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We developed engineering models for forces on rigid, long rods with spherical, ogival, and conical noses that penetrated rate independent, elastic-perfectly plastic targets. The spherical and cylindrical, cavity-expansion approximations simplified the target analyses, so we obtained closed-form penetration equations. To verify our models, we performed terminal-ballistic experiments with 7.1-mm dia., 0.024 kg, marging steel rods and 152-mm dia., 6061-T651 aluminum targets. The models predicted penetration depths that were in reasonable agreement with the data for impact velocities between 0.4-1.4 km/s.

We developed an analytical model for the elastic-plastic response of a compressible material from the uniform expansion of a spherically symmetric cavity. Previous models consider the material as incompressible. Numerical results from both models showed the effect of compressibility.

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We developed engineering models that predict forces and penetration depth for long, rigid rods with spherical noses and rate-independent, strain-hardening targets. The spherical cavity expansion approximation simplified the target analysis, so we obtained closed-form penetration equations that showed the geometric and material scales. To verify our models, we conducted terminal-ballistic experiments with three projectile geometries made of maraging steel and 6061-T651 aluminum targets. The models predicted penetration depths that were in good agreement with the data for impact velocities between 0.3 and 1.0 km/s. IntroductionIn a recent paper, Forrestal, Okajima, and Luk (1988) developed penetration equations for long, rigid rods with spherical, ogival, and conical noses that penetrated rate-independent, elastic, perfectly plastic targets. The cavity expansion approximations (Bishop, Hill, and Mott, 1945) simplified the target analyses, so penetration equations were obtained in closed form. These models predicted penetration depths that were in good agreement with measurements for impact velocities between 0.4 and 1.4 km/s.In this study, we modeled 6061-T651 aluminum targets as an elastic, strain-hardening, rate-independent material. We obtained compression stress-strain data to 100 percent true strain from samples taken from the target material. As shown in Fig. 1, a power-law data-fit closely approximated the post-yield stress-strain data. In a previous article (Forrestal, Okajima, and Luk, 1988) tensile tests were conducted with the target material, and the tensile specimen failed between true strains of 0.052 and 0.059. With this limited data, the authors assumed that the target material was elastic, perfectly plastic, and the flow stress was taken as the tensile failure stress. Therefore, the newly developed large-strain compression test (Kawahara, 1986) and power-law, strain-hardening model provided a more realistic description of the target material.In addition to providing a realistic material description for the target, the penetration equations derived in this study showed the geometric and material scales. To verify our models, we conducted terminal-ballistic experiments with three pro-

We developed models for the dynamic expansion of spherical cavities from zero initial radii for elastic-plastic, rate-independent materials with power-law strain hardening. The models considered the material as incompressible and compressible. For an incompressible material, we obtained closed-form solutions, whereas the compressible results required the numerical solution of differential equations. A comparison of the numerical results from both models showed the effect of compressibility. dr r /dv dv dv\ J Po J r W -uf] = Ipr 1 (1«) (16) where o>, a e are the radial and hoop components of Cauchy Downloaded From: http://appliedmechanics.asmedigitalcollection.asme.org/ on 09/15/2013 Terms of Use: http://asme.org/terms soo 400 as a.