The stress field in the neighborhood of a branched crack in an infinite elastic sheet

The problem of a branched crack consisting of a main crack and a straight branch starting from one of its tip located in an infinite elastic sheet is considered under the assumptions of two-dimensional theory of Elasticity. Employing Kolosov-Muskhelishvili representation of the stress function and other well known techniques the problem is reduced to the solution of an integral equation. The nature of the stress singularity at the re-entrant corner, where the two branches of the crack meet, is discussed. Based upon a numerical solution of the integral equation the stress intensity factors at the two tips are computed for two types of prescribed traction at infinity and various geometric configurations of the branched crack.