Multistage heat treatment
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r e a c t i o n s o f t h i s type a r e t h o s e that a r e a d d i t i v e i n t h e s e n s e that t h e c o u r s e o f t h e r e a c t i o n a t 7"2 i s t h e s a m e a s it w o u l d h a v e b e e n if t h e f r a c t i o n t r a n s f o r m e d a t t e m p e r a t u r e T1 h a d a l l f o r m e d a t t e m p e r a t u r e Tz. F o r m a n y s o l i d s t a t e t r a n s f o r m a t i o n s t h e c o u r s e of t h e i s o t h e r m a l r e a c t i o n i s r e a s o n a b l y w e l l s p e c i f i e d by t h e A v r a m i9 e q u a t i o n : f
= 1 - e x p ( - K t n)
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w h e r e f is t h e f r a c t i o n t r a n s f o r m e d at t i m e t , a n d K i s a t e m p e r a t u r e d e p e n d e n t c o n s t a n t d e t e r m i n e d by t h e n u c l e a t i o n a n d g r o w t h p r o c e s s e s . A r e a c t i o n w i l l be a d d i t i v e i f n in E q . [1] i s i n d e p e n d e n t o f t e m p e r a t u r e so t h a t t h e c o u r s e of t h e r e a c t i o n a t t w o t e m p e r a t u r e s d i f f e r s o n l y by a t i m e f a c t o r . In g e n e r a l , t h i s r e q u i r e m e n t is r a t h e r r e s t r i c t i v e a n d is m o s t frequently s a t i s f i e d when nucleation o c c u r s at heterogeneous s i t e s that s a t u r a t e v e r y e a r l y i n the r e a c t i o n .9 T h e p e a r l i t e r e a c t i o n in s t e e l s is at l e a s t a p p r o x imately additive.5 P r e s u m a b l y , this r e s u l t s from e a r l y site saturation primarily at p r i o r austenite g r a i n boundaries a n d f r o m t h e insensitivity of t h e m o r p h ology t o reaction temperature. In addition, t h e growth r a t e i s not i n f l u e n c e d by p r i o r t r a n s f o r m a t i o n a t a d i f f e r e n t t e m p e r a t u r e s i n c e t h e bulk a u s t e n i t e c o m p o s i t i o n i s n o t , i n g e n e r a l , c h a n g e d by t r a n s f o r m a t i o n t o p e a r l i t e . H i g h c h r o m i u m z2 a n d m a n g a n e s e s t e e l sz4 a r e e x c e p t i o n s , but m u l t i s t a g e t r e a t m e n t s h a v e not b e e n e x a m i n e d i n t h e s e s t e e l s . In t h e b a i n i t e r e a c t i o n , h o w e v e r , n d e p e n d s on r e a c t i o n t e m p e r a t u r e a n d i n c r e a s e s a s t h e t e m p e r a t u r e is lowered, l° T h e r m a l history consequently s h o u l d modify the kinetics of the b a i n i t e r e a c t i o n , a n d s t e p p e d t r a n s f o r m a t i o n s do i n deed have more significant effects o n the formation of b a i n i t e than they do on t h a t o f p e a r l i t e . T h e r a t e o f b a i n i t e f o r m a t i o n c a n be e i t h e r i n c r e a s e d o r d e c r e a s e d by p r i o r t r e a t m e n t d e p e n d i n g on t h e r e l a t i o n s h i p b e t w e e n the i n i t i a l a n d f i n a l t e m p e r a t u r e s . F i g . 1 d e m o n s t r a t e s f o r 4340 s t e e l t h a t t h e b a i n i t e r e a c t i o n is r e t a r d e d w h e n r e a c t i o n is i n i t i a t e d at a higher temperature a n d t h
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