Laboratory impact experiments and numerical simulations on shock pressure attenuation in water ice

Abstract

High‐velocity impact experiments of water ice were conducted to measure the shock pressure profile at various distances from the impact point. A numerical simulation of shock wave propagation in water ice was also conducted for comparison with the experimental results. The numerical model was improved to fit the measured profiles, and it was found that a tensile strength of Yc = 1 MPa was necessary to reproduce the shock pressure profiles above the Hugoniot Elastic Limit. This improved numerical model was then used to study the shock pressure attenuation in water ice at various impact conditions and to refine the crater scaling law. The late‐stage effective energy (LE) is the product of initial shock pressure (P0) and the third power of the projectile size (Lp3). The impact conditions with the same late‐stage effective energy can produce the same shock pressure distribution far from the impact point (so‐called late‐stage equivalence). These impact conditions were investigated by numerical calculations with different projectiles and impact velocities. As a result of our calculation for water ice impacts, we found that a power law index of 2.2 instead of 3, as adopted by previous studies, is suitable for reproducing the late‐stage equivalence in water ice (i.e., LE is proportional to P0 · Lp2.2). By using this improved LE, we can reconcile the inconsistency between the crater size and the LE indicated by previous studies. By using this improved LE, the crater volume Vcr formed on water ice is expressed by the following equation, Vcr = 1.0 exp (ln/2450), with Vcr in cm3, wherein ln (in Pa m2.2) is a constant derived from a fit to the data.