• PDF / 1,175,758 Bytes
• 11 Pages / 612 x 792 pts (letter) Page_size
• 13 Downloads / 250 Views

DOWNLOAD

REPORT

---

P R E D I C T I V E c a l c u l a t i o n s of p r e s s loads, s t r a i n d i s t r i b u t i o n s , and f a i l u r e loci in s h e e t m e t a l f o r m i n g ope r a t i o n s depend on an a c c u r a t e knowledge of p l a s t i c behavior under various strain states. For these r e a sons, the d e v e l o p m e n t of a g e n e r a l y i e l d c r i t e r i o n and p l a s t i c i t y t h e o r y has been p u r s u e d for m a n y y e a r s . The p u r p o s e of the p r e s e n t work is to e x p e r i m e n t a l l y and a n a l y t i c a l l y e x a m i n e p l a s t i c b e h a v i o r u n d e r one of the most widely e n c o u n t e r e d (and often m o s t c r i t i c a l ) s t r a i n s t a t e s in s h e e t s t a m p i n g o p e r a t i o n s : plane strain. J a c k s o n e l al, ~ Hill, 2'3 and D o r n 4 i n d e p e n d e n t l y d e veloped t h e o r i e s of a n i s o t r o p i c p l a s t i c i t y b a s e d on m o d i f i c a t i o n s to the von M i s e s s yield c r i t e r i o n and its a s s o c i a t e d flow r u l e . H i l l ' s o r i g i n a l t h e o r y (let us c a l l this H i l l ' s ' o l d ' theory) is the m o s t widely used today. The a n i s o t r o p y is a s s u m e d to be o r t h o t r o p i c , i.e. possessing three mutually orthogonal s y m m e t r y p l a n e s , with n o r m a l or p l a n a r a n i s o t r o p y being s p e c i a l c a s e s . The p l a s t i c p r o p e r t i e s a r e c o n s i d e r e d u n i f o r m and h o m o g e n e o u s and n e i t h e r B a u s c h i n g e r n o r h y d r o s t a t i c s t r e s s effects a r e i n c l u d e d . I s o t r o p i c h a r d e n i n g is a l s o a s s u m e d ; in t u r n i m p l y i n g that the p l a s t i c p r o p e r t i e s do not depend on the s t r a i n state or s t r e s s . When only n o r m a l a n i s o t r o p y is c o n s i d e r e d ; that is, a l l d i r e c t i o n s in the sheet plane a r e e q u i v a l e n t , the only p a r a m e t e r to be m e a s u r e d for a p p l i c a t i o n of the t h e o r y is the a v e r a g e p l a s t i c a n i s o t r o p y r a t i o , ~. Once this p a r a m e t e r i s d e t e r m i n e d f r o m t e n s i l e t e s t s the t h e o r e t i c a l p r e d i c t i o n s a r e fixed; that is, t h e r e a r e no other a d j u s t a b l e p a r a m e t e r s . H i l l ' s ' o l d ' t h e o r y has r e c e n t l y b e e n t e s t e d u s i n g v a r i o u s sheet a l l o y s . The most c o m m o n t e s t is a c o m p a r i s o n of s t r e s s - s t r a i n c u r v e s o b t a i n e d in b a l a n c e d b i a x i a l t e n s i o n (as in a h y d r a u l i c bulge test) with c u r v e s p r e d i c t e d using the t h e o r y b a s e d on t e n s i l e t e s t d a t a . A s i m i l a r a n a l y s i s has been a p p l i e d to e x p e r i m e n t s c a r r i e d out in p l a n e - s t r a i n c o m p r e s s i o n . 6 The c o n c l u s i o n s r e a c h e d t h r o u g h such t e s t s have R. H. WAGONERis Associate Senior Research Scientist, Physics Department, Gen