Strain localization in the diffuse neck in sheet metal
- PDF / 967,802 Bytes
- 10 Pages / 612 x 783.28 pts Page_size
- 53 Downloads / 223 Views
T H E c o n c e p t of f a i l u r e b y p l a s t i c i n s t a b i l i t y d a t e s b a c k to the t i m e of C o n s i d ~ r e , 1 who i d e n t i f i e d the o n s e t of i n s t a b i l i t y with the condition that, the s t r a i n induced h a r d e n i n g i n c r e m e n t in a d e f o r m i n g m a t e r i a l i s at a b a l a n c e with the i n c r e m e n t in g e o m e t r i c a l s o f t ening. Swift 2 e x t e n d e d t h i s i d e a to the c a s e of plane s t r e s s and Hill 3 a l s o a n a l y z e d the s a m e p r o b l e m , with p a r t i c u l a r r e f e r e n c e to l o c a l i n s t a b i l i t y . K e e l e r and Backofen 4 l a t e r e x p r e s s e d the i n s t a b i l i t y condition a s (d(re/dEe) = a e / Z i , in t e r m s of the e f f e c t i v e s t r e s s and the e f f e c t i v e s t r a i n , w h e r e the c r i t i c a l s u b t a n g e n t Z i (i = d f o r diffuse n e c k i n g and i = l for l o c a l necking) is a function of R and ((r2/(r~). F o r u n i a x i a l t e n s i o n of flat i s o t r o p i c b a r s the two c o n d i t i o n s r e d u c e to (d(rt/det) = (rl (diffuse) and (d(rl/del) = (rl/2 (local). 5 The v a l u e s of E. that s a t i s f y t h e s e c o n d i t i o n s a r e r e s p e c t i v e l y , n and 2n, f o r a m a t e r i a l that e x h i b i t s p a r a b o l i c h a r d e n ing ((r = c~ n) at l e a s t up to a s t r a i n of 2n. However, c h a n g e s in both s t r e s s - s t a t e and s t r a i n r a t e a r e a s s o c i a t e d with diffuse necking, which might m o d i f y the a p p a r e n t s t r a i n h a r d e n i n g b e h a v i o r and r e s u l t in a change in E~ f o r l o c a l necking. The e f f e c t s of the c h a n g e in s t r e s s - s t a t e in the neck have b e e n c o n s i d e r e d b y s e v e r a l i n v e s t i g a t o r s , s-~ the m a i n i n t e r e s t b e i n g in the a x i a l s t r e s s d i s t r i b u t i o n . R e c e n t l y , it h a s b e e n p o i n t e d out that the s t r e s s s t a t e m a y a l s o have an effect on the e f f e c t i v e h a r d e n i n g b e havior. '~ T h i s should a l s o be t a k e n into account while c o n s i d e r i n g the s t r a i n d i s t r i b u t i o n in the neck of a f l a t b a r . As f a r a s s t r a i n r a t e s e n s i t i v i t y is c o n c e r n e d , a g e n e r a l t r e a t m e n t of the t e n s i l e i n s t a b i l i t y for such a m a t e r i a l h a s b e e n m a d e b y H a r t . ~2 He showed that the u n i f o r m s t r a i n is i m p r o v e d when r a t e s e n s i t i v i t y is p o s i t i v e . No a n a l y s i s of s t r a i n d i s t r i b u t i o n o r l o c a l n e c k i n g in f l a t b a r s was c o n s i d e r e d , h o w e v e r . Although a c o m p l e t e a n a l y s i s i s not a t t e m p t e d in the p r e s e n t p a p e r , t h e s e e f f e c t s a r e v i e w e d in an unified m a n n e r , AMIT K. GHOSH is Associate Senior Research Metallurgist, Physics Department, Research Laboratories, GMC, General Motors Technical Center, Warrren,
Data Loading...
