The higher order asymptotic fields for anti-plane oblique crack with physical weak-discontinuity

An Oblique anti-plane crack is studied with its tip at the physical weak-discontinuous line of the structure which is made up of homogeneous material and functionally graded materials (FGMs). The analytic solution of the higher order crack tip fields (similar to the Williams' solution of homogenous material) is obtained by applying the asymptotic series expansion. When non-homogeneous material parameters are degenerated, the solutions become the same as the asymptotic crack tip fields of the homogeneous material. Therefore, the solutions are the basic results of non-homogeneous fracture mechanics, and provide a theoretical basis for solving the fracture problems of one common structure with physical weak-discontinuity.