A phase-field model for spall fracture

As a kind of dynamic tensile failure, the spall fracture usually happened in ductile metals under shock wave loading. Also, its macroscopic softening behavior on the stress caused by the damage is complicated due to the micro-voids nucleation, growth, and coalescence, and finally forming macro-cracks in the material. In addition, the simulated results are often mesh-dependent. Recently, the phase-field model of fracture (PFM) gains popularities in modeling fracture and damage problems. One of its advantages is that the simulated results are mesh independent. The PF-CZM by Wu [J. Mech. Phys. Solids 103, 72–99 (2017)], which is a cohesive zone model regularized by the PFM, can account for different softening behaviors via characteristic functions and proves to be suitable for spall fracture modeling. In this paper, we used the PF-CZM to conduct spall fracture modeling in consideration of constitutive description of elastic-plastic-hydrodynamics (refer to the LS-DYNA theory manual). The free surface velocity profile for plate impact experiments, including the pullback signal, pullback slope, and the first velocity peak after pullback, were simulated and well matched the experimental results. Furthermore, the results show mesh independency. Different softening behaviors were assessed for their accuracy to model the spall fracture, and parameters in this model were discussed in detail. Besides, we directly extended this model to 3D simulation, showing potential engineering applications.