Experimental studies of the force to extrude a rate sensitive material
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T H E force required for frictionless, indirect extrusion can be e s t i m a t e d f r o m the i d e a l o r h o m o g e n e o u s w o r k of d e f o r m a t i o n u s i n g the r e l a t i o n : 1-3 Ph = Wh = ~ lnR
[1]
H e r e -Ph is the e x t r u s i o n p r e s s u r e f o r h o m o g e n e o u s flow, W h is the i d e a l w o r k p e r unit v o l u m e , R is the e x t r u s i o n r a t i o , and ~ is the m e a n flow s t r e s s . The l a t t e r is given by: _
1
lnR
lnR f
[2]
w h e r e q is the u n i a x i a l flow s t r e s s and ~ is the t r u e s t r a i n . ~ is u s u a l l y obtained f r o m i n d e p e n d e n t t e s t s p e r f o r m e d by hot c o m p r e s s i o n , t e n s i o n , o r t o r s i o n at v a r i o u s c o n s t a n t t e m p e r a t u r e s and s t r a i n r a t e s . The e x t r u s i o n f o r c e can a l s o be c a l c u l a t e d u s i n g u p p e r bound t e c h n i q u e s by d e t e r m i n i n g the w o r k of d e f o r m a tion P a within the die r e g i o n , and adding a c o r r e c t i o n for the s h e a r w o r k P s p e r f o r m e d as the m a t e r i a l e n t e r s and l e a v e s the d e f o r m a t i o n zone. Pc~ e x c e e d s P h by a f a c t o r f ( ~ ) ; this c o r r e c t i o n is not p a r t i c u l a r l y s i g n i f i c a n t , a s f ( o t ) only i n c r e a s e s f r o m 1.00 to 1.03 as the die s e m i a n g l e ~ is i n c r e a s e d f r o m 0 to 60 deg. 4 P s a l s o i n c r e a s e s with a , a s w e l l a s with s t r a i n r a t e , and will be d i s c u s s e d in m o r e d e t a i l below. A s e r i o u s s h o r t c o m i n g of t h e s e m e a n s of e s t i m a t i n g e x t r u s i o n p r e s s u r e is that they o v e r l o o k the s t r a i n r a t e s e n s i t i v i t y of the m a t e r i a l a s i t f l o w s t h r o u g h the d i e z o n e . T h i s e f f e c t is of i m p o r t a n c e b e c a u s e , f o r a c o n s t a n t r a m speed, the l o c a l s t r a i n r a t e v a r i e s by two to t h r e e o r d e r s of m a g n i t u d e as the m a t e r i a l flows through the d e f o r m a t i o n zone. In a r e c e n t p a p e r , 5 a T. CHANDRA and J. J. JONAS are Research Assistant and Associate Professor, respectively, Department of Metallurgical Engineering, Physical Sciences Centre, McGill University, Montreal, Canada. Manuscript submitted June 16, 1970. METALLURGICAL TRANSACTIONS
m e t h o d of c a l c u l a t i n g the p r e s s u r e was d e m o n s t r a t e d in which full a c c o u n t is taken of the r a t e s e n s i t i v i t y . F o r e x t r u s i o n r a t i o s of 40 to 160 and a p o w e r law r a t e s e n s i t i v i t y of 0.2, t h i s m e t h o d l e a d s to e s t i m a t e s of e x t r u s i o n p r e s s u r e about 30 to 60 p ct h i g h e r than c o n v e n t i o n a l e s t i m a t e s b a s e d on the i d e a l w o r k , thus e l i m i nating the n e e d f o r an e m p i r i c a l " s h e a r " or " e f f i c i e n c y " f a c t o r . In the p r e s e n t p a p e r , e x p e r i m e n t s a r e d e s
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