Asymmetric Branching of Cracks

Abstract

The problem of asymmetric branching of a crack in an infinite plate under generalized plane stress conditions and loading in a direction perpendicular to the main crack at infinity can be solved by reduction to a system of three complex Cauchy-type singular integral equations or, further, six real Cauchy-type singular integral equations. This system can be numerically solved by reduction to a system of linear equations after applying it at properly selected points of the integration interval and approximating the integrals by using the Gauss and/or Lobatto-Legendre numerical integration rules. The values of the stress-intensity factors at the crack tips, resulting directly from the solution of this system of linear equations, were computed for several geometries of asymmetrically branched cracks and found in satisfactory agreement with the corresponding experimental values determined by the method of caustics.