Effect of air gaps on ballistic resistance of targets for conical impactors

High velocity penetration of a rigid conical impactor into a ductile target with air gaps between the plates is studied using the cylindrical cavity expansion approximation describing impactor–target interaction. It is showed that the latter model predicts improvement of the ballistic performance of the target with the increase of air gaps. It is found analytically that the ballistic limit velocity of the target consisting of N plates with a fixed total thickness with large air gaps increases with the increase of N. The conditions are discussed when the predicted effects can be most pronounced.     

Generation of a magnetic field in the shear deformation region of a conducting material upon high–velocity penetration

It is shown that when a high–velocity impactor penetrates into a conducting target with a transverse magnetic field, conditions for considerable field amplification are produced in the shear deformation region on the lateral surface of the impactor. Field generation in a conducting medium deformed in shear is considered within the framework of a plane one–dimensional problem of magnetohydrodynamics. The results obtained indicate that along the boundary of the cavity produced by the impactor in the target with a magnetic field, a thin layer with a very high field intensity (about 100 T) is formed. The possibility of explosion of this layer due to the magnetic pressure acting in it is analyzed.     

钨球侵彻防弹衣加红松木复合靶的研究

为研究钨球对防弹衣加人体等效靶的侵彻性能,利用12.7 mm弹道枪对钨球侵彻三级软体防弹衣加25 mm厚红松靶开展了实验研究;在此基础上,利用LS-DYNA3D软件对侵彻过程及破坏机理进行了分析,并研究了钨球质量变化对弹道极限及靶板能量吸收的影响;依据量纲分析建立了钨球侵彻防弹衣加红松木复合靶的穿靶能量公式,推导了钨球的弹道极限公式。研究结果表明:0.17、0.21、0.44 g的小钨球侵彻防弹衣加红松木复合靶的弹道极限分别为742.3、692.9、570.1 m/s;侵彻过程中,防弹衣以基体开裂、纤维断裂和拉伸分层破坏为主,纤维层面内出现类似“十”字型的损伤,松木靶以剪切和冲塞剥落破坏为主;随着钨球质量的增加,弹道极限呈幂函数形式降低,靶板的能量吸收率逐渐降低;钨球穿靶能量公式及弹道极限公式的计算结果与实验结果吻合良好,可分别用于计算不同侵彻速度下的穿靶能量和不同质量钨球的弹道极限。     

Shape optimization of impactor penetrating into concrete or limestone targets

The shape of the normally striking impactor that attains the maximum depth of penetration into a concrete or a limestone semi-infinite target for a given impact velocity is found. It is shown that the optimum shape is close to a blunt (in general case) cone and it is independent on the properties of the material of the target in the framework of the employed penetration model. The performance of some other typical shapes of the nose of the impactors (spherical-conic impactors, sharp-conic impactors, truncated-ogive impactors) are analyzed and compared with the optimal impactor.     

某9 mm手枪弹侵彻MDF的弹道特性

为探究某9 mm手枪弹侵彻木质靶板的弹道特性,以中密度板（medium density fiberboard, MDF）为研究对象进行了弹道侵彻试验,通过减装药和角度可调节靶架获得了不同速度和弹着角下弹头的剩余速度和侵彻深度等关键信息;通过Poncelet阻力模型对试验结果进行了分析,并得出侵彻深度与侵彻速度之间的关系式;建立了手枪弹侵彻MDF的数值计算模型,对不同速度和不同弹着角的弹头偏转行为进行了研究,并得到了临界跳飞角度与着靶速度之间的函数关系。结果表明,弹头正侵彻25 mm厚度的MDF时,能量损失量与入射速度具有线性相关性;弹头侵入MDF时均会产生负方向偏转,弹头速度降低或者弹着角减小均会使负方向偏转角度增大,当弹头低速穿透MDF或者弹着角小于45°时,弹头侵彻MDF过程中会产生较大角度偏转,在射出MDF时出现弹道转正现象。     

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。     

Method of calculating the resistance force upon an impact on a composite target

A kinematically possible velocity field allowing calculation of all the necessary integrals in quadratures and obtaining an analytical solution for the resistance force induced by impactor penetration into the target is constructed. The Saint-Venant model of a rigid-plastic body and the theorem on the upper bound of the limit load are used in solving the problem. The essence of the method applied is using the equilibrium equation in the form of the Lagrange equation. The kinematically possible velocity field allows obtaining an upper bound of the limit load, i.e., estimating the resistance force to impactor penetration.     

自由梁中部在平头子弹横向正冲击下的穿透及变形

研究了均匀矩形截面自由梁中部在小尺寸、平头、刚性、圆柱形弹体正撞击下的变形及穿透过程。当子弹冲击速度接近或高于临界穿透速度时 ,在梁上与子弹接触区的周围会形成一个剪切冲塞 ,子弹通过冲塞作用在梁上的剪应力会引起梁的整体弯曲变形。通过动力分析 ,确定了子弹穿透梁的临界穿透速度。对子弹穿透梁的局部剪切过程和梁的各个变形阶段进行了数值计算 ,估算出局部剪切能、梁弯曲变形能、子弹及梁的残余动能在子弹初动能中所占的比例。     

Effect of the impulse of a meteorite on the dimensions of the impact crater

Formulas for the diameter and depth of an explosion crater are obtained which take into account the energy and impulse of the explosion products, rock strength, burial depth of the explosive charge, and gravity. Using the explosive-shock analogy, the obtained relations are extended to the case of meteorite (impactor) impact on the planet’s crust (target). It is shown that in the gravity cratering regime, the influence of the impulse of the impactor is significant and increases with increasing its size. In the strength cratering regime, the impulse has little effect on crater dimensions. It is established that crater dimensions are determined mainly by the kinetic energy of the impactor and, to a lesser degree, by its impulse.     

对厚水层及多层间隙金属靶平面斜侵彻全物理过程的数值模拟研究

2D平面斜侵彻的数值模拟 ,可再现对应的 3D斜侵彻中最严重非对称受力面内的终点弹道效应 ,并为近似估算 3D斜侵彻等效弹迹及等效扩孔横截面积提供基础数据。利用重新设计和改造的LTZ 2D程序 ,解决了阻抗差异大的多物质厚靶的平面斜侵彻的计算问题 ,得到了定性上合理、定量上适用的结果。     

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.     

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.     

椭圆截面截卵形刚性弹体正贯穿加筋板能量耗散分析

为获得椭圆截面截卵形刚性弹体正贯穿加筋板的剩余速度,根据椭圆截面弹体贯穿靶板的破坏特征,认为贯穿过程中靶板的能量耗散方式主要为塞块剪切变形功与塞块动能、扩孔塑性变形功、花瓣动力功、花瓣弯曲变形功、靶板整体凹陷变形功、加强筋侧向凹陷变形功。推导了每种能量计算方法,计算中定量考虑了靶板扩孔、花瓣弯曲、凹陷变形的应变率效应。根据能量守恒关系,得到了椭圆截面弹体剩余速度和弹道极限速度预测公式。并通过实验结果对模型进行了验证。结果表明:考虑靶板应变硬化、应变率效应的贯穿模型可以准确预测弹体剩余速度;随着椭圆截面弹体长短轴之比的增大,靶板的弹道极限速度近似线性增大;长短轴之比小于3时,加筋板的主要耗能为花瓣弯曲变形能、整体凹陷变形能。     

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.     

头部对称刻槽弹体侵彻半无限厚铝合金靶实验与理论模型

在综合考虑弹体结构稳定性及截面比动能的前提下, 提出一种介于尖卵形弹体及尖锥形弹体间的头部对称刻槽弹体, 以期达到提高侵彻深度的目的。以尖卵形弹体侵彻深度为基准, 开展头部对称刻槽弹体侵彻半无限厚铝合金靶实验。在此基础上, 推导得到可描述头部对称刻槽弹体侵彻2A12铝合金靶过程的局部相互作用模型。同时, 结合头部对称刻槽弹体侵彻后靶体破坏现象, 提出适用于头部对称刻槽弹体的靶体响应力, 进而确立头部对称刻槽弹体的侵彻深度模型。实验结果与理论计算表明, 头部对称刻槽弹体具有相对于尖卵形弹体更好的侵彻能力。头部对称刻槽弹体侵彻深度提高的原因是弹体头部结构截面比动能增加及其侵彻过程中的靶体弱化效应, 其中弱化效应是侵彻深度提高的主控因素。     

Equilibrium and stability of a z pinch in a multipole magnetic field

In the theoretical investigation of the dynamic stabilization of a current-carrying plasma filament by a high-frequency multipole magnetic field it is usually assumed that the cross section of the filament has a circular form in equilibrium [1, 2]. This considerably simplifies the calculations but it does not correspond to reality, since the surface of the plasma must be fluted in the multipole field. An attempt to estimate the influence of the deformation of the filament cross section on its stability against bending in the special case of quadrupole field was made in [3], in which the parameters were determined of the elliptical cross section corresponding to a plasma filament with current in a quadrupole field and an expression was found for the electrodynamic force acting on the filament in the case of long-wavelength kink perturbations. However, this force was calculated incorrectly in [3]. In the present paper a study is made of the equilibrium and stability of a current-carrying plasma filament against kink perturbations in the general case of a multipole stabilizing field. Under the assumption that the flute depth is small, the equilibrium form of the cross section of the current-carrying plasma filament in the multipole magnetic field is found and the components of the force exerted by the field on the perturbed filament are calculated. It is shown that the external field interacts with the current in the perturbed filament only in the case of a quadrupole field. The results are discussed in connection with the problem of multipole dynamical stabilization of a z pinch against kink perturbations.     

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.     

弹体斜侵彻混凝土靶的实验研究及其数值模拟

以弹体斜侵彻混凝土的弹道特性为研究内容,通过侵彻实验与数值模拟得到了不同速度下的侵彻深度、开坑尺寸、偏转角等参数,实验结果与模拟结果吻合较好。研究结果表明:倾角对开坑深度和开坑形状影响很大;倾角越大,对侵彻深度和偏转角的影响越明显,弹体偏转角随着速度的增大呈现减小的趋势;当倾角增至一定角度后发生跳弹现象,据此得到跳弹极限角与倾角、侵彻速度的关系。     

基于主-次激波在变截面管中传播的数值模拟

采用二阶精度的单调迎风中心格式(MUSCL)和非结构自适应网格技术与有限体积形式,对轴对称变截面管道中基于主-次的爆轰波传播过程进行了数值模拟。结果表明,基于主-次的爆轰波传播至目标区时,冲击波流场均匀、稳定,波形良好;适当提高驱动段的爆炸能量,目标区能够获得预想的冲击波超压值和作用时间。     

Optimization of two component ceramic armor for a given impact velocity

Using Florence’s model a problem of two-component ceramic-faced lightweight armors design against ballistic impact is solved. Approximate analytical formulas are derived for areal density and thicknesses of the plates of the optimal armor as functions of parameters determining the properties of the materials of the armor components, cross-section and mass of an impactor, and of the expected impact velocity.