An Energy Approach to the Plasticity of a Two-Phase Composite Containing Aligned Inclusions

Abstract

Based on a linear comparison composite (Tandon and Weng, 1988) and an energy criterion for the effective stress of the ductile matrix (Qiu and Weng, 1992), a nonlinear theory is developed to estimate the strain potential and the overall stressstrain relations of a two-phase composite containing aligned spheroidal inclusions. The plastic state of the ductile matrix under a given external load is determined by solving two simultaneous equations, one being its constitutive equation and the other the expression of its effective stress as a function of its secant shear modulus. Then by means of the effective properties of the linear comparison composite, the overall strain and strain potential of the nonlinear system are evaluated. It is demonstrated that, for an elastically incompressible matrix containing either aligned voids or rigid inclusions, the derived strain potential is exactly equal to Ponte Castaneda’s (1991) bound or estimate, respectively, of Willis’ (1977) type. Comparison with an exact solution of a fiber-reinforced composite under the plane-strain biaxial loading also shows an excellent agreement. The theory is generally intended for the condition when the concentration is not high, and is finally applied to examine the aspect-ratio dependence of the overall response for a silicon carbide/aluminum system. It is found that, more so than the elastic behavior, the nonlinear plastic response of the twophase composite is very sensitive to the inclusion shape under most types of loading.