Multiscale homogenization method for the prediction of elastic properties of fiber-reinforced composites

Abstract

An analytical approach based on multiscale homogenization is proposed to enable efficient and accurate characterizations of fiber-reinforced composites with imperfect interfaces. Micromechanical formulations are developed to evaluate transversely isotropic properties of a microscale representative volume element (RVE) consisting of a fiber, the surrounding matrix and their interfaces. We utilized the shear-lag model to derive the longitudinal Young’s modulus, the composite cylinder assemblage (CCA) model to get the in-plane bulk modulus and the axial shear modulus, and the generalized self-consistent (GSC) scheme for the transverse shear modulus. Numerical results given by the detailed finite element analysis (FEA) demonstrate the high accuracy of the obtained material properties. To scale up-to macro-level, the RVEs are homogenized to equivalent inclusions that are perfectly bonded to the matrix, followed by the application of the Mori–Tanaka method to obtain bulk properties of the overall composites. The large-scale FEA model that allows incorporation of periodic boundary conditions and cohesive interfaces between fiber and surrounding matrix confirms the good accuracy of the proposed multiscale homogenization strategy. The proposed strategy does not depend on any computational simulations, providing a very efficient tool to understand effects of imperfect interfaces and an alternative to determine mechanical properties of composites only based on geometric and material parameters.