The stress state of an elastic orthotropic medium with a penny-shaped crack

The static-equilibrium problem for an elastic orthotropic space with a circular (penny-shaped) crack is solved. The stress state of an elastic medium is represented as a superposition of the principal and perturbed states. To solve the problem, Willis’ approach is used, which is based on the triple Fourier transform in spatial variables, the Fourier-transformed Green’s function for an anisotropic material, and Cauchy’s residue theorem. The contour integrals obtained are evaluated using Gauss quadrature formulas. The results for particular cases are compared with those obtained by other authors. The influence of anisotropy on the stress intensity factors is studied.