Three-phase particle reinforced composites: Effective fields and the Mori–Tanaka method

Abstract

The Mori–Tanaka method is a micromechanical effective-field model that approximates the local fields acting on any inhomogeneity phase by the corresponding matrix field. This assumption is tested in a case study using finite-element-based periodic homogenization for numerically evaluating the effective-field inhomogeneity concentration tensors of the reinforcement phases for a set of simple three-phase particle reinforced composites. The numerical predictions show a clear dependence of the mechanical and thermal effective fields on the material properties of the particulate phases. Even though this behavior deviates from the assumption underlying the Mori–Tanaka method, the latter provides useful approximations for the macroscopic stiffnesses and conductivities for the set of composites covered by the study.