An energy approach study of the penetration of concrete by rigid missiles

This paper presents an energy approach for investigating the penetration of concrete by rigid missiles and the associated phenomena. However, the principal assumptions made here must be validated experimentally before giving the proposed subject further considerations. In the following, a new measure for concrete resistance to penetration by hard missiles is presented. The suggested term for this measure is "the Volumetric Crushing Energy Density" of concrete which can be described as the energy required for converting a unit volume of concrete to separate particles under compressive loading so that the particles of the crushed volume meet certain gradation criteria. Using this quantity, an explanation of the scale effect is postulated. Moreover, a dimensionless semi-analytical formula for the penetration depth of a rigid missile in a concrete target is proposed which includes a large number of the variables of the problem. The formula assumes that the penetration incident may include several successive phases where the set of variables that governs the impact is different during each phase, and the variables that characterize the impact during each phase correlate in a different manner as well. Furthermore, many of the penetration depth formulae available in the literature are rewritten according to the formula proposed here where the concrete penetration resistance of any incident is estimated by modifying the resistance of "reference impact incidents." The rewritten formulae show the wide variation of the values of concrete resistance which are implicitly included in the original formulae. Finally, the proposed formula is applied using data of penetration experiments presented by Forrestal et al. [Forrestal, M.J., Altman, B.S., Cargile, J.D., Hanchak, S.J., 1994. An empirical equation for penetration depth of ogive-nose projectiles into concrete targets. Int. J. Impact Eng. 15(4), 395-405; Forrestal, M.J., Frew, D.J., Hickerson, J.P., Rohwer, T.A., 2003. Penetration of concrete targets with deceleration-time measurements. Int. J. Impact Eng. 28, 479-497] to estimate the values of penetration resistance of the concrete targets. (C) 2008 Elsevier B.V. All rights reserved.