The multiple yield phenomenon in single-fiber composites of iron in copper
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of the m e c h a n i c a l b e h a v i o r of f i b e r c o m p o s i t e m a t e r i a l s h a s been shown to be d e s c r i b a b l e by the " r u l e of m i x t u r e s " (or " l a w of c o m b i n e d a c t i o n " ) . In such a f o r m u l a t i o n , a p r o p e r t y of the solid as a whole i s d e t e r m i n e d by the v o l u m e - f r a c t i o n weighted s u m of that p r o p e r t y for the v a r i o u s p h a s e s . Of p e r h a p s m o s t i n t e r e s t has b e e n the e x p e r i m e n t a l o b s e r v a t i o n that the Y o u n g ' s m o d u l u s p a r a l l e l to the f i b e r s g e n e r a l l y obeys the r u l e of m i x t u r e s . F u r t h e r m o r e , c o m p o s i t e p l a s t i c p r o p e r t i e s a l s o s o m e t i m e s obey the s a m e r u l e . Howe v e r , d e t a i l e d i n v e s t i g a t i o n of the p l a s t i c d e f o r m a t i o n of c e r t a i n c o m p o s i t e s has shown that the c o m p o n e n t s m a y i n t e r a c t , r e s u l t i n g in c o m p o s i t e p r o p e r t i e s d i f f e r ing f r o m those p r e d i c t e d by s i m p l e a p p l i c a t i o n of the m i x t u r e r u l e . F o r example, Schoene and Scala 1 and Vennett, Wolf, and Levitt 2 have o b s e r v e d the f o r m a t i o n of m u l t i p l e n e c k s in d e f o r m e d c o m p o s i t e s . Such c o m p o s i t e b e h a v i o r r e s u l t s f r o m the m e c h a n i c a l s t a b i l i z a tion of a n e c k i n g f i b e r by the s u r r o u n d i n g m a t r i x . As a r e s u l t , s e v e r a l n e c k s m a y f o r m in a single f i b e r w h e r e only one is n o r m a l l y o b s e r v e d . In t h i s p a p e r a n o t h e r e x a m p l e of the i n t e r a c t i o n of two p h a s e s d u r i n g the i n h o m o g e n e o u s d e f o r m a t i o n of one is d e s c r i b e d . In the F e - C u c o m p o s i t e s i n v e s t i g a t e d , the F e r r o v a c E i r o n f i b e r d e f o r m s by the L u d e r s m e c h a n i s m following its y i e l d point. During this stage of d e f o r m a t i o n , elongation of the f i b e r s o c c u r s by the p r o p agation of a L u d e r s front, a c r o s s which a r a t h e r l a r g e d e f o r m a t i o n o c c u r s in a short d i s t a n c e J The r e m a i n d e r of the f i b e r r e t a i n s a constant s t r a i n . In o r d e r to m a i n t a i n i n t e r f a c e c o m p a t i b i l i t y with the L u d e r s band, the copper m a t r i x is forced to s h e a r , r e s u l t i n g in a load t r a n s f e r f r o m the f i b e r to the m a t r i x . This load t r a n s f e r m a y r e s u l t in a r e d u c t i o n in effective f i b e r s t r e s s sufficient to cause the L u d e r s band to c e a s e to move. The r e s u l t s of an e x p e r i m e n t a l i n v e s t i g a t i o n of the p h e n o m e n o n a r e p r e s e n t e d , along with a model d i r e c t e d toward an explanation of m u l t i p l e L u d e r s band f o r m a tion in c o m p o s i t e s . EXPERIMENTAL PROCEDURE Composites were fabr
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