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This research conducts 300 small-scale ammunition experiments using moderate bullet speeds and a variety of bullet configurations in order to understand the relationship between penetration behavior and bullet shape. To maximize the survivability of soldiers and reduce their vulnerability and ballistics wounds, it is very important to understand the penetration physics of bullets. Inside human bodies, tumbling and traveling trajectories are important factors to consider when analyzing human injuries due to ballistics. Therefore, many kinds of bullets and armor have been proposed to minimize or maximize human damage. In this study, to support the development of bullets, 10 bullets with different head angle shapes and different diameters were manufactured and fired at speeds less than 200 m/s towards transparent gelatin blocks, and the damage mechanisms, i.e., temporary cavities and permanent cavities, were studied by taking penetration images using a high speed camera. It was found that the tumbling and rotations of bullets are influenced by kinetic energies and the shapes of bullets, and several empirical relationships are derived. The results suggest that the shapes and the diameters are crucial factors for ballistics wounds.

The PELE ammunition is characterized by a low-density filling material surrounded by a high-density brittle jacket material. An analytical model describing the fragmentation of this ammunition behind a target plate is presented. This model assumes uniaxial strain in the filling and uses the Ranking–Hugoniot relations to calculate the material state. In addition, shock and rarefaction wave interactions at the target free surface and the filling/target interface are accounted for, as well as the radial rarefaction originating from the jacket outer surface. This allows the calculation of the pressure evolution in the filling and the radial acceleration of the jacket at any axial position along the projectile. This model aims at improving previously published analytical models where the acoustic wave approximation was used and the wave interactions were neglected. Experimental results (Paulus and Schirm, 2006) are used to validate the analytical model for different target materials (aluminum and steel), target thicknesses (3 mm and 8 mm), filling materials (polyethylene and aluminum) and impact velocities (900 m/s to 3000 m/s). A qualitative comparison based on X-ray photographs reveals similar features between the model and the experiments, such as smaller and lighter fragments with a greater radial velocity at the front of the projectile compared to the fragment characteristics at the back of the projectile. A quantitative comparison based on the maximum radial velocity of the fragments shows on average a 20% difference between the analytical and experimental results for all impact conditions considered. Despite this difference, the analytical trend follows more closely the experimental one compared to the acoustic approximation especially at high impact velocities. In addition, the acoustic approximation fails to reproduce the jacket fragmentation pattern since the fragmentation length of the jacket is significantly under-predicted. A numerical simulation is also presented using the ANSYS Autodyn 14.0 software. The results show that the numerical and analytical pressure evolution in the filling and the radial velocity of the jacket are in very good agreement, verifying the uniaxial strain assumption. This agreement (together with the experimental agreement) thus suggests that the Rankine–Hugoniot relations, the wave interactions and the radial rarefaction wave must all be included in the model to adequately describe the fragmentation of the PELE ammunition behind a thin target plate.

This paper discusses the technique of Digital Speckle Radiography (DSR) and its application to the measurement of the internal flow fields in penetration of sand by long-rod projectiles at velocities up to 200 m/s. Three different rod nose shapes were studied: flat-ended, ogive-2, and hemispherical. Impacts performed on gelatine and concrete gave significantly different displacement fields to sand. Sand, therefore, cannot either be modelled as a fluid or as a conventional solid. Simulations performed using a code written by two of the authors (Bobaru and Promratana) showed that the velocity distribution has a very different appearance to the force distribution. This suggests that processes such as reorganisation, sliding and void filling take place, allowing the grains to move in directions other than the applied force. The resulting velocity distribution bears a strong resemblance to the experimentally measured displacement fields.

A new technique using nickel–chromium wire, called the NiCr (Nichrome®) wire technique, has been presented in a first paper describing the technique [1]. This second paper focuses on the results obtained when this new technique is applied to ballistic fabrics. Strain distributions on the layer impacted, as well as in different layers, are presented. An energy balance based on the strains is shown to provide reasonable values for the elastic energy stored by the yarns. Failure times of the first layer as a function of impact velocity are discussed and a simple momentum balance is shown to predict well the deflection history of the fabric. Ultra-high-speed photography and high-speed videos allowed recording of fabric deflection vs. time. The combination of the four diagnostic techniques, including X-rays, delivers a very complete picture of the impact mechanics in fabrics, both for early-time and late-time phenomena.

An experimental study was made of the pressures generated by a single hydrodynamic ram event. A generic box type fuel tank simulator was fabricated to study the phenomenon and was capable of containing 3785.4 l of liquid thereby isolating the phases of the event from tank wall reflections, and enable separation of the effects of each phase. Tungsten, steel, and aluminum spherical projectiles were fired into the tank and the result was measured using high-speed pressure transducers, which were located throughout the tank, and compared to the pressure waves and events recorded inside the tank simulator with a high-speed video. It was determined that a high-pressure initial wave is generated at impact and is followed by the more gradual drag pressure around the projectile. The angular distribution of the initial wave and the variation with distance were investigated along with the effect of projectile mass on the drag pressure. This region of pressure decreases in the projectile wake, forming a trailing cavity that remains at a low pressure until the cavity begins to collapse. This results in the largest recorded pressure inside the simulator.

This paper presents an investigation regarding the ballistic performance of protection panels of different fabric ply numbers used in body armours. Twaron CT 710 type fabric layers of differing numbers are joined by using three stitch types to form the panels and then the panels are subjected to ballistic tests according to NIJ standards. Ballistic performance of the panels is determined by measuring trauma depth and trauma diameter. The energy absorbed by the fabric layers and the energy transmitted to the back of the fabric layers are determined from the trauma depth and trauma diameter values using a different approach. It is shown that the fabric ply number and stitching type have significant effects on ballistic properties and the effect of conditioning is limited.

When a shotgun or rifle is fired, the shooter experiences an impact to the upper body known as recoil. This force felt by the shooter is a consequence of the momentum transfer from the accelerating ballistic charge to the firearm, which is ultimately transferred to the shooter as he/she restrains the firearm's induced motion. The accelerating ballistic charge responsible for the recoil has two components. The first is the acceleration of the projectile itself. The recoil associated with this action is known as primary recoil. The second component is associated with the acceleration of the gases created by the combustion of the gunpowder propellant. For competitors in the shooting sports, gun recoil can affect performance and create discomfort. An objective method of measuring felt recoil forces would be useful to evaluate methods of recoil reduction. An experimental test apparatus was developed to measure recoil forces of sporting rifles and shotguns. No modifications to the firearms themselves were necessary to make the measurements. Through both inertial and dissipative restraint mechanisms, the apparatus reproduced gun movement that was representative of that experienced by a particular shooter. This should result in measured recoil forces similar to those experienced by the shooter. The apparatus measures the horizontal shoulder force and the vertical force component exerted at the stock comb. The recoil event was found to be quite short, having duration on the order of 10 ms. Peak recoil forces for common shotgun target loads were in the range of 1.6-2.2 kN (360-494 lbf). The apparatus was found sensitive enough to measure recoil force differences among different factory loaded ammunition, and differences in recoil force imparted by different firearms shooting the same ammunition. The apparatus should prove useful for quantifying differences in felt recoil as affected by ammunition type, gunstock geometry, barrel porting, recoil reduction devices, and gun weight, among other factors.

A ricochet model for long rods developed by the author has been revisited in search of solution efficiencies. By replacing a moment-of-momentum governing equation in the original model with a simpler minimization constraint, a solution technique has been developed that avoids the complexity of an iterative solution that characterized the original work. The revised model retains key elements of the original model, including: ricochet by way of plastic hinge formation; rod rebound from the target's ricochet surface; and target gouging as a means to redirect the target force's line of action. Finally, the ricochet equations are analytically rendered so as to give a keen sense of how the critical obliquity for ricochet varies as a function of the initial conditions of the ballistic engagement.

Ballistic limit equations (BLEs) are used for the damage prediction of spacecraft in a meteoroid and space debris environment. For double-wall configurations, the Cour-Palais/Christiansen equations have been modified to yield a general approach including the influence of the shield thickness. The ratio of shield thickness to particle diameter is considered as additional parameter in the equations. These equations result in the single-wall equation when the shield thickness approaches zero. The modifications can also be applied to other BLEs. Impact tests have been performed in order to validate the modified equations. In this paper, the test results are compared to the modified BLEs. Especially in the hypervelocity region, the new equations are more suitable for configurations with very thin shields than the original ones.

We propose the use of “characteristic length,” based on radar cross section, as a metric for comparing the performance of orbital debris impactors of differing shapes, and the use of NASA's standard breakup model (SBM) “flake” shape as the representative particle for predicting orbital debris penetration effects. We also propose the use of a 26-view methodology for examining non-spherical particles such as cylinders, rectangular prisms, octahedrons, etc., with the intent to describe their potential impact orientations while minimizing the number of hydrocode runs needed to develop orientation-dependent ballistic limit curves. Using this methodology and the smooth particle hydrodynamic code (SPHC), we predict the ballistic limit for SBM-based particles against a typical spacecraft dual-wall shield at normal obliquity and velocities of 7, 8, and 12 km/s. Finally, we compare these results with ballistic limits produced by spherical impactors of the same characteristic length as the SBM-based particles.

This paper presents the results of scale size experiments using a tungsten-alloy long-rod projectile fired against 97.5% Al2O3 ceramic targets at 1.8 and 2.6 km/s. Two targets were used, one having lateral steel confinement; the other without. The projectile overmatched the target, and residual projectile length and velocity were recorded using ballistic-syncro photography. Flash radiography was used during penetration of the unconfined target to obtain the penetration velocity. Manganin pressure gauges were also used to obtain additional data on the response of the ceramic target during penetration. Results from the eight experiments indicate that the confinement reduced the residual energy of the projectile at both impact velocities. Expressed in terms of the projectile impact energy, 55–56% was lost in the unconfined target at 2.6 km/s compared with 60% for the confined design. The same trend was found at 1.8 km/s with 68% and 72–73% for the unconfined and confined, respectively. Predictions using the QinetiQ GRIM2D hydrocode and a simplified form of the Johnson–Holmquist ceramic material model agreed well with the experiments for three out of the four test configurations. The predicted projectile erosion and retardation against the confined target at 1.8 km/s was excessively high. Analytical predictions using the Tate modified Bernoulli equation also gave reasonably accurate predictions for three of the tests, but values for the Tate target ‘strength’ extracted from experiments using a different target configuration were not accurate for the target design used in this paper. r 2006 Elsevier Ltd. All rights reserved.

Ballistic limit curves (BLCs) for dual- or multi-wall spacecraft wall systems impacted by spherical projectiles exist for a variety of impact conditions. However, meteoroids and orbital debris particles can take any shape, and non-spherical projectiles can be more damaging than equal mass spherical projectiles under the same impact conditions. In a recent study, a series of BLCs for a typical dual-wall configuration impacted by a variety of non-spherical projectiles were developed and presented in terms of equivalent spherical projectile diameter as a function of impact velocity. In order to be more consistent with debris environment predictions and to be useful for spacecraft design, such BLCs need to be drawn in units that are consistent with environment flux models used in that design process. In this paper, we have recast the equivalent spherical projectile diameter BLCs and now present them using radar cross-section (RCS) diameter as the characteristic length parameter. The recast BLCs are seen to be more tightly grouped and are not as spread out as they were when plotted using equivalent spherical projectile diameter. Thus, the effect of projectile shape on penetrating ability is shown to be somewhat reduced when considering characteristic length as the size parameter as opposed to an equivalent mass diameter.

The Walker–Anderson and Ravid–Bodner analytical models for penetration of projectiles in metallic plates are well known in the ballistics community. The Walker–Anderson model uses the centerline momentum balance in the projectile and target to calculate the penetration history into a semi-infinite medium, while the Ravid–Bodner model uses the upper bound theorem of plasticity theory modified to include dynamic effects. The Ravid–Bodner model also includes a rich selection of failure modes suitable for finite-thick metallic targets. In this paper a blended model is presented: momentum balance is used to calculate the semi-infinite portion penetration (before the back of the target plate begins to flow), and the Ravid–Bodner failure modes are used to determine projectile perforation. In addition, the model has been extended to handle multiple plate impact. Numerical simulations show that after target failure the projectile still continues to erode for some microseconds. This time has been estimated and incorporated into the model. Examples are presented for long-rod projectiles against thick and spaced-plate targets backed by a witness pack that is separated from the main target element(s) by an air gap. Agreement with results from numerical simulations is quite good.

We demonstrate a potentially new concept to enhance the resilience of structures to withstand rapid impulsive loading. The basic idea is to use a high wave speed layer to rapidly spread (μs time scales) the locally applied impact load. We also propose a quantitative measure based on normalized dissipative energy density (NDE) to characterize load spreading. Using this measure, we have studied numerically the effects of wave speed, layering geometry (thickness and configuration), and mechanical properties (impedance and strength) of the layer and substrate on load spreading. The numerical calculations make a good case for the load spreading concept. The NDE measure may also serve as a useful tool to examine the general response of layered composites to impact loading.

Herein, we study the technique of improving the gun performance by installing a diaphragm in the pump tube of the gun. A CFD study is carried out for the 0.28 in. gun in the Hypervelocity Free Flight Radiation (HFF RAD) range at the NASA Ames Research Center. The normal, full-length pump tube is studied as well as two pump tubes of reduced length (approximately 75% and approximately 33% of the normal length). Significant improvements in performance are calculated to be gained for the reduced length pump tubes upon the addition of the diaphragm. These improvements are identified as reductions in maximum pressures in the pump tube and at the projectile base of approximately 20%, while maintaining the projectile muzzle velocity or as increases in muzzle velocity of approximately 0.5 km/sec while not increasing the maximum pressures in the gun. Also, it is found that both guns with reduced pump tube length (with diaphragms) could maintain the performance of gun with the full length pump tube without diaphragms, whereas the guns with reduced pump tube lengths without diaphragms could not. A five-shot experimental investigation of the pump tube diaphragm technique is carried out for the gun with a pump tube length of 75% normal. The CFD predictions of increased muzzle velocity are borne out by the experimental data. Modest, but useful muzzle velocity increases (2.5 - 6%) are obtained upon the installation of a diaphragm, compared to a benchmark shot without a diaphragm.

Summary High-speed metallic jets are squeezed out of the conical cavities in a metallic block when loaded with shock waves. The particulation studies on these jets, which elongate under a strain rate of the order of 10 4 –10 5 s −1 , have been carried out theoretically as well as experimentally. The synchro-streak technique (SST) has been used to measure the unparticulated jet distance (UPJD). The time of particulation calculated from the UPJD has been found to be equal to the total of the collapse time and the stretching time. It has been found that as the angle of conical cavity increases, the jet diameter and the particulation time increase, whereas the jet tip velocity and existing strain rate decrease. From the experimentally measured jet diameter the time of particulation has also been calculated by the Hirsch approximation. This time period is in close agreement with the particulation time calculated by the authors. From the measured jet diameter and jet length, the mass of the jet and the thickness of the block material squeezed into the jet have been estimated. A comparative study on aluminium and copper jets has also been conducted and it has been observed that for the given explosive metal system the jets produced by aluminium are solid and coherent as compared to those produced by copper.

Summary The effect of projectile nose shape on penetration is examined numerically using the nonlinear, large deformation wavecode CTH. In particular, the impact of a tungsten alloy, long rod projectile into a 4340 steel target is investigated for three different nose shapes: blunt, hemispherical, and conical. The pressures are sufficiently high that erosion of the projectile begins immediately upon impact. The decays of the shocks are examined, as are the resulting material flow fields. Later-time effects are also explored, such as how the nose shape affects penetration, and how long each case takes to arrive at a quasi-steady-state flow configuration in which the tungsten-steel interface is completely determined by eroding plastic flow.

Conical penetrators have been shown to give enhanced penetration over flat-ended projectiles up to a certain transition velocity. This transition velocity was found to be associated with a separation of the conical nose from the penetrator body which caused the penetrator to revert to the behaviour of a flat-ended penetrator at higher velocities. An explanation of the marked deformation resistance of the conical noses of these penetrators is presented.

The present investigation is concerned with the generation of controlled tumbling of a blunt-nosed hard-steel projectile and, to some extent, the effect of this tumbling on targets struck subsequently. The mechanism for producing this motion from an initial state of translation in the direction of the projectile axis consisted of the impingement of the bullet on the edge of deflector plates of aluminum, steel or plastic of various thicknesses with various degrees of overlap. These initially plane rectangular plates were rigidly held on three sides and struck at the center of the fourth, or free, edge. This first portion of the study consists of the continuum-mechanical analysis of the impact of the projectile on the plate and the subsequent motion of the projectile. A mode shape analysis is employed to ascertain the deplection of the plate with the impact area modeled as a hexagon. The projection is considered as rigid and its motion as planar prior and subsequent to the impact with the deflector plate, which is modeled as a rigid-perfectly plastic material. The numerical predictions of the theoretical development, the experimental set-up and the data derived from the tests, as well as a comparison between the analytical and measured values, are presented in a companion paper [Ruiz and Goldsmith, Int. J. Impact Engng Vol. 7 , in press (1988)].

Simulation of ballistic impact generally falls into one of two categories: analytical models which assume certain dominant physical phenomena and numerical simulations, where the general continuum conservation equations are integrated in time at all points in a spatial mesh to obtain the spatial time history of stresses, strains, velocities, etc., in the projectile and target. Analytical formulations model the mechanical processes over the full field of influence which leads to approximate conservation equations for the entire region in an impact event. These for mulations have met with considerable success so long as the assumptions inherent in the model are applicable. Numerical simulations (hydrocodes) compute the wave (shock) interactions important at early times. Mechanical effects, e.g. plugging, erosion, etc., require realistic constitutive modeling which includes failure criteria and failure propagation. This paper gives a broad overview of both analytical and hydrocode modeling and examines the technical issues, uncertainties and potential diffuculties for advancement in predictive capability.