Abstract
Friction effects on the optimum shape design for a normal impacting, rigid body are investigated and the optimum 3D- nose shapes of rods are proposed for deep penetration into soil, concrete and metal media. The study is conducted by assuming that the normal and tangent stresses, that act on the impactor nose, are of the Poncelet and Coulomb forms, respectively. The geometrical characteristics of the shapes maximizing penetration depth are compared with those of the minimal resistance bodies obtained at the initial stage of the penetration event. When mass, shank radius and nose length of the rods are fixed, a comparative study of the penetration depths of the optimal impactors and impactors with conical and ogival nose shapes is carried out. The conditions, when the benefits of the optimal configurations in providing deep penetration into soil, concrete and metal media become significant in comparison with other shapes, have been obtained. The model parameters are taken from the published reports on penetration data obtained for striking velocities to 1.5 km/s while the impactors remained rigid and visibly undeformed.
Similar content being viewed by others
References
R. K. Byers, P. Yarrington, and A. J. Chabai, “Dynamic penetration of soil media by slender projectiles,” Int. J. Impact Engng. vol. 16, pp. 835–844, 1978.
E. P. Chen, “Penetration into dry porous rock: a numerical study on sliding friction simulation,” Theor. Appl. Frac. Mech. vol. 11, pp. 135–141, 1989.
E. P. Chen, “Finite simulation of perforation and penetration of aluminum targets by conicalnosed steel rods,”Mech. Mater. vol. 10, pp. 107–115, 1990.
X. W. Chen and Q. M. Li, “Deep penetration of a non-deformable projectile with different geometrical characteristics,” Int. J. Impact Engng. vol 27, pp. 619–637, 2002.
V. M. Fomin (ed.), High-Velocity Interaction of Bodies, Izd. Sib. Otd. Ross. Akad. Nauk, Novosibirsk, 1999.
M. J. Forrestal, “Penetration into dry porous rock,” Int. J. Solids Struct. vol. 22, pp. 1486–1550, 1986.
M. J. Forrestal, K. Okajima, and V. K. Luk, “Penetration of 6061–T651 aluminum targets with rigid long rods,” Trans. ASME J. Appl. Mech. vol. 55, pp. 755–760, 1988.
M. J. Forrestal and V. K. Luk, “Penetration into soil targets,” Int. J. Impact. Engng. vol. 12, pp. 427–444, 1992.
M. J. Forrestal, B. S. Altman, J. D. Cargile, and S. J. Hanchak, “An empirical eqution for penetration depth of ogival-nose projectiles into concrete targets,” Int. J. Impact. Engng. vol. 15, no. 5, pp. 395–405, 1994.
M. J. Forrestal, D. Y. Tzou, E. Askari, and B. D. Longcope, “Penetration into ductile metal targets with rigid spherical-nose steel rods,” Int. J. Impact. Engng. vol. 16, pp. 699–710, 1995.
M. J. Forrestal, D. J. Frew, J. P. Hickerson, and T. A. Rohwer, “Penetration of concrete target with decelaration-time measurements,” Int. J. Impact. Engng. vol. 28, pp. 479–497, 2003.
D. J. Frew, M. J. Forrestal, and S. J. Hanchak, “Penetration experiments with limestone targets and ogival-nose steel projectiles,”Trans ASME J. Appl. Mech. vol. 67, pp. 841–845, 2000.
S. E. Jones and W. K. Rule, “On the optimal nose geometry for a rigid penetrator, including the effects of pressure-dependent friction,” Int. J. Impact Engng. vol. 24, pp. 403–415, 2000.
L. M. Keer, Y. L. Xu, and V. K. Luk, “Boundary effects in penetration and perforation,” Trans. ASME J. Appl. Mech. vol. 65, no. 2, pp. 489–496, 1998.
A. N. Kraiko, D. Ye. Pudovikov, and G. Ye. Yakunina, Theory of aerodynamic shapes close to optimal, Yanus-K: Moscow, 2001.
A. Miele (ed.) Theory of optimum aerodynamic shapes, Academic Press, New York, 1965.
R. S. Montgomery, “Friction and wear at high sliding speeds,” Wear vol. 36, pp. 275–298, 1976.
A. J. Piekutowsky, M. J. Forrestal, K. L. Poormon, and T. L. Warren, “Penetration of 6061-T651 aluminum targets by ogival-nose projectiles with striking velocities between 0.5 and 3.0 km/s,” Int. J. Impact Engng. vol. 23, pp. 723–734, 1999.
J. V. Poncelet, Cours de Mecanique Industrielle, Paris, 1829.
R. Vaziry, D. Delfosse, G. Pageau, and A. Poursartip, “High-speed impact response of particulate metal matrix composite materials—an experimental and theoretical investigation,” Int. J. Impact Engng. vol. 13, no. 2, pp. 329–352, 1993.
G. Ye. Yakunina, “The construction of optimum three-dimensional shapes within the frameworks of a model of local interaction,” J. Appl. Maths. Mech. vol. 64, no. 2, pp. 289–298, 2000a.
G. Ye. Yakunina, “The optimum non-conical and asymmetrical three-timensional configurations,” J. Appl. Maths. Mech. vol. 64, no. 4, pp. 583–591, 2000b.
G. Ye. Yakunina, “On body shapes maximizing penetration depth in dense media,” Doklady Physics, vol. 46, pp. 140–143, 2001a.
G. Ye. Yakunina, “Optimum three-dimensional hypersonic bodies within the framework of a local interaction model,” AIAA Paper no. 2001–1797, 2001b.
G. Ye. Yakunina, “Three-Dimentional Bodies of Minimum Total Drag in Hypersonic Flow,” J. Optimiz. Theory and Appl. vol. 115, no. 2, pp. 241–265, 2002.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Ye Yakunna, G. Effects of Sliding Friction on the Optimal 3D- Nose Geometry of Rigid Rods Penetrating Media. Optim Eng 6, 315–338 (2005). https://doi.org/10.1007/s11081-005-1742-6
Received:
Issue Date:
DOI: https://doi.org/10.1007/s11081-005-1742-6