Micromechanics and overall elastoplasticity of discontinuously reinforced metal-matrix composites

The objective of the present study is to consider the local micromechanics and effective (overall) elasticity and elastoplasticity of discontinuously reinforced metal matrix composites (MMCs). First of all, a new formulation is derived for the exterior-point Eshelby's tensor which represents the strain and stress influence of an ellipsoidal inclusion upon a local material point within the matrix. Second, the effective elastic and elastoplastic constitutive behavior of MMCs containing aligned particle-reinforced composites is proposed. Homogenization procedure is utilized to derive the governing ensemble-volume averaged elastic constitutive field equations and the overall yield function for the composite based on the probabilistic spatial distribution of aligned spheroidal inclusions. The transversely isotropic elastic stiffness fourth-rank tensor is explicitly derived. The plastic flow rule and hardening law are then postulated based on the proposed overall yield function. This micromechanical model can characterize the macroscopic elastoplastic behavior of the composite under three-dimensional arbitrary loading/unloading histories. Third, the effective elastic and elastoplastic models of MMCs with randomly oriented reinforcements are also proposed. The average process over all orientations upon three elastic governing constitutive field equations for aligned particle-reinforced composites is performed to obtain the constitutive relations and isotropic elastic stiffness of MMCs with randomly oriented particles. Orientational averaging procedure is utilized to derive the overall yield function for the composite based on the results for the aligned particle-reinforced MMCs. Elastoplastic constitutive relation for the MMC is established. As applications, the overall elastoplastic stress-strain curves of discontinuously reinforced MMCs under uniaxial loading, pure hydrostatic loading and axisymmetric loading are investigated in detail. Comparisons between present theoretical predictions and experimental data for MMCs are performed to illustrate the capability of the proposed models. Initial yield surfaces for MMCs or void-weakened incompressible materials are discussed. Viscoplastic extension is briefly obtained.