Deformation,fragmentation and acceleration of a controlled fragmentation charge casing

Two different finite element software, LS-DYNA and Impetus, have been evaluated to test their ability to predict the deformation, fragmentation and acceleration of a controlled fragmentation charge casing. The general-purpose program LS-DYNA was used with a multi-material ALE formulation and a mass-preserving erosion criterion coupled to a Johnson-Cook fracture criterion. In the Impetus simulations, a third order Lagrangian element formulation was used for the casing and a node-splitting element erosion treatment coupled to a Cockcroft-Latham failure criterion was used to describe casing fracture. The high-explosive gases were described by a discrete particle formalism.In order to acquire data to validate our computational tools and constitutive models, a series of experiments have been performed using a laboratory charge with an internal grooved casing. In the test series, the charge geometry was fixed except that the groove depth were varied from very shallow to very deep resulting in different deformation patterns, fracture modes and terminal velocities. Various diagnostic tools captured the different stages of the expansion and fragmentation of the casing. A high-speed framing camera depicted the deformation pattern before fragmentation and was used to determine the moment when the casing failed. Three different complementary techniques were used to follow the acceleration of the fragments; a Photon Doppler velocimetry to determine the initial acceleration of the casing, double exposed radiographs to estimate the fragment velocity after break-up and a high-speed video to determine the terminal velocity of the fragment after leaving the fireball. In addition, the fragments were soft recovered in a set of sawdust pit tests and their final shape and weight were measured. A SEM was used to characterise the fracture surfaces and to determine the modus of fracture (tensile or shear failure).Comparisons to experiments show that both software can predict the change in deformation behaviour when the groove depth increases, from tangential necking for shallow grooves to radial punching for deep groves. Both software could also reasonable well predict the acceleration of the fragments, though both overestimates the terminal velocity for the charge with the deepest grooves.     

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。     

Numerical study on the case effect of a bomb air explosion

When considering the bomb explosion damage effect, the air shock wave and high-speed fragments of the bomb case are two major threats. In experiments, the air shock wave was studied by the bare ex-plosives superseding the real cased bomb; in contrast, the bomb case influence was ignored to reduce risk. The air explosion simulations of the MK84 warhead with and without the case were conducted. The numerical simulation results showed that the bomb case significantly influenced the shock wave generated by the bomb: the spatial distribution of shock wave in the near field changed, and the peak value of shock wave was reduced. Breakage of the case and kinetic energy of the fragmentation consumed 3 and 38% of the explosion energy, respectively. The increasing factors of the peak over-pressure induced by the bare explosive on the ground and in the air were 1.43-3.04 and 1.37-1.57, respectively. Four typical stages of case breakage were defined. The mass distribution of the fragments follows the Mott distribution. The initial velocity distribution of the fragments agreed well with the Gurney equation.     

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.     

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.     

破片对反辐射导弹战斗部毁伤效能仿真

分析了“哈姆”反辐射导弹目标特性及破片对其毁伤模式,建立了破片对反辐射导弹战斗部毁伤效能模型,研究了不同质量破片对反辐射导弹战斗部的穿透能力和引爆能力。仿真及试验结果表明：单枚破片质量为15g,速度在1700m/s以上,就足以对反辐射导弹战斗部达到解体性毁伤,它为未来反导弹药战斗部设计提供了重要参考。     

Fracture mechanism of a cylindrical shell cut by circumferential detonation collision

The failure mechanism of a cylindrical shell cut into fragments by circumferential detonation collision was experimentally and numerically investigated. A self-designed detonation wave regulator was used to control the detonation and cut the shell. It was found that the self-designed regulator controlled the fragment shape. The macrostructure and micro-characteristics of fragments revealed that shear fracture was a prior mechanism, the shell fractured not only at the position of detonation collision, but the crack also penetrated the shell at the first contact position of the Chapmen-Jouguet (C-J) wave. The effects of groove number and outer layer thickness on the fracture behavior were tested by simulations. When the thickness of the outer layer was 5–18 mm, it has little effect on fragmentation of the shell, and shells all fractured at similar positions. The increase of the groove number reduced the fracture possibility of the first contact position of the C-J wave. When the groove number reached 7 with a 10 mm outer layer (1/4 model), the fracture only occurred at the position of detonation collision and the fragment width rebounded.     

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。     

某型火箭弹对巡航导弹毁伤概率仿真分析

通过对巡航导弹目标特性分析,论述了目标易损性和毁伤机理(包括破片战斗部对目标的击穿概率模型)。利用破片初速及存速计算模型,分析了战斗部爆破后破片速度衰减规律,并做了模拟仿真,为火箭弹战斗部设计及毁伤效能评估提供了理论依据。最后根据射弹散布规律及毁伤原理建立了毁伤模型,并以某型火箭弹为例,对毁伤概率模型进行了仿真分析。仿真结果表明:该方法为火箭弹战斗部设计和提高对巡航导弹毁伤概率提供了参考。     

随动定向战斗部破片飞散特性研究

针对防空导弹常规破片式杀伤战斗部使用中存在能量利用率低的缺陷,提出采用随动定向战斗部的观点。建立随动定向战斗部的破片动态飞散区和飞散速度的计算模型,采用数值解析方法,解决在复杂弹目交会条件下破片的飞散区域与打击速度的计算问题．并用MATLAB软件对建立的模型进行验证,得出仿真结果与实际结果一致,这表明模型是合理、正确的。     

Effect of tool rotational speed on the particle distribution in friction stir welding of AA6092/17.5 SiCp-T6 composite plates and its consequences on the mechanical property of the joint

This study investigates the effect of tool rotational speed (TRS) on particle distribution in nugget zone (NZ) through quantitative approach and its consequences on the mechanical property of friction stir welded joints of AA6092/17.5 SiC_p-T6 composite. 6 mm thick plates are welded at a constant tool tilt angle of 2° and tool traverse speed of 1 mm/s by varying the TRS at 1000 rpm, 1500 rpm and 2000 rpm with a taper pin profiled tool. Microstructure analysis shows large quantity of uniformly shaped smaller size SiC particle with lower average particle area which are homogeneously distributed in the NZ. The fragmentation of bigger size particles has been observed because of abrading action of the hard tool and resulting shearing effect and severe stress generation due to the rotation of tool. The particles occupy maximum area in the matrix compared to that of the base material (BM) due to the redistribution of broken particles as an effect of TRS. The migration of particles towards the TMAZ-NZ transition zone has been also encountered at higher TRS (2000 rpm). The microhardness analysis depicts variation in average hardness from top to bottom of the NZ, minimum for 1500 rpm and maximum for 2000 rpm. The impact strength at 1000 rpm and 1500 rpm remains close to that of BM (21.6 J) while 2000 rpm shows the accountable reduction. The maximum joint efficiency has been achieved at 1500 rpm (84%) and minimum at 1000 rpm (68%) under tensile loading. Fractographic analysis shows mixed mode of failure for BM, 1000 rpm and 1500 rpm, whereas 2000 rpm shows the brittle mode of failure.     

Force chains based mesoscale simulation on the dynamic response of Al-PTFE granular composites

Force chains based mesoscale simulation is conducted to investigate the response behavior of aluminum-polytetrafluoroethylene (Al-PTFE) granular composites under a low-velocity impact. A two-dimensional model followed the randomly normal distribution of real Al particles size is developed. The dynamic compressive process of Al-PTFE composites with varied Al mass fraction is simulated and validated against the experiments. The results indicate that, force chains behavior governed by the number and the size of agglomerated Al particles, significantly affects the impact response of the material. The failure mode of the material evolves from shear failure of matrix to debonding failure of particles with increasing density. A high crack area of the material is critical mechanism to arouse the initiation re-action. The damage maintained by force chains during large plastic strain builds up more local stresses concentration to enhance a possible reaction performance. In addition, simulation is performed with identical mass fraction but various Al size distribution to explore the effects of size centralization and dispersion on the mechanical properties of materials. It is found that smaller sized Al particle of com-posites are more preferred than its bulky material in ultimate strength. Increasing dispersed degree is facilitated to create stable force chains in samples with comparable particle number. The simulation studies provide further insights into the plastic deformation, failure mechanism, and possible energy release capacity for Al-PTFE composites, which is helpful for further design and application of reactive materials.     

不同网栅结构对MEFP成型影响的对比分析

为了研究不同形状网栅结构对形成的MEFP破片的影响,利用LS-DYNA动力有限元程序,采用Lagrangian方法,分别对十字形网栅切割式MEFP战斗部、星形线形网栅切割式MEFP战斗部、中心圆环形网栅切割式MEFP战斗部、井字形网栅切割式MEFP战斗部成型过程进行了数值模拟研究,并对影响各自破片成型及发散角的因素进行了分析研究。通过对不同方案网栅切割式MEFP速度及散布面积对比分析,结果表明:采用井字形网栅产生的破片集聚性优于十字形、星形线形和中心圆环形结构方案。     

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.     

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。     

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.     

Research on the intermediate phase of 40CrMnSiB steel shell under different heat treatments

In this study, 40CrMnSiB steel cylindrical shells were tempered at 350, 500 and 600 ℃ to study the effect of tempering temperature on the dynamic process of expansion and fracture of the metal shell. A mid-explosion recovery experiment for the metal cylinder under internal explosive loading was designed, and the wreckage of the casings at the intermediate phase was obtained. The effects of different tempering temperatures on the macroscopic and microscopic fracture characteristics of 40CrMnSiB steel were studied. The influence of tempering temperatures on the fracture characteristic parameters of the recovered wreckage were measured and analyzed, including the circumferential divide size, the thick-ness and the number of the circumferential divisions. The results show that as the tempering temper-ature was increased from 350 to 600 ℃, at first, the degree of fragmentation and the fracture characteristic parameters of the recovered wreckage changed significantly and then became essentially consistent. Scanning electron microscopy analysis revealed flow-like structure characteristics caused by adiabatic shear on different fracture surfaces. At the detonation initiation end of the casing, fracturing was formed by tearing along the crack, which existed a distance from the initiation end and propagated along the axis direction. In contrast, the fracturing near the middle position consists of a plurality of radial shear fracture units. The amount of alloy carbide that was precipitated during the tempering process increased continuously with tempering temperature, leading to an increasing number of spherical carbide particles scattered around the fracture surface.     

Fragment spatial distribution of prismatic casing under internal explosive loading

Non-cylindrical casings filled with explosives have undergone rapid development in warhead design and explosion control. The fragment spatial distribution of prismatic casings is more complex than that of traditional cylindrical casings. In this study, numerical and experimental investigations into the fragment spatial distribution of a prismatic casing were conducted. A new numerical method, which adds the Lagrangian marker points to the Eulerian grid, was proposed to track the multi-material interfaces and material dynamic fractures. Physical quantity mappings between the Lagrangian marker points and Eulerian grid were achieved by their topological relationship. Thereafter, the fragment spatial distributions of the prismatic casing with different fragment sizes, fragment shapes, and casing geometries were obtained using the numerical method. Moreover, fragment spatial distribution experiments were conducted on the prismatic casing with different fragment sizes and shapes, and the experimental data were compared with the numerical results. The effects of the fragment and casing geometry on the fragment spatial distributions were determined by analyzing the numerical results and experimental data. Finally, a formula including the casing geometry parameters was fitted to predict the fragment spatial distribution of the prismatic casing under internal explosive loading.     

Real-time calculation of fragment velocity for cylindrical warheads

To simulate explosion fragments, it is necessary to predict many variables such as fragment velocity, size distribution and projection angle. For active protection systems these predictions need to be made very quickly, before the weapon hits the target. Fast predictions also need to be made in real time simulations when the impact of many different computer models need to be assessed. The research presented in this paper focuses on creating a fast and accurate estimate of one of these variables - the initial fragment velocity. The Gurney equation was the first equation to calculate initial fragment velocity. This equation, sometimes with modifications, is still used today where finite element analysis or complex mathematical approaches are considered too computationally expensive. This paper enhances and improves Breech’s two-dimensional Gurney equation using available empirical data and the principals of conservation of momentum and energy. The results are computationally quick, providing improved accuracy for estimating initial fragment velocity. This will allow the developed model to be available for real-time simulation and fast computation, with improved accuracy when compared to existing approaches.     

双球破片冲击柱壳装药的临界起爆条件

为了研究导弹战斗部(柱壳装药)在破片场中的累积毁伤问题,在现有单破片起爆平板装药的Jacobs-Roslund经验准则的基础上,分别建立了考虑破片尺寸、破片撞击角度、柱壳装药的装药半径和壳体厚度的单球破片、双球破片冲击柱壳装药临界起爆条件的工程分析模型.该模型计算结果与数值模拟结果和现有试验结果相吻,证明利用该模型能较...