The influence of projectile hardness on ballistic performance

The ballistic performance of 17 penetrator materials, representing 5 distinct steel alloys treated to various hardnesses along with one tungsten alloy, has been investigated. Residual lengths and velocities, as well as the ballistic limit velocities, were determined experimentally for each of the alloy types for length-to-diameter (L/D) ratio 10 projectiles against finite-thick armor steel targets. The target thickness normalized by the projectile diameter (T/D) was 3.55. For some of the projectile types, a harder target, with the same thickness, was also used. It was found that the ballistic limit velocity decreases significantly when the projectile hardness exceeds that of the target. Numerical simulations are used to investigate some of the observed trends. It is shown that the residual projectile length is sensitive to projectile hardness; the numerical simulations reproduce this experimental observation. However, the observed trend in residual velocity as a function of projectile hardness is not reproduced in the numerical simulations unless a material model is invoked. It is assumed that the plastic work per unit volume is approximately a constant, that is, there is a trade off between strength and ductility. Using this model, the numerical simulations reproduce the experimentally observed trend.     

新型电磁发射拦截弹对钨合金长杆弹拦截效果的数值模拟

本文提出了一种新型电磁发射拦截弹,以拦截弹与钨合金长杆弹碰撞过程为例,使用LS-DYNA程序建立了拦截弹和钨合金长杆弹的三维有限元模型。在拦截弹对钨合金长杆弹的拦截效果问题上进行了数值模拟分析,并得出了不同着角和钨合金长杆弹运动速度对拦截效果影响的关系曲线,给出了拦截弹与钨合金长杆弹碰撞后的速度变化及状态改变情况,结果表明,拦截弹对钨合金长杆弹起到了较好的拦截作用,两者碰撞后,钨合金长杆弹对装甲车辆的穿甲效果明显降低。     

Computational algorithms and applications of element-free Galerkin methods for nonlocal damage models

In using complex material models, especially the strain-gradient-dependent damage models, the convergence of the finite element computation increasingly becomes a problem. Due to large strains in damaging elements the computation may often result in non-convergence. For the higher-order gradient plasticity the special element formulation would often be necessary, which causes additional difficulties in implementation and computations. In recent years, meshless methods have been developed as an alternative to the finite element method (FEM) and can overcome some known shortcomings of FEM. In the present paper an algorithm of element-free Galerkin (EFG) methods for strain-gradient based nonlocal damage models has been developed and used to simulate ductile material damage. The method provides a reliable and robust results for material failure with large damage zones. The strain gradient-dependent terms can be evaluated from the direct differentiation. The investigation confirms that the nonlocal damage model with element-free Galerkin method is suitable for computing the damage problems and predicting the size effects. With the help of the meshless method, material failure in specimens as well as the size effects are predicted accurately.     

Response sensitivity of material and geometric nonlinear force‐based Timoshenko frame elements

Response sensitivity is an essential component to understanding the complexity of material and geometric nonlinear finite element formulations of structural response. The direct differentiation method (DDM), a versatile approach to computing response sensitivity, requires differentiation of the equations that govern the state determination of an element and it produces accurate and efficient results. The DDM is applied to a force‐based element formulation that utilizes curvature‐shear‐based displacement interpolation (CSBDI) in its state determination for material and geometric nonlinearity in the basic system of the element. The response sensitivity equations are verified against finite difference computations, and a detailed example shows the effect of parameters that control flexure–shear interaction for a stress resultant plasticity model. The developed equations make the CSBDI force‐based element available for gradient‐based applications such as reliability and optimization where efficient computation of response sensitivities is necessary for convergence of gradient‐based search algorithms. Copyright © 2016 John Wiley & Sons, Ltd.     

Experimental study of morphology scaling of a projectile obliquely impacting into loose granular media

The morphology scaling of a spherical projectile obliquely impacting into loose granular media is experimentally investigated. The influences of projectile’s releasing distance, diameter and oblique impact angle are mainly considered. Based on the experimental results, four scaling laws are eventually proposed to describe the variations of the length, width, depth of impact crater and the penetration depth of projectile after impacting. We find that when the impact angle is larger than a critical value, these quantities all exhibit power law dependences on the releasing distance, diameter and impact angle of projectile, which are analogous to that obtained in other similar vertical impacting experiments. It is also observed that once the oblique impact angle exceeds this critical value, the tadpole-shaped impact crater may commonly evolve into an elliptical one. At small impact angles, we find that the scaling laws on both the width and the depth of impact crater are still valid, although the corresponding fitting exponents have slightly deviated from those values at larger impact angles. However, the length of crater and the penetration depth of projectile seem to no longer yield such proposed scaling laws, possibly due to the different physical mechanism induced by the rebounding movements of projectile at small impact angles.     

Disintegration behavior of metal rods subjected to hypervelocity impact

The disintegration behavior of projectile rods when impacting plates at velocities above 10 km/s is largely unexplored. Possible material responses include vaporization, melting, solid state phase changes, plastic flow, shear localization, and ductile and brittle tensile fracture. Two primary difficulties have prevented experimental studies of projectile response in this velocity regime, namely the lack of a technique for accelerating a projectile to velocities above 10 km/s, and the lack of a procedure for recovering the projectile remains after impact for examination. These difficulties were overcome recently by using an exploding foil technique to drive an impactor plate and by using a reverse ballistics test arrangement to allow projectile recovery. This paper describes this experimental procedure for investigating the disintegration behavior of projectile rods under hypervelocity impact conditions, presents preliminary results for steel, aluminum and lead, and discusses requirements for computational material response models.     

Oblique penetration of a rigid projectile into an elastic-plastic target

The main objective of the present work is to develop an approximate solution of the problem of oblique penetration of a rigid projectile into an elastic-plastic target of finite thickness. This is accomplished by generalizing the work on normal penetration reported in [1]. Here, an irrotational isochoric velocity field is considered that consists of three parts, each of which together satisfy the condition of impenetrability at the projectile's surface. The first part is associated with the longitudinal motion of the projectile, the second part with the transverse motion, and the third part with the projectile rotation in the plane defined by the initial longitudinal projectile velocity and the normal to the target surface. The target material is assumed to be incompressible and the target region is subdivided into an elastic region ahead of the projectile, and a rigid-plastic region near the projectile. Using the above potential velocity field, inertia effects are included and the linear momentum equation is solved exactly in the elastic region. In the plastic region, the linear momentum equation is integrated numerically along the instantaneous streamlines to determine the pressure field on the projectile surface. Then the decelerating force and moment applied to the projectile are solved numerically. The model developed here predicts the residual velocity, the ballistic limit, as well as the residual angle of obliquity. Moreover, this model is able to describe the phenomenon of ricochet. It is shown that the agreement of the theory with experiments is good even though no adjustable parameters are used. Also, a user-friendly computer program has been developed that is available for distribution along with a Users' Manual.     

Numerical modelling of normal impact on ceramic composite armours

In this paper, the penetration of ceramic targets backed by thin metallic plates when impacted by cylindrical projectiles is studied. To achieve this, a two-dimensional axisymmetric numerical analysis of the normal impact problem is performed. The macroscopic material behaviour in the zone of finely pulverized ceramic ahead of the penetrator is modelled by means of a constitutive model taking into account internal friction and volumetric expansion. The amount of comminution at the computational cells is evaluated through a damage evolution equation, and the yield stress is assumed to be a function of the hydrostatic pressure, internal friction and amount of comminution. For the metallic materials involved, an elasto-plastic behaviour with a rupture condition was considered. Moreover, an erosion condition was included as a limit situation when the ruptured material limits its role in the penetration process to purely inertial effects. In this way, a detailed picture of the penetration process of the target by the impacting projectile was obtained. Then, the results of the numerical analysis were compared with the experimental observations of the projectile-target interaction, previously made by Reijer by using a flash X-ray technique. Under certain conditions, remarkable agreement between computations and experiments is encountered, thus suggesting the adequacy of the main assumptions made in the numerical approach to the physical situation.     

Numerical modelling of the hydrodynamic ram phenomenon

Hydrodynamic ram (HRAM) is a phenomenon that occurs when a high-kinetic energy object penetrates a fluid-filled container. The projectile transfers its momentum and kinetic energy through the fluid to the surrounding structure, increasing the risk of catastrophic failure and excessive structural damage. This is of particular concern in the design of wing fuel tanks for aircraft since it has been identified as one of the important factors in aircraft vulnerability. In the present paper, the commercial finite-element code LS-DYNA has been used to simulate an HRAM event created by a steel spherical projectile impacting a water-filled aluminium square tube. Two different formulations (ALE and SPH) are employed to reproduce the event. Experimental tests which indicate the pressure at different points of the fluid, displacement of the walls and cavity evolution for different impact velocities are compared with the numerical results in order to assess the validity and accuracy of both ALE and SPH techniques in reproducing such a complex phenomenon.     

A material model to reproduce mixed‐mode fracture in concrete

This paper presents a material model to reproduce crack propagation in cement‐based material specimens under mixed‐mode loading. Its numerical formulation is based on the cohesive crack model, proposed by Hillerborg, and extended for the mixed‐mode case. This model is inspired by former works by Gálvez et al but implemented for its use in a finite element code at a material level, that is to say, at an integration point level. Among its main features, the model is able to predict the crack orientation and can reproduce the fracture behaviour under mixed‐mode fracture loading. In addition, several experimental results found in the literature are properly reproduced by the model.     

新型集成装甲对EFP侵彻性能的影响

根据平板装药和陶瓷复合装甲与爆炸成型弹丸（EFP）相互作用的原理，提出了新型集成装甲与EFP作用的计算模型；据此模型进行了EFP残余速度计算，证明了在相同面密度的新型集成装甲和陶瓷复合装甲防护下，EFP的残余速度有明显差异；根据该计算模型可进行集成装甲的优化和EFP的反装甲目标设计。     

弹头高速撞击的有限元分析

弹丸高速撞击是武器设计中的重要研究课题。本文系统地阐述了Lagr-ange有限元方法的守恒方程、本构方程。在空间上采用四节点二维等参元网格离散化,在时间积分上采用显式中心差分法,并引入了抗沙漏节点力来控制弹塑大变形中的沙漏现象,碰撞接触面采用Wilkins滑移面技术。计算结果表明有限元数值分析是高速撞击领域内较有效的工具之一。     

弹体高速侵彻陶瓷复合厚靶的计算模型研究

针对平头弹高速撞击陶瓷复合厚靶的问题,以集中质量法为基础并考虑靶体的内摩擦效应对Fellows模型加以改进,建立侵彻过程的理论计算模型并利用Matlab编程求得不同撞击速度下弹体侵彻复合靶体的侵彻深度,模型得到了试验结果和数值计算结果的验证。参数分析的结果表明,陶瓷厚度的增加可提高复合靶体的抗侵彻能力,但随着初始撞击速度的提高,弹体的侵彻深度增长曲线趋于平缓。     

冲击荷载下钢管混凝土柱模型力学性能试验研究

为研究冲击荷载下钢管混凝土柱（CFT）的力学性能，采用φ57mm轻气炮实验装置和技术，进行了8个钢管混凝土柱模型的冲击试验及模拟分析计算。测得了不同弹体冲击速度下试件表面的应变时程曲线，获取了试件破坏形态及残余变形，比较了不同弹体冲击速度、试件装夹部位、试件外包约束等因素的影响。结果表明，冲击荷载作用下试件残余变形、应变变化直接与弹体冲击速度有关；受弹体碰撞后，试件冲击端的残余变形最大；装夹部位设在试件中部更能真实的模拟试件受力的真实情况．外包碳纤维对试件的抗冲击性能有一定的改善，尤其是在横向变形较大的部位；钢管混凝土柱模型试件的应变量级很大，环境噪声影响较大，可采用大阻值和大量程应变片提高应变准确度。     

A method of computing numerically integrated stiffness matrices

A method of formulating and computing numerically integrated stiffness matrices is presented. Through a better organization of the formulation which is easily achieved by the use of index notation, the computations for integrating and evaluating the element stiffness matrix are substantially reduced. For cases in which the terms of the material property tensor are not functions of position co-ordinates (elastic isotropic and anisotropic materials), a further reduction in computation is achieved by multiplying the material property-tensor after the numerical integration has been carried out.     

不同弹头形式的易碎弹冲击航空有机玻璃的数值分析

利用霍普金森杆(SHPB)实验方法,针对由金属与硫混合而成的易碎弹复合材料及某航空有机玻璃材料,测得了不同应变率下两种材料的动态力学参数。根据实验数据拟合给出易碎弹与航空有机玻璃材料的Johnson-cook强度模型参数,并对参数进行数值仿真验证。在此基础上,利用AUTODYN-3D有限元程序,对具有不同弹头形式的易碎弹冲击航空有机玻璃全过程进行数值模拟,通过对比子弹的破碎效果及对航空有机玻璃的毁伤效果,分析总结了相关规律。结果表明:该复合材料具有较好的易碎效果;空尖易碎弹的破碎效果优于普通易碎弹,并且对航空有机玻璃的毁伤效果逊色于普通易碎弹,更加符合实际应用。     

Linear systems approach to simulation of optical diffraction

The diffractive processes within an optical system can be simulated by computer to compute the diffraction-altered electric-field distribution at the output of the system from the electric-field distribution at the input. In the paraxial approximation the system can be described by an ABCD ray matrix whose elements in turn can be used to simplify the computation such that only a single computational step is required. We describe two rearrangements of such computations that allow the simulation to be expressed in a linear systems formulation, in particular using the fast-Fourier-transform algorithm. We investigate the sampling requirements for the kernel-modifying function or chirp that arises. We also use the special properties of the chirp to determine the spreading imposed by the diffraction. This knowledge can be used to reduce the computation if only a limited region of either the input or the output is of interest.     

高速弹丸撞击1420铝合金过程数值模拟

利用有限差分方法模拟了GCr15钢弹丸高速撞击1420铝合金半无限厚靶过程,结果表明,弹丸前方材料向前方运动,而后方材料则经历减速过程甚至出现反应运动,导致自由表面的突起,弹丸前端最大压应力达到10^10Pa数量级,应力和应变在弹孔周围的分布极不均匀,越靠近弹孔处越大,随着弹丸的深入,弹丸周围的塑变加大。     

圆柱形长杆超高速正碰撞薄板结构破碎效应

超高速碰撞多层板结构破碎效应研究对空间碎片防护及动能武器毁伤效应研究有着重要意义。采用ANSYS/AUTODYN程序的SPH方法,对超高速碰撞碎片云的形成过程进行了数值模拟,某典型时刻一次及二次碎片云形貌的数值模拟结果与实验结果吻合较好,验证了计算方法和模型参数的正确性。在此基础上采用数值模拟方法,对钨合金、轧制均质装甲(Rolled Homogeneous Armor,RHA)及LY12铝三种材料的圆柱形弹体超高速碰撞薄板的破碎规律进行了研究,基于量纲分析方法得出了弹体破碎长度随弹靶材料特性、弹靶尺寸及初始撞击速度变化的关系式。并研究了钨合金及RHA两种材料的长杆弹对八层RHA板结构的超高速碰撞效应。     

The effect of geometric scale on impact induced fragmentation, and its application to the design of dual plate armor

An analysis is presented which predicts that, for a fixed impact velocity, impact induced fragmentation becomes more severe as geometric scale increases. Test data is presented which supports this prediction, and which allows calculation of material dependent coefficients. The analysis was based on a minimization with respect to radius, for an expanding body, of a total energy density term (expansion kinetic energy per unit volume plus surface energy per unit volume). The test configuration was a steel sphere impacting an aluminum plate, with fragmentation recorded by a stack of spaced witness panels. The tests were run at full and half scale. Correlation between testing and analysis was achieved for the number of fragments perforating the front witness panel when a term analogous to a threshold energy was introduced. While the fragment count showed a dependence on geometric scale, the relative depth of penetration (number of witness panels perforated) did not. This suggested that the targets were fragmented, but that the projectile remained in one piece. A reduction in penetration depth with increasing impact velocity was seen, and was attributed to increased projectile deformation. For cases where the projectile would fragment (for example, if a harder target material were used), the effect of geometric scale on the performance of dual plate armor is predicted by analysis. The prediction is that, for impact velocities where projectile breakup at the outer plate of dual plate armor is a factor, the armor required to stop a large scale projectile can be lighter, on a relative basis, than the armor required to stop a small scale projectile.