Normal impact of truncated oval-nosed projectiles on stiffened plates

The objective of this paper is to investigate the perforation capability of projectiles against stiffened plates and to determine how many stiffened plates can be perforated by projectiles. Some important experimental results on the perforation of stiffened plates, of a variety of configurations, by truncated oval-nosed projectiles at normal impact are introduced. A four-stage analytical model is formulated for the dynamic perforation of stiffened plates by rigid projectiles. By adopting an energy method, the model can be used to predict accurately the residual velocity of the projectiles. Numerical simulations have been performed for projectiles against single and layered plates adopted in the experiments. The perforation process is explored and deformation and failure modes are obtained. Good agreement is obtained between the numerical simulations, theoretical predictions and experimental results.     

Direct force measurement in normal and oblique impact of plates by projectiles

An experimental investigation of the forces produced by the penetration and perforation of thin aluminum and steel plates by cylindro-conical and hemispherically-tipped projectiles at 0, 15, 30 and 45° angles of incidence has been performed. Additionally, force histories were recorded for normal impact on Lexan, nylon and ceramic targets by conically-tipped strikers. Similar tests on Kevlar were not successful owing to the generation of voltages by rubbing of fibers that completely overwhelmed the transducer signal. A piezoelectric crystal bonded to the tail of the 12.7 mm diameter, 30 g projectiles followed by an inertial mass and a trailing wire provided the instrumentation. The strikers were propelled by means of a pneumatic gun at velocities ranging from 45 to 170 ms⁻¹. Displacement data obtained from high-speed photography for selected runs allowed curve fits to an analytical function which were compared to the directly recorded force histories.The effects of changes in initial velocity, angle of obliquity and striker tip on the peak force have been analyzed. A simple model has been developed for the perforation of plates by hemispherically-tipped projectiles at oblique incidence, and comparisons have been made with the measured force histories. A model was also devised to predict the peak forces obtained for oblique impact by cylindro-conical projectiles. The peak forces obtained experimentally were found to be relatively independent of the initial projectile velocity for shots where perforation occured. For the tests at speeds below the ballistic limit, the maximum forces were approximately proportional to the initial velocity.     

Perforation of AA5083-H116 aluminium plates with conical-nose steel projectiles—experimental study

The interest regarding use of aluminium alloys in lightweight protective structures is today increasing. Even so, the number of experimental and computational investigations giving detailed information on such problems is still rather limited. In this paper, perforation experiments have been performed on AA5083-H116 aluminium plates with thicknesses varying between 15 and 30 mm impacted by 20 mm diameter, 98 mm long, HRC 53 conical-nose hardened steel projectiles. In all tests, initial and residual velocities of the projectile were measured and a digital high-speed camera system was used to photograph the penetration and perforation process. Based on these measurements, impact versus residual velocity curves of the target plates were constructed and the ballistic limit velocity of each target was obtained. An analytical perforation model from the open literature is then used to predict the ballistic limit velocity, and excellent agreement with the experimental data is found. The experimental results are finally compared to similar experiments on steel and concrete targets, and the capacity of the different materials is evaluated in relation to total weight.     

Perforation of FRP laminates under impact by flat-nosed projectiles

A theoretical study is performed herein on the perforation of fibre-reinforced plastic laminates subjected to impact by flat-nosed projectiles in a wide range of velocities. Ballistic impact on FRP laminates is a very complex problem and it can be generally classified into two categories, i.e. global deformation with local rupture and wave-dominated local failure. Simple analytical models for both global deformation failure as well as wave-dominated local failure are first given, and a shear failure criterion is employed to predict the perforation of FRP laminates which fail in global deformation mode. By combining the wave-dominated local failure model and the concept of Von Karman’s critical impact velocity, a condition for the transition of the above mentioned two failure modes is obtained. It is shown that the model predictions are in good agreement with available experimental observations in terms of ballistic limits and critical conditions for the transition of failure modes.     

尖头弹侵彻延性金属靶板弹道极限的解析模型

现有的尖头弹侵彻金属靶板的弹道极限计算模型往往需要大量的试验数据和靶板材料的动态性能参数,且没有考虑侵彻速度对侵彻效果的影响,这给工程应用带来了很大的不便和误差。基于这一问题,考虑速度效应和靶板材料参数对侵彻的影响,结合流体动力学原理与动态空穴膨胀理论,分别提出了双模式和单模式侵彻模型。双模式侵彻模型的侵彻过程可分为两个阶段：流体动力变形阶段和塑性变形阶段,当侵彻速度小于靶材产生流体动力变形的临界速度时,侵彻进入塑性变形阶段,根据功能原理,建立了计算弹道极限的解析模型;单模式侵彻模型仅考虑塑性变形阶段。解析模型计算的弹道极限与弹道试验结果吻合的较好,且模型中不涉及弹道试验数据和靶板材料的动态性能参数,易于迅速求解,便于工程应用,可用于对延性金属靶板抗尖头弹侵彻能力的评估。     

Response of simulated propellant and explosives to projectile impact—III. Experimental and numerical results of warhead penetration and fragmentation

This paper is the third of a series concerned with the effects of projectile impact on a simulated explosive or propellant, called Propergol. Experiments were conducted to study the fragmentation and perforation response of disks of this material when subjected to impact by blunt and cylindro-conical strikers. Similar tests were conducted on layered targets of Propergol and steel, and also for a simulated warhead that was struck by armor-piercing projectiles. Data were obtained by velocity measurement, high-speed photography and post-mortem target examination including collected fragments.

A fragmentation oriented penetration code, AUTODYN(frag) was developed from the interfacing of a two-dimensional commercial finite difference code, AUTODYN, with a fragmentation subroutine, BFRACT, developed by other investigators. This program was utilized to study the microfracture and fragmentation processes in both monolithic and composite Propergol plates during their penetration by projectiles. In addition, numerical evaluations of the effects of simulated warhead penetration by armor-piercing bullets were conducted using the publicly available finite-element code DYNA2D.

The numerical results were compared with corresponding experimental data and also with the predictions of an analytical representation of the phenomenon, described in the second paper of the series. Reasonable agreement was obtained in the domain where the hypotheses concerning the structure of the analysis and of the computations were applicable.     

Perforation of a thick plate by rigid projectiles

Perforation of a thick plate by rigid projectiles with various geometrical characteristics is studied in the present paper. The rigid projectile is subjected to the resistant force from the surrounding medium, which is formulated by the dynamic cavity expansion theory. Two perforation mechanisms, i.e., the hole enlargement for a sharp projectile nose and the plugging formation for a blunt projectile nose, are considered in the proposed analytical model. Simple and explicit formulae are obtained to predict the ballistic limit and residual velocity for the perforation of thick metallic plates, which agree with available experimental results with satisfactory accuracy.     

Cone formation in targets beneath a penetrating projectile

The penetration and perforation of plates of two aluminium alloys by a cylindrical steel projectile were examined experimentally and simulated numerically. The influence of the impact velocity upon the penetration depth and the deformation and perforation modes were investigated. Particular attention was given to the cone formation in the targets due to a temperature rise and material melting in the sites of intensive plastic shear deformations. An attempt was made to simulate numerically the dynamics of the initiation and development of adiabatic shear bands in plates.     

A generalized formula for the penetration depth of a deformable projectile

A simple analytical algebraic formula is developed for predicting the penetration depth of a deformable projectile into a semi-infinite target. This formula is a simplified version of more general equations that have been developed to predict the time-dependent penetration process in finite thickness targets. Specifically, the formula generalizes the classical hydrodynamic theory to include dependence on elastic properties of the target and on the yield strengths of both the target and the projectile. Moreover, the formula is limited to the case of long-rod penetration where both the projectile and the target experience significant plastic flow. The limiting values of the location of the elastic–plastic boundary in the target have been determined, and a single empirical constant has been introduced to characterize the transition between these limiting values. A value for this empirical constant has been determined which produces theoretical predictions that are in reasonable agreement with experimental data for moderate to high values of the impact velocity of steel and tungsten projectiles penetrating a steel target.     

The effect of target strength on the perforation of steel plates using three different projectile nose shapes

The effect of target strength on the perforation of steel plates is studied. Three structural steels are considered: Weldox 460 E, Weldox 700 E and Weldox 900 E. The effects of strain hardening, strain rate hardening, temperature softening and stress triaxiality on material strength and ductility are determined for these steel alloys by conducting three types of tensile tests: quasi-static tests with smooth and notched specimens, quasi-static tests at elevated temperatures and dynamic tests over a wide range of strain rates. The test data are used to determine material constants for the three different steels in a slightly modified version of the Johnson–Cook constitutive equation and fracture criterion.Using these three steel alloys, perforation tests are carried out on 12 mm-thick plates with blunt-, conical- and ogival-nosed projectiles. A compressed gas gun was used to launch projectiles within the velocity range from 150 to 350 m/s. The initial and residual velocities of the projectile were measured, while the perforation process was captured using a digital high-speed camera system. Based on the test data the ballistic limit velocity was obtained for the three steels for the different nose shapes. The experimental results indicate that for perforation with blunt projectiles the ballistic limit velocity decreases for increasing strength, while the opposite trend is found in tests with conical and ogival projectiles. The tests on Weldox 700 E and Weldox 900 E targets with conical-nosed projectiles resulted in shattering of the projectile nose tip during penetration.Finally, numerical simulations of some of the experimental tests are carried out using the non-linear finite element code LS-DYNA. It is found that the numerical code is able to describe the physical mechanisms in the perforation events with good accuracy. However, the experimental trend of a decrease in ballistic limit with an increase in target strength for blunt projectiles is not obtained with the numerical models used in this study.     

Normal and oblique impact of cylindro-conical and cylindrical projectiles on metallic plates

An experimental program has been undertaken to study the phenomenon of both normal and oblique impact of cylindro-conical and cylindrical projectiles on metallic plates, a domain where almost no test data are available. Hard-steel strikers of 12.7 mm nominal diameter and either 60° conical or blunt tips and blunt soft aluminum cylinders of the same diameter were fired at 2024-0 aluminum targets with thickness from 1.78 to 25.4 mm and at both mild steel and medium carbon steel with thickness up to 19.05 mm. Inital velocities ranged from about 20 to 1025 m s⁻¹, achieved with the aid of a pneumatic cannon at low speeds and a powder gun in the upper velocity range. Initial target obliquity was varied from normal to 50°.The primary results obtained involved the measurement of the velocity drop and change in projectile orientation as the result of passage through the target. The target damage, consisting of dishing, petals, plugs and bands separated from the crater, was examined and metallurgical determinations were executed for a selected set of runs. The information obtained should provide a good basis for understanding the mechanisms involved in this type of impact and perforation. It will also serve as a reliable source of data for comparison with the predictions from analytical models of the process which do not currently exist, but will most certainly be developed in the future.     

分析金属装甲弹道极限的两阶段模型

基于大量弹道试验分析,考虑靶板背面自由边界的影响,提出一个分析刚性尖头弹垂直撞击中等厚度理想弹塑性材料靶板弹道极限的两阶段工程模型.由圆柱形空腔膨胀理论和功能原理导出第一阶段延性扩孔耗能表达式,按薄靶板最小穿透能量的简化分析模型计算第二阶段耗能,由两阶段总的耗能最小确定第一阶段的侵彻深度,从而得到最小穿透能量的解析解.经与金属装甲弹道试验比较,表明两阶段工程模型计算结果与试验吻合较好,比现有单一延性扩孔模型精度高.     

Impact loading of plates — An experimental investigation

The impact of projectiles at sub-ordnance velocities against mild steel, stainless steel and aluminium plates, has been studied in a series of experiments. The projectile mass, nose shape and hardness have been shown to have an important effect on penetration as does the target rigidity and support condition. All materials exhibit a clear ‘kink’ effect related to a change from energy absorption by plastic deformation to perforation with well-defined shear bands and no appreciable bulging.     

Finite element analysis to predict penetration and perforation of thick FRP laminates struck by projectiles

This paper examines the penetration and perforation of fibre-reinforced plastic (FRP) laminates struck by rigid projectiles with different nose shapes within a wide range of impact conditions using ABAQUS/Explicit code. It is assumed that the FRP laminate target response can be represented by a velocity dependent forcing function which eliminates discretizing the target as well as the need for a complex contact algorithm. The forcing function is then applied to the surface of the projectiles as boundary conditions in the numerical model. With this combined analytical and computational technique we can obtain the depth of penetration, residual velocity, ballistic limit, transient response in terms of time-histories of displacement/penetration, velocity and deceleration of the projectile. It is shown that the model predictions are in good correlation with available experimental data.     

卵形弹丸撞击下 FRP层合板的侵彻和穿透

研究了卵形弹丸撞击下FRP层合板的侵彻和穿透性能, 在局部化破坏模式假定的基础上改进了Wen提出的能量简化分析模型。改进模型仍假设弹体在侵彻过程中表面所受靶体的平均压力由靶体材料弹塑性变形所引起的静态阻力和速度效应引起的动阻力两部分组成, 认为侵彻过程中靶体对弹的阻力不再是一个常数, 而是与侵彻速度相关的函数。同时针对不同厚度靶板的破坏模式, 建立了几种不同的侵彻和穿透模型。通过弹头长度与靶板厚度的比较, 将侵彻过程分为部分侵彻和完全侵彻; 穿透过程分为薄板穿透和中厚板穿透。并且根据不同的破坏方式给出了求解卵形弹丸的侵彻深度、 残余速度和极限速度的预测公式。模型预测与实验数据进行了比较, 发现侵彻深度和弹道极限速度的理论预测值与实验数据吻合得很好。      

Q235钢单层板对平头刚性弹抗穿甲特性研究

采用撞击实验和理论模型对单层金属板的抗侵彻性能进行了研究,分析了靶体厚度对抗侵彻性能的影响。通过对比撞击实验和理论模型计算结果,验证了理论模型和参数的有效性。结果表明,采用合适的理论模型能够有效地预测靶板在弹体撞击下的弹道极限。此外,分析了靶体在弹体撞击下的塑性变形总耗能,包括靶板局部变形和整体变形的耗能,同时考虑了靶体材料的应变率效应。在平头弹撞击厚靶的工况中,引入了一个修正函数对靶体厚度进行修正。     

钝头弹高速斜侵彻中厚背水金属靶板的机理研究

为探讨高速钝头弹斜侵彻中厚背水金属靶板的机理,根据不同的受力状态及耗能机制,结合中厚背水靶板抗高速斜侵彻特点,通过厚度等效,将斜侵彻转化为相应的正侵彻。然后,将整个侵彻过程分为压缩镦粗、剪切压缩和剪切扰动三个阶段。基于三阶段侵彻机制,建立了钝头弹高速斜穿甲中厚背水金属靶板后的瞬时余速计算模型,并讨论了该计算模型的局限性。采用该模型计算了3.3 g立方体弹丸斜穿甲5 mm背水钢板后的瞬时余速,理论计算值与试验结果及相应的仿真计算值均吻合较好。由于该模型考虑了靶后水介质的动支撑作用及动能耗散等效应,在一定的适用范围内,能对钝头弹高速斜侵彻中厚背水金属靶板的瞬时余速进行合理地预测,具有一定的理论价值和工程应用价值。     

On the main mechanisms for defeating AP projectiles,long rods and shaped charge jets

Some of the important mechanisms for defeating various projectiles and shaped charge are reviewed in this paper. These mechanisms are based on the compressive strength of the target material (its inherent resistance to penetration) and on the asymmetrical forces which it exerts on the threat, through proper geometrical arrangements. We discuss the basic features of the resistance to penetration, starting with the classical analysis of the cavity expansion process in elasto-plastic solids. This property of the target is responsible for the deceleration of hard cored projectiles and for the erosion of long rods, under normal impact conditions. We then discuss the asymmetrical interaction of armor piercing (AP) projectiles, long rods and shaped charge jets with inclined plates (stationary and moving). These asymmetric forces, exerted on the impacting threat, are responsible for their deflection and breakup. Our work combines experimental observations with numerical simulations and engineering models, which highlight the basic mechanisms behind these complex situations. This understanding is necessary for optimizing the performance of any armor design against a given threat.     

刚性弹侵彻有限直径金属厚靶的机理与模型研究

采用统一强度理论,考虑靶板中间主应力效应和靶体侧面自由边界的影响,得到线性硬化靶材在弹塑性阶段和塑性阶段的空腔壁径向应力的表达式,建立线性硬化靶材的统一侵彻模型,求出中低速(v₀≤1000 m/s)刚性弹体侵彻有限直径金属厚靶时侵彻阻力、侵彻深度计算公式,并利用Simpson算法对其进行求解,分析了包括强度准则差异在内的弹道终点效应的一系列影响因素。结果表明:该文计算方法可以更好地描述侵彻过程中弹靶的动态响应,还可以得到一系列基于不同强度准则的侵彻阻力和深度的解析解、对靶材在不同撞击速度下侵彻深度的区间范围进行有效预测;强度参数、弹体撞击速度、靶体半径和弹头形状对有限直径金属厚靶的抗侵彻性能均有较大的影响,其中强度参数值由1减小为0时,侵彻深度增加了22.45%;随着靶弹半径比的减小,侵彻深度不断增大,当靶弹半径比小于等于16时,侵彻深度增大的程度显著,此时靶体边界尺寸对侵彻性能的影响很大,不能继续按照半无限靶体进行计算。