Interaction Between a Circular Inclusion and an Arbitrarily Oriented Crack

TLDR

The study examines the interaction between a circular elastic inclusion and an arbitrarily oriented crack in an elastic matrix. By employing edge‑dislocation Green’s functions, the authors formulate the through‑crack problem as a smooth arc near the inclusion and derive singular integral equations with Cauchy kernels. They determine the stress singularities at crack tips, express the stress‑intensity factors in terms of asymptotic density functions, and provide these factors for several typical crack orientations.

Abstract

The plane interaction problem for a circular elastic inclusion embedded into an elastic matrix which contains an arbitrarily oriented crack is considered. Using the existing solutions for the edge dislocations [6] as Green’s functions, first the general problem of a through crack in the form of an arbitrary smooth arc located in the matrix in the vicinity of the inclusion is formulated. The integral equations for the line crack are then obtained as a system of singular integral equations with simple Cauchy kernels. The singular behavior of the stresses around the crack tips is examined and the expressions for the stress-intensity factors representing the strength of the stress singularities are obtained in terms of the asymtotic values of the density functions of the integral equations. The problem is solved for various typical crack orientations and the corresponding stress-intensity factors are given.