Phase-field modeling of ductile fracture across grain boundaries in polycrystals

Abstract

In this study, we address damage initiation and micro-crack formation in ductile failure of polycrystalline metals. We show how our recently published thermodynamic framework for ductile phase-field fracture of single crystals can be extended to polycyrstalline structures. A key feature of this framework is that is accounts for size effects by adopting gradient-enhanced (crystal) plasticity. Gradient-enhanced plasticity requires the definition of boundary conditions representing the plastic slip transmission resistance of the boundaries. In this work, we propose a novel type of micro-flexible boundary condition for gradient-plasticity, which couples the slip transmission resistance with the phase-field damage such that the resistance locally changes during the fracturing process. The formulation permits to maintain the effect of grain boundaries as obstacles for plastic slip during plastification, while also accounting for weakening of their resistance during the softening phase. In numerical experiments, the new damage-dependent boundary condition is compared to classical micro-free and micro-hard boundary conditions in polycrystals and it is demonstrated that it indeed produces a response that transitions from micro-hard to micro-free as the material fails. We show that the formulation maintains resistance to slip transmission during hardening, but can generate micro-cracks across grain boundaries during the fracture process. We further show examples of how the model can be used to simulate void coalescence and three-dimensional crack fronts in polycrystals.