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• Thermal modification does not significantly change the ballistic performance of coastal western hemlock CLT. • Density and hardness do no fully encompass the energy absorbing capacity of CLT under small arms ballistic threats. • Empirically fit UFC partial penetration equation formulations fit treatment specific datasets with minimal error. • One global UFC partial penetration equation can be utilized for design with an appropriate safety factor. To test and understand the potential for integration of thermally modified coastal western hemlock CLT systems in military applications, 109 ballistic experiments were conducted at the United States Army Engineer Research Development Center's Fragmentation Simulation Facility. For a range of CLT thicknesses, the depth of penetration and residual velocities were recorded for different striking velocities utilizing a 0.50 caliber steel sphere projectile. This information was used to compare and add to the existing ballistics data for CLT, investigate the effects of thermal modification on high strain rate loading of wood, assess physics-based empirical design equations used by the Unified Facilities Criteria, and evaluate energy absorbing behavior at a range of thicknesses and striking velocities. The experimental results showed that thermal modification does not significantly alter the full and partial penetration performance of coastal western hemlock CLT. However, the mechanism of fracture along the path of the projectile differed, which indicates that the model parameters used in the UFC design equation (density, hardness, and projectile properties) may not fully encompass the ballistic failure mechanisms of CLT. [ABSTRACT FROM AUTHOR]

• Two field tests on concrete targets subjected to a projectile penetration followed by charge explosion were conducted. • The failure mode and stress waves in concrete were experimentally obtained. • Two-step numerical models based on the Kong-Fang concrete material model and SPG method were developed and validated. • The influences of projectile penetration on destructive effects caused by following charge explosion were clarified. The earth penetration weapons (EPWs) usually penetrate into protective structures firstly, and then detonate the charge to induce high-intensity blast stress waves to cause further damage. Existing investigations on the destructive effect caused by the following charge explosion after penetration of EPWs are very limited. To clarify the combined destructive effect in concrete material caused by an EPW, an experimental and numerical investigation on failure mode and stress wave propagation in concrete target subjected to a projectile penetration followed by charge explosion was conducted in the present study. Firstly, two field tests on high strength fiber-reinforced concrete targets subjected to a projectile penetration followed by charge explosion were conducted, in which the failure and blast waves in concrete targets were comprehensively obtained. Then two-step numerical models based on the Kong-Fang concrete material model and SPG method were developed and validated against the experimental data. Finally, based on the validated numerical models, the influences of projectile penetration on the destructive effect caused by following charge explosion were analyzed. The numerical results demonstrated that the damage caused by projectile penetration has significant influences on the final failure mode and stress wave propagation in concrete targets. The research results can provide an important reference for the design of protective structure against EPWs. [ABSTRACT FROM AUTHOR]

Highlights • Cavity dynamics in gelatin was studied. • A motion model of temporary cavity is established in gelatin penetrations of rifle bullets. • The motion model is well consistent with the penetration tests. • The radial movement of cavity is characterized by the behavior of bullet and the characteristic velocity. Abstract In wound ballistics, modeling the penetration-cavitation dynamics will set the basis for evaluating the damaging efficiency of projectiles. In our previous study, a motion model to characterize the behavior of rifle bullets has been established and verified in the gelatin penetration. In order to reveal the cavity production analytically, in combination with parameters obtained from the motion model of rifle bullet, cavity dynamics in gelatin was studied and a motion model of temporary cavity in gelatin penetrations of rifle bullets was proposed and verified by comparison with experimental results in terms of maximum cavity wall radius, radial movement along the penetration trajectory and temporary cavity profiles. It can be concluded that calculated results of the cavity motion model agree well with experiment data for penetration of 7.62 mm and 5.56 mm rifle bullets. And the radial movement of cavity can be characterized by the behavior of bullet and the characteristic velocity. It is significant for the trauma assessment to develop an appropriate cavitation model in gelatin for penetrations of rifle bullet. [ABSTRACT FROM AUTHOR]

We report an increase in penetration resistance of front-facing fluorinated polymer coatings applied to hardened steel substrates. The study included monolithic and laminate configurations and examined their ability to improve the ballistic penetration resistance of selected substrates. Polytetrafluoroethylene (PTFE) coatings substantially improved the V-50 performance and outperformed similar polymer-coated armor composites for thicker coating layers. The thickness and hardness of steel substrates, polymer layer thickness, and cumulative number of laminates collectively influenced the mass efficiency. Since PTFE is a crystalline material that, unlike previously tested polyurea and other elastomers, does not undergo an impact-induced phase transition, its high performance suggests that this material resists flow during impact and, subsequently, reduces the strain imparted to the substrate. The fluoropolymer offers a lightweight and simple solution to enhance ballistic armor systems. [ABSTRACT FROM AUTHOR]

This research deals with the experimental and numerical investigation of ballistic protection provided by a combination of perforated and base armour plates. A 7.62 mm armour piercing projectile was used during the experimentation to determine the ballistic response of an aluminum base armour plate and a combination of steel perforated and aluminum base armour plate. The armour piercing projectiles were able to penetrate the base armour plate while the combination of perforated and base armour plates was able to stop the penetration of the armour piercing projectile. A finite element method based numerical model was developed to investigate the defeating phenomenon of perforated and base armour plate combination. The brittle fracture caused by the bending of the projectile core due to the asymmetric impact was predicted and the resulting fragments of the projectile were unable to penetrate the base armour plate. Craters were formed on the surface of the base armour plate from the impact of the projectile fragments. The numerical model was able to predict the hole growth and penetration of projectile when only the base armour plate was impacted by the projectile. [ABSTRACT FROM AUTHOR]

The penetration of rigid projectiles in polycarbonate (PC) targets is explored through deep indentation tests with conical-nosed indenters and ballistic penetration results for armor piercing 7.62 mm projectiles. We found that the resistance to penetration in both sets of experiments is practically the same, which means that the rate sensitivity of PC does not play a significant role in its resistance to penetration. We account for this observation by including the pressure dependence of the elastic constants and the strength of PC in its constitutive equation, which we implemented in numerical simulations. This pressure-dependent constitutive relation resulted in good agreements between simulation results and experimental data for both penetration depths and residual velocities of armor piercing projectiles impacting PC targets. [ABSTRACT FROM AUTHOR]

Modeling clay is a soft malleable material made from oils and waxes. This material is fundamental for ballistic evaluation of body armors because it is used as backing material in ballistic tests. After a ballistic impact, a back-face indentation is measured to assess performance of the armor. Due to the important role of modeling clay in this particular application, its mechanical characterization and comprehension of penetration mechanics are essential for development of new personal protection systems. This paper presents a two-step computational methodology to calibrate parameters of a Cowper–Symonds material model for modeling clay at characteristic strain rates up to 1.8 × 10 4   s − 1 . In the first stage, a high-speed camera is used to record the penetration of a gas-gun launched cylindrical mass with a hemispherical cap into a block of clay. Image-processing software is used to capture the tail of the projectile as it penetrates into the clay. These data are then used to sample the penetration depth as function of time. In the second stage, an in-house developed model of penetration, based on both the spherical cavity expansion theory and the Tate penetration equation, is used to determine, by inverse analysis, the parameters of the Cowper–Symonds clay model. The proposed constitutive relationship for clay and the determined material parameters can be applied accurately to problems involving high strain rates. [ABSTRACT FROM AUTHOR]

The mechanisms of progressive penetration for two ultrahigh molecular weight polyethylene (UHMWPE) reinforced laminates have been investigated. One used an UHMWPE fiber reinforcement while the other utilized molecularly aligned tape. Both materials had similar out of plane compressive strengths, but the fiber system had a 40% higher in plane tensile strength than the tape. Laminated, 6 mm thick plates with a [0°/90°] ply architecture were impacted by a 12.7 mm diameter sphere under conditions that either allowed out of plane plate deflection or eliminated this deflection by rear support of the target. The depth of penetration and the ballistic limit in the rear-supported tests were identical for the two materials, and proceeded by progressive ply failure. However, tests in the edge clamped condition resulted in a substantially higher penetration resistance, especially for the higher tensile strength fiber-reinforced material. Edge clamped testing of a bilayer target, where the front third was composed of the tape material and the remainder comprised fiber reinforced laminate, had the same ballistic limit as a target composed of only the higher ply tensile strength fiber reinforced material. Penetration in both test support conditions was discovered to occur by tensile ply rupture under the projectile, consistent with a recently proposed mechanism for converting out of plane compression to in plane ply tension. Lateral displacement of plies was also observed near the sides of impact craters in both materials, indicating the existence of a second mechanism impeding penetration of the spherical shaped projectile. [ABSTRACT FROM AUTHOR]

• High hardness steel (HHS) sheet with UHMWPE composite backing were tested against a hardened steel core projectile. • The projectile core was eroded by the HHS sheet and stopped in UHMWPE composite. • It is observed that only a core eroded to a certain length and weight by armor system can be defeated. • In numerical modeling core failure strain was determined from the residual weight of cores. • The numerical model can be used to evolve armor design. Thin high hardness steel sheets can be an alternative to expensive ceramic armor systems designed to defeat hardened core projectiles. A thin high hardness steel sheet backed with UHMWPE fiber-reinforced composite was ballistically tested against a 7.62 × 39 mm hardened steel core projectile in a single-stage gas gun. Thin steel sheets of 530 BHN hardness were adhesively bonded with UHMWPE fiber-reinforced composite to fabricate armor plates. Armor plates were able to defeat the projectile showing considerable potential. Tensile strength of steel sheet and UHMWPE-fiber reinforced ply was also determined. A detailed numerical simulation of the impact event was also performed to understand the phenomenon of defeat and penetration in greater detail. The numerical model was calibrated from the recovered projectile's core after the ballistic test. [ABSTRACT FROM AUTHOR]

Ballistic performance of an armour steel at different tempering conditions against a tungsten heavy alloy long rod kinetic energy projectile has been investigated. The ballistic performance was found to increase with decreasing tempering temperature but the performance increments were not proportional to the strength increase caused by the tempering. Both target and projectile underwent fragmentation at the penetration interface in all the three targets. Apart from the strength target material deformation behaviour also showed considerable influence on ballistic performance. The ballistic performance appears to increase with decreasing toughness for a given strength. [ABSTRACT FROM AUTHOR]

The database for depth of penetration by projectiles into semi-infinite targets is quite extensive. The objective is to use the experimental semi-infinite penetration data to predict finite-thickness target effects. Similitude considerations are used to represent penetration response as a function of a normalized impact velocity, which is the ratio of the penetration pressure to the target strength. Then, a least-squares regression analysis methodology was applied to the normalized experimental data to provide an analytic expression for the normalized depth of penetration as a function of the normalized impact velocity over a very large velocity range, typically a few hundred meters per second to over 3500 m/s. We use the analytic expression, along with some simplifying assumptions, to estimate ballistic limit thickness T 50 and/or the ballistic limit velocity V 50 . If a target is overmatched, i.e., perforated by the projectile, an estimate is also made for the projectile residual velocity and residual length. The experimental data on which the regression fit is based consists of L / D 10 projectiles, so a procedure is also developed to account for different projectile aspect ratios. A series of examples are provided to demonstrate the utility and accuracy of the approach. [ABSTRACT FROM AUTHOR]

Polymer composites comprising ultra-high molecular weight polyethylene (UHWMPE) fibers in a compliant matrix are now widely used in ballistic applications with varying levels of success. This is primarily due to a poor understanding of the mechanics of penetration of these composites in ballistic protection systems. In this study, we report experimental observations of the penetration mechanisms in four model systems impacted by a 12.7 mm diameter spherical steel projectile. The four model targets designed to highlight different penetration mechanisms in Dyneema ® UHWMPE composites were: (i) a bare aluminum plate; (ii) the same plate fully encased in a 5.9 mm thick casing of Dyneema ® ; (iii) the fully encased plate with a portion of the Dyneema ® removed from the front face so that the projectile impacts directly the Al plate; and (iv) the fully encased plate with a portion of the Dyneema ® removed from the rear face so that the projectile can exit the Al plate without again interacting with the Dyneema ® . A combination of synchronized high speed photography with three cameras, together with post-test examination of the targets via X-ray tomography and optical microscopy was used to elucidate the deformation and perforation mechanisms. The measurements show that the ballistic resistance of these targets increases in the order: bare Al plate, rear face cutout target, fully encased target and front face cutout target. These findings are explained based on the following key findings: (a) the ballistic performance of Dyneema ® plates supported on a foundation is inferior to Dyneema ® plates supported along their edges; (b) the apparent ballistic resistance of Dyneema ® plates increases if the plates are given an initial velocity prior to the impact by the projectile, thereby reducing the relative velocity between the Dyneema ® plate and projectile; and (c) when the projectile is fragmented prior to impact, the spatially and temporally distributed loading enhances the ballistic resistance of the Dyneema ® . The simple model targets designed here have elucidated mechanisms by which Dyneema ® functions in multi-material structures. [ABSTRACT FROM AUTHOR]

Abstract: We have used forward ballistic, reverse ballistic and computational analysis techniques to interrogate the effect of the gilding jacket from a 7.62 mm × 51 mm FFV armour-piercing bullet during the penetration of ceramic-faced targets. When the gilding jacket is removed, it is shown that greater damage occurs to the core suggesting that the presence of the jacket is pre-damaging the ceramic before core arrival. This is confirmed through computational analysis. This work highlights possibilities in enhancing protection by pre-stripping the bullet''s jacket prior to ceramic impact. [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: 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: 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: 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: 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: 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 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]

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: 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: 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 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: 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: 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]

The perforation response of a thin or intermediately thick beam/plate struck by a rigid, heavy, flat-nosed projectile traveling at a high velocity is studied analytically. Based on a newly developed expression relating indentation depth to crack length, a shear-plugging model including two stages: indentation and crack growth, is proposed. In this model, shear resistance in the ligament decreases as the cracks propagate through the target thickness. The closed-form solutions for residual velocities, plastic energy, shear zone width, crack propagation speeds, and temperature rise are derived. A coupled shear–tension solution that takes into account global deformation of the plate is also developed. The coupled solution improves prediction for the case with the initial impact velocity near the ballistic limit. Comparisons with experimental results presented in the open literature are made showing rather good correlation, which validates the accuracy of the present solution. [Copyright &y& Elsevier]

The effect of target strength on the perforation of steel plates is studied. Three structural steels are considered: Weldox 460 E, Weldox 700 E and Weldox 900 E. The effects of strain hardening, strain rate hardening, temperature softening and stress triaxiality on material strength and ductility are determined for these steel alloys by conducting three types of tensile tests: quasi-static tests with smooth and notched specimens, quasi-static tests at elevated temperatures and dynamic tests over a wide range of strain rates. The test data are used to determine material constants for the three different steels in a slightly modified version of the Johnson–Cook constitutive equation and fracture criterion.Using these three steel alloys, perforation tests are carried out on 12 mm-thick plates with blunt-, conical- and ogival-nosed projectiles. A compressed gas gun was used to launch projectiles within the velocity range from 150 to 350 m/s. The initial and residual velocities of the projectile were measured, while the perforation process was captured using a digital high-speed camera system. Based on the test data the ballistic limit velocity was obtained for the three steels for the different nose shapes. The experimental results indicate that for perforation with blunt projectiles the ballistic limit velocity decreases for increasing strength, while the opposite trend is found in tests with conical and ogival projectiles. The tests on Weldox 700 E and Weldox 900 E targets with conical-nosed projectiles resulted in shattering of the projectile nose tip during penetration.Finally, numerical simulations of some of the experimental tests are carried out using the non-linear finite element code LS-DYNA. It is found that the numerical code is able to describe the physical mechanisms in the perforation events with good accuracy. However, the experimental trend of a decrease in ballistic limit with an increase in target strength for blunt projectiles is not obtained with the numerical models used in this study. [Copyright &y& Elsevier]

The terminal ballistics of long-rod penetrators is a very complex field of research involving high pressure physics, continuum mechanics, material science and high strain rate phenomena. The research in this field is advanced through experimental data collection, engineering models, and numerical simulations. In the present paper, we summarize some of our recent work which is focused on determining the important material parameters in the interaction of long rods with various targets (both stationary and moving). Our basic goal is to be able to account for various phenomena encountered in the experiments, rather than reproduce the data very accurately. We achieve this goal by using the minimal set of material parameters which is needed in order to highlight the basic features in the interaction. We also show how 3D numerical simulations help to establish a simple model for the complex interaction between a tungsten alloy rod and a moving steel plate. [Copyright &y& Elsevier]

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. [Copyright &y& Elsevier]