The long-standing competition between advancing projectiles penetration power, on one hand, and increasing the efficiency of protective structures, on the other hand, has resulted in a very large body of scientific research along with engineering design methodologies. In the latter context, pre-stressing the target material is a commonly accepted technology aiming at strengthening the resistance to projectile penetration.
The present research aims at deriving a new and simple analytical model for assessing the effect of pre-stressing in improving the ballistic worthiness of targets made of pressure sensitive solids like concrete or sintered powder metals. Analysis is within framework of finite strain continuum mechanics of elastoplastic solids, and centers on the cavity expansion field model.
We begin with a brief review of available studies (mainly experimental) on ballistic response of pre-stressed targets. Next, we address the basic pattern of spherical cavity expansion under internal pressure (simulating the projectile), in presence of remote confining pressure that induces the pre-stresses. New elegant solutions for the cavitation pressure are derived, reflecting the coupled effect of pre-stresses and pressure sensitivity. It is shown that compressive pre-stresses are indeed beneficial in increasing the ballistic velocity (in plate perforation) and decreasing the penetration depth (in deep penetration).
The underlying view in this approach (originally due to work by H. Bethe during WWII) is that the cavity expansion solution provides the specific cavitation energy needed to create a unit of new volume along the projectile path. Our solution has been facilitated by further simplifying assumptions of material incompressibility and perfectly plastic response. The alternative cylindrical cavitation field is analyzed as well, and results are compared with those obtained from the spherical case.
Analytical findings are supported by asymptotic approximations and reduction to known solutions. We shall examine sensitivities of the cavitation pressure to material parameters and level of confining pressure. Applications to ballistic perforation and penetration processes (assuming rigid projectiles and normal impact), and to design of protective structures, will be discussed in view of model limitations and experimental results.
