Similarity Analysis of Projectile Penetration into Concrete
This paper presents a dimensionless model for the depth of penetration (DOP) of a projectile penetrating into a concrete target, based on the similarity theory involving intermediate asymptotics, complete similarity, and incomplete similarity. The calculated numerical results are in good agreement with previous experimental data, including two sets of full-scale and twenty-four sets of sub-scale penetration of non-deformable projectiles into concrete targets. Moreover, compared with several empirical and semi-empirical DOP models, the new model is applicable within a relatively broader range, including the penetration of both sub-scale and full-scale projectiles. For the limitations of the validity, dimensionless parameters Π3 = ϕt/ϕ larger than 12, Π4 = (ϕ3fc)/(Mv02) smaller than 0.1, and the initial impact velocity of the projectile less than about 900 to 1000m/s are necessary for the model.
Roy, P.K.; Rama, R.K. & Patkar, M.R. Penetration dynamics of earth penetration warhead into composite target media. Def. Sci. J., 1987, 37, 347-360.
Sliter, G.E. Assessment of empirical concrete impact formulas. ASCE J. Struct. Div., 1980, 106(ST5), 1023-1045.
Barr P. Guidelines for the design and assessment of concrete structures subjected to impact. Report, UK Atomic Energy Authority, Safety and Reliability Directorate, HMSO, London, 1990.
Adeli H. & Amin, A.M. Local effects of impactors on concrete structures. Nucl. Eng. Design, 1985, 88, 183-203.
Marvin, E.B. & Werner, G. The mechanics of penetration of projectile into targets. Int. J. Eng. Sci., 1978, 16, 1-99.
Yankelevsky, D. Z. Local response of concrete slabs to low velocity missile impact. Int. J. Impact Eng., 1997, 19, 331-343.
Kennedy, R.P. A review of procedures for the analysis and design of concrete structures to resist missile impact effects. Nucl. Eng. Design, 1976, 37,183-203.
Gabi, Ben-Dor. Ballistic impact: recent advances in analytical modeling of plate penetration dynamics – a review. ASME, J. Appl. Mech., 2005, 58, 355-371.
Teland, J.A. A review of empirical equations for missile impact effects on concrete. FFI/RAPPORT-7/05856, Norwegian Defence Research Establishment, 2007.
Li, Q.M.; Reid, S.R.; Wen, H.M. & Telford, A.R. Local impact effects of hard missiles on concrete targets. Int. J. Impact Eng., 2005, 32, 224-284.
Rama Chandra Murthy, A.; Palani, G.S. & Nagesh, R. Iyer Impact Analysis of Concrete Structural Components. Def. Sci. J., 2010, 60, 307-319.
Kosteski, L. E.; Riera, J. D.; Iturrioz, I.; Singh, R. K. & Kant, T. Assessment of empirical formulas for prediction of the effects of projectile impact on concrete structures. Fatigue & Fracture of Engineering Materials & Structures, 2015, 38, 948-959.
Young, C.W. Penetration Equations. SAND97-2426, Sandia National Laboratories, 1997.
Forrestal, M.J.; Altman, B.S.; Cargile, J.D. & Hanchak, S.J. An empirical equation for penetration depth of ogive-nose projectiles into concrete targets. Int. J. Impact Eng., 1994, 15, 395-405.
Forrestal, M.J.; Frew, D.J.; Hickerson, J.P. & Rohwer, T.A. Penetration of concrete targets with deceleration-time measurements. Int. J. Impact Eng., 2003, 28, 479-497.
Frew, D.J.; Hanchak, S.J.; Green, M.L. & Forrestal, M.J. Penetration of concrete targets with ogive-nose steel rods. Int. J. Impact Eng., 1998, 21, 489-497.
Li, Q.M. & Chen, X.W. Dimensionless formulae for penetration depth of concrete target impacted by a non-deformable projectile. Int. J. Impact Eng., 2003, 28, 93-116.
Beth, R.A. Penetration of projectiles in concrete. PPAB Interim Report No. 3, November 1941.
Rosenberg Z. & Dekel E. The penetration of rigid long rods – revisited. Int. J. Impact. Eng. 2009, 36, 551-564.
Forrestal, M.J. & Luk, V.K. Dynamic spherical cavity expansion in a compressible elastic–plastic solid. ASME J. Appl. Mech. 1988, 55, 275-279.
Luk, V.K.; Forrestal M.J. & Amos D.E. Dynamics spherical cavity expansion of strain-hardening materials. ASME J. Appl. Mech. 1991, 58, 1-6.
Barenblatt, G.I. Scaling, self-similarity, and intermediate Asymptotics. Cambridge University Press, Cambridge, 1996.
Barenblatt, G.I. Scaling. Cambridge University Press, Cambridge, 2003.
Frew, D.J.; Forrestal, M.J. & Cargile, J.D. The effect of concrete target diameter on projectile deceleration and penetration depth. Int. J. Impact Eng. 2006, 32, 1584-1594.
Guo, L.; He, Y.; Zhang, X. F.; He, Y. & Qiao, L. Thermal effect on mass loss of projectile during penetration into concrete: experimental and numerical study. 28th International Symposium on Ballistics, 2014, 958-967.
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