E. Dekel

The relation between the penetration capability of long rods and their length to diameter ratio

Summary Recent experimental studies, on the penetration of long rods into semi-infinite steel targets, reveal some features which cannot be predicted by the conventional 1-D penetration model of Alekseevskii and Tate. This paper presents experimental results together with 2-D simulations which were performed in order to investigate this discrepancy. Specifically we are interested in the question of whether the normalized penetration curve— P/L ( P is penetration depth, L is penetrator length)—is dependent on penetrators length to diameter ratio in the range of L/D = 10–40. Both experimental and simulation results show a decrease of about 15% between P/L values for L/D = 10 and 20 rods as well as for L/D = 20 and 30. These, rather large, differences are discussed in terms of material parameters which are resonsible for the discrepancy between the 1-D model and both experiment and simulation. Moreover, we have simulated the penetration of long rods having zero yield strength. Our results show that for large aspect ratios ( L/D > 30) these weaker rods penetrate more than those with their full yield strength. This crossover phenomenon is both counterintuitive as well as opposed to the predictions of the 1-D model for this combination of rod-target materials.

The Deep Penetration of Concrete Targets by Rigid Rods - Revisited

The penetration of rigid long rods into semi-infinite concrete targets is revisited. In particular, we focus on the deceleration of these rods during their penetration, as inferred from the experimental data for penetration depths vs. impact velocities. We find that for a given concrete these decelerations are independent on impact velocity, which enables us to construct a simple relation between the penetration depth and impact velocity. Our model is different from the model which is based on the dynamic cavity expansion analysis to account for the resisting forces on the rod. The cavity expansion model has two terms for the resisting force, a strength term and an inertia term which depends on the velocity of the rod. In the present work we show that there is no physical basis for the inclusion of an inertia term and that the concretes resisting force depends only on its strength, as with metallic targets. We demonstrate the validity of our approach by comparing its predictions with penetration depths from published data for different concrete and grout targets. We also find an empirical relation between the concretes resisting stress and its unconfined compressive strength. Several important issues concerning target dimensions and the strength of the rod are discussed. These issues should be carefully considered as they influence the rigid nature of the rod and the semi-infinite condition of the target.

A critical examination of the modified Bernoulli equation using two-dimensional simulations of long rod penetrators

Summary The modified Bernoulli equation is examined through a series of two-dimensional simulations of long rods penetrating semi-infinite targets. These are copper, aluminium and tungsten alloy rods having zero strength with length-to-diameter ratios of 20. The targets are steel and tungsten alloy with yield strengths in the range of 0–2 GPa. Impact velocities were varied between 1 and 7 km/s. Each simulation results in a definite value for the steady-state penetration velocity, which is substituted in the modified Bernoulli equation to derive an effective resistance to penetration (Rt). The dependence of Rt on target yield strength, impact velocity and projectile and target characteristics is determined.

A parametric study of the bulging process in passive cassettes with 2-D numerical simulations

A series of 2-D numerical simulations of the bulging of passive cassettes, penetrated by shaped charge jets, is described. The purpose of these simulations was to determine the factors affecting the speed of the bulging process in order to be able to design more efficient cassettes. Physical and geometrical parameters, of the different cassette constituents, were varied systematically. These included strengths, elastic moduli, thicknesses and densities of the materials involved.

Hypervelocity penetration of tungsten alloy rods into ceramic tiles: experiments and 2-D simulations

Abstract A series of terminal ballistics experiments and 2-D simulations, with small scale tungsten alloy penetrators, was performed in order to quantify the ballistic efficiency of confined ceramic tiles. The data includes both depth of penetration (DOP), into thick steel backing and X-ray shadowgraphs during the penetration process. Impact velocities ranged between 1.25 to 3.0 km/s. The size of the tiles varied in order to check their performance as a function of thickness and lateral dimensions. We found that the differential ballistic efficiency of alumina tiles is practically independent on impact velocity and tile thickness, within the ranges of velocity and thicknesses, investigated here. A detailed simulation study, using the Eulerian processor of the PISCES 2-D ELK code, was performed in order to better understand the interaction between long-rods and ceramic tiles, and particularly, to adjust a proper failure criterion to the tiles. We found that a simple version of the Johnson-Holmquist model, with a single parameter, is fairly adequate to account for most of the data. These include: lateral confinement, tile thickness and impact velocity influence on the penetration depth. We used the code to further investigate the influence of lateral dimensions on tile performance.

A note on the geometric scaling of long-rod penetration

Abstract The paper describes a set of experiments with copper and tungsten alloy long-rods, which were aimed at finding the sources of non-scaling effects recently discovered in terminal ballistics. Our basic assumption was that geometrical scaling should hold for ductile penetrators (like copper) and that any deviation from this scaling should be attributed to brittle failure mechanisms at the penetrators head. Our experimental results support this assumption as far as the depth of penetration into steel of two penetrators, differing by a factor of 2, is considered. Thus, copper penetrators scaled well, within experimental error, while a difference of about 10% was found between the depth of penetration of 1:2 and 1:4 tungsten alloy penetrators. We also present two-dimensional simulations, which were performed with the PISCES 2DELK code, in order to determine lateral edge effects. These simulations enabled us to choose the right size for our “infinite” targets, avoiding any influence from their lateral-free surface.

Further examination of long rod penetration : the role of penetrator strength at hypervelocity impacts

2D numerical simulations were performed in order to further investigate the role of penetrator strength in the interaction of long rods and semi-infinite targets. These simulations are used to highlight the reasons for several discrepancies between existing data and the well-known 1D model for penetration. In particular, the nature of the secondary penetration of high-density rods, the hydrodynamic limits of high-strength rods, and the predicted maxima in their penetration curves are discussed. The causes for these discrepancies are established by additional numerical simulations which explore the validity of the penetrator strength parameter in the analytical model as a physical entity. It is shown that this is, indeed, the weakest part of the model since it is strongly dependent on both the impact velocity of the rod and its length-to-diameter ratio.

On the role of nose profile in long-rod penetration

The superiority of depleted uranium on tungsten-alloy penetrators has recently been assigned to the self-sharpening mechanism, at the tip of the DU rods, due to the adiabatic shear failure which this material experiences. The purpose of the work presented here was to further investigate the role of deformed nose profile on the deep penetrations of long rods into semi-infinite targets. This was achieved through a series of 2-D numerical simulations and several perforation experiments where we recovered and examined the residual penetrators. The simulations were performed for rigid tungsten-alloy rods having five different nose shapes with the density and elastic properties of tungsten alloys. For the normal impact experiments we chose three rod materials: a tungsten alloy, a copper and a titanium alloy. The residual rods (after perforation of finite thickness targets) were imaged by flash X-ray and softly recovered using sand boxes. As expected, the nose shapes of these rods were very different from each other.

Experiments and 2-D simulations of high velocity penetrations into ceramic tiles

This paper investigates the interaction of long-rod penetrators with thick ceramic tiles, sandwiched between steel plates, through several model experiments and 2-D simulations. Experimental data from low velocity penetrations have been used to calibrate the relevant properties of the ceramic specimens. The influence of increasing impact velocity on tile performance was then investigated through data and simulations of shaped charge jets penetrating the ceramic. We found that the ballistic efficiency of the ceramic tile is lower against high velocity (5 km/s) long-rods, in contrast with the common thesis that their improved performance against shaped charge jets is the result of their enhanced strength. On the other hand, our simulations clearly show that, for high strength ceramics, there is a radial motion of metal and ceramic debris towards the penetration axis. This effect is, probably, the main reason for the considerable improvement in the performance of ceramic tiles against shaped charge jets.

Penetration of tungsten-alloy rods into composite ceramic targets: Experiments and 2-D simulations

A series of terminal ballistics experiments, with scaled tungsten-alloy penetrators, was performed on composite targets consisting of ceramic tiles glued to thick steel backing plates. Tiles of silicon-carbide, aluminum nitride, titanium-dibroide and boron-carbide were 20–80 mm thick, and impact velocity was 1.7 km/s. 2-D numerical simulations, using the PISCES code, were performed in order to simulate these shots. It is shown that a simplified version of the Johnson-Holmquist failure model can account for the penetration depths of the rods but is not enough to capture the effect of lateral release waves on these penetrations.