Penetration dynamics of rods from direct ballistic tests of advanced armor components at 2–3 km/s

The penetration of semi-infinite steel and spaced-plate armors by continuous and segmented rods has been analyzed and measured by direct ballistic tests, hydrocode calculations, and hydrodynamic models at velocities from 2 to 4 km/s. An empirical equation of rod penetration in semi-infinite steel was formulated from hydrodynamic models of rod impact. Penetrations predicted by the equation agreed well with measured values. Increasing the spacing between segments from one to two diameters increased the penetration significantly (20%). Structures to support and align the segments can either increase or decrease the penetration, depending on their design. The relative penetrations of continuous and segmented rods depend on the parameters selected for the comparison: the segmented rod having greater penetration for equal mass and diameter and vice versa for equal mass and length. Tests of segmented rods penetrating spaced-plate armor showed that the armor is defeated by the front segment (or segments) punching a hole in the front plate (or plates) that allows the remaining segmented rod through intact to attack the main armor.     

Effect of alignment on the penetration of segmented rods

The purpose of this investigation is to study the effect of alignment on the performance of segmented penetrators. The Eulerian wave propagation code CTH is used for this purpose. A series of calculations using four L/D = 1 tungsten alloy segment trains at varying degrees of misalignment is performed, impacting a single finite-thickness oblique armor steel plate. Obliquity angles of 30° and 60° were considered. This study was performed primarily to investigate the effects of obliquity and is a continuation of a previous study [1] where semi-infinite armor steel plates were examined. It is shown that the obliquity of the plate can have a significant influence on the performance of the segment train. When misalignment is minimal, the performance of the segment train is not adversely affected, particularly if the misalignment positions the train in an orientation aligned with the plate normal. However, for large misalignments, degradation to the performance of the segment train is significant at all orientations.     

Penetration mechanics and performance of segmented rods against metal targets

Terminal ballistic experiments confirm theoretical predictions that a segmented rod will penetrate a semi-infinite metal target deeper than a continuous rod of the same material and having equal mass, diameter and velocity. For copper segmented rods impacting aluminum targets and tantalum segmented rods impacting 4340 (BHN 300) steel, penetration depths of at least 50 percent greater than that for a corresponding continuous rod are measured at impact velocities of 4 to 5 km/s. Spacing between segments of only about 2.5 segment diameters or more are required to achieve these results. Reducing the Li/D of the segments to less than 1 improves the penetration efficiency of a segmented rod. For segmented rods with segment L_i/D < 1, experiments suggest that penetration may increase with impact velocity rate greater than V^2/3.     

Hydrocode results for the penetration of continuous, segmented and hybrid rods compared with ballistic experiments

Hydrocode calculations of the penetration of various tungsten alloy and stainless steel rod penetrators into semi-infinite steel and aluminum targets are presented and compared with results from ballistic experiments. Good agreement with experimental results is seen for penetration depth, penetration with time, and crater size and profile. The rod penetrator configurations investigated in the calculations include: idealized segmented rods with various segment spacings, the corresponding hybrid rods with axial spacers, and continuous rods of various dimensions. The Eulerian hydrocode results show enhanced penetration performance for idealized segmented rods compared with the parent continuous rods. Penetration performance for the corresponding hybrid segmented rods is significantly greater, even after accounting for the added mass of axial spacers. Results for long rod penetrators of the same mass and length as the hybrid rods, provide evidence that the axial spacers contribute to penetration. Both calculations and experiment show significant differences between the crater profiles of continuous versus ideal segmented or hybrid rods. The profiles generated by continuous rods are smooth, while those by segmented and hybrid rods are scalloped. Hydrocode results show that the scalloped crater profiles arise from successive impacts of rod segments.     

High velocity impact of segmented rods with an aluminum carrier tube

In this paper, we apply the method of ballistic test to investigate the history and mechanism of the tungsten alloy segmented rod with aluminium carrier tube and corresponding continuous rod penetrating into semi-infinite steel target at velocities from 1.8 to 2.0 km / s. The length to diameter ratio of the segmented rod is 1 (L/D = 1), the ratios of length of spacing between segments to diameter (s/d) are 0.5, 1.0 and 2.0 respectively. The results show that the power of penetration of the segmented rod with carrier tube is obviously higher then that of the corresponding continuous rod with carrier tube. Raising of the impact velocity, suitably increasing of the length of spacing between segments and filling the spacing with non-metallic material, etc. all can increase the penetrating power of the segmented rod. When impact velocity is 2.0 km / s, s / D=2.0, the penetrating power of the segmented rod is 10% higher than that of the corresponding continuous rod, if the spacing is filled with glass steel (non-metallic material), the power will be 20% higher. In this paper, we present a simplified model of based on hydrodynamics and penetrating mechanics. This model can properly describe the whole penetrating process of segmented rod penetrating into semi-infinite target. The shape of the crater and depth of penetration, etc. calculated are in good agreement with the results obtained by experiments.     

Energy-efficient penetration and perforation of targets in the hypervelocity regime

In general, the performance of a KE penetrator against most targets increases with velocity regardless of the particular penetrator-target interaction mode. It is possible to show that there exists an optimum velocity which maximizes the performance of an impacting penetrator for a given expenditure of kinetic energy. Simple graphical methods are described that determine the optimum velocity from general performance-velocity plots. These graphical methods may also be applied to experimental data alone. In addition, simple analytic models which describe the velocity dependent penetration/perforation performance of KE penetrators are examined and extended. These models may be used to explicitly assess the influence of parameters such as target strength and density and penetrator mass, strength and density. For some of the models in this analysis, the explicit relations between the optimum striking velocity for a specific kinetic energy value and the penetrator-target parameters are described.     

Experiments with jacketed rods of high fineness ratio

Cylinders of high fineness ratio can show severe integrity and stability problems during acceleration and free-flight phase. The paper describes a method to overcome these problems by adding an envelope to the slender cylinder thereby augmenting the stiffness under flexure. Theoretical considerations treat the pros and cons of jackets with different Young's moduli while looking at various parameters such as maximal deflection, total mass as well as muzzle and impact velocity.

Special emphasis is given to the terminal ballistic efficiency which has been tested using jacketed model penetrators made of tungsten heavy metal with carbon-fibre reinforced plastic (CFRP) and steel envelopes. Some experiments were carried out with cannon-launched CFRP-jacketed tungsten rods of aspect ratios from 45 to 60 being accelerated up to 2000 m/s. In other penetration tests L/D=25 and 40 jacketed penetrators were shot onto homogeneous semi-infinite RHA targets and also spaced targets at 60° incidence at velocities up to 2500 m/s by aid of a light-gas gun.

The experiments with jacketed model penetrators of 3 and 4 mm diameter at high impact velocities showed a good penetration power into homogeneous targets, whereas there is a loss of penetration efficiency into spaced targets of 20% and more. Furthermore it seems that the relative thickness of the jacket should not exceed a certain value in order not to risk a detrimental effect on the penetration performance.     

Novel KE penetrator performance against a steel/ceramic/steel target at 0° over the velocity range 1800 to 2900 m/s

This paper presents scale size firings of two novel shape KE penetrators into a steel/ceramic/steel target at four velocities between 1.8 and 2.9 km/s. The two novel shapes were a three piece segmented rod and a telescopic rod/tube. Two unitary rod designs were also included in the assessment. All the penetrators had a similar mass of 60 grams. Test data against semi-infinite RHA was used to obtain the mass effectiveness (E_m) of the ceramic target for each rod shape and velocity. The performance rankings of the penetrators against the ceramic target were found to be similar to those for semi-infinite RHA. In ascending order of penetration depth the ranking was the 10.6 mm unitary rod, segmented rod, telescopic rod and 6.5 mm unitary rod. It was found that the E_m reached a maximum between 2.3 and 2.6 km/s depending on the penetrator type. The E_m values ranged from 1.8 to 2.4. Hydrocode analysis of the experiments gave some valuable insights into the penetration processes of the two novel penetrator designs. Predicted depth of penetration compared very well with experimental values, but enhancements to the physics of the ceramic model are needed in order to simulate cover plate effects. Crown copyright     

The crater formation due to segmented rod penetrators

The efficiency of segmented rods penetrating into semi-infinite steel targets was investigated numerically by hydrocode simulations with impact velocities varying between 2000 and 5000 m/s.

In a second phase segmented elements were integrated in experimental projectiles and these projectiles were accelerated by means of a powder gun to verify the launchability of such projectiles and to confirm the results of the numerical simulations.

As predicted by the numerical simulations, we observe an increase of the penetration depth in the order of 10% with a 4 segments spaced projectile, in the case of an impact velocity of 2100 m/s.     

Numerical analysis and modeling of jacketed rod penetration

A computational study to assess terminal ballistic performance issues of adding a steel sheath, or jacket, to a depleted uranium (DU) penetrator has been performed. The CTH hydrocode was used to model DU penetrators with steel sheaths of various thicknesses against semi-infinite rolled homogeneous armor (RHA), finite RHA, and oblique plate targets. Guided by the initial results, additional semi-infinite RHA simulations were performed to support the development of a generalized penetration model for jacketed rods. The model computes RHA penetration as a function of impact velocity and normalized jacket thickness (thickness over diameter) and compares very favorably with experimental DU and steel data. The model indicates that “bulk” density (areal density) can considerably underestimate jacketed rod penetration. In addition, some insight into the penetrator and target flow shape factors (k_p and k_t) is obtained.     

The effect of geometric scale on impact induced fragmentation, and its application to the design of dual plate armor

An analysis is presented which predicts that, for a fixed impact velocity, impact induced fragmentation becomes more severe as geometric scale increases. Test data is presented which supports this prediction, and which allows calculation of material dependent coefficients. The analysis was based on a minimization with respect to radius, for an expanding body, of a total energy density term (expansion kinetic energy per unit volume plus surface energy per unit volume). The test configuration was a steel sphere impacting an aluminum plate, with fragmentation recorded by a stack of spaced witness panels. The tests were run at full and half scale. Correlation between testing and analysis was achieved for the number of fragments perforating the front witness panel when a term analogous to a threshold energy was introduced. While the fragment count showed a dependence on geometric scale, the relative depth of penetration (number of witness panels perforated) did not. This suggested that the targets were fragmented, but that the projectile remained in one piece. A reduction in penetration depth with increasing impact velocity was seen, and was attributed to increased projectile deformation. For cases where the projectile would fragment (for example, if a harder target material were used), the effect of geometric scale on the performance of dual plate armor is predicted by analysis. The prediction is that, for impact velocities where projectile breakup at the outer plate of dual plate armor is a factor, the armor required to stop a large scale projectile can be lighter, on a relative basis, than the armor required to stop a small scale projectile.     

线性聚能装药干扰杆式穿甲弹的数值模拟研究

聚能型爆炸反应装甲是目前最先进且具有三防功能的新型爆炸反应装甲。其中,大锥角线性聚能装药结构是反应装甲结构设计中最重要的部分,主要用来拦截来袭高速杆式穿甲弹。运用ANASYS/LS-DYNA有限元数值模拟仿真方法,对线性自锻破片干扰杆式穿甲弹的过程进行了数值模拟研究。通过对线性自锻破片成型过程、线性自锻破片对长杆弹的干扰过程和长杆弹侵彻后效靶板过程进行深入分析,得出了长杆弹被线性自锻破片干扰后穿甲威力下降的两个主要原因。经实验验证,数值模拟与实验结果基本相符。     

Penetration performance of nonideal segmented rods

Five small scale reverse ballistic tests were performed to examine the effects of a thin-walled surrounding tube and/or lexan spacers between segments on the penetration mechanics and performance of tantalum segmented rods against steel targets. Impact velocity was 4.5–5 km/s. The data, although few, suggest that such structures as surrounding tubes and segment spacers do not necessarily degrade the penetration performance of segmented rods.     

新型集成装甲对EFP侵彻性能的影响

根据平板装药和陶瓷复合装甲与爆炸成型弹丸（EFP）相互作用的原理，提出了新型集成装甲与EFP作用的计算模型；据此模型进行了EFP残余速度计算，证明了在相同面密度的新型集成装甲和陶瓷复合装甲防护下，EFP的残余速度有明显差异；根据该计算模型可进行集成装甲的优化和EFP的反装甲目标设计。     

Experimental investigation of the ballistic resistance of steel-fiberglass reinforced polyester laminated plates

The present experimental study is undertaken to investigate the effect of target configuration on ballistic performance when struck by standard bullets of different velocities. At first, single mild steel plates, 1–8 mm thick, are tested, and the effect of thickness and mechanical properties of plate material are explored. Secondly, in-contact laminae comprising an 8 mm-thick target, and spaced laminae of the same total steel thickness, with spacing distances equal to or multiples of the bullet core diameter (6 mm) are tested and the effect of number, thickness, and arrangement of laminae sought.In addition, fiberglass reinforced polyester (FRP) is used as a filler material for targets with spaced steel laminae. The influence of FRP's physical and mechanical properties on the ballistic performance of steel-FRP targets is investigated.In order to perform the ballistic tests, a special setup is constructed, which consists of a launcher, a target clamp and a velocity-measuring device. In each experiment, the change in the projectile velocity (while penetrating the target) divided by the length of penetration is established as a measure of target performance.Results show that single targets are more effective than laminated targets of the same total thickness, regardless of the configuration or striking velocity. It is noted, however, that the difference in performance diminishes as the striking velocity increases. Moreover, the effectiveness of laminated targets, in contact or spaced, increases as the number of laminae comprising each target decreases. Ballistic performance of laminated targets is further enhanced by using the thickest lamina as the back lamina. Results also emphasize the dependence of target performance on mechanical properties.Steel-FRP targets show better performance than weight-equivalent steel targets. Performance of a steel-FRP target is further improved by increasing fiber weight fraction in the FRP.     

线性聚能装药干扰杆式穿甲弹的数值模拟研究

聚能型爆炸反应装甲是目前最先进且具有三防功能的新型爆炸反应装甲。其中,大锥角线性聚能装药结构是反应装甲结构设计中最重要的部分,主要用来拦截来袭高速杆式穿甲弹。运用ANASYS/LS-DYNA有限元数值模拟仿真方法,对线性自锻破片干扰杆式穿甲弹的过程进行了数值模拟研究。通过对线性自锻破片成型过程、线性自锻破片对长杆弹的干扰过程和长杆弹侵彻后效靶板过程进行深入分析,得出了长杆弹被线性自锻破片干扰后穿甲威力下降的两个主要原因。经实验验证,数值模拟与实验结果基本相符。     

Modeling the high strain rate behavior of titanium undergoing ballistic impact and penetration

Titanium is an important candidate in the search for lighter weight armors. Increasingly, it is being considered as a replacement for steel components. It is also an important component in the application of ceramics to armor systems, especially in armor modules that are capable of defeating kinetic energy penetrators while sustaining little or no penetration of the ceramic element. The best alloy available today for ballistic applications is Ti-6Al-4V, an aerospace grade titanium alloy. The principal deterrent to widespread use of this alloy as an armor material is cost, and a significant portion of the cost is in processing. Consequently, the U.S. Army Research Laboratory undertook a program to study a particular lower cost processing technique [1].

The objectives of this work are to characterize the low-cost titanium alloy by generating constants for the Johnson-Cook (JC) and Zerilli-Armstrong (ZA) strength models, and to use and compare these two models in simulations of ballistic experiments. High strain rate strength data for the low-cost titanium alloy are used to generate parameters for the two models. The approach to fitting the JC parameters follows one previously used successfully to model 2-in thick rolled homogeneous armor (RHA) [2]. The approach to fitting the ZA parameters is based on a method described by Gray et al. [3]. The resulting model parameters are used in the shock physics code CTH [4] to model a Ti-6Al-4V penetrator penetrating a Ti-6Al-4V semi-infinite block at impact velocities up to 2,000 m/s. Similar experiments are performed, and the predictions of the two models are compared to each other and to the experimental results.     

Modeling System Effects in Ballistic Impact into Multi-layered Fibrous Materials for Soft Body Armor

An analytical model is developed to study various ‘system effects’ during impact of a flat-faced, cylindrical projectile into a flexible, multi-layered target with no bonding between layers. Each thin layer is assumed to have in-plane, isotropic, elastic mechanical properties. The model allows variation of the mechanical properties from layer to layer as well as the spacings between the layers in order to study their combined effects on the ballistic performance of the system. In particular, we consider such performance measures as the V₅₀ limit velocity, the number of layers penetrated when impacting below this limit, and the residual projectile velocity after complete penetration above this limit. The V₅₀ performance of the target is found to degrade progressively as the spacings between layers are increased relative to the sum of layer thicknesses without spacing. A second finding is that for a given set of layers with differing mechanical properties, both the V₅₀ and the residual velocity depend on the order of layer placement. A third finding is that among systems with identical layers of a given in-plane tensile strength, the V₅₀ velocity increases with increasing strain-to-failure of the layers. However the relative magnitude of this increase diminishes with increasing target-to-projectile areal density ratio. The model builds on the authors’ previous analysis for impact into a single elastic membrane and the results have important design implications for armor design especially for hybrid material configurations.     

A computational study of the relations between material properties of long-rod penetrators and their ballistic performance

The paper summarizes a series of two-dimensional numerical simulations which were performed to study the effects of material properties on the terminal ballistics of long-rod penetrators. Our focus was on the properties of the rod material, unlike recent works which concentrated on a target’s properties. We varied almost all the relevant parameters within a large range of values in order to study the separate effects of each one. These parameters included: compressive and tensile strengths, elastic moduli, melting temperatures and the maximum equivalent plastic strain (failure strain) of the rod material. Most of the simulations were performed for an actual experiment with 300 mm tungsten-alloy long-rod, impacting a semi-infinite steel target. The simulations show that the mechanical and thermal softening mechanisms are the most dominant, as far as the depth of penetration is concerned. In contrast, the elastic moduli and spall strength have a negligible effect as far as penetration depth is concerned.     

Analytical expressions for optimum alignment modes of highly segmented mirrors

The major sources causing deterioration of optical quality in extremely large optical telescopes are misadjustments of the mirrors, deformations of monolithic mirrors and misalignments of segments in segmented mirrors. For active optics corrections, all three errors, which can partially compensate each other, are measured simultaneously. It is therefore of interest to understand the similarities and differences between the three corresponding types of modes which describe these errors. The first two types are best represented by Zernike polynomials and elastic modes respectively, both of them being continuous and smooth functions. The segment misalignment modes, which are derived by singular value decomposition, are by their nature not smooth and in general discontinuous. However, for mirrors with a large number of segments, the lowest modes become effectively both smooth and continuous. This paper derives analytical expressions for these modes, using differential operators and their adjoints, for the limit case of infinitesimally small segments. For segmented mirrors with approximately 1000 segments, it is shown that these modes agree well with the corresponding lowest singular value decomposition modes. Furthermore, the analytical expressions reveal the nature of the segment misalignment modes and allow for a detailed comparison with the elastic modes of monolithic mirrors. Some mathematical features emerge as identical in the two cases.