Fracture dynamics of fusion of two anti-plane cracks

The problem of the fracture dynamics of two two-dimensional coplanar anti-plane shear cracks is considered. Both cracks extend under a critical stress-intensity fracture criterion. The two cracks are initiated at different locations and times. A solution developed by Kostrov [Kostrov, B. V. (1966) J. Appl. Math. Mech. 30, 1241-1248] for isolated cracks is used to determine the tearing loci of the cracks up to the time at which the individual cracks begin to interact. In the interaction interval prior to the fusion of the two cracks, both the stresses and the fracture tip loci are determined sequentially by applying the solution to Abel's equation twice iteratively. This method can be used to solve problems of the fusion of any number of coplanar cracks.