Statistical variability and fragility assessment of ballistic perforation of steel plates for 7.62 mm AP ammunition

The paper describes field test results of 7.62 × 51 mm M61 AP (armour piercing) ammunition fired into mild steel targets at an outdoor range. The targets varied from 10 mm to 32 mm in thickness. The tests recorded penetration depth, probability of perforation (i.e., complete penetration), muzzle and impact velocities, bullet mass, and plate yield strength and hardness. The measured penetration depth exhibited a variability of approximately ±12%. The paper then compared ballistic test results with predictive models of steel penetration depth and thickness to prevent perforation. Statistical parameters were derived for muzzle and impact velocity, bullet mass, plate thickness, plate hardness, and model error. A Monte-Carlo probabilistic analysis was then developed to estimate the probability of plate perforation of 7.62 mm M61 AP ammunition for a range of impact velocities, and for mild steels, and High Hardness Armour (HHA) plates. This perforation fragility analysis considered the random variability of impact velocity, bullet mass, plate thickness, plate hardness, and model error. Such a probabilistic analysis allows for reliability-based design, where, for example, the plate thickness with 95% reliability (i.e. only 1 in 20 shots will penetrate the wall) can be estimated knowing the probabilistic distribution of perforation. Hence, it was found that the plate thickness to ensure a low 5% probability of perforation needs to be 11–15% thicker than required to have a 50/50 chance of perforation for mild steel plates. Plates would need to be 20–30% thicker if probability of perforation is reduced to zero.     

陶瓷/薄钢板复合结构靶板抗高速侵彻性能研究

为探讨陶瓷/薄钢板复合结构靶板(ceramic/thin steel targets,CS靶板)的抗高速侵彻机理,通过弹道试验,分析了3 mm厚SiC陶瓷层和0.6 mm厚钢板层的CS靶板的破坏模式和抗侵彻性能,并与面密度基本相同的纯钢板进行了比较。在此基础上,基于能量守恒原理,建立了CS靶板抗高速侵彻的理论预测模型,并与试验结果进行了对比。结果表明,CS靶板中前陶瓷层的存在,使得后钢板层的破坏模式由剪切冲塞转变为花瓣开裂,大大提升了后钢板层的抗侵彻吸能效率,从而使得CS靶板的整体抗侵彻性能高于等面密度的纯钢板,CS靶板的整体抗侵彻效率较等面密度纯钢板提升15%以上;弹体穿透CS靶板后的剩余速度理论预测值与试验结果吻合较好,相对误差均在5%以内,验证了理论模型的合理性和有效性。     

破片模拟弹侵彻钢板的有限元分析

根据破片模拟弹侵彻钢板的实验研究,采用MSC.Dytran对破片模拟弹侵彻钢板的侵彻过程、侵彻特性、钢板的破坏模式以及弹体的侵彻速度、靶板的侵彻阻力进行了有限元分析,并将分析结果与实验结果进行了比较.分析结果表明,破片模拟弹冲击钢装甲的侵彻过程可大致分为初始接触、弹体侵入、剪切冲塞和穿甲破坏4个阶段.有限元分析的破片模拟弹侵彻特性及靶板破坏模式与实验观测结果有较好的一致性,在靶板破口的正面,与弹体平面凸缘两端接触的部分,变形以剪切为主,而与切削面接触的部分,以挤压变形为主;靶板破口背面为剪切冲塞破坏;有限元模拟的弹体剩余速度与实验结果吻合较好,弹体侵彻过程中弹靶作用界面的速度和侵彻速度近似呈线性变化.有限元分析结果还表明,采用适当的模型,有限元法能较好地模拟破片模拟弹侵彻钢板的侵彻过程、侵彻特性以及钢板的破坏模式.     

Residual Characteristic of High-Velocity Steel Fragments Penetrating UHMWPE FRP Laminates

The mechanical performance of ultra-high molecular weight polyethylene fiber (UHMWPE) and its composites were proposed. Penetrated properties of different thicknesses UHMWPE FRP laminates (URP) impacted by 3.3g cubic high velocity fragments were studied. According to the ballistic experimental results and theoretical analysis, the linear relation between ballistic limit vBL and area density AD was confirmed. The relative parameters of showing experientially residual velocity vr were expressed by the function of AD. In the end, versatile experiential expression between vr and AD was found. Prediction of vr and vBL using obtained expressions under the above stated condition of impacting URP was consistent with the experimentaled results. Consequently, the two experiential relations can be used to predict the residual velocity and ballistic limit of cubic high velocity fragments impacting URP. The residual characteristic of high-velocity steel fragments penetrating UHMWPE FRP laminates can be more exactly forecasted by the two derived experiential formulas.     

Determination of penetration depth at high velocity impact using finite element method and artificial neural network tools

Determination of ballistic performance of an armor solution is a complicated task and evolved significantly with the application of finite element methods(FEM) in this research field.The traditional armor design studies performed with FEM requires sophisticated procedures and intensive computational effort,therefore simpler and accurate numerical approaches are always worthwhile to decrease armor development time.This study aims to apply a hybrid method using FEM simulation and artificial neural network(ANN) analysis to approximate ballistic limit thickness for armor steels.To achieve this objective,a predictive model based on the artificial neural networks is developed to determine ballistic resistance of high hardness armor steels against 7.62 mm armor piercing ammunition.In this methodology,the FEM simulations are used to create training cases for Multilayer Perceptron(MLP) three layer networks.In order to validate FE simulation methodology,ballistic shot tests on 20 mm thickness target were performed according to standard Stanag 4569.Afterwards,the successfully trained ANN(s) is used to predict the ballistic limit thickness of 500 HB high hardness steel armor.Results show that even with limited number of data,FEM-ANN approach can be used to predict ballistic penetration depth with adequate accuracy.     

穿甲子弹垂直侵彻防弹钢试验与理论模型

试验研究了穿甲子弹垂直侵彻高强防弹钢的机理,提出了一个分析靶板极限速度和弹体剩余速度的理论模型,该模型综合考虑了材料的应变率与热软化效应,结果表明,理论值与试验值吻合很好.分析了失效准则的影响,研究了剪切带温度和靶板耗能随入射速度的变化规律.     

碳化硼基3DMC材料抗弹性能的初步探讨

通过7.62穿甲燃烧弹的射击考核,分析了碳化硼基3DMC材料的抗弹性能,发现其综合抗弹性能优于等厚度的某型号装甲钢,并具有抗击连续打击的能力,认为该材料可以独立用于装甲防护。     

穿甲子弹偏心入射陶瓷/钢复合靶板试验

设计并进行了7.62mm穿甲子弹侵彻陶瓷/低碳钢复合靶板的弹道试验,得到了极限速度及陶瓷锥底部半径等数据。分析了锥底半径与入射速度、面板及背板厚度的关系,着重分析了偏心入射时靶板的抗弹机理。结果表明:陶瓷锥可分为破碎区和粉碎区,粉碎区半径约为面板厚度与弹丸半径之和;当弹着点距离陶瓷面板边缘大于5mm时,靶板的抗弹性能变化不大,而弹着点位于距陶瓷面板边缘小于5mm的板边区时,抗弹性能明显降低,靶板的有效防护面积应扣除板边区。     

不同截面形状复合长杆弹对陶瓷复合靶板侵彻研究

采用数值模拟技术研究了由3种不同截面形状的钨芯外包覆一层钢,形成的钢包覆层复合长杆弹在入射速度为1200m/s～1700m/s时对陶瓷/金属复合靶板的侵彻过程。结果表明:对于同一入射速度、相同弹体长度、同种材料的弹芯和包覆层以及靶板材料而言,等面积的六边形截面钨芯复合长杆弹的侵彻深度明显大于圆形及方形截面,方形及六边形截面与和它们等外接圆形成的圆形截面复合长杆弹侵彻深度没有明显差别,本研究认为这是与不同截面钨芯的外接圆直径直接相关。六边形截面长杆弹侵彻过程中的自锐化现象是其侵彻深度明显大于其它两种弹体的主要原因。     

4层横向运动板防护长细杆的数值分析

多层横向运动板对垂直来侵长细杆的挤压、剪切能够使长细杆发生挤压和剪切变形,进而降低长细杆后续的侵彻能力,增强装甲的防护效果。利用LS—DYNA软件对多层横向、邻层反向运动的钢装甲板防护钨合金长细杆进行运动板速度和运动板的厚度分配的相关仿真计算。通过对计算结果中开坑形状、后效板侵深和装甲效能进行分析发现,随着板运动速度的增加,后效板开坑深度减小和开坑形状的非对称性加剧,运动板的干扰作用增强及防护效能提高;在运动板总厚度相同的情况下,板的层数越少,防护性能越好。     

Real-time prediction of projectile penetration to laminates by training machine learning models withfinite element solver as the trainer

Studies on ballistic penetration to laminates is complicated, but important for design effective protection of structures. Experimental means of study is expensive and can often be dangerous. Numerical simu-lation has been an excellent supplement, but the computation is time-consuming. Main aim of this thesis was to develop and test an effective tool for real-time prediction of projectile penetrations to laminates by training a neural network and a decision tree regression model. A large number of finite element models were developed;the residual velocities of projectiles fromfinite element simulations were used as the target data and processed to produce sufficient number of training samples. Study focused on steel 4340tpolyurea laminates with various configurations. Four different 3D shapes of the projectiles were modeled and used in the training. The trained neural network and decision tree model was tested using independently generated test samples using finite element models. The predicted projectile velocity values using the trained machine learning models are then compared with thefinite element simulation to verify the effectiveness of the models. Additionally, both models were trained using a published experimental data of projectile impacts to predict residual velocity of projectiles for the unseen samples. Performance of both the models was evaluated and compared. Models trained with Finite element simulation data samples were found capable to give more accurate predication, compared to the models trained with experimental data, becausefinite element modeling can generate much larger training set, and thus finite element solvers can serve as an excellent teacher. This study also showed that neural network model performs better with small experimental dataset compared to decision tree regression model.     

激光辐照下45#钢板响应特性

采取实验和数值模拟相结合的方法对激光辐照45#钢板的响应特性进行研究。基于连续光纤激光发射系统,开展钢板的激光辐照实验,得到温度场分布及靶板的烧蚀穿孔特性;基于ANSYS建立靶板有限元模型,模拟激光辐照下靶板的热响应过程,得到了靶板厚度、激光功率和光斑直径等因素对靶板温度分布及靶板穿孔特性的影响规律。     

平头弹丸侵彻金属靶板的数值仿真

基于ABAQUS/Explicit非线性有限元分析程序,通过二次开发利用含损伤的Johnson-Cook本构模拟靶板材料,对刚性平头弹丸垂直侵彻不同厚度的金属靶板进行了数值仿真,实现了侵彻过程的可视化。结果表明：网格密度对计算结果有影响,但随着网格密度增加,结果趋于收敛;侵彻过程中,弹丸与靶板发生了多次碰撞,靶板的塑性变形局限在很窄的剪切带内;对数值计算结果与试验结果进行了比较,发现二者吻合得较好。相关结论对防护结构的设计具有指导意义。     

对接厚板表面裂纹的残余应力强度因子

利用线弹簧模型求解对接厚板表面裂纹的残余应力强度因子。基于Reissner板理论和连续分布位错思想,将对接厚板表面裂纹问题归结为一组Cauchy型奇异积分方程,并采用Gauss-Chebyshev方法给出了奇异积分方程的数值结果,并与有限元解进行比较,计算结果表明:用线弹簧模型解决含残余应力表面裂纹问题不仅是合理可行的,而且是一种简单方便的方法,便于工程实际应用。     

Attitude deflection of oblique perforation of concrete targets by a rigid projectile

A perforation model is developed to predict the attitude deflection in the oblique perforation of concrete targets by a rigid projectile, in which the inertial moment of the projectile is introduced, together with taking the attitude deflection during the shear plugging sub-stage into account, and the shape of the plug formed on the rear surface of target is also re-investigated. Moreover, a new classification of concrete targets is proposed based on the target thickness, with which the attitude deflections in different kinds of concrete targets are analyzed. It is found that the numerical results by using the new perforation model are in good agreement with the previous experimental data and simulated results. Furthermore, the variations of the attitude deflection with the initial conditions (the initial attitude angle and the initial impact velocity) are investigated.     

Performance study of jute-epoxy composites/sandwiches under normal ballistic impact

This study is undertaken to explore the use of natural fiber Jute-epoxy (JE), Jute-epoxy-rubber (JRE) sandwich composite for ballistic energy absorption. Energy absorbed and residual velocities for these composites are evaluated analytically and through Finite Element Analysis (FEA). FE analysis of JE plates is carried out for different thicknesses (3, 5, 10 and 15 mm). JE plates and JRE sandwiches having the same thickness (15 mm) are fabricated and tested to measure residual velocity and energy absorbed. The analytical results are found to agree well with the results of FE analysis with a maximum error of 9%. The study on JE composite plate reveals that thickness influences the energy absorption. Experimental and FE analysis study showed that JRE sandwiches have better energy absorption than JE plates. Energy absorption of a JRE sandwich is about 71% greater than JE plates. Damages obtained from FEA and testing are in good agreement. SEM analysis confirms composites failed by fiber rupture and fragmentation.     

横向运动板干扰聚能射流的数值模拟

基于有限元分析软件ANSYS/LS-DYNA和LS-PREPOST,用ALE算法对射流垂直侵彻横向运动防护板的过程进行模拟分析。防护板在不同速度下干扰射流时,对防护板和后效板上的开坑形状进行分析,并计算后效板上的最终侵深及射流轴线上的速度降,得到射流在横向防护板作用下后效板侵深及射流轴线上的速度降随防护板速度变化的曲线。结果表明,防护板抗射流侵彻能力随防护板速度的增加而增强,尤其是防护板横向速度在0～100m/s增加时,抗射流侵彻能力增强较为明显。     

Influence of a liquid-filled compartment structure on the incoming shaped charge jet stability

Liquid-filled compartment structure consists of a bulk steel plate with matrix blind holes which are filled with liquid and a steel front plate to seal up the liquid with rings and bolts.The liquid-filled compart-ment structure can resist the shaped charge warhead effectively.This paper presents experimental and theoretical investigations of the penetration ability of the residual shaped charge jet emerging from the liquid-filled compartment structure after the penetration process at different impact angles.On the basis of shock wave propagation theory,the influence of the liquid-filled compartment structure on jet sta-bility is analysed.The interferences of the liquid backflow caused by a reflected shock wave and a back plate on jet stability under different impact angles are also examined.In addition,the range of the disturbed velocity segments of the jet at different impact angles and the penetration ability of the re-sidual jet are obtained.A theoretical model is validated against the experimental penetration depths.     

Ballistic response of armour plates using Generative Adversarial Networks

It is important to understand how ballistic materials respond to impact from projectiles such that informed decisions can be made in the design process of protective armour systems. Ballistic testing is a standards-based process where materials are tested to determine whether they meet protection, safety and performance criteria. For the V₅₀ ballistic test, projectiles are fired at different velocities to determine a key design parameter known as the ballistic limit velocity (BLV), the velocity above which projectiles perforate the target. These tests, however, are destructive by nature and as such there can be considerable associated costs, especially when studying complex armour materials and systems. This study proposes a unique solution to the problem using a recent class of machine learning system known as the Generative Adversarial Network (GAN). The GAN can be used to generate new ballistic samples as opposed to performing additional destructive experiments. A GAN network architecture is tested and trained on three different ballistic data sets, and their performance is compared. The trained networks were able to successfully produce ballistic curves with an overall RMSE of between 10 and 20 % and predicted the V₅₀ BLV in each case with an error of less than 5 %. The results demonstrate that it is possible to train generative networks on a limited number of ballistic samples and use the trained network to generate many new samples representative of the data that it was trained on. The paper spotlights the benefits that generative networks can bring to ballistic applications and provides an alternative to expensive testing during the early stages of the design process.     

冲击波和高速破片联合作用下固支方板毁伤效应数值模拟

为探讨固支方形钢板结构在空爆冲击波和高速破片联合作用下的动态响应过程及变形破坏模式,利用有限元分析软件ANSYS/LS-DYNA,开展了空爆冲击波和高速破片对固支方板的联合作用数值模拟计算,阐述了固支方板在联合载荷作用下动态响应过程的2个阶段,以及在不同爆距下的变形破坏模式和特点。结果表明,随着爆距增加,在破片密集作用区内,钢板的破坏模式存在从集团冲塞破口到部分穿孔边界撕裂联通,再到无穿孔边界撕裂现象的转换。