Simulation of crack propagation using a gradient-enriched ductile damage model based on dilatational strain

An implicit gradient formulation based on the micro-dilatational approach is applied to the Gurson–Tvergaard–Needleman ductile damage model. The stability of the model is proven analytically for the considered class of materials. The damage model is implemented in an implicit finite-element code in an Updated Lagrangian formulation incorporating an objective time integration scheme and consistent tangent moduli for quadratic convergence. The model is applied to simulate a fracture mechanical test of a typical pressure vessel steel. The investigations are focused on the evolution of ductile damage and stress state at the crack tip. The results show that the model captures the different stages of crack initiation and propagation realistically. A condition for mesh-convergence in terms of the internal length parameter is suggested.