Summary: Well known experiments of projectile impacts on pre-notched plates have demonstrated a transition from brittle to ductile failure with increasing strain rate. At low rates cracks form at the notch tip and propagate at roughly \(70^{\circ}\) counter clockwise from the loading direction. At high rates shear bands form and propagate in a downward curving path. This occurs because of the formation of shear bands, which occurs more readily at the higher velocities, prevents the development of the large principal strains needed to initiate a crack.
In this paper, we present a coupled model that is capable of capturing the failure transition. The finite deformation model consists of a thermoviscoplastic material with strain and strain rate hardening, thermal softening and diffusive regularization. Fracture is modeled with the phase field method, for which a novel modification is presented to account for degradation of the material due to inelastic working.
The numerical model including the discretization and linearization and monolithic scheme is presented and discussed in detail. Numerical simulations of the notched plate impact problem studied by M. Zhou et al. [“Dynamically propagating shear bands in impact-loaded prenotched plates. I: Experimental investigations of temperature signatures and propagation speed”, J. Mech. Phys. Solids 44, No. 6, 981–1006 (1996; doi:10.1016/0022-5096(96)00003-8)] are presented up to the point of shear band or fracture initiation, demonstrating the transition from brittle fracture under minor yielding to ductile failure by shear banding.