Scaling of impact-generated cavity-size for highly porous targets and its application to cometary surfaces

Impact cratering on porous targets in the strength regime

“…The line corresponds to an empirical relationship shown by Eq. 14 obtained for the highly porous targets of foamed polystyrene, sintered glass bead, gypsum, and pumice (Okamoto and Nakamura, 2017). The data for gypsum and pumice used in the fitting of the empirical relationship are also shown in light blue (U > 4 km s -1 ) and dark blue (U < 4 km s -1 ).…”

“…Laboratory high-velocity impact experiments, using millimeter-to-centimeter size projectiles to study cratering in the strength regime, were performed for various targets with porosities ranging from 0% to more than 90%. The morphology and dimensions, i.e., diameter and depth, were studied for weak cemented basalt targets (Housen, 1992), sandperlite-fly ash mixture targets (Housen and Holsapple, 2003), sintered glass bead targets (Love et al, 1993;Michikami et al, 2007;Hiraoka et al, 2008;Okamoto et al, 2015; Okamoto and Nakamura 2017), cement mortar targets (Michikami et al, 2017), gypsum targets Okamoto and Nakamura, 2017), and natural porous rocks (Baldwin, et al, 2007;Kenkmann, et al, 2011;Suzuki et al, 2012;Poelchau, M. H., 2014;Flynn, et al, 2015;Okamoto and Nakamura, 2017). Table 1 summarizes the target density, porosity, strength, impact velocity, and projectile material and diameter of these experiments.…”

“…Craters formed on solid targets with relatively low porosity in the laboratory have a bowl-shaped cavity (pit) with a surrounding thin depression (spall). The shape of the cavity for relatively porous targets is cylindrical, U-shaped or bulb-shaped (Michikami et al, 2007;Flynn et al, 2015;Winkler et al, 2016;Okamoto and Nakamura, 2017). The spall zone is not identified on highly porous targets, such as a sintered glass bead target with 80% porosity, but occurs for those with 60% porosity (Michikami et al, 2007).…”

“…where , , , and are the effective drag coefficient for the impactor when it penetrates a porous target, compressive strength of the target, tensile strength of the impactor, and impact velocity, respectively. An intermediate dependence on the density ratio, i.e., a power law dependence with an index between 0.5 and 1 was obtained for crater depth, of porous targets of foamed polystyrene, sintered glass bead, gypsum, and pumice by curve fitting (Okamoto and Nakamura, 2017):…”

“…The parameters * and * for highly porous sintered glass bead targets, etc. were also determined using the value of * fixed as above but using the compressive strength for (Okamoto and Nakamura, 2017). Figure 4b shows a comparison of the data for porous targets according to Eq.…”