On the ballistic resistance of double-layered steel plates: An experimental and numerical investigation

Civil and military ballistic protection systems often consist of thin, high-strength steel plates. Such plates may either be monolithic or layered with or without spacing. The idea of using layered plates instead of a monolithic one in order to increase the ballistic perforation resistance is not new, and the effect of using targets made up of several thinner plates has been investigated in the literature for a long time. However, results by various authors are contradicting and detailed experimental and numerical work is still required.In the present study, the ballistic perforation resistance of double-layered steel plates impacted by blunt and ogival projectiles was investigated both experimentally and numerically. In the tests, 12 mm thick (monolithic or layered) targets of Weldox 700 E were impacted using a gas-gun at sub-ordnance velocity, and the ballistic limit velocity of the different target combinations was obtained. In general, good agreement was obtained between the numerical simulations and the experimental results. It was found that in the case of blunt projectiles a large gain in the ballistic limit is offered by double-layered systems. These advantages seem to disappear when ogival projectiles are used. However, the main conclusion from both the experimental and numerical studies is that the overall protection level, i.e. the minimum ballistic limit velocity obtained independently of projectile nose shape, seems to increase significantly by double-layering the target.     

Q235钢板对半球形头弹抗侵彻特性

利用轻气炮进行了半球形头杆弹正撞击单层板和等厚接触式三层板的实验, 得到了这两种结构靶体的初始-剩余速度曲线以及弹道极限。采用ABAQUS/EXPLICIT数值模拟软件对杆弹撞击金属板的过程进行了数值模拟研究, 通过对比数值模拟和实验结果, 验证了数值模拟材料模型和参数的有效性。研究了靶体结构对抗侵彻特性的影响, 并分析了弹体对靶体的撞击过程。研究结果表明:多层板的弹道极限高于等厚单层板。单层板主要失效模式为剪切, 而多层板的主要失效模式为整体的蝶形变形和局部的盘式隆起。对于多层板, 靶板具体的失效模式与其在靶中位置相关。     

A study of the perforation of stiffened plates by rigid projectiles

In the present paper, a four-stage perforation model that accurately predicts the residual velocity is developed by adopting an energy method. The four stages are plug formation, dishing formation, petal formation and projectile exit. In addition, some important experimental results are presented and analyzed to validate the present perforation model. In the experiments, high speed camera system is used to record the perforation process. Observations on target damage and measurements of initial velocities and residual velocities with the aid of the system are presented. Numerical simulations are carried out for projectiles against single and layered plates adopted in the experiments. The perforation process is studied and the deformation and failure modes are obtained. The predictions of numerical simulations and analytical model are found in reasonably good agreement with those of experiments, and can be used to predict the ballistic limit and residual velocity of stiffened plates perforated by rigid projectiles. The project supported by the National Natural Science Foundation of China (90305018) The English text was polished by Yunming Chen     

Semi-theoretical analyses of the concrete plate perforated by a rigid projectile

Based on the three-stage perforation model, a semi-theoretical analysis is conducted for the ballistic performances of a rigid kinetic projectile impacting on concrete plates. By introducing the projectile resistance coefficients, dimensionless formulae are proposed for depth of penetration (DOP), perforation limit thickness, ballistic limit velocity, residual velocity and perforation ratio, with the projectile nosed geometries and projectile-target interfacial friction taken into account. Based on the proposed formula for DOP and lots of penetration tests data of normal and high strength concrete targets, a new expression is obtained for target strength parameter. By comparisons between the results of the proposed formulae and existing empirical formulae and large amount of projectile penetration or perforation tests data for monolithic and segmented concrete targets, the validations of the proposed formulae are verified. It is found that the projectile-target interfacial friction can be neglected in the predictions of characteristic ballistic parameters. The dimensionless DOP for low-to-mid speed impacts of non-flat nosed projectiles increases almost linearly with the impact factor by a coefficient of 2/(πS). The anti-perforation ability of the multilayered concrete plates is dependent on both the target plate thickness and the projectile impact velocity. The variation range of the perforation ratio is 1–3.5 for concrete targets.     

A3钢钝头弹撞击45钢板破坏模式的试验研究

为了研究破片模拟弹的终点弹道效应,进行了不同质量A3钢钝头弹(弹径25 mm)撞击45钢板的试验研究,其中A3钢强度弱于45钢。在约200～800 m/s的撞击速度范围内,随着撞击速度的增加,分别观察到弹体出现泰勒撞击、向日葵型花瓣帽形失效及靶板冲塞穿甲三种破坏模式。伴随弹体和靶体经历的不同结构破坏模式,弹材和靶材也经历着相当复杂的材料失效。     

Effect of air gap and order of plates on ballistic resistance of two layered armor

The high velocity normal impact of a three-dimensional rigid conical impactor penetrating into a two-layered ductile armor with an air gap is studied using a simplified model for an impactor–armor interaction. The goal of the study is to investigate analytically the dependence of the ballistic resistance of the armor on the order of the plates in the armor and on the width of an air gap between the plates. It is found that the ratio between the values of a single parameter depending on the material properties of the plates determines this dependence in both cases. This parameter characterizes the properties of the material of the plate; for the most widely used models of impactor–armor interaction, it is the ratio of the distortion pressure to the density of the plate.     

A membrane model for the response of thin plates to ballistic impact

The axisymmetric response of an infinite plate to an impacting projectile is determined analytically on the hypothesis that, for large deformations, a ductile plate behaves to a good approximation like a membrane under uniform tension. The lowest projectile velocity that results in perforation (the ballistic limit), and the residual velocity after perforation, then are determined on the basis of a critical-strain failure criterion. A figure of merit that depends only on the material properties of the target and characterizes the resistance of the material to impact appears naturally in the analysis. Variations in the ballistic limit with target thickness and projectile dimensions can be determined when this figure of merit is known. The theoretical ballistic limit and residual velocity for a steel cylinder impacting a titanium plate are found to agree with available measured values. Further support for the membrane model and an estimate of its range of validity are obtained by comparing the maximum displacement of an impulsively-loaded, circular membrane with experimental data for circular plates.     

Experimental study of turbulence in isothermal and stably stratified homogeneous shear flows: Mean flow measurements

The evolution of freestream turbulence under the combined action of linear shear and stable linear temperature profile is investigated. The experiment is carried out in a small, open circuit, low-speed test cell that uses air as working fluid. The temperature gradient formed at the entrance to the test section by means of an array of 24 horizontal, differentially heated elements is varied to get a maximum Brunt-Vaisala frequency N_o[=({g/T_m}{∂T/∂y})^1/2] of 3.1⁻¹. Linear velocity profiles are produced using screens of variable mesh size. The Reynolds number Re_M based on centre-line velocity and mesh size is varied from 80 to 175. Isothermal studies are carried out in four different experiments with varying velocity gradients. The effect of inlet turbulence level on growth of turbulence is studied in these flows by keeping the shear parameter Sh (=(x/u)(∂u/∂y)) constant. The range of shear parameters considered is 2.5–7.0. Shear and stratification combined produce a maximum gradient Richardson number Ri_g (= N_o²/(∂u/∂y)²) of 0.0145. Results have been presented in terms of evolution of variance of velocity fluctuations, Reynolds shear stress and temperature fluctuations. Measurements show the following: In isothermal flows the growth rate of turbulence quantities depends on both shear parameter and inlet turbulence level. There are distinct stages in the evolution of the flow and that can be identified by the power-law exponent of growth of turbulence. Shear is seen to promote the growth of turbulence and accelerate it towards a fully developed equilibrium state. Stratification initially suppresses the growth of turbulence and, hence, enhances the degree of underdevelopment. Under these conditions shear becomes active and subsequently enhances the growth rate of turbulence quantities.     

W/ZrNiAlCu亚稳态合金复合材料破片对RHA靶的侵彻释能特性

为研究W/ZrNiAlCu亚稳态合金复合材料破片对RHA靶板的侵彻释能特性，采用高速摄影弹道枪侵彻实验和能量方程、Avrami-Erofeev方程理论分析的方法，对破片的侵彻释能过程、侵彻规律、释能规律进行了研究。结果表明，破片在撞击并贯穿靶板的过程中激发了材料的燃烧反应，在靶板前方和后方产生了明显火光，随着撞击速度增加，火光范围增加、亮度提高；破片撞击速度、冲塞体速度的关系符合采用能量法推导的包含质量损失的破片侵彻公式，破片理论弹道极限速度为987.1 m·s?1；在实验速度范围内，材料反应效率随着冲击压力的增加而增加，与实验现象吻合。     

Penetration force measurement of thin plates by laser doppler anemometry

An experimental method is developed by applying laser-Doppler anemometry (LDA) to measure the velocity history of a projectile impact on a target. The force history was obtained by assuming the projectile to be rigid and by differentiating a polynomial which best fitted the obtained velocity data. This method was then applied to the impact of a hemispherically tipped striker on 1-mm thick aluminum plates. The initial velocity of the projectile ranged from several m/s to 93.5 m/s. When these velocities were low enough not to produce cracks on the plate, double-force peaks were observed in each test, and the value corresponding to the higher peak was proportional to the initial velocity of the projectile. Further, this peak force occurred when the projectile just started to rebound, and spring-back behavior of the plate always occurred. Once the cracks on the target started to form, the peak impact force dropped, and the double-peak phenomenon disappeared. It was also found that the peak force was at approximately the same level for impact speeds above the ballistic limit of the plate. On the other hand, a power law was found to perfectly fit the relationship between the absorbed kinetic energy and the initial velocity of the projectile when it was lower than the ballistic limit.     

细长尖头刚性弹对金属靶板的斜侵彻/穿甲分析

给出细长尖头刚性弹（如尖卵、尖锥形）斜侵彻/穿甲金属靶的一个分析模型。在细长尖头弹对中厚度金属靶的斜穿甲中,韧性孔洞扩张为主要的穿甲机理;着靶初期,发生方向角的改变。研究表明,金属靶的斜穿甲仅由4个量纲一参数控制,即冲击函数I、弹体几何函数N、量纲一靶厚和撞击斜角。分析得到显式的侵彻深度、终点弹道极限、剩余速度和撞击方向改变角表达式。该模型可预期跳飞发生的临界条件。理论预期与实验结果吻合较好。     

刚性钝头弹体正冲击GH4169间隔靶的消耗功分析

在380～680 m/s的弹体初速范围内，开展了直径8 mm钨球正冲击GH4169间隔靶实验，测得弹体初速、余速及靶板形貌，明显看出第1层板挠度较小,主要表现为剪切破坏，并产生了杯状挤凿块，第3层板挠度较大，主要表现为拉伸破坏。提出了间隔靶消耗功计算公式，结合剪切冲塞模型和建立的挤凿块速度模型计算了刚性钝头弹体冲击间隔靶中各层板的消耗功。结果表明，第2～3层板的单位面密度消耗功远高于相同面密度的第1层板，这与各层板的变形和失效形式密切相关。消耗功分析可用于定量描述间隔靶中各层板的抗侵彻性能。     

3种点阵金属三明治板的抗侵彻性能模拟分析

对3种不同的点阵金属芯体三明治板受钢质弹丸侵彻作用下的抗侵彻性能进行了有限元模拟研究, 包括空心金字塔三明治板、嵌入陶瓷柱金字塔三明治板和注入环氧树脂陶瓷金字塔三明治板. 随着结构、材料复杂性的递增, 以期望从中得出各子结构、各材料在三明治板抗侵彻过程中的吸能表现. 弹丸作用于板的入射速度及出射速度也是关注的重要参数, 用以量化确定三明治结构各组分对弹丸的弹道极限和抗侵彻能力的影响. 研究表明, 陶瓷材料因其具有高强度和高硬度等特点, 可以显著提高金属三明治板结构的抗侵彻能力; 环氧树脂材料可使离散的板结构保持整体性, 在三明治板受侵彻作用时, 吸收大量能量, 从而实现大幅提高结构的抗侵彻性能的目的; 因其材料/结构的完备性, 注入环氧树脂陶瓷金字塔三明治板具有最高的弹道极限速度, 抗侵彻能力也最强.      

12.7mm动能弹斜侵彻复合装甲的数值模拟研究

通过弹道枪实验对斜置角度为0°～60°的陶瓷复合装甲进行了弹道极限测试，分析了靶板斜置角度对穿燃弹的弹道极限和钢芯质量变化、破坏形态的影响。利用数值模拟的方法对上述实验结果进行验证计算，鉴于数值计算结果与实验结果较好的一致性，进一步研究了陶瓷复合靶板斜置角度对穿燃弹钢芯穿靶偏移角和等效Q235钢靶厚度的影响。结果表明，随陶瓷复合靶板斜置角度的增大:弹道极限近似指数型提高；在相同弹道极限速度下，穿燃弹对Q235钢靶板的极限穿深和对斜置陶瓷复合靶板的极限穿深的等效厚度的比也随之增大；同时，钢芯完整度逐渐降低，穿靶偏移角反向增大。     

带前舱物的钝头弹对金属靶的正穿甲分析

进一步发展了考虑结构响应的剪切冲塞模型,计及前舱物的作用,对带前舱物的钝头弹穿甲金属靶的工程问题进行了刚塑性分析,用于分析终点弹道极限和剩余速度。除剪切破坏之外,模型还考虑了靶板弯曲、膜力拉伸和前舱物撞击引起的靶板预结构响应等。给出了简洁的终点弹道性能公式,与相关实验结果较吻合。     

Drag coefficient and upstream influence in three-dimensional stratified flow of finite depth

A numerical study of the three-dimensional stratified flow past a vertical square flat plate in a channel of finite depth is described. Particular attention is paid to the anomalous dependence of the drag coefficient C_D on parameter K( = ND/-πU), where N is the Brunt-Väisälä frequency, D is the half depth of the channel and U is the upstream velocity. It is shown that C_D generally increases with K, while it decreases locally at integral values of K. Time development of the upstream columnar disturbance and the corresponding variation of C_D reveals that the periodic variation of C_D with time for K > 1 comes from the successive upstream radiation of the columnar disturbances of the first internal wave mode. Although the propagation speed of the columnar disturbance is consistent with the prediction of linear theory, its time-dependent structure is different from the weakly nonlinear theory as has been shown by laboratory experiments.     

Oblique Perforation of Thick Metallic Plates by Rigid Projectiles

Oblique perforation of thick metallic plates by rigid projectiles with various nose shapes is studied in this paper. 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. It is shown that the perforation of a thick plate is dominated by several non-dimensional numbers, i.e., the impact function, the geometry function of projectile, the non-dimensional thickness of target and the impact obliquity. Explicit formulae are obtained to predict the ballistic limit, residual velocity and directional change for the oblique perforation of thick metallic plates. The proposed model is able to predict the critical condition for the occurrence of ricochet. The proposed model is validated by comparing the predictions with other existing models and independent experimental data.The English text was polished by Keren Wang     

平头弹穿透金属靶板的模式分析

对平头弹穿透金属靶的剪切冲塞和绝热剪切冲塞两种可能穿甲模式进行分析. 对作者先前提出的绝热剪切冲塞失效模型进一步发展,给出在绝热剪切冲塞条件下修正的终点弹道极限和剩余速度. 对相关的平头弹穿甲WeldoxE系列钢靶的试验数据进行分析比较,讨论靶板厚度、靶材强度对终点弹道性能的影响. 更多实验数据证实:在一定靶厚时由于靶板的结构响应导致弹道极限附近存在剩余速度跳跃;随靶厚和靶材强度增加,穿甲模式由剪切冲塞向绝热剪切冲塞转换.      

Behaviour of uniaxially preloaded aluminium plates subjected to high-velocity impact

The purpose of this paper is to evaluate the behaviour of structural thin plates made of 7075-T6 aluminium alloy under normal impact of spherical steel projectiles, when they are subjected to uniaxial in-plane tensile preload. Also, nonloaded plates were tested under high-velocity impact. The impact and residual velocity were measured in all tests. From the relationships between the impact and residual velocities, the ballistic limit was estimated by a least-squares method. No significant differences were found between the ballistic limits under the two loaded conditions. Above the ballistic limit in the preloaded plates, unstable cracks that can generate the catastrophic failure of the plate were observed. At similar velocities, this phenomenon was not observed in nonloaded plates.     

Effect of projectile nose shape,impact velocity and target thickness on deformation behavior of aluminum plates

The present study deals with the experimental and numerical investigations of aluminum target plates impacted by blunt, ogive and hemispherical nosed steel projectiles. The projectiles were normally impacted on the target plates of 0.5, 0.71, 1, 1.5, 2, 2.5 and 3 mm thicknesses at different velocities with the help of a pneumatic gun. Effect of projectile nose shape, impact velocity and plate thickness on the deformation of the target plates was studied. Hemispherical nosed projectile caused highest global deformation (dishing) of the target plates. Ogive nosed projectiles were found to be the most efficient penetrator for the case of plates of thicknesses 0.5, 0.71, 1.0 and 1.5 mm. For the case of plates of thicknesses 2.0, 2.5 and 3.0 mm however, blunt nosed projectiles required least energy to perforate the target plates. The ballistic limit velocity of hemispherical nosed projectiles was found to be highest as compared to the other two projectiles. Finite element analysis of the problem was carried out using ABAQUS finite element code. Results of the numerical analysis were compared with the experiments and good correlation between the two was found.