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.     

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.     

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.     

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.     

Energy transfer through chains of impacting rods

A solution has been formulated, which allows one to analyse all the major performance characteristics in a chain of impacting elastic ‘rods’. By allowing one end of the elastic chain to impact against a surface which resists penetration according to a specified penetration law it is possible to analyse the impact system of a variety of mechanical devices such as percussive tools and squeeze film dampers. Virtually, unlimited variety in the number and geometry of the impacting rods, and virtually unlimited complexity in the form of the reaction of the terminal face is permitted. A computer program for treating one or two elastic rods has been developed. The program prints out all important stresses as well as the stress history at several selected points. It also prints out the depth of penetration, the energy transferred from rod to rod, the overall energy transfer into the receiver, rebound velocities and times of separation between rods and between rod and 4receiver. Agreement with exact solutions and experiments is demonstrated.     

Hypervelocity jacketed penetrators

The use of steel jackets was found to significantly improve the penetration efficiency of tungsten alloy rods. Experiments and analyses were conducted with L/D=10 projectiles of constant exterior dimensions at a nominal impact velocity of 2.2 km/s. The fraction of jacket material was varied to see which geometry would have the best performance. For a core-to-jacket diameter ratio (μ) of 0.6, the experiments showed the penetration efficiency (P/KE^1/3) increased by 21% relative to an all-tungsten baseline rod of the same exterior dimensions. Experiments and AUTODYN simulations showed the same penetration efficiency trends. The simulations, however, did not show that the tungsten core outran the jacket, contrary to what was observed in the experiments.     

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 penetration of rigid long rods – revisited

The penetration process of rigid long rods with different nose shapes (ogive, spherical, conical and flat) is analyzed through a series of 2D numerical simulations. Aluminum and steel targets with different strengths (and large dimensions) are used to follow the deceleration process of these rods from impact, at different velocities, to the final penetration point. We find that for low impact velocities the deceleration of these rods is practicably constant, depending only on the strength of the target and the nose shape of the rod. Above a threshold (critical) impact velocity rod deceleration becomes velocity dependent due to the inertial response of the target. These critical velocities depend on the strength of the target and the nose shape of the rod. These observations led us to propose a simple penetration formula which accounts very well for penetration depths data for rigid steel rods with different nose shapes, impacting various aluminum targets at velocities up to about 1.5 km/s. For higher impact velocities, where the dynamic (inertial) contribution to the target resistance is important, we find good agreement between our model predictions and the simulation results for final penetration depths.     

Numerical simulation of segmented penetrator impact

The performance of segmented and continuous penetrators impacting semi-infinite and spaced armor is studied using both the EPIC-2 and HULL hydrocodes. First the performance of a segmented rod is studied, striking semi-infinite armor, for various parameters such as striking velocity, segment spacing and number of segments. Then an actual penetrator configuration proposed by A. Charters is analyzed and the use of normalized penetration is discussed. Finally three-dimensional simulations are presented for segmented and continuous penetrators impacting oblique spaced armor varying such parameters as striking velocity, segment spacing, number of segments, and target thickness.     

On the optimal performance of long-rod penetrators subjected to transverse accelerations

The paper deals with theoretical considerations on the conception and optimization of long-rod penetrators with regard to bending strain and penetration efficiency. In a first step we describe a method allowing to design long penetrators in such a manner that given values of bending stress and deflection are met if the rods are subjected to lateral forces. On the assumption of a constant lateral acceleration this results in rods with various dimensions; the aspect ratio remarkably does not remain constant. Then these penetrators are examined for maximum penetration efficiency while considering rods of equal energy. For the case studied the procedure results in an optimum velocity of about 2700 m/s. This demonstrates a fundamental difference in comparison to the optimization process with L/D-scaled penetrators where a much lower optimum velocity (2300 m/s) is obtained. In comparison to the reference penetrator (L/D=34, V=1800 m/s) the optimum penetrator — still at constant stress level and at an impact velocity of 2700 m/s — has of course a reduced mass, but also a reduced length and diameter showing an aspect ratio of 40. The perforation power could be increased by some 17%. On the other hand, the linearly scaled penetrator at constant energy only shows an increase of about 7% in penetration capability if the impact velocity reaches its optimum value at 2300 m/s. The optimization procedure of the energy-efficient penetration of constant-stress projectiles leads to an optimal velocity well in the hypervelocity regime. Furthermore, the special design of the penetrators with constant stress level results in a gain of penetration efficiency.     

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.     

Phase three penetration

Phase three penetration is defined as the target penetration that occurs after a high-velocity penetrator has fully eroded. Phase 3 penetration is due to one or the combination of after-flow and secondary penetration of the target by the eroded penetrator debris. Recent experimental data for long tungsten rods penetrating confined boron carbide, aluminum nitride, and silicon carbide targets are used to investigate phase 3 penetration. It is found for these three ceramic targets that the onset impact velocity for the occurrence of phase 3 penetration is very roughly 2 km/s. The phase 3 penetration increases with impact velocity approximately as v². For these experiments the phase 3 penetration appears to be due almost entirely to secondary penetration.     

Reverse impact experiments against tungsten rods and results for aluminum penetration between 1.5 and 4.2 km/s

Reverse impact experiments against 0.76 mm diameter L/D = 20 tungsten rods have been conducted with a 38 mm diameter launch tube, two-stage light-gas gun using four 450 kV flash X-rays to measure penetration rates. Techniques for projectile construction, sample placement, alignment, and radiography are described. Data for penetration rate, consumption velocity, and total penetration were obtained for 28 mm diameter 6061-T651 aluminum cylinders at impact velocities between 1.5 and 4.2 km/s. It was found that penetration velocity was a linear function of impact velocity over this velocity range. Above 2 km/s impact velocity, penetration was completely hydrodynamic. There was substantial secondary penetration, and the total penetration increased linearly with impact velocity over the range 1.5 to 2.5 km/s.     

Effects of Sliding Friction on the Optimal 3D- Nose Geometry of Rigid Rods Penetrating Media

Friction effects on the optimum shape design for a normal impacting, rigid body are investigated and the optimum 3D- nose shapes of rods are proposed for deep penetration into soil, concrete and metal media. The study is conducted by assuming that the normal and tangent stresses, that act on the impactor nose, are of the Poncelet and Coulomb forms, respectively. The geometrical characteristics of the shapes maximizing penetration depth are compared with those of the minimal resistance bodies obtained at the initial stage of the penetration event. When mass, shank radius and nose length of the rods are fixed, a comparative study of the penetration depths of the optimal impactors and impactors with conical and ogival nose shapes is carried out. The conditions, when the benefits of the optimal configurations in providing deep penetration into soil, concrete and metal media become significant in comparison with other shapes, have been obtained. The model parameters are taken from the published reports on penetration data obtained for striking velocities to 1.5 km/s while the impactors remained rigid and visibly undeformed.     

Energy partitioning and microstructural observations related to perforation of titanium and steel targets

This paper presents an analysis of two target materials and the associated energetics related to the initial penetration into the target and perforation as the penetrator exits the target. Impact tests were conducted for tungsten alloy rods striking rolled homogeneous armor (RHA) and titanium alloy plates. Rod impact velocities were nominal 1,500 and 2,000 m/s. Target thicknesses were chosen so that the rods would overmatch the targets and lose some 200 m/s during penetration. The tests utilized flash x-rays to determine rod residual lengths and velocities and target plug features to include thicknesses and velocities. From these observables, experimental determination of the corresponding kinetic energies (KEs) and estimates for the fracture energies were obtained. Also, in each case, target material adjacent to penetration channel walls was examined by optical and electron microscopy and x-ray diffraction to gain further insight into deformation processes (cavity expansion) during penetration. The analytic penetration model gave results that were in good agreement with the experimental observables. In addition, it was observed that the RHA follows traditional plastic flow of cavity expansion while titanium alloy shows deformation features that deviate significantly. The paper discusses possible causes for these differences.     

Penetration mechanics of yawed rods

The penetration of rod projectiles is a function of impact yaw. Armor steel targets were struck at 0° obliquity by long steel rods at ~2.15 km/s and various angles of yaw. Crater dimensions varied systematically with yaw angle. Trenching behavior was observed for yaw angles exceeding about 30°. Analysis indicates that the rods collapsed into the targets with no significant rotation, and that penetration chiefly depends on the parameters D and $\text{D}\text{sin θ}$ (where D is rod diameter and θ is yaw angle).     

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.     

On the main mechanisms for defeating AP projectiles,long rods and shaped charge jets

Some of the important mechanisms for defeating various projectiles and shaped charge are reviewed in this paper. These mechanisms are based on the compressive strength of the target material (its inherent resistance to penetration) and on the asymmetrical forces which it exerts on the threat, through proper geometrical arrangements. We discuss the basic features of the resistance to penetration, starting with the classical analysis of the cavity expansion process in elasto-plastic solids. This property of the target is responsible for the deceleration of hard cored projectiles and for the erosion of long rods, under normal impact conditions. We then discuss the asymmetrical interaction of armor piercing (AP) projectiles, long rods and shaped charge jets with inclined plates (stationary and moving). These asymmetric forces, exerted on the impacting threat, are responsible for their deflection and breakup. Our work combines experimental observations with numerical simulations and engineering models, which highlight the basic mechanisms behind these complex situations. This understanding is necessary for optimizing the performance of any armor design against a given threat.     

Heat transfer and fluid friction in bundles of twisted tubes

The results of heat-transfer and friction studies in bundles of twisted tubes and rods with spiral wire-wrap spacers are analyzed, and recommendations are given for calculating the heat-transfer coefficient in heat exchangers using twisted tubes.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 50, No. 6, pp. 885–892, June, 1986.