Abstract
The dynamic behavior of projectiles upon impact with granular media was recorded using two high-speed video cameras for capturing different angles. We used steel, brass, tungsten carbide spheres, and alumina ceramic spheres with diameters in the range of 6–20 mm as the projectiles and polystyrene beads (6 mm in diameter) and glass beads (1.7 mm in diameter) as the granular media. Upon impact, the projectiles penetrated the media, rebounded from the media, or were deflected such that their resulting motion was in a horizontal direction. Post-impact motion of the projectiles depended on the impact angles of the projectiles, the density ratio (bulk density/projectile density), and the diameter ratio (granular diameter/projectile diameter) and not on the impact velocity. The post-impact motion of the projectiles did not follow a clear trend in terms of the transient angle; instead, we observed the existence of a transient region. On the basis of the area of the transient regions, an empirical equation was derived for determining the critical angle of projectiles (the angle at which they can penetrate the granular media) as a function of the density ratio and the diameter ratio.
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References
Kuwabara G., Kono K.: Restitution coefficient in a collision between two spheres. Jpn. J. Appl. Phys. 26, 1230–1233 (1987)
Labous L., Rosato A.D., Dave R.N.: Measurements of collisional properties of spheres using high-speed video analysis. Phys. Rev. E 56, 5717–5725 (1997)
Louge M.Y., Adams M.E.: Anomalous behavior of normal kinematic restitution in the oblique impacts of a hard sphere on an elastoplastic plate. Phys. Rev. E 65, 021303 (2002)
Moon S.J., Swift J.B., Swinney L.H.: role of friction in pattern formation in oscillated granular layers. Phys. Rev. E 69, 031301 (2004)
McNamara S., Falcon E.: Simulations of vibrated granular medium with impact–velocity-dependent restitution coefficient. Phys. Rev. E 71, 031302 (2005)
Uehara J.S., Ambroso M.A., Ojha R.P., Durian D.J.: Low-speed impact craters in loose granular media. Phys. Rev. Lett. 90(19), 194301 (2003)
Walsh A.M., Holloway K.E., Habdas P., de Bruyn J.R.: Morphology and scaling of impact craters in granular media. Phys. Rev. Lett. 91(10), 104301 (2003)
Newhall K.A., Durian D.J.: Projectile-shape dependence of impact craters in loose granular media. Phys. Rev. E 68, 060301 (2003)
Pica Ciamarra M., Lara A.H., Lee A.T., Goldman D.I., Vishik I., Swinney H.L.: Dynamics of drag and force distributions for projectile impact in a granular medium. Phys. Rev. Lett. 92(19), 194301 (2004)
Goldman D.I., Umbanhowar P.: Scaling and dynamics of sphere and disk impact into granular media. Phys. Rev. E 77, 021308 (2008)
de Vet S.J., de Bruyn J.R.: Shape of impact craters in granular media. Phys. Rev. E 76, 041306 (2007)
Zheng X.-J., Wang Z.-T., Qiu Z.-G.: Impact craters in loose granular media. Eur. Phys. J. E 13, 321–324 (2004)
Rioual R., Valance A., Bideau D.: Experimental study of the collision process of a grain on a two-dimensional granular bed. Phys. Rev. E 62(2), 2450–2459 (2000)
Rioual R., Valance A., Bideau D.: Collision process of a bead on a two-dimensional bead packing: importance of the inter-granular contacts. Europhys. Lett. 61(2), 194–200 (2003)
Oger L., Ammi M., Valance A., Beladjine D.: Discrete element method studies of the collision of one rapid sphere on 2D and 3D packings. Europhys. J. E 17, 467–476 (2005)
Crassous J., Beladjine D., Valance A.: Impact of a projectile on a granular medium described by a collision model. Phys. Rev. Lett. 99, 248001 (2007)
Ammi M., Oger L., Beladjine D., Valance A.: Three-dimensional analysis of the collision process of a bead on a granular packing. Phys. Rev. E 79, 021305 (2009)
Holsapple K.A.: The scaling of impact processes in planetary sciences. Annu. Rev. Earth Planet. Sci. 21, 333–373 (1993)
Yamamoto S., Barnouin-Jha O.S., Toriumi T., Sugita S., Matsui T.: An empirical model for transient crater growth in granular targets based on direct observations. Icarus 203, 310–319 (2009)
Gaul D.E., Wedekind J.A.: Experimental studies of oblique impact. Proc. Lunar Planet. Sci. 9, 3843–3875 (1978)
Hartmann W.K.: Impact experiments: 1. Ejecta velocity distributions and related results from regolith targets. Icarus 63, 69–98 (1985)
Yamamoto S.: Measurement of impact ejecta from regolith targets in oblique impacts. Icarus 158, 87–97 (2002)
Takagi, S., Fujiwara, A., Abe, M.: Experimental and theoretical study of reflection of solid body fragments on flat surface. In: Proceedings of Fall Meeting, Japan Society Planetary Science (in Japanese), p. 58 (1998)
Okano, K., Nonaka, S., Takayama, K.: Study on design of projector for Nereus sample return project. In: Proceedings of Symposium on Shock Waves Japan (in Japanese), pp. 53–56 (1999)
Soliman A.S., Reid S.R., Johnson W.: The effect of spherical projectile speed in ricochet off water and sand. Int. J. Mech. Sci. 18, 279–284 (1976)
Al-Raoush R., Alsaleh M.: Simulation of random packing of polydisperse particles. Powder Technol. 176, 47–55 (2007)
Clanet C., Hersen F., Bocquet L.: Secrets of successful stone-skipping. Nature 427(6969), 29 (2004)
Nagohiro S., Hayakawa Y.: Theoretical and numerical approach to magic angle of stone skipping. Phys. Rev. Lett. 94(17), 174501 (2005)
Thoroddsen S.T., Shen A.Q.: Granular jets. Phys. Fluids 13, 4–6 (2001)
Lohse D., Bergmann R., Mikkelsen R., Zeilstra C., van der Meer D., Verluis M., van der Hoef M., Kuipers H.: Impact on soft sand: void collapse and jet formation. Phys. Rev. Lett. 93(19), 198003 (2004)
Lohse D., Rauhe R., Bermann R., van der Meer D.: Creating a dry variety of quicksand. Nature 432, 689 (2004)
Royer J.R., Corwin E.I., Flior A., Cordero M.-L., Rivers M., Eng P., Jaeger H.M.: Formation of granular jets observed by high-speed X-ray radiography. Nat. Phys. 1, 164–167 (2005)
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Nishida, M., Okumura, M. & Tanaka, K. Effects of density ratio and diameter ratio on critical incident angles of projectiles impacting granular media. Granular Matter 12, 337–344 (2010). https://doi.org/10.1007/s10035-010-0186-7
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DOI: https://doi.org/10.1007/s10035-010-0186-7