The Interaction of Collinear Arrays of Griffith Cracks on Two Radial Lines

Abstract

The elastostatic plane problem of an isotropic homogeneous infinite plane with a number of Griffith cracks lying along two radial lines is considered. The analytical technique consists of the joint use of the Mellin transform and the Green’s function. The system of singular integral equations, thus obtained, is solved numerically taking advantage of the fact that the fundamental function is the weight function of the Chebyshev polynomials. The results for several cases are compared with those of previous authors. Stress intensity factors and probable directions of cleavage, which are important from the viewpoint of fracture mechanics, are studied in detail and illustrative numerical results for selected cases of geometry and loading are presented in graphical form.