In this work, we examine a phase-field method for ductile fracture based on a cohesive model. We first present a general framework for constructing variational phase-field fracture models for non-conservative systems, and derive a hyperelastic-plastic-fracture model from a Helmholtz free energy. Simulations of three quasi-static problems are performed to illustrate the effects of different assumptions and modeling choices in the Helmholtz free energy.  The first examines the homogenized response of the model, where we demonstrate the implications of the local dissipation potential and the degradation of the yield surface.  The results also indicate that a specific form or the local dissipation potential is essential to obtain a damage-independent yield stress. In the second problem, we study Mode-I crack propagation in a notched plate. The plate is loaded with displacement-control according to an elasticity solution such that the crack propagates in a stable manner, and the J-integral is evaluated as a function of crack length. The results from this problem indicate that a linear local dissipation potential is critical to obtain convergence in the J-R curve with a diminishing phase-field regularization length.  In the third problem, a three-point bending experiment is simulated after calibration. The results from this problem indicate that the plastic contribution to the damage evolution is decisive in determining the crack path. 

A variational ductile phase-field fracture framework based on a cohesive model

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