Plastic anisotropy of textured steel sheet

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T H E d e e p - d r a w i n g p e r f o r m a n c e of low c a r b o n s t e e l s h e e t is r e l a t e d to the p l a s t i c a n i s o t r o p y r a t i o R, which is defined a s Ewidth/Ethicknes s in a t e n s i l e s h e e t s p e c i men d e f o r m e d well into the p l a s t i c r e g i o n . In an i s o t r o p i c m a t e r i a l R e q u a l s unity; in a good d e e p - d r a w i n g s t e e l R m a y be s o m e w h e r e b e t w e e n 1.5 and 2. It m u s t b e b o r n e in mind, h o w e v e r , that R m a y b e a function R(qb) of the angle ~b b e t w e e n the r o l l i n g d i r e c t i o n and the t e n s i l e d i r e c t i o n ; in p r a c t i c a l c a s e s R(45 deg) will often be s m a l l e r than both R(0 deg) and R(90 deg).* *In practicalcalculationsa differentratio is often used,viz.r = ewidth/ (e thickneu+ ewidtl0.It is relatedto R by R = r/(1 -r). The completerangeof r is from 0 to 1, whereasthe range of R is from 0 to o.. The axisymmetriccaseis representedby R = 1 or r = 0.5. The p l a s t i c a n i s o t r o p y r a t i o is r e l a t e d to the c r y s t a l l o g r a p h i c t e x t u r e . A d e e p - d r a w i n g s t e e l with a high R value generally shows a rather strong {lll}-texture c o m p o n e n t ; the {100} c o m p o n e n t t e n d s to r e d u c e the v a l u e of R d r a s t i c a l l y . S e v e r a l a u t h o r s have s t u d i e d the r e l a t i o n b e t w e e n p l a s t i c a n t s o t r o p y and c r y s t a l l o g r a p h i c t e x t u r e f o r d e e p - d r a w i n g s t e e l s h e e t (bcc). E l i a s e t a l I did t h i s b y c o n s i d e r i n g only the s l i p d i r e c t i o n s n e a r the d i r e c t i o n s of m a x i m u m s h e a r s t r e s s . O b v i o u s l y t h i s is not in a c c o r d a n c e with T a y l o r ' s t h e o r y and, m o r e o v e r , it s e r i o u s l y r e d u c e s the p o s s i b i l i t ~ of e x p l a i n i n g the f a v o r a b l e influence of a s h a r p { l l l ~ - t e x t u r e on R. Fukuda z c a l c u l a t e d the R - v a l u e s of a n u m b e r of s h a r p t e x t u r e c o m p o n e n t s , u s i n g T a y l o r ' s t h e o r y ; s i n c e five s l i p s y s t e m s a r e n e c e s s a r y to p r e s e r v e continuity, he s i m p l y took the five s y s t e m s with the h i g h e s t r e s o l v e d s h e a r s t r e s s . As this i n t e r p r e t a t i o n of T a y l o r ' s t h e o r y is open to c r i t i c i s m , so a r e his r e s u l t s . The w o r k of N a g a s h t m a e t a l s on s i n g l e c r y s t a l s a l s o cannot be a p p l i e d to o u r c a s e , s i n c e in t h e i r c r y s t a l s only one s l i p s y s t e m was a s s u m e d to b e a c t i v a t e d . As the r e s u l t s m e n t i o n e d above a r e not adequate, we d e c i d e d to i n v e s t i g a t e the m e r i t s of a t r u e a p p l i c a t i o n of T a y l o r ' s t h e o r y to the p r o b l e m . THE TAYLOR ANALYSIS In 1938 T a y l o r 4 put f o r w a r d his t h e o r y f o r the fee c a s e , i . e . , {111}(110

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