Matrix strengthening mechanisms of an iron fiber-copper matrix composite as a function of fiber size and spacing
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of t h e m e c h a n i c a l p r o p e r t i e s of c o n t i n u o u s f i b e r c o m p o s i t e m a t e r i a l s , t e s t r e s u l t s a r e oft e n c o m p a r e d w i t h t h e s o - c a l l e d r u l e of m i x t u r e s . I n t h i s c o n t e x t , the r u l e o f m i x t u r e s i s i n t e r p r e t e d t o m e a n that the v o l u m e f r a c t i o n w e i g h t e d s t r e s s e s i n the i n d i v i d u a l p h a s e s a r e a d d e d t o g e t h e r t o give the t o t a l s t r e s s b o r n e by t h e c o m p o s i t e , a l l s t r e s s e s t a k e n a t s o m e c o m m o n s t r a i n v a l u e . T h i s a n a l y s i s , b a s i c a l l y that of p a r a l l e l e l e m e n t s , a s s u m e s that e a c h p h a s e b e h a v e s a s i t w o u l d w h e n d e f o r m e d a p a r t f r o m the c o m p o s i t e , a n d that no r h e o l o g i c a l i n t e r a c t i o n s b e t w e e n the p h a s e s occur. The rule of mixtures analysis has been shownt to describe the Young's moduli of fiber composites quite well. Some investigators2-~ have also found it valid for the range in which one or both phases are deforming plastically while others have observed deviations. Performance below the rule of mixtures standard has been explained by broken fibers, off-axis fibers, degradation of the fibers, or weak internal interfaces. Positive deviations from the rule of mixtures during plastic deformation, with which this work is concerned, have been attributed to either of two sources. Some workers5-7 claim that positive deviations arise from dislocation blocking effects, while otherss'9 believe that they arise from biaxial constraint caused by different Poisson contractions of the two phases. In the first case the dislocations in the matrix are thought to pile up against the fibers. The resulting baekstresses act against dislocation sources, resulting in a higher matrix flow stress. The proposed mechanism is quite ang!pgous to the Petch effect strengthening of polycrystall~ne metals. On the other hand, the difference in Poisson coefficients of two bonded phases results in the generation of stresses normal to the interface when the composite is deformed parallel to the interface. The normal s t r e s s reduces the resolved shear stress in the G. GARMONG, formerly with the Department of Metallurgy and Materials Science, M.1.T., Cambridge, Mass., is with the Science Center, North American Rockwell Corp., Thousand Oaks, Calif. L. A. SHEPARD, formerly with the Department of Metallurgy and Materials Science, M.I.T., is with the Army Materials and Mechanics Research Center, Watertown, Mass, Manuscript submitted June 11, 1970. M[IIAI. tURGI('Ak
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two p h a s e s . Consequently, dislocation m o t i o n , yielding, a n d f l o w o c c u r in e a c h p h a s e at h i g h e r a p p l i e d s t r e s s e s t h a n e x p e c t e d . T h e r e is c u r r e n t l y s o m e q u e s t i o n as to w h i c h of t h e s e two e f f e c t s i s d o m i n a n t i n m e t a l m a t
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