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Abstract: Continuum mechanics codes modeling failure of materials historically have considered those materials to be homogeneous, with all elements of a material in the computation having the same failure properties. This is, of course, unrealistic but expedient. But as computer hardware and software has evolved, the time has come to investigate a higher level of complexity in the modeling of failure. The Johnson–Cook fracture model is widely used in such codes, so it was chosen as the basis for the current work. The CTH finite difference code is widely used to model ballistic impact and penetration, so it also was chosen for the current work. The model proposed here does not consider individual flaws in a material, but rather varies a material’s Johnson–Cook parameters from element to element to achieve inhomogeneity. A Weibull distribution of these parameters is imposed, in such a way as to include a size effect factor in the distribution function. The well-known size effect on the failure of materials must be physically represented in any statistical failure model not only for the representations of bodies in the simulation (e.g., an armor plate), but also for the computational elements, to mitigate element resolution sensitivity of the computations. The statistical failure model was tested in simulations of a Behind Armor Debris (BAD) experiment, and found to do a much better job at predicting the size distribution of fragments than the conventional (homogeneous) failure model. The approach used here to include a size effect in the model proved to be insufficient, and including correlated statistics and/or flaw interactions may improve the model. [Copyright &y& Elsevier]

Abstract: In this work a nondimensional formulation of an analytical model was used to study the ballistic behaviour of composite plates made from woven laminates of E-glass fibres. From this model the influence of two nondimensional ratios (the geometry and density ratios) at the ballistic limit, contact time, and energy-absorption mechanisms were analysed at different impact velocities. The increase in both ratios raises the ballistic limit and varies the contact time between the projectile and plate. At impact velocities that do not cause perforation, the contact time decreases while at impact velocities over the ballistic limit, this time increases. Regardless of the ratio, the main energy-absorption mechanism is the fibre failure at velocities below the ballistic limit, and the cone movement for impact velocities over the ballistic limit. At the ballistic limit the main mechanisms are fibre failure and fibre elastic deformation. [Copyright &y& Elsevier]

Abstract: This paper presents a numerical investigation of the ballistic performance of monolithic, double- and triple-layered metallic plates made of either steel or aluminium or a combination of these materials, impacted by a 7.62-mm APM2 projectile in the velocity range of 775–950 m/s. Numerical models were developed using the explicit finite element code LS-DYNA. It was found that monolithic plates have a better ballistic performance than that of multi-layered plates made of the same material. This effect diminishes with impact velocity. It was also found that double-layered plates with a thin front plate of aluminium and thick back steel plate exhibit greater resistance than multi-layered steel plates with similar areal density. These predictions indicate that multi-layered targets using different metallic materials should be investigated for improved ballistic performance and weight-savings. [Copyright &y& Elsevier]

Abstract: 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. [Copyright &y& Elsevier]

Abstract: The effects of projectile penetration into soft tissue are often studied using the tissue simulant ballistic soap. Consequently, a full understanding of the high strain-rate response of ballistic soap is desirable. Using the plate-impact technique, key shock parameters have been measured for impacts in the range 81–968 m/s, allowing derivation of the Hugoniot equation-of-state for soap in the U S–u P and σ X–u P planes. A polynomial Hugoniot relationship was found in the U S–u P plane, with the general form U S = 1.96 + 2.41uP − 0.72uP 2 (ρ 0 = 1.107 g/cc). Further, embedded lateral manganin stress gauges were employed to interrogate the evolution of lateral stress within the soap. A gradient in lateral stress, whose magnitude increased incrementally with impact stress, was apparent behind the shock for σ X >1 GPa. It is proposed that at higher values of σ X, increased compression of hydrocarbon chains acts to increase the materials resistance to shear, a phenomenon consistent with steric hindrance. [Copyright &y& Elsevier]

Abstract: Reverse ballistic experiments were used to investigate confinement, pre-damaged and intact, and rod size effects on penetration of long, gold rods into silicon carbide (SiC-N). Rod diameters were 1.0mm and 0.75mm, and lengths were 70mm and 50mm, respectively. Within data scatter, penetration velocity was the same for intact (bare or sleeved), pre-damaged (thermally shocked with non-contiguous cracks), and in situ comminuted SiC-N. Penetration velocity was independent of rod diameter within the data scatter. An expression for the penetration velocity versus impact velocity is found using linear regression. It is proposed that the reason there is no difference in the penetration rate between intact and pre-damaged (failed) SiC is because, after the first few microseconds following impact, the rod penetrates failed material in both cases. [Copyright &y& Elsevier]

Abstract: The normal impact of chrome steel spheres upon mild steel and copper plates of various thicknesses was investigated. The bulging of their rear surfaces was monitored during the first 30 μs after impact using stereo digital speckle photography. The experimental data for copper was compared with two path-dependent models, one optimised for annealed and the other for pre-stressed (work-hardened) copper. It was not possible to differentiate between the two copper models using single-point displacement data. However, full-field data revealed clear differences in the shapes of the bulges, with greater global deformation and closer agreement with experiment for the model that included pre-stress. For both mild steel and copper, thin plates resulted in localised bulging whilst thicker plates produced global dishing. The bulge peak also grew earlier and more quickly in thinner specimens. The greater ductility of copper resulted in narrower, faster-growing bulges compared with mild steel of comparable thickness. [Copyright &y& Elsevier]

Abstract: The penetration and perforation of a thick polycarbonate (PC) plate (one and 3 stacked) by an armor piercing 7.62 mm projectile is investigated experimentally and numerically. The characteristic structure of the projectile’s trajectory in the PC plates is studied. It is observed that the trajectory consist of a cavity and a circumferential cracked zone attached to it, which is fully embedded within a cylindrical plastic zone. The size of the plastic zone is approximately twice that of the cavity zone and can be clearly observed due to the change of the refractive properties of the material. Strong local recovery of the PC is shown as well. A 3D transient non-linear adiabatic finite element simulation is performed using the commercial software Abaqus 6.9-EF1. The numerical analyses include two combined failure criteria: “Ductile failure with damage evolution”, and tensile failure. The material properties are strain rate and temperature dependent. The numerical simulations are tested by comparing the numerical trajectory prediction to actual trajectories of inclined impacts of projectiles. It is found that the projectile perforates the plate at angles of inclinations of 30° and higher. The observed agreement between experiments and numerical modeling indicates that the combined effect of the two failure criteria (tensile vs. ductile failure) can reasonably well predict the projectile’s trajectory within a thick PC plate. The numerical analyses are further used to study the effect of the projectile impact velocity on the depth of penetration (DOP). It is found that the DOP scales slightly non-linear with the impact velocity. The core velocity during the penetration process is also slightly non-linear. The deceleration during penetration is almost a linear function of the penetration velocity and it is higher for higher penetration velocities. [Copyright &y& Elsevier]

Abstract: Boron carbide is an attractive candidate for use as armour material because of its lower density combined with high hardness. The ballistic performance of boron carbide tiles were evaluated using standard Depth of Penetration (DOP) test method against hard steel 7.62 mm armour piercing (AP) projectiles. The effect of variation in thickness of tile and the projectile velocity on the ballistic efficiency of the material was studied. It has been found that the differential efficiency factor (DEF) increases with increase in projectile velocity from 600 to 820 m/s. And an insignificant or marginal increase in efficiency was observed for increase in tile thickness from 5.2 mm up to 7.3 mm. The effect of the type of radial confinement on the residual DOP was also studied. It was found that the steel radial confinement produces lower residual DOP values compared to aluminium alloy and with no radial confinement. Results along with photographs have been presented. [Copyright &y& Elsevier]

Abstract: Impact, damage evolution and penetration of thick-section composites are investigated using explicit finite element (FE) analysis. A full 3D FE model of impact on thick-section composites is developed. The analysis includes initiation and progressive damage of the composite during impact and penetration over a wide range of impact velocities, i.e., from 50 m/s to 1000 m/s. Low velocity impact damage is modeled using a set of computational parameters determined through parametric simulation of quasi-static punch shear experiments. At intermediate and high impact velocities, complete penetration of the composite plate is predicted with higher residual velocities than experiments. This observation revealed that the penetration-erosion phenomenology is a function of post-damage material softening parameters, strain rate dependent parameters and erosion strain parameters. With the correct choice of these parameters, the finite element model accurately correlates with ballistic impact experiments. The validated FE model is then used to generate the time history of projectile velocity, displacement and penetration resistance force. Based on the experimental and computational results, the impact and penetration process is divided into two phases, i.e., short time Phase I – shock compression, and long time Phase II – penetration. Detailed damage and penetration mechanisms during these phases are presented. [Copyright &y& Elsevier]

Abstract: This paper reports an initial study into the benefits of determining two-dimensional flow fields for low velocity impact on a small-scale model of explosive reactive armour (ERA) using digital speckle radiography (DSR). The model system consisted of a polymer-bonded sugar (PBS) (otherwise known as a sugar mock) confined between two mild steel plates. The DSR technique relies upon creating a layer within the specimen that is seeded with lead particles. So although radiography itself is mechanically non-invasive, the lead layer needed may change the mechanical properties of the material. DSR revealed where regions of intense shear occurred in normal impact. These regions are likely to be where a polymer-bonded explosive (PBX) would initiate. [ABSTRACT FROM AUTHOR]

Abstract: Depth of penetration experiments were conducted with fragment simulating projectiles launched into Celotex® in order to develop an equation for the strike velocity as a function of the FSP mass and the depth of penetration into Celotex® recovery media. A powder gun launched FSPs, designed in accordance with STANAG-2920 [NATO STANAG-2920 Ballistic Test Method for Personal Armour Materials and Combat Clothing, 2nd ed., 1999.] weighing between 0.13g and 53.78g at striking velocities between 198m/s and 1524m/s. A multiple linear regression analysis was used to determine an empirical relationship for the strike velocity to the impact parameters of depth of penetration, fragment mass, and mean presented area. Sabot launched natural fragments weighing between 2.8g and 15.8g at striking velocities between 532m/s and 1084m/s were used to validate the equation. [Copyright &y& Elsevier]

Abstract: The ballistic impact properties of a borosilicate (‘pyrex’) glass was studied using mild steel rods accelerated using a light gas gun. High-speed photography at sub-microsecond framing rates was used along with schlieren optics to investigate the propagation of elastic shock waves and fracture fronts. Flash X-radiography was used to visualise the deformation of rods as they penetrated the comminuted glass normally. The rod was seen initially to dwell on the surface for at least 3μs creating a Hertzian cone-crack. Later on, between 40 and 60 μs, self-sharpening of the projectile was observed as the ‘wings’ of the heavily deformed front end sheared off. After this event, the front of the rod speeded up. X-rays also showed that the pattern of fissures within the comminuted glass was observed to be very similar shot-to-shot. X-radiography was also used to examine the mechanisms occurring during oblique impact of rods at 45°. In oblique impact, bending of the rod rather than plastic deformation (‘mushrooming’) takes on the role of distributing the load over an area larger than that of the original rod diameter. High-speed photography of the rear surface of a glass block on which a fine grid had been placed confirmed that the comminuted glass moved as larger interlocked blocks. The experiments were modelled using the QinetiQ Eulerian hydrocode GRIM making use of the Goldthorpe fracture model. The model was found to predict well the transition from dwell to penetration. [Copyright &y& Elsevier]

Abstract: A micro-scale computational tool, based upon an explicit digital element method (DEM), has been developed for numerical simulation of ballistic impact and penetration of textile fabrics. In this approach, each yarn is digitized as an assembly of digital fibers. Each digital fiber is further digitized into a short digital rod element chain connected by frictionless pins (nodes). A search is conducted to find contacts between adjacent digital fibers. If a contact is detected, compressive and frictional forces between fibers will be determined, based upon contact stiffness and friction coefficient. Nodal forces are calculated for each time step. Nodal displacements are determined using an explicit procedure. Because the digital element approach operates on a sub-yarn micro-scale, one can determine textile penetration resistance based upon sub-yarn scale properties, such as inter-fiber compression, friction, and fiber strength. Research presented in this paper includes three parts. First, the explicit digital element algorithm used in dynamic simulation is explained. Second, the approach is used to generate 2-D woven fabric micro-geometries and to simulate ballistic penetration processes. Third, numerical results are compared to high resolution experimental impact and ballistic test data. [Copyright &y& Elsevier]

Abstract: In the present study an ultra high strength armour steel was austenatised at 910°C followed by tempering at 200, 300, 400, 500 and 600°C. After heat treatment the properties of tensile strength, ductility, charpy impact strength, hardness and microstructure were evaluated from the mechanical tests and metallographic analysis respectively. The ballistic behavior of the heat-treated plates was evaluated impacting against non-deformable hard steel core projectiles at 840 ± 15 m/s at normal angle of attack. The changes in the microstructure and mechanical properties with heat treatment have been correlated with ballistic performance of the steel. Experimental results showed that 200°C tempering gives the best ballistic performance. [Copyright &y& Elsevier]

Abstract: In this paper, we present and discuss the results of our numerical simulation of the dynamic response and failure modes of circular DH-36 steel plates and DH-36 steel–polyurea bilayers, subjected to impulsive loads in reverse ballistic experiments. In our previous article, we reported the procedure and results of these experiments [MR Amini, JB Isaacs, S Nemat-Nasser. Experimental investigation of response of monolithic and bilayer plates to impulsive loads. accepted]. For the numerical simulations, we have used physics-based and experimentally-supported temperature- and rate-sensitive constitutive models for steel and polyurea, including in the latter case the pressure effects. Comparing the simulation and the experimental results, we focus on identifying the potential underpinning mechanisms that control the deformation and failure modes of both monolithic steel and steel–polyurea bilayer plates. The numerical simulations reveal that the bilayer plate has a superior performance over the monolithic plate if the polyurea layer is cast on its back face (opposite to the blast-receiving side). The presence of the polyurea layer onto the front face (blast-receiving side) amplifies the initial shock loading and thereby enhances the destructive effect of the blast, promoting (rather than mitigating) the failure of the steel plate. In addition, the interface bonding strength between polyurea and steel is examined numerically and it is observed that the interface bonding strength has a significant effect on the performance of the steel–polyurea bilayer plates. The numerical simulations support the experimentally observed facts provided the entire experiment is simulated, employing realistic physics-based constitutive models for all constituents. [Copyright &y& Elsevier]

Abstract: The study of penetrator performance without free-surface effects can require prohibitively large monolithic targets. One alternative to monolithic targets is to use segmented targets made by stacking multiple concrete slabs in series. This paper presents an experimental investigation on the performance of segmented concrete targets. Six experiments were carried out on available small scale segmented and monolithic targets using instrumented projectiles. In all but one experiment using stacked slabs, the gap between slabs remained open. In the final experiment design, grout was inserted between the slabs, and this modification produced a target response that more closely represents that of the monolithic target. The results from this study suggest that further research on segmented targets is justified, to explore in more detail the response of segmented targets and the results of large scale tests when using segmented targets versus monolithic targets. [Copyright &y& Elsevier]

Abstract: 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. [Copyright &y& Elsevier]

Abstract: Various open-literature experimental findings pertaining to the ballistic behavior of glass are used to construct a simple, physically based, high strain-rate, high-pressure, large-strain constitutive model for this material. The basic components of the model are constructed in such a way that the model is suitable for direct incorporation into standard commercial transient non-linear dynamics finite-element based software packages like ANSYS/Autodyn [ANSYS/Autodyn version 11.0, User documentation, Century Dynamics Inc. a subsidiary of ANSYS Inc.; 2007.] or ABAQUS/Explicit [ABAQUS version 6.7, User documentation, Dessault systems, 2007.]. To validate the material model, a set of finite element analyses of the Edge-on-Impact (EOI) tests is carried out and the results compared with their experimental counterparts obtained in the recent work of Strassburger et al. [Strassburger E, Patel P, McCauley JW, Kovalchick C, Ramesh KT, Templeton DW. High-speed transmission shadowgraphic and dynamic photoelasticity study of stress wave and impact damage propagation in transparent materials and laminates using the edge-on impact method. In: Proceedings of the twenty-third international symposium on ballistics. Spain: April 2007, and Strassburger E, Patel P, McCauley W, Templeton DW. Visualization of wave propagation and impact damage in a polycrystalline transparent ceramic-AlON. In: Proceedings of the twenty-second international symposium on ballistics. Vancouver, Canada: November 2005.]. Overall, a good agreement is found between the computational and the experimental results pertaining to: (a) the front-shapes and propagation velocities of the longitudinal and transverse waves generated in the target during impact; (b) the front-shapes and propagation velocities of the “coherent-damage” zone (a zone surrounding the projectile/target contact surface which consists of numerous micron- and sub-micron-size cracks); and (c) the formation of “crack centers”, i.e. isolated cracks nucleated ahead of the advancing coherent-damage zone front. Relatively minor discrepancies between the computational and the experimental results are attributed to the effects of damage-promoting target-fixturing induced stresses and cutting/grinding-induced flaws located along the narrow faces of the target and the surrounding regions. [Copyright &y& Elsevier]

Abstract: Ballistic limit equations are used to predict the damage of spacecraft subjected to impacts by space debris and meteoroids. This paper presents two new ballistic limit equations for impact velocities in the ballistic and shatter regions, respectively. The methodology used to develop the two ballistic limit equations involves the energy balance law and Cohen''s debris cratering model. A very often form for ballistic limit equations based on the crater depth in a semi-infinite target was used for the both equations. The limit velocity between the ballistic and shatter regions was expressed as a non-dimensional equation in this paper. Agreement observed between existing and proposed results confirmed the validity of the presented equations. [Copyright &y& Elsevier]

Abstract: Ballistic perforations of monolithic steel sheets, two-layered sheets and lightweight sandwich panels were investigated both experimentally and numerically. The experiments were performed using a short cylindrical projectile with either a flat or hemispherical nose that struck the target plate at an angle of obliquity. A total of 170 tests were performed at angles of obliquity 0–45°. The results suggest that during perforation by a flat-nosed projectile, layered plates cause more energy loss than monolithic plates of the same material and total thickness. There was no significant difference in the measured ballistic limit speed between monolithic plates and layered plates during oblique impact perforation by a hemispherical-nosed projectile. To develop understanding of the process of fracture development and perforation of a thin stainless-steel sheet resulting from oblique impact by a hard, flat-nosed projectile, numerical simulations by ABAQUS/Explicit finite element code were compared against the experimental fracture patterns, residual velocities and ballistic limits of perforated plates. Effects of projectile length-to-diameter ratio and spacing between layered plates struck by flat-nosed projectiles were investigated. For projectiles of equal mass, a longer projectile (larger ratio of length to diameter, L/D>2) results in a drastic decrease in the ballistic limit speed for a double-layered plate. For thin, layered plates, the ballistic limit speed is affected significantly by the spacing between layers. [Copyright &y& Elsevier]

• Small and medium arms fire can be stopped with a snow-based protective structure. • Snow-filled commercial gabions can be efficiently constructed. • Structures can be construction at a rate of about 0.5 hr/m3 with common equipment. • Snow set-up time of 24 h is recommended. • All but one model of projectile penetration in snow matched our results within 32%. Small (5.56 mm, 7.62 mm and 9 mm) and medium (12.7 mm) arms rounds were fired at snow-filled 1.5m cubic gabions in a mid-winter condition in Fairbanks, Alaska. The rounds were excavated and penetration by each ammunition type was measured. A distribution and average of penetration depth was determined. All 320 rounds fired were captured within 1.5m after entering the snow barrier. Comparison with published models of ballistics penetration of snow showed mixed results with several matching our data within 10% and all but one within 32%. However, most of these models are simplistic in that they accommodate limited variables and therefore may not be expected to perform well in all settings. We conclude that snow-based ballistics protection structures can be quickly and efficiently erected in suitable environments and with minimal size, can provide reliable protection against small and medium arms fire. [ABSTRACT FROM AUTHOR]

Abstract: Laminated ballistic composite panels are an important part of hard-plate protective body armour and may be subjected to a wide variety of impact conditions depending on the projectile, impact velocity and armour construction, to name a few. The ballistic response of laminated composite panels has been investigated through direct impacts of two non-deforming projectiles (7.5mm diameter hardened steel 120° cylindrical–conical, and 9mm hemispherical nosed) selected to enhance different failure mechanisms including penetration and delamination. Experimental and numerical studies were carried out to determine the ballistic response of laminated Kevlar® 29 and 129 composite panels, commonly used in protective body armour. These panels were impacted at velocities between 130 and 250m/s, which were below the penetration limit of the panels. A numerical parametric study was initially undertaken to determine those material properties which reduce back face signature (BFS; maximum dynamic displacement), one of the important performance indicators for assessing personal protection. Experimental material characterization then allowed mechanical property data to be determined for numerical simulations, which showed good agreement with the experimental data, particularly for the conical projectile impacts on both types of Kevlar® panels. Numerical simulations of the impact tests accurately predicted the BFS and dynamic response for the conical projectile impacts, while the BFS for the hemispherical projectiles was slightly low. This can be attributed to the dominant delamination failure mechanisms, which may not be completely captured by the numerical model. Importantly, the numerical analysis accurately predicted the initial velocity of the panel back face for the hemispherical projectiles and the time to reach maximum BFS for the conical projectiles. [Copyright &y& Elsevier]

Abstract: In this paper, the response and failure of sandwich beams with aluminum-foam core are investigated. Quasi-static and low-velocity impact bending tests are carried out for sandwich beams with aluminum-foam core. The deformation and failure behavior is explored. It is found that the failure mode and the load history predicted by a modified Gibson''s model agree well with the quasi-static experimental data. The failure modes and crash processes of beams under impact loading are similar to those under quasi-static loading, but the force-displacement history is very different. Hence the quasi-static model can also predict the initial dynamic failure modes of sandwich beams when the impact velocity is lower than 5m/s. [Copyright &y& Elsevier]

Abstract: In this paper, the ballistic resistance of double-layered steel shields against projectile impact at the sub-ordnance velocity is evaluated using finite element simulations. Four types of projectiles of different weight and nose shapes are considered, while armor shields consist of two layers of different materials. In a previous study of the same authors, it was shown that a double-layered shield of the same metal was able to improve the ballistic limit by 7.0–25.0% under impact by a flat-nose projectile, compared to a monolithic plate of the same weight. Under impact by a conical-nose projectile, a double-layered shield is almost as capable as a monolithic plate. The present paper extends the analysis to double-layered shields with various metallic material combinations. The study reveals that the best configuration is the upper layer of high ductility and low strength material and the lower layer of low ductility and high strength material. This configuration results in some 25% gain in the ballistic limit under moderate detrimental impact. This research helps clarify the long standing issue of the ballistic resistance of the multi-layered armor configuration. [Copyright &y& Elsevier]

Abstract: We present penetration equations for rigid, ogive-nose, rod projectiles that penetrate aluminum targets at normal impact. Comparisons of depth of penetration data and predictions from a previously published penetration equation derived from spherical, cavity-expansion methods show excellent agreement for striking velocities to 1800m/s. We then identify a small parameter in the penetration equation, perform a power-series expansion, and obtain approximate penetration equations. These approximate equations are very accurate for striking velocities to 1300m/s and display clearly the dominant problem parameters. [Copyright &y& Elsevier]

Abstract: 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 10ms. Peak recoil forces for common shotgun target loads were in the range of 1.6–2.2kN (360–494lbf). 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. [Copyright &y& Elsevier]

Abstract: The dynamic stress–strain behaviour of the Spectra Shield® LCR (laminated composite roll) is determined from tests using a tensile split Hopkinson bar, and the experimental results indicate that it is highly strain rate sensitive. The failure strain decreases initially with strain rate up to a critical value, and rises thereafter, while the failure stress increases with strain rate to a similar value of strain rate, after which it decreases. The nature of failure of filaments is observed to change with strain rate, first becoming increasingly brittle and then returning to more ductile modes once the critical strain rate is exceeded. The increase in failure strain and stress are accounted for in terms of strain rate hardening. An explanation of the reduction in failure stress beyond the critical strain rate is proposed with respect to increasing viscoelastic hysteresis and reduction in the time available for filament alignment. [Copyright &y& Elsevier]

Abstract: This paper is devoted to the presentation of a finite element based on a Fourier modal description of physical values on circumferences for a quasi-axisymmetric structure. The finite element detailed in this paper is an advanced version of the COMU element, developed by Combescure [Static and dynamic buckling of large thin shells: design procedure, computation tools, physical understanding of the mechanisms. Nucl Eng Des 1985; 92:339–54, Etude de la stabilité non linéaire géométrique et non linéaire matériau des coques minces. Application aux coques de révolution avec imperfections soumises à des chargements complexes. Habilitation à Diriger des Recherches, INSA Lyon, 1995], in order to extend it for simulating penetration of targets composed of geological materials by steel projectiles. A finite element code with COMU elements is coupled with analytical forcing functions based on the dynamic expansion of a spherical cavity to represent the target. This combined analytical and computational approach is employed to reproduce normal impact of ogive-nosed VAR 4340 steel projectiles striking limestone targets with small angles of pitch and yaw. Results obtained from the cost-effective approach with two-dimensional COMU elements are checked against experimental data [Frew DJ, Forrrestal MJ, Hanchak SJ. Penetration experiments with limestone targets and ogive-nose steel projectiles. J Appl Mech 2000; 67: 841–5] and results from an analogous combined approach using three-dimensional hexahedral continuum elements [Warren TL. Simulations of the penetration of limestone targets by ogive-nose 4340 steel projectiles. Int J Impact Eng 2002;27:475–96]. [Copyright &y& Elsevier]

Abstract: The paper describes a series of 2D numerical simulations which followed the cavity expansion process in an elasto- plastic solid. The results from these simulations, in terms of cavity wall motion as a function of the applied pressures inside the cavity, highlighted several issues concerning cavity expansion process and the terminal ballistics of both rigid and eroding long rods. These issues include the form of the relation between the dynamic radial stress on the cavity wall and its velocity, which can be written in a simple, normalized form, at least for the materials we simulated here. Also, the difference between target resistance to the penetration of rigid and eroding-rod penetration, was quantified with a series of simulations in which the pressures in the cavity were applied on an angular section, rather than on its whole surface. Finally, we explored the inherent differences between spherical and cylindrical cavity expansion processes, which can be helpful for analytical models of the penetration of rigid rods with different nose shapes. [Copyright &y& Elsevier]

Abstract: The present study is based on the experimental and numerical investigations of deformation behavior of layered aluminum plates of different thicknesses under the impact of flat, ogive and hemispherical nosed steel projectiles. Thin-layered plates arranged in various combinations were normally impacted at different velocities with the help of a pneumatic gun. Ballistic limit velocity and the residual velocity of the projectiles for each layered combination were obtained experimentally as well as from the finite element code, and these were compared with those of the single plates of equivalent thicknesses. For two layers, the residual velocity was comparable to that of the single plate, however, when the number of layers was increased the velocity drop was found to be higher in the case of the single plate. Ogive nosed projectile was found to be the most efficient penetrator of the layered target. Hemispherical nosed projectile required maximum energy for perforation. Deformation profiles of the target plates in the layered combinations were measured, and it was found that hemispherical nosed projectile caused highest plastic deformation of target plates. Numerical simulation of the problem was carried out using finite element code ABAQUS. Explicit solution technique of the code was used to analyze the perforation phenomenon. Results of the finite element analysis were compared with experiments and a good agreement between the two was found. [Copyright &y& Elsevier]

Abstract: This paper examines the penetration and perforation of fibre-reinforced plastic (FRP) laminates struck by rigid projectiles with different nose shapes within a wide range of impact conditions using ABAQUS/Explicit code. It is assumed that the FRP laminate target response can be represented by a velocity dependent forcing function which eliminates discretizing the target as well as the need for a complex contact algorithm. The forcing function is then applied to the surface of the projectiles as boundary conditions in the numerical model. With this combined analytical and computational technique we can obtain the depth of penetration, residual velocity, ballistic limit, transient response in terms of time-histories of displacement/penetration, velocity and deceleration of the projectile. It is shown that the model predictions are in good correlation with available experimental data. [Copyright &y& Elsevier]

Abstract: 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. [Copyright &y& Elsevier]

Abstract: In this paper the influence of constitutive relation has been studied in numerical simulations of the perforation of 12-mm thick Weldox 460 E steel plates impacted by blunt-nosed projectiles in the sub-ordinance velocity regime. A modified version of the well-known and much used constitutive relation proposed by Johnson-Cook and both the bcc- and hcp-version of the Zerilli-Armstrong constitutive relation were combined with the Johnson-Cook fracture criterion. These models were implemented as user-defined material models in the non-linear finite element code LS-DYNA. Identification procedures have been proposed, and the different models were calibrated and validated for the target material using available experimental data obtained from tensile tests where the effects of strain rate, temperature and stress triaxiality were taken into account. Perforation tests carried out in a compressed gas gun on 12-mm-thick circular Weldox 460 E steel plates were then used as base in a validation study of plate perforation using LS-DYNA and the proposed constitutive relations. The numerical study indicated that the physical mechanisms during perforation can be qualitatively well predicted by all constitutive relations, but quantitatively more severe differences appear. The reasons for this are discussed in some detail. It was concluded that for practical applications, the Johnson-Cook constitutive relation and fracture criterion seems to be a good choice for this particular problem and excellent agreement with the experimental results of projectile impact on steel plates were obtained under the conditions investigated. [Copyright &y& Elsevier]

Abstract: Protection effectiveness of an oblique metallic plate against a long rod projectile has been evaluated through a three-dimensional dynamic finite element computer program. The parameters considered in the simulations are the impact velocity, oblique plate thickness, gap distance between oblique plate and witness block, and obliquity. It was found that protection performance of an oblique plate was maximized in case that the ratio of line-of-sight (LOS) plate thickness to projectile diameter is around 2.0. This result may be used as a guide for the design of obliquely spaced armour structures against long rod projectiles. [Copyright &y& Elsevier]

Abstract : The Alekseevski–Tate equations are typically used to predict the penetration, penetration velocity, rod velocity, and rod length of long rod penetrators and similar projectiles impacting targets. These nonlinear equations were originally solved numerically and more recently by the exact analytical solution of Walters and Segletes. However, due to the nonlinear nature of the equations, the penetration was obtained implicitly as a function of time, so that an explicit functional dependence of the penetration on material properties was not obtained. The current paper obtains the velocities, length, and penetration as an explicit function of time by employing a perturbation solution of the nondimensional Alekseevski–Tate equations. Simple (algebraic) analytical equations are given. Perturbation solutions of the Alekseevski–Tate equations were first undertaken by Forrestal et al., up to the first–order, and good agreement with the exact solutions was shown for relatively short times. In retrospect, this solution was only valid for penetrators impacting weak targets. The current study obtains a third-order perturbation solution and includes both penetrator and target strength terms, and is applicable for strong targets. The paper compares the exact solution to the perturbation solutions, and a typical comparison between the exact and approximate solutions for a tungsten rod impacting a semi-infinite steel armor target is shown. Also, alternate ways are investigated to normalize the governing equations in order to obtain an optimum perturbation parameter. In most cases, the third-order perturbation solution shows good agreement with the exact solution of the Alekseevski–Tate equations. In addition, simple equations based on the first–order perturbation solution are presented, which are accurate for the perforation of finite thickness (short penetration time) targets. [Copyright &y& Elsevier]

Abstract: 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. [Copyright &y& Elsevier]

Abstract: Recent experimental measurements show that eroding long-rod penetration velocity is a linear function of impact velocity over a very wide range of impact velocities and for an interesting range of rod–target material combinations. These experiments all show that U=a+bV, where U and V are the penetration and impact velocity, respectively, and “a” and “b” are constants for given projectile and target materials. Numerical simulations also show that U=a+bV. The accumulation of these results suggests that a linear relationship between penetration and impact velocity may be fundamental over a very large range of impact velocities. A linear relationship between penetration and impact velocity has a number of implications. Some implications of this result for the Tate–Alekseevskii model are briefly examined in this paper. [Copyright &y& Elsevier]

Abstract: This paper was prepared in response to being awarded the Hypervelocity Impact Society''s Distinguished Scientist Award at HVIS 2003 held in Noordwijk, The Netherlands. It is traditional that the paper associated with the HVIS Distinguished Scientist Award is a retrospective on the recipient''s career. This paper is in that tradition. [Copyright &y& Elsevier]

Abstract: The first experiments with a penetrator with enhanced lateral efficiency (PELE) were carried out in 1996. The unusual behaviour of the penetrator as it perforates a target can generally be described in three main stages. In the first stage the different kinetic energies of the jacket and the filling lead to the enclosure of the filling material. This induces a pressure rise in the filling, which dilates the surrounding jacket in the second stage. During the last stage the high-density jacket breaks into pieces. When a thin target, as in our case, is perforated, a fourth stage must be added to the other three. This new stage describes the interaction between the filling and the plug, which is produced during the impact. For the lateral efficiency of the PELE, the second stage is the important one. The behaviour in this stage (pressure build-up and radial expansion of the jacket) is dominated by only a few physical parameters. For weak shock waves, these parameters are determined by theoretical consideration. A number of experiments were carried out in the velocity range between 900 and 3000m/s in order to obtain an experimental database. In the last section a comparison between the physical model and experimental data gives a short outline of the complex impact behaviour of the PELE projectile. The physical model and the experimental data are in good agreement for impact velocities under 1400m/s. For higher velocities causing stronger shock waves, the theory has to be modified; but the set of physical parameters influencing the terminal ballistic behaviour of PELE remains valid. [Copyright &y& Elsevier]

Abstract: This paper describes a series of smooth particle hydrodynamics (SPH) simulations of tungsten cylindrical and spherical projectiles impacting steel bumper plates at different impact configurations. Comparisons of the destructive capabilities of the spherical and cylindrical projectiles for each impact configuration are presented. Cylindrical geometries were spatially rotated to cover a wide range of impact configurations. The incidence angle of the velocity vector and its magnitude were varied. A rational approach is proposed to quantify the level of damage inflicted on the bumper plates on each impact event. This damage measure is used to create a set of comparative damage matrixes for cylindrical and spherical projectiles that identify under which impact configurations a given geometry is more damaged than the other. [Copyright &y& Elsevier]

Abstract: The mechanical response of rocks to dynamic loading is complex. It is not well understood because of the difficulty of defining an effective shear and tensile strength model. Recently AUTODYN-2D from Century Dynamics is used to simulate the shock-induced damage in granite targets impacted by projectiles at different velocities. The simulated results are compared with experiment data. Johnson–Holmquist shock damage constitutive model for brittle materials is applied to describe the damage and shear strain achieved in a confined volume of granite. A tensile crack softening model is coupled with the JH model to simulate the propagation of radial tensile cracks generated by the principal tensile stress perpendicular to the shock front. The tensile stress is assumed to be equal to the deviatoric stress at radii that experience less than the Hogoniot elastic limit stress. Instead of traditional grid-based methods, a smooth particle hydrodynamics is used to define damaged regions in brittle media. [Copyright &y& Elsevier]

Abstract: Water-filled aluminum tubes were subjected to impact by six steel spherical projectiles of different diameters at impact velocities of 40–200m/s. The effects of the diameter of the steel projectiles and of the material properties of the tubes on cracking and perforation were discussed. Water decreased the wall strength of the aluminum alloy tubes, and the impact velocity at which a steel projectile first passes through the tube wall decreased with increasing diameter of the steel projectile. Using the velocity at which the steel projectile perforates the tube wall, empirical equations of the energies required to perforate the tube wall were derived. Also, the energy balance in the steel projectile during a collision is discussed referring to the pressure history in the filled water and the velocities of the steel projectile before and after collision. [Copyright &y& Elsevier]

Abstract: Experiments were conducted on aluminum plates of 1mm thickness by using a gas gun and projectiles with blunt and hemispherical noses. Target plate was impacted with varying impact velocity. Impact and residual velocities of the projectile were measured. Ballistic limit velocity was found to be higher for hemispherical projectiles than that for blunt projectiles. Effect of nose shape on the deformation of the plate was also studied. Numerical simulations of the impact were conducted by using an explicit finite element code (ABAQUS). Johnson–Cook elasto-viscoplastic model available in the code was used to carryout the analysis. Material property tests were carried out with the help of smooth and notched tensile test specimens. Results obtained from finite element simulations were compared with those of experiments. Good correlation was found between the two. It was observed that the element size significantly affects the numerical results; therefore a sufficiently refined mesh was used. Adaptive meshing was found helpful especially in the case of impact by a hemispherical projectile. [Copyright &y& Elsevier]

Abstract: Greenhill''s Rule for estimating rifling twist in artillery and small arms is interesting both because of its simplicity and longevity. This article describes (a) Greenhill''s Simplified Rule for estimating the twist of rifling; (b) describes his original, more complete, but much less known Rule; (c) summarizes how he got the Rule; and (d) relates it to the modern stability factor. Some comments about twist, bullet stability, and black powder velocities are presented. [Copyright &y& Elsevier]

Abstract: A model to predict the ballistic ricochet of rod penetrators is presented. The model is based on the premise that the phenomenology of ricochet is one where the impacting rod feeds into a plastic hinge located at the rod/target interface, and is thus diverted from a penetrating trajectory. The model is offered in both a full and simple form. The full form of the model arises from the simultaneous solution of a series of six algebraic equations that constitute the momentum-flux/force and moment balances upon the plastic hinge, subject to various material and kinematic constraints. This full model is not solvable in closed form, but rather by way of algorithm. The simple form of the model, by contrast, dispenses with the moment balance and makes several simplifying kinematic assumptions that permit the ricochet criterion to be expressed as a closed-form inequality. Such a simplified form is along the lines of, and thus directly comparable to, several prior ricochet models in the literature. Compared against 24 ballistic tests, comprising two separate ricochet studies, the current model (in both forms) shows an improved ability to predict the ballistic ricochet of impacting rod projectiles. The simple form of the current ricochet model actually proved the best predictor of the ballistic data. [Copyright &y& Elsevier]

Abstract: A finite element analysis was conducted to study the influence of friction during ballistic impact of a rigid sphere onto a square fabric panel that was firmly clamped along its four edges. Projectile-fabric friction and yarn–yarn friction were investigated. Modeling indicates that friction dramatically affects the local fabric structure at the impact region by hindering the lateral mobility of principal yarns. Reduction of lateral yarn mobility allows the projectile to load and break more yarns so that fabric possessing a high level of friction absorbs more energy than fabric with no friction. The projectile-fabric friction delays yarn breakage by distributing the maximum stress along the periphery of the projectile-fabric contact zone. The delay of yarn breakage substantially increases the fabric energy absorption during the later stages of the impact. The yarn–yarn friction hinders the relative motion between yarns and thus resists de-crimping of fabric weave tightness. It induces the fabric to fail earlier during the impact process. The overall influence of projectile-fabric friction and yarn–yarn friction cannot be calculated by simply adding their individual effects. [Copyright &y& Elsevier]

Abstract: In the world today there is an increasing use of small-calibre armour piercing projectiles and these constitute a growing threat. This threat is most eminent for wearers of body armour and to lightly armoured combat vehicles. As part of the solution to this problem, new generations of lightweight armour designs are under development. One promising possibility has been found to be the use of functionally gradient materials as armour materials. In such materials, the high hardness of ceramics is combined with the ductility of metals; in our study the system of Ti–TiB2 was used. As compaction and consolidation process the spark plasma sintering process was used. Though similar to conventional hot pressing, no external heat source is needed; instead a pulsed direct current is passed through the electrically conducting pressure die and through the sample. At low sintering temperatures with short holding times (minutes), fully dense materials can be obtained, benefiting in little grain growth. Mechanical and impact experiments of single ceramic metallic composites layers have been carried out. The ballistic tests were done on discs glued to steel backings, and tungsten core projectiles, calibre 7.62mm, were used. The ballistic results indicate a suitable composition, which does not have to be a pure ceramic, for the outer high hardness armour layer. To verify the suitability of the spark plasma sintered material, a comparison was made on the mechanical and ballistic properties between SPS-(Ti)0.05(TiB2)0.95 and HIP-TiB2, and it was found that the SPS-material was the overall better protective material. [Copyright &y& Elsevier]

Abstract: An experimental study has been carried out on the ballistic performance of 95% and 99.5% alumina ceramic tiles backed by metal plates, when subjected to normal impact of hard steel 12.7mm armour piercing (AP) projectiles at velocities ranging from 500 to 830ms−1. Typical damaged targets and broken projectiles are presented. The depth of penetration is measured in all the experiments, and the ballistic efficiency factor of the ceramic plates are determined. Results show that the efficiency factor increases with increase in projectile velocity. With the increase in thickness of the ceramic tile, the ballistic efficiency factor for a given velocity is observed to decrease in the case of 99.5% grade and increase in the case of 95% grade ceramic. The higher purity alumina (99.5%) shows higher ballistic performance when compared with the 95% alumina. The 99.5% alumina exhibited a predominantly transcrystalline fracture while the 95% alumina showed a less defined fracture surface. Experiments on 7.62mm AP shots were also done keeping the () ratio same as in 12.7mm AP experiments and results are presented. [Copyright &y& Elsevier]

Abstract: Metal foam projectiles are used to generate dynamic pressure–time histories representative of shock loading in water and air. A 1D plastic shock wave analysis is performed for a foam projectile impacting a free but rigid mass. It is shown that the pressure versus time pulse exerted on the mass and the shock arrest distance within the foam depend upon the ratio of foam mass to impacted mass, and upon the ratio of quasi-static to hydrodynamic strength of the foam. The theory is supported by two sets of experiments, one where Alporas foam impacts an instrumented Kolsky pressure bar, and one where the foam is fired at a free mass. It is demonstrated that the magnitude and duration of the pressure pulse can be controlled by suitable adjustment of the velocity, length and density of the foam projectile. [Copyright &y& Elsevier]