Steady State Penetration of Rigid Perfectly Plastic Targets

The problem of steady penetration by a semi-infinite, rigid penetrator into an infinite, rigid/perfectly plastic target has been studied. The rod is assumed to be cylindrical, with a hemispherical nose, and the target is assumed to obey the Von-Mises yield criterion with the associated flow rule. Contact between target and penetrator has been assumed to be smooth and frictionless. Results computed and presented graphically include the velocity field in the target, the tangential velocity of target particles on the penetrator nose, normal pressure over the penetrator nose, and the dependence of the axial resisting force on penetrator speed and target strength. INTRODUCTION IN SIMPLE THEORIES of penetration the material properties of target and penetrator are often represented only by constant characteristic stresses, as for example in Tate [ 1, 21. Although this approach leads to results that are qualitatively correct, it can be difficult to use quantitatively. Some of the problems have to do with actual deformations in target and penetrator including lateral motion, and others are associated with the fact that the plastic flow stress is determined only by the deviatoric components of stress whereas the spherical or pressure component, which may be quite large ahead of the penetrator and contributes significantly to the retardation of the penetrator, is unrelated to flow stress. These and other matters have been discussed recently in some detail by Wright [3]. It would be desirable to account for lateral motion and hydrostatic effects in some simple way, but at present the details are insufficiently known to suggest high quality approximations that might be suitable. In developing an engineering model for penetration and perforation, Ravid and Bodner [4] have attempted to meet this difficulty by assuming simple kinematics for the flow around the penetrator and then adjusting some unknown parameters so as to minimize the plastic dissipation. They characterize this procedure as being “a modification of the upper bound theorem of plasticity to include dynamic effects,” but even if such a modified theorem is actually valid, at present there is no way to tell how close such a bound might be. In this article a detailed numerical solution to an idealized penetration problem is presented in an attempt to shed some light on these matters. The approach taken is as follows. Suppose that the penetrator is in the intermediate stages of penetration so that the active target/penetrator interface is at least one or two penetrator diameters away from either target face, and the remaining penetrator is still much longer than several diameters and is still traveling at a speed close to its striking velocity. This situation is idealized here in several ways. First, it is assumed that the rod is semi-infinite in length and that the target is infinite with a semi-infinite hole. Furthermore, it is assumed that the rate of penetration and all flow fields are steady as seen from the nose of the penetrator. These approximations are reasonable if the major features of the plastic flow field become constant within a diameter or so of the nose of the penetrator, and will be justified a posteriori by the calculation. Next, it is assumed that no shear stress can be transmitted across the target/penetrator interface. This is justified on the grounds that a thin layer of material at the interface either melts or is severely degraded by adiabatic shear. This assumption, together with the previous one, makes it possible to decompose the problem into two parts in which either a rigid rod penetrates a deformable target or a deformable rod is upset at the