Simulation of natural fragmentation of rings cut from warheads

Natural fragmentation of warheads that detonates causes the casing of the warhead to split into various sized fragments through shear or radial fractures depending on the toughness,density,and grain size of the material.The best known formula for the prediction of the size distribution is the Mott formulae,which is further examined by Grady and Kipp by investigating more carefully the statistical most random way of portioning a given area into a number of entities.We examine the fragmentation behavior of radially expanding steel rings cut from a 25 mm warhead by using an in house smooth particle hydrodynamic(SPH) simulation code called REGULUS.Experimental results were compared with numerical results applying varying particle size and stochastic fracture strain.The numerically obtained number of fragments was consistent with experimental results.Increasing expansion velocity of the rings increases the number of fragments.Statistical variation of the material parameters influences the fragment characteristics,especially for low expansion velocities.A least square regression fit to the cumulative number of fragments by applying a generalized Mott distribution shows that the shape parameter is around 4 for the rings,which is in contrast to the Mott distribution with a shape parameter of 1/2.For initially polar distributed particles,we see signs of a bimodal cumulative fragment distribution.Adding statistical variation in material parameters of the fracture model causes the velocity numerical solutions to become less sensitive to changes in resolution for Cartesian distributed particles.     

Numerical simulation of the natural fragmentation of explosively loaded thick walled cylinders

The ability to predict the natural fragmentation of an explosively loaded metal casing would represent a significant achievement. Physically-based material models permit the use of small scale laboratory tests to characterise and validate their parameters. The model can then be directly employed to understand and design the system of interest and identify the experiments required for validation of the predictions across a wide area of the performance space. This is fundamentally different to the use of phenomenologically based material algorithms which require a much wider range of characterisation and validation tests to be able to predict a reduced area of the performance space. Eulerians numerical simulation methods are used to describe the fragmentation of thick walled EN24 steel cylinders filled with PBXN-109 explosive. The methodology to characterise the constitutive response of the material using the physically based Armstrong–Zerilli constitutive model and the Goldthorpe path dependent fracture model is described, and the results are presented. The ability of an Eulerian hydrocode to describe the fragmentation process and reproduce the experimentally observed fragment mass and velocity distributions is presented and discussed. Finally the suitability of the current experimental analysis methodology for simulation validation is addressed.     

圆柱形装药驱动轴向预制破片飞散特性

为了增强柱形战斗部轴向威力,在无壳柱形战斗部底面布置单层离散的预制破片。开展圆柱形TNT装药驱动轴向预制破片飞散试验,获得预制破片的最大初速、飞散角等特征参数;运用LS-DYNA软件对装药驱动预制破片过程进行数值模拟,阐述预制破片群飞散过程;对装药驱动整体平板理论计算公式进行改进,获得预制破片的最大初速。结果表明:破片初速理论计算结果、数值计算结果和试验结果吻合良好;随着与装药底部中心距离的加大,破片初速、径向飞散角分别近似呈“抛物线”减小、增大;试验实测、理论计算得到的破片最大初速值超过2500 m/s,试验实测的径向飞散角最大约为22°,而周向飞散角则普遍较小,均值在5°以内。     

Experimental and numerical study of the fragmentation of expanding warhead casings by using different numerical codes and solution techniques

There has been increasing interest in numerical simulations of fragmentation of expanding warheads in 3D. Accordingly there is a pressure on developers of leading commercial codes, such as LS-DYNA, AUTODYN and IMPETUS Afea, to implement the reliable fracture models and the efficient solution techniques. The applicability of the Johnson–Cook strength and fracture model is evaluated by comparing the fracture behaviour of an expanding steel casing of a warhead with experiments. The numerical codes and different numerical solution techniques, such as Eulerian, Lagrangian, Smooth particle hydrodynamics (SPH), and the corpuscular models recently implemented in IMPETUS Afea are compared. For the same solution techniques and material models we find that the codes give similar results. The SPH technique and the corpuscular technique are superior to the Eulerian technique and the Lagrangian technique (with erosion) when it is applied to materials that have fluid like behaviour such as the explosive and the tracer. The Eulerian technique gives much larger calculation time and both the Lagrangian and Eulerian techniques seem to give less agreement with our measurements. To more correctly simulate the fracture behaviours of the expanding steel casing, we applied that ductility decreases with strain rate. The phenomena may be explained by the realization of adiabatic shear bands. An implemented node splitting algorithm in IMPETUS Afea seems very promising.     

On the continued acceleration of bomb casing fragments following casing fracture

It has been said that, once a bomb casing has fractured, “detonation gases will then stream around the fragments or bypass them, and the acceleration process stops there.” However, while apparently copious gas flow through casing fractures indicates some pressure release, it is also an indication of significant gas drive pressure, post casing fracture. This paper shows two approaches to the problem of calculating the actual loss of drive. One presents first-order analytical calculations, in cylindrical geometry, of pressure loss to the inside surface of a fractured casing. The second shows the modelling of a selected example in the CTH code. Both approaches reveal that gas escape, while occurring at its own sound-speed relative to the adjacent casing fragments, has to compete with rapid radial expansion of the casing. Together with some historic experiments now publicly available, our calculations indicate that post-fracture casing fragment acceleration is, for most systems, unlikely to be reduced significantly.     

Strain rate dependency and fragmentation pattern of expanding warheads

For the characterization of the behaviors of a metal material in events like expanding warheads, it is necessary to know its strength and ductility at high strain rates, around 104e105/s. The flyer plate impact testing produces the uniform stress and strain rates but the testing is expensive. The Taylor test is relatively inexpensive but produces non-uniform stress and strain fields, and the results are not so easily inferred for material modeling. In the split-Hopkinson bar(SHB), which may be used in compression, tension and torsion testing, the strain rates never exceeds 103/s. In the present work, we use the expanding ring test where the strain rate is 104e105/s. A streak camera is used to examine the expanding ring velocity, and a water tank is used to collect the fragments. The experimental results are compared with the numerical simulations using the hydrocodes AUTODYN, IMPETUS Afea and a regularized smooth particle(RSPH) software. The number of fragments increases with the increase in the expansion velocity of the rings. The number of fragments is similar to the experimental results. The RSPH software shows much the same results as the AUTODYN where the Lagrangian solver is used for the ring. The IMPETUS Afea solver shows a somewhat different fragmentation characteristic due to the node splitting algorithm that induces pronounced tensile splitting.     

冲击波和高速破片联合作用下固支方板毁伤效应数值模拟

为探讨固支方形钢板结构在空爆冲击波和高速破片联合作用下的动态响应过程及变形破坏模式,利用有限元分析软件ANSYS/LS-DYNA,开展了空爆冲击波和高速破片对固支方板的联合作用数值模拟计算,阐述了固支方板在联合载荷作用下动态响应过程的2个阶段,以及在不同爆距下的变形破坏模式和特点。结果表明,随着爆距增加,在破片密集作用区内,钢板的破坏模式存在从集团冲塞破口到部分穿孔边界撕裂联通,再到无穿孔边界撕裂现象的转换。     

装药长径比对EFP成型作用效果影响分析

针对装药长径比对EFP成型的影响,基于一种球缺型药型罩EFP,利用ANSYS／LS-DYNA仿真软件对其成型过程进行建模仿真,研究EFP成型过程及其各项参数．在该基础上,改变装药高度得到不同的装药长径比数据,并对不同长径比EFP形成过程进行仿真,得到不同装药长径比EFP的速度、速度增长率及炸药能量利用率等数据,为选择最佳装药长径比提供依据．     

可变形定向破片战斗部模型试验和数值模拟研究

基于可变形定向破片战斗部的作用原理,设计了试验结构模型,并对其进行了静爆试验研究。根据试验结果,建立了有限元分析模型,利用LS-DYNA程序对可变形定向战斗部变形过程以及破片的飞散过程进行了数值模拟。结果表明,在目标方向破片密度和速度都有较大幅度增益,数值模拟与试验结果比较吻合。     

蒙特卡洛剖分投影法的爆震弹破片平均比动能评估

为了评估爆震弹封装壳体破片致死、致伤半径,并削弱其平均比动能,基于蒙特卡洛剖分投影法建立破片平均比动能计算模型。通过LS-DYNA及自编程联合仿真方法对爆震弹自然破片、半预制破片比动能计算模型进行仿真求解,获得了全破片全时域的质量分布、初始速度、垂直靶分布、平均比动能阈值及安全半径等指标。结果表明:在相同装药参数下,半预制破片相比于自然破片,质量分布、初始速度阈值更低且更集中;在小于等于2.5 m范围内半预制破片平均比动能阈值比自然破片更低,大于2.5 m后半预制破片平均比动能阈值比自然破片更高。相比于自然破片,采用半预制破片可显著减小爆震弹破片的致死半径,但并不能明显增大其安全半径。     

杀爆弹对主战坦克毁伤评估仿真

在全面分析杀爆弹对主战坦克毁伤效应的基础上，针对冲击波和破片对坦克外部件的毁伤，利用计算机仿真方法进行杀爆弹对主战坦克毁伤评估。利用射击线技术构建了杀爆弹对主战坦克毁伤评估模型；基于蒙特卡洛随机模拟试验法，开发了计算程序，进行了以破片杀伤为主的杀爆弹对主战坦克毁伤效应仿真评估，得到了车体命中破片数随炸点坐标变化规律，以及坦克整体毁伤概率随杀爆弹终点速度变化规律。研究结果为主战坦克目标易损性分析与毁伤评估提供了重要参考。     

Field test and probabilistic analysis of irregular steel debris casualty risks from a person-borne improvised explosive device

Person-borne improvised explosive devices (PBIEDs) are often used in terrorist attacks in Western countries. This study aims to predict the trajectories of PBIED fragments and the subsequent safety risks for people exposed to this hazard. An explosive field test with a typical PBIED composed of a plastic explosive charge and steel nut enhancements was performed to record initial fragment behaviour, including positions, velocity, and trajectory angles. These data were used to predict the full trajectory of PBIED fragments using a probabilistic analysis. In the probabilistic analyses a probability of fatality or serious injury was computed. Based on the results presented, many practical conclusions can be drawn, for instance, regarding safe evacuation distances if a person were exposed to a suspected PBIED.     

圆形减压环力学试验与壁厚对其耗能性能的影响

圆形减压环主要由钢管、铝管套筒和钢丝绳组成,由于其耗能特性强,因此在被动防护系统中得到了广泛应用。在边坡防护工程中,将钢丝绳一端固定,另一端连接在防护阻挡结构上,通过钢管与铝管套筒的摩擦和钢管的大变形来散耗冲击动能。首先分析了圆形减压环的工作原理,并对其力学性能进行了拟静力试验,再利用ANSYS/LS-DYNA软件,研究了圆形减压环在荷载作用下,不同钢管壁厚对其耗能性能的影响。结果表明：随着钢管壁厚的增加,圆形减压环的启动荷载也随之增大;在低速荷载作用下,钢管壁厚对圆形减压环的耗能性能影响较弱,但是随着加载速度的提高,钢管壁厚对其耗能性能的影响明显增加,耗能总量上升明显。     

Effect of the end cap on the fragment velocity distribution of a cylindrical cased charge

The prediction of the fragment velocity distribution of a cylindrical cased charge with end caps is one of the key issues to assess the damage efficiency of the warhead. However, limited work has been con-ducted to predict the fragment velocity distributions along the axis of cylindrical cased charges with end caps. This paper presents a study of the velocity distribution of fragments caused by the explosion of a cylindrical cased charge with end caps. The fragment velocity distribution and the end cap velocity were determined by an X-ray radiography method, and the axial fragment distribution was determined by witness plates. It was found that the velocities of fragments, especially near the edge, were increased when the end caps were added, and the position of maximum velocity is closer to the non-detonation end. The fragment velocities were increased, and the fragment projection range was decreased with the increase of the thickness of the end cap. A formula for fragment velocity distributions of a cylindrical cased charge with end caps, which is based on Huang's formula, was proposed by the theoretical analysis and data fitting and validated experimentally. The results indicate that the proposed formula is accurate in predicting the fragment velocity distribution along the axis of a cylindrical cased charge with end caps detonated at one end.     

横向运动板干扰聚能射流的数值模拟

基于有限元分析软件ANSYS/LS-DYNA和LS-PREPOST,用ALE算法对射流垂直侵彻横向运动防护板的过程进行模拟分析。防护板在不同速度下干扰射流时,对防护板和后效板上的开坑形状进行分析,并计算后效板上的最终侵深及射流轴线上的速度降,得到射流在横向防护板作用下后效板侵深及射流轴线上的速度降随防护板速度变化的曲线。结果表明,防护板抗射流侵彻能力随防护板速度的增加而增强,尤其是防护板横向速度在0～100m/s增加时,抗射流侵彻能力增强较为明显。     

基于FEM/SPH算法的弹丸侵彻土体数值模拟

基于有限元法(FEM)和光滑粒子流体动力学(SPH)结合的算法,用数值模拟了钢质弹丸对钢筒约束土体的侵彻过程。基于ANSYS/LS-DYNA显式动力分析和LS-PrePost后处理软件,形象再现了钢质弹丸冲击作用下土体飞溅形成漏斗坑和直线通道的物理过程。侵彻深度计算结果与实验数据吻合较好,钢质弹丸的速度和加速度时程曲线图与理论分析一致,体现了FEM/SPH算法的精确性。研究结果表明FEM/SPH算法在模拟侵彻土体方面具有可行性和有效性。     

薄壳结构跌落冲击仿真与试验研究

为了验证薄壳结构跌落冲击问题动态数值仿真的方法途径,设计制作了带有配重的薄壳结构,测定了材料主要力学性能,利用非线性有限元软件对该结构进行单次和累积结果的多次跌落冲击数值仿真,并进行了验证试验。对该结构的跌落冲击过程、典型位置的加速度响应、塑性变形的仿真、验证试验结果进行了对比分析,结果表明：采用的数值仿真方法和途径能够较好地研究分析薄壳结构的跌落冲击及其他同类问题。     

Numerical simulation study on penetration performance of depleted Uranium (DU) alloy fragments

Due to its high strength, high density, high hardness and good penetration capabilities, Depleted ura-nium alloys have already shined in armor-piercing projectiles. There should also be a lot of room for improvement in the application of fragment killing elements. Therefore, regarding the performance of the depleted uranium alloy to penetrate the target plate, further investigation is needed to analyze its advantages and disadvantages compared to tungsten alloy. To study the difference in penetration per-formance between depleted uranium alloy and tungsten alloy fragments,firstly, a theoretical analysis of the adiabatic shear sensitivity of DU and tungsten alloys was given from the perspective of material constitutive model. Then, taking the cylindrical fragment penetration target as the research object, the penetration process and velocity characteristics of the steel target plates penetrated by DU alloy frag-ment and tungsten alloy fragment were compared and analyzed, by using finite element software ANSYS/LS-DYNA and Lagrange algorithm. Lastly, the influence of different postures when impacting target and different fragment shapes on the penetration results is carried out in the research. The results show that in the penetration process of the DU and tungsten alloy fragments, the self-sharpening properties of the DU alloy can make the fragment head sharper and the penetrating ability enhance. Under the same conditions, the penetration capability of cylindrical fragment impacting target in vertical posture is better than that in horizontal posture, and the penetration capability of the spherical fragment is slightly better than that of cylindrical fragment.     

Influence of shaped charge structure parameters on the formation of linear explosively formed projectiles

The research of LEFP (linear explosive forming projectile) is of great value to the development of new warhead due to its excellent performance. To further improve the damage ability of the shaped charge warhead, a special shell overhanging structure was designed to increase the charge based on the traditional spherical charge, in which case the crushing energy of LEFP could be guaranteed. LS-DYNA was used to simulate different charge structures obtained by changing the number of detonation points, the length of shell platform, the radius of curvature and the thickness of liner. The RSM (response surface model) between the molding parameters of LEFP and the structural parameters of charge was established. Based on RSM model, the structure of shaped charge was optimized by using multi-objective genetic algorithm. Meanwhile, the formation process of jet was analyzed by pulsed X-ray photography. The results show that the velocity, length-diameter ratio and specific kinetic energy of the LEFP were closely related to the structural parameters of the shaped charge. After the optimization of charge structure, the forming effect and penetration ability of LEPP had been significantly improved. The experimental data of jet velocity and length were consistent with the numerical results, which verifies the reliability of the numerical results.     

Analysis on damage characteristics and detonation performance of solid rocket engine charge subjected to jet

To further explore the damage characteristics and impact response of the shaped charge to the solid rocket engine (SRE) in storage or transportation, protective armor was designed and the shelled charges model (SCM)/SRE with protective armor impacting by shaped charge tests were conducted. Air overpressures at 5 locations and axial acceleration caused by the explosion were measured, and the experimental results were compared with two air overpressure curves of propellant detonation obtained by related scholars. Afterwards, the finite element software AUTODYN was used to simulate the SCM impacted process and SRE detonation results. The penetration process and the formation cause of damage were analyzed. The detonation performance of TNT, reference propellant, and the propellant used in this experiment was compared. The axial acceleration caused by the explosion was also analyzed. By comprehensive comparison, the energy released by the detonation of this propellant is larger, and the HMX or Al particles contained in this propellant are more than the reference propellant, with a TNT equivalent of 1.168–1.196. Finally, advanced protection armor suggestions were proposed based on the theory of woven fabric rubber composite armor (WFRCA).