M.Sc Thesis

M.Sc StudentMendelson Dana
SubjectInfluence of Confining Pressure on Ballistic Shielding
Effectiveness of Porous Solids
DepartmentDepartment of Aerospace Engineering
Supervisor PROFESSOR EMERITUS David Durban
Full Thesis textFull thesis text - English Version


In recent decades, extensive research has been carried out on ballistic penetration and perforation processes. These studies employ computational, analytical and experimental methods, covering a wide range of target materials and projectile characteristics. The main research directions aim at improving ballistic performance of projectiles, on one hand, and improving protective efficiency of target material on the other. At present, a considerable body of knowledge is available in published literature, though several issues are still outstanding.

A well-established method of improving ballistic efficiency of protective structures is by applying remote confining pressure on target materials. All the same so when the target is made of pressure sensitive solid, which consumes deformation energy by admitting plastic volume changes.

However, existing studies on the influence of confining pressure are mainly experimental or numerical. There is a definite need of simple theoretical analysis of perforation and penetration processes in presence of remote confining pressure, particularly for pressure sensitive solids.

The present work aims to provide an initial analytical study for practical assessment of both penetration depth and residual velocity, in ballistic deep penetration and plate perforation, respectively, for pressure sensitive target material.

To this end we assume that cavitation pressure, either spherical or cylindrical, captures the essential features of ballistic impact, at least over a range of firearms bullets velocity. That assumption is supported by numerous studies on penetration and perforation of conventional engineering solids. Thus, this research examines cavitation phenomena in pressure sensitive solids, in spherical and cylindrical geometries. The central idea in employing the cavity expansion model, for ballistic impact problem, is that to reasonable approximation the cavitation pressure can be identified with the specific energy needed to create a unit volume along the projectile path tunnel.

Material behavior is described by the non-associated Drucker-Prager constitutive relation, along with further simplifying assumptions. Rigid pointed head projectiles at normal impact are considered, and friction effects are neglected.

Within that framework, we have derived new formulae for cavitation pressure. These expressions show that confining pressure increases the cavitation pressure in two different ways; by providing external support to the protective structure, and by generating an apparent yield stress which is higher than the material yield stress. The latter effect is coupled with the effective stress pressure sensitivity parameter in the Drucker-Prager solid.

A further contribution is due to plastic compressibility in the non-associated model. These findings are of practical significance, in providing simple analytical tools, for assessing reduction in penetration depth, and in residual velocity, upon improving shielding effectiveness by applying confining pressure. In that context, pressure sensitive solids exhibit a clear preference in design of protective structures.