Summary -We conducted depth of penetration experiments into grout and concrete targets with ogive-nose steel projectiles. Powder guns launched 0.064 kg, 12.9 mm diameter projectiles into grout targets with unconfined compressive strengths of 13.5 M Pa (2.0 ksi} and 21.6 MPa (3.1 ksi). For the concrete targets, powder guns launched projectiles with length-to-diameter ratios of 10; a 0.48 kg, 20.3 mm diameter rod, and a 1.60kg, 30.5 mm diameter rod. Concrete targets had unconfined compressive strength of 62.8 M Pa (9.1 ksi) for the 0.48 kg rods and unconfined compressive strength of 51.0 MPa (7.4 ksi) for the 1.60 kg rods. For these experiments, penetration depth increased as striking velocity increased until nose erosion became excessive. Thus, we determined experimentally the striking velocities corresponding to maximum penetration depths. Predictions from a previously published model are in good agreement with data until nose erosion becomes excessive.

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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-

Glass bars and plates were subjected to impact loading. Failure waves were observed to propagate behind the compression waves. Material traversed by the failure wave suffers total loss of tensile strength and substantial drop in shear strength. Failure wave propagation velocities exceed the maximum crack propagation speed, but are not constant. In bars, failure wave speed range from 2.3 to 5.2 mm/μs, increasing with increasing impact velocity; in plates, the wave speed is about 2 mm/μs. The failure is ‘‘explosive’’ in nature, leading to radial expansion in bars and an increase in mean stress in plates.