Interaction of newly defined stress intensity factors for angular corners in a row of diamond-shaped inclusions

Abstract

This paper deals with a row of equally spaced equal diamond-shaped inclusions with angular corners under various loading conditions. The problem is formulated as a system of singular integral equations with Cauchy-type singularities, where the unknown functions are the densities of body forces distributed in infinite plates having the same elastic constants of the matrix and inclusions. In order to analyze the problems accurately, the unknown functions of the body force densities are expressed as a linear combination of two types of fundamental density functions and power series, where the fundamental density functions are chosen to represent the symmetric stress singularity of $1/r^{1 - \lambda _1 }$ and the skew-symmetric stress singularity of $1/r^{1 - \lambda _2 }$. Then, newly defined stress intensity factors for angular corners are systematically calculated for various shapes, spacings, elastic constants and numbers of the diamond-shaped inclusions in a plate subjected to uniaxial tension, biaxial tension and in-plane shear. For all types of diamond-shaped inclusions, the stress intensity factor is shown to be linearly related to the reciprocal of the number of diamond-shaped inclusions.