Two-phase composite model taking into account the matricity of microstructure and its application to functionally graded materials

In this investigation, a model for two-phase composites with interpenetrating microstructure has been developed by introducing the concept of matricity into a constitutive relation of particle-reinforced composites. Firstly we consider two models for particle-reinforced composites, namely an αM-model for an α-phase matrix composite and a βM-model for an α-phase particle composite. Elastic and plastic deformation of these composites can be predicted by a theory for particle-reinforced composites based on the Eshelby’s equivalent inclusion method and Mori-Tanaka’s mean field concept. Secondly, a matricity-model is developed under the assumption that the composite with an α-phase volume fraction fα and matricity Mα consists of the parts of αM-model and βM-model in a volume ratio of Mα to 1 − Mα. The model can reasonably predict the elastic–plastic deformation of the composites in a full range of phase composition. This model is also incorporated into a finite element method, and finite element analysis is carried out on the deformation behavior of a functionally graded material.