The branch crack problem in plane elasticity was modelled by assuming a reasonable distribution of the dislocations. A new integration scheme was proposed in which a point dislocation was placed at the branch point, and the distributed dislocations were assumed to lie along all the branches. Thus, a singular integral equation and a constraint equation could be formulated for the branch crack problem. A semi-open quadrature rule was used which ensured that the number of unknowns was equal to the number of equations. The results of the numerical solution were directly related to the stress intensity factors at the branch tip.

New Integration Scheme for the Branch Crack Problem. Y.Z.Chen, N.Hasebe: Engineering Fracture Mechanics, 1995, 52[5], 791-801