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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
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.
Projectile Interactions in Granular Impact Cratering
Physical Review Letters, 2008
We present evidence for the interactions between a ball and the container boundaries, as well as between two balls, that are mediated by the granular medium during impact cratering. The presence of the bottom boundary affects the final penetration depth only for low drop heights with shallow filling, in which case, surprisingly, the penetration becomes deeper. By contrast the presence of the side wall causes less penetration and also an effective repulsion. Repulsion is also found for two balls dropped side-by-side.
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.
Granular dynamics during impact
Physical review letters, 2014
We study the impact of a projectile onto a bed of 3 mm grains immersed in an index-matched fluid. We vary the amount of prestrain on the sample, strengthening the force chains within the system. We find this affects only the prefactor of the linear depth-dependent term in the stopping force. We propose a simple model to account for the strain dependence of this term, owing to increased pressure in the pile. Interestingly, we find that the presence of the fluid does not affect the impact dynamics, suggesting that dynamic friction is not a factor. Using a laser sheet scanning technique to visualize internal grain motion, we measure the trajectory of each grain throughout an impact. Microscopically, our results indicate that weaker initial force chains result in more irreversible, plastic rearrangements, suggesting static friction between grains does play a substantial role in the energy dissipation.
Projectile penetration in granular material
SHOCK COMPRESSION OF CONDENSED MATTER - 2019: Proceedings of the Conference of the American Physical Society Topical Group on Shock Compression of Condensed Matter, 2020
Penetration depth is the most important parameter in terminal ballistics. Here only the case of projectiles penetrating granular medium is considered. Laboratory and field tests have shown that projectile characteristics such as mass, size, and nose shape, and target characteristics such as strength and density determine the depth of penetration. Analyses of full flight data recorded by onboard data acquisition system (G-Rec) are presented. These tests have revealed very high decelerations at impact with extensive particle fracture along the path of the projectile. Particle size distribution analysis of the sample collected from the projectile tip shows two to three orders of magnitude reduction in size. For similar impact velocities and target densities, Poncelet's coefficient does not vary with tip shape.
Penetrating a granular medium by successive impacts
Physical Review E, 2022
We consider the penetration dynamics of a vertical cylinder into a dry granular medium subjected to successive impacts. The depth of the impactor below the free surface z_N first evolves linearly with the impact number N and then follows a power-law evolution z_N ∝ N^1/3. The depth reached by the cylinder after a given number of impacts is observed to increase with the impact energy, but to decrease with its diameter and the density of the granular medium. We develop a model that accounts for the quasistatic and inertial granular forces applying on the cylinder to rationalize our observations. This approach reveals the existence of two intrusion regimes for large and small impact numbers, allowing all data to be rescaled on a master curve. Then, we extend the study to the effect of sidewalls on the dynamics of the impactor. We show that lateral confinement changes the dependence of the impactor depth on the impact number z_N(N). This effect is accounted for by considering the increase of the granular drag with the lateral confinement.
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 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.
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.