Target Penetration Research Articles

The analytical model ATOS-M for computing of the shaped charge jet penetration parameters

The ATOS-M computer program uses the shaped charge jet parameters as initial conditions for calculation of the jet penetration. Parameters of the jet produced by the shaped charge are calculated using two-dimensional MCD hydrocode. The ATOS-M model includes the following main components: - a set of simplifying axioms permitting to use one-dimensional simulation of the shaped charge jet evolution at the flight and the target penetration phases; - kinematical penetration scheme for elementary jet sections using analytical solutions for continuous and particulated jets; - semi-empirical formulas for calculation of the jet break-up time; - a set of semi-empirical formulas for calculation of profile of the penetration cavern; - algorithm for calculation of the cut-off' velocity taking into account the lateral drift velocity; - analytical solutions for calculation of the relative penetration velocities with taking into account the compressibility and strength effects. Comparison of the ATOS-M calculations to the experimental data (sinchro-streak, time of arrival and penetration) shows good agreement.

Analytical model for the disruption of a metal jet penetrating detonating high explosive

We investigate the interaction of a constant-velocity, long-rod penetrator with detonating high explosive. An analytical flow-field model extending the Birkhoff model of inert target penetration is developed and compared with numerical simulations. We propose a rod-disruption model, discuss the effect of enhanced “anomalous” rod erosion on penetration history, and estimate the maximum coherent penetration depth. The model is extended to idealized stretching jet penetrators and its predictions are compared with jet-high-explosive (HE) interaction experiments. We predict a strong dependence of the high-explosive penetration on penetrator diameter and a very high “virtual” HE density in agreement with experimental observations.

Savings estimates for the E nergy S tar® voluntary labeling program

E nergy S tar ® is a voluntary labeling program designed to identify and promote energy-efficient products. Operated jointly by the Environmental Protection Agency (EPA) and the US Department of Energy (DOE), E nergy S tar labels exist for more than 20 products, spanning office equipment, residential heating and cooling equipment, new homes, commercial and residential lighting, home electronics, and major appliances. We present estimates of the energy, dollar and carbon savings already achieved by the program and provide savings forecasts for several market penetration scenarios for the period 2001–2010. The target market penetration forecast represents our best estimate of future E nergy S tar savings. It is based on realistic market penetration goals for each of the products. We also provide a forecast under the assumption of 100% market penetration; that is, we assume that all purchasers buy E nergy S tar-compliant products instead of standard efficiency products throughout the analysis period. Finally, we assess the sensitivity of our target penetration case forecasts to greater or lesser marketing success by EPA and DOE, lower-than-expected future energy prices, and higher or lower rates of carbon emissions by electricity generators.

Eroded length model for yawed penetrators impacting finite thickness targets at normal and oblique incidence

Summary A simple expression is derived to estimate the residual length of a yawed, long-rod penetrator impacting finite thickness targets at both normal and oblique incidence. The unique feature of this model is a determination of the different penetration path through the plate which is not simply a line-of-sight thickness. The presence of yaw results in a penetration path which is determined by the magnitude and direction of the penetration velocity vector which is dependent upon the penetrator velocity component along that path. Hence, the material thickness penetrated through the finite target is an explicit, and variable, function of the impact geometry, (obliquity and yaw), impact velocity, and relative penetrator and target properties (densities and strengths). The eroded penetrator length is also dependent on both the penetration path angle and on the velocity component along that path and thus becomes an explicit function of these variables. Two simple expressions are derived to determine the eroded penetrator length and implications for deep target penetration degradation due to yaw are discussed.

An analytic model for the prediction of incoherent shaped charge jets

It is now a well recognized fact that the jet from a shaped charge can be overdriven in the sense that the fastest moving particles are not produced as a cohesive mass of material. Rather, the tip material may be produced as a number of discrete particles which possess different nonzero radial components of velocity and hence spread out from the axis of symmetry of the charge. Such a jet is classed as incoherent and when this incoherency occurs the jet’s target penetration capability is invariably degraded. This physical phenomenon is the subject matter of this article. Several experimental results using common shaped charge materials are presented first. An analytic model which predicts the jet speed at the transition point between a coherent and incoherent state is then described. This model is based on the assumption that a stagnant core with circular boundaries exists in the flow region. Further, the flow field is assumed to be compressible with circular streamlines. The Murnaghan equation of state is used to relate the pressure and density in the flow region where the jet is produced. It is postulated that the transition between a coherent and incoherent state occurs when the circular flow becomes wholly supersonic. The critical Mach number for coherency is shown to be approximated to high accuracy by a simple formula depending on the collapse angle of the flow and the incoming flow speed. Excellent agreement between the model predictions and the experimental data is demonstrated.

Spatio-temporal diversity in the microenvironments for neural cell adhesion molecule, neural cell adhesion molecule-polysialic acid, and L1-cell adhesion molecule expression by sensory neurons and their targets during cochleo-vestibular innervation

Sixteen phases in the microenvironments were defined for the structural development and innervation of the cochleo-vestibular ganglion and its targets. In each phase the cell adhesion molecules, neural cell adhesion molecule, neural cell adhesion molecule-polysialic acid, and L1-cell adhesion molecule, were expressed differentially by cochleo-vestibular ganglion cells, their precursors, and the target cells on which they synapse. Detected by immunocytochemistry in staged chicken embryos, in the otocyst, neural cell adhesion molecule, but not L1-cell adhesion molecule, was localized to the ganglion and hair cell precursors. Ganglionic precursors, migrating from the otocyst, only weakly expressed neural cell adhesion molecule. Epithelial hair cell precursors, remaining in the otocyst, expressed neural cell adhesion molecule, but not L1-cell adhesion molecule. Post-migratory ganglion cell processes expressed both molecules in all stages. The cell adhesion molecules were most heavily expressed by axons penetrating the otic epithelium and accumulated in large amounts in the basal lamina. In the basilar papilla (cochlea), cell adhesion molecule expression followed the innervation gradient. Neural cell adhesion molecule and L1 were heavily concentrated on axonal endings peripherally and centrally. In the rhombencephalon, primitive epithelial cells expressed neural cell adhesion molecule, but not L1-cell adhesion molecule, except in the floorplate. The neuroblasts and their axons expressed L1-cell adhesion molecule, but not neural cell adhesion molecule, when they began to migrate and form the dorsal commissure. There was a stage-dependent, differential distribution of the cell adhesion molecules in the floorplate. Commissural axons expressed both cell adhesion molecules, but their polysialic acid disappeared within the floorplate at later stages. In conclusion, the cell adhesion molecules are expressed by the same cells at different times and places during their development. They are positioned to play different roles in migration, target penetration, and synapse formation by sensory neurons. A multiphasic model provides a morphological basis for experimental analyses of the molecules critical for the changing roles of the microenvironment in neuronal specification.

Fragmentation of targets during ballistic penetration events

An analytical target fragmentation model is developed to predict the number of armor debris fragments produced in a ballistic penetration event. The model employs an energy balance to estimate the energy available to propagate cracks in the target material and thus produce an estimate of the mean number of behind-armor debris fragments. The expected number of behind-armor debris fragments agrees well with the results of conventional ordnance velocity target penetration behind-armor debris tests. This analytical fragmentation model and test results were used as the basis for the development of a means of calibrating the parameters of a Weibull statistical distribution function to predict the probability distribution of the number of debris fragments produced in a ballistic impact. It was concluded that the armor fragmentation model was a good predictor of the number of fragments produced in a ballistic penetration event deserving further investigation.

PENETRATION OF A LONG ROD INTO A SEMI-INFINITE METALLIC TARGET AT HIGH VELOCITY

The one-dimensional hydrodynamic theory proposed by Tate [1.2] is considered as a standard reference for describing the penetration of long rods into semi-infinite metallic targets. In this paper, a modified analytical approach using Tate's theory has been developed, wherein the penetration process is considered to consist of three phases: hydrodynamic, deformation and rigid. These phases are related to the situations of the rod front during target penetration. For each rod phase, the target penetration is described consisting of two stages: erosion and deformation. The plastic wave theory is used with the equations of motion to predict the sequence of penetration stages that associate with each rod penetration phase and represent the complete penetration process. In addition, the strength factors for both rod and target materials, respectively, are assumed not to vary during their erosion. The governing equations of the analytical approach are programmed using FORTRAN. The input data consist of rod impact velocity, length, diameter, density and Brinell hardness number as well as target density. Young's modulus and Brinell hardness number. The present results are concerned with the predictions of the produced hole diameter and penetration depth in semi-infinite targets due to their impact by long rods with high velocities. The predicted results are compared with the experimental results of other investigators: good agreement is obtained. Moreover, the program is used to discuss the influence of the different penetration parameters on penetration depth and produced hole diameter.

Concatenated Approach to Trajectory Optimization

the covariance simulationincorporatesthe equations developedpreviously.Inasmuchasthe Tomahawkmissileis being considered,the terrain scene is a terminal area digital scene matching and area correlation(DSMAC) scene. Shown in Fig. 2 is a typical CEP plot from the covariance simulation, which illustrates that the highly accurate positional solution obtained from the relative GPS correction vector scheme degrades only minimally between the DSMAC scene and the target. For target penetration considerations, the results presented here incorporate a terminal trajectory with a high-angle dive to impact the target. At the target, the navigational error contributes 2.6%, the steering error 10.2%, the scene center location error 20.9%, and the relative target location error 66.3%, which is consistent with the earlier discussion regarding relative error magnitudes. An examination of Fig. 2 also reveals that the correction vector scheme affords a substantial improvement over the situation where the Kalman e lter accepts a high-quality DSMAC positional update and, subsequently, the missile e ies in a free inertial manner to the target (the mode of operation for the current Block III Tomahawk missile ). Because improvements in satellite imaging technology are expected to permit larger DSMAC scene to target separations while maintaining the same scene/target relative error, free inertial navigation to the target will clearly become less desirable, and relative GPS schemes such as the one proposed herein more desirable. Summary

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 v 2. For these experiments the phase 3 penetration appears to be due almost entirely to secondary penetration.

Plastic Guidance Fins for Long Rod Projectiles .

Projectile tail fins on long rod kinetic energy (KE) penetrators serve the same purpose as fletchings (feathers) on an arrow, namely, they help align the projectile axis with its velocity vector. This reduces the projectile's yaw and hence reduces its aerodynamic drag. In addition, a low yaw angle at target impact helps to maximise the projectile's target penetration. It is typical for projectiles to exit the gun muzzle and enter free flight at some ndn-zero yaw angle. Aerodynamic forces acting on yawed tail fins create a stabilising torque about the projectile's centre of gravity (CG). This torque can be increased by making the fin material lighter. Most conventional long rod penetrators fired from high performance guns have tail fins made from aluminium. However, aluminium can undergo catastrophic oxidation (rapid burning) in-bore. Coating aluminium with Al/sub 2/O/sub 3/ {hardcoat) prevents ignition of the substrate, provided solid propellant grain impacts do not chip the brittle hardcoat off the surface. Plastic is lighter than aluminium and less exothermic when oxidized. Therefore, other factors aside, it is conceivable that plastic fins could increase projectile stability while incurring less thermal erosion than aluminium. However, thermal loads are not the only concern when considering plastic as an alternative tail fin material. The mechanical strength of plastic is also a critical factor. This paper discusses some of the successes and failures of plastic fins, at least relatively thin fins, for use as KE stabilisers.

Tactical applications for electromagnetic launchers

The major advantage of electromagnetic (EM) propulsion, at least for the anti-armor mission, is the ability to reach higher impact velocities where the lethality can be much greater for fixed energy delivered to the breech. We describe a methodology we are developing for optimizing EM gun systems for tactical applications. To demonstrate the methodology we provide an analysis which describes the most effective configuration for a large-bore tactical gun firing monolithic tungsten long-rod penetrators against semi-infinite rolled homogeneous armor (RHA). The criterion used in estimating system effectiveness is maximizing target penetration while minimizing launch energy.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

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.

A model of a pneumatic jackhammer system

A complete model of a pneumatic jackhammer system has been developed. Application of this model requires that two preliminary experiments be performed. The first experiment produces the relationship between piston impact velocity and the pressures acting on the top and bottom surfaces of the piston, while the second determines the force-indentation behavior for the bit/target system. The model analysis leads to the prediction of the jackhammer efficiency and target response, including target penetration and crack propagation. This model is not dependent on the jackhammer type or size, and may be applied to any such system.

Significance of Quality Control of Liner-Wall Symmetry on Shaped-Charge Perforator Performance

Summary The objectives of this investigation were to demonstrate experimentally the significance of liner-wall mass uniformity and concentricity on the penetrating effectiveness (total target penetration and target hole size and symmetry) of conical shaped charges and to devise a systematic approach for selecting the optimum manufacturing conditions for the production of acceptably uniform shaped-charge liners. Experimental results indicated that total target penetration decreased with increasing liner-wall mass nonuniformity. Moreover, a statistical quality-control method was implemented to investigate systematically the variation in the symmetry of newly produced liners as a function of several manufacturing parameters, such as die vibration, die rotation, die pressing loads, and die dwelling/shaping times.

Computational techniques for penetration of concrete and steel targets by oblique impact of deformable projectiles

This article summarizes progress made in numerically modeling and simulating the penetration and perforation of concrete slabs and steel plate targets by oblique impact of large deformable projectiles. Two modeling efforts are described: (1) concrete target penetration modeling including the effects of concrete compressive and tensile strength on penetration and (2) steel plate perforation modeling including modeling of plate stiffeners. The computational results section includes a discussion of key results and findings obtained in applying the above modeling techniques to practical problems of interest, and comparisons of computed results with experiments.

Range corrections using non-analyte spiking

It is shown by using non-analyte spiking to correct for range variations in sample and standard in proton-induced prompt γ-ray spectrometry, the error introduced by using total ranges instead of effective ranges as a measure of target penetration is negligible, thus making knowledge of the appropriate thresholds irrelevant.

On the hydrodynamic theory of long-rod penetration

The hydrodynamic theory of long-rod penetration is reexamined by applying the modified Bernoulli equation to the forces acting on both sides of the moving rod-target interface. Using a ratio of 2 for the effective cross sectional areas of the mushroomed and rigid parts of the rod, it is shown that analytical expressions can be used to calculate the resistance to target penetration. The analytical expression used to calculate this resistance is the cylindrical cavity expansion, which yields resistance values of 3–4 times the compressive yield strength of the target material. Calculations based on our model show good agreement with experimental data, for steel and tungsten long rods penetrating various steel targets.

Factors Affecting Perforating Charge Performance and Relationship to Port Plug Condition

Summary A series of perforating tests was run in surface targets to determine whether the conditions of the port plug from a perforating gun could be used as a relative indication of entrance hole shape and perforation penetration. Tests that used centralized and decentralized guns in large cement targets showed that a strong correlation exists between casing-entrance hole shape and the shape of the hole in the port plug of the gun. Also, if the charge was misaligned or double-jetted, resulting in cutting of the side of the port plug or the gun, target penetration was sharply reduced. Data were also collected on such influences as gun clearance, charge weight and liner type, multiple casing strings, defective charges, and age of charges.

Recent Developments in Shaped Charge Technology

AbstractShaped‐charge principles, including analytical work, computer‐code simulations, and experimental results, are reviewed. It is assumed that the reader has a basic understanding of the functioning of shaped charges, and emphasizes developments in recent years. The survey is divided into four sections: Liner Collapse, Jet Formation, Jet Breakup, and Target Penetration. Only traditional shaped charges are covered; kinetic‐energy penetrators and self‐forging‐fragment warheads are not included. Ninety‐nine references are cited.