Crack path prediction near an elliptical inclusion

Abstract

A technique is presented which will predict the path of a naturally growing crack where the stress field can be modeled as two dimensional. The Green function for an arbitrarily oriented edge dislocation interacting with a rigid inclusion (or void) is used in an integral formulation of the elasticity problem. The technique uses a boundary integral approach to solve for the dislocation density along an arbitrarily shaped crack interacting with a rigid elliptical inclusion or void. The crack path is parameterized as a cubic spline, and a first order perturbation solution is employed to account for the generally curvilinear nature of the crack. The singular integrals are solved using a numerical technique which describes the distribution of dislocations along the crack as a piecewise quadratic polynomial to transform the integral equations into algebraic equations well suited to a matrix-type solution. Results of each step of the analysis have been verified with previously published results, and with experimental results of a crack propagating near an open circular hole. New results are also presented as paths of cracks interacting with inclusions of differing ellipticity ratios and at different orientations with respect to the initial crack.