Normal and oblique impact of small arms bullets on AA6082-T4 aluminium protective plates

Normal and oblique impact on 20 mm thick AA6082-T4 aluminium plates are studied both experimentally and numerically. Two types of small arms bullets were used in the ballistic tests, namely the 7.62 × 63 mm NATO Ball (with a soft lead core) and the 7.62 × 63 mm APM2 (with a hard steel core), fired from a long smooth-bore Mauser rifle. The targets were struck at 0°, 15°, 30°, 45° and 60° obliquity, and the impact velocity was about 830 m/s in all tests. During testing, the initial and residual bullet velocities were measured by various laser-based optical devices, and high-speed video cameras were used to photograph the penetration process. Of special interest is the critical oblique angle at which the penetration process changes from perforation to embedment or ricochet. The results show that the critical oblique angle was less than 60° for both bullet types. A material test programme was also conducted for the AA6082-T4 plate to calibrate a modified Johnson-Cook constitutive relation and the Cockcroft-Latham failure criterion, while material data for the bullets mainly were taken from the literature. 3D non-linear FE simulations with detailed models of the bullets were finally run. Good agreement between the FE simulations and the experimental results for the APM2 bullets was in general obtained, while it was more difficult to get reliable FE results for the soft core Ball bullets.     

An engineering fragmentation model for the impact of spherical projectiles on thin metallic plates

In this paper, an engineering fragmentation model is presented for the case of hypervelocity impact of a spherical projectile on a thin bumper plate at normal incidence. The range of impact velocities covered is the solid fragmentation regime up to the limits of complete melting of projectile and target material. The model was developed for an axisymmetric fragment cloud by consideration of the conservation laws for mass, momentum, and energy, as well as making a few assumptions on the morphology of the cloud. The fragment cloud is modeled discretely, i.e. each particle of the fragment cloud is considered separately in the analytical calculation. The model consists of mainly analytical relationships and a few empirical fit functions, where no analytical formulation was available. The model distinguishes between fragments originating from the projectile and fragments originating from the bumper plate. The projectile fragments are split into the central fragment and spall fragments. An exponential distribution function is assumed for the mass distribution of the projectile's spall fragments. The fragments from the bumper are assumed to have a uniform mass. All fragments are assumed to be of spherical shape. The fragmentation model was applied and calibrated during experiments, in which Al spheres impact on thin Al plates. The calibration experiments, performed using a two-stage light gas gun, were in the range of impact velocities between 4.8 and 6.7 km/s. In this velocity range, the model was calibrated against residual velocities measured and fragment mass distribution, which was indirectly determined by measuring the crater depth distributions in rear walls.     

Experimental study of dynamic crushing of thin plates stiffened by stamping with V-grooves

Experimental study was made for the dynamic crushing of thin plates stiffened by stamping with 1–3 parallel V-grooves in a clamped-end condition. The length of the blanks was set at the same value of 300 mm, while the width was of 70, 140 and 210 mm at a thickness of 1 mm, otherwise specified. The depth of V-grooves was set at values of 4, 7 and 10 mm. In both static and dynamic tests, the results show that the ability of the plates to resist crushing and to absorb deformation energy was substantially enhanced by stamping with V-grooves. Stamped with 1 or 2 grooves of smaller values in depth, the plates 210 mm wide had larger resistance to dynamic crushing than those of greater values in depth did. In general, increases in number and depth of grooves caused an increase in the plates’ capacity of energy absorption. However, the ability of the plates to resist crushing and to absorb deformation energy cannot be determined only in accordance with the second moment of area of cross section, because the plates sufficiently wide stamped with any number of grooves deformed plastically before buckled in dynamic tests and, the interaction between deep grooves during deformation also enhanced the capacity of energy absorption.     

Damage evaluation of concrete plates by high-velocity impact

This paper describes the evaluation of the local damage of concrete plates by the impact of high-velocity rigid projectiles. A new launching system of mushroom-shaped projectiles has been developed. Impact tests for concrete plates have been conducted by using the system to examine failure modes of the local damage of concrete plates. The damage or failure behavior has been discussed on the basis of the failure process captured by a high speed video camera and the strain histories obtained by strain gauges on the concrete plate. Numerical simulations have been also carried out in order to explain the mechanism of the local damage observed by the experiment. A reasonable numerical model has been discussed in terms of a constitutive model and strain rate effect of concrete material. Mechanism of the local damage of concrete plates has been illustrated schematically.     

Response of high performance concrete plates to impact of non-deforming projectiles

The relatively recent technology, which enables the production of high strength concrete (HSC), makes HSC a prospective material for the construction of impact-resisting barriers. However, current penetration formulae are based on test data of normal strength concrete (NSC) and their extrapolation to higher concrete strengths is unsafe. The response of 80×80 cm high performance concrete (HPC) plate specimens to an impact of non-deforming steel projectiles was examined in an experimental study. The tests were planned with an aim to observe the influence of the concrete mix ingredients and amount and type of reinforcement on the performance of HSC under this type of loading. The variants that were examined were the aggregates (different types and maximum size), addition of micro-silica (MS) and steel fibers, and reinforcement details. The main findings show that design of HPC barriers to withstand impact loads involves several aspects. These are aimed at achieving enhanced properties of the structural element, where only one of which is the concrete's compressive strength.     

A new finite element for buckling analysis of laminated stiffened plates

A new stiffened plate element for stability analysis of laminated stiffened plates has been presented. The basic plate element is a combination of Allman's plane stress triangular element and a Discrete Kirchhoff–Mindlin plate bending element. The element includes transverse shear effects. The model accommodates any number of arbitrarily oriented stiffeners within the plate element and eliminates constraints on the mesh division of the plate. The element has no problem associated with shear locking – a phenomenon usually encountered in isoparametric elements. The stability analysis of laminated stiffened plates has been carried out under different loading conditions with the present element.     

Comparative analysis of perforation models of metallic plates by rigid sharp-nosed projectiles

Based on the mode of ductile hole enlargement, the present paper compares the models of a rigid sharp-nosed projectile perforating the ductile metallic target plate, given by Chen and Li [1] and Forrestal and Warren [2], respectively. It indicates that the formulae of ballistic limit and residual velocity of these two perforation models are consistent in form but with different applicable range, which due to them employing the spherical cavity expansion theory and cylindrical cavity expansion theory, alternately. Further analyses are conducted to discuss the effects of target material and plate thickness on the terminal ballistic performance with referring the experimental results of aluminum alloy and Weldox E steel plates. It is confirmed that the perforation mechanisms may transform with increasing the plate thickness and the strength of target material.     

Ballistic penetration of steel plates

This paper presents a research programme in progress where the main objective is to study the behaviour of Weldox 460 E steel plates impacted by blunt-nosed cylindrical projectiles in the lower ordnance velocity regime. A compressed gas gun is used to carry out high-precision tests, and a digital high-speed camera system is used to photograph the penetration process. A coupled constitutive model of viscoplasticity and ductile damage is formulated and implemented into the non-linear finite element code LS-DYNA, and the material constants for the target plate are determined. The proposed model is applied in simulations of the plate penetration problem and the results are compared with test data. Good agreement between the numerical simulations and the experimental results is found for velocities well above the ballistic limit, while the ballistic limit itself is overestimated by approximately 10% in the numerical simulations.     

Experimental and numerical study on the perforation process of mild steel sheets subjected to perpendicular impact by hemispherical projectiles

In this paper a study is presented on the experimental and numerical analysis of the failure process of mild steel sheets subjected to normal impact by hemispherical projectiles. The experiments have been performed using a direct impact technique based on Hopkinson tube as a force measurement device. The tests covered a wide range of impact velocities. Both lubricated and dry conditions between specimen and projectile have been applied. Different failure modes for each case were found. For lubricated conditions a petalling was observed, whereas for dry conditions a radial neck along with a hole enlargement reduces the formation of petalling. The perforation process has been simulated by the application of 3D analysis using ABAQUS/Explicit FE code. The material behavior of the circular specimen was approximated by three different constitutive relations. The main task was to study the influence of the material definition on the response of the sheet specimen with special attention to the failure mode.     

Perforation resistance of five different high-strength steel plates subjected to small-arms projectiles

Thin plates of high-strength steel are frequently being used both in civil and military ballistic protection systems. The choice of alloy is then a function of application, ballistic performance, weight and price. In this study the perforation resistance of five different high-strength steels has been determined and compared against each other. The considered alloys are Weldox 500E, Weldox 700E, Hardox 400, Domex Protect 500 and Armox 560T. The yield stress for Armox 560T is about three times the yield stress for Weldox 500E, while the opposite yields for the ductility. To certify the perforation resistance of the various targets, two different ballistic protection classes according to the European norm EN1063 have been considered. These are BR6 (7.62 mm Ball ammunition) and BR7 (7.62 mm AP ammunition), where the impact velocity of the bullet is about 830 m/s in both. Perforation tests have been carried out using adjusted ammunition to determine the ballistic limit of the various steels. In the tests, a target thickness of 6 mm and 6 + 6 = 12 mm was used for protection class BR6 and BR7, respectively. A material test programme was conducted for all steels to calibrate a modified Johnson–Cook constitutive relation and the Cockcroft–Latham fracture criterion, while material data for the bullets mainly were taken from the literature. Finally, results from 2D non-linear FE simulations with detailed models of the bullets are presented and the different findings are compared against each other. As will be shown, good agreement between the FE simulations and experimental data for the AP bullets is in general obtained, while it was difficult to get reliable FE results using the Lagrangian formulation of LS-DYNA for the soft core Ball bullet.     

弹丸超高速撞击半无限厚铝板数值模拟

微流星体及空间碎片的超高速撞击威胁着长寿命、大尺寸航天器的安全运行,导致其严重的损伤和灾难性的失效.撞击损伤特性研究是航天器防护设计的一个重要问题.本文采用AUTODYN软件的Lagrange法对半无限铝板的超高速斜撞击和与其具有相同法向速度的正撞击进行了模拟,给出了不同撞击角和不同法向速度下半无限厚铝板弹坑深度、宽度、长度的变化规律及多弹坑的形成过程,并与经验方程进行了比较分析.结果发现:随撞击角的增加,弹坑的深度和宽度减小,而弹坑的长度增加;随撞击速度的增加弹坑的直径和深度增加;在撞击角大于70度时出现多弹坑.     

Structural response of all-composite pyramidal truss core sandwich columns in end compression

With the equivalent mechanical properties of composite materials, analytical formulae of critical load for an all-composite sandwich column with pyramidal truss core are derived. Four failure modes are considered: macro Euler buckling, macro shear buckling, face-sheet wrinkling and face-sheet crushing. Failure mechanism maps are constructed with the four competing failure modes, and the relationship between the failure mechanism maps and material mechanical properties is discussed. Selected experiments validate the analytical predictions, and reasonable agreement is obtained. Macro shear buckling is the main failure mode for the sandwich column specimens, which is attributed to the low stiffness of core. The final failure loads is related to the strength of the nodes between face-sheets and truss core, so the node strength is the key of improving the failure load. Given by numerical simulations, the failure loads and failure modes agree well with analytical predictions.     

Quasi-brittle fracture during structural impact of AA7075-T651 aluminium plates

The stress–strain behaviour of the aluminium alloy 7075 in T651 temper is characterized by tension and compression tests. The material was delivered as rolled plates of thickness 20 mm. Quasi-static tension tests are carried out in three in-plane directions to characterize the plastic anisotropy of the material, while the quasi-static compression tests are done in the through-thickness direction. Dynamic tensile tests are performed in a split Hopkinson tension bar to evaluate the strain-rate sensitivity of the material. Notched tensile tests are conducted to study the influence of stress triaxiality on the ductility of the material. Based on the material tests, a thermoelastic–thermoviscoplastic constitutive model and a ductile fracture criterion are determined for AA7075-T651. Plate impact tests using 20 mm diameter, 197 g mass hardened steel projectiles with blunt and ogival nose shapes are carried out in a compressed gas-gun to reveal the alloy's resistance to ballistic impact, and both the ballistic limit velocities and the initial versus residual velocity curves are obtained. It is found that the alloy is rather brittle during impact, and severe fragmentation and delamination of the target in the impact zone are detected. All impact tests are analysed using the explicit solver of the non-linear finite element code LS-DYNA. Simulations are run with both axisymmetric and solid elements. The failure modes are seen to be reasonably well captured in the simulations, while some deviations occur between the numerical and experimental ballistic limit velocities. The latter is ascribed to the observed fragmentation and delamination of the target which are difficult to model accurately in the finite element simulations.     

Hypervelocity penetration of gold rods into SiC-N for impact velocities from 2.0 to 6.2 km/s

This paper presents the experimental design and results of an advanced set of reverse ballistic experiments with long gold rods, impacting SiC-N ceramics at impact velocities from 2.0 to 6.2 km/s. Important issues for these experiments were the high accuracy and position requirements necessary to detect a possible failure wave or failure kinetics in SiC-ceramics as might be evidenced by a change in the slope of the penetration velocity–impact velocity curve. New and sophisticated evaluation methods were developed for this purpose and produced very reliable results. Analyses of the experimental results show clearly that there is no change in the slope of the penetration velocity–impact velocity curve, contrary to that inferred from previous data and analysis.     

High-velocity impact of low-density projectiles on structural aluminum armor

The US Army Research Laboratory has been studying the impact physics of low-density projectiles on urban and light-armor structures for use in electro-magnetic cannons. In this paper, results of low-aspect ratio projectiles of nylon, aluminum and steel impacting aluminum armor at velocities above 2000 m/s will be presented. Both computational solid mechanics and analytic modeling techniques were used to supplement experiments to derive a toolkit for assessing target response and character of the debris created from different constant energy impact conditions.     

On the influence of constitutive relation in projectile impact of steel plates

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.     

Influence of conical projectile diameter on perpendicular impact of thin steel plate

A numerical study of conical projectiles for perpendicular impact on a thin steel plate is reported. The target material considered, Weldox 460 E steel, is frequently used for this kind of application and several results of experiments are available in the international literature to verify numerical simulations. The Johnson-Cook constitutive relation coupled with the Johnson-Cook failure criterion have been applied to analyse penetration of the target and also the failure process. The analysis has been focussed on the influence of the projectile diameter on the perforation process, assuming the same projectile mass. The aim was to preserve the same initial kinetic energy and identical nose angle. The goal is to estimate the ballistic limit, the residual velocity, the plastic work, and the temperature levels produced during the penetration process. The analysis has shown a linear increase of the ballistic limit with the projectile diameter.     

Contact force history analysis of composite sandwich plates subjected to low-velocity impact

Usually the modified Hertzian contact law or experimental static indentation law has been used to analyze low-velocity impact response of composite laminates. In composite laminated plates subjected to low-velocity impact, usually indentation by impact is very small and also energy absorption by indentation is negligible, so ‘spring element method’, which proposed by author recently, can be well applied to investigate impact response. In the present study ‘lumped mass method’ also had been proposed by author to approximately calculate contact force history of composite laminates will be conceptually described as well as the spring element method. And it will be discussed that how the spring element method can be applied to composite sandwich plates. Finally numerical results easily obtained from finite element analysis based on the spring element method using general-purpose commercial FEM software is compared with experimental results. The comparison shows overall agreement.     

On the plant-specific impact of different pressurization rates in the estimation of containment failure mode probabilities

The explicit consideration of different pressurization rates (e.g. fast and slow) in estimating the probabilities of containment failure modes (e.g. leak, rupture, and/or catastrophic rupture) might have a profound effect on the confidence of the containment performance evaluation that is so critical for risk assessment of nuclear power plants. We have performed a bounding analysis for the impact of different pressurization rates on the leak and rupture mode probabilities using models for fast and slow pressurizations. The present models are based on the evaluations of probability distributions that are characterized with the median pressures and their standard deviations, for individual mechanisms of structural failure modes and the nominal break sizes. As a result, we have obtained a quantitative and plant-specific estimate of the impact of the pressurization rates on the leak and rupture containment failure probabilities. The present study showed that the impact was not significant for the specific cases considered in this study and confirmed that the treatment used in the specific cases was conservative.     

Experimental study on expansion characteristics of debris clouds produced by oblique hypervelocity impact of LY12 aluminum projectiles with thin LY12 aluminum plates

Tests of hypervelocity projectile impacts to a double-wall structure made of LY12 aluminum were performed using a two-stage light gas gun. In the bumper plate hole analysis, empirical equations that relate hole dimensions to impact parameters such as velocity, angle of obliquity and bumper plate thickness are obtained. The laser shadowgraphs in order to get the expansion of debris clouds were taken and the characteristic parameters obtained. The damage effects of the back wall varying with impact parameters were studied. The expansion of debris clouds was determined.