Enhanced fracture resistance of high strength steel produced by extrusion of nickel coated steel powder
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dt
face controlled coarsening, there exists a certain class of initial fractional frequency functions for which the square of critical particle size varies linearly with time during the entire coarsening process.
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Enhanced Fracture Resistance of High Strength Steel Produced by Extrusion of Nickel Coated Steel Powder
/minimum
Let rio, (1/p)i, and (I/p2)i be the values of fo(~-), (l/p), and (~/pZ) in the beginning of the coarsening process (i. e. ~- = 0, t = 0). Suppose we choose an initial fractional frequency function f(p, 0) such that:
In principle, it is possible to choose different initial fractional frequency Eq. [23] holds. In such a case, from follows that:
dt ] i n i t i a l
infinitely many functions for which Eqs. [21] to [23] it
~ dt r m i n i m u m
T h u s , f o r a c l a s s of i n i t i a l f r a c t i o n a l f r e q u e n c y f u n c t i o n s f o r w h i c h E q . [23] h o l d s , t h e d~3/dr is a l r e a d y at i t s m i n i m u m p o s s i b l e v a l u e in t h e b e g i n n i n g of t h e c o a r s e n i n g p r o c e s s . In s u c h a c a s e (d~3/dt) c a n n o t d e c r e a s e b e l o w t h i s m i n i m u m v a l u e , and h e n c e it m u s t remain constant during the entire coarsening process. H o w e v e r , the f r a c t i o n a l f r e q u e n c y f u n c t i o n d o e s c h a n g e w i t h t i m e , u n t i l it a p p r o a c h e s the u n i v e r s a l t i m e i n v a r i a n t f o r m . One c a n c o n c l u d e t h a t t h e r e e x i s t s a c l a s s of i n i t i a l d i s t r i b u t i o n f u n c t i o n s f o r w h i c h d~3/dt r e m a i n s c o n s t a n t d u r i n g the e n t i r e c o a r s e n i n g p r o c e s s . T h e i n i t i a l f r a c t i o n a l f r e q u e n c y f u n c t i o n f(p, 0) is b a s i c a l l y d e t e r m i n e d by t h e n u c l e a t i o n and g r o w t h b e h a v i o r d u r i n g the precipitation process, v Whether the normal prec i p i t a t i o n p r o c e s s p r o d u c e s an i n i t i a l s i z e d i s t r i b u t i o n f u n c t i o n s u c h t h a t E q . [23] is s a t i s f i e d s t i l l r e m a i n s to be explored. The above conclusions are valid for the volume diff u s i o n c o n t r o l l e d p a r t i c l e c o a r s e n i n g d e s c r i b e d by E q . [1]. S i m i l a r a r g u m e n t s c a n b e a d v a n c e d f o r t h e i n t e r f a c e c o n t r o l l e d p a r t i c l e c o a r s e n i n g t h a t l e a d to a s i m i l a r c o n c l u s i o n . E v e n if f(p, T) d i f f e r s f r o m the t i m e i n v a r i a n t f u n c t i o n a l f o r m g i v e n by W a g n e r 3 f o
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