The application of a dislocation model to the strain and temperature dependence of the strain hardening exponent n in th
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THEr e l a t i o n s h i p b e t w e e n t r u e
s t r e s s (o.) and t r u e and so f r o m what was stated in the p r e v i o u s s e n t e n c e , s t r a i n (c) d u r i n g d e f o r m a t i o n of i r o n and s t e e l can often a t r e n d f r o m d o u b l e - n to s i n g l e - n is expected as the be c o n v e n i e n t l y d e s c r i b e d m a t h e m a t i c a l l y by the Ludwik- t e m p e r a t u r e is d e c r e a s e d or the s t r a i n r a t e i n c r e a s e d . H o l l o m o n r e l a t i o n s h i p 1'2 i . e . In the p a s t , the d o u b l e - n a p p r o x i m a t i o n has b e e n taken as i n d i c a t i v e of a change in d e f o r m a t i o n m e c h a n o.= K. e n [1] i s m at the s t r a i n ~.5 However this point is s t i l l not w h e r e K is u s u a l l y r e f e r r e d to as the s t r e n g t h c o e f f i c l a r i f i e d in a s a t i s f a c t o r y way and in view of the c i e n t and n as the s t r a i n h a r d e n i n g index. F o r f r e q u e n t u s e made of Eq. [1] in d i s c u s s i n g m e c h a n i c a l inhomogeneously-yieldingpolycrystalline materials, b e h a v i o r in i r o n and s t e e l (and other m e t a l s ) , s o m e this e x p r e s s i o n is v a l i d f r o m the end of the L u d e r s kind of q u a n t i t a t i v e p h y s i c a l i n t e r p r e t a t i o n is long s t r a i n u n t i l n e c k i n g . The a l t e r n a t i v e equation o v e r d u e . In this p a p e r a r e c e n t l y p u b l i s h e d m o d e l , 6 which p r e d i c t s a r e l a t i o n b e t w e e n t r u e s t r e s s and t r u e o. = o'o + K " s n [2] s t r a i n for i r o n and s t e e l in t e r m s of the v a r i o u s p o s has also b e e n p r o p o s e d ~ for m e t a l s having a t e m p e r a s i b l e d i s l o c a t i o n m e c h a n i s m s , will be u s e d in an a t t u r e - d e p e n d e n t y i e l d s t r e s s e.g. i r o n and s t e e l . Howt e m p t to f u r t h e r i l l u m i n a t e the i m p o r t a n t p r i n c i p l e s e v e r , the p r e s e n t c o n t e n t i o n is that the l a t t e r r e l a t i o n i n v o l v e d . The p r o c e d u r e adopted is to c o m p a r e the ship is no l e s s e m p i r i c a l than Eq. [1] w h i l s t having the t h e o r e t i c a l e x p r e s s i o n m e n t i o n e d above with Eq. [1] added c o m p l i c a t i o n of a t h i r d p a r a m e t e r . F o r this and to d e r i v e an e x p r e s s i o n for the s t r a i n h a r d e n i n g r e a s o n the d i s c u s s i o n h e r e will be r e s t r i c t e d to the index n (which f r o m Eq. [1 ] is d i n ~ / d l n e ) in t e r m s of simple Ludwik-Hollomon expression. the p h y s i c a l l y s i g n i f i c a n t d i s l o c a t i o n p a r a m e t e r s . It is In m a n y i n s t a n c e s , a log o.-log ~ plot is n o n l i n e a r then p o s s i b l e not only to e s t a b l i s h the r e a s o n for a but can be a p p r o x i m a t e d by t w o s t r a i g h t l i n e s i n t e r d o u b l e - n b e h a v i o r but also to p r e d i c t its o c c u
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