Frobenius’ method for curved cracks

The distribution of stresses produced by an undulated crack in a plane elastic solid, and in particular, at its tips where stresses approach infinity, requires the solution of two coupled singular integral equations. Except for simple crack geometries such as rectilinear and circular arcs in infinite plates, for which explicit analytic solutions have been obtained, the integral equations require numerical solutions. We propose a treatment of the integral equations by Frobenius’ method, which is particularly suitable for evaluating the stress intensity factors of slightly curved cracks.