Comparison of strain hardening in polycrystals and <111> single crystals: The example of copper
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R E C E N T w o r k on the r e l a t i o n of p o l y c r y s t a l s t r a i n h a r d e n i n g to that of i s o l a t e d s i n g l e c r y s t a l s h a s gene r a l l y upheld the a n a l y s i s of T a y l o r . hz Not only have a n u m b e r of T a y l o r ' s a s s u m p t i o n s b e e n shown to be v a l i d , ~ but the p a r a l l e l a n a l y s i s of Bishop and HIll 4'5 h a s b e e n p r o v e d to b e wholly e q u i v a l e n t to T a y l o r ' s . 6 An I m p o r t a n t a s s u m p t i o n was that h a r d e n i n g r a t e s on a l l s l l p s y s t e m s a r e equal. Although t h e r e have b e e n s o m e d i f f i c u l t i e s tn d e m o n s t r a t i n g t h a t a s s u m p t i o n to be Independent of s l i p mode, 7'8 p l a n e s t r a i n c o m p r e s s i o n t e s t s a p p e a r to s u p p o r t such Independence. %~~ F t n a l l y , an e x t e n d e d T a y l o r a n a l y s i s has b e e n u s e d b y Chin ~ to m a k e r a t h e r s u c c e s s f u l t e x t u r e p r e d i c t i o n s . It would t h e r e f o r e s e e m difficult to s a y , a s M a y e r and Backofen d i d s i x y e a r s ago, 7 that " t h e p r o b l e m of the s t r a i n h a r d e n i n g of p o l y c r y s t a l s . . . Is s t i l l l a r g e l y unsolved." Yet some aspects of the Taylor view of hardening remain under challenge. One such challenge can be summarized as follows. Kocks pointed out ~2 that the appropriate single crystal for comparison to polycrystals was one which deformed by multiple slip, or '~polysllp." His experiments on aluminum showed that the strain hardening of
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