Uncoupled characteristics of three-dimensional planar cracks

Abstract

The uncoupled characteristics of three-dimensional planar cracks under arbitrary loading is investigated by boundary integral equation method. From theoretical analysis, the crack displacements under normal loading and shear loading on the crack surface are uncoupled. For a crack under shear loading (mode II and III), the special case of the crack with uncoupled displacements is investigated, whereby the self-similar crack expansion (SSCE) method, proposed in a previous paper by Xu et al. (1996, Journal of Applied Mechanics) is used for the analysis of three-dimensional cracks under shear loading. A number of cracks with arbitrary geometry and mixed mode loading conditions are calculated in this paper. For cracks with uncoupled displacements under various loading conditions, the numerical results by the SSCE method show good accuracy, with errors in stress intensity factors around the penny-shaped crack edge less than 1%. Results of a penny-shaped crack under torsional loading show good applications of uncoupled characteristics to the stress analysis for three-dimensional cracks.