Effect of projectile nose shape,impact velocity and target thickness on deformation behavior of aluminum plates

The present study deals with the experimental and numerical investigations of aluminum target plates impacted by blunt, ogive and hemispherical nosed steel projectiles. The projectiles were normally impacted on the target plates of 0.5, 0.71, 1, 1.5, 2, 2.5 and 3 mm thicknesses at different velocities with the help of a pneumatic gun. Effect of projectile nose shape, impact velocity and plate thickness on the deformation of the target plates was studied. Hemispherical nosed projectile caused highest global deformation (dishing) of the target plates. Ogive nosed projectiles were found to be the most efficient penetrator for the case of plates of thicknesses 0.5, 0.71, 1.0 and 1.5 mm. For the case of plates of thicknesses 2.0, 2.5 and 3.0 mm however, blunt nosed projectiles required least energy to perforate the target plates. The ballistic limit velocity of hemispherical nosed projectiles was found to be highest as compared to the other two projectiles. Finite element analysis of the problem was carried out using ABAQUS finite element code. Results of the numerical analysis were compared with the experiments and good correlation between the two was found.     

3D numerical simulations of ductile targets subjected to oblique impact by sharp nosed projectiles

Three-dimensional numerical simulations have been performed to study the behaviour of ductile targets subjected to normal and oblique impact by sharp nosed cylindrical projectiles. Twelve-mm-thick Weldox 460 E steel targets were impacted by 20 mm diameter projectiles with conical nose and 1-mm-thick 1100-H12 aluminum targets were impacted by 19 mm diameter ogive nosed projectiles. In both the cases, the targets were impacted at 0°, 15°, 30°, 45° and 60° obliquity or until the ricochet of the projectile occurred. The ballistic limit of 12 mm steel targets was found to be almost same up to 30° obliquity and thereafter it increased sharply. However, in the case of 1 mm aluminum targets a consistent increase in the ballistic limit was observed with increase in obliquity. The critical angle of projectile ricochet was found to increase with increase in impact velocity. Both the targets failed through ductile hole enlargement. Petal formation occurred in the aluminum targets and four petals were generally formed in each plate, however, the size of the upper two petals decreased and that of the lower two petals increased with increase in target obliquity. In the case of the steel targets the perforation occurred through the formation of a hole enclosed by a bulge. Both the bulge and the hole were circular in normal impact and elliptical in oblique impact. Petal formation in steel targets was observed at 60° obliquity. The ABAQUS/explicit finite element code was used to carry out numerical simulations.     

Effect of projectile nose shape on the ballistic resistance of ductile targets

Three-dimensional numerical simulations were carried out to study the ballistic resistance of ductile targets subjected to normal impact by the projectiles. 12 mm thick Weldox 460 E steel targets were impacted by 20 mm diameter conical nosed projectiles and 1 mm thick 1100-H12 aluminum targets were impacted by 19 mm diameter ogive nosed projectiles. The internal nose angle of conical projectile was varied (33.4°–180°) and found to have significant effect on the ballistic limit of 12 mm thick Weldox 460 E steel target. Similarly, the caliber radius head (CRH) of ogive nosed projectile was varied (0–2.5) and found to have significant effect on the ballistic limit of 1 mm thick 1100-H12 aluminum target. The ballistic limit of 12 mm thick Weldox 460 E steel target increased almost linearly with the decrease in the projectile nose angle. While the ballistic limit of 1 mm thick 1100-H12 aluminum target increased as the CRH increased from 0 to 0.5 and with further increase in CRH to 1.0, 1.5, 2.0 and 2.5 its values were found to drop quite significantly. ABAQUS/Explicit finite element code was used to carry out the numerical simulations.     

Q235钢板对半球形头弹抗侵彻特性

利用轻气炮进行了半球形头杆弹正撞击单层板和等厚接触式三层板的实验, 得到了这两种结构靶体的初始-剩余速度曲线以及弹道极限。采用ABAQUS/EXPLICIT数值模拟软件对杆弹撞击金属板的过程进行了数值模拟研究, 通过对比数值模拟和实验结果, 验证了数值模拟材料模型和参数的有效性。研究了靶体结构对抗侵彻特性的影响, 并分析了弹体对靶体的撞击过程。研究结果表明:多层板的弹道极限高于等厚单层板。单层板主要失效模式为剪切, 而多层板的主要失效模式为整体的蝶形变形和局部的盘式隆起。对于多层板, 靶板具体的失效模式与其在靶中位置相关。     

Incremental deformation and penetration analysis of deformable projectile into semi-infinite target

In this paper, a new analytical method for projectile deformation and penetration into a semi-infinite target has been developed. This method is based on separated, successive and incremental steps. In deformation step, the target assumed rigid and the increment of projectile deformation was evaluated, whilst in penetration step, the projectile assumed rigid and the increment of penetration was evaluated. These sequential steps continued untill the projectile stopped.Furthermore, a series of ballistic tests have been carried out with ogival projectiles with striking velocity of 600–900 m/s. The projectiles and target plates material has been chosen from 4 types of steel. In this way, 210 tests for 48 combinations of projectile, target and velocity have been carried out. Numerical simulation has been also performed using the LS-DYNA code.Comparison between the depth of penetration obtained by this analytical method and those of the experimental and numerical ones shows a good agreement.     

Semi-theoretical analyses of the concrete plate perforated by a rigid projectile

Based on the three-stage perforation model, a semi-theoretical analysis is conducted for the ballistic performances of a rigid kinetic projectile impacting on concrete plates. By introducing the projectile resistance coefficients, dimensionless formulae are proposed for depth of penetration (DOP), perforation limit thickness, ballistic limit velocity, residual velocity and perforation ratio, with the projectile nosed geometries and projectile-target interfacial friction taken into account. Based on the proposed formula for DOP and lots of penetration tests data of normal and high strength concrete targets, a new expression is obtained for target strength parameter. By comparisons between the results of the proposed formulae and existing empirical formulae and large amount of projectile penetration or perforation tests data for monolithic and segmented concrete targets, the validations of the proposed formulae are verified. It is found that the projectile-target interfacial friction can be neglected in the predictions of characteristic ballistic parameters. The dimensionless DOP for low-to-mid speed impacts of non-flat nosed projectiles increases almost linearly with the impact factor by a coefficient of 2/(πS). The anti-perforation ability of the multilayered concrete plates is dependent on both the target plate thickness and the projectile impact velocity. The variation range of the perforation ratio is 1–3.5 for concrete targets.     

平头弹穿透金属靶板的模式分析

对平头弹穿透金属靶的剪切冲塞和绝热剪切冲塞两种可能穿甲模式进行分析. 对作者先前提出的绝热剪切冲塞失效模型进一步发展,给出在绝热剪切冲塞条件下修正的终点弹道极限和剩余速度. 对相关的平头弹穿甲WeldoxE系列钢靶的试验数据进行分析比较,讨论靶板厚度、靶材强度对终点弹道性能的影响. 更多实验数据证实:在一定靶厚时由于靶板的结构响应导致弹道极限附近存在剩余速度跳跃;随靶厚和靶材强度增加,穿甲模式由剪切冲塞向绝热剪切冲塞转换.      

A study of the perforation of stiffened plates by rigid projectiles

In the present paper, a four-stage perforation model that accurately predicts the residual velocity is developed by adopting an energy method. The four stages are plug formation, dishing formation, petal formation and projectile exit. In addition, some important experimental results are presented and analyzed to validate the present perforation model. In the experiments, high speed camera system is used to record the perforation process. Observations on target damage and measurements of initial velocities and residual velocities with the aid of the system are presented. Numerical simulations are carried out for projectiles against single and layered plates adopted in the experiments. The perforation process is studied and the deformation and failure modes are obtained. The predictions of numerical simulations and analytical model are found in reasonably good agreement with those of experiments, and can be used to predict the ballistic limit and residual velocity of stiffened plates perforated by rigid projectiles.     

A study of the perforation of stiffened plates by rigid projectiles

In the present paper, a four-stage perforation model that accurately predicts the residual velocity is developed by adopting an energy method. The four stages are plug formation, dishing formation, petal formation and projectile exit. In addition, some important experimental results are presented and analyzed to validate the present perforation model. In the experiments, high speed camera system is used to record the perforation process. Observations on target damage and measurements of initial velocities and residual velocities with the aid of the system are presented. Numerical simulations are carried out for projectiles against single and layered plates adopted in the experiments. The perforation process is studied and the deformation and failure modes are obtained. The predictions of numerical simulations and analytical model are found in reasonably good agreement with those of experiments, and can be used to predict the ballistic limit and residual velocity of stiffened plates perforated by rigid projectiles. The project supported by the National Natural Science Foundation of China (90305018) The English text was polished by Yunming Chen     

Oblique Perforation of Thick Metallic Plates by Rigid Projectiles

Oblique perforation of thick metallic plates by rigid projectiles with various nose shapes is studied in this paper. 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. It is shown that the perforation of a thick plate is dominated by several non-dimensional numbers, i.e., the impact function, the geometry function of projectile, the non-dimensional thickness of target and the impact obliquity. Explicit formulae are obtained to predict the ballistic limit, residual velocity and directional change for the oblique perforation of thick metallic plates. The proposed model is able to predict the critical condition for the occurrence of ricochet. The proposed model is validated by comparing the predictions with other existing models and independent experimental data.The English text was polished by Keren Wang     

Perforation of 5083-H116 Aluminum Armor Plates with Ogive-Nose Rods and 7.62 mm APM2 Bullets

We conducted an experimental and analytical study to understand the mechanisms and dominant parameters for ogive-nose rods and 7.62 mm APM2 bullets that perforate 5083-H116 aluminum armor plates. The 20-mm-diameter, 95-mm-long, ogive-nose, 197 g, hard steel rods were launched with a gas gun to striking velocities between 230–370 m/s. The 7.62-mm-diameter, 10.7 g, APM2 bullet consists of a brass jacket, lead filler, and a 5.25 g, ogive-nose, hard steel core. The brass and lead were stripped from the APM2 bullets by the targets, so we conducted ballistic experiments with both the APM2 bullets and only the hard steel cores. These projectiles were fired from a rifle to striking velocities between 480–950 m/s. Targets were 20, 40, and 60-mm-thick, where the 40 and 60-mm-thick targets were made up of layered 20-mm-thick plates in contact with each other. The measured ballistic-limit velocities for the APM2 bullets were 4, 6, and 12% smaller than that for the hard steel cores for the 20, 40, and 60-mm-thick targets, respectively. Thus, the brass jacket and lead filler had a relatively small effect on the perforation process. In addition, we conducted large strain, compression tests on the 5083-H116 aluminum plate material for input to perforation equations derived from a cavity-expansion model for the ogive-nose rods and steel core projectiles. Predictions for the rod and hard steel core projectiles are shown to be in good agreement with measured ballistic-limit and residual velocity data. These experimental results and perforation equations display the dominant problem parameters.     

靶板厚度对卵形弹丸垂直贯穿中等厚度混凝土靶的影响

为研究卵形弹丸贯穿中等厚度混凝土靶体的贯穿规律,开展直径60 mm尖卵形弹丸贯穿不同厚度混凝土靶体的侵彻实验,获得了不同撞击速度的弹丸贯穿不同厚度混凝土靶体的剩余速度规律。结合无网格SPH方法、RHT混凝土本构以及状态方程,对贯穿实验进行数值模拟,对不同工况下的弹丸过载规律以及靶体的损伤过程的分析发现:弹丸贯穿中等厚度混凝土靶体的贯穿过程分为开坑阶段、隧道稳定侵彻阶段以及靶背影响出靶阶段,在相同初始撞击速度下的靶背影响区的厚度随着靶体厚度的增加而增大。实验结果与数值模拟结果对比,表明模型能够有效模拟弹丸贯穿混凝介质问题,研究结果可为贯穿机理的研究提供参考。     

A3钢钝头弹撞击45钢板破坏模式的数值分析

不同速度范围内的A3钢钝头弹撞击45钢靶板分别表现为泰勒撞击、向日葵型花瓣帽形失效和靶板冲塞穿甲等3种不同的破坏模式,利用LS-DYNA对这种复杂的破坏机理和相应的影响因素进行了数值模拟研究。采用Johnson-Cook强度模型和累积损伤失效模型描述弹靶材料的力学性能,并考虑了塑性变形的绝热温升效应。数值模拟再现了不同破坏模式的失效过程,得到了与实验一致的结果。研究还指出,弹靶的冲塞穿甲实际是在高速撞击下,弹体发生花瓣帽形变形失效后继续穿甲靶板的后续结果。     

平头弹穿透间隙式双层靶的穿甲模式

平头弹贯穿单层金属靶,随着靶厚的增加和弹速的增高,穿甲模式均可能由剪切冲塞向绝热剪切冲塞转换。因此,对于双层或多层靶的穿甲,其不同层的靶板失效模式可能是不同的。本文中对相关的平头弹穿甲Weldox 700E单层及双层间隙式钢靶的实验数据进行分析,讨论其穿甲模式。弹速较高时,贯穿第1层靶发生绝热剪切失效,弹速降低,贯穿第2层靶板发生绝热剪切失效或剪切冲塞失效, 最终失效模式为绝热剪切和剪切冲塞混杂。     

Perforation of 7075-T651 Aluminum Armor Plates with 7.62 mm APM2 Bullets

We conducted an experimental and analytical study to better understand the mechanisms and dominant parameters for 7.62 mm APM2 bullets that perforate 7075-T651 aluminum armor plates. The 7.62-mm-diameter, 10.7 g, APM2 bullet consists of a brass jacket, lead filler, and a 5.25 g, ogive-nose, hard steel core. The brass and lead were stripped from the APM2 bullets by the targets, so we conducted ballistic experiments with both the APM2 bullets and only the hard steel cores. These projectiles were fired from a rifle to striking velocities between 600 and 1,100 m/s. Targets were 20 and 40-mm-thick, where the 40-mm-thick targets were made up of layered 20-mm-thick plates in contact with each other. The measured ballistic-limit velocities for the APM2 bullets were 1% and 8% smaller than that for the hard steel cores for the 20 and 40-mm-thick targets, respectively. Thus, the brass jacket and lead filler had a relatively small effect on the perforation process. Predictions from a cylindrical cavity-expansion model for the hard steel core projectiles are shown to be in good agreement with measured ballistic-limit and residual velocity data. The results of this study complement our previous paper with 5083-H116 aluminum target plates in that the ultimate tensile strength of 7075-T651 is about 1.8 times greater than that of 5083-H116. We also present a scaling law that shows a square root relationship between ballistic-limit velocity and plate thickness and material strength.     

带前舱物的钝头弹对金属靶的正穿甲分析

进一步发展了考虑结构响应的剪切冲塞模型,计及前舱物的作用,对带前舱物的钝头弹穿甲金属靶的工程问题进行了刚塑性分析,用于分析终点弹道极限和剩余速度。除剪切破坏之外,模型还考虑了靶板弯曲、膜力拉伸和前舱物撞击引起的靶板预结构响应等。给出了简洁的终点弹道性能公式,与相关实验结果较吻合。     

卵形头部刚性弹侵彻厚靶的半解析模型

基于确定靶体中速度势和速度场的方法分析刚性卵形头部弹体对有限厚靶的侵彻问题。推导了靶体中速度场与应力场的计算方法,利用据此编制的计算程序,计算了卵形头部钢弹体对铝靶的侵彻与穿透问题,给出了侵彻深度与剩余速度同初始碰撞速度的关系。结果表明,在对实验参数不经过任何调整的情况下,得到了同试验曲线相吻合的结果。可以看出该方法的有效性。     

Rigorous model-based uncertainty quantification with application to terminal ballistics—Part II. Systems with uncontrollable inputs and large scatter

This Part II of this series is concerned with establishing the feasibility of an extended data-on-demand (XDoD) uncertainty quantification (UQ) protocol based on concentration-of-measure inequalities and martingale theory. Specific aims are to establish the feasibility of the protocol and its basic properties, including the tightness of the predictions afforded by the protocol. The assessment is based on an application to terminal ballistics and a specific system configuration consisting of 6061-T6 aluminum plates struck by spherical 440c stainless steel projectiles at ballistic impact speeds in the range of 2.4–2.8 km/s. The system's inputs are the plate thickness, plate obliquity and impact velocity. The perforation area is chosen as the sole performance measure of the system. The objective of the UQ analysis is to certify the lethality of the projectile, i.e., that the projectile perforates the plate with high probability over a prespecified range of impact velocities, plate thicknesses and plate obliquities. All tests were conducted at Caltech's Small Particle Hypervelocity Range (SPHIR), which houses a two-stage gas gun. A feature of this facility is that the impact velocity, while amenable to precise measurement, cannot be controlled precisely but varies randomly according to a known probability density function. In addition, due to a competition between petalling and plugging mechanisms for the material system under consideration, the measured perforation area exhibits considerable scatter. The analysis establishes the feasibility of the XDoD UQ protocol as a rigorous yet practical approach for model-based certification of complex systems characterized by uncontrollable inputs and noisy experimental data.     

A3钢钝头弹撞击45钢板破坏模式的试验研究

为了研究破片模拟弹的终点弹道效应,进行了不同质量A3钢钝头弹(弹径25 mm)撞击45钢板的试验研究,其中A3钢强度弱于45钢。在约200～800 m/s的撞击速度范围内,随着撞击速度的增加,分别观察到弹体出现泰勒撞击、向日葵型花瓣帽形失效及靶板冲塞穿甲三种破坏模式。伴随弹体和靶体经历的不同结构破坏模式,弹材和靶材也经历着相当复杂的材料失效。