Deformation and perforation of spherical shells by normal impact of blunt-ended projectiles

An approximate quasi-static theory is developed to predict large plastic deformation and perforation of spherical shells subjected to impact by blunt-ended projectiles at normal incidence. Based on experimental observations for quasistatic load-displacement characteristics, the problem of a spherical shell under normal impact by a flat-ended missile may be analyzed through the solutions to that of an equivalent circular plate struck transversely by the same missile. It is shown that the approximate theoretical predictions with alpha = 30 (here alpha is an empirical constant) are in good agreement with experimental data, in terms of maximum permanent transverse displacements and dimple radii. Furthermore, a theoretical formula for ballistic limits of spherical shells under missile impact is presented and the range of applicability of the theory is discussed.