Edge crack in front of anisotropic wedge interacting with anti-plane singularity

Abstract

This paper analyzes the anisotropic elastic problem of an edge crack of length a in front of the wedge tip interacting with an anti-plane singularity such as a screw dislocation or anti-plane line force. The derivation is based on complex potential in conjunction with the conformal mapping method. Explicit closed-form analytical solutions are obtained and used to calculate the stress intensity factors and the strain energy density factors of the crack. The results can be reduced to the existing ones when the wedge angle is taken to be limiting case or the materials are assumed to be isotropic or orthotropic. Numerical calculations show that the stress intensity factors can be positive and negative for different applied loadings but the strain energy density factors are all positive. Stress intensity factors are used to discuss the influences of the wedge angle and singularity on the anti-shielding or shielding effects but they are inconvenient to be used as a criterion for predicting the crack extension. The positive definite characteristic of the strain energy density factor makes it suitable to predict the fracture behavior of the cracked structure.