The relation between shock-state particle velocity and free surface velocity: A molecular dynamics study on single crystal Cu and silica glass

Abstract

We investigate the ratio Rrp of the free surface velocity to the shock-state particle velocity during shock wave loading with molecular dynamics simulations on two representative solids, single crystal Cu, and silica glass. The free surface velocity is obtained as a function of the particle velocity behind the shock front (or shock stress) for loading on Cu along ⟨100⟩, ⟨110⟩, and ⟨111⟩, and on the isotropic glass. Rrp≥1 for Cu and Rrp<1 for silica glass, and it increases with shock strength; the simulations agree well with the experimental results. For supported shock loading of silica glass at 30–90 GPa, the SiIV–SiVI transition occurs upon shock, inducing substantial densification and thus small Rrp (0.65–0.78). For single crystal Cu, Rrp deviates from 1 near the Hugoniot elastic limit and reaches ∼1.2 at 355 GPa for ⟨100⟩ shock. Rrp is anisotropic, e.g., it is about 1.02, 1.08, and 1.06 for shock loading to about 80 GPa along ⟨100⟩, ⟨110⟩, and ⟨111⟩, respectively. Such an anisotropy is mostly due to that in the degree of stress relaxation at low pressures and that in solid state disordering at high pressures. These results suggest that Rrp is materials dependent and the assumption of Rrp=1 is only valid in a limited stress range. Caution should be exercised when interpreting the free surface velocity measurements as regards the shock states.