Analysis of cracks in transversely isotropic, linear elastic half-space by weakly singular boundary integral equation method

Abstract

This dissertation presents an efficient numerical technique for the analysis of stress intensity factors and T-stress components for arbitrary-shaped cracks in a homogeneous, linear elastic half-space under various conditions on the free surface. The key governing equations are established in a form of weakly singular boundary integral equations involving both unknown relative and sum of the crack-face displacements. A systematic regularization technique based on the integration by parts and special decompositions of singular kernels is adopted to regularize all involved strongly singular and hyper-singular integrals to those containing only weakly singular kernels and requiring only continuous crack-face data for their validity. Besides the direct consequence of the weakly singular nature, the governing integral equations also possess several positive features such as no requirement of free-surface discretization and the capability to treat material anisotropy, non-planar crack geometry and general crack-face loading conditions. In numerical implementations, a weakly singular, symmetric Galerkin boundary element method along with the special near-front approximation is employed to solve the traction integral equation for the relative crack-face displacement. The sum of the crack-face displacement is then obtained by solving the displacement integral equation via standard Galerkin method. The stress intensity factors and the T-stress components along the crack are extracted directly from the near-front relative and sum of the crack-face displacement data. Obtained numerical results for various scenarios clearly demonstrate the accuracy, convergence and capability of the proposed technique.