Theoretical study of the effective modulus of a composite considering the orientation distribution of the fillers and the interfacial damage

Abstract

In the manufacturing process of a filler-reinforced composite, the fillers in the matrix are aligned due to the shear flow occurring during the drawing stage, and the interface between the matrix and the fillers form various imperfections that lead to debonding and slip under mechanical loading. Hence, there have been numerous micromechanics studies to predict effective moduli of the composites in the presence of partial alignment of fillers and interface imperfections. In this study, we present an improved theory that overcomes two limitations in the existing micromechanics based approaches. First, we find that the interface damage tensor, which has been developed to model the weakened interface between matrix and fillers, has singularities that cause non-physical predictions (such as infinite or negative effective moduli). We correct the mathematical mistakes to remove singularities and derive analytic expressions of the damage tensor for ellipsoidal inclusions. Second, we reveal that the previous theory on the effective moduli with axisymmetric filler orientation distribution fails because the longitudinal and transverse moduli do not converge in the limit of random orientation distribution. With appropriate corrections, we derive an analytic expression for the orientation average of arbitrary transversely isotropic 4th order tensor under general axisymmetric orientation distribution. We apply the improved method to compute the effective moduli of a representative composite with non-uniform filler orientation and interface damage.