Projectile Interactions in Granular Impact Cratering (original) (raw)
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Unified force law for granular impact cratering
Nature Physics, 2007
Experiments on the low-speed impact of solid objects into granular media have been used both to mimic geophysical events [1-5] and to probe the unusual nature of the granular state of matter [6-9]. While the findings are all strikingly different from impact into ordinary solids and liquids, no consensus has emerged regarding the interaction between medium and projectile. Observation that the final penetration depth is a power of the total drop distance was interpreted by a stopping force that is a product of powers of depth and speed [6]. Observation that the penetration depth is linear in initial impact speed was interpreted by a force that is linear in speed [7]. Observation that the stopping time is constant was interpreted by a force that is constant but proportional to the initial impact speed [8]. Observation that depth vs time is a sinusoid for a zero-speed impact was interpreted by a force that is proportional to depth [9]. These four experimental results, as well as their interpretations, would all seem to be in conflict. This situation is reminiscent of highspeed ballistics impact in the 19 th and 20 th centuries, when a plethora of empirical rules were proposed [10,11]. To make progress, we developed a means to measure projectile dynamics with 100 nm and 20 s precision. For a 1-inch diameter steel
Unified force law for granular impact cratering 48 PUBLICATIONS 463 CITATIONS SEE PROFILE
Experiments on the low-speed impact of solid objects into granular media have been used both to mimic geophysical events [1-5] and to probe the unusual nature of the granular state of matter [6-9]. While the findings are all strikingly different from impact into ordinary solids and liquids, no consensus has emerged regarding the interaction between medium and projectile. Observation that the final penetration depth is a power of the total drop distance was interpreted by a stopping force that is a product of powers of depth and speed [6]. Observation that the penetration depth is linear in initial impact speed was interpreted by a force that is linear in speed [7].
Impact cratering depends on projectile-to-grain and grain-to-grain interactions during the very short time of impact. This study investigates the effects of different media composition, namely the ratio between beach sand and silica sand of the impacted medium, on crater diameter and depth. Pure silica sand, pure beach sand, and ratios of 1:2, 1:1 and 2:1 of silica:beach sand were tested, and a plastic ball was dropped from various heights for different media. The recorded crater diameters and depths indicate that impact cratering is a more complex process than previously thought mainly because of the increased randomness in grain-to-grain contacts and force chain distributions produced by mixing different granular materials. It seems that mixtures of smaller grains and larger grains create a quasi-alloy state where smaller grains fill in the gaps between larger grains to increase the number of grain-to-grain contacts and force chains, and hence increase the rigidity of the medium. An equal partitioning of silica sand and beach sand seem to maximize this effect, as the medium with a volume ratio of 1:1 silica:beach sand has the smallest scaling factor for crater diameter. Although the crater depths result did not follow the 1/3 to 1/4 scaling factor proposed by previous studies, the shallower depths with larger compositions of silica sand confirm that crater depth decreases as grain sizes increase. The data also suggest that the quasi-alloy state of mixed medium redirects the energy of the projectile from deeper penetrations instead to wider and shallower displacements of sand.
Low-Speed Impact Craters in Loose Granular Media
Physical Review Letters, 2003 dsim(rhob3/2Db2H)1/3d\sim({\rho_{b}}^{3/2}{D_{b}}^{2}H)^{1/3}dsim(rhob3/2Db2H)1/3. The scaling with properties of the medium is also established. The crater depth has significance for granular mechanics in that it relates to the stopping force on the ball.
Low Speed Granular–Granular Impact Crater Opening Mechanism in 2D Experiments
Quasi-2D, low-velocity experiments of colliding granular projectiles against granular targets were performed by means of a 7 m-long Hele-Shaw cell. The processes involved in the crater-opening mechanism of low-velocity granular-against-granular collisions are described. We show that the crater is opened mainly by a compaction process of the target. The projectile is fragmented and its lower section suffers a severe compaction; this projectile remnant forms a central dome or peak inside the crater. When the target reaches its maximum degree of compaction, the excess of momentum generates fast avalanches sliding on the slopes of the confined material, and exerts pressure on the crater walls, increasing its diameter. We propose that low-velocity collisions between granular aggregates are a possible mechanism that allows the growth of small planetary objects or the aggregation after catastrophic or high-energy collisions.
Morphology and scaling of impact craters in granular media
Physical Review Letters, 2003
We present the results of experiments on impact craters formed by dropping a steel ball vertically into a container of small glass beads. As the energy of impact increases, we observe a progression of crater morphologies analogous to that seen in craters on the moon. We find that both the diameter and the depth of the craters are proportional to the 1=4 power of the energy. The ratio of crater diameter to rim-tofloor depth is constant for low-energy impacts, but increases at higher energy, similar to what is observed for lunar craters.
Impact craters in loose granular media
The European Physical Journal E - Soft Matter, 2004
The craters formed by the impact of steel balls with a loose sand bed are experimentally studied. Both crater size and morphology depend strongly on the impact angle. Two scaling laws, corresponding to length and width, respectively, are proposed.
Drag-force regimes in granular impact
Physical Review E, 2014
We study the penetration dynamics of a projectile incident normally on a substrate comprising of smaller granular particles in three-dimensions using the discrete element method. Scaling of the penetration depth is consistent with experimental observations for small velocity impacts. Our studies are consistent with the observation that the normal or drag force experienced by the penetrating grain obeys the generalized Poncelet law, which has been extensively invoked in understanding the drag force in the recent experimental data. We find that the normal force experienced by the projectile consists of position and kinetic-energy-dependent pieces. Three different penetration regimes are identified in our studies for low-impact velocities. The first two regimes are observed immediately after the impact and in the early penetration stage, respectively, during which the drag force is seen to depend on the kinetic energy. The depth dependence of the drag force becomes significant in the third regime when the projectile is moving slowly and is partially immersed in the substrate. These regimes relate to the different configurations of the bed: the initial loose surface packed state, fluidized bed below the region of impact, and the state after the crater formation commences.
Sphere penetration by impact in a granular medium: A collisional process
Europhysics Letters, 2009
The penetration by a gravity-driven impact of a solid sphere into a granular medium is studied by two-dimensional simulations. The scaling laws observed experimentally for both the final penetration depth and the stopping time with the relevant physical parameters are here recovered numerically without the consideration of any microscopic solid friction but with dissipative collisions only. Dissipative collisional processes are thus found as essential in catching the penetration dynamics in granular matter whereas microscopic frictional processes can only be considered as secondary effects.
Cratering experiments on the self armoring of coarse-grained granular targets
Icarus, 2012
Recently published crater statistics on the small asteroids 25143 Itokawa and 433 Eros show a significant depletion of craters below approx. 100 m in diameter. Possible mechanisms that were brought up to explain this lack of craters were seismic crater erasure and self armoring of a coarse, boulder covered asteroid surface. While seismic shaking has been studied in this context, the concept of armoring lacks a deeper inspection and an experimental ground truth. We therefore present cratering experiments of glass bead projectiles impacting into granular glass bead targets, where the grain sizes of projectile and target are in a similar range. The impact velocities are in the range of 200 to 300 m s −1 . We find that craters become fainter and irregular shaped as soon as the target grains are larger than the projectile sizes and that granular craters rarely form when the size ratio between projectile and target grain is around 1:10 or smaller. In that case, we observe a formation of a strength determined crater in the first struck target grain instead. We present a simple model based on the transfer of momentum from the projectile to this first target grain, which is capable to explain our results with only a single free parameter, which is moreover well determined by previous experiments. Based on estimates of typical projectile size and boulder size on Itokawa and Eros, given that our results are representative also for km s −1 impact velocities, armoring should play an important role for their evolution.