Difficulty of coarsening of silica inclusions in slowly and rapidly solidified iron
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Author's Reply ROGER N. WRIGHT H-C. Chao was the f i r s t to d e m o n s t r a t e c o n e l u s i v e l y a c o r r e l a t i o n between the r o p i n g p h e n o m e n o n and a t e x t u r e mix I and, thus, his c o m m e n t a r y is m o s t w e l c o m e . Nonetheless, the a r g u m e n t s s e t forth in Fig. 1 of his d i s c u s s i o n s e e m s e l f - c o n t r a d i c t o r y . The r - v a l u e c a l c u l a t i o n s , p e r s e , a r e a c c u r a t e and c o n s i s t e n t with the p r e v i o u s work. 1-3 The p r o b l e m l i e s in the o v e r a l l (111)[11~ m a t r i x d e f o r m a t i o n i m p l i c i t in Fig. l ( b ) . It a p p e a r s in the F i g u r e that the m a t r i x m a t e r i a l at the ends of the slot is somehow not d e f o r m i n g when, in fact, it would be e x p e r i e n c i n g the s a m e E y a s the m a t r i x m a t e r i a l at the s i d e s of the slot. Moreover, it i s of c o u r s e the s t r a i n of the m a t r i x m a t e r i a l at the slot ends which c o n t r o l s Gapf. In short, the e n t i r e s h e e t of (111)[115] m a t e r i a l should be d e c r e a s i n g in width with t e n s i l e s t r a i n i n g and the slot m u s t d e c r e a s e in width with the m a t r i x sheet. T h i s b e h a v i o r has b e e n d i s c u s s e d q u a n t i t a t i v e l y in p r e v i o u s work 3' 4 and is f u n d a m e n t a l to the p l a s t i c buckling model. Now the s l o t - e n d m a t r i x m a t e r i a l c o n s t r a i n t shown in Fig. l ( b ) could be produced by t e n s i l e grip effects. H o w e v e r such c o n s t r a i n t s should not be p r e s e n t in the t e n s i l e gage s e c t i o n p r o p e r and not a s g e n e r a l b e h a v i o r in sheet f o r m i n g o p e r a t i o n s . The s t a t e m e n t that the (100)[011] m a t e r i a l c o n s i s t s of thin b a n d s with t h i c k n e s s e s well below that of the s h e e t is i n t e r e s t i n g , but u n s u b s t a n t i a t e d . In any c a s e , a l l that is r e q u i r e d for the b u c k l i n g m e c h a n i s m is that c e r t a i n t h r o u g h - t h e - t h i c k n e s s " b a n d s " or s e c t i o n s be r e l u t i v e l y r i c h ~n (100)[011 ] t e x t u r e i n c o m p a r i s o n to a m a t r i x r e l a t i v e l y r i c h in (111)[117 t e x t u r e (or a 1010-VOLUME 8A, JUNE 1977
s i m i l a r t e x t u r e such a s (111)[01"1] ). The l o n g i t u d i n a l s t r a i n at which b u c k l i n g e n s u e s will depend on how p r o n o u n c e d the t e x t u r e v a r i a t i o n is, a s d i s c u s s e d p r e viously. 3 The r e m a r k s c o n c e r n i n g d e l a m i n a t i o n and c l e a v a g e a r e , again, v e r y i n t e r e s t i n g . Hopefully, well defined e v i d e n c e f o r the c a u s e - e f f e c t r e l a t i o n s h i p s w i l l be f o r t h c o m i n g in f u t u r e p u b l i c a t i o n s . The p l a s t i c buckling model w a s set forth a s a s p e cific m e c h a n i c a l e x p l a n a t i o n for roping. Unlike other model
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