PENETRATION OF A RIGID PROJECTILE INTO AN ELASTIC-PLASTIC TARGET OF FINITE THICKNESS

This paper considers the problem of non-steady penetration of a rigid projectile into an elastic-plastic target of finite thickness. A speci fic blunt projectile shape in the form of an ovoid of Rankine is used because it corresponds to a reasonably simple velocity field which exa ctly satisfies the continuity equation and the condition of impenetrab ility of the projectile. The target region is subdivided into an elast ic region ahead of the projectile where the strains are assumed to be small, and a rigid-plastic region near the projectile where the strain s can be arbitrarily large. Using the above mentioned velocity field, the momentum equation is solved exactly in both the elastic and the ri gid-plastic regions to find expressions for the pressure and stress fi elds. The effects of the free front and rear surfaces of the target (w hich is presumed not to be too thin) and the separation of the target material from the projectile are modeled approximately, and the force applied to the projectile is calculated analytically. An equation for projectile motion is obtained which is solved numerically. Also, a use ful simple analytical solution for the depth of penetration or the res idual velocity is developed by making additional engineering approxima tions. Moreover, the solution procedure presented in this paper permit s a straight forward approximate generalization to accommodate a proje ctile with arbitrary shaped tip. Theoretical predictions are compared with numerous experimental data on normal penetration in metal targets , and the agreement of the theory with experiments is good even though no empirical parameters are used. Also, simulations for conical and h emispherical tip shapes indicate that the exact shape of the projectil e tip does not significantly influence the prediction of integral quan tities like penetration depth and residual velocity.