AN ENERGY APPROACH TO THE PLASTICITY OF A 2-PHASE COMPOSITE CONTAINING ALIGNED INCLUSIONS

Based on a linear comparison composite (Tandon and Weng, 1988) and an energy criterion for the effective stress of the ductile matrix (Qiu a nd Weng, 1992), a nonlinear theory is developed to estimate the strain potential and the overall stress-strain relations of a two-phase comp osite containing aligned spheroidal inclusions. The plastic state of t he ductile matrix under a given external load is determined by solving two simultaneous equations, one being its constitutive equation and t he other the expression of its effective stress as a function of its s ecant shear modulus. Then by means of the effective properties of the linear comparison composite, the overall strain and strain potential o f the nonlinear system are evaluated. Ir is demonstrated that, for an elastically incompressible matrix containing either aligned voids or r igid 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 composi te under the plane-strain biaxial loading also shows an excellent agre ement. The theory is generally intended for the condition when the con centration is not high, and is finally applied to examine the aspect-r atio dependence of the overall response for a silicon carbide/aluminum system. It is found that, more so than the elastic behavior, the nonl inear plastic response of the two-phase composite is very sensitive to the inclusion shape under most types of loading.