Effective elastic constants of participate composites with inhomogeneous interphases

We consider a composite material reinforced with spherical inclusions, which are arranged in a matrix in a statistically isotropic way and they are bonded to the matrix via an interphase. We represent the interphase as an inhomogeneous region (a functionally graded material) and consider an idealized model in which the interphase is linear elastic and isotropic and has the Young's modulus and Poisson's ratio varying in radial direction. We predict effective elastic constants of such a composite and study the influence of the spatial inhomogeneity of interphase on these constants. In the analysis we use the composite spheres assemblage method [1] to evaluate the effective bulk modulus and the generalized self-consistent method [2] to obtain the effective shear modulus. We show that the radial variation in the Young's modulus of interphase has an influence on the effective elastic moduli as compared with the corresponding uniform interphase case when particles are stiffer than the matrix and the effect is negligible when particles are softer than the matrix for the composite systems considered. We also show that the variation in Poisson's ratio has a much smaller influence on the effective bulk modulus than the inhomogeneity in the Young's modulus.