An arbitrarily curved crack under uniform remote in-plane stresses

An effective approach based on conformal mapping and distributed dislocation techniques is proposed to solve the plane problem of an arbitrarily curved crack in an infinite homogeneous and isotropic elastic plane under uniform remote in-plane stresses. A Cauchy-type singular integral equation is constructed in the image plane. The singular integral equation is solved numerically using the Gauss–Chebyshev integration formula to arrive at the stress intensity factors at the two crack tips. Numerical examples of an elliptical arc crack, a hypotrochoidal arc crack and a cycloid crack are presented to demonstrate the effectiveness of the proposed solution method.