Size-dependent Probabilistic Micromechanical Damage Mechanics for Particle-reinforced Metal Matrix Composites

A size-dependent micromechanical framework is proposed to predict the deformation responses of particle-reinforced metal matrix composites by incorporating the essential features of the dislocation plasticity. Within the framework of probabilistic micromechanical formulation, the damage caused by the manufacturing process and by the external mechanical loading in the presence of thermal residual stresses is considered. The effective elastic moduli of four-phase composites, consisting of a ductile matrix and randomly located spherical intact or damaged particles are derived. Subsequently, the size-dependent plastic deformation behavior of particle-reinforced metal matrix composites is predicted with a dislocation theory. Specifically, the density of dislocations due to the thermal contraction misfit and the plastic deformation misfit is taken into consideration within the micromechanical methodology to account for the dislocation strengthening. To predict the overall elastoplastic damage behavior of composites, a size-dependent hybrid effective yield function is presented on the basis of the ensemble-volume averaging and the modified matrix yield strength. The comparisons between our predictions and available experimental data illustrate the potential capability of the proposed framework. Numerical simulations are also performed to exhibit the salient features of the proposed methodology.