the c i r c u m v e n t i o n the net r e s u l t  isolated  of the o v e r a l l p r o c e s s  of o b s t a c l e s  i s the p r o d u c t i o n of s e s s i l e  loops  which w i l l a c t as s t r o n g b a r r i e r s t o f u r t h e r d i s l o c a t i o n motion. 89  The  o b s e r v a t i o n s o f L a l l y and H i r s c h i n d i c a t e t h a t d u r i n g the  Stage I d e f o r m a t i o n  o f magnesium, the d i s l o c a t i o n s t r u c t u r e c o n s i s t s o f a  h i g h d e n s i t y o f e l o n g a t e d edge d i p o l e s . . V e r y few was  screws were  observed..It  p o s t u l a t e d t h a t the edge d i p o l e s were formed by the t r a p p i n g o f edge  components from d i f f e r e n t  sources  on nearby g l i d e p l a n e s . Screws of o p p o s i t e  -•130 s i g n . o n the  o t h e r hand can a n n i h i l a t e l e a d i n g t o a low  screw d e n s i t y . Under  such c o n d i t i o n s , i t c o u l d be p o s t u l a t e d , t h a t dynamic r e c o v e r y i s a s s o c i a t e d w i t h the temperature at which c r o s s s l i p a lower o v e r a l l d i s l o c a t i o n d e n s i t y and  S i m i l a r observations  -  i n magnesium  can o c c u r  leading.to  a different dislocation configuration.  t o those  of L a l l y cannot be made on z i n c  or cadmium because of the h i g h e r e f f e c t i v e temperature a t +20°C which  will  g i v e r i s e t o a c o n s i d e r a b l e d i s l o c a t i o n rearrangement d u r i n g the time necessary  f o r f o i l p r e p a r a t i o n . The  observations  of importance i n t h a t i t i s tempting t o invoke  on magnesium however are  c r o s s s l i p as the mechanism  o f dynamic r e c o v e r y . However on a more macroscopic s c a l e the i n t e r p r e t a t i o n becomes more complex. C o n r a c t ' " ^ a s observed a s i m i l a r temperature dependence, 6  of  9 /G  i n magnesium t o t h a t observed i n z i n c and  Q/Gc remains c o n s t a n t  below a p p r o x i m a t e l y  t h i s temperature'.... the h a r d e n i n g the  . Therefore  T^ =  cadmium. S p e c i f i c a l l y  .23 and  d e c r e a s e s above  the e f f e c t i v e temperature above which  r a t e decreases i n a l l t h r e e m e t a l systems i s  same. However the ease o f c r o s s s l i p  approximately  i s r e l a t e d t o the s t a c k i n g  energy i n t h a t the p a r t i a l s must recombine b e f o r e the p r o c e s s  can  fault  occur.  Although there i s considerable  c o n t r o v e r s y w i t h r e g a r d t o the magnitude  of  in. the t h r e e systems, i t ; i s g e n e r a l l y thought  the  stacking f a u l t energies  t h a t the s t a c k i n g f a u l t energy o f magnesium i s a p p r e c i a b l y h i g h e r than t h a t of  e i t h e r z i n c or cadmium.  Because of and  cross s l i p  the a s s o c i a t i o n between the  i t would not be  stacking fault  expected t h a t a l l t h r e e metals w i l l  energy undergo  dynamic r e c o v e r y a t the same e f f e c t i v e t e m p e r a t u r e . . T h e r e f o r e i t i s not p o s s i b l e t o l i n k dynamic r e c o v e r y t o c r o s s  slip.  - 131 3.2.2.  . D i f f u s i o n C o n t r o l l e d Processes  D i s l o c a t i o n climb when governed by t h e s e l f d i f f u s i o n energy U  D  was n o t observed  by P r i c e a t temperatures  below  T ..= .4 H  ..Therefore  it  cannot be c o n s i d e r e d as a dynamic r e c o v e r y mechanism i n t h e r e g i o n o f  T  = .26 .  H  •Kroupa and P r i c e  8 8  have observed, t h a t above TTT = .26 i n z i n c n  circular c + a  or  c  l o o p s produced b e h i n d  £L122|0-123^ screws can move  under t h e s t r e s s a s s o c i a t e d w i t h t h e i n t e r a c t i o n o f t h e l o o p s w i t h approaching basal d i s l o c a t i o n s  ( F i g . 78 ). T h i s motion was t e r m e d . c o n s e r v a t i v e  climb  s i n c e i t d i d n o t i n v o l v e s e l f d i f f u s i o n but r a t h e r the g e n e r a t i o n o f v a c a n c i e s on one s i d e o f t h e l o o p and t h e i r subsequent motion a l o n g t h e l o o p t o the o t h e r s i d e . . The a c t i v a t i o n energy f o r c o n s e r v a t i v e climb w i l l t h e r e f o r e be t h e p i p e d i f f u s i o n e n e r g y  U.  • Such l o o p i n s t a b i l i t y  i s a mechanism o f dynamic r e c o v e r y s i n c e ,  as observed by P r i c e , t h e n o r m a l l y s e s s i l e l o o p s a c t as s t r o n g b a r r i e r s t o b a s a l d i s l o c a t i o n motion. Loop motion by c o n s e r v a t i v e climb s h o u l d t h e r e f o r e r e s u l t i n a c o n s i d e r a b l e r e l i e f o f the back s t r e s s a s s o c i a t e d w i t h p i l e - u p s behind t h e l o o p s .  I n t h e p r e s e n t work, e x t e n s i v e  [1122}(112.3} s l i p was  i n p o l y c r y s t a l l i n e z i n c and cadmium. T h e r e f o r e a s i g n i f i c a n t o f b a s a l l o o p s s h o u l d be formed.. The v a l u e o f A G at temperatures  above T = .26 was determined H  b o t h z i n c and cadmium a t .6 ± .1 e.v.  Q  concentration  at y i e l d for poycrystals  t o be almost  identical for  96  F r i e d e l has s t a t e d t h a t t h e expected  v a l u e s o f t h e p i p e d i f f u s i o n e n e r g y . i n z i n c and cadmium a r e .57 e.v.  observed  .62 e.v..and  r e s p e c t i v e l y . From an e n e r g e t i c p o i n t o f view i t i s t h e r e f o r e  - 132 -  F i g . 77  ( c )  Sequence of transmission electron micrographs showing the ' conservative climb ' motion of a dislocation loop with a [0001] Burgers vector due to its interaction with a moving edge dislocation with a ^[1120] Burgers vector. The plane of the micrograph is parallel to the basal plane of the zinc platelet. (after Price  ).  p o s s i b l e t o p o s t u l a t e t h a t dynamic r e c o v e r y  i s a s s o c i a t e d w i t h the  conserv-  a t i v e climb of b a s a l l o o p s . S i n c e the energy r e q u i r e d f o r e l o n g a t e d breakup ( U may  + U. ) i s g r e a t e r than t h a t J j  p  of c o n s e r v a t i v e  be argued t h a t the r a t e c o n t r o l l i n g p r o c e s s  climb  (U ), i t P  i s a c t u a l l y t h a t of l o o p  breakup.However because of the h i g h e r d i s l o c a t i o n d e n s i t y i n r e a l as opposed t o P r i c e ' s specimens, i t i s p r o b a b l e  i  loop  crystals  t h a t the edge d i p o l e w i l l  j  tend t o p i n c h o f f e a r l i e r i n the sequence of l o o p formation.. T h e r e f o r e process  of l o o p s p l i t t i n g  i s not as  important  a  In order f o r such a c o n s e r v a t i v e valid for single crystals,  i t i s neccessary  the  process.  climb i n t e r p r e t a t i o n t o be  t o p o s t u l a t e t h a t some £ll22}  ^1123^> s l i p can occur d u r i n g b o t h Stage I and Stage I I s i n g l e c r y s t a l deformation. 13  Basinski  has  shown t h a t the C o t t r e l l - S t o k e s law  i s only  s t r i c t l y obeyed i n magnesium at temperatures below 46°K.•However the i a t i o n s t h a t occur a t h i g h e r temperatures are not p a r t i c u l a r l y any  case t h e r e i s a c o n s i d e r a b l e  ormation which was forest  increase i n y  severe..In  d u r i n g b o t h stages  of  def-  i n t e r p r e t e d by B a s i n s k i i n terms of an i n c r e a s i n g  concentration. E s s e n t i a l l y s i m i l a r r e s u l t s were o b t a i n e d  d u r i n g t h i s work on  cadmium s i n g l e c r y s t a l s . A l t h o u g h the C o t t r e l l - S t o k e s law was d u r i n g Stage I , t h e r e was  -20 5 x 10  not  -196°C "v" decreased  from  30 x 10  2  °  cm.  3  3 cm.  t o approximately  Based on an i n t e r s e c t i o n mechanism t h i s a 30  corresponds  f o l d i n c r e a s e i n the f o r e s t d e n s i t y d u r i n g Stage I .  I t would appear t h e r e f o r e t h a t t h e r e i s some non b a s a l a c t i v i t y Stage I and  obeyed  a c o n s i d e r a b l e decrease i n the a c t i v a t i o n , volume  at a l l temperatures s t u d i e d . A t  to  dev-  t h i s could lead to a s i g n i f i c a n t  during  c o n c e n t r a t i o n of b a s a l l o o p s .  - 134 Dynamic r e c o v e r y t o t h i s p o i n t has been a s s o c i a t e d o n l y w i t h nd the c o n s e r v a t i v e climb o f b a s a l loops produced behind screws. However the p i p e d i f f u s i o n p r o c e s s may  2  order  a l s o have a  pyramidal  significant  e f f e c t on the nature and m o b i l i t y of the o t h e r types of l o o p d e b r i s ment i o n e d i n the p r e v i o u s s e c t i o n . S i n c e t h i s d e b r i s i s produced o n l y as a r e s u l t of b a s a l d i s l o c a t i o n motion, i f s i m i l a r p r o c e s s e s  involving  conserv-  a t i v e climb can occur, then . i t i s not n e c e s s a r y t o p o s t u l a t e a change i n the f o r e s t d e n s i t y d u r i n g s i n g l e c r y s t a l d e f o r m a t i o n  i n order t o e x p l a i n  dynamic r e c o v e r y . Before t h i s i n t e r p r e t a t i o n can proceed  i t will  be  n e c e s s a r y t o know more about the a n n e a l i n g c h a r a c t e r i s t i c s of d e b r i s . As an a l t e r n a t i v e t o a p i p e d i f f u s i o n mechanism, t h e r e i s a d i s t i n c t p o s s i b i l i t y t h a t r e c o v e r y may  be a s s o c i a t e d w i t h the  annealing  c h a r a c t e r i s t i c s o f excess v a c a n c i e s produced d u r i n g d e f o r m a t i o n .  Resistivity  90  s t u d i e s made by Sharp, M i t c h e l l and C h r i s t i a n on cadmium , s i n g l e and p o l y c r y s t a l s deformed 12$,  crystals  i n d i c a t e d . t h e e x i s t e n c e of an a n n e a l i n g  peak i n the v i c i n i t y of T t o be  .25  = .25 . They determined the a c t i v a t i o n energy H * .2 e.v. and a s s o c i a t e d the peak w i t h s i n g l e vacancy m i g r a t i o n . .91  P e i f f e r and Stevenson a n n e a l i n g peaks, one a t  T  9 2  i n a s i m i l a r study observed  = .23 and another a t H  e n e r g i e s were.24 and peaks was  =  .28.  The  activation  H  .30.e.v. r e s p e c t i v e l y . They b e l i e v e d t h a t one  o f the  a s s o c i a t e d w i t h s i n g l e vacancy m i g r a t i o n a l t h o u g h they were not  sure which one.  The  expected  v a l u e f o r the energy a s s o c i a t e d w i t h vacancy  1  motion  T  two  i n cadmium i s  .41 e.v.  9  7  T h i s i s somewhat lower than the  .6 *  e.v. a c t i v a t i o n energy found t o c o n t r o l the dynamic r e c o v e r y . o f z i n c cadmium. However due t o the approximations e x p r e s s i o n s when a p p l i e d t o d e f o r m a t i o n ,  .1  and  i n v o l v e d in. the r a t e t h e o r y  i t i s not o u t s i d e the realm  of  p r o b a b i l i t y t h a t vacancy m i g r a t i o n and dynamic r e c o v e r y are somehow l i n k e d .  The  exact n a t u r e  of such a r e l a t i o n s h i p i s r a t h e r vague. I f  the net r e s u l t of m i g r a t i o n i s the p r o d u c t i o n of b a s a l d i s l o c a t i o n l o o p s by vacancy  c o n d e n s a t i o n , then i t would be expected t h a t such l o o p s w i l l  t r i b u t e t o h a r d e n i n g and w i l l not l e a d t o a r e c o v e r y e f f e c t . On the  conother  hand by a n n e a l i n g out a t edge d i s l o c a t i o n s excess v a c a n c i e s can cause climb a l l o w i n g f o r . the c i r c u m v e n t i o n of o b s t a c l e s . Climb t h e r e f o r e can o c c u r a t lower temperatures  = .k and under such c o n d i t i o n s i s c o n t r o l l e d H o n l y by the vacancy m i g r a t i o n energy.- A l t h o u g h P r i c e d i d not observe climb  below T  H  than T  = .k , i t i s p r o b a b l e t h a t the excess vacancy  p l a t e l e t s used  f o r study was  c o n c e n t r a t i o n i n the  q u i t e low due t o the low d i s l o c a t i o n d e n s i t y  and the a v a i l a b i l i t y of the specimen s u r f a c e . . In summary.it must be concluded t h a t the e x a c t cause o f the dynamic r e c o v e r y o c c u r i n g i n the v i c i n i t y of T^ =  .26  cannot  be  definitely  e s t a b l i s h e d a t t h i s t i m e . However because o f the b e t t e r c o r r e l a t i o n of e n e r g i e s , i t i s thought  t h a t the most l i k e l y p r o c e s s i s one  p i p e d i f f u s i o n l e a d i n g t o the c o n s e r v a t i v e climb of n o r m a l l y  involving sessile  basal d i s l o c a t i o n loops.  .3.3.  -THE  MECHANICAL EQUATION OF STATE  I t was  shown i n s e c t i o n  2.2.3. t h a t a m e c h a n i c a l  equation  of s t a t e c o u l d be f o r m u l a t e d f o r : p o l y c r y s t a l s i n the r e g i o n s o f l i n e a r h a r d e n i n g below  T  = .26  .-Only under these c o n d i t i o n s i s i t p o s s i b l e t o  H o b t a i n e q u i v a l e n t s t a t e s a t an e q u a l v a l u e o f s t r a i n when d e f o r m a t i o n at d i f f e r e n t  occurs  temperatures. The  concept  of dynamic r e c o v e r y b e i n g a s s o c i a t e d w i t h the  c o n s e r v a t i v e climb o f l o o p s i s c o n s i s t e n t w i t h the above o b s e r v a t i o n s . B a s a l l o o p s s h o u l d remain s t a b l e i n the l i n e a r h a r d e n i n g  regions.- The  r  -136 -  '  o v e r a l l d i s l o c a t i o n c o n f i g u r a t i o n at a g i v e n v a l u e of s t r a i n w i l l be  independent of temperature. However once c o n s e r v a t i v e  that equivalent erature  3.4.  s t a t e s . w i l l be  dependence o f the  THE  law was  not  o c c u r , . i t i s not  expected  found, at e q u a l s t r a i n s because of the as observed by  temp-  Price.  observed t h a t a t a l l temperatures. the  Cottrell-Stokes  s t r i c t l y obeyed d u r i n g the Stage I d e f o r m a t i o n o f cadmium  Acr cr  means t h a t the increase  can  LAW  s i n g l e c r y s t a l s or d u r i n g cases the  climb  r a t e of l o o p a n n e a l i n g  COTTRELL-STOKES  I t was  of  the  early, s t r a i n r e g i o n s  rate of increase  cr  of p o l y c r y s t a l s . In b o t h  r a t i o decreased, w i t h i n c r e a s i n g s t r a i n . In e f f e c t t h i s  G  of  cr was  somewhat l e s s t h a n the  . In p o l y c r y s t a l s t h i s may  e f f e c t s . • T h i s e a r l y region up  therefore  be  rate  r e l a t e d . to., g r a i n boundary  of s t r a i n i s a s s o c i a t e d w i t h the  g r a d u a l buildv.  o f a s t a b l e d i s l o c a t i o n c o n f i g u r a t i o n a t the g r a i n b o u n d a r i e s ( p i l e  This  c o n t r i b u t i o n t o s t r e s s w i l l be  It i s therefore of  cr  expected t h a t the  which i s a s s o c i a t e d . w i t h  A T  Although  athermal, c o n t r i b u t i n g only t o  increase  in  cr  intragranular  of  w i l l be  G processes.  ups).  cr  G somewhat i n excess  d e c r e a s e s d u r i n g Stage I h a r d e n i n g . t h e r e i s  X  a s i g n i f i c a n t decrease i n the  a c t i v a t i o n volume. T h i s  implies.that  there  _ *-  i s an  increase  great  as. the  i n the v a l u e of  increase  in  *X G  T  . This  w i t h i n c r e a s i n g s t r a i n although not observation  i s not  consistent with  as the  24  t h e o r y of Seeger that  %/G  can be  regarding  Stage I hexagonal m e t a l d e f o r m a t i o n . He  c a l c u l a t e d , by  only considering•the  between i n d i v i d u a l p a r a l l e l d i s l o c a t i o n s and from J  i s n e g l i g i b l e . For  elastic  t h a t the  such' a t h e o r y t o be  assumes  interactions  contribution to  ©j/G  c o r r e c t , the a c t i v a t i o n  volume must remain c o n s t a n t d u r i n g Stage I . Because of the marked change  - 137 i n "v" i n cadmium, i t must be concluded t h a t c o n t r i b u t i o n t o t h e observed  3.4.1.  Qj/G r e p r e s e n t s an important  r a t e o f h a r d e n i n g and.cannot be n e g l e c t e d .  Obeyance  The C o t t r e l l - S t o k e s law i s obeyed o n l y - d u r i n g . the hardening  linear  r e g i o n s o f p o l y c r y s t a l s and d u r i n g t h e Stage I I h a r d e n i n g o f  s i n g l e c r y s t a l s below r e l a t i o n s h i p between  T = .26 ..In o r d e r t o p o s t u l a t e the o r i g i n and H C*and cr i t i s n e c e s s a r y t o know how. t w i n n i n g may f \ . G  a f f e c t t h e two s t r e s s components.-As observed  i n single c r y s t a l s the  f o r m a t i o n o f a t w i n does n o t a f f e c t - t h e flow s t r e s s r e q u i r e d f o r f u r t h e r d e f o r m a t i o n . B a s a l s l i p . w i t h i n a twinned  r e g i o n t h e r e f o r e must r e p r e s e n t  an important  o n l y immediately  c o n t r i b u t i o n t o deformation  f o r m a t i o n b e f o r e the macroscopic  observed  a f t e r t h e twin  stress returns t o i t s previous  v a l u e . T h e r e f o r e a l t h o u g h t w i n n i n g may. a f f e c t t h e work, h a r d e n i n g  rate,it  does n o t changexthe i n s t a n t a n e o u s r e l a t i v e v a l u e s o f the. two s t r e s s components. T h i s ^ s t a t u s quo" c o n d i t i o n d u r i n g . d e f o r m a t i o n may a l s o be a p p l i e d t o t h e nature  o f t h e d i s l o c a t i o n c o n f i g u r a t i o n i n t h e neighbourhood  of g r a i n boundaries.- Once a s t a b l e c o n f i g u r a t i o n i s o b t a i n e d i t w i l l be assumed t h a t h a r d e n i n g becomes i n t r a g r a n u l a r and t h e component o f <3~ a s s o c i a t e d w i t h boundaries  need n o t be c o n s i d e r e d • w i t h r e g a r d , t o t h e  C o t t r e l l - S t o k e s law.  The  athermal  w i t h some combination  component o f s t r e s s is. t h e r e f o r e a s s o c i a t e d  o f t h e f o l l o w i n g components:  i ) t h e i n t e r a c t i o n o f f o r e s t and g l i d e i i ) t h e i n t e r a c t i o n o f l o o p s and g l i d e  dislocations dislocations  - 138 I t w i l l be assumecL t h a t  cr  a r i s e s due  t o an i n t e r s e c t i o n  mechanism. The C o t t r e l l - S t o k e s obeyance can t h e r e f o r e be  interpreted in  terms, of an i n c r e a s i n g f o r e s t d e n s i t y w i t h i n c r e a s i n g s.train . • o~ p r o p o r t i o n a l t o b o t h a t h e r m a l s t r e s s components because the b a s a l  remains loop  d e n s i t y w i l l be a f u n c t i o n of the f o r e s t d e n s i t y .  3.4.2.  - Dynamic Recovery  I t has been shown c r y s t a l s , dynamic r e c o v e r y T h i s means, t h a t the 0~*  . . I f recovery  p r o p o r t i o n of  cr  t h a t i n b o t h s i n g l e c r y s t a l s and  i s associated with  r a t e of i n c r e a s e  of  cr  G  i n c r e a s i n g values  Ao~ o~ i s somewhat l e s s than t h a t  i s r e l a t e d , t o loop i n s t a b i l i t y G  poly-  and  if a  of  of  significant  i s derived, from the nature o f l o o p - d i s l o c a t i o n i n t e r -  -actions, then i t i s expected t h a t because o f the r e l i e f  c T ^ . w i l l i n c r e a s e a t a lower r a t e  of back s t r e s s which occurs because of o b s t a c l e ^  motion. 3.5.  -RATE CONTROLLING '.PROCESSES BELOW. T - = TT  _ I t was rolling  process  .26  ^  p r o p o s e d , t h a t f o r e s t i n t e r s e c t i o n i s the  rate  cont-  g o v e r n i n g y i e l d i n s i n g l e c r y s t a l s and p o l y c r y s t a l s below  T  = .26 . T h i s was done w i t h o u t any. c o n s i d e r a t i o n of p o s s i b l e a l t e r n a t e Hmechanisms.. These w i l l now be d i s c u s s e d . 3.5.I.  .Peierls Stress  The P e i e r l s s t r e s s f o r the motion of b a s a l d i s l o c a t i o n s i s v e r y low because of the  close-packed  t h e r e f o r e be  as a r a t e c o n t r o l l i n g p r o c e s s .  considered  n a t u r e of the b a s a l plane.. I t cannot However d u r i n g  p o l y c r y s t a l l i n e d e f o r m a t i o n when non b a s a l s l i p must occur,  the P e i e r l s  - 139 s t r e s s a s s o c i a t e d w i t h movement on the s i g n i f i c a n t and  The  c o r r u g a t e d p y r a m i d a l p l a n e s may  -  be  rate c o n t r o l l i n g .  25ji cadmium a t -196°C based  a c t i v a t i o n -volume a t y i e l d i n  on a shear s t r e s s c o n v e r s i o n a b a s a l d i s l o c a t i o n where  of  _  y  =  cr  .  a = 2.97  .30  , was  x 10  -20  cm.  3  . I n terms  2  A* , t h i s gave a v a l u e o f 110b  3  .  of  •However  3 i n terms of a  c+a  p y r a m i d a l d i s l o c a t i o n t h i s reduces t o about 17b  a much  more a c c e p t a b l e v a l u e f o r . t h e P e i e r l s mechanism. However i t was volume i n c r e a s e d  a l s o o b s e r v e d . ( T a b l e 9)  t h a t the a c t i v a t i o n  w i t h i n c r e a s i n g g r a i n s i z e , a t r e n d not  P e i e r l s mechanism. From F i g . 68  i t was  expected f o r  observed, t h a t f o r a g i v e n  the  grain size  "v" d e c r e a s e d s u b s t a n t i a l l y • w i t h i n c r e a s i n g s t r a i n . - I f the P e i e r l s mechanism i s r a t e c o n t r o l l i n g .the a c t i v a t i o n volume should not  - S i n c e the  P e i e r l s mechanism i s not  experimental observations,.it  can be  vary with  strain.  compatible w i t h a l l of  the  r e j e c t e d as a p o s s i b l e c o n t r o l l i n g  mechanism.  3.5.2. . Cross. S l i p  C r o s s s s l i p has  been c o n s i d e r e d  mechanism of dynamic recovery.. I t may  a l s o be  c o n t r o l y i e l d a t temperatures below T . = H b a s a l d i s l o c a t i o n s t o move onto non e x t e n t of non the  o n l y non  [ll22J0-123^ in section  i n s e c t i o n 3-3»  .26  argued t h a t  as a cross  possible slip  could  i f i t i s required.in order f o r  b a s a l p l a n e s and  thereby c o n t r o l  the  b a s a l s l i p . However-this argument cannot be v a l i d a t e d i n t h a t b a s a l t r a c e s t h a t are s l i p . T h i s i s not  observed i n z i n c and  a cross  slip  cadmium.arise from  system. A l s o as p o i n t e d  out  1.4.1., when [ll22J<(ll23>sl.ip.occurs, the number of independent  systems t h a t  can  operate i s s u f f i c i e n t  ..to promote e x t e n s i v e p o l y c r y s t a l l i n e  - iko deformation. Therefore cross s l i p  i s not a necessary process i n order f o r  deformation t o proceed.  3.5-3-  The Non C o n s e r v a t i v e - M o t i o n o f Jogs 98  Frank  f i r s t p o s t u l a t e d t h a t a jogged screw d i s l o c a t i o n can  move o n l y i f t h e j o g l e a v e s b e h i n d i t e i t h e r a row o f v a c a n c i e s o r i n t e r s t i t i a l s depending on i t s . s i g n and d i r e c t i o n o f motion.- The c o n s e r v a t i v e motion o f vacancy jogs i s thought t o be a s s o c i a t e d w i t h a r e l a t i v e l y h i g h a c t i v a t i o n energy, and t h e r e f o r e need n o t be c o n s i d e r e d . . I t i s u s u a l l y not p o s s i b l e t o d i s t i n g u i s h between a j o g or an i n t e r s e c t i o n mechanism merely from t h e v a l u e s o f r a t e t h e o r y parameters. Both p r o c e s s e s a r e expected; t o have s i m i l a r v a l u e s o f a c t i v a t i o n volume i n t h e range from  2  3  -10 b  to 10  4  3  b .  The concept o f a j o g mechanism b e i n g r a t e c o n t r o l l i n g i s n o t - 99 s t r o n g l y s u p p o r t e d by e x p e r i m e n t a l o b s e r v a t i o n s . . I t was advanced by Mott m a i n l y t o e x p l a i n the n a t u r e o f t h e flow s t r e s s v a r i a t i o n s i n copper  single  c r y s t a l s . . I n copper i t has been observed t h a t the flow s t r e s s i s almost temperature  independent between  T  = .2 and  T  = .5  .-At h i g h e r temperatures  t h e r e i s a s i g n i f i c a n t drop i n s t r e s s . Mott t h e r e f o r e proposed t h a t a t tempe r a t u r e s below TJJ = -5 > "the s e l f d i f f u s i o n p r o c e s s r e q u i r e d f o r ..the  mech-  anism t o procede cannot occur a t an a p p r o p r i a t e r a t e i n terms o f the a p p l i e d s t r a i n r a t e . The vacancy n u c l e a t i o n a t t h e j o g i s t h e r e f o r e c o m p l e t e l y a t h e r m a l l e a d i n g t o a temperature independent flow s t r e s s . . I t was a l s o assumed b y Mott t h a t energy i s n o t a v a i l a b l e f o r vacancy m i g r a t i o n away from t h e r e g i o n o f t h e j o g . Under such c o n d i t i o n s any t h e r m a l f l u c t u a t i o n w i l l t e n d t o move t h e j o g forward a s i n g l e atomic spacing, but i f t h e vacancy  -.141produced i s not m o b i l e , the j o g can be p u l l e d back by the i n t e r a c t i o n w i t h the vacancy produced. T h e r e f o r e t h e flow s t r e s s s h o u l d not be dependent  below  temperature  T =. .5 . Above t h i s temperature however where t h e energy . H  f o r s e l f d i f f u s i o n i s a v a i l a b l e , the v a c a n c i e s produced s h o u l d be mobile and a temperature dependent  flow s t r e s s s h o u l d r e s u l t .  There are some q u e s t i o n a b l e f e a t u r e s o f t h i s t h e o r y . F i r s t all  i t i s n o t c l e a r why  of  the n u c l e a t i o n o f a vacancy a t a j o g s h o u l d be a  c o m p l e t e l y a t h e r m a l p r o c e s s . The t h e r m a l energy a v a i l a b l e i n t h i s  temperature  range s h o u l d be s u f f i c i e n t t o p r o v i d e a p o r t i o n o f t h e energy needed f o r vacancy n u c l e a t i o n .  S e c o n d l y , even i f vacancy n u c l e a t i o n i s an a t h e r m a l p r o c e s s , the temperature a t which a temperature dependent  f l o w s t r e s s occurs s h o u l d be  a s s o c i a t e d o n l y w i t h t h e energy f o r vacancy m i g r a t i o n . T h i s s h o u l d o c c u r a t temperatures w e l l below  T  ..= .5 H  .In z i n c and cadmium.it can o c c u r a t - a p p r e c i a b l e r a t e s above  i s b e l i e v e d ; t h a t s i n g l e vacancy motion T  = .25  . T h e r e f o r e below t h i s  temperature a c c o r d i n g t o t h e j o g mechanism, the f l o w s t r e s s of z i n c and cadmium w i l l be governed by the a t h e r m a l p r o c e s s o f vacancy n u c l e a t i o n . T h i s s h o u l d l e a d t o a temperature independent f l o w s t r e s s . T h i s was observed  .There  systems below  T  not  i s a c o n s i d e r a b l e i n c r e a s e i n the flow s t r e s s i n b o t h H  = .26. I t i s t h e r e f o r e u n l i k e l y t h a t the non  conservative  motion of jogs i s the r a t e c o n t r o l l i n g p r o c e s s a t low temperatures i n z i n c and cadmium.  3.5.4.  Intersection  The p o s t u l a t e o f f o r e s t  i n t e r s e c t i o n was  not made merely  -  because o t h e r mechanisms c o u l d not e x p l a i n i o n s . There are no major i n c o n s i s t e n c i e s estimate of f o r e s t  2  -196°C from  :.is. w i t h i n  1.1  x 10  the expected  non  b  The v a r i a t i o n o f a c t i v a t i o n volumes 4  for. 25u  ..,3  cadmium t o 1.1 .x 10 bb  for single  i s not due  f o r e s t mechanism to. be due  difference  i n the f o r e s t  t o a change i n the f o r c e w i t h temperature  s p a c i n g as the  grain  d i s t a n c e curve.. The  can be i n t e r p r e t e d  e i t h e r t o a change i n the s t a c k i n g  from  fault  o r t o a change i n the e f f e c t i v e v a l u e o f the f o r e s t  due t o the manner i n which a d i s l o c a t i o n bows out under the i n f l u e n c e stress.  crystals  range f o r i n t e r s e c t i o n . - The v a r i a t i o n has been shown  l i n e a r v a r i a t i o n o f AG  w i t h temperature  observat-  w i t h the f o r e s t mechanism. The  3  t o a r i s e from the expected s i z e changes and  -  spacings of T a b l e 9 made from . a c t i v a t i o n volume d a t a are  r e a s o n a b l e f o r the systems i n v o l v e d .  at  a l l of the e x p e r i m e n t a l  142  the energy spacing of a  - 1U3 , 4.  SUMMARY AND.CONCLUSIONS  The  o b s e r v a t i o n s and  a c t e r i s t i c s , of z i n c and  1)  cadmium may  i n t e r p r e t a t i o n s of the d e f o r m a t i o n  char-  be summarized.as f o l l o w s :  Negative work h a r d e n i n g beyond .the p o i n t o f maximum- s t r e s s i n p o i y c r y s - : t a l l i n e z i n c and  cadmium a t temperatures  above T  • w i t h r e c r y s t a l l i z a t i o n . However a t temperatures  = ,4  i s associated  up t o a t l e a s t  T  =  r e c r y s t a l l i z a t i o n does not go t o completion d u r i n g d e f o r m a t i o n . A t 50$  2)  .5  least  of the s t r u c t u r e o u t s i d e the necked a r e a remains u n r e c r y s t a l l i z e d .  G r a i n boundary m i g r a t i o n can o c c u r i n the i n i t i a l h a r d e n i n g r e g i o n s and i s p a r t i c u l a r l y important  as a r e c o v e r y mechanism above  T  = ,4  .  H S l i g h t boundary c o r r u g a t i o n s were observed  i n cadmium, a t  temperatures  down t o -95°C s u g g e s t i n g t h a t the change i n f r a c t u r e mode from  ductile  shear t o i n t e r g r a n u l a r f r a c t u r e which o c c u r s at -120°C i s a s s o c i a t e d w i t h the c e s s a t i o n o f r e c o v e r y by boundary m i g r a t i o n .  3)  J1122}0-123)" i s the o n l y non b a s a l s l i p system observed d u r i n g p o l y c r y s t a l l i n e d e f o r m a t i o n . . I t i s more p r e v a l e n t as the decreases.-At  +20°C i t i s more e x t e n s i v e i n z i n c than i n cadmium.at  e q u i v a l e n t temperature.  4)  The non b a s a l t r a c e s are wavy and  at  e l e v a t e d temperatures.-At  to  c o n c e n t r a t e i n t o bands. Q u a l i t a t i v e l y i t appears  non b a s a l s l i p  The  temperature  low temperatures  i n c r e a s e s as the g r a i n s i z e  f o r m a t i o n of low angle b o u n d a r i e s  an  discontinuous  t h e y are s t r a i g h t  and.tend  t h a t the amount.of  decreases.  during deformation  b o t h systems.and does not v a r y i n n a t u r e or e x t e n t w i t h  i s similar in temperature.  -  -M 5)  I n cadmium s i n g l e c r y s t a l s t h e r e s o l v e d b a s a l s h e a r s t r e s s a t  which  Stage I ends i s independent  -50°C t o  of temperature  i n the range  from  -196°C.  6)  Twinning  i s a g e n e r a l f e a t u r e of Stage  atures below  7)  -50°C.  'a  A r e g i o n of temperature develops below  T  and  .26  =  i  IV-.:.,  I I cadmium d e f o r m a t i o n a t t e m p e r j  s t r a i n rate independent  i n both polycrystalline  l i n e a r work  z i n c and  hardening  cadmium.  The  H amount o f s t r a i n a s s o c i a t e d w i t h l i n e a r h a r d e n i n g i n c r e a s e s a s t h e e r a t u r e d e c r e a s e s . The 8)  rate of hardening i s s i m i l a r  Cadmium s i n g l e c r y s t a l s a l s o show c o n s t a n t S t a g e ening rates below  T  =  .26  i n both  I and Stage  temp-  systems. I I hard-  and c o n t i n u o u s l y d e c r e a s i n g h a r d e n i n g  rates  H above t h i s t e m p e r a t u r e . T h i s i s s i m i l a r t o t h e b e h a v i o u r o f z i n c  and  magnesium. 9)  The  maximum l i n e a r h a r d e n i n g r a t e o f p o l y c r y s t a l l i n e  varies linearly with  d  - 1  . The  corresponds t o the t e n s i l e Stage  extrapolated value of  0 to  I I hardening rate of single  T h i s c h a n g e i n h a r d e n i n g r a t e c a n be e x p l a i n e d i n t e r m s i n the frequency  1 0 ) The  o r s t r a i n r a t e change t e s t s .  of  ACT  H  =  .26.  _ l 2  0  =  crystals. change  obeyed f o r e i t h e r ,  temperature  Obeyance i s o n l y o b s e r v e d d u r i n g t h e  h a r d e n i n g o f p o l y c r y s t a l s and T  of a  d  o f |jL122^<1123)slip.  C o t t r e l l - S t o k e s law i s not s t r i c t l y  below  -196°C  cadmium a t  d u r i n g Stage  I I single  crystal  linear  hardening  Dynamic r e c o v e r y i s a s s o c i a t e d w i t h i n c r e a s i n g v a l u e s  ,  cr  11)  In polycrystalline  z i n c and  cadmium e q u i v a l e n t s t a t e s a t e q u a l  strains  - 14-5 are o n l y o b t a i n e d d u r i n g l i n e a r - h a r d e n i n g . - T h e r e f o r e o n l y i n these can a m e c h a n i c a l  12)  e q u a t i o n o f s t a t e be  Y i e l d a t temperatures  below  T = .H  .26  formulated.  can be  i n t e r p r e t e d i n terms of a  f o r e s t i n t e r s e c t i o n mechanism.. T h e ' t o t a l a c t i v a t i o n cannot of . 8 e.v.  regions  D.vc  i s somewhat i n excess  13)  I t i s p r o b a b l e t h a t dynamic recovery-above  be e s t i m a t e d but  i n cadmium . TJJ =  a d i f f u s i o n c o n t r o l l e d p r o c e s s . The most l i k e l y  .26  i s associated with  mechanism.involves.the  c o n s e r v a t i v e climb of n o r m a l l y s e s s i l e b a s a l l o o p s by a p r o c e s s o f p i p e - d i f f u s i o n . The  e x p e r i m e n t a l a c t i v a t i o n energy  z i n c and cadmium i s  .6  *  .1  e.v.  for yield in polycrystalline  -ike 5.  • SUGGESTIONS FOR FUTURE WORK  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 a r e immediately from t h e r e s u l t s o f t h i s work. These  1)  below -196°C  e s t a b l i s h t h e flow s t r e s s - t e m p e r a t u r e  . A thorough e l e c t r o n microscopy  recognized  include:  An e x t e n s i o n o f t e s t i n g t o temperatures completely  2)  -  i n order t o  relationships.  r e p l i c a study on s l i p t r a c e s  i n order  t o e s t a b l i s h t h e s i g n i f i c a n c e o f c r o s s s l i p i n p o l y c r y s t a l l i n e z i n c and cadmium.  3)  An e x t e n s i v e r e s i s t i v i t y  study o f v a r i o u s deformed s t a t e s  i n order t o  e s t a b l i s h t h e r e l e v a n c e o f s i n g l e vacancy motion t o dynamic  recovery.  APPENDIX  -  -1^7  I  I ;.'.vi.:,Rate,, Theory  As mentioned i n s e c t i o n  2 . 1 . when d e f o r m a t i o n i s goverened  a. s i n g l e r a t e c o n t r o l l i n g . . p r o c e s s , the shear s t r a i n r a t e may  by  be e x p r e s s e d  )f = Jo e  by  (1)  81 A more g e n e r a l e x p r e s s i o n as i n d i c a t e d . b y Dorn , i s g i v e n by  y  SJ  5=  J .e  L  AQt/kT . . . . . . . . . . . . . . . . . . . . . . . . . . . . ( 2 )  0  th where " i "  r e f e r s t o the i  ' k i n d o f mechanism.  • S e v e r a l d i f f e r e n t 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 e s can operate a t the same time. I f t h e y occur s e q u e n t i a l l y t h e n the s t e a d y s t a t e s t r a i n  rate  observed d u r i n g c r e e p / w i l l be a s s o c i a t e d w i t h the slowest p r o c e s s , i . e .  the  p r o c e s s w i t h the h i g h e s t a c t i v a t i o n energy.' I f - t h e s t r a i n r a t e i s f i x e d as i s u s u a l i n a , t e n s i l e t e s t , . t h e n the magnitude o f the s t r e s s w i l l  reflect'the  p a r t i c u l a r c o n t r o l l i n g p r o c e s s i n t h a t any a c t i v a t i o n p r o c e s s occurs under the combined i n f l u e n c e o f t h e r m a l energy and the e f f e c t i v e  stress.  An example o f s e q u e n t i a l p r o c e s s e s would be the movement o f a jogged screw d i s l o c a t i o n d u r i n g p y r a m i d a l g l i d e i n a hexagonal m e t a l . must be s u p p l i e d f o r the n o n - c o n s e r v a t i v e motion  Energy  o f the j o g , f o r f o r e s t  i n t e r s e c t i o n , t o overcome the P e i e r l s s t r e s s and f o r p o s s i b l e c r o s s s l i p around  o b s t a c l e s . . I f t h i s , sequence o f processes, must occur b e f o r e  can p r o c e e d , t h e n one  deformation  o f the p r o c e s s e s w i l l be r a t e c o n t r o l l i n g . . W h i c h one  w i l l depend on the nature o f the e f f e c t i v e s t r e s s on.the d i s l o c a t i o n a t stage o f the p r o c e s s . The  stress w i l l  energy a v a i l a b l e a t t h a t temperature  i n c r e a s e , t o a v a l u e a t which the i s s u f f i c i e n t t o continue  any thermal  deformation  -148 a t the r e q u i r e d s t r a i n r a t e . Under such a s e q u e n t i a l system i t i s q u i t e p o s s i b l e t h a t t h e r a t e c o n t r o l l i n g p r o c e s s can change d u r i n g d e f o r m a t i o n from one o f t h e aforementioned  processes t o another.  - I f however, two o r more independent r a t e , then, the t o t a l s t r a i n r a t e i s g i v e n by  p r o c e s s e s c o n t o l the s t r a i n ^  a p p l i c a t i o n o f simple r a t e t h e o r y t o d e f o r m a t i o n  )( ^  and. t h e  i s not p o s s i b l e .  . I f i t assumed t h a t a s i n g l e p r o c e s s i s r a t e c o n t r o l l i n g from  then  (1)  =  A G  -kT  In-i/j  .........................(3)  I f i t i s now assumed t h a t a t a c o n s t a n t d i s l o c a t i o n c o n f i g u r a t i o n thei. s t r a i n r a t e i s g i v e n bjp  i  = i(  T,  ................ 4) (  t h e n by d i f f e r e n t i a t i n g . (4) w i t h i . r e s p e c t t o temperature s t r e s s and  at constant  effective  recombining  AG =  I  -kT /^m 2  c)T*\  +  T  /  G>AG\  S i n c e i n g e n e r a l the a c t i v a t i o n e n t r o p y i s g i v e n by  As =-MAG\  .......(6)  t h e n the a c t i v a t i o n e n t h a l p y i s g i v e n by  A H = -kT  2  /  3 m  i/i*  \  I  ................a)  -•149 -  The a c t i v a t i o n volume d e f i n e d as  v = bdl  ...(8)  ..................... where  b = Burgers v e c t o r d = a c t i v a t i o n distance 1 = length of d i s l o c a t i o n . undergoing a c t i v a t i o n .  i s g i v e n by the s t r e s s dependence o f  =-/_p\AG_\  v  =  AG  such t h a t  kT / din  jl  \  ..................  (|)  . T h e r e f o r e a c t i v a t i o n energy and a c t i v a t i o n volume can be determined from r e v e r s i b l e temperature and s t r a i n r a t e changes  during  d e f o r m a t i o n . P r o b a b l y the l a r g e s t source of e r r o r i n t h i s type o f c a l c u l a t i o n can be t r a c e d t o the l a c k o f r e v e r s i b i l i t y i n some systems. I f  , which  i s a f u n c t i o n o f the a c t i v e d i s l o c a t i o n d e n s i t y , changes d u r i n g the r a t e change, o f v,  AG,  t h e n the measured v a l u e o f A l  and  AH  calculated values  w i l l be i n e r r o r .  In o r d e r t o c a l c u l a t e  M i t r a and Dorn  AC-., i t i s n e c e s s a r y t o d e v e l o p an e x p r e s s i o n  ... / c) AG \  whereby the e n t r o p y term a l data.  and subsequent  strain  so  can be r e a d i l y e v a l u a t e d . from .experiment-  \ d T fa* u s i n g a g r a p h i c a l t e c h n i q u e have attempted such a  c a l c u l a t i o n but i n the p r o c e s s appear t o have i n t e r c h a n g e d f r e e energy and 74  e n t h a l p y . Schoeck  ±  n  a  c o n s i s t e n t thermodynamic treatment has a r r i v e d a t energy change ( t h e r m a l  AG = AH +  d  %  T  n  T  dn dT  P-  V  ..(10)  - 'I50 = T h i s he c l a i m s makes p o s s i b l e it  only  c o n t a i n s terms t h a t  However h i s f o r m u l a t i o n  can be e a s i l y determined from e x p e r i m e n t a l d a t a .  i s based on t h e q u e s t i o n a b l e r e l a t i o n s h i p  i  T h i s d i f f e r s from (4)  a simple c a l c u l a t i o n o f A G s i n c e  =  y  (  T,  T  )  a  i n t h e use o f t h e a p p l i e d  . . . . . . . . . . . . . . . . . . . . . . ( i i )  stress ^  instead  a  o f the  e f f e c t i v e s t r e s s Q'"*" . The s t r a i n r a t e f o r a g i v e n system under c e r t a i n conditions  o f temperature and a p p l i e d  stress i s associated  with a certain  .  r a t e c o n t r o l l i n g mechanism. T h i s mechanism operates under t h e combined influence  7  o f t h e t h e r m a l energy a v a i l a b l e and t h e e f f e c t i v e s t r e s s  Ultimately  therefore  •  t h e s t r a i n r a t e and t h e e f f e c t i v e s t r e s s a r e dependent  v a r i a b l e s and t h e dependence o f \  f  on t h e macroscopic f l o w s t r e s s  is  unjustified. If  1  i s substituted  T3. i n Schoeck s e x p r e s s i o n  for  r e l a t i o n s h i p s i m i l a r t o ( 1 0 ) but containing  T  instead  of T  (10), a  i s obtained. a  Because o f t h e unknown n a t u r e o f make any r e a s o n a b l e e s t i m a t e o f  J  during  deformation, i t i s d i f f i c u l t t o  AG.  Much o f t h e c o n f u s i o n i n t h e l i t e r a t u r e c o n c e r n i n g r a t e involves  t h e statement o f t h e b a s i c r a t e e q u a t i o n (1).. I t has been common  to substitute  it  expressions  ZVH, t h e e n t h a l p y change f o r /\G i n ( 1 ) . When t h i s i s done, • S/'k  i s assumed t h a t t h e e n t r o p y term  e x p o n e n t i a l term  Vo  e  i s incorporated  i n t o the p r e -  . This approximation of the rate equation i s v a l i d  only  i f t h e e n t r o p y change does n o t r e p r e s e n t a s i g n i f i c a n t c o n t r i b u t i o n t o t h e o v e r a l l f r e e energy change and i f i t does n o t v a r y a p p r e c i a b l y or  w i t h temperature  stress. 73 As  o u t l i n e d by Conrad.  , attempts have been made t o c a l c u l a t e t h e  energy o f a c t i v a t i o n , i n c l u d i n g t h e work done by t h e e f f e c t i v e s t r e s s  during  t h e r m a l a c t i v a t i o n . I n t h i s case t h i s " t o t a l " a c t i v a t i o n energy i s u s u a l l y  151 e x p r e s s e d as  AH = AH  +  0  Fd  ....(12)  :  where F= the f o r c e on the d i s l o c a t i o n segment Since  Fd  =  lbd^f*=  AH where  v j  = AH  0  represents  v j * ,  therefore  +  (15)  .  v i *  the work done by the a p p l i e d s t r e s s d u r i n g  thermal  activation. However the e n e r g i e s  i n (15)  represented  should  be  free  energies  so t h a t >  AG  D  = AG  v!r*  +  diagram i s shown i n F i g . 7 8  A t y p i c a l force distance the v a r i o u s  energy terms. The  term  a c t i v a t i o n energy s i n c e i t does not stress before  ained AG  o n l y i f the  = AG  can be  0  *  AG  AGo  must be  ;  0  l a b e l l e d o n l y as  illustrate  the"apparent"  t r u e a c t i v a t i o n energy i s g i v e n  force distance  curve  = 0  ). T h i s can be  by  ascertT =  0,  c r i t i c a l temperature where T  =  c o n d i t i o n s under which T • However even i f the  (AGo  are known. When  a c c u r a t e l y e s t a b l i s h e d , i t must be assumed t h a t the  curve does not  to  i n c l u d e the work done by the e f f e c t i v e  the a c t i v a t e d event. The  the t o t a l a r e a under the  (14)  change w i t h temperature i f the v a l u e  of AG„  force  0  distance  found a t  T c  i s a p p l i e d t o o t h e r temperatures where the i s thought t o o c c u r . Even i f the range o f temperatures, i f the t h e n f o r some p r o c e s s e s the  same r a t e c o n t r o l l i n g p r o c e s s  same p r o c e s s i s thought t o occur over a  s t a c k i n g f a u l t energy changes w i t h temperature  shape o f the  f o r c e - d i s t a n c e diagram can  change  w i t h temperature. The  c a l c u l a t i o n of AG  o  Is t h e r e f o r e  r e s t r i c t e d to  conditions  -152 -  ft* o f y i e l d when J can be e s t i m a t e d from t h e y i e l d s t r e s s - t e m p e r a t u r e r e l a t i o n ship . 11  Gregory  developed a s i m i l a r r e l a t i o n s h i p t o e x p r e s s i o n (13)  i n o r d e r t o c a l c u l a t e t h e " t o t a l " a c t i v a t i o n energy. However he used t h e applied and  stress  T  instead  can l e a d t o s e r i o u s  o f y*~ i n t h e l a s t term. T h i s i s u n j u s t i f i e d  errors  e s p e c i a l l y when  Ta '* jT . >  - 153 A G  =  VT* = A G  Q  =  AG* =  ABCA ACxgX-jA x-^Cx^x  x ABCx^x 0  B  Distance  Fig.  7 8  Typical.Force-Distance  curve f o r a t h e r m a l l y a c t i v a t e d process.  deformation  - 15+ APPENDIX  2  U n l o a d i n g Y i e l d P o i n t s i n Cadmium.  [  D u r i n g the e a r l y s t a g e s of d e f o r m a t i o n when c y c l i n g 25p. and kOOp. cadmium between -140°C and--196°C, s l i g h t y i e l d p o i n t s as shown i n F i g . 7 9 were observed on r e l o a d i n g a t T-196°C .  stress  strain  F i g . 79  -Unloading y i e l d p o i n t i n p o l y c r y s t a l l i n e  These made the d e t e r m i n a t i o n o f  Aer  cadmium  d i f f i c u l t because  o f the  ambiguity o f the y i e l d s t r e s s a t -196°C.  S e v e r a l authors have observed u n l o a d i n g y i e l d p o i n t s i n f . c . c .  100 m e t a l s . Haasen and K e l l y  101 and Makin  observed y i e l d p o i n t s i n s i n g l e  c r y s t a l s o f aluminum, copper and n i c k e l produced by u n l o a d i n g and They p o s t u l a t e d t h a t  reloading.  C o t t r e l l - L o m e r s e s s i l e s are produced d u r i n g u n l o a d i n g  c a u s i n g a h i g h e r y i e l d s t r e s s on r e l o a d i n g . Boiling  102  u s i n g p o l y c r y s t a l l i n e A g , " A l , Cu, N i and Pb, found t h a t  - 155 unloading  y i e l d p o i n t phenomena i s a common o c c u r e n c e i n f . c . c . . m e t a l s .  f u r t h e r observed,that  He  t h e m a g n i t u d e o f t h e s t r e s s i n c r e a s e was dependent on  t h e amount o f u n l o a d i n g  a n d - i n d e p e n d e n t o f time.. Y i e l d p o i n t s w e r e o n l y  however when r e c o v e r y d u r i n g t h e u n l o a d i n g  c y c l e Has  observed  negligible.  B i r n b a u m , t e s t i n g z i n c a n d m a g n e s i u m s i n g l e c r y s t a l s b e t w e e n 7 7 C~ and  293°K f o u n d n o y i e l d p o i n t s a f t e r r e l o a d i n g . F u r t h e r h e o b s e r v e d  c o p p e r s i n g l e c r y s t a l s , t h e m a g n i t u d e o f t h e s t r e s s i n c r e a s e was  that i n  orientation  i n d e p e n d e n t , a n o b s e r v a t i o n n o t c o n s i s t e n t w i t h t h e c o n c e p t o f C o t t r e l l - "•L o m e r s e s s i l e p r o d u c t i o n . He t h e r e f o r e p o s t u l a t e d t h a t a c h a n g e o c c u r s unloading  i n the nature  of glide-forest dislocation  during  interactions.  In order t o obtain a b e t t e r understanding  of the y i e l d  phenomena  i n c a d m i u m , 25u a n d kOOp, s p e c i m e n s w e r e e x a m i n e d V a t -196°C. T h e y w e r e ormed u s i n g 2$ s t r a i n i n c r e m e n t s  followed by unloading  t o a given  of t h e f l o w s t r e s s . Specimens were t h e n h e l d f o r v a r i o u s p e r i o d s before  def-  percentage o f time  reloading. I t was f o u n d t h a t t h e h o l d i n g t i m e  up t o f i v e m i n u t e s h a d n o e f f e c t  on t h e m a g n i t u d e o f t h e f l o w s t r e s s o n r e l o a d i n g . H o w e v e r t h e o c c u r r e n c e y i e l d p o i n t s was a f u n c t i o n o f t h e amount o f u n l o a d i n g b y B o i l i n g . No y i e l d p h e n o m e n a was o b s e r v e d was  observed^  u n t i l a t l e a s t 40$ o f t h e l o a d  removed. -At  low values  increasing deformation, observed  of strain  a  cr  ( F i g . 80  a  ) , However w i t h o~ . B o i l i n g c  and e x p l a i n e d i t i n terms o f creep  during the  cycle. Fig. 8l illustrates  strain.  o~ =  o*" became somewhat g r e a t e r t h a n  s i m i l a r behaviour  unloading  I n a l l cases  the variation of  0^/05  with increasing  s p e c i m e n s w e r e u n l o a d e d t o 10$ o f t h e f l o w s t r e s s a n d  h e l d f o r f i v e minutes before and  as p r e v i o u s l y  of  took about t e n seconds.  r e l o a d i n g . The u n l o a d i n g  o p e r a t i o n was  continuous  -156 -  Fig.Qp  Unloading y i e l d point  terminology  - 157 I t i s observed from F i g . 8 l  t h a t the y i e l d e f f e c t i s c o n s i d e r a b l y  g r e a t e r in.400u cadmium t h a n i n 25". The v a l u e s o f  ^b/c%  remain approx-  i m a t e l y c o n s t a n t up t o a v a l u e o f s t r a i n which has been p r e v i o u s l y i d e n t i f i e d w i t h t h e s t a r t o f dynamic r e c o v e r y a t -196°C. Beyond t h i s v a l u e o f s t r a i n , Ob/og  decreased and t h e y i e l d e f f e c t g r a d u a l l y d i s a p p e a r e d . Specimens were a l s o t e s t e d a t -95°C and no y i e l d e f f e c t s were  observed.  I n f a c t s l i g h t s t a t i c r e c o v e r y o c c u r r e d . The drop i n s t r e s s assoc}  i a t e d w i t h u n l o a d i n g and: t h i r t y second h o l d i n g a t 10$ o f t h e flow i s shown as a f u n c t i o n o f t h e flow s t r e s s i n F i g . 82  .Therefore d u r i n g  C o t t r e l l - S t o k e s t e s t s , a p p r o p r i a t e c o r r e c t i o n s were made t o  i n t o account temperatures.  stress,  A o~ AT  t o take  t h e s t a t i c r e c o v e r y o c c u r r i n g d u r i n g t h e o p e r a t i o n o f changing  -158 -  - 159 -  Fig.82  The decrease i n flow s t r e s s due t o s t a t i c r e c o v e r y d u r i n g i n t e r r u p t e d t e s t i n g o f 25u cadmium a t -95°C. ( 30 second h o l d i n g a t 10$ o f the f l o w s t r e s s ).  .-•i6o APPENDIX  The D e t e r m i n a t i o n  o f A°~  j  f r o m - S t r a i n Rate Change T e s t s  An i d e a l s t r a i n r a t e change s h o u l d occur i n an ;  instantaneous  f a s h i o n without an i n t e r m e d i a t e drop i n l o a d o r a measurable time l a g d u r i n g the change. These f a c t o r s become o f extreme importance i f one i s a t t e m p t i n g t o a n a l y z e m a t e r i a l s a t h i g h e f f e c t i v e temperatures  When u s i n g an Instron, m e c h a n i c a l  where r e c o v e r y can occur.  d i f f i c u l t i e s a r e sometimes  r e s p o n s i b l e f o r a c o n s i d e r a b l e e r r o r i n the d e t e r m i n a t i o n o f ACT . A l t h o u g h i  the I n s t r o n used d u r i n g t h i s work was equipped crosshead  speed change, a c o n s i d e r a b l e time l a g was observed  c r e a s e i n s t r a i n r a t e . When t h e crosshead to  ,002"/min. t h e r e was a d e l a y time  machine stopped. When changing was  w i t h an automatic  of  push b u t t o n  d u r i n g a de-r  speed was changed from  .02"/min.  1.6 seconds d u r i n g which time the  from .2"/min. t o .02"/min. the d e l a y  time  .8 seconds. However a t these h i g h e r speeds t h e r e was a l s o a s l i g h t  r e v e r s a l o f the screws d u r i n g the change which caused a.drop i n l o a d on the specimen. There was no measurable d e l a y time a s s o c i a t e d w i t h a change t o a n . i n c r e a s e d crosshead  speed. T h e r e f o r e a l l j A " 0  v a l u e s were o b t a i n e d  d u r i n g an i n c r e a s e i n s t r a i n r a t e . In many m a t e r i a l s i t i s n e c e s s a r y t o obtain  Ao~  from a decrease i n s t r a i n r a t e because o f t h e appearance o f  d i s t i n c t y i e l d p o i n t s on i n c r e a s i n g the s t r a i n r a t e . F o r t h i s work i t was d e c i d e d t h a t any e r r o r a r i s i n g from any' s l i g h t y i e l d phenomenon would be much l e s s than t h a t r e s u l t i n g from t h e time dellay d u r i n g a decrease rate.  i n strain  -.:i6l Fig.83  i l l u s t r a t e s t h e nature  o f the change i n flow s t r e s s  d u r i n g s t r a i n r a t e change t e s t s under v a r i o u s c o n d i t i o n s .  (a)  below  T  = .26  i n l i n e a r hardening  regions .  v  Fig.83  The nature o f the flow s t r e s s o b t a i n e d tests i n polycrystals  d u r i n g s t r a i n r a t e change  - 162 Obtaining  values  a t low temperatures was r e l a t i v e l y  easy  because o f t h e abrupt n a t u r e o f y i e l d a f t e r a change i n s t r a i n r a t e ( F i g . 83 a) . W i t h i n c r e a s i n g s t r a i n however y i e l d became more g r a d u a l t o that obtained  a t a l l values  Under t h e s e c o n d i t i o n s  similar  o f s t r a i n a t temperatures above  /L\a~ was obtained  and work h a r d e n i n g r e g i o n s . ( F i g . 8 3  = .26 .  by e x t r a p o l a t i n g the e l a s t i c  b) .  As t h e temperature i n c r e a s e d  t o the r e g i o n of  T  = .hO a  i t became extremely d i f f i c u l t t o o b t a i n r e l i a b l e v a l u e s  o f Ao~  because  of t h e almost c o m p l e t e l y p a r a b o l i c n a t u r e o f y i e l d a f t e r an i n c r e a s e i n s t r a i n rate  (Fig.83 c ) . F o r t h i s reason r a t e t h e o r y  not attempted above ;  c a l c u l a t i o n s were  = .k-0  T H  Some work s o f t e n i n g o c c u r r e d at a l l temperatures above  on d e c r e a s i n g  the s t r a i n  T .= .26 .=This gave f i s e . t o a more H  rate  gradual  decrease i n t h e observed flow s t r e s s a f t e r the s t r a i n r a t e change had been made. T h i s became more pronounced w i t h i n c r e a s i n g temperature ( F i g . 83 c ) . I f the l o a d was removed and immediately r e a p p l i e d ifenefe was no evidence o f any y i e l d p o i n t w h i c h i s u s u a l l y a s s o c i a t e d w i t h work s o f t e n i n g . However y i e l d p o i n t s were observed d u r i n g  s t r a i n r a t e changes  ok on cadmium s i n g l e c r y s t a l s s i m i l a r t o t h o s e r e p o r t e d by Langenecker i n aluminum and z i n c . I t would t h e r e f o r e appear t h a t i n p o l y c r y s t a l s a t e l e v a t e d temperatures c o n s i d e r a b l e  d i s l o c a t i o n rearrangement can o c c u r  i n t h e time n e c e s s a r y f o r a d e c r e a s e i n s t r a i n r a t e . One i s f a c e d w i t h the difficulty  o f e s t a b l i s h i n g the flow  s t r e s s along  a-b (Fig.83 c) a t which  y i e l d i s o c c u r r i n g a t the reduced s t r a i n r a t e . S i n c e i n v o l v e s up t o a t l e a s t .5$ s t r a i n t h e r e determination  t h i s region usually  i s considerable  r e a l l y r e f l e c t s a r e v e r s i b l e change.  doubt i f any such  - 163 Some ambiguity  i s a l s o 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 s t r a i n 1  r a t e . However i t s h o u l d be somewhat l e s s due t o the absence of the d e l a y times observed d u r i n g a decrease Tg = .kO  t h e work hardening  i n s t r a i n r a t e . A t temperatures  above  r a t e a f t e r an i n c r e a s e i n s t r a i n . r a t e i s not  s u f f i c i e n t l y l i n e a r t o a l l o w f o r an e x t r a p o l a t i o n as i n Fig.83  b . Under  such c o n d i t i o n s A<3~ s h o u l d be o b t a i n e d by e x t r a p o l a t i n g the work hardening r a t e a t a c e r t a i n c o n s t a n t vjalue o f s t r a i n  1  (Fig.83 c ) .  - 164 BIBLIOGRAPHY'',.  1)  E . Macherauch,  55, 91, (1964)..  2)  L.M. C l a r e b r o u g h and M.E. Hargreaves,  Z. Msrtallkunde,  Progress i n Metal Physics  8, .5)  P.B. F e l t h a m and J.D. Meakin,  4)  B. R u s s e l l and D. J a f f r e y ,  5)  S.K. M i t r a and J . E . Dom,  6)  H. Conrad and S. F r e d e r i c k ,  7)  H. Conrad and. L. Hayes,  •8) 9) 10  H. .Conrad,  T r a n s . A.I.M.E.•.227,  (1957)-  1015,  56, 249, (1963)-  I98, 364, (I96I). 8, 791, (i960).  A c t a Met.,  5_, 745, (i960).  11  D. P. Gregory, A.N. S t r o h and G.H. Rowe,  12  Z.S. 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