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.     

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.     

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.     

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.     

Characteristics structure analysis on debris cloud in the hypervelocity impact of disk projectile on thin plate

In this paper, the gauge points setting is introduced in the SPH simulation to analyze the debris cloud structure generated by the hypervelocity impact of disk projectile on thin plate. Compared with the experiments, more detailed information of the debris cloud structure can be classified from the numerical simulation. However, due to the solitary dispersion and overlap display of the particles in the SPH simulation, accurate comparison between numerical and experimental results is difficult to be performed. To track the velocity and spatial distribution of the particles in the debris cloud induced from disk and plate, gauge points are locally set in the single-layer profile in the SPH model. By analyzing the gauge points’ spatial coordinate and velocity, the location and velocity of characteristic points in the debris cloud are determined. The boundary of debris cloud is achieved, as well as the fragments distribution outside the main structure of debris cloud.     

Discriminating between the Weibull and log‐normal distributions

Log‐normal and Weibull distributions are the most popular distributions for modeling skewed data. In this paper, we consider the ratio of the maximized likelihood in choosing between the two distributions. The asymptotic distribution of the logarithm of the maximized likelihood ratio has been obtained. It is observed that the asymptotic distribution is independent of the unknown parameters. The asymptotic distribution has been used to determine the minimum sample size required to discriminate between two families of distributions for a user specified probability of correct selection. We perform some numerical experiments to observe how the asymptotic methods work for different sample sizes. It is observed that the asymptotic results work quite well even for small samples also. Two real data sets have been analyzed. © 2004 Wiley Periodicals, Inc. Naval Research Logistics, 2004     

Reaction degree of composition B explosive with multi-layered compound structure protection subjected to detonation loading

The explosive reaction degree and protection from explosions are concerns in the military field.In this work,the reaction degree of the composition B explosive was investigated experimentally.Multi-layered compound structures were used as barriers to weaken the blast loads.A comprehensive experiment using a high-speed camera and image processing techniques,side witness plates,and bottom witness plates was presented.Using the experimental fragment velocities,fragment piercing patterns,and damage characteristics,the reaction degree of the explosive impeded by different multi-layered com-pound structures could be precisely differentiated.Reaction parameters of the explosive obstructed by compound structures were obtained by theoretical analysis and numerical simulations.Unlike the common method in which the explosive reaction degree is only distinguished based on the initial pressure amplitude transmitted into the explosive,a following shock wave reflected from the side steel casing was also considered.Different detonation growth paths in the explosive formed.Therefore,all these shock wave propagation characteristics must be considered to analyze the explosive response impeded by compound structures.     

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。     

高超声速尖双锥流动高精度数值模拟

以25°/55°尖双锥外形的高超声速低焓层流流动模拟为例,对高阶加权紧致非线性格式模拟激波/边界层干扰流动的能力进行验证和确认。空间离散采用二阶MUSCL和三阶、五阶加权紧致非线性格式,时间离散采用二阶精度双时间步方法,通量函数采用混合Roe-Rusanov,AUSMPW+,Van Leer等,对比了不同精度空间离散格式对时间、网格收敛特性和通量函数耗散特性的影响。数值模拟结果表明采用高精度空间离散格式能在较疏的网格上获得收敛解,并能消除结果对通量函数的敏感性,但收敛需要推进更久的计算时间。数值模拟结果与实验测量结果吻合良好,满足工程精度要求。     

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.     

超空泡鱼雷有关流体动力分析

针对从理论上难以解析计算超空泡鱼雷流体动力的问题,阐述了一种超空泡鱼雷流体动力数值计算的简单而有效的方法,该算法具有计算量小、执行速度快的特点,数值计算的结果与试验结论吻合.同时,对超空泡高速鱼雷的有关控制力问题进行了分析.     

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。     

Study on energy release characteristics of reactive material casings under explosive loading

Reactive Materials (RMs), a new material with structural and energy release characteristics under shock-induced chemical reactions, are promising in extensive applications in national defense and military fields. They can increase the lethality of warheads due to their dual functionality. This paper focuses on the energy release characteristics of RM casings prepared by alloy melting and casting process under explosive loading. Explosion experiments of RM and conventional 2A12 aluminum alloy casings were conducted in free field to capture the explosive fireballs, temperature distribution, peak overpressure of the air shock wave and the fracture morphology of fragments of reactive material (RM) warhead casings by using high-speed camera, infrared thermal imager temperature and peak overpressure testing and scanning electron microscope. Results showed that an increase of both the fireball temperature and air shock wave were observed in all RM casings compared to conventional 2A12 aluminum ally casings. The RM casings can improve the peak overpressure of the air shock wave under explosion loading, though the results are different with different charge ratios. According to the energy release characteristics of the RM, increasing the thickness of RM casings will increase the peak overpressure of the near-field air shock wave, while reducing the thickness will increase the peak overpressure of the far-field air shock wave.     

雾化过程的多尺度仿真算法

提出了一种雾化过程多尺度仿真算法:对大块液团运动,采用流体体积法直接模拟;将与网格尺度相当或更小的液滴简化成粒子,采用一种基于虚网格的拉格朗日粒子法进行追踪;湍流运动采用了湍流动能单方程输运模型的大涡模拟。基于新算法开发了一套仿真程序,并对此程序进行了验证,对影响模型精度的重要参数进行了深入研究。采用该算法对单股射流的雾化过程进行了仿真,雾场的瞬态和统计特性分析表明,仿真结果与试验结果吻合较好。     

基于面元法的三维机翼数值设计

利用一种数值迭代方法设计出具有给定目标压力分布形式和环量及厚度分布的三维机翼.取一初始机翼,应用考虑尾涡衰减及卷曲的面元法计算三维机翼的流体动力性能,对机翼几何形状进行小的扰动并计算由此引起的压力变化,形成雅可比行列式,求解出几何修正因子以改变机翼几何形状,多次迭代后得到具有目标压力分布形式的机翼.再由给定的环量及厚度分布修改目标压力,重新设计机翼,最后得到符合设计要求的三维机翼.重点讨论了数值设计中尾涡模型、目标压力分布形式、几何控制点对设计结果的影响,及如何加快计算收敛.算例分析表明,设计方法收敛快速、有效可行,计及尾涡衰减及卷曲能够得到更准确的设计结果,目标压力分布形式和几何控制点的选取决定了设计机翼的光顺性.     

Spalart-Allmaras湍流模型在高超声速气动加热计算中的应用

将AUSM+格式与LU SGS隐式迭代相结合,采用一方程的Spalart Allmaras湍流模型和二阶迎风MUSCL格式,研究了火星"探路者号"实验模型在10马赫来流条件下的气动热问题。采用量热完全和热完全两种气体模型的计算结果与实验数据进行了比较。热完全气体模型模拟的热流分布规律与实验吻合较好,但是对分离区的热流估计过高。在网格合理划分,尤其是满足近壁面的网格分辨率要求的前提下,该方法能够合理反映高超声速流场除分离区以外的气动热特性。     

伪谱法模拟各向异性/非均匀介质中弹性波的传播

数值模拟一直是研究弹性波在复杂介质中传播问题的有效手段之一。各向异性问题和非均匀问题日益引起关注。伪谱法是近年来发展较快、建立在弹性波动方程基础上的一种数值模拟方法。它的主要特征是将波动方程中的空间微分变换成频域中的乘法运算 ,从而只需要较少的空间格点就可以得到较高的计算精度。介绍了伪谱法及其稳定性条件 ;编制了一个适合于小型工作站或者PC机的模拟地震波在二维各向异性均匀 /非均匀介质中传播的数值模拟程序 ,模拟了各向异性 /非均匀介质中弹性波传播理论 ,分析了裂纹以及各向异性界面对波传播的影响     

非结构网格上解二维Hamilton-Jacobi方程的自适应算法

提出了一种非结构网格上解Hamilton Jacobi方程的自适应局部加密方法。讨论了加密方法关键的一步:光滑度指标的确定,通过采取无振荡插值,得到了无振荡数值格式,典型算例表明,该方法只需增加少量的点和计算量却能够提高计算精度和对间断的分辨能力。     

杀伤战斗部破片定向飞散特性研究

研究了钢预制破片壳体在四种装药爆轰驱动下的飞散特性。求得了使破片飞行路径呈平行型的预制破片壳体的临界半径及相应的破片初始速度。     

五阶HWCNS格式在低速复杂流场中的应用

采用五阶精度显式HWCNS格式求解雷诺平均NS方程，利用多块对接结构网格技术，对30P-30N多段翼型进行网格收敛性研究，在不考虑转捩的情况下采用SA一方程湍流模型研究HWCNS格式与二阶精度MUSCL格式对该翼型压力分布和典型站位速度型的影响，并与实验结果进行对比分析。采用HWCNS格式和SA一方程湍流模型模拟梯形翼高升力构型低速复杂流场，通过对总体气动特性和压力分布的分析，探讨五阶精度显式HWCNS格式在低速复杂外形流动中的应用能力。