Development of the distributed dislocation dipole technique for the analysis of closure of complex fractures involving kinks and branches

This paper presents the development of the distributed dislocation dipole technique (DDDT) for the analysis of straight, kinked and branched cracks where parts of the cracks may close during loading. The method has been developed for plane problems. Crack cases in which closure occurs are analyzed by reformulating the Bueckner's principle, taking into account the contact stresses at the contacting portions of the crack surfaces. Stress intensity factors corresponding to opening and the in-plane sliding mode of deformation at the crack tips are computed. Several test cases involving straight, kinked and/or branched cracks where parts of the cracks undergoes crack surface closure when subjected to the outer loading are analyzed. The results obtained from the DDDT are compared to those obtained from a Finite Element Method (FEM) analysis of the same crack cases. This comparison shows that the computation of stress intensity factors for the cases involving crack surface closure are less accurate than those for fully open crack cases. However, for the cases under consideration, the stress intensity factors were still computed with a maximum difference of approximately 2 per cent compared to the FEM calculations if Jacobi polynomial expansions of at least the twelfth order were used to represent the crack surface opening and sliding displacements. In most cases under consideration, sixth order Jacobi polynomial expansions were sufficient to obtain results within that margin of deviation.