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.     

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.     

An efficient SPH methodology for modelling mechanical characteristics of particulate composites

Particulate composites are one of the widely used materials in producing numerous state-of-the-art components in biomedical, automobile, aerospace including defence technology. Variety of modelling techniques have been adopted in the past to model mechanical behaviour of particulate composites. Due to their favourable properties, particle-based methods provide a convenient platform to model failure or fracture of these composites. Smooth particle hydrodynamics (SPH) is one of such methods which demonstrate excellent potential for modelling failure or fracture of particulate composites in a Lagrangian setting. One of the major challenges in using SPH method for modelling composite materials depends on accurate and efficient way to treat interface and boundary conditions. In this paper, a master-slave method based multi-freedom constraints is proposed to impose essential boundary conditions and interfacial displacement constraints in modelling mechanical behaviour of composite materials using SPH method. The proposed methodology enforces the above constraints more accurately and requires only smaller condition number for system stiffness matrix than the procedures based on typical penalty function approach. A minimum cut-off value-based error criteria is employed to improve the compu-tational efficiency of the proposed methodology. In addition, the proposed method is further enhanced by adopting a modified numerical interpolation scheme along the boundary to increase the accuracy and computational efficiency. The numerical examples demonstrate that the proposed master-slave approach yields better accuracy in enforcing displacement constraints and requires approximately the same computational time as that of penalty method.     

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.     

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.     

SPH算法在超高速碰撞数值模拟中的应用

采用大型动力学软件Ls-dyna中的SPH求解器,对球形弹丸超高速碰撞靶板的过程进行数值模拟。给出由于碰撞速度不同,而引起的不同的碎片云图像,以及不同的靶板破碎孔的尺寸。同时模拟了入射角度不同,而得到不同的超高速碰撞物理过程。初步分析结果表明数值模拟结果是合理的,较清晰地模拟了超高速碰撞下碎片云的生成、膨胀过程。另外,通过数值模拟结果与实验结果的比较分析,表明SPH方法得到的结果能描述相应的超高速碰撞现象。所以采用SPH算法针对超高速碰撞物理过程进行数值模拟是可行的。     

Rayleigh-Taylor不稳定性的SPH模拟

采用SPH方法模拟了流体界面的Rayleigh Taylor不稳定性,给出了界面初始扰动的发展过程,得到了蘑菇状的扰动图像,并对两种不同初始分布的扰动过程进行了比较。分析表明,计算结果合理,SPH方法适合于界面不稳定性的模拟。     

改进的接触算法及其在光滑粒子流体动力学中的应用

采用以黎曼解描述粒子间相互作用的接触算法,模拟一维情况下包含间断的流场。在弱间断的条件下,采用弱波近似的黎曼解来描述粒子间的相互作用;在强间断的条件下,则引入非迭代黎曼解来描述粒子间的相互作用。并引入Taylor展开思想,提高了接触算法在自由边界的计算精度。该算法无需引入人为粘性,程序结构简洁。数值计算表明,改进后的接触算法能很好地描述强间断,并有效改善了原始接触算法在自由面的计算缺陷。     

Experimental and numerical study of the blast wave decrease using sandwich panel by granular materials core

Among the intrinsic properties of some materials, e.g., foams, porous materials, and granular materials, are their ability to mitigate shock waves. This paper investigated shock wave mitigation by a sandwich panel with a granular core. Numerical simulations and experimental tests were performed using Autodyn hydro-code software and a shock tube, respectively. The smoothed particle hydrodynamics (SPH) method was used to model granular materials. Sawdust and pumice, whose properties were determined by several compression tests, were used as granular materials in the sandwich panel core. These granular materials possess many mechanisms, including compacting (e.g., sawdust) and crushing (e.g., pumice) that mitigate shock/blast wave. The results indicated the ineffectiveness of using a core with low thickness, yet it was demonstrated to be effective with high thickness. Low-thickness pumice yielded better results for wave mitigation. The use of these materials with a core with appropriate core reduces up to 88% of the shock wave. The results of the experiments and numerical simulations were compared, suggesting a good agreement between the two. This indicates the accuracy of simulation and the ability of the SPH method to modeling granular material under shock loading. The effects of grain size and the coefficient of friction between grains have also been investigated using simulation, implying that increasing the grain size and coefficient of friction between grains both reduce overpressure.     

Evaluation of effectiveness of polymer coatings in reducing blast-induced deformation of steel plates

Incorporating elastomers such as polymers in protective structures to withstand high energetic dynamic loads, has gained significant interest. The main objective of this study is to investigate the influence of a Polyurea coating towards the blast-induced response in steel plates. As such, Polyurea coated steel plates were tested under near-field blast loads, produced by the detonation of 1 kg of spherical nitromethane charges, at a standoff distance of 150 mm. Mild steel (XLERPLATE 350) and high-strength steel (BIS80) plates with thicknesses of 10 mm were Polyurea coated with thicknesses of 6 mm and 12 mm on either the front (facing the charge) or the back face. The deformation profiles were measured using 3D scanning. Numerical simulations were performed using the non-linear finite element code LS-DYNA. The strain-dependent behaviour of the steel and Polyurea were represented by Johnson-cook and Money-Rivlin constitutive models, respectively. The numerical models were validated by comparing the plate deflection results obtained from the experiments and were then used in the subsequent parametric study to investigate the optimum thickness of the Polyurea coating. The results indicate that back face coating contributes towards an approximately 20% reduction in the residual deformation as well as the absence of melting of the Polyurea layer, while the front-face coating can be used a means of providing additional standoff distance to the steel plates.     

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。     

“9·11”世贸大楼坍塌原因数值分析

数值分析表明,"9·11"恐怖袭击事件造成纽约世贸大楼的内部竖向承重钢结构的防火保护层在爆炸中严重脱落,火灾高温使钢材强度大幅度降低,导致着火层群柱失稳,上部巨大的冲击荷载把下层柱逐层压渍,引发连续坍塌.最后对超高层建筑的结构设计提出建议.     

A combination of Lagrangian relaxation and column generation for order batching in steelmaking and continuous‐casting production

This article considers the order batching problem in steelmaking and continuous‐casting production. The problem is to jointly specify the slabs needed to satisfy each customer order and group all the slabs of different customer orders into production batches. A novel mixed integer programming model is formulated for the problem. Through relaxing the order assignment constraints, a Lagrangian relaxation model is then obtained. By exploiting the relationship between Lagrangian relaxation and column generation, we develop a combined algorithm that contains nested double loops. At the inner loop, the subgradient method is applied for approximating the Lagrangian dual problem and pricing out columns of the master problem corresponding to the linear dual form of the Lagrangian dual problem. At the outer loop, column generation is employed to solve the master problem exactly and adjust Lagrangian multipliers. Computational experiments are carried out using real data collected from a large steel company, as well as on large‐scaled problem instances randomly generated. The results demonstrate that the combined algorithm can obtain tighter lower bound and higher quality solution within an acceptable computation time as compared to the conventional Lagrangian relaxation algorithm. © 2011 Wiley Periodicals, Inc. Naval Research Logistics, 2011     

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.     

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.     

Numerical simulation of warhead transportation

The new numerical approach for analysis of the warhead transportations is suggested.This approach allows to control the warhead operability before its experimental analysis.The approach is implemented by the adequate models for the software ANSYS.Analysis of the loads at land operations and trans-portations of the warhead by natural roads,water and aviation allows to obtain the maximal values of loads,which are used in numerical simulations of the warhead.These loads give an opportunity to analyze the operability and the fatigue strength of the cartridge warhead.The numerical simulations of the attachments of the warhead combat elements are performed on the basis of the suggested method.The data of the numerical simulations verifies the operability of the fastener system of the warhead combat elements.     

Microstructure and corrosion behaviour of gas tungsten arc welds of maraging steel

Superior properties of maraging steels make them suitable for the fabrication of components used for military applications like missile covering, rocket motor casing and ship hulls. Welding is the main process for fabrication of these components, while the maraging steels can be fusion welded using gas tungsten arc welding(GTAW) process. All these fabricated components require longer storage life and a major problem in welds is susceptible to stress corrosion cracking(SCC). The present study is aimed at studying the SCC behaviour of MDN 250(18% Ni) steel and its welds with respect to microstructural changes. In the present study, 5.2 mm thick sheets made of MDN 250 steel in the solution annealed condition was welded using GTAW process. Post-weld heat treatments of direct ageing(480 C for 3 h), solutionizing(815 C for 1 h) followed by ageing and homogenizing(1150 C for 1 h) followed by ageing were carried out. A mixture of martensite and austenite was observed in the microstructure of the fusion zone of solutionized and direct aged welds and only martensite in as-welded condition. Homogenization and ageing treatment have eliminated reverted austenite and elemental segregation. Homogenized welds also exhibited a marginal improvement in the corrosion resistance compared to those in the as-welded, solutionized and aged condition. Constant load SCC test data clearly revealed that the failure time of homogenized weld is much longer compared to other post weld treatments, and the homogenization treatment is recommended to improve the SCC life of GTA welds of MDN 250 Maraging steel.     

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.     

SPH数值模拟中固壁边界的一种处理方法

在光滑粒子流体动力学 (SPH)数值模拟中尝试了一种处理固壁边界的边界力方法 ,给出了一种新的边界力形式。利用SPH方法及边界力方法对水坝坍塌和涌波进入静止水塘这两个自由表面流动问题作了数值模拟。数值模拟结果表明 ,在SPH计算中使用本文所给边界力处理固壁是行之有效的