The average volume of martensite plates during transformation
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T H E O R I E S of the k i n e t i c s of m a r t e n s i t e f o r m a t i o n ~-3 a t t e m p t to d e s c r i b e the e x p e c t e d r a t e of n u c l e a t i o n of m a r t e n s i t e p l a t e s . Using the a s s u m p t i o n that growth is v i r t u a l l y i n s t a n t a n e o u s , the t h e o r i e s a r e capable of p r e d i c t i n g the n u m b e r o f m a r t e n s i t e p l a t e s p e r unit v o l u m e (N v) as a function of t i m e and t e m p e r a t u r e . On the o t h e r hand, the c o n v e n i e n t e x p e r i m e n t a l t e c h n i q u e s for following m a r t e n s i t e f o r m a t i o n , (e.g., e l e c t r i c a l resistivity, magnetic saturation, dilatation, metallog r a p h i c point counting, and so forth) m e a s u r e the v o l u m e f r a c t i o n o f m a r t e n s i t e ( f ) in a s a m p l e . Thus, a n e c e s s a r y step in linking t h e o r y and e x p e r i m e n t is m e a s u r e m e n t of the a v e r a g e v o l u m e o f the m a r t e n s i t e p l a t e s ( ~ ) which by definition
v-f
Nv
[a]
r e l a t e s N v to f . The p u r p o s e of the p r e s e n t work i s to e x p e r i m e n t a l l y e x a m i n e the d e p e n d e n c e of V u p o n f and to c o m p a r e this d e p e n d e n c e with the t h e o r e t i c a l prediction. FISHER'S ANALYSIS Twenty y e a r s ago, F i s h e r ~'4,s f o r m u l a t e d a t h e o r y which p r e d i c t s that the a v e r a g e v o l u m e (V) d e c r e a s e s s t r o n g l y as the t r a n s f o r m a t i o n p r o c e e d s . The t h e o r y is b a s e d on the o b s e r v a t i o n that the i n i t i a l m a r t e n s i t e p l a t e s divide the s a m p l e into p r o g r e s s i v e l y s m a l l e r c o m p a r t m e n t s - - t h u s , the l a t e r f o r m i n g p l a t e s should tend to be s m a l l e r , Fig. 1. In o r d e r to explicitly s t a t e the a s s u m p t i o n s involved and to f a c i l i t a t e l a t e r d i s c u s sion, a s i m p l e d e r i v a t i o n of the equation which follows f r o m h i s a s s u m p t i o n s is given h e r e . F i s h e r a s s u m e d that the a m o u n t of t r a n s f o r m a t i o n p e r plate ( d f / d N v ) is a c o n s t a n t f r a c t i o n (m) of the v o l u m e of the c o m p a r t m e n t within which it f o r m s . M o r e o v e r , the a v e r a g e a m o u n t of t r a n s f o r m a t i o n p e r plate (at a given f ) was a s s u m e d to be D. G. McMURTRIE, formerly Student, University of Michigan, Ann Arbor, Mich. and Summer Employee, Scientific Research Staff, Ford Motor Co., Dearborn, Mich., is with Product Development Engineering, Ford Motor Co. C. L. MAGEE is with the Scientific Research Staff, Ford Motor Co. Manuscript submitted April 24, 1970. METALLURGICALTRANSACTIONS
[2]
d f : m(a - Y)-Vc dNv
w h e r e Vc ts the a v e r a g e c o m p a r t m e n t s i z e and (1 - f ) is the volume f r a c t i o n of a u s t e n i t e a v a i l a b l e for t r a n s f o r m a t i o n . Since the a v e r a g e volume of a c o m p o n e n t is the r e
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