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Deformation of alpha-uranium. St. John, Charles Falding 1964

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DEFORMATION OF ALPHA-URANIUM  -BY  CHARLES' FALDING .ST. JOHN . . B . A . S c . , . The U n i v e r s i t y of B r i t i s h C o l u m b i a ,  1962  A.THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE. REQUIREMENTS'FOR.THE DEGREE.OF MASTER .OF APPLIED .SCIENCE  i n the  Department of  METALLURGY  We a c c e p t t h i s standard  t h e s i s as  conforming t o  r e q u i r e d from c a n d i d a t e s  the  for.the  degree of MASTER OF ' APPLIED. ,SC IENCE.  .Members o f the Department of M e t a l l u r g y  THE:UNIVERSITY OF BRITISH.COLUMBIA September,.196^  In presenting t h i s the  requirements  for  B r i t i s h Columbia, available mission  for  for  I  an a d v a n c e d agree that  reference  extensive  representatives.  cation  of t h i s  Department  of  It  thesis  w i t h o u t my w r i t t e n  and s t u d y .  by the  further thesis  agree for  that  freely per-  scholarly or by  t h a t , c o p y i n g or  f i n a n c i a l g a i n s h a l l not  permission*  1964  the U n i v e r s i t y o f  Head o f my Department  Metallurgy  October 1,  I  this  The U n i v e r s i t y o f B r i t i s h C o l u m b i a , V a n c o u v e r 8, Canada Date  at  f u l f i l m e n t of  L i b r a r y s h a l l make i t  i s understood  for  in partial  degree  the  copying of  p u r p o s e s may be g r a n t e d his  thesis  publi-  be a l l o w e d  ABSTRACT  . An i n v e s t i g a t i o n as t o the  characteristics  o f f l o w and  f o r a l p h a - u r a n i u m were c a r r i e d out over the temperature to 270°C.  -The parameters r e l e v a n t  range  fracture  -196°C  t o g r a i n s i z e and s t r a i n r a t e were  investigated. It  was e s t a b l i s h e d , t h a t  i n the s e m i - b r i t t l e (l/D^^) .  the flow s t r e s s a n d . t h e  fracture  region vary,-linearly with-the grain size  stress  parameter  E v i d e n c e suggests t h a t ' t h e s e n s i t i v i t y of f l o w s t r e s s t o  s i z e i s d i r e c t l y , r e l a t e d . t o the  grain  importance of g l i d e d i s l o c a t i o n a c t i o n  a's. the d e f ormation mode.  •• S t r a i n r a t e change i r r e v e r s i b i l i t y was found t o exist- at strains  f o r a l l .temperatures  w i t h the e f f e c t  investigated.  of g r a i n s i z e ,  i n d i c a t e s t h a t massive  occur i n the e a r l y stages of f l o w . microscopy r e s u l t s  This evidence,  correlated  structural  T h i s agrees w i t h e l e c t r o n  as e s t a b l i s h e d b y other  workers.  low  changes  transmission  ACKNOWLEDGEMENT  The a u t h o r w o u l d l i k e t o e x t e n d h i s t h a n k s t o h i s r e s e a r c h d i r e c t o r , - Dr. E. T e g h t s o o n i a n , f o r guidance t h r o u g h o u t the, c o u r s e o f t h i s work.  Thanks a r e a l s o extended t o R . J . R i c h t e r f o r t e c h n i c a l  a s s i s t a n c e , • M i s s J . K n i f f e n f o r m a n u s c r i p t p r e p a r a t i o n and t o f e l l o w g r a d u a t e s t u d e n t s and f a c u l t y members f o r t h e i r h e l p f u l a d v i c e .  F i n a n c i a l s u p p o r t was r e c e i v e d from, t h e Canadian Uranium :  Research Foundation i n the form o f r e s e a r c h f e l l o w s h i p s . i s g r a t e f u l l y acknowledged.  .This s u p p o r t  TABLE OF CONTENTS Page I. • II.  INTRODUCTION . . . .  1  EXPERIMENTAL  5  A. M a t e r i a l  5  .B..Tensile Specimen Preparation :  6  .  1 . . R o l l i n g Schedules . 2 . Specimen Dimensions  6 8 8  J . . R e c r y s t a l l i z a t i o n Procedures  9  • C . Metallography- and G r a i n S i z e D e t e r m i n a t i o n • D . • T e n s i l e Experiments E . Temperature  .  .10  :  11  Control  . I I I . EXPERIMENTAL.RESULTS  1  12  - A.. R o l l i n g and Beta Quenching 1. Hot R o l l i n g . 2.. C o l d . R o l l i n g and Beta Quenching :  12 13  5..Warm R o l l i n g B. G r a i n Growth 1.  13 13  .  13  C r i t i c a l S t r a i n Anneals  2 . . L a r g e S t r a i n Anneals  15 16  C. T e n s i l e Experiments 1.  General.Flow. C h a r a c t e r i s t i c s  16  2. G r a i n S i z e S e n s i t i v i t y o f Flow 3 . S t r a i n Rate S e n s i t i v i t y o f Flow k,- F r a c t u r e and D u c t i l i t y  22 37 50 59  D. - Summary, o f R e s u l t s . IV.  2  DISCUSSION • A.. G e n e r a l Flow C h a r a c t e r i s t i c s 1.  63  . . . .  .  63  Parabolic Beginning  . 2. Work Hardening (a) Region I ....... (b) Region I I .3. Temperature. Dependence o f Flow S t r e s s  63  . . . . .  6k 6k 67 70  - Table o f Contents  Continued Page  B. G r a i n S i z e S e n s i t i v i t y 1.  71  o f Flow  l/2 (a) A p p l i c a b i l i t y o f ( l / D ) Parameter (b) P i l e - U p T h e o r i e s (c) G r a i n Boundary Source Theory . 2.  71  P e t c h Slope as a F u n c t i o n o f S t r a i n  P e t c h Slope as a -Function o f Temperature . (a). P.ile-Up T h e o r i e s . (b) G r a i n Boundary- Source Theory (c) D i s l o c a t i o n ' M o b i l i t y :  . . . .  71 , 75 78 80 80 8l ; 8l  3. -Petch Slope as a F u n c t i o n o f O r i e n t a t i o n  8k  k.  86  Characteristics  ,C. S t r a i n Rate S e n s i t i v i t y  o f Flow  .  87  1..Irreversibility . 2 . - A c t i v a t i o n Volumes D. F r a c t u r e and D u c t i l i t y 1. F r a c t u r e 2. D u c t i l i t y  87 95 9I4. gk 95  V.  -CONCLUSIONS  96  VI.  APPENDICES  97  V I I . - REFERENCES  1  1  1  vi. • LIST OF FIGURES  Figure 1.  Page  • A s - r e c e i v e d M a t e r i a l Showing Secondary'Phases  2.  Specimen Dimensions  3.  Microstruetures•of (c)  'k. E f f e c t  (a)  Hot R o l l e d , . ( b ) . Beta Quenched,  lh  o f Temperature on T e n s i l e Curve Form  6.  • Temperatures Comparison o f T e n s i l e Curves . Preferred  Orientation  17  with Strain  .19  .  ...  .  ...  .  .  .  Effect  o f Temperature on Flow- S t r e s s at  8.  Effect  o f Temperature on the S t r a i n - H a r d e n i n g  T r a n s i t i o n Region  11. 12. 13.  lh.  .  for  of .Specimens w i t h Random and  7.  10.  and  Warm.Rolled M a t e r i a l  V a r i a t i o n o f S t r a i n Hardening Exponent  Effect  .  .  .20  6 Per Cent S t r a i n  .  .  of G r a i n S i z e on S t r a i n Hardening Exponent  21  . . . .  23  . . . . . . .  2h  V a r i a t i o n - o f Flow S t r e s s w i t h G r a i n S i z e f o r S e r i e s E-*X-2 (-196°C) V a r i a t i o n o f Flow S t r e s s w i t h G r a i n S i z e f o r S e r i e s E - X - l (20°C) . V a r i a t i o n o f Flow S t r e s s w i t h G r a i n S i z e f o r S e r i e s E.-X.-4 (100°C) V a r i a t i o n o f Flow S t r e s s w i t h G r a i n S i z e (270°C) and S e r i e s E - X - 5 (170°C)  for'Series  25 26 27  E-X-3 28  V a r i a t i o n o f Flow S t r e s s w i t h G r a i n S i z e f o r ' S e r i e s  A-X-l 30  15.  V a r i a t i o n of k w i t h - S t r a i n  16.  V a r i a t i o n of k w i t h S t r a i n f o r S e r i e s A,  18.  .  Exponent  (20°C)  17.  6 8  !§.  9.  . . . . . . . . .  -Effect  of Temperature on  f o r S e r i e s D and E . . . . . . . . .  Cmax.and  V a r i a t i o n of Maximum a n d ' C o n s t a n t f o r S e r i e s D and-E ... .  19.  V a r i a t i o n of  .20.  . Comparison o f for-Series  32  ^const.  .  .  ....  .  .  . 33  k V a l u e s w i t h Temperature . ... . . . . - 3 5  with S t r a i n f o r : D and.E Series  \T°  31  36  Curve f o r S e r i e s . A w i t h T e n s i l e Curve B  38  List  Figure 21.  - A T y p i c a l S t r a i n R a t e . Change T e s t  22.  .Extrapolation  23.  .30..  31.  32.  .33-  .36.  37-  .  39  .......  .  kO  170°C and- 270°C  -kl  average f o r - I n c r e m e n t a n d Decrement  -196°C, 20°C and 100°C  \2  I A T " \ V e r s u s Per Cent S t r a i n f o r Increment and Decrement A £ at 170°C and- 270°C E f f e c t of Temperature on S t r a i n at Change R e v e r s i b i l i t y .  S t a r t of S t r a i n Rate . . . . . . . . . ...  E f f e c t o f G r a i n S i z e on S t r a i n Rate Change Series-E-X-4 (100°C)  kj>  .  kk  .  kS  ^7  - A c t i v a t i o n Volumes as a F u n c t i o n of S t r e s s f o r S t r a i n Rate Changes . A c t i v a t i o n Volumes as a . F u n c t i o n S t r a i n Rate Changes  .  .  Sensitivity-for  Decrement  of S t r a i n f o r  kQ  Decrement 49  A c t i v a t i o n Volumes as a F u n c t i o n o f S t r e s s f o r Increment S t r a i n Rate Changes - A c t i v a t i o n Volume as a F u n c t i o n - o f S t r a i n f o r S t r a i n Rate Changes . Fracture'Modes, C r a c k , , (c)  (a). T r a n s c r y s t a l l i n e C a v i t a t i o n Voids  Crack,  Increment '  (b)'  • J>k. . V a r i a t i o n o f F r a c t u r e • S t r e s s w i t h G r a i n S i z e at ;.20°C f o r S e r i e s D and E .35.  .  V e r s u s Per Cent S t r a i n f o r Increment and Decrement cJk. at 20°C and 100°C . . . . . . . . . . . . . . .  25.  29.  Method f o r S t r a i n Rate Change A n a l y s i s  Versus at  28.  .  ;  2k.  27.  • Page  |/VT| V e r s u s T " average f o r Increment and Decrement at  26.  vii.  of Figures Continued  . V a r i a t i o n o f F r a c t u r e S t r e s s w i t h G r a i n - S i z e at and 270°C f o r S e r i e s D and E . . . - E f f e c t of Temperature and E Effect  of Temperature  for Series  .  52  Intercrystalline 53 -196°C and 55 100°C,  170°C 56  on F r a c t u r e - P e t c h Slope- f o r S e r i e s D .  57  o n - F r a c t u r e S t r e n g t h and P e t c h I n t e r c e p t  D and-E  38".  Effect  of Temperature  39-  Effect  of C o l d R e d u c t i o n on A n n e a l e d , G r a i n S i z e f o r  - A and B  .51  58  on D u c t i l i t y .  60 Series 99  viii. List  of Figures  Continued  Figure  Page 1/2  kO.  l/D  kl.  Histogram S h o v i n g G r a i n S i z e D i s t r i b u t i o n f o r Three G r a i n S i z e s from S e r i e s E  101  A r r h e n i u s P l o t o f G r a i n S i z e and A n n e a l i n g Temperatures Series D and,E  103  h2.  as a F u n c t i o n of D  100  for  LIST.. OF TABLES Page Table I . Table I I .  List  of T y p i c a l Reactor Grade.Impurities  .Temperature C o n t r o l Media  . . . . .  5 H  . I . • •INTRODUCTION Much a t t e n t i o n  i n r e c e n t years has been d i r e c t e d , t o w a r d s  p h y s i c a l p r o p e r t i e s , of a l p h a - u r a n i u m - a s a r e s u l t development.  the  of r e a c t o r m e t a l l u r g y  The m a j o r i t y o f t h i s . w o r k , however, has been  w i t h f a b r i c a t i o n and heat treatment o f r e a c t o r f u e l r o d s .  associated The n a t u r e  of  1_R the d e f o r m a t i o n systems p e r se have a l s o been e x t e n s i v e l y examined  .  The e x a c t i n t e r r e l a t i o n between the m i c r o s c o p i c d e f o r m a t i o n modes and the macroscopic  t e n s i l e b e h a v i o u r i s not w e l l known.  d i s l o c a t i o n theories ,to alpha-uranium.  In p a r t i c u l a r ,  current  of y i e l d i n g and work h a r d e n i n g have not been a p p l i e d  The r e l a t i v e l y abnormal p r o p e r t i e s , of a l p h a - u r a n i u m as  compared t o f . c . c  or h . c . p . metals presumably has been the  deterring  factor. ,The c r y s t a l l © g r a p h i c c o n f i g u r a t i o n o f a l p h a - u r a n i u m . i n unique i n that, the atoms form corrugated, l a y e r s lattice metals  points.  t h a t do not l i e on the  Moreover, the orthorhombic l a t t i c e  very'rarely  orthorhombic occurs  and i s more o f t e n a s s o c i a t e d w i t h c o v a l e n t l y bonded m a t e r i a l s .  structure  therefore  presents  which i n t u r n cause e l a s t i c  s t r o n g l y a n i s o t r o p i c bonding and p l a s t i c  anisotropies.  for The  characteristics  - A comparison between  the. t e n s i l e behaviour- of a l p h a - u r a n i u m and t h a t of the more common m e t a l s , with r e s p e c t . t o established d i s l o c a t i o n t h e o r i e s ,  would make an  interesting  study. - A g r a i n s i z e study w i t h r e s p e c t t o a l p h a - u r a n i u m d e f o r m a t i o n was chosen b e c a u s e . o f  the a b i l i t y - t o d e r i v e m i c r o s c o p i c b e h a v i o u r as  by d i s l o c a t i o n t h e o r y from a . r e l a t i v e l y  predicted  simple a n a l y s i s of t e n s i l e  curves.  • Many.-of the more common-metallic systems have been subjected^ t o g r a i n s t u d i e s - t h e r e b y making a v a i l a b l e s u i t a b l e  comparisons.  size  --2 -  The r e l a t i o n between y i e l d or flow s t r e s s , T~ , • a n d , t h e D, was f i r s t proposed by H a l l  T  =  £>  and- l aate t e ri b y P e t c h  7  and  grain  size,  co-workers.  1/2  T °  + k/D  where ^q-  = s t r e s s r e s i s t i n g flow i n the absence of any g r a i n boundary i n f l u e n c e D = s u b g r a i n or g r a i n s i z e k •;= c o n s t a n t f o r any s t r a i n . 0  T h i s r e l a t i o n was found a l s o t o be a p p l i c a b l e t o the f r a c t u r e  strengths  Q  8 and d e t a i l e d a n a l y s e s to account.for  have been advanced by C o t t r e l l  the d u c t i l e - b r i t t l e  proposed t o account  f o r the  and l a t e r by Johnson  t r a n s i t i o n of b . c . c .  metals.  .Theories  k parameter i n terms of d i s l o c a t i o n t h e o r y may  be c l a s s i f i e d as those w h i c h i n v o l v e d i s l o c a t i o n p i l e - u p s a n d ,  alternatively,  those w h i c h i n v o l v e g r a i n boundary d i s l o c a t i o n d o n a t i o n s . • The m i c r o s c o p i c mechanism suggested by H a l l and P e t c h a pile-up.of dislocations  of l i k e  s i g n generated  involves  f r o m . a Frank-Read  source.  The y i e l d i n g or f l o w occurs when the p i l e - u p e x e r t s s u f f i c i e n t s t r e s s the g r a i n boundary so t h a t p l a s t i c to another.  . The P e t c h s l o p e ,  k,  d e f o r m a t i o n can propagate  at  from one g r a i n  f o r t h i s mechanism has been shown t o be" "^ 1  -  1/2  TT.(1 - ^ ) Lp where  I f the  T i ~ lp = jl b =  average s t r e n g t h of boundary average p i l e - u p . l e n g t h shear modulus Burgers V e c t o r Poissons. R a t i o  s l i p bands e x t e n d . t h r o u g h o u t  be independent o f g r a i n s i z e .  the g r a i n , t h e n  the r a t i o  A m o d i f i c a t i o n and e x t e n s i o n  (D/lp)  will  of P e t c h ' s  8 mechanism was l a t e r suggested by C o t t r e l l force  .  P i l e - u p s i n t h i s case d i d not  d i s l o c a t i o n s t h r o u g h g r a i n boundaries but a c t i v a t e d  sources i n adjacent g r a i n s .  The r e s u l t i n g • s t r e s s  other  relaxation  Frank-Read  allowed  -3  Lttders band p r o p a g a t i o n from one g r a i n t o a n o t h e r . the  -  C o t t r e l l . obtained  following k r e l a t i o n , 1/2  * - r, where  7  *  ^Tp = u n p i n n i n g s t r e s s o f Frank-Read sources ^ l / 2 = average d i s t a n c e between the Frank-Read sources and g r a i n boundary. 11  Armstrong et a l .  s u b s e q u e n t l y extended C o t t r e l l s mechanism t o i n c l u d e  f l o w o t h e r t h a n j u s t y i e l d and Lttders band p r o p a g a t i o n . t e n s i l e curve can t h e r e b y be s u b j e c t e d . t o  a Petch a n a l y s i s ;  • An i m p o r t a n t o b j e c t i o n t o t h e o r i e s is. the l a c k o f d i r e c t  The e n t i r e  involving dislocation pile ups T  o b s e r v a t i o n of t h i s c o n f i g u r a t i o n i n many m e t a l s .  A l t e r n a t i v e l y , . d i s l o c a t i o n s have been o b s e r v e d . t o be generated boundaries, or o t h e r  from g r a i n  interfaces  a n d - t o form t a n g l e s at e a r l y stages of s t r a i n 13 •Based on these o b s e r v a t i o n s L i has p r o p o s e d a mechanism.in w h i c h g r a i n boundary l e d g e s donate d i s l o c a t i o n s i n e a r l y - s t a g e s .  The f l o w s t r e s s was  l/2 shown t o be a  l/D '  f u n c t i o n o f g r a i n s i z e based on d i s l o c a t i o n - d e n s i t i e s .  The k s l o p e was p r e d i c t e d . t o b e ,  0\ u  where  m  b ji  Li  b  ^8m^  . „ YL/2  = ledge d e n s i t y on g r a i n b o u n d a r i e s = k parameter on d i s l o c a t i o n = " depending ' about 0 . 4 = Eurgers V e c t o r .= shear modulus.  showed t h a t the s t r e n g t h s  strength,•Frank-Read'source  arrangement,  r e l a t e d t o each mechanism - g r a i n boundary strength,  and d i s l o c a t i o n d e n s i t y s t r e n g t h -  are a l l a p p r o x i m a t e l y e q u i v a l e n t w i t h r e s p e c t t o the magnitude o f k .  12  -k  The o b j e c t  of t h i s  study i s to i n v e s t i g a t e  dependence of f l o w and f r a c t u r e The e f f e c t  the g r a i n  i n terms of the v a r i o u s  size  proposed;theories.  of s t r a i n r a t e i s a l s o examined as means of p r o c u r i n g  complementary and independent e v i d e n c e . s t u d y encompasses,the  ductile-brittle  • The,temperature  transition.  -  range  under  II.  EXPERIMENTAL  A. M a t e r i a l The uranium for. t h i s s t u d y was  s u p p l i e d by-the Atomic Energy  Company-of Canada L i m i t e d , C h a l k R i v e r , i n t h e form ©f c y l i n d r i c a l r e a c t o r f u e l rods. 3 / 8  i n c h i n d i a m e t e r . . F u e l . r o d s a r e produced by a  hot r o l l i n g s c h e d u l e f o l l o w e d by a b e t a a n n e a l t o e l i m i n a t e , as much as p o s s i b l e , a n y - p r e f e r r e d  orientation.  -A t y p i c a l a n a l y s i s f o r r e a c t o r grade uranium i s shown i n T a b l e I  TABLE I . L i s t o f T y p i c a l R e a c t o r Grade I m p u r i t i e s ,.P_pm .. Carbon Hydrogen -Chloride Silica Nitrogen - Iron -Manganese Chromium Nickel Magnesium The p r i n c i p a l i s t h e c u b i c isomorphous  '  kOO 1 5 50 50 50 .13 . 20 .kO 5  s e c o n d a r y phase p e c u l i a r t o r e a c t o r grade uranium s e r i e s UN, UQ. and UO.  These may  f o r m as i n d i v i d -  u a l compounds or they-may form s o l u t i o n s w i t h each o t h e r , as U(C,N) or U(0,C,N). -A t y p i c a l p h o t o m i c r o g r a p h i s shown i n F i g u r e  1.  - 6  -  150X F i g u r e 1.  As-received  B. T e n s i l e Specimen 1.  M a t e r i a l Showing Secondary Phases  Preparation  R o l l i n g Schedules Two d i s t i n c t r o l l i n g s c h e d u l e s e r i e s were i n i t i a t e d i n o r d e r t o  produce f l a t t e n s i l e specimens w i t h s u i t a b l e m e t a l l u r g i c a l h i s t o r i e s . S e r i e s 1.  - t o produce upon a n n e a l i n g  a range o f g r a i n s i z e w i t h a  minimum o f p r e f e r r e d o r i e n t a t i o n . Series 2.  -  t o produce upon a n n e a l i n g  a range o f g r a i n s i z e w i t h a h i g h  degree of p r e f e r r e d o r i e n t a t i o n . Three r o l l i n g s c h e d u l e s were u t i l i z e d i n an attempt t o induce s t r e s s e s s u f f i c i e n t t o cause r e c r y s t a l l i z a t i o n w i t h a minimum o f p r e f e r r e d orientation.  - 7 -  Schedule A - hot r o l l  (625°C) t o 80 p e r cent r e d u c t i o n i n t h i c k n e s s  - a n n e a l i n . b e t a range (725°C) f o r 15 m i n u t e s t h e n quench i n water - remove oxide i n 8 I HN0  3  (20°C) from 0 t o 2.5 p e r cent r e d u c t i o n i n t h i c k n e s s .  - cold r o l l  Schedule B - same.as Schedule A b u t w i t h o u t the water • Schedule C - same as Schedule A b u t w i t h o u t the c o l d  One  rolling  quench rolling.  schedule-was adapted.to induce a h i g h degree o f  p r e f e r r e d o r i e n t a t i o n i n the r e c r y s t a l l i z e d  specimens.  • Schedules. D and' E - hot r o l l . (625°C) r o d . t o a r e c t a n g u l a r  cross-section  - warm r o l l ( 3 0 0 ° C ) t o 4 0 p e r cent r e d u c t i o n i n t h i c k n e s s - vacuum a n n e a l a t - warm r o l l  525°C  f o r 1 hour  (300°C) t o 90 p e r cent r e d u c t i o n o f r e m a i n i n g  thickness.  • A l l r o l l i n g was c a r r i e d out on a .2 h i g h , k i n c h r o l l i n g equipped w i t h a. v e n t i l a t i o n hood.to p r e v e n t i n g e s t i o n o f . U 0  2  i n s u r e c o n t i n u i t y o f r o l l i n g temperature t h e maximum r o l l i n g was  mill  d u s t . ,To speed o f 14-5 f t / m i n  used and t h e s t r i p was r e h e a t e d - a f t e r each p a s s .  • The h e a t i n g medium, used i n . t h e h o t r o l l i n g • o p e r a t i o n s  consisted  of a e u t e c t i c m i x t u r e o f 35 weight p e r cent LiC03 and 65 weight p e r cent K C0 2  3  salts.  T h i s c o m p o s i t i o n has a . f r e e z i n g p o i n t of,510°C and an upper  w o r k i n g range s u f f i c i e n t  f o r b e t a heat t r e a t i n g .  medium was a h i g h f l a s h - p o i n t  The warm r o l l i n g  (360°C) p e t r o l e u m base o i l .  -AH  heating  cutting  o p e r a t i o n s were done.under water because o f t h e p y r o p h o r i c n a t u r e o f uranium.  . - 8 2. Specimen Dimensions F l a t t e n s i l e specimens were c h o s e n . f o r t h i s work f o r two r e a s o n s ; f i r s t , , t o f a c i l i t a t e pre-deformation m e t a l l o g r a p h i c examination,•and s e c o n d , . t o a v o i d the d i f f i c u l t i e s i n v o l v e d w i t h t h e m a c h i n i n g o f uranium.  T e n s i l e specimens were stamped from.the r o l l e d . s t r i p p r i o r , t o the  r e c r y s t a l l i z a t i o n p r o c e d u r e and had t h e f o l l o w i n g d i m e n s i o n .  ••2.20"-  1.20" 0.80  "I  o OJ  C—  T j  F i g u r e 2.  -Specimen Dimensions  The u r a n i u m s t r i p w a s . r o l l e d t o a t h i c k n e s s range o f 0 . 0 1 5 " to  0.020". 3 . . R e c r y s t a l l i z a t i o n Procedure , P r i o r . t o r e c r y s t a l l i z a t i o n , t h e t e n s i l e specimens were d e b u r r e d  u s i n g . a f i n e f i l e and t h e adherent b l a c k o x i d e removed by an e l e c t r o p o l i s h as d e s c r i b e d i n t h e M e t a l l o g r a p h y s e c t i o n .  .Most heat t r e a t m e n t s were c a r r i e d . o u t i n b a t c h e s o f s i x specimens w i t h a v a c u u m a n n e a l t u b e - f u r n a c e , under p r e s s u r e s . o f l e s s t h a n - 1 0 ~ -  Hg. - The temperature, c o n t r o l was b e t t e r t h a n ±  ^>°C.  5  mm  of  - 9 -  C.: M e t a l l o g r a p h y and G r a i n - S i z e  Determination  .Because .of t h e importance o f a c c u r a t e g r a i n - s i z e and  the inherent d i f f i c u l t i e s involved.with  determination,  t h e p o l i s h i n g o f uranium;  c o n s i d e r a b l e importance was p l a c e d on m e t a l l o g r a p h i c t e c h n i q u e .  A t e n s i l e . t e s t specimen t h a t was t o be e x a m i n e d • m e t a l l o g r a p h i c a l l y p r i o r - t o t h e d e f o r m a t i o n t e s t was mounted i n a,removable j i g t h a t an end-of t h e specimen t o be p o l i s h e d w i t h o u t any a c c i d e n t a l .For  allowed  bending.  s u i t a b l e g r a i n and t w i n d i s t i n c t i o n , . i t was necessary, t o  employ p o l a r i z e d , l i g h t i n g w h i c h r e q u i r e d  c a r e f u l e l e c t r o p o l i s h i n g procedures  . The b e s t r e s u l t s were o b t a i n e d when e l e c t r o p o l i s h i n g was i n t r o d u c e d d i r e c t l y a f t e r g r i n d i n g t o k/O emery paper. • S e v e r a l e l e c t r o p o l i s h i n g s o l u t i o n s were i n v e s t i g a t e d and t h e f o l l o w i n g two were found t o g i v e t h e b e s t r e s u l t s . (1), Chromium. T r i o x i d e -Water G l a c i a l Acetic Acid 200.ma/cm  2  for  25 gm JO m l .300 m l  seconds.  (.2) O r t h o p h o s p h o r i c A c i d . (85^) 100ml Ethylene Glycol 100ml E t h y l A l c o h o l (95$)160 m l 10-30 ma/cm f o r .5 t o 10 m i n u t e s ; p a s s i v a t e s , p o l i s h e d and kept c o o l . 2  must be f l a s h  .The chromium/acetic a c i d p o l i s h was a l s o u s e d . t o remove adherent o x i d e f r o m tensile  specimens. .Two g r a i n s i z e measuring t e c h n i q u e s were used;, one f o r t h e l a r g e r  grain.sizes smaller  o f 0.060 mm. and o v e r , and a n o t h e r more a c c u r a t e method, f o r ' t h e  grain sizes.  The l e s s a c c u r a t e t e c h n i q u e i s an a d a p t a t i o n t o uranium  o f t h e A.S.T.M. Comparative Method as c a l c u l a t e d b y J e f f r i e s ' . P l a n i m e t r i c M e t h o d : a n d , c o n s i s t s . o f v i s u a l l y comparing t h e g r a i n s i z e o f a specimen t o a  - 10  standard.  -  Heyn's Intercept'-Method was used f o r t h e a c c u r a t e g r a i n  s i z e d e t e r m i n a t i o n s and c o n s i s t e d o f c o u n t i n g - a t an a p p r o p r i a t e m a g n i f i c a t i o n the number o f g r a i n b o u n d a r i e s . i n t e r c e p t e d - b y two l i n e s , o f known l e n g t h s . Two m u t u a l l y , p e r p e n d i c u l a r l i n e s i n s c r i b e d on an e y e - p i e c e were c a l i b r a t e d , u s i n g • a m a g n i f i c a t i o n s t a n d a r d , to. v a r i o u s o b j e c t i v e l e n s e s so t h a t t h e i r r e p r e s e n t a t i v e l e n g t h s were a c c u r a t e l y , known.  -On e x a m i n a t i o n  of a-tensile  specimen,. t h e s e l i n e s were p o s i t i o n e d a l o n g . t h e w i d t h and t h i c k n e s s d i r e c t i o n s i n a plane perpendicular t o t h e . r o l l i n g d i r e c t i o n . g r a i n s i z e , . a n d , t h e shape of• t h e g r a i n s , w e r e  thus  The average  obtained.  I n t h e p r o c e s s o f d e t e r m i n i n g t h e more a c c u r a t e g r a i n t o 1400 g r a i n s would be counted.  sizes,1200  When a n n e a l i n g was done i n b a t c h e s , s e v e r a l  specimens were examined and t h e i r g r a i n s i z e c o n s i d e r e d r e p r e s e n t a t i v e .  • A . t a b l e o f a n n e a l i n g t i m e s and-temperatures a n d , t h e - r e s u l t a n t g r a i n s i z e s , i s g i v e n i n Appendix-1. -D. - T e n s i l e - E x p e r i m e n t s The t e n s i l e t e s t s were performed on an I n s t r o n t e n s i l e , t e s t i n g machine equipped w i t h an i n s t a n t a n e o u s s t r a i n . r a t e change mechanism. .The g r i p p i n g a p p a r a t u s was a s e l f - t i g h t e n i n g d e s i g n and was, mounted s o as t o p e r m i t complete.immersion i n c o n t r o l l e d ; t e m p e r a t u r e b a t h s . Two t y p e s . o f t e n s i l e t e s t s were i n v e s t i g a t e d over a range o f g r a i n s i z e and  temperature (1)  Continuous. T e s t s  (2) . S t r a i n Rate Change-Tests  - 11  The c o n t i n u o u s t e n s i l e t e s t specimens were s t r a i n e d a t a . c o n s t a n t o f c r o s s - h e a d t r a v e l of 0.01  h i g h t h e s t r a i n r a t e was  rate  i n c h e s p e r minute. . T h i s corresponds, t o a  s t r a i n r a t e of about 1 p e r cent p e r minute. was  -  I n t e s t s where t h e d u c t i l i t y  i n c r e a s e d a f t e r 10 p e r c e n t e l o n g a t i o n .  The  s t r a i n r a t e change t e s t s were i n t r o d u c e d a t v e r y low s t r a i n s and l o a d s and c o n t i n u e d , . evenly, spaced, t o t h e u l t i m a t e l o a d . were made f r o m t h e b a s i c cross^-head, t r a v e l o f 0.01 s t r a i n . r a t e i n c r e a s e s were a f a c t o r o f 10, conducted w i t h a , f a c t o r o f 5 and 20. t e s t s were performed-over  A l l s t r a i n . r a t e changes i n c h e s p e r m i n u t e . - Most  b u t some i n c r e a s e s were, a l s o  .Both c o n t i n u o u s and s t r a i n r a t e change  the t e m p e r a t u r e range  -196°C t o 270°C w h i c h  encompasses t h e b r i t t l e , t o d u c t i l e . t r a n s i t i o n .  . The e x t r a n e o u s d e f o r m a t i o n due t o e l a s t i c s t r a i n i n g of t h e g r i p p i n g apparatus, was  r e c o r d e d on a c a l i b r a t i o n c u r v e .  A l l load-elongation-curves  as r e c o r d e d by the I n s t r o n s t r i p r e c o r d e r were t h u s c o r r e c t e d .  E. - Temperature C o n t r o l T e n s i l e t e s t s were conducted a t the f o l l o w i n g . f i v e  temperatures.  - TABLE I I . . .Temperature C o n t r o l Media Temperature  Immersion Medium  -196°C 22°C 100°C 170°C 270°C  Liquid Nitrogen Ambient A i r Boiling-Water Petroleum O i l Petroleum,Oil  T e n s i l e specimens immersed i n l i q u i d n i t r o g e n b a t h s were a l l o w e d •10 m i n u t e s . t o i n s u r e temperature tensile testing.  e q u i l i b r a t i o n before being subjected.to  • The . t e m p e r a t u r e s  w i t h a Wheelco t e m p e r a t u r e  o f t h e p e t r o l e u m , o i l b a t h s we're . c o n t r o l l e d  c o n t r o l l e r and d i d n o t v a r y more t h a n ±  3°C.  - 12 i  I I I . • EXPERIMENTAL RESULTS A. R o l l i n g and B e t a Quenching 1  1.  Hot  Rolling  The hot r o l l i n g , segments o f t h e r o l l i n g s c h e d u l e s -vjere d e s i g n e d t o modify, t h e dimensions and m i c r o s t r u c t u r e o f t h e " a s - r e c e i v e d " r e a c t o r f u e l r o d s t o t h o s e s u i t a b l e f o r subsequent  b e t a heat t r e a t i n g and warm o r  cold, r o l l i n g . The d u c t i l i t y o f uranium i n t h e temperature p r o v e d t o be more, t h a n adequate i n r e d u c i n g ' t h e 3/8  r e g i o n o f 625°C  inch rod t o s t r i p  s u i t a b l e f o r w a r m . r o l l i n g • o r a c t u a l t e n s i l e specimens.  Reductions i n area  o f more t h a n 95 p e r cent were a c h i e v e d w i t h no edge c r a c k i n g . s u r f a c e o f t h e hot r o l l e d s t r i p was  The  r a t h e r rough and c o v e r e d w i t h a . c o a r s e ,  f l a k i n g o x i d e . - This, o x i d e was e a s i l y s t r i p p e d c h e m i c a l l y .  i  . I f t h e r o l l i n g and soaking' t e m p e r a t u r e s were k e p t above 625°C but below-the  a l p h a - b e t a . t r a n s i t i o n (663°C), t h e n r e d u c t i o n s o f ^5 p e r cent  were adequate t o cause r e c r y s t a l l i z a t i o n and g r a i n r e f i n e m e n t .  This i s  shown - i n F i g u r e . 3 where.the b e t a quenched and. t h e hot r o l l e d m i c r o s t r u c t u r e s can be compared. 2. . C o l d R o l l i n g and B e t a Quenching The b e t a quenching p r o c e d u r e d i d not improve t h e s t r i p s u r f a c e except t o e x p l o s i v e l y , remove.most of t h e c o a r s e o x i d e .  The i r r e g u l a r g r a i n  p r o f i l e . a n d t w i n n i n g i s t y p i c a l and i n d i c a t i v e o f a b e t a quench. . C o l d , r o l l i n g improved.the  hot r o l l e d . s u r f a c e somewhat but t h e  c o n t r o l o f s m a l l r e d u c t i o n s was u n s a t i s f a c t o r y . s t r u c t u r e from,the unworked, a n n e a l e d s t a t e was  The  change i n m i c r o -  slight.  \  As b e t a quenching a n d c o l d r o l l i n g proved, u n s a t i s f a c t o r y i n s u b s e q u e n t l y p r o d u c i n g an adequate g r a i n s i z e r a n g e , t h e s e  rolling  schedules, were n o t i m p o r t a n t .  3 • •• Warm R o l l i n g • The warm r o l l i n g s c h e d u l e was adopted, t o produce..most' o f t h e t e n s i l e t e s t specimens and gave a smooth s u r f a c e c o v e r e d w i t h a . t h i n , t i g h t l y adherent b l a c k oxide. t o a l l o w t h e 90 P  e r  The uranium.was d u c t i l e enough a t 300°C  cent r e d u c t i o n s w i t h o u t any edge c r a c k i n g . . F i g u r e - 3  shows t h a t no r e c r y s t a l l i z a t i o n h a s , o c c u r r e d and t h a t t h e g r a i n s t r u c t u r e . i s h i g h l y worked.  B•  G r a i n Growth 1..Critical  1  Strain-Anneals  . R o l l i n g - s c h e d u l e s A and B. were d e s i g n e d . t o e x p l o i t t h e r a n g e . o f grain sizes associated with the c r i t i c a l strain-anneal. :  The c r i t i c a l  strain 15  f o r uranium.has been f o u n d t o be about 2.5 p e r c e n t r o l l i n g r e d u c t i o n F i g u r e 39 in-Appendix- I . shows -the maximum g r a i n s i z e o b t a i n e d from  strain-  a n n e a l s e r i e s B t o o c c u r a t about 2 p e r cent r o l l i n g r e d u c t i o n . . I t i s . ;  i n t e r e s t i n g . t o note t h a t t h e a d d i t i o n a l s t r e s s , i n t r o d u c e d i n t o s e r i e s A t h r o u g h t h e b e t a quench p r o c e d u r e has s h i f t e d . t h e curve t o about 6 p e r c e n t r e d u c t i o n lower than the B s e r i e s ,  •The i n t e r n a l s t r e s s e s a s s o c i a t e d w i t h  the ^ quench a r e t h e r e f o r e e q u i v a l e n t t o about 6 p e r cent  rolling•strain.  A l t h o u g h t h e g r a i n s i z e range o f s e r i e s B i s 190 m i c r o n s , t h e H a l l - P e t c h l/2 -l/2 parameter ( l / D ) i s o n l y about 3 mm . - S e r i e s C , - w h i c h ' c o n s i s t e d .of a n n e a l i n g b e t a quenched m a t e r i a l f o r v a r i o u s t i m e s and t e m p e r a t u r e s , p r o v i d e d a g r a i n s i z e range o f only.- 30 .microns w i t h a c o r r e s p o n d i n g H a l l - P e t c h range o f about 1- mm  -1/2  ' .  F i g u r e 3.  Microstructures  (a)  100X  (c)  UOOX  of (a) Hot R o l l e d (b) B e t a Quenched, and (c) Warm R o l l e d M a t e r i a l .  - 15  The  -  c r i t i c a l strain-anneal technique f o r producing an adequate  grain size range was  abandoned because of the low Hall-Petch parameter  range,-the largeness of the grain sizes with respect to the specimen dimensions, the lack of accurate grain size control, and.the poor specimen surface. 2. Large. S t r a i n - A n n e a l s .The use o f f i n e g r a i n e d m a t e r i a l was d e s i r a b l e because o f t h e s e n s i t i v i t y o f the. H a l l - P e t c h parameter t o g r a i n s i z e a t s m a l l , g r a i n  sizes,  as shown i n F i g u r e kO i n " Appendix- I . -The warm, r o l l i n g s c h e d u l e s D and E p r o v i d e d a h i g h l y t w i n n e d m i c r o s t r u c t u r e w h i c h s e r v e d . t o produce a h i g h density of nucleation sites f o r fine g r a i n e d ; r e c r y s t a l l i z a t i o n ^ . 1  This  p r q c e d u r e gave a g r a i n s i z e range o f k t o 35 m i c r o n s and a c o r r e s p o n d i n g l/2  H a l l - P e t c h p a r a m e t e r range o f 5 t o 16 mm"  ' .  The m a j o r i t y o f t h e t e n s i l e  t e s t specimens were p r o d u c e d i n t h i s manner. F i g u r e kl  i n Appendix I shows t h e c h a r a c t e r o f t h e g r a i n  d i s t r i b u t i o n w i t h i n i n d i v i d u a l specimens.  size  The f r e q u e n c y f u n c t i o n s f o r a l l  g r a i n s i z e s a r e skewed i n t h e d i r e c t i o n . o f l a r g e r g r a i n s i z e s w h i l e t h e s t a n d a r d d e v i a t i o n i n c r e a s e s w i t h t h e l a r g e r g r a i n - s i z e d specimens.  Although  t h e g r a i n s i z e . d i s t r i b u t i o n range i n c r e a s e s w i t h i n c r e a s i n g g r a i n s i z e , t h e c o r r e s p o n d i n g H a l l - P e t c h parameter range a c t u a l l y d e c r e a s e s .  It is  i m p o r t a n t t o n o t e . t h a t specimens a n n e a l e d i n t h e r e g i o n o f 600°C and over d e v e l o p a c h a r a c t e r i s t i c double peak.  .Exaggerated g r a i n g r o w t h o f t h i s 17  n a t u r e has been r e p o r t e d t o o c c u r i n . t h i s . t e m p e r a t u r e r e g i o n The m a j o r i t y o f t h e t e n s i l e specimen g r a i n s were not e q u i a x e d and showed an e l o n g a t i o n o f about 10 p e r cent i n . t h e r o l l i n g p l a n e .  There  16  -  was  some e v i d e n c e o f "banding" but not t o any s i g n i f i c a n t  -  degree.  - When, t e n s i l e specimens'were annealed- i n b a t c h e s t h e  average  g r a i n s i z e -of i n d i v i d u a l specimens d i d n o t d e v i a t e more than. 5 p e r c e n t .  The r a t e e q u a t i o n c o n s t a n t s f o r g r a i n growth a r e c a l c u l a t e d and shown i n A p p e n d i x . I .  The  c h a r a c t e r o f t h e a c t i v a t i o n energy  plot,  • F i g u r e k-2, i s s i g n i f i c a n t i n t h a t two g r a i n growth r e g i o n s a r e e v i d e n t . F o r r e a s o n s shown i n Appendix  I , i t can be c o n c l u d e d , t h a t specimens  a n n e a l e d a t about 600°C and above undergo an i m p u r i t y c o a l e s c e n c e and ; hence may  e x h i b i t d i f f e r e n t t e n s i l e deformation c h a r a c t e r i s t i c s  than  .those a n n e a l e d below 600°C. .This e v i d e n c e i s . c o r r o b o r a t e d - b y t h e  double  p e a k s . e x h i b i t e d by, t h e h i g h temperature g r a i n s i z e d i s t r i b u t i o n .  Whenever  the r e s u l t s . o f t h e s e c o a l e s c e d specimens were i n doubt they-were  considered  as s p u r i o u s d a t a .  .C. - T e n s i l e 1.  Experiments  G e n e r a l Flow  Characteristics  .. S t r e s s - s t r a i n c u r v e s f o r uranium a r e unique i n . t h a t t h e y a r e ' c h a r a c t e r i z e d by t h e absence o f a measurable curves a t the lower temperatures from t h e onset o f s t r a i n .  l i n e a r or e l a s t i c r e g i o n .  The  s i m u l a t e a. s t a g e III t y p e o f h a r d e n i n g  As t h e d e f o r m a t i o n temperature  increases the  c u r v e s appear t o approach a " y i e l d " t y p e o f b e h a v i o u r as shown i n F i g u r e k. Some speqimens show an upper and l o w e r y i e l d p o i n t f o r s m a l l g r a i n s i z e s a t 270°C. P l a s t i c d e f o r m a t i o n f o r s e r i e s D and: E m a y b e d i v i d e d - i n t o d i s t i n c t r e g i o n s w i t h r e g a r d t o t h e s t r a i n h a r d e n i n g exponent,  n.  A t low  s t r a i n s , r e g i o n I,.the deformation curves.obey h i g h s t r a i n hardening •exponents  from 0.5 t o 0.8  depending  on t h e t e m p e r a t u r e .  two  Region I i s  - 18  f o l l o w e d by a g r a d u a l t r a n s i t i o n t o r e g i o n I I . The s t r a i n h a r d e n i n g exponent f o r r e g i o n I I i s 0.08 f o r a l l t e m p e r a t u r e s . h a r d e n i n g exponents  strain  f o r r e g i o n I and* I I a r e not u s u a l and a r e e x t r e m a l  t o t h o s e o f most m e t a l s . lower s t r a i n s  The  The t r a n s i t i o n r e g i o n i s s h i f t e d t o b o t h  and. l o w e r s t r a i n h a r d e n i n g exponents" w i t h i n c r e a s i n g  t e m p e r a t u r e as shown i n F i g u r e 5i s temperature  The low s t r a i n h a r d e n i n g exponent  independent.  The t e n s i l e c u r v e s f o r s e r i e s A and B a r e g e n e r a l l y  similar  t o t h o s e o f D and E, e x c e p t f o r t h e magnitudes o f f l o w s t r e s s e s work h a r d e n i n g r a t e s .  and  The random o r i e n t a t i o n o f g r a i n s i n s e r i e s A  and B has l o w e r e d t h e f l o w s t r e s s c o n s i d e r a b l y as shown i n F i g u r e 6.  .The  f l o w s t r e s s e s f o r t h e randomly o r i e n t e d specimens i s a p p r o x i m a t e l y . 60 p e r cent o f t h o s e f o r s e r i e s D and E w i t h a h i g h l y p r e f e r r e d ' o r i e n t a t i o n . .The  s t r a i n hardening rate f o r r e g i o n . I I of the A s e r i e s . t e n s i l e  curve  i s o v e r 2 l / 2 t i m e s l a r g e r t h a n t h a t o f the D and E s e r i e s , as shown i n F i g u r e 6. F i g u r e 7 shows t h e v a r i a t i o n o f f l o w s t r e s s i n r e g i o n I I w i t h temperature.  As t h e t e m p e r a t u r e i s i n c r e a s e d , . t h e s e n s i t i v i t y o f f l o w A t h i g h t e m p e r a t u r e s , above 300°C, t h e  s t r e s s to. t e m p e r a t u r e d e c r e a s e s .  f l o w s t r e s s tends t o become t e m p e r a t u r e independent and approaches  a  v a l u e w h i c h c o i n c i d e s w i t h t h e t h e o r e t i c a l t e m p e r a t u r e independent f l o w l8  stress^  as c a l c u l a t e d from d i s l o c a t i o n d e n s i t i e s  the t e m p e r a t u r e independent b  y where  f  G  p  1 / / 2  v, y, Q  TT-  ' — '  )i r\  be r e p r e s e n t e d  b  m G n  = = =  orientation factor — k to 5 shear modulus ( 1 0 p s i ) d i s l o c a t i o n d e n s i t y (2.3 X 1 0 f o r s t r a i n s over  b  =  B u r g e r s V e c t o r (3 X 10"  r\r\r\  4-^  cn  7  1  3.5$)  +  i . e . assuming t h a t  component o f f l o w s t r e s s may  m 0.2  =  '  nnn  cm)  -  1  2  5  6  7  8  9  (per c e n t ) . F i g u r e 6.  Comparison o f T e n s i l e Curves o f Specimens w i t h Random and Preferred Orientation.  io  F i g u r e 7.  E f f e c t o f Temperature on Flow S t r e s s a t 6 P e r Cent S t r a i n  -22  -  . F i g u r e 8 i l l u s t r a t e s t h e t e m p e r a t u r e dependence o f t h e s t r a i n hardening regions. the  . I t c a n be seen t h a t as t h e t e m p e r a t u r e i s i n c r e a s e d  domain o f r e g i o n - I I extends t o lower- s t r a i n s a t t h e expense o f t h e  t r a n s i t i o n and r e g i o n I . . E x t r a p o l a t i n g t h e c u r v e s t o h i g h e r t e m p e r a t u r e s w i l l r e s u l t i n t h e e l i m i n a t i o n o f a l l s t r a i n hardening r e g i o n s except r e g i o n I I i n t h e v i c i n i t y o f 300°C.  A t t h i s temperature and above, t h e  e n t i r e t e n s i l e curve w i l l obey t h e low work h a r d e n i n g  The s t r a i n hardening•exponent dependent a s shown i n F i g u r e 9 the  was:not found, t o be g r a i n s i z e  The e f f e c t o f g r a i n s i z e was t o i n c r e a s e  work h a r d e n i n g c o e f f i c i e n t w i t h d e c r e a s i n g g r a i n .2Grain  exponent.  size.  S i z e S e n s i t i v i t y , t o Flow  S i n c e p l a s t i c flow- i n i t i a t e s e s s e n t i a l l y a t t h e onset -of l o a d a p p l i c a t i o n and no l i n e a r o r e l a s t i c r e g i o n e x i s t s t h e n some d i f f i c u l t y  arises  as t o t h e l o a d - e l o n g a t i o n curve a n a l y s i s . .The u s u a l method o f a n a l y s i s for  c u r v e s p o s s e s s i n g a d e f i n i t e l i n e a r r e g i o n i s t o measure v a l u e s o f  p l a s t i c s t r a i n a l o n g , t h e a b s c i s s a and draw i n t e r s e c t i n g . l i n e s p a r a l l e l t o the  l i n e a r r e g i o n - o f t h e t e n s i l e curve t o o b t a i n t h e c o r r e s p o n d i n g l o a d . As  t h i s t e c h n i q u e p r e s e n t e d some d i f f i c u l t y on a p p l i c a t i o n t o uranium c u r v e s , t h e f o l l o w i n g method was adopted.  tensile  V a l u e s o f s t r a i n were measured  on.the a b s c i s s a .and. v e r t i c a l i n t e r s e c t i n g l i n e s were drawn. -The l o a d s o b t a i n e d i n t h i s manner t h e n c o r r e s p o n d e d t o v a l u e s o f t o t a l s t r a i n ;  elastic  p l u s p l a s t i c . . T h e r e f o r e s t r a i n v a l u e s i n a l l p l o t s i n c l u d e an e l a s t i c segment. The e x p e r i m e n t a l s c a t t e r - f o r t h e E s e r i e s  (preferred orientation)  H a l l - P e t c h p l o t s , ( F i g u r e s 10-to-13 i n c l u s i v e l y ) . a p p e a r s t o i n c r e a s e w i t h , strain.  Specimens E - l - 3 and E - 1 0 - 3 , w h i c h were a n n e a l e d a t 600°C  and-over,  200  I  I  I  j  I  1 I I I I  0.1  1 l o  F i g u r e 9-  S  I .  ( €. ) ( P  |  I  I  I  I I I | 10  e r  15  cent)  E f f e c t o f G r a i n S i z e on S t r a i n Hardening Exponent  ro  3  - 25  d  o  OJ  d  -  c—  d  H  vo  O o  VO ON  Po  OJ  Xi !•  fe CD CD •H  H  fn CU  CO OJ  u  o  <H  CD N •H CO  O  OJ  •H  r)  1  •  ON  •  O  CO  -fl -P •H  OJ CQ CQ CD  u -p  CO  8 H O  •  fl  O •H  -P  oi  •ri  > o CD  •H  fe OJ  H  o H  O  o H  O ON  O CO  O  o  VO  o  ITS  ( 0 T X'Tstt) 'ssajq.s S  -4-.. O  *OT&:  o  KN  O OJ  O  r-i  -26 -  - 93 -  - 29  -  gave h i g h v a l u e s and have been n e g l e c t e d f o r reasons d e s c r i b e d p r e v i o u s l y .  The H a l l - P e t c h p l o t , ' F i g u r e X k ,  f o r s e r i e s ; A and B (random  o r i e n t a t i o n ) has been d r a w n • c o n s i d e r i n g - t h e  A p o i n t s - o n l y . -The  B tensile  specimens had g r a i n s i z e s o f t h e same o r d e r o f magnitude a s . t h e dimensions.  specimen  The B specimens-would t h e r e f o r e behave i n a manner s i m i l a r  t o s i n g l e c r y s t a l s . - C o n s i d e r i n g t h e B specimens as e q u i v a l e n t . t o s i n g l e l/2  c r y s t a l s and. t r a n s p o s i n g t h e i r l/D  values, t o z e r o w o u l d be d o u b t f u l  compensation because o f t h e p o s s i b i l i t y o f f o r c e d s l i p . F i g u r e 15 and E.  -The  shows t h e v a r i a t i o n 'of k w i t h s t r a i n f o r s e r i e s D  curves f o r a l l temperatures  t o a common c h a r a c t e r i s t i c s form.  except t h a t f o r -196°C adhere  .The. k /values i n c r e a s e r a p i d l y from a  •low v a l u e at- v e r y l o w - s t r a i n s t o a maximum a t 0.5 p e r cent s t r a i n , t h e n g r a d u a l l y - d e c r e a s e t o a - c o n s t a n t v a l u e a t h i g h e r s t r a i n s . - Uranium.has a . n e g l i g i b l e s e n s i t i v i t y t o g r a i n s i z e a t -196°C. A l t h o u g h t h e g r a i n s i z e s e n s i t i v i t y , k,.. ,  determined  from a s m a l l l / D  for series A i s  1/2  range, t h e t r e n d i s v e r y s i m i l a r t o the  E s e r i e s e q u i v a l e n t , as shown in" F i g u r e 16.  The magnitudes o f k ._. r  a r e somewhat h i g h e r f o r t h e random o r i e n t a t i o n t h a n f o r t h e h i g h l y p r e f e r r e d orientation. . Two u n i q u e s t r a i n v a l u e s a r e e v i d e n t ; a t w h i c h k g,x.ocaurs a n d t h e s t r a i n , £ m  , r e g i o n b e g i n s . • F i g u r e :17 w i t h temperature.  t h e strain,£  max.,  c o n s t . , a t w h i c h the...k -|cons  shows t h e v a r i a t i o n o f t h e s e s t r a i n v a l u e s ,  I t can be seen t h a t w h i l e t h e €.max. v a l u e i s  0.5 p e r cent and c o n s t a n t , t h e £ c o n s t . v a l u e s decrease l i n e a r l y w i t h i n c r e a s i n g temperature.  approximately  An e x t r a p o l a t i o n o f t h e s e  curves  Figure lk.  V a r i a t i o n of Flow S t r e s s ' w i t h Grain S i z e f o r Series A*X-1 (20°C) :  6 (per c e n t ) F i g u r e 15.  V a r i a t i o n o f k w i t h S t r a i n f o r S e r i e s D and  E  8  -.54 -  g i v e s the temperature at which t h e C m a x .  and. £ c o n s t ,  supposedly c o i n c i d e .  330°C  t r a n s i t i o n between  . I n the v i c i n i t y of k  m a x <  and the k  F i g u r e 15 shows a g e n e r a l . F i g u r e 18 i l l u s t r a t e s  temperature. . and k  c o n s  -k  c o n s  ^  presumably a p r e c i p i t i o u s  r e g i o n would ensue.  increase  of k w i t h i n c r e a s i n g  the. r e l a t i o n s h i p between  v a l u e s as a f u n c t i o n of temperature , ..The  appear, t o i n c r e a s e  v a l u e s would  k  c  o  n  S  k^x values  4 -  -196°C  l i n e a r l y w i t h temperature from a z e r o v a l u e a t  3/2 t o 1.1 k g / m m '  at 270°C.  ambiguous s i n c e k a l s o be z e r o . T h e .  c o n s  However the r e g i o n between 20°C and -196°C i s  v a l u e s f o r temperatures h i g h e r than -196°C may  t  .The alignment of the  -196°C p o i n t may w e l l be f o r t u i t o u s .  v a l u e s when c o r r e c t e d f o r e l a s t i c  y  temperature  s t r a i n i n g are  approximately  independent.  -The  manner i n which the g r a i n s i z e  t o flow, s t r e s s ,  ^  ,  0  independent  contribution  changes w i t h s t r a i n i s o f i n t e r e s t because of  s i m i l a r i t y to single c r y s t a l  stress-strain  t h a t w i t h i n c r e a s i n g temperature the curves  character  F i g u r e 19 shows  t e n d t o assume  stage form o f work h a r d e n i n g , . t y p i c a l o f f . c . c .  the  a.three-  single crystals.  'This  i s e s p e c i a l l y e v i d e n t i n the 270°C curve where an "easy g l i d e " r e g i o n f o l l o w e d by a h a r d e n i n g r e g i o n - i s between since  \J"  ^vT  0  0  r e a d i l y d i s c e r n i b l e . - This  and. the f l o w s t r e s s f o r a s i n g l e c r y s t a l  i s not  similarity unlikely  r e p r e s e n t s the s t r e s s r e s i s t i n g d i s l o c a t i o n a n d / o r t w i n  p r o p a g a t i o n . t h r o u g h an i n f i n i t e l y l a r g e . p e r t u r b a t i n g g r a i n boundary e f f e c t s .  grain  (single  c r y s t a l ) w i t h o u t any  . T h e 170°C has been o m i t t e d because  a c c u r a t e d a t a i n . t h e r e g i o n o f 1 p e r cent s t r a i n and l e s s was not Note the curve.  -196°C 'vf  0  curve e x h i b i t s a curve form s i m i l a r t o the  available.  tensile  - 37  • F i g u r e 20  compares the  T°  -  curve f o r s e r i e s ' A t o t h e t e n s i l e  curve f o r s e r i e s . B. • The t e n s i l e curve f o r s e r i e s B does n o t behave as a specimen w i t h i n f i n i t e l y l a r g e g r a i n s . -At low s t r a i n s t h e f l o w s t r e s s o f t h e B curve i s h i g h e r t h a n t h e A s e r i e s i n t e r c e p t v a l u e s , but the d e c r e a s i n g s t r a i n h a r d e n i n g r a t e causes t h e f l o w s t r e s s t o f a l l below at higher s t r a i n s .  T h i s d i s s i m i l a r i t y may.be due t o t h e importance  of  " f o r c e d s l i p " i n . t h e A s e r i e s specimens.  3 . .. S t r a i n -Rate S e n s i t i v i t y o f Flow .. S t r a i n r a t e change t e s t s were p e r f o r m e d i n o r d e r t o examine a n y - p o s s i b l e c o r r e l a t i o n between a c t i v a t i o n volumes and t h e s e n s i t i v i t y of p l a s t i c flow to g r a i n s i z e .  I n the course o f e f f e c t i n g t h i s  b o t h p o s i t i v e and n e g a t i v e changes were a n a l y z e d .  The  examination,  s t r a i n r a t e changes  were i n i t i a t e d . f r o m t h e onset o f p l a s t i c f l o w i n t h e r e g i o n o f 0.1 s t r a i n or l e s s and c o n t i n u e d t o h i g h s t r a i n s ,  per  but t e r m i n a t e d b e f o r e  cent  necking  occurred. A t y p i c a l s t r a i n r a t e change, t e s t i s shown i n F i g u r e 21. f l o w s t r e s s a t t h e i n i t i a t i o n o f p l a s t i c f l o w was e x t r a p o l a t i o n t e c h n i q u e as  determined  by  The  an  22.  shown i n F i g u r e +  S i n c e b o t h p o s i t i v e A.^T and n e g a t i v e ' i V T " , s t r e s s changes were measured,. t h e n o m i n a l s t r e s s a t w h i c h t h e s t r a i n r a t e change was e f f e c t e d must be the average s t r e s s l e v e l , d e s i g n a t e d  °r  XTav  =  T i  ^Tav  =  T i  -1/2 +  |^r 1/2  ^~  a v  i  100  £ F i g u r e 21.  (per c e n t )  -A T y p i c a l S t r a i n Rate Change T e s t  - .40 -  -Figure22.  E x t r a p o l a t i o n Method f o r S t r a i n Rate Change A n a l y s i s  F i g u r e s 23 and 24 show t h e change i n f l o w . s t r e s s a s . a f u n c t i o n o f t h e average  s t r e s s f o r a l l t e s t i n g , temperatures.  s i m i l a r i n t h a t t h e y e x p e r i e n c e an i n i t i a l stresses, which converges  These curves a r e a l l  i r r e v e r s i b l e r e g i o n a t low  t o a r e v e r s i b l e r e g i o n a t h i g h e r s t r e s s e s . . The  n e g a t i v e s t r a i n r a t e changes i n t h e i r r e v e r s i b l e r e g i o n s show a c l a s s i c a l C o t t r e l l - S t o k e s obeyance, w h i l e t h e p o s i t i v e divergent behaviour.  The p o s i t i v e  s t r a i n r a t e .changes show a  s t r a i n r a t e . changes a r e i n t e r e s t i n g i n  t h a t t h e y a l l e x p e r i e n c e a minima which i s preceded by a h o r i z o n t a l r e g i o n , the e x t e n t o f w h i c h d e c r e a s e s a s - t h e temperature v i c i n i t y of the p o s i t i v e  i s increased. . In the  s t r a i n r a t e change.minima,.the n e g a t i v e  s t r a i n r a t e changes cease t o b e , l i n e a r and curve so as t o become c o i n c i d e n t w i t h t h e p o s i t i v e s t r a i n . r a t e change curve.  F i g u r e s . 2 5 and 26 show t h e s t r a i n rate.change o f s t r a i n f o r a l l temperatures. w i t h d e c r e a s i n g temperature.  ,  d a t a as a f u n c t i o n  ..The e x t e n t o f i r r e v e r s i b i l i t y i n c r e a s e s  . I f t h e s t r a i n a t which r e v e r s i b i l i t y , b e g i n s  - kl -  -k2 -  o H X!  •H CO ft  5  50  100 Average  150  200  ( p s i X 10 ) 3  1 X •H w ft  ^"Average ( p s i X 10 ) Figure 2k.  Versus  average f o r Increment and Decrement -196°C, 20°C and 100°C  A£, at  rH  X •H  ra Pi  5 0 .10  8  V  (psi  H X! 6  %  k  Increment 100°C  —  <£ /<£i = 10 2  E-13-4 E-12-4  .2  o  l  2  3  4 £  F i g u r e 25.  5  6  7  8  (per c e n t )  Versus Per Cent S t r a i n f o r Increment and Decrement  A€. a t 20°C and 100°C \  -4  5  -  are p l o t t e d a g a i n s t t h e t e s t i n g t e m p e r a t u r e s an a p p a r e n t l i n e a r and d e c r e a s i n g . t e m p e r a t u r e dependence i s shown, as i n F i g u r e 27.  The  s i m i l a r i t y , between t h i s curve and. t h e c u r v e s f o r the onset o f t h e low work h a r d e n i n g r e g i o n and. f o r t h e onset o f t h e k  c  o  n  s  ^ r e g i o n s h o u l d be  noted. • The e f f e c t o f g r a i n s i z e on s t r a i n r a t e was i n v e s t i g a t e d  f o r a s e r i e s , of. g r a i n s i z e s a t 100°C. ;  •shown i n F i g u r e 28 were d e r i v e d f r o m . s t r a i n region.  change  No g r a i n  rate  sensitivity  . A l l d a t a as  changes i n t h e r e v e r s i b l e  size effect was.established.  .• A c t i v a t i o n volumes,.V*, • may be d e r i v e d , from, t h e w e l l  established  rate theory, r e l a t i o n s , i . e . , k  T  ^ln€. . ^T"  where  V^ L  = =  d b  = =  J  T  Lbd length of d i s l o c a t i o n involved interaction i n t e r a c t i o n distance Burgers V e c t o r  The a c t i v a t i o n volumes were c a l c u l a t e d  i n obstacle  f o r b o t h t h e increment and decrement  s t r a i n r a t e changes and a r e p l o t t e d as a f u n c t i o n  o f t h e average f l o w  stress.  The a c t i v a t i o n volumes f o r t h e decrement changes a r e shown i n Figure.29.  The c u r v e s a r e u n i q u e i n t h a t t h e a c t i v a t i o n volumes d e c r e a s e  i n v e r s e l y w i t h the ^ a p p l i e d  stress  i n a manner w h i c h i s independent o f t h e  temperature.  .The a c t i v a t i o n volumes f o r t h e increment changes, F i g u r e 31 show maxima.as a r e s u l t o f t h e minima e x h i b i t e d  by t h e s t r e s s change c u r v e s .  I 100  I 110  X" Average Figure 28.  I  I 120  (psiX  .130  10 ) 3  E f f e c t o f G r a i n .Size on S t r a i n Rate Change S e n s i t i v i t y , f o r S e r i e s E-X-k  (100°C)  -50-  The i n d i v i d u a l curves tend-to a common curve form, as in-Figure 2.9, with the onset of r e v e r s i b i l i t y . Figure J l also shows the e f f e c t of increasing and decreasing the magnitude of the-strain rate change by a factor of two.  .The e f f e c t  of doubling the s t r a i n rate.change i s shown f o r the 270°C curve and i l l u s t r a t e s the independence of activation volume to s t r a i n rate change ". magnitude. - A similar result is. shown i n the 170°C curve, f o r a; decrease i n : s t r a i n rate change magnitude.  .k.  •  Fracture and D u c t i l i t y Specimens tested'at -196°C and-20°C f a i l e d cataclysmically  without p r i o r "necking":  that i s , fracture occurred;before.the ultimate  strength (maximum.:.load) was'achieved.  The fracture p r o f i l e s at these  temperatures were perpendicular to the t e n s i l e axis and:the fracture surface had: a " c r y s t a l l i n e " appearance.  Microscopic examination showed  that crack;propagation was•mostly, t r a n s c r y s t a l l i n e as shown i n Figure 33• • Specimens-tested at 100°C to•270°C i n c l u s i v e l y f a i l e d i n regions of the. t e n s i l e curve a f t e r the maximum.load.  The fracture p r o f i l e s of the  100°C specimens consisted of varying proportions of U5 degree and perpendicular segments. .The perpendicular segments were c r y s t a l l i n e , while the. 4.5 degree segments.were :more-fibrous. . Intergranular and transgranular cracks were evident.  The 170°C. and 270°C specimens f a i l e d i n heavily  necked regions with a: "V" type of fracture p r o f i l e ,  the "V" p r o f i l e being  the two-dimensional analogy-to the c l a s s i c a l cup and cone type of ductile fracture.  The cracks were mainly i n t e r c r y s t a l l i n e with heavy cavitation  i n the 270°C specimens. are shown i n Figure 3 3 .  Examples, of i n t e r c r y s t a l l i n e cracking and cavitation  (per F i g u r e 32. — :  ;  cent)  A c t i v a t i o n Volume as a F u n c t i o n o f S t r a i n f o r Increment Changes f o r S e r i e s D and E .  (a)  Transcrystalline  Cracks  (3OOX)  (b)  Intercrystalline  Cracks  (llOOX)  (c)  C a v i t a t i o n Voids Figure  (225X) 55.  -.54 -  •The e f f e c t F i g u r e s 34 and-35. to the l / D  of g r a i n s i z e o n . f r a c t u r e s t r e s s i s shown i n  .The f r a c t u r e  s t r e s s e s make a r e a s o n a b l y good f i t  f u n c t i o n - f o r specimens t e s t e d at  -196°C and 20°C.  At  100°C t h e s c a t t e r i s l a r g e and a. .unique k - f r a c t u r e v a l u e cannot be assigned.  S i m i l a r p l o t s : w e r e t e n t a t i v e l y a p p l i e d t o the 170°C and  l/2 270°C specimens and a. l / D scatter.  obeyance seems:to h o l d w i t h r e a s o n a b l e  However,, o n l y . f i v e p o i n t s were a v a i l a b l e f o r the 170 C  series.  C  F i g u r e 36 shows k - f r a c t u r e as a f u n c t i o n o f t e m p e r a t u r e . can be seen t h a t a r a p i d drop o f k - f r a c t u r e f o r t r a n s c r y s t a l l i n e o c c u r s between -196 0 C and 20°C.  Between 20°C and 170°'C the  v a l u e s i n c r e a s e t h r o u g h a s c a t t e r band at  100°C.  It  It fracture  k-fracture  is difficult  to  ,1/2 a s c e r t a i n whether the 100°C and 170°C v a l u e s adhere t o a l / D s h i p due t o the s c a t t e r a t  relation-  100°C and the l a c k o f s u f f i c i e n t e x p e r i m e n t a l  p o i n t s at 170°C. 3/2 .The k - f r a c t u r e a g a i n decreases ;  t o about 1.1  kg/mm  . T h i s v a l u e i s i d e n t i c a l w i t h t h a t f o r the k ' . i n t h e . k o n s t . C  plastic  at  270°C.  region f o r  flow. . F i g u r e 37 shows the temperature dependence o f the average  fracture  -1/2 stresses  ( 10  .mm" '  ) and the. i n t e r c e p t v a l u e s , T ° f  experience an i n c r e a s e t o a maximum at t o lower v a l u e s . fracture  strengths  The  £  r  a  c  t  r  a  c  t  Both curves  100°C f o l l o w e d by a sharp  curve appears t o e x t r a p o l a t e  i n t h e r e g i o n near 0°K.  decrease  t o v e r y low  200  h  F i g u r e 35. V a r i a t i o n o f F r a c t u r e S t r e s s w i t h G r a i n S i z e a t 100°C,.170°C and. 270°C f o r S e r i e s . D a n d E.  F i g u r e 36.  . E f f e c t o f Temperature on F r a c t u r e Petch' S l o p e _ f o r S e r i e s . D and E  T Figure $ 7 .  (°K)  . E f f e c t o f Temperature on-Fracture S t r e n g t h and P e t c h I n t e r c e p t f o r S e r i e s D and E  -.59 -  F i g u r e 38 i l l u s t r a t e s t y p i c a l of u r a n i u m . occurs, i n . the  the  semi-brittle  to ductile  transition  F o r the m a t e r i a l u s e d . i n the p r e s e n t work,  0°C t o 150°C temperature r e g i o n .  . A maximum occurs at  h i g h temperature end- o f the t r a n s i t i o n r e g i o n , . w h i c h has a l s o previously  was observed f o r  been  higher d u c t i l i t y w i t h decreasing; g r a i n  -196°C and- 2Q°C specimens.  no g r a i n s i z e dependence was  Summary o f  size  F o r other temperatures  noted.  Results  G e n e r a l Flow- C h a r a c t e r 1.  the  reported"^.  A trend: towards  D.  this  -  .The " y i e l d " becomes i n c r e a s i n g l y sharper w i t h  and a . s o f t u p p e r - l o w e r type  of y i e l d occurs at  increasing.temperature  270°C f o r the  finer grain  .2.  . T h e f l o w s t r e s s tends t o become temperature independent  .3.  .The s t r a i n at which the  sizes.  over300°C.  low s t r a i n h a r d e n i n g r e g i o n b e g i n s  decreases  w i t h increasing, temperature.  .4.  5-  The low s t r a i n h a r d e n i n g s l o p e i s independent  Preferred  orientation  of- t e m p e r a t u r e .  has a marked e f f e c t on f l o w s t r e s s and  hardening.  6.  The s t r a i n hardening, exponent  is  independent o f g r a i n  size.  strain  - 61 -  G r a i n S i z e S e n s i t i v i t y of Flow -  The f l o w s t r e s s , obeys the P e t c h r e l a t i o n w i t h c l o s e s t  .1. at  lower  2.  3.  strains.  . The P e t c h s l o p e i s dependent on p r e f e r r e d  The k v a l u e s show an i n i t i a l maximum a t  by a g r a d u a l t r a n s i t i o n t o a c o n s t a n t . r e g i o n  k.  agreement  The P e t c h s l o p e i s z e r o at  at  orientation.  0.5 p e r cent s t r a i n f o l l o w e d higher  strains.  -196°C and increases, w i t h i n c r e a s i n g  temperature.  5.  The s t r a i n at w h i c h the c o n s t a n t  decreases w i t h i n c r e a s i n g  6.  The T °  curves  Petch slope region, begins  temperature.  show, an " e a s y g l i d e " r e g i o n a t  becomes more dominant w i t h i n c r e a s i n g  low s t r a i n s  that  temperature.  • S t r a i n Rate S e n s i t i v i t y of Flow -  1.  -The f l o w s t r e s s changes  changes are not r e v e r s i b l e at  .2. changes  3.  k.  lower  The i n c r e m e n t a l f l o w . s t r e s s  strain  rate  strains.  changes  show minima w h i l e the  decremental  obey C o t t r e l l - S t o k e s , l a w .  There i s a c l o s e  a f f e c t s »the s t r a i n s slope,  f o r increment and decrement  s i m i l a r i t y i n the manner i n which  temperature  a t which the low s t r a i n h a r d e n i n g , constant  and r e v e r s i b l e r e g i o n s  Petch  initiate.  The s t r a i n r a t e change s e n s i t i v i t y i s independent o f g r a i n  size.  - 62 -  .5-  .The a c t i v a t i o n volumes r e l a t e d t o the decrement  changes  decrease  w i t h i n c r e a s i n g f l o w s t r e s s i n a,manner which i s independent of temperature.  The i n c r e m e n t a l a c t i v a t i o n volumes show, maxima.  The a c t i v a t i o n volumes are  6.  magnitude i n the. r e v e r s i b l e  . Fracture  crystalline occurs  .2.  -  mode changes  higher,  The t r a n s c r y s t a l l i n e  h.  ;  to  inter-  , The. f r a c t u r e  s t r e s s e s obey a P e t c h  the b r i t t l e r e g i o n o n l y .  :  relation  origin.  s t r e s s shows a•maximum at about  D u c t i l i t y increases  -Fracture  temperatures.  fracture  which does not pass t h r o u g h the  J.  from transcrystalline  c r a c k i n g ' i n the b r i t t l e - d u c t i l e t r a n s i t i o n r e g i o n .  t h r o u g h y i e l d i n g at  change  regions.  and D u c t i l i t y  1. -The f r a c t u r e  independent of s t r a i n r a t e  100°C.  generally, with decreasing g r a i n s i z e  in  63  • IV. '.A. G e n e r a l Flow  DISCUSSION  Characteristics  1.•Parabolic  Beginning  The curve forms of' t h i s work are t y p i c a l o f - u r a n i u m i n t h a t t h e y show no e l a s t i c  r e g i o n and e x h i b i t a p a r a b o l i c form from the  onset 20- 21  of l o a d a p p l i c a t i o n .  Suggestions  i n v o l v e the h i g h a n i s o t r o p y  advanced t o account  of thermal expansion.  d i r e c t i o n s have b o t h p o s i t i v e and n e g a t i v e 16 c  p o s i t i v e while  b  i s negative  .  f o r t h i s phenomenon  The orthorhombic  expansion c o e f f i c i e n t s ; 20  .Friedel  attributes this  c o o l e d from h i g h a n n e a l i n g t e m p e r a t u r e s .  about an average v a l u e of zero would be a p p l i c a b l e .  d i s t r i b u t i o n range was o f the  curve  a  and  specimens:  As a rough a p p r o x i m a t i o n  these i n t e r n a l s t r e s s e s were assumed t o behave so t h a t a g a u s s i a n  f o r m i n ' conjunction with a t e n s i l e  lattice  smooth .  p a r a b o l i c b e g i n n i n g t o i n t e r n a l s t r e s s e s e s t a b l i s h e d when t e n s i l e are  '  distribution  On a p p l y i n g t h i s  i t was found t h a t the  curve  stress  o r d e r o f s i n g l e c r y s t a l y i e l d s t r e n g t h s and  t h a t these s t r e s s e s c o u l d be i n d u c e d through a temperature decrease  of  only 30°C. M e t a l l o g r a p h i c examination  of annealed t e n s i l e  specimens  of  this  study a l l showed evidence o f quench s t r a i n i n g i n . the form o f t w i n s . Presumably, s l i p would a l s o have  occurred.  Attempts t o c o r r e l a t e t e n s i l e s t r e s s d i s t r i b u t i o n showed a sharper i n his study.  curve  "yield"  data w i t h a g a u s s i a n  internal  r e g i o n than found by F r i e d e l  T h i s was e s p e c i a l l y , t r u e f o r the D and E s e r i e s specimens w i t h  i a highly preferred orientation. made a b e t t e r  fit.  T h e ' A s e r i e s specimens  of random o r i e n t a t i o n  - 6k -  Presumably the i n a b i l i t y t o f i t a g a u s s i a n d i s t r i b u t i o n i s due to preferred o r i e n t a t i o n .  If this  i s the  case t h e n the  specimens  d e s i g n a t e d t o have a randomly o r i e n t a t e d g r a i n d i s t r i b u t i o n s t i l l , h a v e remnants  of preferred  orientation.  The p a r a b o l i c f l o w c h a r a c t e r : o f a l p h a - u r a n i u m may - a l s o be the result  of i n t e r n a l l o c a l i z e d s t r e s s c o n c e n t r a t i o n s  anisotropy.  caused by an  The atomic b o n d i n g i n the ac p l a n e i s thought t o be  w h i l e bonding between t h e p l a n e s i s c o n s i d e r e d m e t a l l i c . measurements  of the e l a s t i c  elastic covalent  Ultrasonic  moduli., v a r y by as much as 15 p e r cent depending  on the s t a t e of p r e f e r r e d o r i e n t a t i o n  22 2^ > . y  2. Work Hardening (a)  Region I  - H i g h Work Hardening  '.The h i g h work h a r d e n i n g r e g i o n may.be p a r t i a l l y , due t o d i s l o c a t i o n substructure  as w e l l a s t o t h e  elasticity  contribution.  Well defined p o l y 25  2k  gonized substructure  has been o b s e r v e d - t o  The. p o l y g o n i z e d network w i l l  before  e x p e c t e d , t o be t h e  substructure  factor  t h a t the hardening•rate  .In.the  i n i t i a l stages of p l a s t i c  breakdown, t h i s , mechanism would,be . 20  determining flow s t r e s s .  Friedel  due t o d i s l o c a t i o n s which a r e  s u b g r a i n b o u n d a r i e s i s v e r y h i g h a n d can approach the small polygonized, b l o c k s ,  l' f  '  .  impede d i s l o c a t i o n movement i n a manner s i m i l a r  t o t h a t o f a g r a i n boundary network. or m i c r o s t r a i n ,  occur i n annealed m a t e r i a l  has shown  piled-up.against shear modulus f o r  i.e.  = s i z e . o f polygonized blocks = f r a c t i o n of sources t h a t emit" l o o p s .  flow  - 65  Then -^P- ^ ~  Q  approaches p. if- the s i z e o f p o l y g o n i z e d  -  substructure  i s comparable t o t h e Frank network.  . Hultgren^ hardening  i n an i n v e s t i g a t i o n of g r a i n boundary and  substructure  i n aluminum found; t h a t t h e c o n t r i b u t i o n s o f g r a i n b o u n d a r i e s  and s u b s t r u c t u r e a r e a d d i t i v e . • S u b g r a i n b o u n d a r i e s e x e r t e d the i n f l u e n c e a t room t e m p e r a t u r e . . I t i s i m p o r t a n t  t o note t h a t  greater  Hultgren  a t t r i b u t e d t h e i n c r e a s e i n f l o w s t r e s s t o t h e r e l a t i o n s h i p between d i s l o c a t i o n  13 d e n s i t y and s u b g r a i n s i z e as t h e o r e t i c a l l y p r e d i c t e d by L i e f f e c t has a l s o been s t u d i e d f o r copper and  . . This  iron.  S t u d i e s i n v o l v i n g subgrains i l l u s t r a t e the importance o f temperature. .Subgrain  subgrain  s t r u c t u r e s i z e s a r e e f f e c t e d by t h e  annealing  annealing  t e m p e r a t u r e and hence v a r y the f l o w . s t r e s s i f s u b s t r u c t u r e i s an factor.  important 1  . The t r a n s i t i o n t o the low work h a r d e n i n g  region i s a gradual  as p r e d i c t e d by F r i e d e l ^ s r e s i d u a l i n t e r n a l s t r e s s t h e o r y .  Any  phenomenon i s masked by the l a r g e i n t e r n a l s t r e s s d i s t r i b u t i o n . e v i d e n t by the low h a r d e n i n g  one  yield It is  r a t e i n r e g i o n I I t h a t any p i l e - u p mechanisms  as d e s c r i b e d by F r i e d e l have b r o k e n down w i t h the p o s s i b l e d i s p e r s a l o f the p o l y g o n i z e d  s t r u c t u r e . .A t r a n s m i s s i o n m i c r o s c o p y s t u d y . b y Douglass  18 et a l  on d i s l o c a t i o n d e n s i t i e s as a f u n c t i o n o f c o l d work g i v e s e v i d e n c e  o f c o n s i d e r a b l e d i s l o c a t i o n p r o d u c t i o n i n the e a r l y s t a g e s o f s t r a i n i n g . . S t r a i n s i n t h e v i c i n i t y o f k p e r cent and l e s s i n c r e a s e the d e n s i t y by a f a c t o r o f 100,  w h i l e c o n t i n u e d s t r a i n i n g does not  appreciable dislocation density increase. l i n e a r l y with s t r a i n .  dislocation  This process  cause  The t w i n d e n s i t y i n c r e a s e d  of d i s l o c a t i o n m u l t i p l i c a t i o n . i s  - 66 -  commonly observed f o r metals  and i s  i n s t i g a t e d , by moving d i s l o c a t i o n s .  I n - t h i s mechanism,.the. i n i t i a l mobile d i s l o c a t i o n s at  the  onset of  plastic  27 flow produce bursts, of d i s l o c a t i o n s  i n t h e i r wake  .  In r e l a t i o n to  s u b g r a i n s t r u c t u r e , these i n i t i a l d i s l o c a t i o n s may be the r e s u l t angle b o u n d a r i e s g e n e r a t i n g - m o b i l e , d i s l o c a t i o n s . t o d e p i n these d i s l o c a t i o n s 1  i s the  subgrain s i z e .  i s . of the  o r d e r of  The s t r e s s ^  of low necessary  1  2 y\ 0/TT l ' (l-'O)  where  -Any r e g i o n o f Iiiders band p r o p o g a t i o n or lower  y i e l d p o i n t phenomenon i s - m a s k e d by the i n t e r n a l s t r e s s d i s t r i b u t i o n . The e f f e c t  of i n c r e a s i n g , t e m p e r a t u r e  i s t o s t a b i l i z e the low  work h a r d e n i n g r e g i o n at the expense of the h i g h work hardening•and transition regions.  In e f f e c t , , the t e n s i l e  curves take on the  o f a sharp " y i e l d " r a t h e r t h a n a g r a d u a l p a r a b o l i c curve.. form:of p l a s t i c i. ii.  appearance  This  "yield"  f l o w i n i t i a t i o n i s p r o b a b l y due t o two a d d i t i v e  effects;  i n c r e a s e d d i s l o c a t i o n m o b i l i t y w i t h r e g a r d , t o temperature j decreased p r i o r , i n t e r n a l s t r e s s d i s t r i b u t i o n with regard  to  temperature.  16 It  i s a w e l l known f a c t  t h a t the  fraction-of plastic  t o g l i d e d i s l o c a t i o n a c t i o n i n c r e a s e s w i t h temperature at. the o f t w i n n i n g modes. sensitive  temperature i s  expense  D i s l o c a t i o n v e l o c i t y i s a l s o thought t o be much more  to a p p l i e d s t r e s s than twin propogation;  " y i e l d i n g " as  flow due  such would:be i n c r e a s i n g l y s e n s i t i v e  It  then f o l l o w s that  t o s t r e s s as  the  i n c r e a s e d ..thereby r e s u l t i n g , i n a sharper t r a n s i t i o n t o , the  low work h a r d e n i n g r e g i o n - I I .  The number o f s l i p modes i n c r e a s e s w i t h  temperature as w e l l , . t h e r e b y i n c r e a s i n g the r a t e o f m o b i l e d i s l o c a t i o n production.  - 67 -  The s e c o n d . f a c t o r which would suppress the p a r a b o l i c curve form w i t h i n c r e a s i n g temperature  i s . t h e r e d u c t i o n of " q u e n c h e d - i n "  r e s i d u a l s t r e s s e s due t o t h e r m a l expansion a n i s o t r o p i c s . d e f o r m a t i o n - t e m p e r a t u r e would t e n d t o - which g i v e - r i s e t o heterogeneous  -Increased  compensate the i n t e r n a l s t r e s s e s  y i e l d i n g amongst i n d i v i d u a l  grains.  Heterogeneous y i e l d i n g - m a s k s t h e t r u e homogeneous or coherent point.  A d i f f i c u l t y i n t h i s regard a r i s e s  s t r e s s e s were i n d u c e d by c o o l i n g , so t o o , The p o i n t of c o n j e c t u r e  however.  J u s t as  yield internal  may; t h e y be i n d u c e d by h e a t i n g .  i s t h e amount o f " t e m p e r a t u r e  t o cause p l a s t i c f l o w i n - o r d e r t o . r e l i e v e . t h e  change  necessary  induced s t r e s s e s .  From  . m e t a l l o g r a p h i c e x a m i n a t i o n a l l specimens showed s i g n s of s t r e s s therefore  the' temperature  change i s l e s s t h a n about, 4 0 0 ° C ,  c o o l i n g range. '..  that the d i s l o c a t i o n f a c t o r strain,does  the minimum  S i n c e the y i e l d . b e h a v i o u r i s o b s e r v e d t o  become p r o g r e s s i v e l y s h a r p e r w i t h i n c r e a s i n g - temperature  ,yield"  relaxation,  i s the more dominant one.  occur at a l l  (b) R e g i o n I I  is  thought  Considerable "pre-  temperatures.-..  --Low Work Hardening  The, i n t e r e s t i n g f e a t u r e  of region II  work h a r d e n i n g r a t e . w i t h temperature T h i s i s not expected  it  i s the constancy o f the  f o r the. temperature  i n t h e l i g h t o f the d r a s t i c  -mechanism o c c u r i n g i n t h i s temperature  range.  changes  range examined'. i n deformation  .The temperature  independence  seems t o i n d i c a t e . t h a t h a r d e n i n g mechanisms i n v o l v i n g d i s l o c a t i o n - t w i n 25  interactions  as d e s c r i b e d by L e t e u r t r e  are u n i m p o r t a n t , , s i n c e the  p r o p o r t i o n s o f each deformation-mode are a s t r o n g f u n c t i o n o f  relative  temperature.  - 68  -  A second n o t a b l e f e a t u r e i s t h a t the s t r a i n h a r d e n i n g r a t e i s •28-2Q a l s o independent o f g r a i n s i z e .  E x p e r i m e n t a l e v i d e n c e on o t h e r systems  shows a l a r g e r a b s o r p t i o n  o f s t o r e d energy and/or d i s l o c a t i o n d e n s i t y  for smaller grain s i z e s .  At h i g h s t r a i n s however, the a b s o r p t i o n  '  rates  become c o i n c i d e n t . - T h i s a l s o appears t o be the case f o r a l p h a - u r a n i u m s i n c e t h e g r a i n . s i z e e f f e c t on work h a r d e n i n g i s e v i d e n t l o w e r s t r a i n s , . r e g i o n I.and. t r a n s i t i o n  only at  the  region.  - I f the P e t c h or C o t t r e l l r e l a t i o n s h i p . b e t w e e n  grain size  and  flow, s t r e s s , i s assumed, i ,e., ~-  where  then  dT" d  if  j_  •=  ,  i s e i t h e r ( i ) ' g r a i n boundary s t r e n g t h ( P e t c h ) or ( i i ) s t r e s s . t o a c t i v a t e a;Frank-Read source (Cottrell) dT°  ,-.+  d^sT  d e.  ^ d^T"  *  f  • dTj  ±  d~e~  O 4  (D)  t h e n t h e flow, mechanismsr elated,-to d£  1/2  •=  ^  do not v a r y w i t h s t r a i n , i . e . ,  0.  . I f i t can be assumed;that d i s l o c a t i o n - t w i n and- d i s l o c a t i o n - g r a i n boundary mechanisms do not determine the work h a r d e n i n g r a t e t h e n the alternative vis dislocation-dislocation interactions. unlikely.because  only  T h i s i n t u r n seems  o f t h e i n c r e a s i n g , number o f d i s l o c a t i o n s l i p systems w i t h  t e m p e r a t u r e w h i c h would change the n a t u r e . o f t h e i n t e r a c t i o n s .  The occurrence of a r e g i o n o f f o r c e d s l i p .boundaries may be the mechanism.that  determines  - 69 -  9• at  the  grain  the work, h a r d e n i n g r a t e  i n a manner independent of g r a i n s i z e and d e f o r m a t i o n temperature.  Forced  s l i p a r i s e s because c o n t i n u i t y ' o f s t r e s s and s t r a i n has t o be m a i n t a i n e d at the g r a i n boundaries d u r i n g d e f o r m a t i o n . to maintain t h i s  .The number o f systems n e c e s s a r y  c o n t i n u i t y has been t h e o r e t i c a l l y  c a l c u l a t e d by Taylor^*-  t o be a minimum o f f i v e and s i x have been observed i n p r a c t i c e . the d e f o r m a t i o n mechanisms a c t i v e i n the  central  q u i t e a p a r t from the p e r i p h e r a l mechanisms. operative  regions  1  Therefore  of the g r a i n  are  The n e c e s s i t y , o f 5 or 6  systems must i n c l u d e b o t h t w i n n i n g and s l i p i n p r o p o r t i o n s , t h a t  are much l e s s  temperature dependent than t h a t which occurs i n s i n g l e  crystals.  •Studies  made on b o t h s i n g l e and p o l y c r y s t a l l i n e m a t e r i a l  have  shown only, 6 w e l l known and r e a s o n a b l y f r e q u e n t l y o c c u r i n g d e f o r m a t i o n . 3 t w i n n i n g and 3 s l i p systems.-  Therefore  it  i s reasonable  t o assume  systems; that  a l l the r e a d i l y a v a i l a b l e d e f o r m a t i o n systems must be u t i l i z e d i n the. f o r c e d s l i p process regardless  It  of  the•temperature.  i s a l s o i n t e r e s t i n g t o examine  work h a r d e n i n g : r a t e s .of .randomly o r i e n t a t e d , crystal  specimens.  work- h a r d e n i n g ' r a t e s •orientation. crystals^  i n . t h i s r e g a r d the  relative  p r e f e r r e d o r i e n t e d and s i n g l e  - T h i s , work ..has e s t a b l i s h e d , t h a t the randomly o r i e n t e d are  s u b s t a n t i a l l y h i g h e r than those of  preferred  . C o m p a r i s o n . t o the c o n s t a n t work h a r d e n i n g r a t e s of  single  shows, a work h a r d e n i n g r a t e t h a t i s again, lower than t h a t  the p r e f e r r e d m a t e r i a l . R.O.  The work h a r d e n i n g r a t i o s are  : P.O.  :.S.C.  =  lh  : 6 : 1  approximately  of  -70-  • Comparisons between s i n g l e c r y s t a l and  polycrystalline  work h a r d e n i n g . r a t e s f o r m e t a l s o f h i g h e r c r y s t a l l o g r a p h i c symmetry show 32  an approximate  equivalence  .  The g r a i n boundary c o n t i n u i t y has  little  e f f e c t on. t h e r a t e o f work h a r d e n i n g f o r t h e s e m e t a l s . . Because o f t h e marked .difference.between t h e work h a r d e n i n g r a t e s o f the randomly o r i e n t e d and s i n g l e c r y s t a l specimens i t i s e v i d e n t t h a t the g r a i n boundary c o n t i n u i t y c o n t r i b u t i o n t o work h a r d e n i n g i s a s t r o n g . f u n c t i o n o f p r e f e r r e d o r i e n t a t i o n . ..Therefore, i n t h e l i g h t o f t h i s i t can be c o n c l u d e d t h a t f o r c e d s l i p i s an i m p o r t a n t . 3 •  factor.  Temperature Dependence o f Flow' S t r e s s The manner i n which.the  t e n s i l e curves change w i t h  i s .quite s i m i l a r t o t h o s e o f b . c . c o r • h . c . p .  metals.  temperature  Temperature has  l i t t l e e f f e c t on t h e work h a r d e n i n g - s l o p e s o f t h e s e m e t a l l i c systems but a l a r g e change on.the magnitude o f f l o w s t r e s s . for' f . c c  m e t a l s i n . t h a t temperature  The  situation i s different  has a g r e a t e r e f f e c t on t h e work  h a r d e n i n g - s l o p e . . T h i s l a t t e r c a s e . i s deduced, t o be t h e r e s u l t o f subs t a n t i a l s t r u c t u r e changes ( d i s l o c a t i o n d e n s i t y , f o r example) w i t h for  temperature  any g i v e n s t r a i n .  . I t would appear t h a t , l i k e b . c . c . m e t a l s , uranium has a l a r g e P e i e r l ' s . f o r c e and. t h a t d i s l o c a t i o n , density,'does not change s u b s t a n t i a l l y with.temperature>  a l t h o u g h t h e m o b i l e d i s l o c a t i o n d e n s i t y may  change.  The, f a c t t h a t a ,large P e i e r l ' s . f o r c e e x i s t s i s s u b s t a n t i a t e d b y t h e o f ' t w i n n i n g • a n d t h e .temperature systems.  occurrence  dependence o f ' t h e number o f a v a i l a b l e  slip  - 71  The  f l o w stress'shows  -  a temperature-sensitive.to temperature-  i n s e n s i t i v e t r a n s i t i o n w i t h increasing.temperature  t h a t seems t o make a good  f i t w i t h the• t h e o r e t i c a l t e m p e r a t u r e independent f l o w s t r e s s . . The 1  t h e o r e t i c a l flow, s t r e s s was c a l c u l a t e d - f r o m room .temperature d i s l o c a t i o n d e n s i t i e s , i n d i c a t i n g a t e m p e r a t u r e independence o f t h e d i s l o c a t i o n distribution.  The r e l a t i v e amount.of s t r a i n r e s u l t i n g f r o m , d i s l o c a t i o n with'  a c t i o n w i l l change/temperature however. B.. G r a i n ' S i z e S e n s i t i v i t y o f Flow 1. P e t c h S l o p e as a - F u n c t i o n  ofStrain l/2  (a) A p p l i c a b i l i t y o f ( l / D The  ) Parameter  P e t c h parameter u t i l i z e d i n t h i s study/was a g e o m e t r i c f a c t o r  r e l a t e d t o the. g r a i n s i z e .  The f l o w s t r e s s s e n s i t i v i t y f a c t o r , k, i s , :~  o f c o u r s e , r e l a t e d - t o , t h e geometry o f t h e f l o w mechanism(s), w h i c h i n a c t u a l i t y may n o t depend on t h e average g r a i n s i z e . . T h e r e f o r e  t h e assignment  l/2  of a (l/D  ;) parameter b a s e d on average g r a i n s i z e measurements w i l l  give  measured k v a l u e s . (k ) w h i c h may, be c o n s i d e r a b l y a t v a r i a n c e w i t h t h e ffi  e f f e c t i v e k values ( k ^ ) . The. f o i l o w i n g . e f f e c t s w i l l p e r t a i n t o t h e v a l i d i t y o f t h e average g r a i n s i z e as. t h e p a r a m e t e r d e t e r m i n i n g  flow s t r e s s .  (i)'Residual internal stresses : ( i i ) Heterogeneous, f l o w , w i t h r e s p e c t t o g r a i n s i z e d i s t r i b u t i o n ( i i i ) Subgrain boundaries ( i v ) Twin b o u n d a r i e s - E f f e c t s ( i ) , . ( i i ) w o u l d b e . i m p o r t a n t only- i n t h e i n i t i a l .of f l o w w h i l e  ( i v ) and' p o s s i b l y - ( i i i ) a p p l y t h r o u g h o u t . 1  stages  -72  R e s i d u a l i n t e r n a l s t r e s s e s may  -  t e n d t o a l t e r , t h e measured  g r a i n s i z e s e n s i t i v i t y of flow. i n . t h e same manner i n w h i c h t h e y mask t h e yielding stress.  The e x t e n t and manner o f t h e a l t e r a t i o n i s d i f f i c u l t  t o a n a l y s e q u a n t i t a t i v e l y ; .'. Q u a l i t a t i v e l y , one would expect any a r i t y o r " s h a r p maximum.in. t h e .k a range o f s t r a i n s .  versus  singul-  curve t o be smeared out over  At h i g h e r s t r a i n s the r e s i d u a l s t r e s s  factor  would disappear.  I f t h e g r a i n s i z e i s the c o r r e c t g e o m e t r i c .parameter  determining  flow..in i t s i n i t i a l s t a g e s t h e n . t h e e x t e n t o f g r a i n s i z e d i s t r i b u t i o n w i t h i n a n y - p a r t i c u l a r specimen w i l l , a l t e r the observed f l o w s e n s i t i v i t y t rue v a l u e . - A c c o r d i n g t o . t h e P e t c h r e l a t i o n s h i p , t h e a b i l i t y  of a  from,the slip  band-to c o n c e n t r a t e s t r e s s v a r i e s w i t h the square r o o t o f t h e g r a i n s i z e . . T h e r e f o r e . i n t h e i n i t i a l s t a g e s o f f l o w t h e l a r g e r g r a i n s w i t h i n a specimen w i l l tend,. on t h e average,, t o cause f l o w .  The c o r r e c t g r a i n s i z e  parameter  i n t h i s case w o u l d n o t be the average g r a i n s i z e but some l a r g e r v a l u e . The e x t e n t t o w h i c h t h i s mechanism w i l l a l t e r t h e observed o r measured k can b e . e s t i m a t e d i n the. f o l l o w i n g Let  •=  way.  measured k effective k  then  km  A.T ACI/D// )  '= .  2  Ad/D V2 e  )  - 73  -  From:the g r a i n s i z e d i s t r i b u t i o n s shown i n Appendix I , the l a r g e s t g r a i n s i n any p a r t i c u l a r specimen a r e a p p r o x i m a t e l y the d e s i g n a t e d  twice  average.  .Therefore  i f  D Ac  e  e  —  •2 • D  ^  2AD  m  f f i  •• .  then ^  i„5  k . m  From t h i s : a p p r o a c h , . t h e  g r a i n s i z e s e n s i t i v i t y as m e a s u r e d f r o m :  a v e r a g e d g r a i n s i z e s i s . 5 0 ' p e r cent l o w e r t h a n t h e e f f e c t i v e s e n s i t i v i t y i f on t h e average t h e l a r g e s t g r a i n s d e t e r m i n e t h e i n i t i a l flow, s t r e s s .  -This  e r r o r w o u l d tend, t o v a n i s h as t h e e f f e c t i v e o r o p e r a t i v e g r a i n s i z e approaches t h e measured v a l u e s . - The e r r o r c a l c u l a t e d above i s an a b s o l u t e maximum s i n c e r e s i d u a l s t r e s s e s and random o r i e n t a t i o n w i l l l o w e r t h e maximum o p e r a t i v e g r a i n s i z e . strains.  F u r t h e r , t h i s would apply only a t v e r y low  The o b s e r v e d v a r i a t i o n o f k w i t h £  w i l l not vary appreciably  from, t h e e f f e c t i v e curve due t o t h i s e f f e c t s i n c e t h e v a l u e s a r e l o w a t s m a l l s t r a i n s anyway.  . The. r o l e s u b g r a i n b o u n d a r i e s t a k e i n d e t e r m i n i n g f l o w s t r e s s i s •i not c e r t a i n as t o s t r e s s magnitudes o r t o e x t e n t o f t e n s i l e s t r a i n s . I f they a r e important  i n r e s i s t i n g f l o w t h e n t h e o p e r a t i v e s t r a i n regions-  would be a t low s t r a i n s , due.to t h e p o s s i b i l i t y o f s u b s t r u c t u r e d i s p e r s a l  - 7^  at higher s t r a i n s .  -  F u r t h e r , t h e e f f e c t on t h e measured.k i s a l s o  u n c e r t a i n . . I f t h e s u b g r a i n s t r u c t u r e i s independent o f g r a i n - s i z e t h e n . t h e e f f e c t i v e k would be z e r o .  On t h e o t h e r hand t h e s u b g r a i n s i z e s  c o u l d v a r y l i n e a r l y w i t h the g r a i n s i z e . s e n s i t i v i t i e s w o u l d be t o o h i g h .  (D)  .In t h i s case t h e  observed  T h e . i n i t i a l , r a p i d i n c r e a s e of'k,  w i t h s t r a i n can be r a t i o n a l i z e d ; b y . i n v o k i n g t h e n o t i o n t h a t , i n i t i a l l y  y  s u b g r a i n s t r u c t u r e d e t e r m i n e s . f l o w . s t r e s s and t h a t the s u b g r a i n s i z e i s independent o f g r a i n s i z e .  T h i s i s c o n s i s t e n t and s u b s e q u e n t i a l w i t h  F r i e d e l s h i g h work h a r d e n i n g - t h e o r i e s i n c o n n e c t i o n w i t h s u b g r a i n boundaries.  T h e r e f o r e a t the onset o f f l o w s u b g r a i n  boundariesdetermine  f l o w and t h e s e n s i t i v i t y t o g r a i n s i z e would be z e r o . -As s t r a i n  continues  t h e s u b g r a i n b a r r i e r s g r a d u a l l y , b r e a k down and t h e s l i p bands p e n e t r a t e t o the g r a i n boundaries.  .In t h i s manner t h e g e o m e t r i c f a c t o r would  g r a d u a l l y be t r a n s f e r r e d from-the s u b g r a i n s i z e t o t h e g r a i n s i z e accompanied by an i n c r e a s e o f g r a i n s i z e s e n s i t i v i t y , t o f l o w . : I t i s n o t a b l e t h a t the maximum g r a i n s i z e flow, s e n s i t i v i t y - always o c c u r s a t O.5 s t r a i n r e g a r d l e s s of temperature.  .The  :  simultaneous  e r  cent  s t r a i n n e c e s s a r y t o cause s u b g r a i n  d i s p e r s a l would not be e x p e c t e d t o v a r y w i t h  The  P  temperature.  d e f o r m a t i o n mechanism - t w i n n i n g - a n d  the  r e s u l t a n t t w i n b o u n d a r i e s - s h o u l d be examined as a p o s s i b l e p e r t u r b a t i n g . f a c t o r on t h e assessment o f " g r a i n s i z e " . .Twin d e n s i t i e s are known t o increase gradually, w i t h s t r a i n , u n l i k e d i s l o c a t i o n d e n s i t i e s . o f t h e c o m p l e x i t y of t h e a l p h a - u r a n i u m  Because  c r y s t a l system t h e t w i n boundary  i n t e r f a c e s a r e under c o n s i d e r a b l e s t r e s s .  The atoms, o f t h e  orthorhombic  c e l l do not l i e . o n l a t t i c e p o i n t s and hence.the s t a c k i n g sequence p r e s e n t s a.problem o f accommodation a c r o s s . t h e t w i n i n t e r f a c e .  Further, a reaction  - 75 between. S h o c k l y d i s l o c a t i o n s a s s o c i a t e d w i t h t h e t w i n (121) the d i s l o c a t i o n s (010)  [100]  -  and  ( 0 0 1 ) [ 1 0 0 ] has been o b s e r v e d .  and  1 1  .This r e s u l t s i n the f o r m a t i o n o f s e s s i l e Frank d i s l o c a t i o n s . Therefore  i t would-appear, t h a t t w i n i n t e r f a c e s may. w e l l a c t as pseudo  g r a i n boundaries;  perhaps, t o a g r e a t e r e x t e n t . t h a n  i n s i m p l e r c r y s t a l systems,  I n t h i s case the o p e r a t i v e g r a i n s i z e s would become p r o g r e s s i v e l y s m a l l e r w i t h s t r a i n and the measured k would.become p r o g r e s s i v e l y h i g h e r t h a n the a c t u a l s e n s i t i v i t y , i . e . . i f t h e t e n d e n c y t o t w i n i s . independent o f g r a i n size,  then, D  e.=  D  m  (1+Q)  Cj  where  =  number- t w i n s / g r a i n  assuming from o b s e r v a t i o n t h a t  q =  K  e  then D  e  =  .  D  m  KC ) and  AD  =  e  A (1  then from  D +  m  K£).  (1)  (b) P i l e - U p The  Theories  g r a i n boundary, or s u b g r a i n boundary s t r e n g t h theory, as  advanced by H a l l and l a t e r - b y P e t c h g i v e s - r i s e t o a . g r a i n s i z e p r o p o r t i o n a l t o t h e magnitude o f t h e boundary, s t r e n g t h , i . e . 1/2  k  =  Tjr  1  b  1  •n(i--o-) ip  sensitivity  -.76-  where  _1  r a t i o o f g r a i n s i z e t o p i l e - u p l e n g t h ZZL c o n s t .  =  P *~  •• =  i  s t r e n g t h o f g r a i n boundary  The parameters t h a t c o u l d p o s s i b l y , - v a r y w i t h s t r a i n - a r e T ^ and p o s s i b l y l p .  , I f the c o r r e c t g e o m e t r i c f a c t o r i s the g r a i n s i z e , , the. o c c u r r e n c e of p e r i p h e r a l r e g i o n s o f f o r c e d s l i p ; w o u l d , t e n d - t o i n c r e a s e " ^ , t u r n would t e n d t o . i n c r e a s e , t h e k. 0.5  p e r cent s t r a i n . • The  temperature.  The  which i n  .In f a c t a marked- .decrease o c c u r s  sharpness:of  from  the. d e c r e a s e i n c r e a s e s w i t h  o n s e t o f f o r c e d s l i p would-be more g r a d u a l as. the  temperature i n c r e a s e d .  I n l i g h t o f t h i s , a s i m p l e mechanism i n v o l v i n g  boundary s t r e n g t h s does not seem l i k e l y . progresses  the r a t i o  distances  lp-  j-  . F u r t h e r , . a s work  hardening  would increase through a decrease i n p i l e - u p °  . The d e p i n n i n g  s t r e n g t h theory,, a f t e r C o t t r e l l , - p r e d i c t s a g r a i n  s i z e s e n s i t i v i t y dependent on s t r e s s e s r e s i s t i n g . d i s l o c a t i o n a c t i o n and the i n t e r a c t i o n . d i s t a n c e , i . e . , l / 2 r  k  Np  r  . . I n . t h i s case,, d i s l o c a t i o n s o u r c e s . t h a t are i n i t i a l l y s t r o n g l y locked:.would-cause a r a p i d d e c r e a s e o f k w i t h s t r a i n .  On the o t h e r hand  an absence o f d i s l o c a t i o n p i n n i n g ' would, cause work hardening, t o i n c r e a s e  k.  Any- e v i d e n c e o f an u p p e r - l o w e r y i e l d point-phenomenon, that- would.: i n d i c a t e the p r e s e n c e o f s t r o n g d i s l o c a t i o n l o c k i n g i s p r o b a b l y , masked by, t h e r e s i d u a l , i n t e r n a l . s t r e s s e s . . The  o b s e r v a t i o n of - a . " s o f t " u p p e r - l o w e r y i e l d  p o i n t a t h i g h temperature, does not n e c e s s a r i l y , imply, l o c k i n g ; massive-' d i s l o c a t i o n p r o d u c t i o n may.be the- e x p l a n a t i o n . . F u r t h e r m o s t i m p u r i t i e s i n - a l p h a - u r a n i u m , h a v e v e r y low s o l i d s o l u b i l i t i e s . :  These  complications  77 -make t h e i n t e r p r e t a t i o n  o f the. k w i t h r e s p e c t t o ^ T " i n c o n c l u s i v e , 1/2  The density.  i n t e r a c t i o n distance  r  could;be a . f u n c t i o n - o f d i s l o c a t i o n  A t room.temperature t h e . d i s l o c a t i o n  density, increases by a  f a c t o r o f ICO up t o k per- cent s t r a i n . . . T h e r e f o r e t h e i n t e r a c t i o n d i s t a n c e , i f determined.by d i s l o c a t i o n d e n s i t y , w o u l d . d e c r e a s e . r a t h e r r a p i d l y i n t h i s strain interval.  .This- dependence i s o b s e r v e d : t o o c c u r a t room t e m p e r a t u r e .  An e s t i m a t i o n o f t h e e f f e c t o f a 1 0 0 - f o l d . d i s l o c a t i o n d e n s i t y on t h e g r a i n s i z e s e n s i t i v i t y c a n be made. Assuming t h a t r  2  then  ~  where  then  V100  1/2  comparing.to t h e e x p e r i m e n t a l , r a t i o o f t h e maximum and c o n s t a n t const. •^max. k  •=  k values  1  ^  I t w o u l d appear t h r o u g h a comparison o f .the t h e o r e t i c a l - , , t o t h e observed; k r a t i o s t h a t t h e d i s l o c a t i o n d e n s i t y - d o e s  determine t h e  i n t e r a c t i o n d i s t a n c e , , r . However, i f t h e w i d t h o f s l i p , bands becomes, large.the a b i l i t y t o concentrate  stress•decreases.  The i n t e r a c t i o n  d i s t a n c e i n . t h i s case-would,be.determined,by t h e s l i p band w i d t h . F o r c e d s l i p a t • h i g h e r s t r a i n s would f u r t h e r t h e c o m p l i c a t i o n s .  ( c ) . G r a i n Boundary Source Theory The. g r a i n boundary source t h e o r y advanced.by L i - a s an alternative t o theories applicable basic  involving dislocation pile-ups  t o a •Lu'ders band type o f f l o w .  is strictly  However, u t i l i z i n g t h e  concepts,, the t h e o r y may be expended;to.flow: a t a n upper y i e l d  p o i n t and a t s t r a i n s a f t e r I i i d e r s . p r o p a g a t i o n .  The  most i m p o r t a n t o b j e c t i o n  t o the Fetch o r C o t t r e l l  i s the lack of d i r e c t observation of p i l e - u p s .  theorie  .For i r o n , i n p a r t i c u l a r  . d i s l o c a t i o n s , a p p e a r - t o be g e n e r a t e d . f r o m , g r a i n b o u n d a r i e s o r o t h e r interfaces.  These d i s l o c a t i o n s f o r m c l u s t e r s and t a n g l e s w i t h i n . t h e  g r a i n at? e a r l y , s t a g e s o f s t r a i n i n g . - L i 'proposed ..a/ mechanism;.whereby d i s l o c a t i o n s a d s o r b e d onto t h e g r a i n b o u n d a r i e s i n t h e form, o f l e d g e s , .move upon y i e l d i n g . ; i n t o t h e l a t t i c e .  . The e x t e r n a l  stress  required,.to  g e n e r a t e d i s l o c a t i o n s f r o m t h e s e l e d g e s i s s m a l l and t h e f l o w s t r e s s a t the. t i m e o f y i e l d i n g - w i l l be t h e s t r e s s , r e q u i r e d through the r e s u l t a n t  f o r e s t . - The t h e o r e t i c a l ; P e t c h  ,k -m  •= =  cK = The  slope f o r t h i s  _ - \ l / 2 1/2 jx b U8m)^ /D  mechanism i s  • where  t o move d i s l o c a t i o n s  :ledge  density  constant  g r a i n boundary donor t h e o r y can be extended t o t h e upper  y i e l d s t r e s s . b y a s s u m i n g : t h a t t h e d i s l o c a t i o n d i s t r i b u t i o n a t t h e upper y i e l d p o i n t s i s s l i g h t l y d i f f e r e n t from that a t the lower y i e l d , p o i n t . The. "donor" d i s l o c a t i o n s w i l l - be. a r r a n g e d t e m p o r a r i l y i n a. u n i f o r m d i s t r i b u t i o n near the g r a i n boundaries. established  The l o w e r y i e l d p o i n t i s  by a rearrangement i n t o c l u s t e r s o r c e l l u l a r  structures.  - 79  -The  -  i n t e r n a l s t r e s s e s due t o t h e two d i f f e r e n t arrangements can be • 33  d i f f e r e n t by as much as. a f a c t o r o f 2 i n a s i m i l a r manner.  .  The. P e t c h s l o p e s - w i l l behave  T h i s mechanism p r e d i c t s t h e observed, b e h a v i o u r  o f t h e g r a i n - s i z e f l o w s e n s i t i v i t y i n . t h e i n i t i a l stages: o f s t r a i n i n g . The e x t e n s i o n o f L i ' s . ; t h e o r y t o h i g h s t r a i n s must i n v o l v e d i s l o c a t i o n p r o d u c t i o n other than t h a t of g r a i n boundaries.  The  dislocation  p r o d u c t i o n r a t e o f t h e g r a i n i n t e r i o r i s e s t i m a t e d by assuming f i r s t • o r d e r . k i n e t i c s f o r d i s l o c a t i o n g e n e r a t i o n and second o r d e r k i n e t i c s f o r r e c o v e r y . The g r a i n boundary k i n e t i c s was grain size.  Utilizing  found, t o be i n v e r s e l y p r o p o r t i o n a l t o t h e  t h e s e concepts the P e t c h s l o p e was  t h e o r e t i c a l l y i f dynamic r e c o v e r y i s o c c u r r i n g .  found t o  decrease  I n f a c t the Petch slope  s h o u l d reduce t o n e a r l y z e r o and t h e r e b y e l i m i n a t e g r a i n boundary b e h a v i o u r i n t h e work hardened s t a t e .  This study e s t a b l i s h e d a constant  Petch  s l o p e i n - t h e low work h a r d e n i n g r e g i o n a l t h o u g h t h e e x p e r i m e n t a l  scatter  i n c r e a s e d . • T h e . f a c t t h a t the g r a i n s i z e s e n s i t i v i t y does n o t reduce t o z e r o a s . p r e d i c t e d by t h i s theory-may i m p l y a f o r c e d s l i p dependence. r e l a t i o n s h i p between-forced f  s l i p flow- s t r e s s and g r a i n s i z e i s n o t  -The  clear^  .-but ' t h e s p e c i f i c volume o f f o r c e d s l i p would.be e x p e c t e d t o i n c r e a s e 1  w i t h d e c r e a s i n g , g r a i n s i z e because o f the i n c r e a s e d g r a i n boundary a r e a p e r u n i t volume. As.a the b e h a v i o u r  summary o f t h e p o s s i b l e e x p l a n a t i o n s advanced t o e x p l a i n of k w i t h s t r a i n i t s h o u l d be e v i d e n t t h a t a c o n c i s e adherence  .'of-the e x p e r i m e n t a l r e s u l t s t o t h e o r y i s l a c k i n g .  Conversely a rough  c o r r e l a t i o n can be made w i t h segments o f a l l t h r e e t h e o r i e s . the decrease  o f k may  F o r example,  be a t t r i b u t e d . t o a - C o t t r e l l type- o f d e p i n n i n g , a  . d e c r e a s i n g i n t e r a c t i o n d i s t a n c e - o r a d i s l o c a t i o n rearrangement as  suggested  -  by L i .  80  -  The m u l t i p l i c i t y o f parameters involved-makes the i n t e r p r e t a t i o n  o f the. k b e h a v i o u r a.matter o f c o n j e c t u r e . p l a y s i s not c e r t a i n .  Moreover t h e r o l e t w i n n i n g  Any d e f i n i t e s t a t e m e n t s as t o t h e e x a c t mechanisms  o c c u r r i n g s h o u l d be complimented w i t h d i r e c t • • o b s e r v a t i o n v i a t r a n s m i s s i o n microscopy. 2.  • P e t c h S l o p e as - a F u n c t i o n o f  Temperature  (a) P i l e - U p T h e o r i e s . T h e o r i e s concerned w i t h t h e i n t e r a c t i o n between d i s l o c a t i o n p i l e - ' ups and g r a i n boundary, o r m u l t i p l i c a t i o n source s t r e n g t h s would a - marked^decrease  indicate  of g r a i n s i z e 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.  The s t r e n g t h parameters i n t h e r e s p e c t i v e k - t h e o r i e s s h o u l d . r e f l e c t t h e s t r o n g t e m p e r a t u r e dependence o f t h e m a c r o s c o p i c f l o w s t r e s s .  Further  i t i s unreasonable t o envisage a decrease i n d i s l o c a t i o n d e n s i t y which i n t u r n would i n c r e a s e t h e i n t e r a c t i o n d i s t a n c e , r . t r e n d i s expected.  In f a c t the reverse  These parameters t h u s p r e d i c t a d e c r e a s i n g P e t c h s l o p e  w i t h temperature c o n t r a r y t o t h e e x p e r i m e n t a l r e s u l t s .  . The o r i e n t a t i o n f a c t o r s m' and m"  should decrease w i t h i n c r e a s i n g  temperature as t h e number o f a v a i l a b l e s l i p s y s t e m s • i n c r e a s e s w i t h t e m p e r a t u r e . T h i s d e c r e a s e w o u l d enhance t h e d e c r e a s e o f t h e - s t r e n g t h p a r a m e t e r s . The p i l e - u p t h e o r i e s on f a c e v a l u e appear t o c o n t r a d i c t t h e o b s e r v e d t e m p e r a t u r e dependence o f the P e t c h s l o p e . • T h i s - c o n t r a d i c t i o n may be an i n h e r e n t f a u l t o f a p p l i c a t i o n o f t h e s e t h e o r i e s t o a l p h a - u r a n i u m o r a n o t h e r o v e r l y i n g f a c t o r i s d e t e r m i n i n g t h e temperature dependence.  - 81  -  (b) G r a i n Boundary Source Theory • The g r a i n boundary source t h e o r y p r e d i c t s a temperature dependence o f t h e P e t c h s l o p e . t h a t i s a f u n c t i o n o f t h e r e l a t i o n s h i p between t h e ledge d i s l o c a t i o n d e n s i t y and t h e i m p u r i t i e s .  F o r impure m a t e r i a l , t h e  Petch slope w i l l . d e c r e a s e w i t h temperature i f the i m p u r i t y s t a b i l i z a t i o n e f f e c t i s s t r o n g . . I f , however t h e i m p u r i t y s t a b i l i z a t i o n j u s t b a l a n c e s t h e f r e e energy o f l e d g e f o r m a t i o n w i t h o u t i m p u r i t i e s t h e n t h e P e t c h s l o p e i s i n s e n s i t i v e t o temperature.  The l e d g e t h e o r y p r e d i c t s ; t h e r e f o r e an  i n s e n s i t i v i t y or a decrease i n , k w i t h i n c r e a s i n g temperature.  I t i s i m p o r t a n t t o note t h a t t h e above argument i s based on a thermodynamic approach and t h e r e f o r e n e c e s s i t a t e s e q u i l i b r i u m c o n d i t i o n s . E q u i l i b r i u m : , c o n d i t i o n s may not be s a t i s f i e d , a t t h e t e n s i l e t e s t i n g tempe r a t u r e s and t h e temperature dependence i s t h e n a f u n c t i o n o f the a n n e a l i n g temperature.  T h i s f a c t p l u s t h e e f f e c t o f a n n e a l i n g t e m p e r a t u r e on s u b s t r u c t u r e  i l l u s t r a t e s t h e importance o f t h e a n n e a l i n g c o n d i t i o n s on P e t c h p a r a m e t e r s .  The P e t c h s l o p e has been shown t o be e i t h e r temperature  insensitive  3^-38 o r a d e c r e a s i n g f u n c t i o n o f t e m p e r a t u r e f o r many,metals  . .In g e n e r a l  the change i s s m a l l e r f o r b . c . c . metals, t h a n f o r f . c . c . o r h.c.p. (c) . D i s l o c a t i o n M o b i l i t y D i s l o c a t i o n p i l e - u p and g r a i n boundary source t h e o r i e s p r e d i c t a.-Petch s l o p e t e m p e r a t u r e s e n s i t i v i t y t h a t i s a t v a r i a n c e w i t h t h e experimental r e s u l t s i n t h i s study. .Apparentlyatemperature e f f e c t indigenous t o a l p h a - u r a n i u m i s o v e r - r i d i n g t h e b e h a v i o u r p r e d i c t e d by t h e o r y .  The  d o m i n a t i n g t e m p e r a t u r e dependence i n c o n n e c t i o n w i t h d e f o r m a t i o n mechanisms i s the v a r y i n g t w i n / d i s l o c a t i o n p r o p o r t i o n s . •  82  -  -  I t i s w e l l known t h a t s l i p i s r a r e . a t v e r y low t e m p e r a t u r e s with deformation  o c c u r i n g almost s o l e l y by t w i n n i n g .  As the t e m p e r a t u r e  i s i n c r e a s e d t h e predominance of t w i n n i n g g r a d u a l l y d e c r e a s e s u n t i l a t t e m p e r a t u r e s above 400°C s l i p becomes predominant^.  From t h e g r a i n s i z e  i n s e n s i t i v i t y e s t a b l i s h e d i n t h i s work f o r d e f o r m a t i o n  a t -196°C,,the  a s s u m p t i o n t h a t t w i n n i n g i n a l p h a uranium i s g r a i n s i z e independent may advanced. . L i n d l e y a n d Smallman, i n c o n t r a s t found a f i n i t e occurrence  twinning  Petch slope f o r vanadium^ .  The  w i t h s l i p as t h e d e f o r m a t i o n  mode w i l l t h e r e f o r e a c t as a p e r t u r b a t i n g  1  of twinning i n competition  e f f e c t on t h e g r a i n s i z e dependence o f s l i p . twinning i s favoured,  be  I n t h e l i m i t i n g . c a s e where o n l y  (low temperature),, t h e r e i s no g r a i n s i z e  effect;  w h i l e a t t h e o p p o s i t e extreme where o n l y s l i p , o c c u r s , t h e g r a i n s i z e e f f e c t w i l l be f u l l y m a n i f e s t .  A t t e m p e r a t u r e s i n between t h e s e  extremes,, t h e k v a l u e s w i l l e x p e r i e n c e  two  a transition.  . The m a c r o s c o p i c s t r e s s n e c e s s a r y t o cause t w i n n i n g i s not  considered  t o be u n i q u e and p o s s i b l y , i s t h e r e s u l t o f r e l a x a t i o n n e c e s s i t a t e d by extremely h i g h s t r e s s e s a s s o c i a t e d w i t h d i s l o c a t i o n p i l e - u p s .  Further,  s t r e s s e s necessary, t o cause t w i n n i n g seem, t o b e . t e m p e r a t u r e independent. variation  of. t w i n n i n g w i t h t e m p e r a t u r e i s , t h e r e f o r e a c t u a l l y t h e t e m p e r a t u r e  dependence o f s l i p and t h e a b i l i t y t o cause s t r e s s r e l a x a t i o n b y s l i p . m a c r o s c o p i c s t r e s s e s may  'e  VN  • = flow  .The  t h e n be c o n s i d e r e d on t h e average t o be a d d i t i v e , *  i  The  A  T  . •+ slip  T, . twin  where A and B a r e f u n c t i o n s , o f t e m p e r a t u r e and a r e r e l a t e d . t o t h e r e l a t i v e p r o p o r t i o n s of s l i p and  twinning.  - 83  Then the  • A.(^f°  =  + k/D  1/2 7  ) . +  T.  B  -  t w i n  measured g r a i n - s i z e s e n s i t i v i t y i s now .m k  where  A  =  A  k  1  <  As t h e r e l a t i v e preponderance  of s l i p t o t w i n n i n g i n c r e a s e s ,  A w i l l i n c r e a s e from a low v a l u e a t low t e m p e r a t u r e s t o t h e l i m i t i n g value of u n i t y at h i g h temperatures.  P e t c h s l o p e s as measured i n temperature  r e g i o n s where A i s not u n i t y a r e t h e r e f o r e low.  The above r e s u l t i s i n t e r e s t i n g i n t h a t t h e e f f e c t has an analogy i n connection w i t h the v a r i a t i o n of the Petch slope w i t h s t r a i n . A t low s t r a i n s , . d e f o r m a t i o n i s observed, t o be almost e n t i r e l y due t o d i s l o c a t i o n a c t i o n . . I n t h i s case A i s c l o s e t o u n i t y and the.measured ;  Petch slope i s - v a l i d .  A t some c r i t i c a l s t r a i n and above, d i s l o c a t i o n  a c t i o n appears t o d e c r e a s e t o a-low and c o n s t a n t v a l u e . - A w i l l : t h e r e f o r e decrease-and so w i l l t h e measured P e t c h s l o p e .  The i n i t i a l maxima  e x h i b i t e d a t a l l t e m p e r a t u r e s can t h e n be a t t r i b u t e d t o .a s t r a i n r e g i o n o f peak d i s l o c a t i o n a c t i o n .  An e x t r a p o l a t i o n of-;]s  1Dax  and k  c o n s  ^  values with  t e m p e r a t u r e shows an i n t e r s e c t i o n i n t h e r e g i o n o f 400°C t o 500°C. t h i s t e m p e r a t u r e r a n g e , s l i p w i l l be - Therefore i f the k max.  At  predominant.  v a l u e s a r e c o n s i d e r e d t o be r e p r e s e n t a t i v e '  o f . t h e a c t u a l g r a i n s i z e s e n s i t i v i t y o f d i s l o c a t i o n motion t h e n t h e P e t c h slope i s roughly i n s e n s i t i v e . t o temperature.  .This b r i n g s the e x p e r i m e n t a l  variation into line with the.theoretical predictions.  - 84 -  3.  . P e t c h S l o p e as a F u n c t i o n The  of Orientation  C o t t r e l l . d e p i n n i n g - t h e o r y s u g g e s t s two o r i e n t a t i o n , f a c t o r s  t h a t may v a r y i n d e p e n d e n t l y ,  i.e.  ( i ) m - w h i c h r e l a t e s , average r e s o l v e d s h e a r s t r e s s t o t h e macroscopic t e n s i l e s t r e s s . ( i i ) m" - w h i c h i n d i c a t e s t h e average m i s o r i e n t a t i o n amongst the g r a i n s , Increased  p e r f e c t i o n o f p r e f e r r e d o r i e n t a t i o n w i l l l o w e r t h e m" f a c t o r  t o l i m i t i n g , v a l u e s approaching, u n i t y , as i n a s i n g l e c r y s t a l .  The e f f e c t  i o f p r e f e r r e d o r i e n t a t i o n on m  i s n o t n e c e s s a r i l y , t h a t o f m . .This  f a c t i s i l l u s t r a t e d by comparing, t h e r e s p e c t i v e f l o w s t r e s s and P e t c h slope values  o f t h e p r e f e r r e d and "randomly" o r i e n t e d m a t e r i a l .  macroscopically while  microscopically  T  experimentally if  Tq-°=  £  . . ,k  m  m" t c  1/2 (r)  o v a l u e s a r e s i m i l a r a t low s t r a i n s , t h e n m  R0  —  experimentally if  =  °'^^"PO  —  0  m'  °-  6  m  P0  - po 2k  (X r / ) values are similar at low strains,, then 1  2  • (mm") 2r: R0  therefore  m^  0  The  3l / 3  2  (m'm")  po  0  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 has lowered, the mis-  o r i e n t a t i o n f a c t o r , m", between t h e g r a i n s b y a f a c t o r o f 3 l / 3 •  •In the lower l i m i t i s not  ideal preferred  of  m^  i d e a l and  .5  ^_  the m^Q  orientation  would be  o r i e n t a t i o n f a c t o r f o r randomly  has. been c a l c u l a t e d t o be  about 6 l / 2 assuming, b a s a l  • Alpha-uranium i s s i m i l a r i n t h a t one  slip  system.(010)  is:known t o be predominant a t room temperature. - T h e r e f o r e a would be  expected between the  uranium. An  the  somewhat, h i g h e r .  !  only.  land  l / 3 . Hpwever,. the p r e f e r r e d . o r i e n t a t i o n .  F o r h.c.p. systems a S a c h s oriented, grains  ^  85  [100],  similarity  o r i e n t a t i o n f a c t o r f o r h.c.p.. and  T h e r e f o r e an upper l i m i t f o r m^Q about 5-  average v a l u e would: t h e n be  would be  slip  alpha-  approximately 6 l / 2 .  --If "the "randomly"  oriented  specimens are p e r f e c t l y random then  ^0  —  ~  ^0  5  therefore  m"  11/2  "PO  i  The  -  8  t e n s i l e specimens w i t h p r e f e r r e d  o r i e n t a t i o n are not  well  17 oriented  f o r deformation.  show a s t r o n g .The o t h e r and  .This i s s u b s t a n t i a t e d  (010)[100] t e x t u r e  J  i n v o l v e d w i t h the  t o m a g n i f y i n g the  Petch slope.  metals o f lower symmetry and o f t e x t u r e . • The et a l  that  v a r y i n d e p e n d e n t l y of each  importance of ..other parameters  T h i s would be  e s p e c i a l l y important f o r  specimens h a v i n g . v a r i e d degrees or type  o r i e n t a t i o n dependence has  f o r magnesium.  1  about the t e n s i l e a x i s .  o r i e n t a t i o n f a c t o r s can t h e r e f o r e  contribute  by p o l e f i g u r e s  been a l s o e s t a b l i s h e d  by  Wilson  - 86  k,  \T° Characteristics The  e x a m i n a t i o n o f k has  a c t i v i t y i n . t h e i n i t i a l stages dominant t w i n n i n g and  indicated a concentration of d i s l o c a t i o n  o f s t r a i n f o l l o w e d by a r e g i o n of p r e -  forced s l i p .  T h i s sequence o f events must be  r e f l e c t e d by t h e l a t t i c e f r i c t i o n s t r e s s . • F i g u r e 19,  -196°C  The  p l o t of \j*  0  versus  ]  €.  shows an i n i t i a l r e g i o n of r e l a t i v e l y easy flow f o l l o w e d  a rapid-work h a r d e n i n g At  -  stage l e a d i n g ' t o the low work h a r d e n i n g  can be d e s i g n a t e d  region.  :  t h i s , easy flow r e g i o n does not  occur.  The  as t h e consequence 'of a.Ltlders type  easy flow o f flow  by  region  propagation.  I n t h i s r e g i o n d i s l o c a t i o n s are b e i n g generated i n t o r e g i o n s of low  dislocation  d e n s i t y v i a e i t h e r Frank-Read m u l t i p l i c a t i o n as i n the C o t t r e l l t h e o r y g r a i n boundary d o n a t i o n s to stage  as i n the L i t h e o r y .  or  T h i s mechanism i s comparable  I of the c l a s s i c a l s i n g l e c r y s t a l t e n s i l e  behaviour.  . T h i s massive d i s l o c a t i o n motion produces - s t r u c t u r a l c o n f i g u r a t i o n s t h a t impede f u r t h e r d i s l o c a t i o n m o b i l i t y and The  t r a n s i t i o n of d e f o r m a t i o n  i n c r e a s e s t h e work h a r d e n i n g  mechanism p l u s the occurrence r a t e i n t o the stage  I t i s i n t e r e s t i n g t o compare t h e ^ r t e n s i l e , curve  f o r s e r i e s B.  hence n e c e s s i t a t e  0  I I and  curve  twinning.  of forced  slip  Illregions.  f o r series A with  the  Both s e r i e s have a.random o r i e n t a t i o n , but  the B specimens had g r a i n s i z e s comparable t o the specimen t h i c k n e s s .  The  B specimens would t h e r e f o r e deform i n a.manner c l o s e r t o - t h a t o f a s i n g l e crystal.  • F i g u r e 20 shows t h a t B f l o w s t r e s s i s i n i t i a l l y h i g h e r than A  but becomes lower a t h i g h e r s t r a i n s .  The  lower work h a r d e n i n g  the B specimens i s a t t r i b u t a b l e t o a decreased  rate for  s e v e r i t y of forced  s i n c e the r a t i o of g r a i n s exposed at the specimen s u r f a c e i s high..  slip At  .  - 8  7  -  low. s t r a i n s i n t h e r e g i o n o f y i e l d i n g t h e r e i s enough g r a i n s i z e e f f e c t • to r a i s e . t h e B f l o w s t r e s s over t h a t o f t h e l a t t i c e f r i c t i o n s t r e s s as r e p r e s e n t e d i s therefore  by theT° curve.  The i n f l u e n c e o f g r a i n boundary c o n t i n u i t y  important.  C. • S t r a i n Rate S e n s i t i v i t y o f Flow 1.  Irreversibility The most, i n f o r m a t i v e r e s u l t s t o be d e r i v e d f r o m t h e s t r a i n r a t e  change e x p e r i m e n t s appear t o be t h e n a t u r e  o f " i r r e v e r s i b i l i t y " and t h e  r e l a t i o n s h i p w i t h s t r a i n and t e m p e r a t u r e .  R e v e r s i b i l i t y w i t h regard t o  deformation  mechanisms i s u s u a l l y c o n s i d e r e d  t o be t h e a b i l i t y t o c y c l e  between e x t e r n a l l y a p p l i e d r a t e dependent c o n d i t i o n s i n a manner w h i c h i s independent of... change d i r e c t i o n .  Considering  t h e v a s t amount o f c u r r e n t  research i n the f i e l d o f r a t e theory i t i s s i g n i f i c a n t that l i t t l e mention i s made o f i r r e v e r s i b l e e f f e c t s .  Evidently irreversibility i s rarely  ko observed or, a l t e r n a t i v e l y , overlooked  and i g n o r e d . • M a r t i n s o n  marked s t r a i n r a t e change i r r e v e r s i b i l i t y f o r L i F .  noted a  Some w o r k e r s i n f e r  i r r e v e r s i b i l i t y by d e f i n i n g e i t h e r the p o s i t i v e or negative  stress*changes  as r e v e r s i b l e and u t i l i z e o n l y t h e s e d a t a i n a p p l i c a t i o n t o r a t e  theory.  I r r e v e r s i b i l i t i e s t h a t show s i m i l a r t r e n d s f o r p o s i t i v e and n e g a t i v e i n c r e m e n t s may be due t o i n c o n s i s t e n c i e s i n h e r e n t i n t h e measuring  stress technique.  R e s u l t s w h i c h e x h i b i t d i v e r g i n g . t r e n d s , as i n t h i s work, cannot be r a t i o n a l i z e d , except by i n v o k i n g a t r u e i r r e v e r s i b l e deformation  phenomenon  o c c u r i n g d u r i n g t h e s t r e s s change. J o h n s t o n and S t e i n ^  1  suggest t h a t a c o n s i d e r a b l e change i n  m o b i l e d i s l o c a t i o n d e n s i t y may o c c u r d u r i n g a . s t r e s s change. • The e x p e r i m e n t a l l y observed i m p l i c a t i o n s were examined i n t h e f o l l o w i n g way.  - 88 AT  Empirically  =  (^  /f  Q  )  m  where VA = d i s l o c a t i o n v e l o c i t y m and ~t  0  are constant shear  £  theoretically where  =  0 = b = n •=  of the m a t e r i a l  stress 0  bnVT  orientation factor Burgers. V e c t o r mobile d i s l o c a t i o n d e n s i t y  combining and d i f f e r e n t i a t i n g ft  m  =  5  3  ln€l  m  l n t  E x p e r i m e n t a l l y , • m' has been shown t o i n c r e a s e w i t h s t r a i n . f o r L i F and f o r s i l i c o n i r o n . a stress  T h i s i m p l i e s a d i s l o c a t i o n d e n s i t y change w i t h  increment. Christian  k2 s u g g e s t s t h a t c o n s i d e r a b l e d i s l o c a t i o n re-arrangement  or m u l t i p l i c a t i o n may occur d i r e c t l y a f t e r a s t r e s s i n c r e m e n t . Johnston^  Oilman and  found t h a t m, when d e f i n e d , b y t h e e x t e r n a l l y a p p l i e d s t r e s s ,  increases with s t r a i n f o r L i F . s t r e s s due t o work h a r d e n i n g  A l s o , the increase i n macroscopic flow  i s approximately  equal- t o t h e s t r e s s  increment  needed t o m a i n t a i n a p a r t i c u l a r d i s l o c a t i o n v e l o c i t y . . U t i l i z i n g . t h i s n o t i o n o f an e f f e c t i v e s t r e s s , t h e d i s l o c a t i o n v e l o c i t y f o r m u l a may be r e d e f i n e d as  .ft  m  - not to be c o n f u s e d w i t h m' r e l a t e d . t o p r e f e r r e d o r i e n t a t i o n .  8  combining w i t h  d^T = then  0 bnV/""  =  9  -  and d i f f e r e n t i a t i n g  (^T- T(st) ( d i n t , T  -d Ln n)  .+  dT(st)  m  approximately  A'T =  (^T-^fst)  ( Aln 4- - A i n n)  +  A\(st)  m F o r an i d e a l r e v e r s i b l e d i s c o n t i n u o u s s t r e s s change AT(st)  Alnn then  = o  =  AX=  0  (T-V(st)  A  l n £  -  m and i f  ^ "NT"  _  \T~  (st) t h e n a - C o t t r e l l - S t o k e s obeyance w i l l h o l d  A^T =  (a  -  K)^  A, me  (2)  a w i t h s l o p e o f (1-K) A l ^ C .  .  I f K can be e s t i m a t e d , an e v a l u a t i o n o f m can be  attempted  from s t r a i n r a t e change d a t a p r o v i d i n g C o t t r e l l - S t o k e s l a w . i s m a i n t a i n e d . • F o r a, d i s c o n t i n u o u s s t r e s s change i n v o l v i n g a ..massive change i n s t r u c t u r e b u t e s s e n t i a l l y t h e same.mobile d i s l o c a t i o n d e n s i t y , . i . e . A^(s$  Alnn  *  o  =  0  The A ^ ~ ( s t ) i s d i s c o n t i n u o u s and w i l l n o t n e c e s s a r i l y be l i n e a r l y , r e l a t e d tq  the flow stress.  The s t r u c t u r a l c o n f i g u r a t i o n o b t a i n e d from a. d i s c o n t i n u o u s  90  -  s t r e s s change may  be q u i t e d i f f e r e n t from t h a t produced d u r i n g a g r a d u a l  stress increase.  The s t r a i n r a t e change r e s u l t s w i l l , t h u s be dependent  on-the ^ \ ^ [ ( s t ) =  -  term, i . e . , T  ( i --K) m  A ink  •+  A^~( t)  T h i s work showed i r r e v e r s i b i l i t i e s  (3)  s  i n the i n i t i a l stages of kO  s t r a i n i n g t h a t a r e comparable t o t h o s e shown by M a r t i n s o n  . -The  positive  s t r e s s increments e x p e r i e n c e a.minimum w i t h s t r e s s w h i l e i n t h e same r e g i o n t h e n e g a t i v e s t r e s s increments obey C o t t r e l l - S t o k e s , law.  The  positive  and n e g a t i v e s t r e s s increments t h e r e f o r e converge and c o i n c i d e a t h i g h e r s t r a i n s i n a.manner w h i c h i s temperature  dependent„  The p o s i t i v e  stress  i n c r e m e n t s a r e l a r g e r than t h e n e g a t i v e . i n c r e m e n t s . Because o f t h e e x t r a p o l a t i o n t e c h n i q u e u t i l i z e d  i n t h i s work  t h e s t r e s s i n c r e m e n t s were e s t i m a t e d a f t e r some s t r a i n i n g had  occurred.  Any s t r u c t u r a l changes r e s u l t i n g d i r e c t l y from t h e d i s c o n t i n u o u s i n c r e a s e i n s t r e s s a r e t h e r e b y i n c l u d e d i n t h e measured s t r e s s i n c r e m e n t s . •• S i n c e t h e p o s i t i v e s t r e s s v a l u e s a r e t h e g r e a t e r , i t would.appear t h a t c o n s i d e r a b l e s t r u c t u r a l . c h a n g e s a r e o c c u r r i n g d u r i n g t h e s t r e s s change.  A subsequent  s t r e s s decrement would not r e v e r s e t h e s t r u c t u r e change and hence i s s m a l l e r than the s t r e s s increment.  I t can be, t h e n c o n c l u d e d t h a t t h e s t r e s s " d e c r e -  ments more n e a r l y approximate  a " r e v e r s i b l e " change,than.the s t r e s s kk  T h i s v i e w . i s a l s o h e l d by M i t r a e t a l  ; a l t h o u g h , because of  increments., r convenient  geometry, t h e p o s i t i v e v a l u e s a r e u s u a l l y quoted by o t h e r w o r k e r s . .The  manner i n which t h e i r r e v e r s i b l e r e g i o n s o f t h e t e n s i l e  curve v a r y w i t h temperature, i s n o t a b l e .  The  s t r a i n s a t w h i c h t h e low  work h a r d e n i n g , c o n s t a n t P e t c h s l o p e , and c o n s t a n t d i s l o c a t i o n d e n s i t y  -  .regions.begin are a l l . reasonably c o i n c i d e n t w i t h t h a t f o r the r e v e r s i b l e region.  .  T h i s s i m i l a r i t y h o l d s f o r a l l ; t e m p e r a t u r e s t e s t e d except f o r  -196°C and i n t h i s case f r a c t u r e o c c u r r e d p r e m a t u r e l y . . of these:experimental involved.  91-  The  consistency  o b s e r v a t i o n s i n d i c a t e s . t h a t a common mechanism i s  An e x p l a n a t i o n t o account f o r the n a t u r e o f the s t r a i n r a t e  change r e s u l t s s h o u l d , t h e r e f o r e r e f l e c t . t h e n o t i o n s advanced p r e v i o u s l y .  • As p r e v i o u s l y , - a n d t e n t a t i v e l y e s t a b l i s h e d : the i n i t i a l of deformation  stages  e x p e r i e n c e r e l a t i v e l y d r a s t i c s t r u c t u r a l .changes; n o t a b l y ,  . a . r a p i d - i n c r e a s e . o f d i s l o c a t i o n d e n s i t y e i t h e r f r o m a, d e p i n n i n g o r a g r a i n boundary mechanism, a p o s s i b l e breakdown o f s u b g r a i n . b o u n d a r i e s , . r e l a x a t i o n o f "quenctjed-in" s t r e s s e s .  A discohtinu'pus. stress.  w i l l cause a marked s t r u c t u r a l .change t h r o u g h , t h e a l l o f t h e s e mechanisms.  The J^fi  st)  and  a  increment-  o p e r a t i o n o f any  or  would, t h e r e f o r e . r e f l e c t t h e e x t e n t .  and d u r a t i o n o f t h e s e changes w i t h r e g a r d t o s t r a i n . .The  s t r e s s decrement  would not b e . r e l a t e d t o much d i s c o n t i n u o u s s t r u c t u r a l .change and would . i n d i c a t e the t h e r m a l component o f f l o w stress.. - The p o s i t i v e s t r e s s increments  i n the i r r e v e r s i b l e . - r e g i o n s are .  t h e r e f o r e r e l a t e d , t o t h e a v a i l a b i l i t y o f s o u r c e s t h a t cause ..rapid s t r u c t u r a l changes. .The may  i n i t i a l h o r i z o n t a l regions t h a t occur a t lower temperature  i n d i c a t e a c o n s t a n t r a t e : o f s t r u c t u r a l change:;  At h i g h e r temperatures  . t h e d e p l e t i o n rate-iwould be h i g h e r and no h o r i z o n t a l .'region-exists . 1  rapid.decrease  t o a .minimum would be•due t o a d e p l e t i o n o f s o u r c e s , such as  g r a i n boundary, l e d g e s . .The  e x t e n t o f t h e i r r e v e r s i b l e r e g i o n s a f t e r the  minima are. t e m p e r a t u r e dependent and may availability.  The  be t h e r e s u l t o f the. s l i p system  - 92 The l i n e a r C o t t r e l l - S t o k e s r e g i o n o f t h e decrement changes s u g g e s t s t h a t the.: t h e r m a l s t r e s s component i n c r e a s e s p r o p o r t i o n a t e l y w i t h t h e a t h e r m a l component. at  The s l o p e s o f the c u r v e s v a r y from  low. t e m p e r a t u r e - t o l/20 a t t h e h i g h e r t e m p e r a t u r e s .  l/30  Applying  r e l a t i o n s h i p (2) t o t h e s e s l o p e s , an i n d i c a t i o n as t o t h e magnitude o f m may be estimated;, i . e . , m  =  (1 - K) A l n € . AV  Experimentally  A^T  The l i m i t s o f K a r e 45 t o 70 depending  v a r i e s from 0 t o 1.  l/20 t o l / 3 0 a n d  Aln£- • =  2.3.  The maximum-values o f m.are t h e n - a p p r o x i m a t e l y  on t e m p e r a t u r e .  The minimum v a l u e i s z e r o .  . . C h r i s t i a n has shown. t h a t m s h o u l d decrease w i t h i n c r e a s i n g temperature as f o u n d i n t h i s work. . R e s u l t s f o r K = 0 have been r e p o r t e d for  l i t h i u m f l u o r i d e , lk.5  m a t e r i a l s , 1.5  he  45  -'27  , s i l i c o n iron, kO :  ; and f o r some s e m i c o n d u c t i n g  •  • A t h i g h e r s t r a i n s t h e decrement changes d e v i a t e f r o m t h e C o t t r e l l - Stokes l i n e a r i t y and curve upwards :  . t r e n d o f t h e increment changes.  so as t o c o i n c i d e w i t h or. p a r a l l e l t h e  T h i s p o s i t i v e d e v i a t i o n - m a y be  attributed  t o t h e t h e r m a l component., i n c r e a s i n g d i s p r o p o r t i o n a t e l y t o t h e a t h e r m a l component. .The  r a t e d e t e r m i n i n g p r o c e s s i n the r e v e r s i b l e r e g i o n does not  a p p e a r - t o b e . t h e r e s u l t o f f o r c e d , s l i p s i n c e t h e s t r a i n r a t e change r e s u l t s were independent o f g r a i n - s i z e .  T h i s c o n c l u s i o n , however, i s based on t h e  a s s u m p t i o n t h a t f o r c e d s l i p i s a f u n c t i o n - o f g r a i n size.. t h e r a t e a t • w h i c h • t h e a t h e r m a l component.increases  Alternatively  may depend on the l o n g  range s t r e s s f i e l d s as d e t e r m i n e d by t h e average d i s l o c a t i o n d e n s i t y .  Therefore  the d e v i a t i o n . f r o m t h e C o t t r e l l - S t o k e s r e g i o n i s the r e s u l t o f a d e c r e a s i n g rate of d i s l o c a t i o n d e n s i t y increase.  - 93 -  I t i s i n t e r e s t i n g t o note t h a t - t e s t s performed a t -196°C showed a - s t r a i n r a t e dependence.  Twinning or the a s s o c i a t e d emissary .  ok dislocations  must t h e r e f o r e be t h e r m a l l y a c t i v a t e d .  The o c c u r r e n c e o f kl  t w i n n i n g i s known t o be s t r a i n rate.dependent f o r o t h e r m e t a l s  . .The  role that twinning plays i n the i r r e v e r s i b l e or reversible region i s uncertain. The manner i n w h i c h t h e i r r e v e r s i b l e . r e g i o n s v a r y w i t h t e m p e r a t u r e and s t r a i n appear t o c o r r o b o r a t e and compliment.the g r a i n s i z e and g e n e r a l tensile  observations.  2. A c t i v a t i o n Volumes The v a r i a t i o n o f t h e " a c t i v a t e d volume" as i n d i c a t e d . b y t h e Increment s t r a i n r a t e changes i s d i f f i c u l t t o r a t i o n a l i z e i n , t e r m s o f a rapid-initial  d i s l o c a t i o n density increase.  I f the rate determining process  i s based on a . f o r e s t i n t e r s e c t i o n mechanism, t h e n t h e a c t i v a t i o n volume s h o u l d n o t e x p e r i e n c e an i n i t i a l i n c r e a s e t o a maximum.  Therefore i t i s  d o u b t f u l t h a t t h e increment s t r e s s change v a l u e s i n t h e i r r e v e r s i b l e r e g i o n are  related t o a thermally activated process.  A c t i v a t i o n volume c u r v e s o f ko  t h i s form as d e t e r m i n e d f r o m p o s i t i v e s t r e s s changes have been r e p o r t e d No r a t i o n a l i z a t i o n was a t t e m p t e d however. I f t h e a c t i v a t i o n volumes; r e l a t e d t o decrement s t r e s s changes a r e assumed,to be t h e more r e p r e s e n t a t i v e of, t h e t h e r m a l l y a c t i v a t e d mechanisms, t h e n two c o n c l u s i o n s can be e s t a b l i s h e d . • F i r s t ; , t h e a c t i v a t i o n volumes i s  s o l e l y a . f u n c t i o n of the a p p l i e d  s t r e s s and hence i s e x p l i c i t l y independent o f t e m p e r a t u r e .  Further rate  t h e o r y e x p e r i m e n t s , such as temperature change t e s t s , should.be i n v e s t i g a t e d  - 4 9  b e f o r e t h e t e m p e r a t u r e . i n d e p e n d e n t r a m i f i c a t i o n s can be  Second;  -  illuminated.  i f t h e a c t i v a t i o n volume i s r e l a t e d t o d i s l o c a t i o n  d e n s i t y , t h e n d e c r e a s i n g the t e m p e r a t u r e a l l o w s an i n c r e a s i n g s t a b l e dislocation density to exist.  However, t h e o r e t i c a l a c t i v a t i o n volumes  as c a l c u l a t e d f r o m d i s l o c a t i o n d e n s i t i e s a r e somewhat h i g h e r t h a n  the  e x p e r i m e n t a l v a l u e s , . E i t h e r t h e f o r e s t i n t e r s e c t i o n mechanism.is determined  by l o c a l i z e d r e g i o n s o f h i g h d i s l o c a t i o n d e n s i t y o r some o t h e r  mechanism i s r a t e d e t e r m i n i n g . • F u r t h e r r a t e t h e o r y experiments  are  mandatory here as w e l l .  • D. • F r a c t u r e and D u c t i l i t y  -  I.- F r a c t u r e The - f r a c t u r e s t r e n g t h s o f a l p h a ^ u r a n i u m  have been r e p o r t e d 19,  t o show a maximum w i t h r e s p e c t t o t e s t i n g ' t e m p e r a t u r e  k  9  .  The  peak  f r a c t u r e s t r e n g t h occurs i n the b r i t t l e t o d u c t i l e t r a n s i t i o n r e g i o n which u s u a l l y o c c u r s between Q°C  and 100°C. • F u r t h e r , a l p h a - u r a n i u m  fails  by  ' t r a n s c r y s t a l l i n e c r a c k p r o p a g a t i o n i n t h e b r i t t l e r e g i o n and changes t o i n t e r c r y s t a l l i n e c r a c k i n g i n . t h e v i c i n i t y of the b r i t t l e - d u c t i l e -At h i g h t e m p e r a t u r e s , regions.  little  r a c  f a i l u r e i s due t o e x c e s s i v e f l o w i n h i g h l y , necked  T h e . r e s u l t s o f t h i s i n v e s t i g a t i o n v e r i f y • t h e known b e h a v i o u r . The  the k j .  transition.  ^.  t r a n s i t i o n o f f r a c t u r e mechanisms s h o u l d be r e f l e c t e d  behaviour.  The'Petch p l o t s f o r -196°C and 20°C show, r e a s o n a b l y  s c a t t e r i n d i c a t i n g a t r a n s c r y s t a l l i n e c r a c k i n g mechanism.  i n t e r c e p t s o f / t h e s e p l o t s do n o t p a s s . t h r o u g h ,  by  -The  t h e o r i g i n as suggested  in  8  C o t t r e l l s theory  for semi-brittle fracture.  A r e c e n t i n v e s t i g a t i o n by  50  'Taplin  suggests, t h a t an a p p r o x i m a t e . l i n e a r agreement e x i s t s between t h e  -95 I _L/ C  b r i t t l e f r a c t u r e s t r e s s . a n d t h e g r a i n s i z e parameter, 1/D  .  Due t o  an i n s u f f i c i e n t number o f e x p e r i m e n t a l p o i n t s a d e f i n i t e P e t c h obeyance was n o t e s t a b l i s h e d .  The f r a c t u r e s t r e s s i n t e r c e p t s were non-zero.  .However t h e r e s u l t s o f Lemogue  do obey C o t t r e l l s r e l a t i o n s h i p f o r  v e r y pure m a t e r i a l . a t -196°C. • The e x p e r i m e n t a l p o i n t s a t 100°C show c o n s i d e r a b l e s c a t t e r . .This o b s e r v a t i o n c o u p l e d w i t h m e t a l l o g r a p h i c e v i d e n c e i n d i c a t e a t r a n s i t i o n r e g i o n d u r i n g w h i c h i n t e r c r y s t a l l i n e c r a c k i n g i s becoming the d o m i n a t i n g  f r a c t u r e mode.  A t 270°C t h e k f  r a c  -t'  ^  s  equivalent• t o •  t h e a p p r o p r i a t e . k v a l u e s f o r flow, i n d i c a t i n g a y i e l d t y p e o f r u p t u r e . .Heavy c a v i t a t i o n i s s i g n i f i c a n t f o r t h i s type o f f a i l u r e . of  the.k|'  r a C  4  :  The v a r i a t i o n  .values can t h e r e f o r e be i n t e r p r e t e d t h r o u g h f r a c t u r e mode  transitions. 2.  Ductility The  t r a n s i t i o n t e m p e r a t u r e range from, t h i s s t u d y a g r e e s w e l l w i t h  51 previous d a t a . f o r hydrogen-free m a t e r i a l at approximately  ..  The d u c t i l i t y hump o c c u r r i n g  170°C has been r e p o r t e d b y T a p l i n ^ .  The apparent d e c r e a s e  i n d u c t i l i t y above t h i s t e m p e r a t u r e i s p r o b a b l y due t o t h e i n c r e a s i n g i n s t a b i l i t y of the necked.region w i t h i n c r e a s i n g temperature. .The.grain  s i z e e f f e c t on d u c t i l i t y i s due t o t h e l a r g e  k  f r a e t  values a t t h e lower temperatures w i t h respect t o t h e k values f o r flow. observation i s supported  This  by a p r e v i o u s l y e s t a b l i s h e d g r a i n s i z e dependence  50 of t h e b r i t t l e - d u c t i l e t r a n s i t i o n temperature  - 96 V. CONCLUSIONS l/2  1.  The flow- s t r e s s v a r i e s  l i n e a r l y - w i t h t h e parameter  (l/D• ' ) .  2. . The v a r i a t i o n o f t h e P e t c h s l o p e , k,, and t h e i n t e r c e p t , T - °> w i t h t e m p e r a t u r e and s t r a i n • i s - t h o u g h t  t o "be d i r e c t l y r e l a t e d t o t h e  importance o f g l i d e d i s l o c a t i o n a c t i o n r e l a t i v e t o t w i n n i n g . J.  Attempts t o c o r r e l a t e  the macroscopic g r a i n s i z e s e n s i t i v i t y o f  f l o w s t r e s s t o t h e m i c r o s c o p i c mechanisms as suggested by e i t h e r pile-up  k.  o r g r a i n boundary d o n a t i o n t h e o r i e s , were The t e m p e r a t u r e independence  dislocation  inconclusive.  o f t h e work h a r d e n i n g r a t e a t  - h i g h e r s t r a i n s i s t h o u g h t . t o be a t t r i b u t a b l e t o t h e importance o f g r a i n boundary 5.  continuity  and t h e r e s u l t i n g " f o r c e s l i p "  .The n a t u r e o f s t r a i n . r a t e  (or twinning).  change i r r e v e r s i b i l i t y a t l o w s t r a i n s  i s t h o u g h t t o be t h e r e s u l t o f massive s t r u c t u r a l changes; i n p a r t i c u l a r , dislocation 6.  density.  The t r a n s c r y s t a l l i n e c r a c k i n g f r a c t u r e  stress varies  linearly  l/2  w i t h t h e parameter  (l/D  ) and does n o t pass t h r o u g h t h e o r i g i n .  - 97 VI.  APPENDICES  APPENDIX I . G r a i n Growth .A.  A n n e a l i n g Data  .Specimen No.  A- 1  2 3 .4 B- 1 2 •3 4 5 C - -1 2 15 ,16 17 . 18 19 20 21 22 D- 1 2 3 4 5 6 7 8 9  15 16 17 18 19 20 21  -Annealing Temperature °C  625 625 625 625 625 625 625 625 625 625 550 625 . 625 655 655  58O-66O  625 660 660 525 425 625 575 475 640 525 575 625 + 640 575 575 500 625 600 500 475  Annealing Time hrs.  Grain Size microns  60 45  3/4 3/4 3/4 3/4 3/4 3/4 3/4 5/4 3/4 3/4 1/2 5 5 9 9 9 3/4  40  35 180 220 180 130 45 40 30 79 65 49 62 73  46  55 49 7-8  l  1/3 1 3 16 3 8 24 l 1/2 1 7 3 1/2 1/3 2 1/2 1 31 2 -3/4 3 1/4  not r e c r y s t a i  26.5 14.4 6.4 34.8 6.9 10.0  25.5 10.0 9,4 12.5 5-9 8.3 13.7 5-2 continued.  - 98 Specimen No.  Annealing Temperature °C  E- 1 (6 specimens)  2 3 k  5 6 7 8 9 10 11  " ••" " " " " " " "  Annealing Time hrs.  Grain Size microns  640  2 l/2  27.3  575 500 600 475 550 500 475 475 625 640  5 1/2 12 1/2 5  H-9  l  5  .3 A k 1/2 1.3A  l/3  1  ,  6.72 13-6 3-93 9-^0 5.13 5-^5 ^-95 15.2 220  - 99 -  O.JO  0,25  E-l  E-4  E-5  S 0.20^ •rH CQ  fl •H  cS  o  w  a3  0.15  fl o  -H  •P  § fe  o.iol-  o.05_  4  6  8  10  12  14  16  18  20  22  24  20  25  30  35  1  4o  45  J  50  L  55  G r a i n S i z e (microns) Figure 4 l .  H i s t o g r a m Showing G r a i n S i z e D i s t r i b u t i o n f o r Three G r a i n S i z e s from S e r i e s E  60  - 102 B.  G r a i n Growth K i n e t i c s .• Assuming t h a t f o r g r a i n growth n D  and  K  then  log  = D =  -  Ae  - Q  /  log'A  K R  t  T  - .-Q  2.3.R  .1  +  n  log t  T  U t i l i z i n g the. above form o f t h e r a t e e q u a t i o n and o n l y w e l l known a n n e a l i n g v a l u e s ,  t h e r a t e c o n s t a n t s n and Q were  calculated.  The time constant^ n , was determined t o be l / l O f o r a l l annealing.temperatures.  The A r r h e n i u s p l o t shown i n F i g u r e k2 shows two d i s t i n c t energy r e g i o n s .  The a c t i v a t i o n energy f o r ' t e m p e r a t u r e s . b e l o w  activation  600°C i s  c a l c u l a t e d .to be 11 k i l o c a l o r i e s p e r mole w h i l e above 60Q°C t h e a c t i v a t i o n energy seems t o i n c r e a s e .  ,This  "apparent"  • .  a c t i v a t i o n energy i s d e s c r i b e d by Rath and  Gordon-^ i n c o n n e c t i o n w i t h t h e i r aluminum. to.be  A t h i g h temperatures  studies  o f g r a i n boundary motion i n  the g r a i n boundary m i g r a t i o n was found  s o l u t e - i n d e p e n d e n t w i t h a low a c t i v a t i o n energy w h i l e a t low temperatures  t h e m i g r a t i o n was s o l u t e "breakaway" temperature  dependent w i t h a h i g h e r a c t i v a t i o n energy. l a y a t some i n t e r m e d i a t e v a l u e .  ..the. break i n t h e curve i s p r e c i p i t o u s , but i n p r a c t i c e because  Theoretically, i t i s more g r a d u a l  o f l o c a l inhomogeneities i n d r i v i n g energy and- s o l u t e  ..The. t r a n s i t i o n r e g i o n was f o u n d - t o g i v e " a p p a r e n t "  The  activation  concentration. energies  t h a t - a r e very. h i g h .  Therefore,  f o r uranium a n n e a l e d below 600°C t h e s o l u t e atoms a r e  d i s p e r s e d and a c t . a s b a r r i e r s  t o g r a i n growth.  Above 600°C t h e i m p u r i t i e s  16 b e g i n t o c o a l e s c e and cease t o be e f f e c t i v e b a r r i e r s  t o g r a i n growth  .  .  - 104 -  T h i s t r a n s i t i o n :reg.ion has than the  "apparent"  a c t i v a t i o n energies, much h i g h e r  s o l u t e - d e p e n d e n t , r e g i o n and, i n t h i s c a s e ,  k i l o c a l o r i e s p e r mole.  i s about  30  - 105 APPENDIX I I .  T e n s i l e Experiments A. G r a i n Size'.Experiments .Flow s t r e s s , v a l u e s were o b t a i n e d f r o m approximately.'10 s t r a i n v a l u e s f o r a l l t h e f o l l o w i n g specimens. - A l l specimens were t e s t e d a t a s t r a i n r a t e o f 1 p e r c e n t p e r minute. pecimen E-l-2 2 3 k  5 6 7 8 9 10  :  Test  Temperature °C -196 -196 -I96  -196 -196 -196 -196 -196 -196 -196  A-1-1 2 3  20 20 20 20  B-l-l 3  20 20 20  k  .k  C-15-1 16 17 • 18 19 20 21 22  20 20 20 20 . 20 20 20 20  B-k-1  . 20 20 20 20 ' 20 20  5 6 •7 .8 . 9 E-l-l 2 3 •5-  Specimen  20 20 20 20 •20  Temperature °C  E-6-1 7 8 .. 9 10 11  20 20 20 •20 20 20  E-l-4 2 3  100 100 100 100 100 100 100 100 100 100  k  5 6 7 8 9 10 D-15-5 16 17 18 19 20  170 170 " 170 170 170 170  E-l-3 2 3  270 270 270 270 270 270 270 270 .270 270  k  ;  Test  .5 6 7 8 •9 .10  -  -106 B.  S t r a i n Rate Change Experiments  Specimen  Temperature ^C  S t r a i n Rate R a t i o . (inch/min)  E-12-2  -196  0.01/0.1  •E-12-1 13  20 20  0.01/0.1 0.01/0.1  E-12-4 13 1 2 3 4 .5 6 7 8 9  100 . 100 ,100 100 100 100 100 100 100 100 100  0.01/0.1 0.01/0.1 0.01/0.1 0.01/0.1 0..01/0.1 0:Ol/O.l 0.01/0.1 0.01/0.1 0.01/0.1 0.01/0.1 0.01/0.1  •.E-10-5  170  0.01/0.1  D-15-5 16 17 18 19  170 170 170 170 170  E-3-3 4 5 J6 7 8 9 10 7  270 270 270 270 270 270 270 ,270 270  , j :  Remarks  Specimens E - l t o 9-4 t o investigate grain s i z e e f f e c t on  0.01/0.05 O.OI/0.O5 0.01/0.05 O.OI/0..O5 0.01/0i05  Specimens D-15-19-5 s u b j e c t e d . t d one t e s t p e r specimen,  0.01/0.2 0.01/0.2' 0.01/0.2 0.01/0.2 0.01/0.2 0.01/0.2 0.01/0.2 0.01/0.2 0.01/0.1  Specimens E-3 t o 10-3 s u b j e c t e d t o one t e s t p e r specimen.  - 107 APPENDIX- I I I . • Estimates'of Error A.- Grain Size Determination For the accurate grain size determinations, from which the majority of the t e n s i l e specimens were taken (series-D and E), the grain size was determined from an average of about 1400 grains, -Taking batch E-8 as an example the probable error from - the mean may be estimated from Peter's formula: P.E.  0.84$  .=  V where  =  < £ \ | .j v  n (n-1)  i = 1, 2 —  n  i  difference between the calculated-mean and the j_th measurement.  -Experiment observations i n one d i r e c t i o n only, about 700 grains, gave a calculated mean of 17.7 grains/unit length. Measurement Grains/unit length  1 2 . •3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 1920 21 22 23 24 25  J  .24  - 25 14  18 18 24  17 15 18 20 13 13 20 20 16 11 17 17 15  •. 14  18 17 19 20 18  Vj_  6.3 7.3 3,7 0.3 0.3 6.3 0.7 2.7 0.3 2.3 .4.7  4.7 2.3 . 2,3 1.7 6.7 0.7 . 0.7 2.7 3-7 .0.3 0.7 1-3 .2.3 0.3  - 108 Grains/unit  Measurement  26 27 28 29 30 31 32 33 3^ 35 36 37 38 39 40  length  16 10 15 .18 22 .18 17 21 19 19 17 18 20  1,7 7-7 2.7 0.3 4.3 0.3 0.7 3-3 1.3 1.3 0.7 0.3 2.3 6.3 • 2.7  :2k  15  1*0  n =  and  P.E.  =  1  0.84^  (101.2)  =  2.16  V(40.)(39) . T h e r e f o r e t h e mean number o f g r a i n s / u n i t  Since  D  where  then  A D Cn  =  length  = =  17-7 * 2.2 X ;  K X"  K i s a microscope c a l i b r a t i o n f a c t o r .  K X  A  X  2  d  therefore  97.0  .(17.-7)*  (2.2)  the mean g r a i n D .-  .5.47  =  0.68 microns  size i s ±.  0.68 m i c r o n s .  The a c c u r a c y i s a c t u a l l y somewhat b e t t e r than t h i s . s i n c e t h e g r a i n f o r b o t h p e r p e n d i c u l a r d i r e c t i o n s were, o b t a i n e d and averaged.  sizes  - 109 l / 2 becomes  • The e r r o r involved, w i t h the P e t c h parameter l / D i n c r e a s i n g l y important w i t h decreasing g r a i n s i z e , i . e . A <I/D ) ~ 1/2  i4a,  / ?  -l/2 For t h i s example,. E-8,, the. ( l / D s i z e i s one o f t h e s m a l l e s t . A (l/D / ) d - 1 2 1  ) e r r o r i s l i m i t i n g since the g r a i n ( 0 . 6 8 X lo"?mm) (5.47 X 10~ mmp/^  2  3  0.84  mm  •1/2  T h e r e f o r e t h e mean P e t c h parameter i s  (I/D / ) 1  2  =  13.5 ••* 0.8  The  e r r o r r e l a t e d , t o the l a r g e r g r a i n s i z e s decreases  B.  T e n s i l e Stress- Parameters D i f f e r e n t i a t i n g the r e l a t i o n T  <JV T The  .=  ~^ F  =  F(load) A(area)  considerably.  yields  2 c)X  *  F  X  e r r o r i n measuring.the specimen dimensions i s e s t i m a t e d t o  be a p p r o x i m a t e l y 1 p e r c e n t , i . e . ,  c) X Ci-0.01 The  e r r o r i n measuring t h e f l o w s t r e s s o r change i n f l o w  stress  i s e s t i m a t e d to.be a s f o l l o w s : -. ( i )  Flow s t r e s s a c c u r a c y  =  *  O.5H0S  F o r a minimum f l o w s t r e s s o f - 3 0 l b s , t h e e r r o r i s O.5/30 — 1.5 p e r c e n t . The maximum e r r o r i s t h e n  =  T  0.015  +  2 (0.01) ~  3.5 p e r cent  - no -  (ii).The is  critical  a c c u r a c y i n d e t e r m i n i n g the change i n flow s t r e s s ,  AT,  and c a n . b e : e s t i m a t e d by p u t t i n g  ~b ( A T ) AT  =  "pTg* A T  The minimum-value of  was 5 l b s and the a c c u r a c y was * 0 . 5 l b s .  Therefore d  (AM")  AT  =  0.5  +.5 5  =  20 p e r cent  -•in V I I .•• REFERENCES 1. .2.  Calm, R . W . ,  A c t a M e t . 1,  L l o y d , - L . . T . ,• C h i s w i k ,  3-  Teeg,,R.  k.  LeMogne, A . , Lacombe,  %  (1953).  H . . H . • , • T r a n s . . A . I . M . E . . 203,  1206 (1955).  0.,- O g i l v i e , R . . E . , J . N u c l . M a t e r . , 3 ( 1 ) , 8 l - ( 1 9 6 l ) . P . , J . Nucl..Mater.,  8 (1),  116  (1963).  . 5 . - A n d r e , J . P . , G r e n i e r , • P . , • C o m p t e s R e n d u s , g5_6 ( 7 ) , 1511(1963). 6. 7.  Hall,E.  0., Proc.  Phys. - Soc.,  •P e t c h , - N . J . , J . Iron Steel  London,.B64, 7V7 (1951)-  I n s t . , . ljA,  25 (1953)-  8.  C o t t r e l l , , A . H . , Trans. Met. • Soc. • A ; I . M . E . ,  9.  Johnson,A.  10. 11.  Eshelby,  A . , Phil.  M a g . J , . (7^), I77 (1962).  J . D . , • Frank, F. C , Nabarro,  -Armstrong,  212,,192 (1958).  R . , et a l . , P h i l .  F . R. N . , P h i l .  M a g . 42, 3^1 (1951)  M a g . J_, 45 (1962).  12.  Brandon, D. G . , N u t t i n g , J . , J . T r o n S t e e l  13.  L i , J . . C . M . , • Trans . M e t . S o c - A . I . M . E . ,  14.  Harrington, C. D . , Ruehle,  Inst.  227 ( 1 ) ,  196, 160 ( i 9 6 0 ) . 259 (1963).  A . E . , "Uranium-Production  Technology",  V a n N o s t r a n d , N . J . , . 2 6 8 (1959). 15.  Taub,  J . M . , D o l l , , D . T . , Hanks, G. S . , " C o l d Working o f Uranium",  U.S.A.E.C 16.  R e p o r t LA-2071, 95 (1957).  Holden,. A. N . , . "Physical Metallurgy  116  of Uranium",.Addison-Wesley,  Mass.,  (1958).  17.  L l o y d , L . . T . , • M u e l l e r , M. H . , " R e c r y s t a l l i z a t i o n i n R o l l e d Uranium S h e e t " , U . S . A , E . C . R e p o r t , . ANL-6327, 22 (1962).  18.  D o u g l a s s , • D . - L . ,• B r o n i s z ,  S . •E . , . Trans . M e t . S o c . A. I . M . E .  22J_, 1151  (1963). 19.  Taplin,,D. M. R . M a r t i n , J . W., J . Nucl.-Mater.  20.  F r i e d e l , J . , "Internal Stresses and Fatigue Rassweiler,  W. L . G r u b e , , E l s e v i e r ,  21  McLean,-D.,- "Mechanical Properties  22.  Laquer,  25.  Reynolds,  24.  Ruedl, E . , Amelinckx,  25.  Lefeurtre,  H. L.,,Trans.  A.S.M.  10, 154  (I965).  i n Metals,- E d . . G . M.  N . Y . , , 257 (1959).  of Metals",.Wiley,,N.Y.,  85.  42, 7 7 1 ( 1 9 5 0 ) .  M . B . , , T r a n s . - A . S . M . 4_5_, 859 (1953). S. A . J . Nucl. Mater,  J . , J . Nucl. Mater.  9 . ( 1 ) 1 1 6 (1963).  6 ( 3 ) , 338 (1962).  (I962).  -112  -  • References Continued....  26.  H u l t g r e n , F.,  27.  • Stein,. D.F.,  28.  T r a n s . Met. Low,  Soc-  A.I.M.E.,  230 (4), 898 (1964).  J . - A p p l . Phys. 31,  J . R.,,  362 ' ( i 9 6 0 . ) .  Clarebrough,.L.•M., Hargreaves,• M.E.,• L o r e t t o ,  M. . H. ,• A c t a .  Met.  6 725 (1958). 29.  Weissmann, S.,  Keh,  C r y s t a l s " , Ed.  255 (1963).  30.  Taylor,  31.  Lacombe, P.,  G.  A . S . , • " E l e c t r o n M i c r o s c o p y and G.  Thomas,,J.. Washburn, I n t e r s c i e n c e ,  33-  34.  N.Y.,  " R e c r i s t a l l i s a t i o n e t C r o i s s a n c e de Gros C r i s t a u x  McLean, D.,  "Mechanical P r o p e r t i e s  of M e t a l s " , W i l e y , N.Y.,  -Wronski,. A.S.,. Johnson,,A.A., P h i l . Mag. Armstrong,- R.,  36.  Conrad, H.,  37.  Lindley,  J_  123 (1962).  SmalLman, R..E., A c t a . Met..11  .Wilson,.D. V.,  Chapman, J . A.,  P h i l . Mag.  39.  Sachs,. G.,'Z. V e r . d t s c h Ing.  40.  Martinson,. R.H. ,..M.A-.Sc. T h e s i s ,  41.  J o h n s t o n , .W.  42.  C h r i s t i a n , - J . W.,  43.  Gilman, J . J . , J o h n s t o n , W.  44.  M i t r a , • S . K.,  (5), (1963),  8 (93)  1543  (I963).  J_2, 734 (1928). University  G.,-Stein,..-D.F.,, A c t a . Met.  11,  o f B r i t i s h Columbia 317  (1963) .  (I963).-  12, 99.(1964).  A c t a . . Met.  ;  ;  19_8, August (196l)'364.  J . Iron S t e e l Inst.  T.C.,  Ed.  (74) 213 (1962).  X, 45 (1962).  et a l . P h i l . Mag.  d'Uranium- ' "  15_, (i960).  L i , J . M. C., " E l e c t r o n M i c r o s c o p y and S t r e n g t h of C r y s t a l s " , G.- Thomas, J . Washburn,. I n t e r s c i e n c e , N.Y., (1963).  35.  38.  of  62, 307 (1938).  I . , • J . Inst. Metals  from. "Nouveau t r a i t ^ de Chimie Mine'rale"  32.  Strength  G . , J . A p p l . Phys.  31, 687 (i960).  Osborne, P. W.,.Dorn,.J.E., T r a n s . Met.-Soc.-A.I.M.E.  1206 (1961). 45.  J o h n s t o n , W.G.,  46.  Chaudhuri,-A.R., e t a l . J . A p p l . Phys.  47.  Causey, A.R.,-M-.A-.Sc. T h e s i s ,  Gilman, J  .J.,. J . - A p p l . Phys .. 3_0, 129 (1959) •  33, 2737 (1962).  University  o f B r i t i s h Columbia  (1963).  221  - 113 References  48.  Gregory,  49.  Lemogne,-A.,  D . P . , A c t a . Met. Morin,  Continued.  11, 455 (1963).  J . , Lacombe,  P.,  Comptes R e n d u s ,  257 (1^) 20J2  (1963). 50.  T a p l i n , D . , M. • R . , • M a r t i n J . W . , J . Less-Common M e t a l s  51.  Marsh, L . L . , "Effect  o f H y d r o g e n on t h e  Uranium",. U.S. A . E . C . 52.  Tensile  R e p o r t BMI-98O  7 89 (1964).  Transition in  (1955).  R a t h , y B . B . , Gordon P . , " S i n g l e Boundary M i g r a t i o n i n Deformed C r y s t a l s o f Aluminum',' P h . D . • T h e s i s , I l l i n o i s I n s t i t u t e o f T e c h n o l o g y .  

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