Stephan Bless

Calculation of penetration resistance of brittle materials using spherical cavity expansion analysis

Abstract In this paper, we show that the ‘target resistance’ of brittle materials can be calculated accurately using spherical cavity expansion analysis and a conventional brittle material model. The stress field ahead of the tip of the penetrator is assumed to have spherical symmetry. The brittle material is modeled as an elastic material which cracks under tension. The cracked material is considered to be pulverized when it fails in compression, which is then characterized as a Mohr-Coulomb material with pressure dependent shear strength. The target resistance value found from this analysis compares well with the reported experimental values for AD995 alumina (Al 2 O 3 ) and aluminum nitride (A1N).

On the LD effect for long-rod penetrators

Abstract A common measure of penetration efficiency is given by the depth of penetration P into a semi-infinite target normalized by the original length of the projectile L. It has been known for over 30 years that P L depends upon the aspect ratio L D for projectiles with relatively small aspect ratios, e.g. 1 ⩽ L D ⩽ 10 . This influence of L D on penetration is referred to as the L D effect. Although observed, the L D effect for large aspect ratio rods is not as well documented. Further, published penetration equations have not included the L D effect for high aspect ratio rods. We have compiled a large quantity of experimental data that permits the quantification of the L D effect for projectiles with aspect ratios of 10 ⩽ L/D ⩽ 30. Numerical simulations reproduce the observed experimental behavior; thus, no new physics is required to explain the phenomenon. The numerical simulations allow investigation of the fundamental mechanics leading to a decrease in penetration efficiency with increasing aspect ratio.

Penetration of semi-infinite AD995 alumina targets by tungsten long rod penetrators from 1.5 to 3.5 km/s

The performance of confined AD995 Alumina against LD 20 tungsten long rod penetrators was characterized through reverse ballistic testing. The semi-infinite ceramic target was cylindrical with a diameter approximately 30 times the rod diameter. The target configuration included a titanium confinement tube and a thick, aluminum coverplate. The impact conditions ranged from 1.5 to 3.5 km/s with three or four tests performed at each of six nominal impact velocities. Multiple radiographs obtained during the penetration process allowed measurement of the penetration velocity into the ceramic and the consumption velocity, or erosion rate, of the penetrator. The final depth of penetration was also measured. Primary penetration approaches 75% of the hydrodynamic limit. Secondary penetration is very small, even at 3.5 km/s. The effective Rt value decreased from 90 kbar to 70 kbar with increasing impact velocity over the range of velocities tested. In tests in which the ratio of target diameter to penetrator diameter was reduced to 15, Rt, dropped by 30% to 50%. When a steel coverplate was used, total interface defeat occurred at 1.5 km/s.

Computational modeling of the penetration response of a high-purity ceramic

This paper describes computational modeling of the penetration response of a high-purity ceramic, namely the AD-99.5 alumina. This material is the most widely investigated ceramic, and extensive materials testing and ballistic data are available. The model development is based on constitutive relationships inferred from bar impact and plate impact data. The model is then incorporated into the EPIC Lagrangian finite element code. A novel element removal scheme for ceramics is presented, and the code is then used to investigate the penetration response of AD-99.5 alumina in the depth of penetration and semi-infinite configurations. The computations are found to be in excellent agreement with the experimental results. The interface defeat problem is also investigated numerically, and the results are used to suggest an explanation for interface defeat.

The penetration of steel targets finite in radial extent

An experimental, analytical, and computational effort was undertaken to examine the effect of confinement on penetration in armor-like steel targets. For the experiments, LD 10, tungsten-alloy projectiles were fired at 1.5 km/s into 4340 steel cylindrical rounds of various diameters. Penetration efficiencies, as measured by the depth of penetration normalized by the original projectile length (PL), were determined and the results plotted as a function of normalized target diameter DtD, where Dt is the target diameter and D is the projectile diameter. As DtD changed from 20 to 5, PL increased by 28%, although PL was approximately independent of DtD for DtD ⪆ 15. An analytical model using a modified cavity expansion theory was developed to estimate the resistance to penetration for targets of finite lateral extent. The analytical model shows decreasing target resistance as DtD decreases below approximately 30; in particular, target resistance decreases rapidly for DtD < 20. Numerical simulations were performed and the computational predictions are in excellent agreement with the experimental results; simulations were used to extend DtD between 3 and 78. Plastic strain contours are plotted to assess the extent of plastic flow within the target; the results of the simulations demonstrate that PL begins to increase when the extent of plastic flow in the target reaches the radial boundary.

On the velocity dependence of the L/D effect for long-rod penetrators

Abstract At ordnance velocities (1.0 – 1.9 km/s), there is a pronounced decrease in penetration efficiency, as measured by P / L , when projectiles of larger L / D are used. The influence of L / D on penetration is referred to as the L / D effect d. We numerically examine the L / D effect at higher velocities, from 2.0 km/s to 4.5 km/s. It is found that as the velocity increases, there is a change in mechanism for the L / D effect. At ordnance velocities the L / D effect is mostly due to the decay in penetration velocity during the “steady-state” region of penetration. At higher velocities, the steady-state region of penetration shows no L / D dependence, and the L / D effect is due primarily to the penetration of the residual (non-eroding) rod at the end of the penetration event. This change in mechanism is related to the change in slope of the penetration-versus-impact velocity “S-shaped” curve for eroding projectiles.

SAND PENETRATION BY HIGH‐SPEED PROJECTILES

Tungsten projectiles were shot into sand at velocities between 600 and 2200 m/s. Penetration was maximum at about 775 m/s. Below that velocity, projectiles were apparently stabilized by a fin set. Above that velocity, projectiles were broken by transverse loads. High‐speed penetration resulted in comminution of sand particles, reducing their size by about 1000 times.

Cavity expansion resistance of brittle materials obeying a two-curve pressure–shear behavior

We derived a closed-form solution for the pressure required to open a spherical or a cylindrical cavity in brittle materials which demonstrate a two-curve pressure–shear behavior. The material is allowed to crack under tension and fail under shear; only both failure modes result in comminution. Since the cavity expansion pressure is closely related to the penetration resistance of a target material, this solution identifies the material parameters that are important in impact and penetration problems. It is found that cracking and comminution can be prevented when a large enough confinement pressure is present, and the resulting high cavity expansion resistance could explain the intriguing phenomenon of interface defeat. The effects of dilatancy, and shear strength of comminuted ceramic on cavity expansion pressure are explicitly revealed.

Penetration of hard layers by hypervelocity rod projectiles

Abstract The penetration resistance of hard layers, such as ceramics and hardened steels, struck by high velocity long rod projectiles can be characterized by the depth of penetration (DOP) test. The DOP test can be used to calculate average penetration resistance, which can be expressed as R T . The tests can also be used to compute differential efficiency. For hard materials, these values differ markedly from those for conventional armor steel (RHA). Implications for the effectiveness of hypervelocity penetrators are that the optimum velocity for energy efficient penetration will be much higher for hard materials than for RHA. Furthermore, ceramics will continue to substantially outperform armor steels, while high hardness steels will lose their relative advantages against long rod projectiles above 3 km/s.

Failure wave effects in hypervelocity penetration

It has been known for several years that glass is a relatively effective armor against shaped charge jets [1] even though its performance against conventional long-rod projectiles is mediocre. Some of the authors have earlier postulated that this effect is due at least in part to an increase of the R t value at hypervelocity. This enhancement is due to the fact that in long-rod penetration of brittle materials, a failure wave is generated in front of the penetrator which prematurely damages the material; however, if the penetrator is supersonic relative to this failure velocity, penetration is always occurring in intact material. Consequently, the true strength of a brittle material is only measured in hypervelocity experiments. In order to avoid the uncertainties of analyzing shaped charge penetration data, we have conducted experiments with L/D = 10 W alloy rods (ρ = 17.2 g/cm 3 ) against glass targets (ρ = 2.5 g/cm 3 ) to unambiguously search for this effect. In low velocity experiments, the penetration was essentially hydrodynamic, while above 3.9 km/s, the R t -Y value was on the order of 5.7 to 7.2 GPa. This substantiates the failure wave hypothesis.