An analysis of plastic instability in pure shear in high strength AISI 4340 steel
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TANAKA
AND
JOSEPH
W.
SPRETNAK
The phenomenon of p l a s t i c i n s t a b i l i t y in p u r e s h e a r was s t u d i e d at r o o m t e m p e r a t u r e in heat t r e a t e d h i g h - s t r e n g t h AISI 4340 s t e e l s , e m p l o y i n g the t o r s i o n t e s t . The i n s t a b i l i t y o c c u r s a f t e r s a t u r a t i o n of s t r a i n h a r d e n i n g by the d i s p e r s e d c a r b i d e p a r t i c l e s . The s t r a i n at o n s e t of i n s t a b i l i t y i s s e n s i t i v e l y d e p e n d e n t on r a t e of s t r a i n i n g . The e f f e c t i v e s t r e s s ( t o t a l s t r e s s m i n u s the s t r e s s r e s u l t i n g f r o m d i s p e r s i o n hardening) m a y be a r e s u l t of Snoek r e l a x a t i o n o r the C o t t r e l l d r a g , depending on s t r a i n r a t e ; the m a g n i t u d e of this s t r e s s i s l i n e a r l y p r o p o r t i o n a l to the d i s s o l v e d c a r b o n content. E x p e r i m e n t a l o b s e r v a t i o n s i n d i c a t e that i n s t a b i l i t y i n t e r f a c e s a d v a n c e s p i r a l l y in the a x i a l d i r e c t i o n of the s p e c i m e n . It is p r o p o s e d that the i n t e r f a c e i s s t a b l e in a t h e r m o d y n a m i c s e n s e and that the d r i v i n g f o r c e for m i g r a tion d e p e n d s only on r a t i o of the s p e e d of the f r o n t to the m a c r o s c o p i c s t r a i n r a t e . When the i n t e r f a c e b e c o m e s s t a t i o n a r y , f r a c t u r e i s n u c l e a t e d at an a x i a l d i s t o r t i o n in the i n t e r f a c e . F r a c t u r e by the i n s t a b i l i t y o c c u r s by a t r a n s l a t o r y m o t i o n of one now r i g i d body with r e s p e c t to a s e c o n d r i g i d body along the c h a r a c t e r i s t i c (slip) s u r f a c e . P o r e s m a y be found in the f r a c t u r e s u r f a c e , but t h e s e a r e i n c i d e n t a l to the i n t e n s e flow along the c h a r a c t e r i s t i c , and a r e not the c a u s e of the i n s t a b i l i t y . T H E R E is now sufficient e v i d e n c e on f r a c t u r e in m e t a l s and a l l o y s to conclude that it o c c u r s a s a r e s u l t of p l a s tic s t r a i n i n g and that a p r e r e q u i s i t e to f r a c t u r e i s the l o c a l i z a t i o n of p l a s t i c flow within the p l a s t i c z o n e , r e f e r r e d to a s p l a s t i c i n s t a b i l i t y . The c o m m o n p r o t o t y p e of such an i n s t a b i l i t y i s the load i n s t a b i l i t y in the t e n s i l e t e s t , o r phenomenon of " n e c k i n g d o w n " . R e s e a r c h in t h i s l a b o r a t o r y has r e v e a l e d a m o r e b a s i c i n s t a b i l i t y which d o e s not involve the phenomenon of necking, n a m e l y the l o c a l i z a t i o n of p l a s t i c flow in d i r e c t i o n s of p u r e s h e a r , which a r e d i r e c t i o n s of z e r o e x t e n s i o n a l s t r a i n . T h e s e a r e d i r e c t i o n s of the c h a r a c t e r i s t i c s ( s l i p lines)
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