Interaction of multiple straight cracks and elliptical inclusions in a finite plate due to mismatched thermal expansion

Abstract

The purpose of this paper is to study the interaction between multiple elliptical inclusions and straight cracks in a finite plate due to a uniform temperature change. In this solution, Eshelby’s equivalent inclusion method involving both interior Eshelby’s tensor and exterior Eshelby’s tensor is applied to calculate the thermal stress fields of an infinite plate containing multiple elliptical inclusions under a uniform temperature change first. Then the multiple cracks and the boundary are modeled by continuous distributions of dislocation densities in an infinite plate. Based on the stress boundary conditions of the cracks and boundary, a system of singular integral equations with Cauchy kernels are obtained. After solving the singular integral equations with Gauss–Chebyshev numerical quadrature, the stress intensity factor of each crack can be calculated. Besides, the finite element method is employed to examine the accuracy and efficiency of the presented method. Finally, the effects of the material and geometric parameters on the normalized stress intensity factors of the cracks are studied.