Binary inclusion model for the overall elasticity of imperfectly bonded composites

Abstract

A micromechanical approach is developed to estimate the overall elastic moduli of composite materials with imperfectly bonded spherical fillers. The randomly dispersed particles are assumed to satisfy linear interfacial conditions where both tangential and normal interface displacement discontinuities are linearly related to the respective surface tractions. Using the generalized version of Eshelby’s equivalent inclusion method proposed by Furuhashi et al. [6] the analysis of the heterogeneous medium reduces to the study of a corresponding homogeneous medium containing spherical inclusions with a proper distribution of eigenstrain and Somigliana dislocation fields. Based on the estimated pair-wise average of strain fields in two interacting imperfect fillers embedded in the homogeneous infinite matrix, the ensemble phase volume average of field quantities has been evaluated within a representative volume element containing a finite number of imperfect particles. For the case of a constant radial distribution function, results are in reasonable agreement with those based on the generalized self-consistent method and composite sphere assemblage proposed by Hashin [11].