A statistical micromechanics-based multi-scale framework for effective thermomechanical behaviours of particle reinforced composites

Abstract

Particle-reinforced composite materials have been widely used as they can exhibit nearly isotropic material properties and are often easy to process. Some silicon carbide particle reinforced aluminium composites with high volume concentration of reinforcement exhibit excellent thermophysical properties and can be used in advanced electronic packaging. In this paper, a statistical micromechanics-based multi-scale material modelling framework is introduced to describe the macroscopic effective thermomechanical properties of the particle-reinforced composite. The formulation differs from most of the existing methods in that the interaction effects among the reinforcing particles are directly accounted for by considering pair-wise interaction and statistical information on particle distribution is included. The strain and stress concentration factor tensors that relate the local average strain and stress fields, respectively, to the corresponding global average fields are derived according to the theory of average fields. The effective coefficient of thermal expansion for the particle-reinforced composite material is derived. Comparisons of the prediction from the proposed framework to the results from other existing methods are presented. The results are expressed in analytical closed-form in terms of the thermal and mechanical properties of the two constituent phases and the volume fraction of particles. No parameter estimation or data fitting is required.