A Theory for the mechanical properties of metal-matrix composites at ultimate loading
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W H E N s t r o n g m e t a l f i b e r s a r e i n c o r p o r a t e d into a m e t a l m a t r i x u n i d i r e c t i o n a l l y , the e x t e n s i o n a l p r o p e r t i e s p a r a l l e l to the f i b e r s depend on the p r o p e r t i e s of the c o m p o n e n t s and the r e l a t i v e a m o u n t of each p r e s ent. 1 In the a b s e n c e of d e l e t e r i o u s effects (e.g. b r i t t l e i n t e r m e t a l l i c compounds) m o d u l u s and flow s t r e s s have been found e x p e r i m e n t a l l y to obey a s i m p l e v o l u m e - f r a c t i o n a v e r a g e of the c o r r e s p o n d i n g component p r o p e r t i e s . At r e l a t i v e l y high v o l u m e f r a c t i o n s of a b r i t t l e - f i b e r phase, the u l t i m a t e composite s t r e n g t h follows a v o l u m e - f r a c t i o n a v e r a g e of fiber s t r e s s and m a t r i x s t r e s s , both e v a l u a t e d at f i b e r f a i l u r e s t r a i n ; at low v o l u m e f r a c t i o n s d e v i a t i o n s o c c u r due to the a b i l i t y of the m a t r i x to work h a r d e n a f t e r fiber f a i l u r e . S i m i l a r l y , when the f i b e r s a r e ductile and fail by necking, the o b s e r v e d u l t i m a t e s t r e n g t h s have been c o m p a r e d to a v o l u m e - f r a c t i o n a v e r a g e of fiber s t r e s s at n e c k i n g and the s t r e s s in the m a t r i x at the fiber necking s t r a i n ( s i m p l e a v e r a g i n g theory). While this a p p r o a c h y i e l d s f a i r l y good c o r r e l a t i o n s at high v o l u m e f r a c t i o n s of f i b e r , t h e r e is again a p o s i t i v e deviation from the p r e dicted u l t i m a t e s t r e n g t h at low fiber v o l u m e f r a c t i o n s . The explanation of this o b s e r v a t i o n is m o r e c o m p l i c a t e d than for the b r i t t l e fiber c a s e , and a n u m b e r of m i c r o scopic c a u s e s have been d i s c u s s e d . P i e h l e r 2 has a t t r i buted such d e v i a t i o n s to h y d r o s t a t i c s t r e s s e s g e n e r a t e d in the m a t r i x upon necking a n d / o r the i n c r e a s e d u n i f o r m s t r a i n beyond n e c k i n g of the monolithic f i b e r . Kelly and Davies ~ and Kelly and T y s o n 3 have e l a b o r a t e d on P i e h l e r ' s second s u g g e s t i o n : At fiber n e c k i n g , the m a t r i x h a r d e n i n g r a t e may s t i l l be sufficiently l a r g e for the composite to be stable to i n h o m o g e n e o u s d e f o r m a tion at higher s t r a i n and s t r e s s l e v e l s . Thus a p o s i t i v e deviation f r o m the p r e d i c t i o n s of the s i m p l e a v e r a g i n g theory is expected. Subsequent to the work of Refs. 1 to 3, Ahmad and B a r r a n c o 4 p r o p o s e d an a l t e r n a t i v e to the s i m p l e G. GARMONGand R. B. THOMPSONare Members of Technical Staff, North American Rockwell Science Center, Thousand Oaks, Calif. 91360. Manuscript submitted March 3, 1972. METALLURGICALTRANSACTIONS
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