Penetration of limestone targets by ogive-nosed VAR 4340 steel projectiles at oblique angles: experiments and simulations

In this paper, we document the results of a combined experimental, analytical, and computational research program that investigates the penetration of steel projectiles into limestone targets at oblique angles. We first conducted a series of depth-of-penetration experiments using 20.0 g, 7.11-mm-diameter, 71.12-mm-long, vacuum-arc-remelted (VAR) 4340 ogive-nose steel projectiles. These projectiles were launched with striking velocities between 0.4 and 1.3 km/s using a 20-mm powder gun into 0.5 m square limestone target faces with angles of obliquity of 15° and 30°. Next, we employed the initial conditions obtained from the experiments with a technique that we have developed to calculate permanent projectile deformation without erosion. With this technique we use an explicit, transient dynamic, finite element code to model the projectile and an analytical forcing function based on the dynamic expansion of a spherical cavity to represent the target. Due to angle of obliquity we developed a new free surface effect model based on the solution of a dynamically expanding spherical cavity in a finite sphere of incompressible Mohr–Coulomb target material to account for the difference in target resistance acting on the top and bottom sides of the projectile. Results from the simulations show the final projectile positions are in good agreement with the positions obtained from post-test castings of the projectile trajectories.     

刚性尖头弹侵彻圆柱形金属厚靶分析模型

考虑金属厚靶侧面自由边界的影响,研究了刚性尖头弹侵彻有限平面尺寸金属厚靶问题。基于有限柱形空腔膨胀理论和线性硬化材料模型,得到了空腔壁径向压力的解析式,建立了刚性尖头弹侵彻有限直径圆柱形金属厚靶工程模型。与试验和数值模拟比较表明,该文工程模型计算精度很好。基于所建立的工程模型,研究了靶板半径对侵彻深度和侵彻阻力的影响,结果表明:当靶板与弹丸半径比值小于20时,靶板半径对侵彻阻力和侵彻深度有显著影响,不能按无限尺寸靶板计算;当靶板与弹丸半径比值大于20时,靶板半径对侵彻阻力和侵彻深度影响较小,可近似按无限尺寸靶计算。     

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.     

A generalized formula for the penetration depth of a deformable projectile

A simple analytical algebraic formula is developed for predicting the penetration depth of a deformable projectile into a semi-infinite target. This formula is a simplified version of more general equations that have been developed to predict the time-dependent penetration process in finite thickness targets. Specifically, the formula generalizes the classical hydrodynamic theory to include dependence on elastic properties of the target and on the yield strengths of both the target and the projectile. Moreover, the formula is limited to the case of long-rod penetration where both the projectile and the target experience significant plastic flow. The limiting values of the location of the elastic–plastic boundary in the target have been determined, and a single empirical constant has been introduced to characterize the transition between these limiting values. A value for this empirical constant has been determined which produces theoretical predictions that are in reasonable agreement with experimental data for moderate to high values of the impact velocity of steel and tungsten projectiles penetrating a steel target.     

The penetration of rigid long rods – revisited

The penetration process of rigid long rods with different nose shapes (ogive, spherical, conical and flat) is analyzed through a series of 2D numerical simulations. Aluminum and steel targets with different strengths (and large dimensions) are used to follow the deceleration process of these rods from impact, at different velocities, to the final penetration point. We find that for low impact velocities the deceleration of these rods is practicably constant, depending only on the strength of the target and the nose shape of the rod. Above a threshold (critical) impact velocity rod deceleration becomes velocity dependent due to the inertial response of the target. These critical velocities depend on the strength of the target and the nose shape of the rod. These observations led us to propose a simple penetration formula which accounts very well for penetration depths data for rigid steel rods with different nose shapes, impacting various aluminum targets at velocities up to about 1.5 km/s. For higher impact velocities, where the dynamic (inertial) contribution to the target resistance is important, we find good agreement between our model predictions and the simulation results for final penetration depths.     

侵彻单层靶时着靶姿态对装药损伤的影响规律研究

为研究着靶姿态对高速侵彻弹装药损伤的影响,依据实际战斗部的结构尺寸设计了小尺寸模型试验弹,在125 mm口径的滑膛炮发射平台上开展了试验弹以不同攻角斜侵彻单层钢靶试验。通过理论计算得到着靶姿态对侵彻过程能量损失的影响。利用CT扫描无损检测技术观测不同着靶姿态下试验弹内部的损伤情况。运用LS-DYNA对试验弹侵彻钢靶过程中装药的力学响应过程进行模拟计算。结果表明:在斜侵彻单层钢靶的过程中,着角一定时,能量损耗与攻角呈指数关系;试验弹的倾角越大,装药尾部受到的应力波拉伸压缩反复作用越明显,装药在侵彻过程中长度变化越大,更易出现深度裂纹、塌边等损伤;壳体外形变化会引起装药受到的压缩应力阻碍微裂纹的扩展和滑移,减少宏观损伤的出现。     

An Analytical Model for Predicting Stab Resistance of Flexible Woven Composites

Flexible woven composites have been widely used in geotextiles and light weight building structures. The stab resistance behavior of the flexible woven composite is an important factor for the application design. This paper reports an analytical model for predicting stab resistance of flexible woven composites under perpendicular stab with a blunt steel penetrator. The analytical model was established based on the microstructure and the deformation shape of the flexible woven composite under normal penetration. During the quasi-static stab penetration, the strain energies of warp and weft yarns and resins have been calculated. The stab resistance was calculated from the strain energies of the flexible woven composite. Furthermore, the contributions of the warp and weft yarns, resins to the stab resistance have been analyzed. It was found the three constituents have near the same contribution to the stab resistance. The higher value of weaving density, strength of yarns and especially the higher strength coating resins will lead the higher stab resistance. With the analytical model, the stab resistance would be expected to be designed in an efficient way with an acceptable precision.     

An examination of long-rod penetration

The one-dimensional modified Bernoulli theory of Tate [J. Mech. Phys. Solids 15, 287–399 (1967)] is often used to examine long-rod penetration into semi-infinite targets. The theory is summarized and the origins of the target resistance term examined. Numerical simulations were performed of a tungsten-alloy, long-rod projectile into a semi-infinite hardened steel target at three impact velocities sufficiently high to result in projectile erosion. The constitutive responses of the target and projectile were varied parametrically to assess the effects of strain hardening, strain-rate hardening, and thermal softening on penetration response. The results of one of the numerical simulations were selected to compare and contrast in detail with the predictions of the Tate model.     

Perforation of AA5083-H116 aluminium plates with conical-nose steel projectiles – Calculations

The use of aluminium alloys in lightweight protective structures is increasing. Even so, the number of experimental and computational investigations that give detailed information on such problems is limited. In an earlier paper by some of the authors, perforation experiments were performed with 15–30 mm thick AA5083-H116 aluminium plates and 20 mm diameter, 98 mm long, HRC 53 conical-nose hardened steel projectiles. In all tests, initial and residual velocities of the projectile were measured and the ballistic limit velocity of each target plate was determined. In the present paper, an analytical perforation model based on the cylindrical cavity-expansion theory has been reformulated and used to calculate the ballistic perforation resistance of the aluminium plates. In addition, non-linear finite element simulations have been carried out. The target material was modeled with the Johnson–Cook constitutive relation using 2D axisymmetric elements with adaptive rezoning. To allow ductile hole growth, a pin-hole was introduced in the target. The analytical and numerical results have been compared to the experimental findings, and good agreement was in general obtained. A parametric study was also carried out to identify the importance of the different terms of the Johnson–Cook constitutive relation on the perforation resistance of the target. The results indicate that thermal softening cannot be neglected, so an alternative procedure for identification of the material constants in the power-law constitutive relation used in the cavity-expansion theory has been proposed.     

高速长杆弹对有限直径金属厚靶的侵彻分析EI北大核心CSCD

采用基于统一强度理论的有限柱形空腔膨胀理论,结合Tate磨蚀杆模型,考虑中间主应力、靶体侧面自由边界的影响及高速(1500 m/s~2200 m/s)侵彻弹体的变形和消蚀现象,推导线性硬化有限直径金属厚靶在长杆弹高速侵彻时的空腔壁径向应力,建立侵彻阻力和侵彻深度计算模型,并利用MATLAB软件编程求解,分析包括强度准则差异在内的弹道终点效应的一系列影响因素。结果表明:该文计算方法可以更好地描述弹靶的动态响应,还可以得到一系列基于不同强度准则的侵彻阻力和深度的解析解、对不同靶弹半径比的靶材侵彻深度的区间范围进行有效预测;强度参数、弹体撞击速度和靶体半径对有限直径金属靶体的抗侵彻性能均有较大的影响,其中强度参数值由1减小为0时,侵彻阻力可减小33.33%,侵彻深度可增加15.93%;当靶弹半径比小于等于20时,侵彻深度增大的程度显著,当靶弹半径比由19.88减小至4.9时,侵彻阻力减小了41.30%,侵彻深度增长了32.61%,此时靶体边界尺寸对侵彻性能的影响很大,不能继续按照半无限靶体进行计算。     

层压玻璃钢板的侵彻阻抗的试验研究

本文给出层压玻璃钢板和钢板的侵彻阻抗的试验研究结果。撞击速度范围为V=600～800m/s,弹丸为钢球。试验结果表明,对于同样的撞击极限速度,层压玻璃钢靶比钢靶约轻(30～40)%。      

Effect of joint design on ballistic performance of quenched and tempered steel welded joints

A study was carried out to evaluate the effect of joint design on ballistic performance of armour grade quenched and tempered steel welded joints. Equal double Vee and unequal double Vee joint configuration were considered in this study. Targets were fabricated using 4 mm thick tungsten carbide hardfaced middle layer; above and below which austenitic stainless steel layers were deposited on both sides of the hardfaced interlayer in both joint configurations. Shielded metal arc welding process was used to deposit for all layers. The fabricated targets were evaluated for its ballistic performance and the results were compared in terms of depth of penetration on weld metal. From the ballistic test results, it was observed that both the targets successfully stopped the bullet penetration at weld center line. Of the two targets, the target made with unequal double Vee joint configuration offered maximum resistance to the bullet penetration at weld metal location without any bulge at the rear side. The higher volume of austenitic stainless steel front layer and the presence of hardfaced interlayer after some depth of soft austenitic stainless steel front layer is the primary reason for the superior ballistic performance of this joint.     

Improved Metal Wear After Dynamic Treatment by Powder Impact

Investigations of the reinforcement of metals via super-deep penetration is discussed. It is shown that dynamic impulse treatment of the steel target by powder increases wear resistance and hardness.     

Multiple impact penetration of semi-infinite concrete

An experimental study was performed to gather multiple impact, projectile penetration data into concrete. A vertical firing range was developed that consisted of a 30-06 rifle barrel mounted vertically above a steel containment chamber. 0.41 m cubes of an Air Force G mix concrete were suspended in wet sand and positioned in the steel chamber. The concrete targets were subjected to repeated constant velocity impacts from 6.4 mm diameter steel projectiles with an ogive nose shape and a length to diameter ratio of 10. A laser sight was adapted to the rifle to ensure alignment, and a break screen system measured the projectile velocity. After each impact, the projectile penetration and crater formation parameters were recorded. The penetration and crater formation data were consistent with single impact penetration data from previous studies conducted at Sandia National Laboratories. In addition, an analytic/empirical study was conducted to develop a model that predicted the penetration depth of multiple impacts into concrete targets. Using the multiple impact penetration and crater formation data, a single impact penetration model, developed by Forrestal at Sandia National Laboratories, was extended to account for the degradation of the target strength with each subsequent impact. The degradation of the target was determined empirically and included in the model as a strength-modifying factor. The model requires geometry parameters of the ogive nose projectile, projectile velocity, the number of impacts, and target compressive strength to calculate the overall penetration depth of the projectile.     

刚性弹侵彻有限直径金属厚靶的机理与模型研究

采用统一强度理论,考虑靶板中间主应力效应和靶体侧面自由边界的影响,得到线性硬化靶材在弹塑性阶段和塑性阶段的空腔壁径向应力的表达式,建立线性硬化靶材的统一侵彻模型,求出中低速(v₀≤1000 m/s)刚性弹体侵彻有限直径金属厚靶时侵彻阻力、侵彻深度计算公式,并利用Simpson算法对其进行求解,分析了包括强度准则差异在内的弹道终点效应的一系列影响因素。结果表明:该文计算方法可以更好地描述侵彻过程中弹靶的动态响应,还可以得到一系列基于不同强度准则的侵彻阻力和深度的解析解、对靶材在不同撞击速度下侵彻深度的区间范围进行有效预测;强度参数、弹体撞击速度、靶体半径和弹头形状对有限直径金属厚靶的抗侵彻性能均有较大的影响,其中强度参数值由1减小为0时,侵彻深度增加了22.45%;随着靶弹半径比的减小,侵彻深度不断增大,当靶弹半径比小于等于16时,侵彻深度增大的程度显著,此时靶体边界尺寸对侵彻性能的影响很大,不能继续按照半无限靶体进行计算。     

Penetration into low-strength (23 MPa) concrete: target characterization and simulations

A combined experimental, analytical, and computational research and development program investigates the penetration of steel projectiles into low-strength concrete. Laboratory-scale material property tests conducted at the US Army Waterways Experiment Station on the concrete provide the data used in parameter estimation for a geomaterial constitutive model. The experiments and the model are described as well as the procedure used to fit the material model to the experimental data. The model accurately reproduces the data and predicts experimental results not used in the evaluation of model constants. The model, used in conjunction with an explicit transient dynamic finite element code, accurately predicts deceleration and depth of penetration of 3 CRH ogive-nosed 4340 steel penetrators.     

Penetration of boron carbide, aluminum, and beryllium alloys by depleted uranium rods: Modeling and experimentation

As part of the US stockpile stewardship program, it is necessary to perform experiments with various metallic components and explosives. These experiments will be conducted within specially designed blast vessels to ensure that the debris from the experiment is contained. The debris includes fragments that are launched at hypervelocities. The blast vessels are built primarily of steel, but have windows of either aluminum or beryllium alloys for diagnostic equipment requirements. To contain the hypervelocity depleted uranium fragments, ceramic armoring of the windows and steel vessel is used. To develop the necessary design tools, a program of experiments and modeling was begun. Preliminary pre-test predictions were made to design experiments. The experiments were conducted with targets representative of the armored windows in the vessel. To assist in the vessel design, two- and three-layered target analytical models were developed to predict the penetration of depleted uranium rods striking at velocities up to 2 km/s into layered targets of ceramic (boron carbide and silicon carbide) and aluminum, beryllium and steel alloys. The agreement between the pre-test predictions, the developed layered-target analytical model, and the experiments is good.     

Modeling the impact of a molten metal droplet on a solid surface using variable interfacial thermal contact resistance

An analytical model of the true area of contact between molten metal and a rough, solid surface has been used to calculate thermal contact resistance and to predict how it changes with surface roughness, substrate thermal properties and contact pressure. This analytical model was incorporated into a three-dimensional, time-dependent numerical model of free-surface flows and heat transfer. It was used to simulate impact, spreading and solidification of molten metal droplets on a solid surface while calculating contact resistance distributions at the liquid–solid interface. Simulations were done of the impact of 4 mm diameter molten aluminum alloy droplets and 50 μm diameter plasma sprayed nickel particles on steel plates. Predicted splat shapes were compared with photographs taken in experiments and simulated substrate temperature variation during droplet impact was compared with measurements.