Isotropic fiber coarsening in unidirectionally solidified eutectic alloys
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A t h e o r y of c o a r s e n i n g h a s been d e v e l o p e d f o r the c a s e of f i b e r s of c i r c u l a r c r o s s s e c t i o n in u n i d i r e c t i o n a l l y s o l i d i f i e d e u t e c t i c a l l o y s . The f i b e r s a r e a s s u m e d to be r a n d o m l y d i s t r i b u t e d throughout the u n o c c u p i e d s p a c e in t h e m a t r i x ( u n i f o r m l y d i s t r i b u t e d ) , and diffusion of s o l u t e i s a s s u m e d to o c c u r u n d e r s t e a d y - s t a t e c o n d i t i o n s with c y l i n d r i c a l s y m m e t r y . The t h e o r y p r e d i c t s that the cube of the a v e r a g e f i b e r r a d i u s i n c r e a s e s l i n e a r l y with t i m e for a l l f i b e r v o l u m e f r a c t i o n s . A s the v o l u m e f r a c t i o n i n c r e a s e s , the c o a r s e n i n g r a t e i n c r e a s e s and the t h e o r e t i c a l d i s t r i b u t i o n of f i b e r r a d i i b e c o m e s b r o a d e r . It is shown that i s o t r o p i c f i b e r c o a r s e n i n g o c c u r s at a p p r o x i m a t e l y half the r a t e at which t h e s a m e p h a s e would c o a r s e n if it w e r e in the f o r m of s p h e r i c a l p r e c i p i t a t e s f o r v o l u m e f r a c t i o n s up to 0.6. It i s a l s o d e m o n s t r a t e d that the f i b e r s w i l l c o a r s e n at a f a s t e r r a t e when they a r e u n i f o r m l y d i s t r i b u t e d than when t h e y a r e a r r a n g e d on an h e x a g o n a l l a t t i c e . T H E a n i s o t r o p i c m i c r o s t r u c t u r e s found in u n i d i r e c tionally solidified eutectic alloys possess attractive properties for elevated temperature structural applic a t i o n s . The p e r f o r m a n c e of t h e s e m a t e r i a l s d e p e n d s , to a c e r t a i n extent, upon the s t a b i l i t y of the l a m e l l a r o r f i b r o u s m o r p h o l o g y which d e v e l o p s d u r i n g the s o l i d i f i c a t i o n p r o c e s s . T h e r e a r e p r i m a r i l y two i m p o r tant t y p e s of i n s t a b i l i t i e s which can l e a d to a d e g r a d a tion of the m e c h a n i c a l p r o p e r t i e s of such m a t e r i a l s : 1) m o r p h o l o g i c a l i n s t a b i l i t y , o r a change of s h a p e which i s e s s e n t i a l l y e q u i v a l e n t to s p h e r o i d i z a t i o n of the m i c r o s t r u c t u r e ; 2) s i z e i n s t a b i l i t y , which is e q u i v a l e n t to c o a r s e n i n g of the m i c r o s t r u c t u r e while the b a s i c m o r p h o l o g y i s m a i n t a i n e d . It would a p p e a r odd that s i z e i n s t a b i l i t i e s could o c c u r without b e i n g a c c o m p a n i e d by s e v e r e m o r p h o l o g i c a l i n s t a b i l i t i e s , b e c a u s e the l a m e l l a r o r f i b r o u s " p a r t i c l e s " a l m o s t c e r t a i n l y do not have a t h e r m o d y n a m i c e q u i l i b r i u m shape in the unidirectionally solidified microstructure. Neverthel e s s , s e v e r a l i n v e s t i g a t o r s
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