J. B. Stevens and R. C. Batra
Department of Engineering Science and Mechanics
Virginia Polytechnic Institute and State University
Blacksburg, VA 24061-0219

Ballistic tests using tungsten and depleted uranium rods and mild steel targets indicate that for the same input of the kinetic energy, uranium rods result in deeper tunnels than tungsten rods. This led Magness to conjecture that adiabatic shear bands, which are narrow regions of intense plastic deformation, form sooner in uranium rods near the target/penetrator interface resulting in a conical nose shape which facilitates its penetration into the target. We have simulated numerically the normal impact of cylindrical rods of tungsten and uranium against a flat rigid plate (the Taylor anvil test) and their penetration into stationary and stress free steel targets. Animations of Uranium (mpeg) (QuickTime) and Tungsten (mpeg) (QuickTime)pentrators show differences in shear band formation. The rods are initially stress free and are moving with a uniform speed. The steel, tungsten, and the uranium are modeled as strain hardening, strain-rate hardening and thermal softening with the flow stress given by the Johnson-Cook relation. Thermal conduction is not included in the analysis due to the high rates involved and 100 % of the plastic work done is assumed to be transferred to thermal energy. Continuity of normal displacements and normal tractions at the target/penetrator interface are imposed by the penalty method and the tangential tractions there are assumed to depend upon the relative speed between the contacting particles.

The images above are colormaps depicting the effective stress distribution at various times after impact with a rigid wall. The Taylor impact test (a.k.a. Taylor anvil or reverse ballistic impact test) is the normal impact of a right circular cylinder with a flat, rigid surface. Taylor [6] analysed this impact configuration by assuming that when the flow stress is exceeded in the impacting projectile cylinder, a mushroomed region forms near the impacted end. The mushroomed region can be regarded as stationary and separate from the undeformed material which continues to move in the direction of impact. Taylor assumed a constant flow stress of the material and related it to the final dimensions of the deformed projectile. Jones et al. [7,8] improved upon Taylor's analysis of the problem by dividing it into two phases. The first high strain-rate phase ends with the attenuation of shock waves initiated by the impact. It is followed by a period of lower strain-rate plastic deformations characterized by plastic waves propagating at a uniform speed. These analyses are essentially one-dimensional and cannot predict details of the deformed configuration of the projectile. Extensive experimental studies have shown that the Taylor model yields very approximate values of the dynamic yield strength of the rod material. The foregoing studies have not reported any information on the occurrence of adiabatic shear bands in the mushroomed region. Dick et al. [13] conducted reverse ballistic impact tests (a.k.a. Taylor Impact) on WHA rods with ellipsoidal tungsten particles in an Fe-Ni matrix and also examined the deformed rods for fracture. At an impact speed of 173 m/s, the mushroomed end had a slight ellipticity which they attributed to radial cracks distributed in the body. At the higher impact speed of 228 m/s, the deformation was found to be more localized along a curved path extending from the transition between the mushroomed region and the undeformed rod toward the impact face. Diametrically opposite to this section, they observed ductile fracture along a similar path. The images below show the typical deformed shape and a section cut from the mushroomed region where the shear band forms.

We simulated the Taylor impact test for both uranium and tungsten heavy alloy rods. Both materials were modeled as thermoviscoplastic via the Johnson-Cook flow law. We also investigated the effect of replacing the standard Johnson-Cook thermal softening function by one proposed by Zhou et al.. The animations of the impact event modeled with the Johnson-Cook thermal softening show that no shear band forms at the mantle of either rod Uranium (mpeg) (QuickTime) and WHA(mpeg) (QuickTime). Using the thermal softening function proposed by Zhou et al., which yields a more pronounced softening effect, a shear band forms in the WHA(mpeg) (QuickTime) rod but not in the Uranium (mpeg) (QuickTime) rod. Further enhancing the softening function by increasing the thernal softening power causes a shear band to form in both rods, but more readily in WHA(mpeg) (QuickTime) than in Uranium (mpeg) (QuickTime). While shear bands form more readily in WHA rods than Uranium rods in the computed Taylor impact test ...

The simulation of the penetration of WHA rod into a mild steel target yields relatively homogeneous deformation compared to the Uranium which undergoes periodic localization.