Numerical simulations of oblique-angle penetration by deformable projectiles into concrete targets

Numerical simulations of oblique-angle penetration by deformable projectiles into concrete targets are performed in this paper by using the three-dimensional finite element code LS-DYNA, into which a combined dynamic constitutive model which can simultaneously describe both the compressive and tensile damage of concrete is implemented. As a consequence, the ballistic trajectories and the depths of penetration under different oblique angles (from 10° to the ricochet angle) are obtained. Moreover, the damage distribution of concrete after oblique penetration is procured, which can really reflect the tensile and compressive damage of concrete. The numerical results for the depths of penetration are compared with experimental data obtained by previous authors and show good agreement.     

Hypervelocity impact of rod projectiles with L/D from 1 to 32

Beside a short remark on the “hydrodynamic theory of rod projectiles”, the paper deals with the terminal ballistic behaviour of cylindrical projectiles against semi-infinite targets. Experimental data of EMI, completed by results of some other authors, are presented. Crater parameters like depth, diameter and volume and their dependence on projectile velocity (up to 5000 m/s), projectile and target material properties, as well as L/D-ratios (1–32), will be discussed. Mainly the projectile materials steel and tungsten sinter-alloys are considered. Target materials are mild steel and high strength steel, an Al-alloy and a tungsten sinter-alloy. The results show that the influence of material density on the crater dimensions is considerably greater than the influence of strength. The L/D ratio determines the velocity dependence of crater depth, diameter and volume. At high velocities in the hydrodynamic regime, the crater depth of short cylinders (L/D 1) is approximately proportional to v_p^2/3 (V_p=projectile velocity). With increasing L/D-ratio, the slope of the penetration curves decreases and converges for rods (L/D 1) versus a saturation, i. e. becomes nearly independent on v_p. A consequence of this saturation is the existence of a so-called “tangent velocity”, above which an optimal increase of efficiency is only realized by increasing the projectile mass and not the velocity. Furthermore, ballistic limits of real targets like single plates and symmetric double plates meteorite bumper shield) are taken into account. The expected better performance of “segmented rods” is also discussed.     

Hypervelocity penetration of concrete

Experiments have been conducted with 6.25 mm diameter tungsten rods striking concrete at 2.2 km/s. Three concretes were used—one was 2.35 g/cm³ and the other two were 2.27 g/cm³. The erosion rates were measured to be T/ΔL = 2.4–3.1 depending on the density of the concrete. This is greater than the hydrodynamic value, which shows that the strength of the penetrator is affecting the penetration. The cratering efficiency was computed (which included surface spall) and was found to be commensurate with the strength of the concrete, 28–34 MPa. CTH calculations were conducted using the brittle fracture kinetics (BFK) and Holmquist–Johnson–Cook (HJC) material models for concrete. Density in the calculations was 2.25 g/cm³. It was not possible to match erosion rates at 2.2 km/s, which were too high in the calculations. Also, computed crater volumes were much too small, mainly due to spall in the experiments that was not shown in the computations. Another significant inaccuracy of the calculations was the damage extent, which became unrealistically widespread as time increased in the BFK model.     

Hypervelocity penetration of ceramics

The penetration resistance of alumina was found to decrease with velocity for armor-piercing bullets. However, it was relatively independent of velocity for rods and fragment-simulating projectiles. These results are explained in terms of compressive yielding caused by high velocity pointed projectiles.     

High velocity penetration of homogeneous, segmented and telescopic projectiles into alumina targets

Segmented and telescopic projectiles are designed to make efficient use of the higher impact velocities achievable with new acceleration techniques. This concept has been found to work against steel armour. In this study, we compare the penetration capability into an alumina target for these unconventional projectiles with that of a homogeneous projectile. The influence of segment separation distance and core-to-tube diameter ratio were simulated for the impact velocities 2.5, 3.0 and 3.5 km/s. The simulated final penetrations are compared to test results for one type of each of the homogeneous, segmented and telescopic projectiles at 2.5 and 3.0 km/s. Both simulations and tests show that the unconventional projectiles have better penetration capability than a homogeneous projectile with the same initial geometry.     

Yaw impact of rod projectiles

The purpose of this numerical study is to investigate the penetration regimes for L/D 30 tungsten-alloy rod projectiles for cases where the impact yaw angle varies from 0 to 90° and for impact velocities from 1.4 to 2.6 km/s. The target is modeled as a semi-infinite or half-space block of rolled homogeneous armor (RHA) at zero obliquity. For cases of mild interference, the penetration channel is still deep and narrow but may be skewed with respect to the original shot-line. While penetration is degraded the efficiency of the rod projectile remains relatively high. With increasing yaw angle the rod may deform due to transverse loading to the extent such that it contacts and produces gouges on the opposite side of the penetration channel. Additionally, lateral loading may induce angular acceleration to the extent such that the tail of the projectile rotates (in the plane of symmetry) and also contacts the opposite side of the penetration channel. In the next discernible penetration regime, the long-rod deforms under transverse load but the tail does not rotate significantly. It is seen that nearly the entire rod length experiences the lateral load with the result that the original shot-line is significantly altered. The deformed rod, again, has multiple contact or loading points (or regions) and the resultant angular acceleration appears to be insufficient to induce rotation of the projectile tail. Thus, rather than ricochet, the projectile cuts a significant slot into the target. Finally, for very large yaw angles the crater becomes indistinguishable from one produced by a side-on or 90° impact even though the impact yaw angle may be significantly less than 90°.     

Penetration of hard layers by hypervelocity rod projectiles

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.     

Dynamic penetration of soil media by slender projectiles

In the investigation of earth penetration by projectiles, new experimental techniques, refined constitutive models, and multidimensional wavecodes are providing insights into the complex mechanisms which control the penetration process.     

基于A-T模型的长杆弹超高速侵彻陶瓷靶体强度分析

Alekseevskii-Tate(A-T)模型广泛应用于长杆弹超高速冲击的终点效应分析中。A-T模型对于金属弹靶强度有明确的表达式,而对于陶瓷靶体强度尤其是弹体初始冲击速度大于1 500 m/s时还没有统一的结论。基于长杆钨弹超高速(1 500~5 000 m/s)侵彻三种陶瓷(Al N,B4C,Si C)/铝复合靶体的缩比逆弹道实验数据;基于A-T模型,给出了上述陶瓷材料在不同侵彻速度范围内的靶体强度表达式。进一步通过与47发长杆钨弹超高速(1 250~2 500 m/s)侵彻陶瓷(Al N,B4C,Si C,AD85)/RHA钢复合靶体DOP实验数据对比,验证了提出的陶瓷靶体强度表达式的适用性。     

Perforation of a thick plate by rigid projectiles

Perforation of a thick plate by rigid projectiles with various geometrical characteristics is studied in the present paper. The rigid projectile is subjected to the resistant force from the surrounding medium, which is formulated by the dynamic cavity expansion theory. Two perforation mechanisms, i.e., the hole enlargement for a sharp projectile nose and the plugging formation for a blunt projectile nose, are considered in the proposed analytical model. Simple and explicit formulae are obtained to predict the ballistic limit and residual velocity for the perforation of thick metallic plates, which agree with available experimental results with satisfactory accuracy.     

主控因素对异型头弹丸半侵彻金属靶深度的影响特性研究

为研究异型头弹丸半侵彻金属靶的侵深特性,基于量纲方法对影响侵深的主控因素进行了分析,采用弹道枪加载和LS-DYNA软件对异型头弹丸半侵彻金属靶的作用过程进行了试验和数值模拟研究,分析了异型头弹丸结构、弹丸初速、靶板厚度等因素对侵彻深度的影响规律,获得了侵深随弹丸初速以及靶板厚度的变化曲线。研究结果表明,弹丸初速和靶板厚度是影响侵彻深度的关键因素,并拟合得到了弹丸初速和靶板厚度综合影响下的半侵彻侵深经验公式。研究结果可为半侵彻作用的研究及新型侵彻的工程计算方法等提供参考。     

Experimental study of perforation of multi-layered targets by hemispherical-nosed projectiles

In this paper, perforation of single and three layered metallic targets by hemispherical-nosed cylindrical projectiles are studied experimentally. The circular targets of Al 1100 have a diameter of 220 mm and the hemispherical-nosed projectiles are silver steel cylinders with a mass of 12.15 g which are hardened to 56RC. The single layer target is 3 mm thick and the thicknesses of layers of the three layered targets are 0.5, 1 and 1.5 mm. The multi-layered targets are tested both when the layers are in-contact and spaced (with air gaps). Tests are carried out using a one stage gas gun. The ballistic limit velocity is obtained and the effects of order of layers and the width of air gaps between them on the ballistic limit velocity are investigated. The results show that the single layer targets have greater ballistic limit velocities than multi-layered targets. Furthermore, the ballistic limit velocity of in-contact layered targets is greater than that of spaced layered targets.     

The influence of confinement on the penetration of ceramic targets by KE projectiles at 1.8 and 2.6 km/s

This paper presents the results of scale size experiments using a tungsten-alloy long-rod projectile fired against 97.5% Al₂O₃ ceramic targets at 1.8 and 2.6 km/s. Two targets were used, one having lateral steel confinement; the other without. The projectile overmatched the target, and residual projectile length and velocity were recorded using ballistic-syncro photography. Flash radiography was used during penetration of the unconfined target to obtain the penetration velocity. Manganin pressure gauges were also used to obtain additional data on the response of the ceramic target during penetration. Results from the eight experiments indicate that the confinement reduced the residual energy of the projectile at both impact velocities. Expressed in terms of the projectile impact energy, 55–56% was lost in the unconfined target at 2.6 km/s compared with 60% for the confined design. The same trend was found at 1.8 km/s with 68% and 72–73% for the unconfined and confined, respectively. Predictions using the QinetiQ GRIM2D hydrocode and a simplified form of the Johnson–Holmquist ceramic material model agreed well with the experiments for three out of the four test configurations. The predicted projectile erosion and retardation against the confined target at 1.8 km/s was excessively high. Analytical predictions using the Tate modified Bernoulli equation also gave reasonably accurate predictions for three of the tests, but values for the Tate target ‘strength’ extracted from experiments using a different target configuration were not accurate for the target design used in this paper.     

Impact of conical tungsten projectiles on flat silicon carbide targets: Transition from interface defeat to penetration

Normal impact of conical tungsten projectiles on flat silicon carbide targets was studied experimentally and numerically for half apex angles 5° and 5–15°, respectively, and comparisons were made with cylindrical projectiles. A 30 mm powder gun and two 150 kV and four 450 kV X-ray flashes were used in the impact tests. The numerical simulations were run with the Autodyn code in two steps. In the first, the surface loads were determined for different impact velocities under assumed condition of interface defeat. In the second, these surface loads were applied to the targets in order to obtain critical states of damage and failure related to the transition between interface defeat and penetration, and the corresponding critical velocities. In the impact tests, interface defeat occurred below a transition velocity, which was significantly lower for the conical than for the cylindrical projectiles. Above the transition velocity, the initial penetration of conical projectiles differed markedly from that usually observed for cylindrical projectiles. It occurred along a cone-shaped surface crack, qualitatively corresponding to surface failure observed in the simulations. The transition velocity for the conical projectile was found to be close to the critical velocity associated with this surface failure.     

Impact and penetration by L/D ≤ 1 projectiles

Calculations of steel target penetration by L/D ≤ 1 tungsten and tungsten alloy projectiles have been extended to L/D = 1/32 over the velocity range 1.5 to 5 km/s. The ratio of crater to projectile diameter tends to 1 as L/D decreases over this entire velocity range. For impact velocities of 1.5 and 3 km/s, penetration depth normalized by projectile length, P/L, increases with decreasing projectile L/D up to a maximum value and then decreases for still lower L/D. Experiments at impact velocities of 2 and 3 km/s confirm these results. For 5 km/s impact velocity, the calculations show P/L increasing with decreasing projectile L/D over the entire range 1/32 ≤ L/D ≤ 1. The projectile L/D for which the maximum P/L occurs appears to depend on the impact velocity. P/L generally scales with impact velocity as P/L v^f(L/D) where f(L/D) ranges from 0 for a long rod to, we believe, 2 in the limit as projectile L/D approaches zero. The calculations show for 1/8 ≤ L/D ≤ 1/2, P/L v^0.9; for L/D = 1/16, P/L v^1.5; and for L/D = 1/32, the new results give P/L v^1.9.     

A combined numerical and theoretical study on the penetration of a jacketed rod into semi-infinite targets

A combined numerical and theoretical study is conducted herein on the penetration of semi-infinite targets by jacketed rods with different r_j0/r_c0 ratios where r_j0 and r_c0 are the radii of the jacket and the core, respectively. The numerical results show that for smaller r_j0/r_c0 ratios the u–v relationship changes only a little compared to that of unitary long rod penetrator of the same core material, hence, the u–v relationship of unitary (homogeneous) long rod penetration is also applicable for jacketed rod penetration. Model for cratering in semi-infinite targets by jacketed rods is then suggested by using the laws of conversation of mass, momentum and energy, together with the u–v relationship of unitary (homogeneous) long rod penetration and an analytical model for predicting the depth of penetration has also been given for jacketed long rods penetrating semi-infinite targets in co-erosion mode. A new criterion for transition from bi-erosion to co-erosion is proposed. It transpires that the present model is in good agreement with the experimental observations for EN24 steel jacketed tungsten alloy long rods penetrating semi-infinite armor steel targets in terms of crater diameter and penetration depth.     

MESA 3-D calculations of armor penetration by projectiles with combined obliquity and yaw

We introduce and briefly describe MESA, a new 3-D Eulerian hydrodynamic code, developed specifically for simulations of armor and anti-armor systems. The code's current capabilities and its planned model improvements and additions are discussed. MESA models hydrodynamic flow and the dynamic deformation of solid materials. It uses simple elastic-perfectly plastic material strength models as well as models with thermal softening and strain and strainrate hardening. Future versions will incorporate advanced fracture models. It treats detonations in explosives using a programmed burn. The code's current capabilities are illustrated with simulations of experiments on yawed rods obliquely impacting armor plates at 1.29 km/s. With nominal elastic-perfectly plastic strength parameters MESA predicts well the experiment measurements of rod length, velocity deflection, and emergent yaw rates but underpredicts exit rod velocities. An artificial simulation of fracture indicates that fracture modeling would further improve agreement with experiment. The utility of MESA to treat hypervelocity impacts is demonstrated with simulations of a rod obliquely impacting a thin plate at 5 km/s. At this much higher impact velocity, hole sizes are much larger and material strength plays a minor role in hole size and rod deformation.     

Quantitative analysis of debris from SiC-fiber-reinforced aluminum-alloy targets impacted by spherical projectiles

Silicon-carbide-continuous-fiber-reinforced aluminum matrix composite targets were impacted with duralumin projectiles at velocities from 2.9 km/s to 4.3 km/s. The debris from the composite targets was monitored by flash, soft x-ray radiography. The spatial distribution of the leading half of the debris were quantified in terms of mass, velocity, and kinetic energy and compared with that of debris from monolithic aluminum-alloy targets. A material effect on the debris production was found through the experiment so that fragments from the composite targets were smaller in mass and size, but more in number than those from the monolithic bumper. An increase of the impact velocity brought the enhancement of fragmentation in the leading edge part of the debris produced from both the composite and the monolithic targets in comparison with lower velocity impacts. The 4.3 km/s impact for the composite gave the spatial densities of debris mass and kinetic energy biased toward the periphery of the debris cloud, while other lower velocity impacts gave the different densities biased toward a gun axis. Such peripheral distribution of debris was found at an impact velocity of 3.5 km/s for the monolithic target. In the present velocity range, the composite debris always exhibited its larger peripheral distribution than the monolithic one did.