THE INFLUENCE OF INCLUSION SHAPE ON THE OVERALL ELASTOPLASTIC BEHAVIOR OF A 2-PHASE ISOTROPIC COMPOSITE

A mean-field, approximate theory is developed for the determination of the overall stress-strain relation of a two-phase composite, consisting of randomly oriented elastic, spheroidal inclusions and a ductile matrix. The theory is intended for a low-volume concentration of inclusions. It is versatile enough to provide results under any proportionally increasing combined stresses, and yet simple enough to require no iterations. To preserve the virtue of simplicity, the simpler deformation theory is used over the incremental one. More so than the elastic behavior, the elastoplastic response of the composite is found to be extremely sensitive to the inclusion shape, with the discs providing the most remarkable reinforcement. Explicit results of the overall secant moduli are established for the three extreme inclusion shapes of disc, needle (fiber) and sphere. An interesting consequence of this analysis is that while both the particle and fiber-reinforced composites become plastically compressible, the disc-reinforced composite-as the ductile matrix itself-remains plastically incompressible. When applied to a silicon-carbide/aluminum system, the theory indicates that within the aspect ratio alpha < 10, the prolate and oblate inclusions with inversed aspect ratios (i.e. alpha and 1/alpha) have almost the same effect on the flow stress of the composite, but beyond this the discoriented inclusions begin to show a more superior influence. The theory also compares reasonably with the experimental data when the carbides exist in the form of randomly oriented platelets, with alpha = 1/4.