Analytical formulas for penetration of a long rigid projectile including the effect of cavitation

Analytical expressions for penetration of a long rigid projectile with a nose shape of an ovoid of Rankine into a semi-infinite incompressible elastic–perfectly-plastic target have been developed earlier. Using these expressions it is shown that the drag force applied by the target on the projectile can be approximated as a bilinear function of the square of the penetration velocity in terms of three non-dimensional constants {Σc, αc, βmax}. The value of Σc characterizes the constant value of the drag force for low penetration velocities. Cavitation (separation of the target material from the projectile’s surface) first occurs when the penetration velocity reaches a value associated with αc. The parameter βmax controls the dependence of the drag force on the square of the penetration velocity as the separation point on the projectile’s surface approaches its tip. Analytical expressions for these constants are determined in terms of the material parameters of the target material. Also, a simple formula for the penetration depth is developed and a method is proposed for determining the constants {Σc, αc, βmax} directly from experimental data.