Analysis of the plastic zones of cracks in an elastic-perfectly plastic half-space under contact loading

In this paper, a semi-analytic solution is proposed to solve the subsurface stress distribution and plastic zones of an elastic-perfectly plastic half-space with cracks under contact loading. The cracks can be treated as a distribution of edge dislocations with unknown densities based on the distributed dislocation technique. These unknown dislocation densities, contact area and surface pressure distribution can be obtained iteratively when the surface displacement due to the substrate cracks and contact loading is converged by a numerical algorithm according to the conjugate gradient method. The plastic zones at crack tips can be determined by canceling the stress intensity factor (SIF) due to the closure stress and that due to the external applied load based on the Dugdale model of small scale yielding. It is noticed that the plastic zone sizes are affected by the original crack length and depth, yield strength of substrate and loading conditions. This solution might provide guidance for the fracture mechanics analysis of materials with cracks in a half-space.