SHOCK ATTENUATION ASSOCIATED WITH HYPERVELOCITY IMPACT EVENTS (Invited Presentation)
In continuous materials (gas, liquid, solids) SPD may be presented with several branches: close to the point of impact “isobaric core” (IB), steep decay with the distance R just beyond IB (~R-3), less steep decay at larger R, and the asymptotic far field decay ~R-1 (seismic waves) or (R×lnR)-1 for Landau’s (1946) solution.
Scaling of attenuating shock waves has no complete analytical solution but may be studied with numerical modeling techniques. The concept of the “late stage equivalence” (Dienes and Walsh, 1970) assumes that shock wave may be scaled with the unique parameter L×va = const (L is the projectile size, v is the impact velocity, a is the scaling exponent). Similar approach for gases reveals that a depends on heat capacity ratio γ. For solids only numerical modeling allows us to study scaling. We present here a large set of the 1D planar and central symmetry numerical modeling of SPD after impact. We find that for solids (Tillotson’s EOS) the a exponent is not constant but depends on the impact velocity range. One can discriminates the low velocity range (LVR) where SPD is close to the momentum scaling a~1 (Holsapple, 1993), and the high velocity range (HVR) where a ~ 1.5 is close but smaller than the energy scaling (a=2). The transition from LVR to HVR is defined by the ratio of the impact velocity, v, to the target sound speed, c0. In the planar case the HVR scaling is possible at v/c0 > 5 to. For the central symmetry (impact at the spherical cavity surface) HVR seems to be valid at smaller v/c0.
Comparing numerical modeling and field observation of shocked rocks we have additional problems (non-uniform layered targets with air and/or water saturated porosity in rocks, variably fractured during their pre-impact geologic history, oblique impacts etc.). The first problem in complex craters is the central mound uplifting, which distorts initial isobars. Here filed estimates of shock recorded in minerals is important to verify numerical models of impact cratering.