An efficient homogenization scheme for analyzing the elastic properties of hybrid nanocomposites filled with multiscale particles

Abstract

Designing material requires the establishment of structure–property relationships for multiscaled nanoparticle/microparticle-reinforced polymer hybrid nanocomposites. This fundamental task is the first step in developing a reliable new method. In the present study, two micromechanical analytical models are proposed to develop an efficient homogenization scheme, in the case of calculating elastic properties for a multiscaled hybrid nanocomposite consisting of silica nanoparticles and glass microparticles embedded in the epoxy matrix. In the small scale, we consider homogenous interphase surrounding the nanoparticle which the first model takes into consideration. In the small scale, considering the thickness of this interphase as variable and characteristic length scale, the influence of nanoparticle size on the overall elastic properties is calculated. In the large scale, an interface model of homogenization is proposed; this model too calculates the elastic properties of the overall nanocomposite as a function of inclusion size in microsize representative volume elements. In the large scale, the existence of surface stress and strains is a result of “sticking” behavior of the matrix to the inclusion surfaces. By combining these two models, we can determine the effective elastic properties of a hybrid nanocomposite as a function of nanoparticle size, microscale inclusion size, interphase thickness, and volume fractions. The model predictions are in good agreement with the experimental data provided in the literature.