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.     

弹体高速侵彻陶瓷复合厚靶的计算模型研究

针对平头弹高速撞击陶瓷复合厚靶的问题,以集中质量法为基础并考虑靶体的内摩擦效应对Fellows模型加以改进,建立侵彻过程的理论计算模型并利用Matlab编程求得不同撞击速度下弹体侵彻复合靶体的侵彻深度,模型得到了试验结果和数值计算结果的验证。参数分析的结果表明,陶瓷厚度的增加可提高复合靶体的抗侵彻能力,但随着初始撞击速度的提高,弹体的侵彻深度增长曲线趋于平缓。     

An investigation on failure mechanisms of ceramic/metal armour subjected to the impact of tungsten projectile

The failure mechanism of AD95 ceramic/4340 steel armour subjected to the penetration of the tungsten projectile was investigated at the nominal velocity of 820 m/s. Typical failure modes of the targets with various boundary conditions were presented. The effect of cover plate and confinement on failure mechanisms of the target was analyzed. The results showed that the cover plate can effectively reduce the damage of the target due to it can force the ejected ceramic fragments to decelerate the projectile, and a ceramic powders column was formed beneath the eroded projectile in the confined ceramic sandwiched between cover and support plate during penetration. Compared to the confinement, cover plate is more effective to reduce the damage of the support plate. Based on the experimental results, the failure mechanisms and penetration process of different target configuration have been discussed.     

A time-dependent model for long-rod penetration

The one-dimensional, quasi-steady-state, modified Bernoulli theory of Tate [J. Mech. Phys. Solids, 15, 287 (1967)] is often used to examine long-rod penetration into semi-infinite targets. In general., the time histories of penetration predicted by the Tate model can be in good agreement with those computed from numerical simulations. However, discrepancies exist between the model and numerical simulations at the beginning and at the end of penetration. From insights provided by numerical simulations, assumptions are made concerning the velocity and stress profiles in the projectile and the target. Using these assumptions, the time-dependent, cylindrically-symmetric, axial momentum equation is explicitly integrated along the centerline of the projectile and target to provide the equation of motion. The model requires the initial interface velocity—which can be found, for example, from the shock jump conditions-and material properties of the projectile and target to compute the time history of penetration. Agreement between the predictions of this one-dimensional, time-dependent penetration model are in good agreement with experimental results and numerical simulations.     

陶瓷/金属复合靶抗侵彻性能的数值模拟方法研究

采用自主开发的欧拉型二维爆炸与冲击问题仿真软件EXPLOSION-2D对钨杆侵彻陶瓷/金属复合靶板进行了数值模拟研究。为了描述陶瓷材料的损伤特性,在软件中嵌入JH-2本构模型及通过平板撞击实验结果拟合得到的高压状态方程。在质点网格法的基础上,给出了在欧拉算法下脆性材料累积损伤、破坏的数值算法。采用上述模型及算法研究了不同陶瓷片厚度条件下陶瓷/金属复合靶板的抗侵彻性能,分析了陶瓷靶损伤演化规律和侵彻过程。数值模拟结果与DOP(侵彻深度实验)结果吻合得较好,验证了该文模型和算法的有效性。     

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.     

Reliability analysis of projectile penetration into geological targets

The present study is dedicated to the reliability analysis of projectile penetration into a buried concrete target. The expressions for depths of penetration in the buried target have been derived for crater and tunnel regions separately using the methodology proposed by earlier investigators. These penetration depths have then been employed for subsequent reliability analysis using first-order reliability method. Design points, important for probabilistic design, have been located on the failure surface. Sensitivity analysis has been carried out to study the influence of various random variables on projectile reliability. Some parametric studies have also been included to obtain some results of field interest.     

动能弹侵彻多层陶瓷靶板数值模拟研究

结合试验对钨合金长杆弹垂直侵彻多层陶瓷靶板进行了三维数值模拟,得出了侵彻的物理图像及各种参量的变化规律。模拟结果中,后置钢靶剩余穿深和陶瓷破碎锥形状与试验基本一致。对于多层陶瓷靶板,每一层都会有漏斗形的破碎锥出现,且这些破碎锥的形状基本一致。随着陶瓷层数的增多,弹体的速度和动能下降速率逐渐变小。比较了相同厚度的多层和单层陶瓷靶板的抗弹性能,结果表明两者的陶瓷破坏形式不同,多层靶板的抗弹性能要优于相同厚度的单层陶瓷靶板,且仅在一定厚度范围内这种优势才较为明显。     

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。     

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.     

Penetration of a rigid projectile into an elastic-plastic target of finite thickness

This paper considers the problem of non-steady penetration of a rigid projectile into an elastic-plastic target of finite thickness. A specific blunt projectile shape in the form of an ovoid of Rankine is used because it corresponds to a reasonably simple velocity field which exactly satisfies the continuity equation and the condition of impenetrability of the projectile. The target region is subdivided into an elastic region ahead of the projectile where the strains are assumed to be small, and a rigid-plastic region near the projectile where the strains can be arbitrarily large. Using the above mentioned velocity field, the momentum equation is solved exactly in both the elastic and the rigid-plastic regions to find expressions for the pressure and stress fields. The effects of the free front and rear surfaces of the target (which is presumed not to be too thin) and the separation of the target material from the projectile are modeled approximately, and the force applied to the projectile is calculated analytically. An equation for projectile motion is obtained which is solved numerically. Also, a useful simple analytical solution for the depth of penetration or the residual velocity is developed by making additional engineering approximations. Moreover, the solution procedure presented in this paper permits a straight forward approximate generalization to accommodate a projectile with arbitrary shaped tip. Theoretical predictions are compared with numerous experimental data on normal penetration in metal targets, and the agreement of the theory with experiments is good even though no empirical parameters are used. Also, simulations for conical and hemispherical tip shapes indicate that the exact shape of the projectile tip does not significantly influence the prediction of integral quantities like penetration depth and residual velocity.     

陶瓷金属复合靶板工程模型及耗能分析

基于实验和数值模拟,将穿甲子弹侵彻陶瓷金属复合靶板的过程分为两个阶段,分别计算弹体侵彻陶瓷面板的动能损失、粘结层及金属背板的耗能,建立了计算弹道极限的工程分析模型,其结果与实验吻合较好。基于所建立的工程模型,分析了复合靶板各组分对其抗弹性能的影响。结果表明,陶瓷/金属复合靶板的耗能机制主要是背板耗能和弹丸质量损失耗能,分别约占初始动能的60%―95%和5%―40%。     

An investigation on mass loss of ogival projectiles penetrating concrete targets

Mass loss of an ogival projectile during its normal penetration in concrete target was investigated in this paper. Experiments of 38CrSi short-rod projectiles with ogival nose shape penetrating into concrete targets were conducted in the striking velocity range of 500–1500 m/s. Discussions revealed that projectile mass loss derives mainly from the nose part for both short-rod and long-rod projectiles during the penetration process. Furthermore, an engineering model was proposed to determine upper limit of rigid penetration regime as the maximum value of the striking velocity, which was based on the feature of projectile mass loss in the hydrodynamic transition between rigid penetration regime and semi-hydrodynamic penetration regime. Good agreements are obtained between engineering predictions and experimental results.     

A modified model for the penetration into moderately thick plates by a rigid,sharp-nosed projectile

The deep penetration model based on cavity expansion analysis (Int. J. Impact Eng. 27 (2002) 619) is modified to take account of the increase of the contact area between the projectile nose and the target medium before the projectile nose fully penetrates into the target. The modified penetration model is applicable to those penetration problems where the length of the projectile nose is comparable to the penetration depth. The predicted results are in good agreement with experimental results from Diskshit and Sundararajan (Int. J. Impact Eng. 12(3) (1992) 373) and Diskshit et al. (Int. J. Impact Eng. 16(2) (1995) 293).     

弹体侵彻陶瓷/金属复合靶板问题的研究

针对弹体侵彻陶瓷/金属复合靶板的问题,将弹体的墩粗变形、陶瓷面板碎裂及陶瓷锥的形成变化和金属背板的变形结合起来,建立了可变形弹体垂直侵彻陶瓷/金属靶板的理论分析模型。利用大型非线性有限元程序LS-DYNA3D,对平头弹侵彻陶瓷/金属复合靶板的问题进行数值模拟,得到了陶瓷/金属复合靶板受弹体侵彻的变形过程。最后给出了典型位置的位移随时间的变化曲线,理论模型分析结果和数值模拟结果与实验结果进行了对比,吻合很好。说明理论分析模型的正确性和数值模拟结果的可靠性,可以为复合靶板的设计提供有利依据。     

Modeling and validation of full fabric targets under ballistic impact

The impact of three different projectiles (0.357 Magnum, 9-mm FMJ and 0.30 cal FSP) onto Kevlar® was modeled using a commercial finite-element program. The focus of the research was on simulating full-scale body armor targets, which were modeled at the yarn level, by reducing to a minimum the number of solid elements per yarn. A thorough validation of the impact physics was performed at the yarn level, single-layer level, and a full body armor system. A verification was performed by checking the numerical model against analytical predictions for yarn impact. For one-layer and multiple-layer targets validation consisted on matching experimental data of pyramid formation recorded by an ultra-high-speed camera. The full-scale targets were also instrumented with nickel–chromium wires that stretch with the yarn during the penetration event. The wires provided a second validation data set since the numerical model can reproduce the signal recorded by the wires. The third and final validation of the model is provided by a comparison of the ballistic limit predicted by the model and data obtained in tests. This is a check of the failure model used in the numerical simulations. This paper shows that the main features of the impact physics are well reproduced by the finite-element model. Prediction of ballistic limits for the 9-mm FMJ and FSP projectiles were within the scatter of the tests, while for the 0.357 projectile the difference was only 15%.     

蜂窝铝的侵彻实验研究与有限元模拟

目的 研究弹体侵彻蜂窝铝的力学行为。方法 在实验中, 通过轻气炮加速的尼龙弹体冲击蜂窝铝靶体。利用Ansys/LS-DYNA建立了弹体侵彻蜂窝铝的壳单元有限元模型。结果 实验给出了冲击速度为140和167 m/s时弹体的加速度曲线。运用壳单元模型对蜂窝铝的侵彻进行模拟, 得到了弹体的加速度曲线以及蜂窝铝在侵彻过程中的变形图。结论 将模拟结果与实验结果进行了对比, 发现模拟结果与实验结果符合较好, 证明了壳单元有限元模型模拟蜂窝铝侵彻行为的可靠性。     

A fuzzy model of the penetration resistance of concrete targets

The penetration resistance of a concrete target varies greatly with the strike velocity of the projectile from low and intermediate impact velocities to high impact velocities. A fuzzy model of the penetration resistance of a concrete target is proposed to describe this characteristic. A complete analysis is conducted of the penetration process during which a rigid projectile penetrates a semi-infinite concrete target based on the proposed fuzzy model. Good agreement is observed between the experimental and predicted results based on the proposed fuzzy model.     

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。