Hard projectile penetration and trajectory stability

We present a general framework to describe the dynamics of a hard projectile penetrating into a solid target. Rigid body dynamics, differential area force law and semi-empirical resistance function are used to formulate the motion of the hard projectile. The proposed model is capable of predicting the projectile trajectory under various oblique and yaw angles. Critical conditions for the occurrences of the instability and the reverse of the projectile trajectory are discussed. It was found that the relative location of mass centre of the projectile has strong influence on the control of the rotation of the projectile, and thus, the projectile stability and the change of trajectory direction. The validity of the proposed model is limited to deep penetration and when the wake separation and reattachment between projectile body and target have negligible influence on the target resistance to the projectile.     

The effect of annular multi-point initiation on the formation and penetration of an explosively formed penetrator

Using LS-DYNA software, this paper studies the problem of an annular multi-point initiation circuit applied to an EFP charge, and the effects on the penetrator formation parameters, such as velocity and length-diameter ratio, by examining the number of initiation points, the initiation position, and the synchronized initiation deviation of the annular multi-point initiation circuit. It reaches the conclusion that when there are six or more initiation points, the formed EFP of a multi-point initiation project is similar to the result of a peripherally initiated charge. It also finds that the change of across velocity gradient is the main cause of bending distortion of the penetrator, and that the formed penetrator cannot bend if the multi-point synchronized initiation deviation is less than 200 ns. The simulation results were validated through X-ray imaging experimentation. Both results are in good agreement. It was found that, with the increase of the initiation annular radius, the EFP velocity improves by 24%, and the length-diameter ratio increases by more than 5 times.     

A numerical study of the cavity expansion process and its application to long-rod penetration mechanics

The paper describes a series of 2D numerical simulations which followed the cavity expansion process in an elasto- plastic solid. The results from these simulations, in terms of cavity wall motion as a function of the applied pressures inside the cavity, highlighted several issues concerning cavity expansion process and the terminal ballistics of both rigid and eroding long rods. These issues include the form of the relation between the dynamic radial stress on the cavity wall and its velocity, which can be written in a simple, normalized form, at least for the materials we simulated here. Also, the difference between target resistance to the penetration of rigid and eroding-rod penetration, was quantified with a series of simulations in which the pressures in the cavity were applied on an angular section, rather than on its whole surface. Finally, we explored the inherent differences between spherical and cylindrical cavity expansion processes, which can be helpful for analytical models of the penetration of rigid rods with different nose shapes.     

Experimental impact study using an explosive driven projectile accelerator and numerical simulation

This paper presents a projectile impact experiment using a compact accelerator driven directly by explosives, and a numerical simulation of the impact. The compact projectile accelerator has been developed to evaluate the perforation resistance of structural materials. Projectile shooting tests were conducted and the relationship between the explosive weight and the injected projectile velocity was obtained. A series of impact tests on the targets, with varying projectile velocity, was examined using the developed accelerator. The projectile was made of SNCM (nickel–chromium–molybdenum special steel of the Japanese Industrial Standard) and the targets were aluminum 5052S alloy plates. The projectile track and the impact process on the targets were observed with a SHIMAZU HPV-1 high-speed video camera and the velocity of the projectile and interactive behavior were evaluated. A numerical simulation study was conducted using the parallel version of the non-linear finite element code of LS-DYNA to follow the impact experiments and determine the ballistic limit of the projectile for the targets.     

基于等质量变壁厚球缺罩聚能杆式射流成型特性研究*

基于变壁厚球缺罩质量恒定假设,通过改变药型罩内表面曲率半径rx 和罩顶厚度s,调整药型罩的结构,建立了δs与rx 设计参数计算模型;采用LS-DYNA3D显式非线性动力有限元程序,对不同结构变壁厚球缺罩形成聚能杆式射流的过程进行三维数值模拟;设计出罩顶厚度改变量δs 在（-1．2～＋1．2） mm范围内的7种不同结构变壁厚球缺罩方案,研究其形成聚能杆式射流的形态和各项性能参数的变化规律,并与等壁厚药型罩形成的聚能杆式射流参数进行对比分析。研究结果表明：变壁厚球缺罩对杆式射流的形状、长度、密实度和断裂时间等性能参数均有较显著影响;当δs ＝-0．4mm时,杆式射流头部速度为3317m/s,并且速度梯度分布合理,杆式射流的综合性能较优。     

A combined numerical and theoretical study on the penetration of a jacketed rod into semi-infinite targets

A combined numerical and theoretical study is conducted herein on the penetration of semi-infinite targets by jacketed rods with different r_j0/r_c0 ratios where r_j0 and r_c0 are the radii of the jacket and the core, respectively. The numerical results show that for smaller r_j0/r_c0 ratios the u–v relationship changes only a little compared to that of unitary long rod penetrator of the same core material, hence, the u–v relationship of unitary (homogeneous) long rod penetration is also applicable for jacketed rod penetration. Model for cratering in semi-infinite targets by jacketed rods is then suggested by using the laws of conversation of mass, momentum and energy, together with the u–v relationship of unitary (homogeneous) long rod penetration and an analytical model for predicting the depth of penetration has also been given for jacketed long rods penetrating semi-infinite targets in co-erosion mode. A new criterion for transition from bi-erosion to co-erosion is proposed. It transpires that the present model is in good agreement with the experimental observations for EN24 steel jacketed tungsten alloy long rods penetrating semi-infinite armor steel targets in terms of crater diameter and penetration depth.     

Penetration of a rigid projectile into a multi-layered target: theory and numerical computations

The main objective of the present work is to develop an adequate analytical model for penetration of multi-layered targets by rigid projectiles. The theoretical approach presented here generalizes the single-layer models described in [1] and [2]. As in [1] and [2] an analytical solution is developed for which the momentum equation is satisfied pointwise in the target region, while the boundary and continuity conditions are satisfied only approximately. Also, a single particular velocity field is assumed for all target layers. The predictions of the analytical solution are compared with numerical simulations obtained using the hydrocode Autodyn2D [3]. Attention is focused on two cases of a two-layered target: one consisting of materials which differ only by their hardnesses (yield strengths); and the other consisting of significantly different materials (RHA and Aluminum). The predictions of the analytical model are in reasonably good agreement with those of Autodyn2D for both cases, independently of whether the hard layer is first or second. It should also be mentioned that the computational time is reduced from several hours for Autodyn2D to only a few minutes for the analytical model.     

Experimental and numerical study on the orthogonal and oblique impact on water filled pipes

A 300 mm long piece of copper (ASTM B280) pipe with an outer diameter of 35 mm and 0.7 mm wall thickness was subjected to a rigid steel pipe impact under a drop weight loading configuration where the pipe was simply supported at its ends. Differences in deformation features for a pipe filled with water and an empty pipe were investigated for two configurations namely orthogonal and oblique impact. Compared to orthogonal pipe impact the oblique pipe impact has not been reported in the literature. It is hoped that current work would serve as a first step in this direction. Finite Element Method coupled with Smooth Particle Hydrodynamics (SPH) available in LS-DYNA was used to simulate the empty and water filled pipe impacts under orthogonal and oblique configurations respectively. Fluid structure interaction (FSI) during the water filled pipe impact was successfully modeled using SPH which is a simple method for predicting the short duration FSI events. Experimental results of the effect of varying D/T ratio on the empty and water filled pipes have been reported.     

A fresh look at the free flight dynamics of a spinning projectile

In the first part of the paper, several equations of motion by different groups of workers are critically examined. Exact equations of motion are then developed. This form is then quasi-linearised into a ballistic formulation. The geometrical motion of a spinning projectile, in the presence of a cubic restoring moment is analysed in the cross-flow plane. It is observed that the trajectories assume a cuspidal form at the lower and upper range of the travel, when the angular momentum parameter coincides with these points. In general, both steady and unsteady precessional motions are presented.     

The dependence of penetration velocity on impact velocity

Recent experimental measurements show that eroding long-rod penetration velocity is a linear function of impact velocity over a very wide range of impact velocities and for an interesting range of rod–target material combinations. These experiments all show that U=a+bV, where U and V are the penetration and impact velocity, respectively, and “a” and “b” are constants for given projectile and target materials. Numerical simulations also show that U=a+bV. The accumulation of these results suggests that a linear relationship between penetration and impact velocity may be fundamental over a very large range of impact velocities. A linear relationship between penetration and impact velocity has a number of implications. Some implications of this result for the Tate–Alekseevskii model are briefly examined in this paper.     

爆炸成型弹丸速度计算方法研究

从炸药装药的瞬时爆轰产物飞散理论出发,根据动量守恒原理得出药型罩装药形成爆炸成型弹丸的速度计算模型,并根据装药高度与 直径之比对弹丸速度的影响修正了计算模型。应用该计算模型计算了大锥角药形罩和球缺药型罩装药形成的爆炸成型弹丸速度,计算结果与实 验和数值模拟得到的结果吻合较好,此速度计算模型适合于工程应用。     

基于地磁测量的火箭弹滚转角解算误差补偿方法研究

为实现火箭弹弹道修正,需实时解算弹体的滚转角。根据地磁场基本特性,采用两轴磁传感器测量地磁场分量,并同时测量弹道倾角以解算弹体姿态角。提出一种火箭弹弹体滚转角解算的误差补偿方法,进行某型火箭弹打靶试验,利用该方法对火箭弹飞行试验过程中的姿态角数据进行实时解算,并与陀螺测量到的滚转角数据进行比较。试验结果表明:利用该方法解算滚转角准确度在4°以内,能够满足火箭弹弹道修正的要求。     

风致飞掷物冲击建筑浮法玻璃试验和数值模拟

通过试验和有限元数值模拟的方法研究风致飞掷物对建筑浮法玻璃的冲击破坏效应。首先进行钢球冲击浮法玻璃面板的破坏试验,然后基于LS-DYNA建立与试验对应的飞掷物冲击浮法玻璃有限元模型,并通过对比试验和数值模拟的结果验证有限元模型的可靠性。最后基于验证后的有限元模型,以板状飞掷物为代表,研究风致飞掷物的冲击位置、冲击姿态和外形等特性对其冲击效应的影响。结果表明,建筑浮法玻璃在风灾中非常容易受到飞掷物的冲击而破坏。采用JH-2作为浮法玻璃的本构模型并以SIGP1=75 MPa作为失效准则,能够较准确地模拟浮法玻璃在冲击荷载下的破坏特性。板状飞掷物的冲击位置对其冲击效应影响不大,但其冲击姿态和边厚比对冲击效应有较大的影响。     

空气夹层对含液结构在球形弹体侵彻作用下动态响应的影响

基于一维应力波理论对高强水中冲击波在不同介质间的传播进行分析,提出了2种防护含液结构的空气夹层形式,建立了数值仿真模型。在验证数值仿真方法的基础上,分析了含液结构在弹体侵彻过程中空穴演化、冲击波传播、空气夹层结构变形等的动态变化过程及弹体速度衰减规律,讨论了不同舱室结构在球形弹体侵彻作用下的冲击波特点和结构不同组成部分的能量转换关系,对比了不同弹速下前后板的塑性变形。研究结果表明:(1)在含液结构中添加空气夹层能有效降低含液结构前板和后板的冲量、能量和塑性变形;(2)空气夹层影响前后板变形的主要原因为阻抗失配和空气夹层变形引起的稀疏波及液体空化;(3)从整体看,双层间隔板结构衰减前后板变形能力优于方格夹层板结构,但随着弹速的增加,双层间隔夹层板的前后壁变形相互制约,2种结构对含液塑性变形的改变逐渐接近。     

圆锥-球缺药型罩聚能战斗部结构优化设计？

针对现代舰船抗爆炸与冲击能力的日益提升,提出了一种圆锥-球缺组合药型罩聚能战斗部在鱼雷上的应用,建立了该战斗部水中接触爆炸钢质靶板的力学物理模型,并通过试验对数值模拟结果进行了验证性研究。采用正交设计方法,设计了16种不同参数的圆锥-球缺聚能战斗部的结构,利用该模型进行了数值计算,得到了战斗部的最佳结构,为高效聚能战斗部的设计提供了理论依据。     

双层药型罩内罩开槽对EFP形成尾翼的影响？

为了研究内层药型罩周向对称开槽对爆炸成型弹丸（ EFP）形成尾翼的影响,利用LS-DYNA显示动力分析有限元程序,采用Lagrange算法,对双层药型罩聚能装药的成型过程进行数值模拟。对不同开槽参数的数值模拟结果进行对比分析,选择数值模拟最佳结果进行试验验证。数值模拟与试验研究所得结论基本吻合。结果表明：内层药型罩周向对称开槽结构能够形成带尾翼的串联EFP。当L/Da ＝0.20、W/Da ＝0.05时（ Da 为装药直径,L为开槽长度、W为开槽宽度）,前后EFP长径比最大,带尾翼的串联EFP的成型效果最佳。     

Finite element modeling of impact, damage evolution and penetration of thick-section composites

Impact, damage evolution and penetration of thick-section composites are investigated using explicit finite element (FE) analysis. A full 3D FE model of impact on thick-section composites is developed. The analysis includes initiation and progressive damage of the composite during impact and penetration over a wide range of impact velocities, i.e., from 50 m/s to 1000 m/s. Low velocity impact damage is modeled using a set of computational parameters determined through parametric simulation of quasi-static punch shear experiments. At intermediate and high impact velocities, complete penetration of the composite plate is predicted with higher residual velocities than experiments. This observation revealed that the penetration-erosion phenomenology is a function of post-damage material softening parameters, strain rate dependent parameters and erosion strain parameters. With the correct choice of these parameters, the finite element model accurately correlates with ballistic impact experiments. The validated FE model is then used to generate the time history of projectile velocity, displacement and penetration resistance force. Based on the experimental and computational results, the impact and penetration process is divided into two phases, i.e., short time Phase I - shock compression, and long time Phase II - penetration. Detailed damage and penetration mechanisms during these phases are presented.     

Experimental and numerical study of peculiarities at high-velocity interaction between a projectile and discrete bumpers

A high-velocity impact interaction of a polyethylene projectile (15 mm diameter) and aluminium projectile (6.35 mm diameter) with string and mesh bumpers (made of steel strings of 0.5–1.0 mm in diameter) was investigated experimentally and numerically. The study was aimed on detecting the projectile fragmentation peculiarities during projectile interaction with discrete bumpers. Since polyethylene has lower penetration resistance than aluminium, the effects inherent to discrete bumper penetration into the projectile must be more obvious for polyethylene. The string bumper is a set of parallel strings lying in a plane. The geometry of the string bumper which is simpler than the geometry of the mesh one also allowed one to get more understandable distribution of fragments on a thick aluminium witness-plate which was imposed behind the studied bumper to register the results of impact interaction for further analysis. The projectile velocity varied in the range of 1.7–3.8 km/s. The geometrical properties of such bumper-projectile system were characterized by two geometrical parameters: the parameter κ characterizing the bumper discreteness and equal to cell aperture-string diameter ratio, and the parameter ? defining the average number of cells falling within the projectile diameter.     

Simulation of perforation and penetration in metal matrix composite materials using coupled viscoplastic damage model

In the first part of the two companion papers, theoretical formulation of the multiscale micromechanical constitutive model that couples the anisotropic damage mechanism with the viscoplastic deformation is presented. In the second part of these companion papers the numerical simulation of the computational aspects of the theory are elaborated. The perforation and penetration problem of metal matrix composites (MMCs) due to high impact loading is simulated. In this sense, the computational aspects of the developed theory are elaborated here. First, the verification of the developed model is performed through its numerical implementation in order to test the model predictions of the material characteristic tests. This encompasses uniaxial monotonic loading and unloading under different strain rates, uniaxial cyclic loading, and uniaxial loading and relaxation. The verified material routine of the developed model is then implemented in the explicit finite element code ABAQUS via the user defined subroutine VUMAT at each integration point in order to analyze the projectile impact and penetration into laminated composite plates.     

Finite element analysis of projectile size and shape effects on the probabilistic penetration response of high strength fabrics

The effects of projectile characteristics on the probabilistic impact response of single-layer fully-clamped flexible woven fabrics is numerically studied using a yarn-level fabric model with a statistical implementation of yarn strengths. Six small and large sized spherical, cylindrical, and conical projectiles of the same mass are considered. Probabilistic velocity response curves which describe the probability of fabric penetration as a function of projectile impact velocity are generated for each projectile type through a series of forty impact simulations at varying impact velocities. The probabilistic fabric impact response is observed to be strongly dependent on the shape of the projectile’s impact face and the manner of projectile–yarn interactions at the impact site.