On the double- n behavior of iron
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On the Double-n Behavior of Iron S. N . M O N T E I R O A N D R . E .
t w o s e t s o f r e s u l t s , we w o u l d l i k e t o m a k e s o m e a d d i t i o n a l c o m m e n t s . C o n f l i c t s of t h i s n a t u r e w o u l d p r o b a b l y not a r i s e i f t h e s t r e s s - s t r a i n c u r v e a n a l y s i s due t o C r u s s a r d a n d J a o u l4-6 w e r e t o be m o r e g e n e r a l l y employed. C r u s s a r d and J a o u l ' s method has attractive advantages over a log a v s log e plot for determining t h e v a l u e o f n i n E q . [1]. I n m a n y c a s e s t h e e x p e r i m e n t a l d a t a , w i t h i n l i m i t s d e f i n e d by t h e t r a n s i t i o n s t r a i n s , c o n f o r m s m u c h b e t t e r to L u d w i k ' s e q u a t i o n e = ao + k e n
[2]
t h a n t o E q . [1]. T h i s is p a r t i c u l a r l y true in m e t a l s w i t h a s t r o n g temperature-dependent y i e l d s t r e s s such a s iron or t i t a n i u m . H o w e v e r , t h e p a r a m e t e r s ~o, k , a n d n do not n e c e s s a r i l y have a s i m p l e physical significance. F o r e x a m p l e , n e g a t i v e v a l u e s of co, k , a n d n a r e p o s s i b l e u n d e r s p e c i f i c d e f o r m a t i o n c o n d i t i o n s . 6'7 It i s b e c o m i n g increasingly e v i d e n t t h a t t h e s e p a r a m e t e r s , in p a r t i c ular n , are representative o f t h e n a t u r e o f t h e w o r k h a r d e n i n g p r o c e s s . I n s u b s e q u e n t p a p e r s i t w i l l be s h o w n t h a t n e g a t i v e v a l u e s of k a n d n c o r r e s p o n d t o deformation u n d e r conditions such a s work-softening w h e r e d y n a m i c r e c o v e r y is v e r y s t r o n g . By t a k i n g t h e d e r i v a t i v e o f e i t h e r e x p r e s s i o n , [1] o r [2], a n d p l o t t i n g t h e s l o p e v s t h e s t r a i n on a l o g - l o g g r a p h , t h e v a l u e o f n c a n be o b t a i n e d i n d e p e n d e n t o f t h e e x i s t e n c e o f Co. C o n s e q u e n t l y , if in a g i v e n r e g i o n o f t h e s t r e s s - s t r a i n c u r v e t h e p a r a m e t e r ~o h a s a f i n i t e v a l u e a n d E q . [2] r a t h e r t h a n E q . [1] i s a p p l i c a b l e , t h e t r a n s i t i o n s t r a i n e l a s w e l l a s t h e w o r k - h a r d e n i n g e x p o n e n t s n l a n d n2 w i l l n o r m a l l y be m o r e a c c u r a t e l y d e t e r m i n e d by a m e t h o d s u c h a s that d e v e l o p e d by C r u s s a r d a n d J a o u l . O n t h e o t h e r h a n d , if a s t r e s s - s t r a i n c u r v e i s t h o r o u g h l y r e p r e s e n t e d by a n e q u a t i o n o f t h e H o l l o m o n t y p e , C r u s s a r d a n d J a o u l ' s m e t h o d will s t i t l p r o v i d e the c o r r e c t answers. Fig. 1 s h o w s o n e o f C r u s s a r d ' s c u r v e s f o r a v e r y p u r e i r o n d e f o r m e d a t r o o m t e m p e r a t u r e . Not j u s t o n e , but a c t u a l l y t w o t r a n s i t i o n p o i n t s c a n be s e e n i n
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