The Role of Absolute Size in Cratering, Momentum Enhancement, and Fragmentation

In impact studies, we often intuitively think that things scale linearly in size. By this, we mean that if we perform an impact experiment at one scale, and then we double the target and projectile size (radius) and perform an impact at the same impact speed, then the crater depth and diameter will be twice what they were in the first experiment. It turns out that our intuition is not correct for crater radius: the relative crater radius is larger for the larger impact. This effect is even more pronounced for crater ejecta mass and momentum enhancement. We have studied this effect for the past 15 years in aluminum, rocks, and concrete. The most detailed information is for two aluminum alloys, Al 2024-T351 and Al 1100-O, for impacts with aluminum spheres of diameters from 0.16 to 3.0 cm from 0.5 to 8 km/s using two-stage light gas guns (NASA Ames and SwRI). It was found that absolute size mattered in the crater radius, the amount of mass ejected, and the momentum enhancement. Interestingly, though a saturation (approaching linear size scaling) is seen in ejecta mass as impactor size increased, no saturation was observed for momentum enhancement, a major finding of our recent 3.0 cm impacts. Examination of the recovered ejecta shows a bilinear distribution in fragment sizes, likely due to ejecta from crater interiors vs. fragments produced near crater rims. A material model was developed that included an absolute size (a fixed finite slip distance to failure in a shear band). This model replicated the ejecta mass behavior observed in the experiments, but not the momentum enhancement behavior. Early numerical modeling was high resolution (60 cells across the projectile radius), 2D axisymmetric computations (CTH). More recent work in full 3D computations has shown the same ejecta mass-momentum enhancement behavior. Thus, the failure to replicate the more surprising size scale behavior in momentum enhancement is not due to 2D computations, but either resides in inadequate material models or (more likely) the inability of the computational tools to model well the post-cratering material separation as fragments are formed. Work has shown similar behavior in rocks and concrete. This information is directly relevant in extrapolating the results of the DART impact to other hypervelocity impacts into asteroids or comet nuclei, as will be discussed.