Effective elastic properties of cracked composites with periodically distributed particulates

Abstract

A composite with periodically distributed particulate reinforcements is usually preferred in some industrial engineering areas to enhance the damage resistance of materials. The bonding of the matrix and enhancements may be fractured during manufacturing or operating by cracks that are evenly distributed. In this study, a cracked composite is simplified as an infinite plane with repeatedly distributed units containing inhomogeneities and cracks. The inhomogeneities can be in arbitrary shapes and cracks are assumed horizontally oriented. In formulating the governing equations, each inhomogeneity is homogenized according to the Equivalent Inclusion Method with equivalent eigenstrains to be determined, and each crack of mixed modes I and II is modeled as a distribution of climb and glide dislocations using the Distributed Dislocation Technique with dislocation densities to be determined. The fast Fourier transform is used to speed up the calculation while taking into account the interactions of the inhomogeneities and cracks in the plane. Effective moduli of the composites are obtained from average stresses and strains and samples are reported to demonstrate the generality of the model.