Microstructural observations on the terminal penetration of long rod projectile

Present study focuses on the terminal penetration of tungsten heavy alloy(WHA) long rod penetrator impacted against armour steel at an impact velocity of 1600 m/s. The residual penetrator and armour steel target recovered after the ballistic test have been characterized using optical microscope, scanning electron microscope(SEM) and electron probe micro analyzer(EPMA). Metallurgical changes in target steel and WHA remnant have been analysed. Large shear stresses and shear localization have resulted in local failure and formation of erosion products. Severe plastic deformation acts as precursor for formation of adiabatic shear band(ASB) induced cracks in target steel. Recovered WHA penetrator remnant also exhibits severe plastic deformation forming localized shear bands, ASB induced cracks and shock induced cracks.

Analytical models for the penetration of semi-infinite targets by rigid,deformable and erosive long rods

A theoretical study is presented herein on the pen- etration of a semi-infinite target by a spherical-headed long rod for Yp 〉 S, where Yp is the penetrator strength and S is the static target resistance. For Yp 〉 S, depending upon initial impact velocity, there exist three types of penetration, namely, penetration by a rigid long rod, penetration by a deforming non-erosive long rod and penetration by an erosive long rod. If the impact velocity of the penetrator is higher than the hydrodynamic velocity （VH）, it will penetrate the target in an erosive mode; if the impact velocity lies between the hydrodynamic velocity （VH） and the rigid body velocity （VR）, it will penetrate the target in a deformable mode; if the impact velocity is less than the rigid body velocity （VR）, it will penetrate the target in a rigid mode. The critical conditions for the transition among these three penetration modes are proposed. It is demonstrated that the present model predictions correlate well with the experimental observations in terms of depth of penetration （DOP） and the critical transition conditions.

Approximate solutions of the Alekseevskii–Tate model of long-rod penetration

The Alekseevskii–Tate model is the most successful semi-hydrodynamic model applied to long-rod penetration into semi-infinite targets. However, due to the nonlinear nature of the equations, the rod(tail) velocity, penetration velocity, rod length, and penetration depth were obtained implicitly as a function of time and solved numerically By employing a linear approximation to the logarithmic relative rod length, we obtain two sets of explicit approximate algebraic solutions based on the implicit theoretica solution deduced from primitive equations. It is very convenient in the theoretical prediction of the Alekseevskii–Tate model to apply these simple algebraic solutions. In particular, approximate solution 1 shows good agreement with the theoretical(exact) solution, and the first-order perturbation solution obtained by Walters et al.(Int. J. Impac Eng. 33:837–846, 2006) can be deemed as a special form of approximate solution 1 in high-speed penetration. Meanwhile, with constant tail velocity and penetration velocity approximate solution 2 has very simple expressions, which is applicable for the qualitative analysis of long-rod penetration. Differences among these two approximate solutions and the theoretical(exact) solution and their respective scopes of application have been discussed, and the inferences with clear physical basis have been drawn. In addition, these two solutions and the first-order perturbation solution are applied to two cases with different initial impact velocity and different penetrator/target combinations to compare with the theoretical(exact) solution. Approximate solution 1 is much closer to the theoretical solution of the Alekseevskii–Tate model than the first-order perturbation solution in both cases, whilst approximate solution 2 brings us a more intuitive understanding of quasi-steady-state penetration.

Analysis Model on Penetration Depth of Concrete by Eroding Long-Rod Projectiles

Mass loss should be considered while calculating the penetration depth of concrete by eroding long-rod projectiles of high velocity.The penetration process is divided into two phases：eroding phase and rigid phase.During eroding phase,a model to predict the penetration depth is established on the assumption that there is a chipping region in the bottom of crater.During rigid phase,Forrestal formula is adopted to calculate the penetration depth.Using this model,the depth of concrete penetration by a tungsten alloy long-rod projectile is calculated.When the critical eroding velocity is between 950 m/s and 1 000 m/s,the result is in good agreement with the experimental data.

Long-rod penetration:the transition zone between rigid and hydrodynamic penetration modes

Long-rod penetration in a wide range ol" velocity means that the initial impact velocity varies in a range from tens of meters per second to several kilometers per second.The long rods maintain rigid state when the impact velocity is low,the nose of rod deforms and even is blunted when the velocity gets higher,and the nose erodes and fails to lead to the consumption of long projectile when the velocity is very high clue to instantaneous high pressure.That is,from low velocity to high velocity,the projectile undergoes rigid rods,deforming non-erosive rods,and erosive rods.Because of the complicated changes of the projectile,no well-established theoretical model and numerical simulation have been used to study the transition zone.Based on the analysis of penetration behavior in the transition zone,a phenomenological model to describe target resistance and a formula to calculate penetration depth in transition zone are proposed,and a method to obtain the boundary velocity of transition zone is determined.A combined theoretical analysis model for three response regions is built by analyzing the characteristics in these regions.The penetration depth predicted by this combined model is in good agreement with experimental result.

Alekseevskii-Tate revisited:An extension to the modified hydrodynamic theory of long rod penetration

The modified hydrodynamic theory of long rod penetration into semi-infinite targets was established independently by Alek-seevskii and Tate over forty years ago and since then many investigators contributed much to the development of the high speed penetration mechanics.However,in all the models proposed so far,the target resistance Rt is not well defined and usually determined by adjusting it until the predicted depth of penetration comes to an agreement with experimental data.In this paper,assumptions are first made about particle velocity and pressure profiles together with response regions in the target and then an extension is made to the modified hydrodynamic theory of long rod penetration into semi-infinite targets,in which Rt has explicit form and is dependent on penetration velocity as well as thermo-mechanical properties of target material.The present model is compared with long rod penetration tests for different material combinations.It transpires that the present model predictions are in good agreement with the experimental data and numerical simulations in terms of penetration depth although many assumptions and simplifications are introduced into the paper.

Predicting the penetration of long rods into semi-infinite metallic targets

Analytical equations are presented herein to predict the penetration of semi-infinite metallic targets struck normally by long rods at high velocities for Yp<S where Yp is the rod strength and S is the static target resistance.The equations are derived based on energy balance method.It is assumed that the kinetic energy loss of a long rod is related to the energy dissipated by the plastic deformations in the target,the energy consumed by the long-rod penetrator itself and the energy carried by the eroded rod debris.Secondary penetration is also examined in the present paper due to the fact that the eroded rod debris forms a tube which can penetrate the target further if the density of the rod is greater than that of the target and the impact velocity is high enough.The present analytical equation is found to be in good agreement with the experimental data for a wide range of impact velocities.

Analytical model for cratering of semi-infinite metallic targets by long rod penetrators

Analytical model is presented herein to predict the diameter of crater in semi-infinite metallic targets struck by a long rod penetrator. Based on the observation that two mechanisms such as mushrooming and cavitation are involved in cavity expansion by a long rod penetrator, the model is constructed by using the laws of conservation of mass, momentum, energy, together with the u-v relationship of the newly suggested 1D theory of long rod penetration (see Lan and Wen, Sci China Tech Sci, 2010, 53(5): 1364–1373). It is demonstrated that the model predictions are in good agreement with available experimental data and numerical simulations obtained for the combinations of penetrator and target made of different materials.

超高速钨合金长杆弹侵彻花岗岩靶的毁伤效应

为研究钨合金长杆弹超高速侵彻花岗岩靶的毁伤规律,文章选用长径比为10∶1的钨合金长杆弹,应用二级轻气炮平台开展弹体在1.6~3.85km/s弹速下的侵彻花岗岩靶的试验,并基于LS-DYNA软件对超高速侵彻过程进行数值模拟。结果表明:(1)不同弹速下花岗岩靶的成坑模式不同,在相对低速(1.6~1.8km/s)时,呈现两边高中间低的“漏斗形”,在相对高速(1.99km/s及以上)时,呈现中间高两边低的“蘑菇头形”,且弹速越高,蘑菇头越扁平;(2)侵彻深度与弹速呈现“上升—下降—上升”的三段式非正比例形态,在1.99km/s后出现侵彻逆减现象,直到2.32km/s后侵彻深度再次随弹速增加而增加;(3)不同弹速下的裂纹数量和最大裂纹长度随弹速的增加而增加,并不受侵彻机制转变的影响。研究结果可为动能弹打击地下工事花岗岩掩体提供参考,具有十分重要的工程价值。

钢制长杆弹斜侵彻中厚靶板数值模拟

利用大型动力有限元分析软件 ,采用 Johnson- Cook动态本构模型 ,对长杆弹侵彻中厚靶问题进行了数值模拟 ,给出了弹体与靶体的破坏变形发展过程及应力波传播过程 ,得到了弹体的受力曲线 。

不同头部形状长杆弹侵彻过程的数值模拟

采用数值模拟技术研究了4种不同头部形状长杆弹体侵彻半无限厚轧制均质装甲(RHA)靶板的过程,重点考察弹体头部结构对侵彻过程的影响。结果表明:当靶板为高强度材料时,在相同的条件下,长杆弹体的侵彻深度是由弹体材料的失效机制决定,弹体头部形状对其影响较小;但长杆弹体头部的轮廓在撞击初始阶段对靶板的破坏有一定的影响,尤其是靶板开坑截面的大小。

Al_2O_3陶瓷复合靶抗长杆弹侵彻性能和机理实验研究

用DOP(depthofpenetration)实验研究了质量分数为 90 %的Al2 O3 陶瓷复合靶抗长杆弹侵彻性能。实验表明 :随陶瓷厚度的增加 ,以差分效益系数和靶平均阻力表征的陶瓷复合靶的抗长杆弹侵彻性能降低 ;盖板能增强陶瓷复合靶抗侵彻性能。对回收陶瓷和盖板的破坏特征分析表明 :长杆弹对陶瓷复合靶侵彻过程大致可分为初期侵彻和稳定侵彻两个阶段 ,但对薄靶和厚靶 。

长杆弹侵彻半无限厚土的旋转效应分析

利用刚流撞击模型以及土壤介质变形沿合力方向假设,建立了微元合力与介质移动速度之间的关系。在此基础上,建立了长杆弹侵彻土壤时考虑旋转效应的动力学方程。由这些非线性动力学方程的数值解,确定了撞击力和侵入位移。计算结果表明,随着初始角速度的增大,侵入位移的幅值明显增大。

陶瓷复合靶板抗长杆弹侵彻的数值模拟分析

采用LS-DYNA非线性有限元程序对长杆弹垂直入射陶瓷／金属靶板的侵彻过程进行了数值模拟分析．重点研究了弹体入射速度在600～1400m／s情况下，陶瓷面板侧向约束的影响，发现侧向约束板存在最佳厚度，此时靶板的防护系数最高．

超高速钨合金长杆弹对混凝土侵彻及损伤破坏的数值分析

采用二维拉格朗日弹塑性流体力学计算程序LTZ-2D,分析了超高速钨合金长杆弹侵彻混凝土靶板的过程以及靶板的损伤破坏情况.计算结果表明,与低速侵彻规律相同,截卵形弹头以及较大的长径比更有利于弹体对靶板的侵彻,但对混凝土靶板造成的损伤相对较小;由于弹体失效的影响,存在一个临界速度,当弹体的着靶速度高于临界速度时,弹体对靶板的侵彻能力随着撞击速度的提高而降低.

长杆弹侵彻半无限靶板的影响因素及其影响规律

针对长杆弹垂直侵彻半无限厚靶板的问题,理论上分析了影响弹体侵彻效率的主要因素,并就其对长杆弹归一化侵彻深度的影响规律及机理进行了系统的探讨,得出了长杆弹截面形状、头部形状、长径比、入射速度、弹靶材料密度比、弹靶材料泊松比、弹靶材料强度在长杆弹侵彻过程中的影响机理和其对最终归一化侵彻深度的影响规律。这些结论能够对长杆弹、防护装甲以及防护工事的设计提供一定的科学依据。

圆管与圆杆组合体对半无限均质钢靶侵彻深度研究

依据圆管、圆杆初始撞击动能与弹坑体积之比相等的假设,建立了同材料圆管与圆杆对半无限均质靶板侵彻深度之比的简化理论模型。推导出圆管与圆杆的侵彻深度之比是两者的长度比、初始撞击速度比、坑径比和圆管内外径比的函数。在同一初始撞击速度、相同长度、圆杆直径不大于圆管内径条件下,对影响圆管和同长度同材料圆管与圆杆组成的圆管—圆杆异型侵彻体侵彻深度的参量进行了讨论,并给出圆管与圆杆侵彻深度之比的变化范围。圆管与圆杆侵彻深度之比在同材料同长度下理论计算值与实验数据有很好的一致性。所有这些都为伸缩式、大长径比新型动能穿甲弹结构设计提供了理论基础。

长杆射弹侵彻三种混凝土靶的实验研究

为了研究钻地武器的侵彻性能,在57mm口径的气炮上发射长杆射弹对三种靶体进行模拟侵彻实验。靶体为水泥砂浆石靶、钢纤维混凝土靶和含单层密排刚玉球的钢纤维混凝土靶。实验结果表明,弹头形状对侵彻深度有明显影响;当长杆射弹和撞击速度都相同时,与侵彻钢纤维混凝土靶相比,含单层密排刚玉球的钢纤维混凝土靶中的侵彻深度大约降低了11%,而水泥砂浆石靶中的侵彻深度增加了12%。

钨合金长杆弹侵彻半无限钢靶的数值模拟及分析

利用显式动力有限元程序ANSYS/LS-DYNA,采用ALE方法和Steinberg本构模型,对钨合金长杆弹侵彻半无限厚钢靶进行了数值模拟,给出了侵彻过程4个阶段的完整图像和相关物理量的时程变化曲线,分析了弹、靶的压力分布、质点速度以及材料的流动特性。结果表明:在较大速度范围内,模拟计算的侵彻深度与实验结果吻合得很好;沿侵彻轴线,弹靶交界面附近的材料行为主要由静水压力控制。

杆式动能体侵彻移动靶板数值仿真研究

为研究不同速度的杆式动能体以不同攻角、不同着角对不同移动速度的靶板侵彻毁伤效果,运用ABAQUS软件对侵彻过程进行数值模拟,仿真得到不同初速的动能体以不同攻角、不同着角侵彻不同速度移动靶板后的速度、偏转角、扭转角、剩余质量及对靶板的毁伤面积。结果表明:就穿甲能力而言,攻角在60°左右最好;就毁伤效应而言,在一定的速度下应是攻角越小或者越大越好;相对于正穿靶,动能体以一定着角斜穿靶其毁伤效果大幅下降。