Multiscale homogenization model for thermoelastic behavior of epoxy-based composites with polydisperse SiC nanoparticles

Abstract

A multiscale statistical homogenization method based on a finite element analysis is proposed to predict the embedded filler size-dependent thermoelastic properties of nanoparticulate polymer composites. A molecular dynamics simulation is used to predict the particle size-dependent elastic constants and coefficient of thermal expansion (CTE) of nanocomposites. Because of the densified interphase zones formed in the vicinity of nanoparticles, and their relative dominance according to particle size, the thermoelastic properties are more prominently increased by smaller nanoparticles. The equivalent continuum microstructure of a nanocomposite is modeled as a three-phase periodic unit cell consisting of the nanoparticle, matrix, and effective interphase zone. An inverse numerical scheme is proposed to predict the thermoelastic properties of the effective interphase zone from the known properties of nanocomposites. In order to account for more realistic variation of the nanoparticle radius and spatial distribution in nanocomposites, statistical homogenization is performed by assigning randomness to the particle size using a beta distribution and to the spatial distribution through larger many-particle embedded representative volume elements (RVEs). Compared with the result from a regular homogenization method using a mono-particle RVE, the mean value of the elastic moduli increases, while that of the CTE decreases in the many-particle RVEs whose mean particle radius corresponds to that of the mono-particle RVE at the same volume fraction of nanoparticles.