The influence of polycrystal grain size upon the creep ductility of copper
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T H E p r e s e n c e of g r a i n b o u n d a r i e s m a y s t r e n g t h e n o r w e a k e n a m a t e r i a l depending upon the t e m p e r a t u r e , s t r e s s , and s t r a i n rate of the t e s t . The H a l l - P e t c h r e l a t i o n (flow s t r e s s p r o p o r t i o n a l to the r e c i p r o c a l s q u a r e root of the g r a i n d i a m e t e r ) has b e e n shown to hold at low t e m p e r a t u r e s (T ( 0.3T m) and high s t r e s s e s for a v a r i e t y of m a t e r i a l s w h e r e s l i p is the m a j o r mode of d e f o r m a t i o n . This r e s u l t is o b t a i n e d as long as the g r a i n b o u n d a r i e s offer s o m e r e s i s t a n c e to the d e f o r m a t i o n s y s t e m s o p e r a t i n g within the g r a i n s and so long as the d e f o r m a t i o n is p r e d o m i n a n t l y i n t r a g r a n u l a r . At t e m p e r a t u r e s above 0.4T m and at low s t r a i n r a t e s and s t r e s s e s , the g r a i n b o u n d a r i e s can c o n t r i b u t e to w e a k e n i n g m a t e r i a l s . In this c o n t e x t m a y be cited the p h e n o m e n o n of e x c e e d i n g l y soft " s u p e r p l a s t i c " b e h a v i o r at high t e m p e r a t u r e s with m a t e r i a l s having g r a i n s i z e s of a r o u n d 5 g m a v e r a g e d i a m e t e r or l e s s . This w e a k e n i n g effect can a r i s e b e c a u s e : a) g r a i n b o u n d a r y s l i d i n g o c c u r s in an i n c r e a s i n g a m o u n t as the g r a i n size d e c r e a s e s , so b e c o m i n g the p r e d o m i n a n t mode of d e f o r m a t i o n ; b) with d e c r e a s i n g g r a i n s i z e , the n u m b e r of s u b boundaries restricting dislocation motion across a g r a i n d e c r e a s e s until at v e r y fine g r a i n s i z e s , the g r a i n s m a i n t a i n v e r y low d i s l o c a t i o n d e n s i t i e s ; c) the g r a i n b o u n d a r i e s e n h a n c e diffusion p r o c e s s e s and h e n c e r e c o v e r y r a t e s ; d) at fine g r a i n s i z e s N a b a r r o - H e r r i n g diffusion c r e e p c a n c o n t r i b u t e s i g n i f i c a n t l y to softening; e) the g r a i n b o u n d a r i e s c a n m i g r a t e so e n h a n c i n g r e c o v e r y : the r a t e of r e c o v e r y by this p r o c e s s will be g r e a t e r the f i n e r the g r a i n s i z e . Although s o m e a t t e m p t s have b e e n made to r a t i o n a l ize t h i s b e h a v i o r of c o m p e t i n g s t r e n g t h e n i n g and w e a k e n i n g p r o c e s s e s in a q u a n t i t a t i v e m a n n e r , these have not yet b e e n c o m p l e t e l y s u c c e s s f u l . B a r r e t t , Lytton, and Sherby 1 have i n v e s t i g a t e d this p h e n o m e n o n d u r i n g the c r e e p of copper and o b s e r v e d R. G. FLECK and D. M. R. TAPLIN are Graduate Student and Associate Professor, respectively, Department of MechanicalEngineering, Solid MechanicsDivision, University of Waterloo, Waterloo, Ontario, Canada. G. J. COCKS is Graduate Student, Department
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