A dislocation model for simulating two-dimensional quasi-static crack propagation was presented. The crack and plastic flow along slip planes were described using dislocation dipoles. A stationary crack could be modelled as well as a propagating crack along a straight line inclined at an arbitrary angle to a free surface of a semi-infinite medium. Cracks were also allowed to kink. A super-dipole algorithm was introduced to save simulation time without losing important information and necessary geometric details. It reduces the number of dislocation dipoles on slip planes in the plastic wake. The paper gave results on crack shapes for stationary and advancing cracks as well as it described how the size of the plastic zone depended upon crack inclination angles. Results on stress intensity factors were given using two different approaches as well as kinking cracks were introduced and stress intensity factors at kinked crack tips were calculated.

Dislocation Modeling of Quasi-Static Crack Propagation in an Elasto-Plastic Medium. A.Stoll, A.J.Wilkinson: International Journal of Fracture, 2010, 164[1], 103-15