Axisymmetric crack in transversely isotropic FGM Full-space under tractions on crack surfaces

This paper develops a discontinuous displacement method to analyze an axisymmetric crack in an infinite functionally graded material (FGM) with transverse isotropy. The fundamental solution for a transversely isotropic layered solid of infinite extent subjected to point concentrated loads is employed to establish boundary integral equations only over one side of crack surfaces. Both continuous and discontinuous elements are employed to discretize the crack surface. A discretization technique is utilized to model arbitrary variations of the FGM along a graded direction. Verifications are conducted to illustrate that the numerical solutions presented by the proposed approach are in very good agreement with the classical analytical solutions. Examples are given for penny-shaped cracks in isotropic and transversely isotropic FGMs under different types of tractions, and the stress intensity factors (SIF) for two types of elastic media are analyzed and compared in detail. Results illustrate the effect of the heterogeneity and anisotropy of the materials on the fracture behavior of crack problems.