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HE i n f l u e n c e s of m a t e r i a l p r o p e r t i e s of m e t a l s on s t r e t c h f o r m i n g a r e often s t u d i e d by t e s t i n g a wide r a n g e of m a t e r i a l s . 1 A n a l y s i s of t h e s e data is then used to i n f e r the effect of each of the v a r i o u s p a r a m e t e r s on f o r m a b i l i t y . Although this a p p r o a c h has cont r i b u t e d a g r e a t d e a l to our u n d e r s t a n d i n g of the p l a s tic d e f o r m a t i o n of sheet m e t a l s , it is s o m e t i m e s difficult to s e p a r a t e the effects of a l l the p a r a m e t e r s . F o r e x a m p l e , it is known that i n c r e a s e d s t r a i n h a r d e n i n g and s t r a i n - r a t e h a r d e n i n g both c o n t r i b u t e to i n c r e a s e d f o r m a b i l i t y , but the p r e c i s e c h a r a c t e r i z a t i o n of t h e s e i n c r e a s e s depends on the p a r t i c u l a r shape b e i n g f o r m e d and on other m a t e r i a l p r o p e r t i e s . To e l i m i n a t e s o m e of t h e s e d i f f i c u l t i e s , we study only a s i n g l e m a t e r i a l , 5182-0 a l u m i n u m . By v a r y i n g t e m p e r a t u r e and s t r a i n r a t e , we can change the s t r a i n h a r d e n i n g and s t r a i n - r a t e h a r d e n i n g of this m a t e r i a l 2-4 t h e r e b y v a r y i n g the total e l o n g a t i o n (Fig. 1). T h e s e p a r a m e t e r s a r e a l s o known to affect punch s t r e t c h ing.~ In p a r t i c u l a r , t e n s i l e t e s t s at t e m p e r a t u r e s of 25, 130, and 200~ a r e used to m e a s u r e the s t r a i n h a r d e n i n g and s t r a i n - r a t e h a r d e n i n g . Also, f o r m i n g l i m i t d i a g r a m s a r e e s t a b l i s h e d at the s a m e t e m p e r a t u r e s and at punch v e l o c i t i e s of 50, 500, and 5000 m m / min, and s t r a i n d i s t r i b u t i o n s in full cups a r e m e a s u r e d . F i n a l l y , a m a t h e m a t i c a l m o d e l of the t e n s i l e data is c o n s t r u c t e d and is used in a finite e l e m e n t p r o g r a m to p r e d i c t s t r a i n d i s t r i b u t i o n s in h e m i s p h e r i cal punch s t r e t c h i n g . Both the e x p e r i m e n t a l and a n a l y t i c a l r e s u l t s a r e a n a l y z e d to d e t e r m i n e the effects of changing s t r a i n h a r d e n i n g and s t r a i n - r a t e h a r d e n i n g on punch s t r e t c h ROBERT A. AYRES is Senior Research Scientist, Physics Department, General Motors Research Laboratories, Warren, MI 48090. MICHAEL L. WENNER is Senior Research Engineer, Mathematics Department, General Motors Research Laboratories, Warren, MI 48090. Manuscript submitted May 24, 1978. METALLURGICAL TRANSACTIONSA

ing of 5182-0 a l u m i n u m . The effects of v a r y i n g punch v e l o c i t i e s at e l e v a t e d t e m p e r a t u r e s a r e also d i s c u s s e d . The r e s u l t s p r e s e n t e d h e r e can be i n t e r p r e t e d u n a m b i g u o u s l y , s i n c e other m a t e r i a l p r o p e