A rate-dependent phase-field model for dynamic shear band formation in strength-like and toughness-like modes

The phase-field model has proven a promising tool to simulate crack propagation, and special attention has recently been paid to the prediction of crack nucleation. Dynamic shear banding (or the so-called adiabatic shear banding) is a significant ductile failure mechanism in metals and alloys under impact loading, and its nucleation has been considered either strength-like or toughness-like in the literature. In this work, a rate-dependent phase-field model incorporating stored-energy-based shear banding criteria is proposed to simulate dynamic shear band formation within a thermodynamically consistent framework, emphasizing the capability to capture shear band nucleation in all possible modes, be it strength-like, large-scale yielding, or small-scale yielding. The model is first applied on dynamic shear banding under coupled damage and thermal softening, where the phase-field length scale is demonstrated to play an important role in energy dissipation when either the rate- or temperature-dependence during shear band formation is non-negligible, which is significantly different from its interpretation in quasi-static conditions. Then the capability of the proposed model in capturing shear band nucleation is thoroughly investigated by simulating both designed numerical tests and reported physical experiments. Strain-based and stress-based criteria for shear band nucleation can be well retrieved with the energy-based phase-field model. Validation against shear banding experiments of all possible modes over a wide range of specimen geometries, material properties, and loading rates is performed to demonstrate the performance of the model and shed light on a unified understanding of shear band formation in various scenarios.