Impact and penetration by L/D ≤ 1 projectiles

Calculations of steel target penetration by L/D ≤ 1 tungsten and tungsten alloy projectiles have been extended to L/D = 1/32 over the velocity range 1.5 to 5 km/s. The ratio of crater to projectile diameter tends to 1 as L/D decreases over this entire velocity range. For impact velocities of 1.5 and 3 km/s, penetration depth normalized by projectile length, P/L, increases with decreasing projectile L/D up to a maximum value and then decreases for still lower L/D. Experiments at impact velocities of 2 and 3 km/s confirm these results. For 5 km/s impact velocity, the calculations show P/L increasing with decreasing projectile L/D over the entire range 1/32 ≤ L/D ≤ 1. The projectile L/D for which the maximum P/L occurs appears to depend on the impact velocity. P/L generally scales with impact velocity as P/L v^f(L/D) where f(L/D) ranges from 0 for a long rod to, we believe, 2 in the limit as projectile L/D approaches zero. The calculations show for 1/8 ≤ L/D ≤ 1/2, P/L v^0.9; for L/D = 1/16, P/L v^1.5; and for L/D = 1/32, the new results give P/L v^1.9.     

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.     

Variation of crater geometry with projectile L/D for L/D ≤ 1

A series of hydrocode calculations and terminal ballistics experiments were performed to investigate the penetration mechanics of projectiles with L/D ≤ 1. Projectile L/D ranged from 1/32 to 1; impact velocity ranged from 1.5 to 5 km/s. Projectiles were tungsten or tungsten alloy, targets were RHA. The paper concentrates on the effect of projectile L/D on the size and geometry of the target crater. Normalized crater depth (or penetration) increases with decreasing projectile L/D and achieves a maximum at about L/D=1/8 for 1.5 km/s and 1/16 for 3 km/s, and then decreases with further decrease in L/D. For 5 km/s, P/L increases with decreasing L/D over the entire range studied. P/L scales with impact velocity as P/L V^f(L/D) where, we believe, f(L/D) approaches 2 as L/D 0. The ratio of crater to projectile diameter D_c/D decreases with decreasing L/D and approaches a value of 1 as L/D approaches zero for all velocities studied. The crater shape measured by P/D_c decreases with decreasing L/D; i.e., as L/D decreases, the crater changes from approximately hemispherical for L/D = 1 to a very shallow disk shape. The kinetic energy required per unit crater volume, KE/V_c, increases with decreasing L/D for L/D < 1/4. That is, cratering efficiency decreases with decreasing projectile L/D. For the impacts studied, KE/V_c increases from about 5 kJ/cm³ to 12 kJ/cm³ as projectile L/D is reduced from 1 to 1/32.     

Estimation of a crater volume formed by impact of a projectile on a metallic target

The crater volume has been an important factor in ballistics and has many influences such as material strength, initial projectile velocity, angle of incidence, and nose shape. The goal of this research is to predict the resulting crater volume of a long rod penetration based on the initial projectile velocity and mass. Mooney’s (Bull Seism Soc Am 64(2):473, 1974) displacement equations were used to calculate the elastic crater volume for a given impulse force, P, varying as a delta function in time on the surface of an isotropic, semi-infinite solid. This estimated elastic volume, V_elastic is linearly related to the experimental ballistic volume, V_experimental by an “energy dissipation factor”, k. V_elastic = kV_experimental. The energy dissipation factor “lumps” together elastic and plastic deformation mechanisms. Terminal ballistic data for a steel long-rod projectile into “semiinfinite” steel or aluminum target will be compared to the crater volume calculated through the use of k.     

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.     

高速长杆弹对有限直径金属厚靶的侵彻分析EI北大核心CSCD

采用基于统一强度理论的有限柱形空腔膨胀理论,结合Tate磨蚀杆模型,考虑中间主应力、靶体侧面自由边界的影响及高速(1500 m/s~2200 m/s)侵彻弹体的变形和消蚀现象,推导线性硬化有限直径金属厚靶在长杆弹高速侵彻时的空腔壁径向应力,建立侵彻阻力和侵彻深度计算模型,并利用MATLAB软件编程求解,分析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、对不同靶弹半径比的靶材侵彻深度的区间范围进行有效预测;强度参数、弹体撞击速度和靶体半径对有限直径金属靶体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,侵彻阻力可减小33.33%,侵彻深度可增加15.93%;当靶弹半径比小于等于20时,侵彻深度增大的程度显著,当靶弹半径比由19.88减小至4.9时,侵彻阻力减小了41.30%,侵彻深度增长了32.61%,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。     

Hypervelocity impact of rod projectiles with L/D from 1 to 32

Beside a short remark on the “hydrodynamic theory of rod projectiles”, the paper deals with the terminal ballistic behaviour of cylindrical projectiles against semi-infinite targets. Experimental data of EMI, completed by results of some other authors, are presented. Crater parameters like depth, diameter and volume and their dependence on projectile velocity (up to 5000 m/s), projectile and target material properties, as well as L/D-ratios (1–32), will be discussed. Mainly the projectile materials steel and tungsten sinter-alloys are considered. Target materials are mild steel and high strength steel, an Al-alloy and a tungsten sinter-alloy. The results show that the influence of material density on the crater dimensions is considerably greater than the influence of strength. The L/D ratio determines the velocity dependence of crater depth, diameter and volume. At high velocities in the hydrodynamic regime, the crater depth of short cylinders (L/D 1) is approximately proportional to v_p^2/3 (V_p=projectile velocity). With increasing L/D-ratio, the slope of the penetration curves decreases and converges for rods (L/D 1) versus a saturation, i. e. becomes nearly independent on v_p. A consequence of this saturation is the existence of a so-called “tangent velocity”, above which an optimal increase of efficiency is only realized by increasing the projectile mass and not the velocity. Furthermore, ballistic limits of real targets like single plates and symmetric double plates meteorite bumper shield) are taken into account. The expected better performance of “segmented rods” is also discussed.     

Hypervelocity impact on isotropic composites with metal or ceramic inclusions

Experimental results of studying the hypervelocity impact on isotropic heterogeneous composites consisting of an epoxy or aluminum matrix containing fine-grained metal (Al, Pb) or ceramic (SiO₂) inclusions are given. The aim of the study is to develop composite materials offering higher penetration resistance to a high-velocity projectile than the component material. This resistance is characterized by the magnitude of the ratio of the crater depth in a thick target to the diameter of spherical projectile. In the case of two particulate composites studied it is shown that the crater depth from impact of steel projectiles is lower about by one projectile diameter than for homogeneous lead or aluminum over the impact velocity ranged from 3 up to 11 km/s.     

Yaw impact of rod projectiles

The purpose of this numerical study is to investigate the penetration regimes for L/D 30 tungsten-alloy rod projectiles for cases where the impact yaw angle varies from 0 to 90° and for impact velocities from 1.4 to 2.6 km/s. The target is modeled as a semi-infinite or half-space block of rolled homogeneous armor (RHA) at zero obliquity. For cases of mild interference, the penetration channel is still deep and narrow but may be skewed with respect to the original shot-line. While penetration is degraded the efficiency of the rod projectile remains relatively high. With increasing yaw angle the rod may deform due to transverse loading to the extent such that it contacts and produces gouges on the opposite side of the penetration channel. Additionally, lateral loading may induce angular acceleration to the extent such that the tail of the projectile rotates (in the plane of symmetry) and also contacts the opposite side of the penetration channel. In the next discernible penetration regime, the long-rod deforms under transverse load but the tail does not rotate significantly. It is seen that nearly the entire rod length experiences the lateral load with the result that the original shot-line is significantly altered. The deformed rod, again, has multiple contact or loading points (or regions) and the resultant angular acceleration appears to be insufficient to induce rotation of the projectile tail. Thus, rather than ricochet, the projectile cuts a significant slot into the target. Finally, for very large yaw angles the crater becomes indistinguishable from one produced by a side-on or 90° impact even though the impact yaw angle may be significantly less than 90°.     

Experimental study of morphology scaling of a projectile obliquely impacting into loose granular media

The morphology scaling of a spherical projectile obliquely impacting into loose granular media is experimentally investigated. The influences of projectile’s releasing distance, diameter and oblique impact angle are mainly considered. Based on the experimental results, four scaling laws are eventually proposed to describe the variations of the length, width, depth of impact crater and the penetration depth of projectile after impacting. We find that when the impact angle is larger than a critical value, these quantities all exhibit power law dependences on the releasing distance, diameter and impact angle of projectile, which are analogous to that obtained in other similar vertical impacting experiments. It is also observed that once the oblique impact angle exceeds this critical value, the tadpole-shaped impact crater may commonly evolve into an elliptical one. At small impact angles, we find that the scaling laws on both the width and the depth of impact crater are still valid, although the corresponding fitting exponents have slightly deviated from those values at larger impact angles. However, the length of crater and the penetration depth of projectile seem to no longer yield such proposed scaling laws, possibly due to the different physical mechanism induced by the rebounding movements of projectile at small impact angles.     

The influence of plate hardness on the ballistic penetration of thick steel plates

This investigation describes and analyses the experimental results pertinent to the penetration of steel plates of varying hardness in the range HV295–HV520 and of thickness 20 and 80 mm by ogive-shaped 20-mm-diameter projectiles over the velocity range 300–800 m s⁻¹. All the tests were carried out at normal impact angle, i.e. zero obliquity. The experimental results presented include the variation of depth of penetration, crater volume, lip height, bulge height and diameter, plugged length and diameter and specific energy absorption capacity with impact velocity for tests on each plate of a given hardness and thickness. Selected data and observations relating to the plastic zone size and shape surrounding the penetrating projectile, incidence and extent of adiabatic shear band (ASB) formation and plate spalling have also been presented. These experimental data have been interpreted in terms of the appropriate penetration mechanisms like ductile hole formation, bulging followed by star cracking, ASB-induced shear plugging, etc., and also by making use of the fact that the projectile undergoes substantial deformation when penetrating the harder plates (HV450 and HV520). It is also demonstrated that the resistance to penetration and hence the mechanism of penetration is very much dependent on whether the penetration occurs under plane strain or plane stress conditions. For example, ASB-induced plugging occurs only under plane stress conditions while projectile deformation is dominant only under plane strain conditions even in harder plates.     

Oblique penetration of a rigid projectile into a thick elastic–plastic target: theory and experiment

A model of oblique penetration of a rigid projectile into a thick elastic–plastic target has been developed (Roisman et al., Int J Impact Engng 1997; 19: 769–95) which incorporates stress-free boundary conditions at the rear surface of the target. The main objective of the present work is to validate the theoretical model by comparison with new experimental results for normal and oblique penetration of a rigid projectile into a thick plate of Al 6061-T651. Good agreement between theory and experiment is exhibited for the projectile residual velocity and the crater shape.     

A numerical comparison of the ballistic performance of unitary rod and segmented-rods against stationary and moving oblique plates

The purpose of this paper is to investigate the ballistic performance of segmented-rods against stationary or moving oblique plates. To do this, a series of three-dimensional numerical simulations for the impact characteristics of segmented-rods (5 of L/D=1) into stationary or moving oblique thin-plate targets is conduced. To provide a base line data, an L/D=5 unitary rod projectile which has the same mass and kinetic energy is also considered. The ballistic characteristics of the projectiles are evaluated by examining the crater profile in a thick witness target that is placed behind the oblique plate. The impact velocities considered are 1400, 1800 and 2200 m/s. The results for the test range show that the unitary rod projectile shows better performance in the moving oblique target than the stationary one and the segmented-rods always show slightly better performance in the stationary target. From the impact velocity of 2200 m/s, the outstanding penetration performance of the segmented-rods can be observed. This trend is due to the interaction between the reactive plate and projectile. The extent of the interaction relies on the relative velocities of the plate and projectiles, the plate angle and extended total length of the segmented-rods     

结构参数对截锥弹低速正侵彻装甲靶的影响

采用数值模拟和实验研究相结合的方法,对截锥形动能弹低速正侵彻装甲靶作用行为进行了分析,获得了弹头锥角、前级半径和着靶速度对侵彻性能的影响特性,并对目前常用的侵彻理论模型进行了验证。数值模拟结果表明,弹头锥角和前级半径是影响截锥形动能弹侵彻性能的重要因素;着靶速度对侵彻深度和侵彻过载有显著影响,对弹体变形也有一定影响。实验结果与数值模拟结果吻合较好,而侵彻理论模型与实验结果有较大差别,侵彻模型并不适合分析存在一定变形的弹靶侵彻问题。     

High-speed penetration into sand

The series of experiments aimed at the exploring high-speed impact of bullet on non-solid target were carried out at IPE RAS. The electro-discharge launcher (EDL) employed in these experiments can reach the projectile velocities of 4 km/s. The following topics were considered: the phenomena related to the high-speed penetration into non-solid targets, the parameters that influence the penetration depth and the projectile design suitable for the deepest penetration into sand. Experimental equipment allows the measurement of the penetration depth of bullet, its path inside the sand and the shock waves caused by the high-speed bullet impact. Experiments had shown the absence of significant deviation from a straight-line trajectory for the any tested bullet shapes at the impact velocity of 1.5–3.0 km/s. The most interesting result is the existence of a critical velocity for this type of interaction. The full bullet wear due to the friction with sand occurs at this velocity. The critical velocity value depends on bullet material and dimensions. Experiments show that exceeding the critical velocity leads to reduce in penetration depth. The influence of bullet material, shape and velocity on its penetration depth into sand was measured. These data allow a determination of the main characteristics of projectile for deep penetration into sand.     

Observations and simulations of the low velocity-to-hypervelocity impact crater transition for a range of penetrator densities into thick aluminum targets

Projectile/target impact crater systems involving soda-lime glass/1100 aluminum, ferritic stainless steel/1100 aluminum, and tungsten carbide/1100 aluminum (corresponding to projectile densities of 2.2, 7.89, and 17 Mg (m³) at impact velocities ranging from 0.56 to 3.99 km/s were examined by light metallography, SEM, and TEM. Plots of crater depth/crater diameter ratio (p/D _c) versus impact velocity exhibited anomalous humps with p/D _c ranging from 0.8 to 5.5 between 1 and 2 km/s, with hypervelocity threshold or steady-state values of p/D _c (>5 km/s) ranging from 0.4 to 1.0; with the p/D _c values increasing with increasing projectile density in each case. This hump-shaped regime, with exaggerated target penetration depths, appears to occur because projectiles remain relatively intact and unfragmented. The crater geometry begins to change when the projectile fragmentation onset velocity (>2 km/s) is exceeded and fragmentation increases with increasing impact velocity. Computer simulations and validation of these simulations were developed which fairly accurately represented residual crater shapes/geometries and correlated experimentally measured microhardness maps with simulated residual yield stress contour maps. Validated computer simulations allowed representative extrapolations of impact craters well beyond the laboratory where melting and solidification occurred at the crater wall, especially for hypervelocity impact (>5 km/s).     

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。     

Development of functionally-graded cementitious panel against high-velocity small projectile impact

A functionally-graded (FG)-cementitious panel consisting of PE-fibrous ferrocement, calcined bauxite aggregates and conventional mortar was developed to resist high-velocity small projectile penetration. A total of 72 specimens measuring 200 mm by 200 mm by 100 mm were fabricated and subjected to ogive-nosed (Caliber Radius Head, CRH = 2.5) projectile impacts at velocities ranging from 300 m/s to 600 m/s. The results indicated that FG-panels have superior impact resistance compared to plain mortar targets in which all FG-panels remained intact, whereas the latter disintegrated into several pieces when the projectile velocity exceeded 300 m/s. The FG-panels also suffered minor front face damages with much smaller average crater diameters (<48 mm) compared to plain mortar targets (>100 mm). However, penetration depths in the FG-panels were slightly larger at impact velocity less than 400 m/s compared to the mortar panels due to the lower compressive strength of PE-fibrous ferrocement. At higher impact velocity, all penetration depths in FG-panels were smaller than those in plain mortar targets. The effects of thickness variation of each functional layer were also investigated and results showed that thickening the calcined bauxite aggregate layer was most effective in reducing the penetration depth for all impact velocities, but the average inner and outer crater diameters were slightly increased.     

Oblique hypervelocity impacts into graphite

Investigations have been conducted into the morphology of craters formed by impacts of aluminium and HDPE projectiles at oblique angles to graphite target plates. The experiments were conducted with a two-stage gas gun capable of launching projectiles of differing density and strength to speeds of about 6 kms⁻¹ at right angles into target plates. It was found that, as the impact angle is decreased from the normal, the crater dimensions scaled as the normal component of the impact velocity as predicted by the ‘2/3 power law’ until a critical normal velocity was reached below which the conditions for a hypervelocity impact no longer apply. In this regime, new scaling laws were derived for the crater dimensions. It was also possible to identify a fragmentation angle below which the projectile remains intact as it ricochets across the target surface.     

Cavity and crater depth in hypervelocity impact

We discuss the depth of cavities and craters caused by hypervelocity impacts as a function of impact parameters such as impact velocity, projectile and target densities, and projectile diameter, in two extreme cases: the penetration of intact projectiles at low impact pressure and the hemispherical excavation at very high impact pressure. The relations between the depth and the impact parameters are obtained. Then, previous experimental results are compiled; crater depth normalized by projectile diameter and the ratio of projectile and target densities is plotted for glass, plastic, and metal projectiles and metal, rock, ice, foam, sheet-stack, and aerogel targets. The trends of the data are consistent with the relations in the extreme cases.