Three-dimensional fracture mechanics for transversely isotropic materials
横观各向同性材料的三维断裂力学问题

In this paper,based on three-dimensional elastic theory for transversely isotropic materials,the fundamental solutions for a displacement-jump(dislocation)were derived with Hadamard's finite-part concepts. Subsequently,the limit theory was used to reduce the three-dimension problems for arbitrary-shaped planar cracks in an infinite transversely isotropic solid to the solutions of a set of hypersingular integral equations.With a dominant-part analysis of two-dimensional hypersingular integrals,the stress singular indices and singular stress fields near smooth periphery of the crack front were exactly derived and thus the stress intensity factors and the energy release rate for local extension of the crack were expressed in the form of the displacement jumps on the crack surfaces.As applications of the results obtained,two examples are given,an exact solution for a penny-shaped crack problem and a numerical solution for a square crack.The exact analytical method for hypersingular integral equations under axially uniform extension loading for the penny-shaped crack was discussed.The closed solutions of the displacement jumps and the stress intensity factors were obtained.These solutions agree with available results.