Variational Estimates for the Elastoplastic Response of Particle-Reinforced Metal-Matrix Composites

Abstract

Ductile solids reinforced by aligned elastic spheroidal inclusions, with overall transversely isotropic symmetry, are examined analytically in this paper. Estimates for the effective constitutive behavior of this class of composite materials are obtained in terms of simple optimization problems for general loading conditions, as functions of the particle stiffness, concentration and shape. In particular, explicit expressions are obtained for the yield functions of the composites. The results apply to composites with inclusion shapes ranging from continuous fibers (or needles in the limit of vanishingly small concentration), to approximately spherical, to continuous flat layers (or disks). As an example, we investigate a model composite of the type used in many structural applications, namely, 2124 Al–SiC which is made of a ductile matrix phase (Al) reinforced by hard brittle particles (SiC). The predicted stress-strain responses for these composites are compared with available experimental measurements and numerical calculations. Thus, it is shown that the constitutive model developed in this work predicts fairly accurately the uniaxial tensile experiments of Christman et al. (1989). In addition, the constitutive model is in good agreement with the periodic finite-element calculations of Tvergaard (1990) and Hom (1992), also for uniaxial loading conditions. A significant advantage of the analytical model proposed herein is that it can provide the constitutive response of composites under arbitrary loading conditions, without requiring complex numerical computations.