Phase field formulation for the fracture of a metal under impact with a fluid formulation

This work is concerned with the impact problems of metals involving intense shock waves. To account for different fracture modes, we develop a phase field model with a new formulation of the thermodynamic driving force. This driving force is based on a new history variable dependent on two critical energy release rates, one for volumetric loading and the other for shear loading. The formulation is based on an updated Lagrangian framework. In contrast to most existing phase field models, usually implemented under total Lagrangian framework, we have adopted an equation of state for pressure, and artificial viscosity to deal with the strong shock waves. Besides, the hypoelastic elastoplastic constitutive model and the Johnson–Cook model are adopted to consider the strain hardening, strain rate hardening, and thermal softening at finite deformation, high temperature, and high strain rate situations. Another feature of the proposed model compared with existing models is that the former needs two or three fewer parameters. The proposed model is validated by experimental results. Moreover, parametric studies on the impact velocity and the Taylor–Quinney coefficient are conducted, which shows that different fracture modes can be captured, and the Taylor–Quinney coefficient has a significant effect on the results. Besides, global sensitivity analysis is performed to study the effect of a few key parameters on the fracture characteristics. •A phase field model based on hydrocode and updated Lagrangian for impact problems.•A new formulation for thermodynamic driving force for phase field is developed.•Fracture by volumetric loading and shear banding with different critical energies.•The equation of state and artificial viscosity to handle the intense shock waves.