Deep penetration of a non-deformable projectile with different geometrical characteristics

A general non-dimensional formula based on the dynamic cavity-expansion model is proposed to predict penetration depth into several mediums subjected to a normal impact of a non-deformable projectile. The proposed formula depends on two dimensionless numbers and shows good agreement with penetration tests on metal, concrete and soil for a range of nose shapes and impact velocities. The validity of the formula requires that the penetration depth is larger than the projectile diameter and the projectile nose length while projectile remains rigid without noticeable deformation and damage.     

弹体冲击混凝土半无限靶的侵彻阻力与深度计算

假设弹体是刚性的,将弹体侵彻冲击作用下的混凝土靶体划分为粉碎区、径向裂缝弹性区与原始弹性区,并认为侵彻粉碎区域内的混凝土材料处于类似于流体动力学状态,可采用水动力模型.根据伯努利方程推得了细长杆弹侵彻阻抗力的公式,进而求出锥形弹头侵彻阻抗力的等效平面解,得到了弹体的侵彻深度.利用实弹进行了以不同速度侵彻不同强度的混凝土靶体的验证计算,并与多个经验公式做了对比.结果表明,该模型是合理的,与经验公式相比计算结果趋于保守.     

Resistance of high-strength concrete to projectile impact

This paper presents the results of an experimental study on the impact resistance of concrete with compressive strengths of 45–235 MPa when subjected to impact by 12.6 mm ogive-nosed projectile at velocities ranging from ∼620 to 700 m/s. The results indicate that the penetration depth and crater diameter in target specimens exhibit an overall reduction with an increase in the compressive strength of the concrete. However, the trend is not linear. Further increase in the compressive strength requires a reduction in the water-to-cementitious material ratio and the elimination of coarse aggregates. However, doing these does not result in reduction of the penetration depth and crater diameter. The presence of coarse granite aggregates appears to be beneficial in terms of reducing penetration depth, crater diameter, and crack propagation, thus contributing to impact resistance. Incorporation of steel fibers in the concrete reduced the crater diameter and crack propagation, but did not have a significant effect on penetration depth. An increase in the curing temperature from 30°C to 250°C did not alter the impact resistance of the concrete significantly. Based on the present findings and cost consideration, high-strength fiber-reinforced concrete with a compressive strength of ∼100 MPa appears to be most efficient in protection against projectile impact.     

Multiple impact penetration of semi-infinite concrete

An experimental study was performed to gather multiple impact, projectile penetration data into concrete. A vertical firing range was developed that consisted of a 30-06 rifle barrel mounted vertically above a steel containment chamber. 0.41 m cubes of an Air Force G mix concrete were suspended in wet sand and positioned in the steel chamber. The concrete targets were subjected to repeated constant velocity impacts from 6.4 mm diameter steel projectiles with an ogive nose shape and a length to diameter ratio of 10. A laser sight was adapted to the rifle to ensure alignment, and a break screen system measured the projectile velocity. After each impact, the projectile penetration and crater formation parameters were recorded. The penetration and crater formation data were consistent with single impact penetration data from previous studies conducted at Sandia National Laboratories. In addition, an analytic/empirical study was conducted to develop a model that predicted the penetration depth of multiple impacts into concrete targets. Using the multiple impact penetration and crater formation data, a single impact penetration model, developed by Forrestal at Sandia National Laboratories, was extended to account for the degradation of the target strength with each subsequent impact. The degradation of the target was determined empirically and included in the model as a strength-modifying factor. The model requires geometry parameters of the ogive nose projectile, projectile velocity, the number of impacts, and target compressive strength to calculate the overall penetration depth of the projectile.     

An examination of long-rod penetration

The one-dimensional modified Bernoulli theory of Tate [J. Mech. Phys. Solids 15, 287–399 (1967)] is often used to examine long-rod penetration into semi-infinite targets. The theory is summarized and the origins of the target resistance term examined. Numerical simulations were performed of a tungsten-alloy, long-rod projectile into a semi-infinite hardened steel target at three impact velocities sufficiently high to result in projectile erosion. The constitutive responses of the target and projectile were varied parametrically to assess the effects of strain hardening, strain-rate hardening, and thermal softening on penetration response. The results of one of the numerical simulations were selected to compare and contrast in detail with the predictions of the Tate model.     

Normal penetration of an eroding projectile into an elastic–plastic target

The main objective of the present work is to describe normal penetration of a deformable projectile into an elastic–plastic target. The force imposed on the projectile by the target is generally a complex function of the strength of the target material, the projectile velocity, its diameter and shape, as well as the instantaneous penetration depth. When this force exceeds a certain critical value the projectile begins to deform. At moderate-to-high values of the impact velocity, the projectile's tip material flows plastically with large deformations causing the formation of a mushroom-like configuration. This process is accompanied by erosion of the projectile material. In the rear (“elastic”) part of the projectile the deformations remain small and the region can be approximated as a rigid body being decelerated by the projectile's yield stress. The general model allows one to predict the penetration depth, the projectile's eroded length and the crater diameter. It has been shown that in the limit of very high impact velocities the present model reduces to the well-known form of the hydrodynamic theory of shaped-charge jets. Also, a simplified asymptotic formula for the crater radius has been derived which includes the effect of the target's yield stress and compares well with experimental data for very high impact velocities.     

Tungsten long-rod penetration into confined cylinders of boron carbide at and above ordnance velocities

The purpose was to investigate the influence of impact velocity and confinement on the resistance of boron carbide targets to the penetration of tungsten long-rod projectiles. Experimental tests with impact velocities from 1400 to 2600 m/s were performed using a two-stage light-gas gun and a reverse impact technique. The targets consisted of boron carbide cylinders confined by steel tubes of various thicknesses. Simulations were carried out using the AUTODYN-2D code and Johnson–Holmquist's constitutive model with and without damage evolution. The experimental results show that the penetration process had different character in three different regions. At low-impact velocities, no significant penetration occurred. At high-impact velocities, the relation between penetration velocity and impact velocity was approximately linear, and the penetration was steady and symmetrical. In between, there was a narrow transition region of impact velocities with intermittent and strongly variable penetration velocity. In the lower part of this region, extended lateral flow of the projectile took place on the surface of the target. The influence of confinement on penetration velocity was found to be small, especially at high-impact velocities. The simulated results for penetration velocity versus impact velocity agreed fairly well with the experimental results provided damage evolution was suspended below the transition region.     

三维编织复合材料弹道侵彻准细观层次有限元计算

三维编织复合材料相比于层合复合材料有较高的层间剪切强度和断裂韧性,因而具有更高的冲击损伤容限。用钢芯弹对三维编织复合材料作弹道贯穿测试,得到弹体的入射速度和剩余速度,并考察侵彻破坏模式。目前对三维编织复合材料弹道侵彻性能计算主要建立在连续介质假设上,从真实细观结构计算三维编织复合材料弹道冲击性能尚有一定难度,用三维结构复合材料的纤维倾斜模型在准细观结构层次上分解三维编织复合材料,就其中的一块倾斜单向板作弹道侵彻有限元计算,由弹体动能损失得到贯穿整个复合材料靶体后弹体的剩余速度。有限元计算及与弹道测试结果的比较证明在准细观层次上计算三维编织复合材料弹道冲击性能的有效性。      

Penetration analysis for geo-material based on unified strength criterion

A unified strength criterion is applied for penetration analysis of geo-materials. Based on the cylindrical cavity-expansion theory the relation between the radial traction on the cavity surface and the impact velocity of a rigid projectile is derived. The finial penetration depth of the projectile is analytically obtained and the effect of strength criterion on the penetration depth is investigated. By comparing with existing test results, it is found that the proposed penetration model is effective in the analysis of a rigid projectile penetrating into a semi-infinite geo-material target.     

Finite element modeling of impact, damage evolution and penetration of thick-section composites

Impact, damage evolution and penetration of thick-section composites are investigated using explicit finite element (FE) analysis. A full 3D FE model of impact on thick-section composites is developed. The analysis includes initiation and progressive damage of the composite during impact and penetration over a wide range of impact velocities, i.e., from 50 m/s to 1000 m/s. Low velocity impact damage is modeled using a set of computational parameters determined through parametric simulation of quasi-static punch shear experiments. At intermediate and high impact velocities, complete penetration of the composite plate is predicted with higher residual velocities than experiments. This observation revealed that the penetration-erosion phenomenology is a function of post-damage material softening parameters, strain rate dependent parameters and erosion strain parameters. With the correct choice of these parameters, the finite element model accurately correlates with ballistic impact experiments. The validated FE model is then used to generate the time history of projectile velocity, displacement and penetration resistance force. Based on the experimental and computational results, the impact and penetration process is divided into two phases, i.e., short time Phase I - shock compression, and long time Phase II - penetration. Detailed damage and penetration mechanisms during these phases are presented.     

Depth of penetration of high-speed penetrator with including the effect of mass abrasion

Mass abrasion is observed on the nose of projectile when a projectile strikes concrete target at high velocity. To evaluate the influence of the mass abrasion on the depth of penetration (DOP) limit, the relationship between the nose factor of the residual projectile after abrasion and the initial impact velocity is suggested according to the experimental data. Based on the dynamic cavity expansion theory, with considering the effects of varying nose factor and mass of projectile, a modified model is proposed to calculate the depth of penetration of kinetic energy penetrator. The model predicts that a theoretical maximum DOP exists due to the mass abrasion of the projectile. The model is checked by the different experimental data.     

On the hydrodynamic approximation for long-rod penetration

Steady-state hydrodynamic theory, or variations thereof, has been applied to long-rod penetration since the 1940s. It is generally believed that projectile strength is of little consequence at high velocities, and that hydrodynamic theory is applicable to long-rod penetration when penetration pressures are much greater than the target flow stress. Substantiating this belief is the observation that at approximately 2.5 km/s, for tungsten alloy projectiles into armor steel, normalized penetration (P/L) nominally saturates to the classical hydrodynamic limit of the square root of the ratio of the projectile to target densities. Experimental data herein, however, show penetration velocities and instantaneous penetration efficiencies fall below that expected from hydrodynamic theory, even at impact velocities as high as 4.0 km/s. Numerical simulations, using appropriate strength values, are in excellent agreement with the experimental data. Parametric studies demonstrate that both projectile and target strength have a measurable effect even at such high impact velocities.     

蜂窝铝的侵彻实验研究与有限元模拟

目的 研究弹体侵彻蜂窝铝的力学行为。方法 在实验中, 通过轻气炮加速的尼龙弹体冲击蜂窝铝靶体。利用Ansys/LS-DYNA建立了弹体侵彻蜂窝铝的壳单元有限元模型。结果 实验给出了冲击速度为140和167 m/s时弹体的加速度曲线。运用壳单元模型对蜂窝铝的侵彻进行模拟, 得到了弹体的加速度曲线以及蜂窝铝在侵彻过程中的变形图。结论 将模拟结果与实验结果进行了对比, 发现模拟结果与实验结果符合较好, 证明了壳单元有限元模型模拟蜂窝铝侵彻行为的可靠性。     

The dependence of penetration velocity on impact velocity

Recent experimental measurements show that eroding long-rod penetration velocity is a linear function of impact velocity over a very wide range of impact velocities and for an interesting range of rod–target material combinations. These experiments all show that U=a+bV, where U and V are the penetration and impact velocity, respectively, and “a” and “b” are constants for given projectile and target materials. Numerical simulations also show that U=a+bV. The accumulation of these results suggests that a linear relationship between penetration and impact velocity may be fundamental over a very large range of impact velocities. A linear relationship between penetration and impact velocity has a number of implications. Some implications of this result for the Tate–Alekseevskii model are briefly examined in this paper.     

An investigation on mass loss of ogival projectiles penetrating concrete targets

Mass loss of an ogival projectile during its normal penetration in concrete target was investigated in this paper. Experiments of 38CrSi short-rod projectiles with ogival nose shape penetrating into concrete targets were conducted in the striking velocity range of 500–1500 m/s. Discussions revealed that projectile mass loss derives mainly from the nose part for both short-rod and long-rod projectiles during the penetration process. Furthermore, an engineering model was proposed to determine upper limit of rigid penetration regime as the maximum value of the striking velocity, which was based on the feature of projectile mass loss in the hydrodynamic transition between rigid penetration regime and semi-hydrodynamic penetration regime. Good agreements are obtained between engineering predictions and experimental results.     

粗骨料种类对刚性弹贯穿混凝土靶剩余速度的影响

针对弹体贯穿混凝土靶问题,混凝土细观尺度模型能够反映混凝土中各介质对混凝土力学行为的影响。本研究编写了三维随机球形粗骨料的生成和投放程序,并采用一种基于背景网格的材料识别技术建立了含有水泥砂浆和粗骨料两种网格的三维混凝土细观有限元模型,同时将界面过渡区简化为这两种网格之间的一种可失效的接触。基于这一模型,运用连续有限元软件对刚性弹贯穿混凝土过程进行了数值仿真,并分析了三个不同种类的粗骨料对剩余速度的影响。结果表明,粗骨料的强度和密度分别在较低和较高的着靶速度下对剩余速度有一定影响。     

考虑攻角的长杆弹斜穿透中厚铝靶机理

攻角对长杆弹斜侵彻有重要影响,该文通过大量数值模拟研究了攻角对长杆弹斜穿透中厚铝板的影响机理。基于实验验证的有限元模型,开展了变速度和攻角的多工况数值模拟,得到了侵彻过程中弹体的减加速度大小、速度方向以及整体弯曲的变化规律,分析了侵彻速度、倾角和攻角对侵彻阻力、弹体弯曲和弹道偏转的影响。结果表明:带攻角斜侵彻时,负攻角对弹体弯曲的影响明显大于正攻角,且弹体弯曲随着侵彻速度的增大而减小;随着斜侵彻速度的增大,攻角引起弹体甩尾和弹道偏转越明显,此时带攻角的斜侵彻过程的能量损耗机理明显不同于正侵彻和无攻角的斜侵彻。     

Finite element calculation of 4-step 3-dimensional braided composite under ballistic perforation

The ballistic perforation test results of 4-step 3-dimensional (3D) braided Twaron^®/epoxy composites, which were subjected to impact by conically cylindrical steel projectile, are presented. The residual velocities of projectile perforated composites target at various strike velocities were measured and also compared with that from finite element calculation. ‘Fiber inclination model’ for 3D textile composites was adopted to decompose the 3D braided composite at quasi-microstructure level for the geometrical modeling in preprocessor of FEM. The material modeling was also based on this simplified model. The finite element code of Ls-Dyna was used to simulate the impact interaction between projectile and inclined lamina. The residual velocity of projectile perforating the entire 3D braided composite can be calculated from the sum of kinetic energy loss of the projectile that obtained from FEM. From the simulation of ballistic penetration process and comparison between numerical results and experimental results, it proves that the analysis scheme of quasi-microstructure level in this paper is valid and reasonable. The simplified method in this paper could be extended to model other kinds of 3D textile composites under ballistic impact.