Analysis of the size effect on the penetration depth of earth-penetrating projectiles and practical calculating formula

The penetration depth of the earth-penetrating projectile is a basic problem in the design of protection engineering. Scaled testing is an important method to study the penetration law. The size effect between the model test results and the prototype is a problem that must be solved to establish the calculation method of penetration using scaled tests. In this study, the stress and strain state evolution of the rock-like target medium subjected to the penetration of earth-penetrating projectiles and the penetration resistance function of the projectiles were derived using cavity expansion theory. The formula for the caliber coefficient characterizing the size effect was obtained, and a simplified analysis of the nose shape coefficient and caliber coefficient was conducted using curve fitting and Taylor expansion within the penetration velocity range of the conventional earth-penetrating weapons. A practical calculation formula for the penetration depth of conventional earth-penetrating weapons into rock-like media was proposed, whose coefficients can be directly determined by parameters of target and projectiles. The results show that the main influencing factor of the projectile’s penetration resistance is the impedance of the target. The source of the size effect is originated from the fact that the ranges of the target damage zones do not satisfy the geometric similarity law. The nose shape coefficient can be simplified into a linear function of the projectile’s aspect ratio, and the nose shape coefficient of a flat-nosed projectile is 0.57. The caliber coefficient of the projectile is determined by the ratio of the cavity radius of the penetration to the radius of the fracture zone and can be taken as 1.2−1.4 for conventional earth-penetrating weapons. The theoretical calculation formula of penetration depth is in good agreement with experimental results, and thus, has high reliability.