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.      

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。     

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。     

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     

On the ballistic resistance of double-layered steel plates: An experimental and numerical investigation

Civil and military ballistic protection systems often consist of thin, high-strength steel plates. Such plates may either be monolithic or layered with or without spacing. The idea of using layered plates instead of a monolithic one in order to increase the ballistic perforation resistance is not new, and the effect of using targets made up of several thinner plates has been investigated in the literature for a long time. However, results by various authors are contradicting and detailed experimental and numerical work is still required.In the present study, the ballistic perforation resistance of double-layered steel plates impacted by blunt and ogival projectiles was investigated both experimentally and numerically. In the tests, 12 mm thick (monolithic or layered) targets of Weldox 700 E were impacted using a gas-gun at sub-ordnance velocity, and the ballistic limit velocity of the different target combinations was obtained. In general, good agreement was obtained between the numerical simulations and the experimental results. It was found that in the case of blunt projectiles a large gain in the ballistic limit is offered by double-layered systems. These advantages seem to disappear when ogival projectiles are used. However, the main conclusion from both the experimental and numerical studies is that the overall protection level, i.e. the minimum ballistic limit velocity obtained independently of projectile nose shape, seems to increase significantly by double-layering the target.     

Deformation and Failure Modes of Soft Steel Projectiles Impacting Harder Steel Targets at Increasing Velocity

The present paper describes an experimental and numerical study concerning the impact of blunt steel projectiles against harder steel plates, at impact velocities between 200 and 800 m/s. In contrast with previously published observations, three modes of deformation and failure of the soft steel projectiles were observed in the present study. These included: Taylor cylinder mushrooming, sunflower-like petalling and plugging perforation. Individual velocity ranges and the transitions between the deformation/failure modes are identified by both experiments and numerical simulations. Complex material failure mechanisms of projectile and target play conflicting roles in the various penetration stages. Johnson–Cook models of strength and accumulative damage failure are employed in 3D numerical simulation to describe material behavior of both projectile and target. Computational evolutions of each scenario are offered in detail to understand the deformation and failure of projectile and target plate.     

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。     

On the deep penetration and plate perforation by rigid projectiles

We present results of a large number of 2D numerical simulations in which we investigated various aspects in the deep penetration of rigid short projectiles into semi-infinite targets, as well as their perforation through thin metallic plates. In particular, we analyze the effect of the entrance phase on the penetration characteristics of short ogive and spherical nosed projectiles. The second issue which we investigate here concerns the perforation of metallic plates by sharp nosed projectiles. Our simulation results show that a simple model, which is based on energy conservation, accounts for the residual velocities when the target is penetrated by the ductile hole enlargement process. In addition, we define a new concept, the effective resisting stress which the plate exerts on the projectile during perforation. We show that it has some valuable insights for the process of perforation and we perform a parametric study to understand its dependence on various parameters. This effective stress, which determines the ballistic limit velocity of the projectile, depends on the strength of the plate, as well as on its thickness, as we show here.     

细长尖头刚性弹对金属靶板的斜侵彻/穿甲分析

给出细长尖头刚性弹（如尖卵、尖锥形）斜侵彻/穿甲金属靶的一个分析模型。在细长尖头弹对中厚度金属靶的斜穿甲中,韧性孔洞扩张为主要的穿甲机理;着靶初期,发生方向角的改变。研究表明,金属靶的斜穿甲仅由4个量纲一参数控制,即冲击函数I、弹体几何函数N、量纲一靶厚和撞击斜角。分析得到显式的侵彻深度、终点弹道极限、剩余速度和撞击方向改变角表达式。该模型可预期跳飞发生的临界条件。理论预期与实验结果吻合较好。     

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.     

细长薄壁弹体的屈曲和靶体等效分析

利用金属靶开展动能深侵彻弹的穿甲屈曲实验研究。实验观察到长/短型弹体动塑性屈曲破坏分别表现为轴向皱褶型和轴向外翻撕裂型2种基本模式。不同的屈曲破坏模式与弹体几何、撞击初条件以及靶材等密切相关。区别于刚性尖头弹穿甲金属靶的韧性隧道开孔,尖头弹因屈曲破坏易变形为钝头形,导致弹体穿透靶板表现为挤凿穿甲。利用薄壁中空柱壳的弹性欧拉屈曲分析和弹体塑性屈服的极限分析给出弹体动塑性屈曲的临界条件。同时给出屈曲实验中混凝土靶和金属靶的等效条件。     

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     

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.     

刚性尖头弹垂直撞击金属厚靶板极限速度分析

研究了刚性尖头弹垂直撞击金属厚靶板扩孔冲塞型和延性扩孔型穿孔模式,提出分析最小穿透能量的两阶段工程模型．应用功能原理和圆柱形空腔膨胀理论得到第一阶段侵彻扩孔耗能．考虑靶板背面自由边界的影响,应用Taylor扩孔理论计算延性扩孔型穿孔第二阶段耗能;考虑加速塞块和剪断塞块所损耗的能量,由动量和能量原理导出扩孔冲塞型穿孔第二阶段剪切冲塞耗能．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．与铝合金和装甲钢靶板弹道试验数据比较表明,该文两阶段模型的计算结果与试验结果吻合较好。     

Experiments and modeling of ballistic penetration using an energy failure criterion

One of the most intricate problems in terminal ballistics is the physics underlying penetration and perforation. Several penetration modes are well identified, such as petalling, plugging, spall failure and fragmentation (Sedgwick, 1968). In most cases, the final target failure will combine those modes. Some of the failure modes can be due to brittle material behavior, but penetration of ductile targets by blunt projectiles, involving plugging in particular, is caused by excessive localized plasticity, with emphasis on adiabatic shear banding (ASB).Among the theories regarding the onset of ASB, new evidence was recently brought by Rittel et al. (2006), according to whom shear bands initiate as a result of dynamic recrystallization (DRX), a local softening mechanism driven by the stored energy of cold work. As such, ASB formation results from microstructural transformations, rather than from thermal softening. In our previous work (Dolinski et al., 2010), a failure criterion based on plastic strain energy density was presented and applied to model four different classical examples of dynamic failure involving ASB formation. According to this criterion, a material point starts to fail when the total plastic strain energy density reaches a critical value. Thereafter, the strength of the element decreases gradually to zero to mimic the actual material mechanical behavior.The goal of this paper is to present a new combined experimental–numerical study of ballistic penetration and perforation, using the above-mentioned failure criterion. Careful experiments are carried out using a single combination of AISI 4340 FSP projectiles and 25[mm] thick RHA steel plates, while the impact velocity, and hence the imparted damage, are systematically varied. We show that our failure model, which includes only one adjustable parameter in this present work, can faithfully reproduce each of the experiments without any further adjustment.Moreover, it is shown that the most common failure criterion based on a critical strain is simply inadequate to reproduce the results, due to the linear nature of the damage evolution. The advantages of the energy-based failure criterion are discussed in detail.     

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.     

Simulations of a top-hat section subjected to axial crushing taking into account material and geometry variations

Simulations of top-hat thin-walled sections of dual-phase steel DP800 subjected to axial crushing have been performed taking into account process history and measured geometric imperfections, thickness variations and material variations. The simulations were based on experiments performed by Fyllingen et al. [Fyllingen, Ø., Hopperstad, O.S., Langseth, M., 2008. Robustness study on the behaviour of top-hat thin-walled high-strength steel sections subjected to axial crushing. International Journal of Impact Engineering, in press, doi:10.1016/j.ijimpeng.2008.03.005], who investigated the robustness of a top-hat section subjected to axial crushing. The geometry variation and spatial strain hardening variation were mapped onto the model. The fracture parameter and strain-rate sensitivity were based on values obtained from one of the batches. It was emphasised to use an element type, element size, a fracture criterion and a spot-weld model typically used by the industry. Compared to nominal models especially the thickness variations, geometric imperfections and material failure criterion influenced the behaviour. The material batch variation resulted in large differences in the batch means of the mean crushing forces and the variation in the geometric imperfections and thickness resulted in variation in the mean crushing force within each batch. Compared to the experiments the model generally under-predicted the mean crushing force.     

厚壁压力管道侧向冲击破坏的实验研究

本文报导了三跨连续压力管道侧向受平头、半球头及锥头弹体冲击破坏的实验研究结果,管的外径为45mm,厚度为3mm,内充液体压力分别为0MPa,5MPa,10MPa,15MPa和20MPa五级,获得了不同工况下的临界破坏速度及相应的破坏模式,实验过程中测量并记录了圆管的变形、冲击力时程曲线。实验结果表明,内充介质的存在降低了临界破坏能量,同时临界破坏能量随内充介质压力的增加而减小。     

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.     

Experimental Study on the Perforation Process of 5754-H111 and 6082-T6 Aluminium Plates Subjected to Normal Impact by Conical,Hemispherical and Blunt Projectiles

This paper presents an experimental investigation on the perforation behaviour of 5754-H111 and 6082-T6 aluminium alloys. The mechanical response of these materials has been characterized in compression with strain rates in the range of $10^{-3}~s^{-1} < \dot {\varepsilon } < 5 \cdot 10^{3}~s^{-1}$ . Moreover, penetration tests have been conducted on 5754-H111 and 6082-T6 plates of $4~mm$ thickness using conical, hemispherical and blunt projectiles. The perforation experiments covered impact velocities in the range of $50~m/s < V_{0} < 200~m/s$ . The initial and residual velocities of the projectile were measured and the ballistic limit velocity obtained for the two aluminium alloys for the different nose shapes. Failure mode and post-mortem deflection of the plates have been examined and the perforation mechanisms associated to each projectile/target configuration investigated. It has been shown that the energy absorption capacity of the impacted plates is the result of the collective role played by target material behaviour, projectile nose shape and impact velocity in the penetration mechanisms.