An accurate semi-analytical method for an arbitrarily oriented edge or interior crack in an anisotropic homogeneous elastic solid

In this work, a general semi-analytical method for the determination of the elastic fields within an anisotropic homogeneous elastic solid with an inclined edge or interior crack is developed. In this method, the displacement field is represented as a sum of a function and a finite series of functions with unknown coefficients. The functions are constructed in such a way that all the essential homogeneous and inhomogeneous boundary conditions are satisfied exactly and, moreover, the displacement discontinuity across the crack faces as well as the exact singular behaviour of the stress field at the crack-tip are captured. The unknown coefficients are determined by utilizing the principle of minimum potential energy; the obtained coefficients matrix involves some singular integrands which for their accurate integrations over the domain in the vicinity of the crack-tip the generalized Duffy transformation is employed. Following the calculations of the unknown coefficients, the displacement field and subsequently the remaining field quantities are obtained. The fracture parameters, stress intensity factor SIF and the crack opening displacement COD are readily evaluated. Comparisons of the solutions of several examples obtained by the current approach with the exact solutions reveal the efficacy of the proposed method.