Ductile fracture modelling based on the Drucker-Prager plasticity and phase field approach

In this paper, a coupled plasticity-phase field model for ductile fracture is proposed. The Drucker-Prager plasticity model, which have been applied to metals, concrete, polymers, foams, and other pressure-dependent materials, is coupled with the phase field method. The governing equations are determined by a minimization principle that results in balance laws for the coupled displacement-fracture phase field problem. Furthermore, the finite element implementation, discretization and integration algorithms for the proposed model are presented for three-dimensional, plane strain and plane stress states. In addition, to control the influence of the plastic work and its effect on the crack propagation process, a threshold variable is introduced. Using a numerical example, it is demonstrated that a specific length scale and a certain minimum element size is necessary such that the regularized crack surface converges to the sharp crack. The accuracy of the proposed model and integration algorithm is verified by comparing the obtained results with existing experimental data. In addition, the Arcan sample, by means of a special test setup, allows to load a sample at different direction, and thus performing mixed mode fracture investigation using the model.