Ballistic Limit of Single and Layered Aluminium Plates

Abstract: This paper presents an experimental and finite‐element investigation of ballistic limit of thin single and layered aluminium target plates. Blunt‐, ogive‐ and hemispherical‐nosed steel projectiles of 19 mm diameter were impacted on single and layered aluminium target plates of thicknesses 0.5, 0.71, 1.0, 1.5, 2.0, 2.5 and 3 mm with the help of a pressure gun to obtain the ballistic limit in each case. The ballistic limit of target plate was found to be considerably affected by the projectile nose shape. Thin monolithic target plates as well as layered in‐contact plates offered lowest ballistic resistance against the impact of ogive‐nosed projectiles. Thicker monolithic plates on the other hand, offered lowest resistance against the impact of blunt‐nosed projectiles. The ballistic resistance of the layered targets decreased with increase in the number of layers for constant overall target thickness. Axi‐symmetric numerical simulations were performed with ABAQUS/Explicit to compare the numerical predictions with experiments. 3D numerical simulations were also performed for single plate of 1.0 mm thickness and two layered plate of 0.5 mm thickness impacted by blunt‐, ogive‐ and hemispherical‐nosed projectiles. Good agreement was found between the numerical simulations and experiments. 3D numerical simulations accurately predicted the failure mode of target plates.     

The effect of target strength on the perforation of steel plates using three different projectile nose shapes

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.     

Effect of projectile nose shape,impact velocity and target thickness on the deformation behavior of layered plates

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.     

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.     

Experimental study of perforation of multi-layered targets by hemispherical-nosed projectiles

In this paper, perforation of single and three layered metallic targets by hemispherical-nosed cylindrical projectiles are studied experimentally. The circular targets of Al 1100 have a diameter of 220 mm and the hemispherical-nosed projectiles are silver steel cylinders with a mass of 12.15 g which are hardened to 56RC. The single layer target is 3 mm thick and the thicknesses of layers of the three layered targets are 0.5, 1 and 1.5 mm. The multi-layered targets are tested both when the layers are in-contact and spaced (with air gaps). Tests are carried out using a one stage gas gun. The ballistic limit velocity is obtained and the effects of order of layers and the width of air gaps between them on the ballistic limit velocity are investigated. The results show that the single layer targets have greater ballistic limit velocities than multi-layered targets. Furthermore, the ballistic limit velocity of in-contact layered targets is greater than that of spaced layered targets.     

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.     

Penetration of 6061-T6511 aluminum targets by ogive-nosed VAR 4340 steel projectiles at oblique angles: experiments and simulations

In this paper we present the results from a combined experimental, analytical, and computational penetration program. First, we conducted a series of depth-of-penetration experiments using 0.021 kg, 7.11 mm diameter, 71.12 mm long, vacuum-arc-remelted 4340 ogive-nose steel projectiles. These projectiles were launched with striking velocities between 0.5 and 1.3 km/s using a 20 mm powder gun into 254 mm diameter, 6061-T6511 aluminum targets with angles of obliquity of 15°, 30°, and 45°. Next, we employed the initial conditions obtained from the experiments with a new technique that we have developed to calculate permanent projectile deformation without erosion. With this technique we use an explicit, transient dynamic, finite element code to model the projectile and an analytical forcing function derived from the dynamic expansion of a spherical cavity (which accounts for compressibility, strain hardening, strain-rate sensitivity, and a finite boundary) to represent the target. Results from the simulations show the final projectile positions are in good agreement with the positions obtained from post-test radiographs.     

Highy oblique impacts into thick and thin targets

Hypervelocity impact (HVI) tests have been conducted at the JSC Hypervelocity Impact Test Facility (HIT-F) with aluminum projectiles impacting semi-infinite (thick) and thin aluminum plates (with plate thickness to projectile diameter ratios of 6.4 and 0.14, respectively) at impact angles ranging from normal to the plate (0°) to highly oblique (88°). The targets were impacted by solid homogeneous aluminum spheres from 1 mm to 3.6 mm diameter. Results of the HVI tests were not unusual up to 65°, where impact damage is characterized as smooth craters and holes that become progressively elliptical and distended along the projectile flight path. Above 65° angles, however, a transition occurs to an irregularly shaped hole in thin materials and rough bottomed crater in thick targets. Above 80°, multiple damage sites in the targets were formed with the damage areas separated by variable distances of undamaged target surface. Analytical and numerical simulations of the impact process at oblique angles above 65° demonstrates that shock compression and release of the projectile into multiple fragments occurs before the projectile fully engages the target. The resulting projectile fragments are then responsible for the multiple impact sites observed on the targets.     

刚性尖头弹扩孔贯穿金属靶板理论模型的讨论

针对延性扩孔破坏模式,讨论了刚性尖头弹贯穿韧性金属靶板的已有六个理论模型（F-W、C-L、JZG、WHM、S-W和JBL）对于靶板厚度和弹头形状的适用范围,统一了各模型参数的选取准则,分别给出了JZG模型尖锥头形和尖卵头形弹体半锥角和无量纲曲率半径（CRH）的适用范围。基于12组冲击速度为200~1600m/s,厚径比（靶体厚度与弹身直径之比H/d）为0.605~9.17的多种弹靶材料的穿甲实验,得出：对于尖锥头形弹体贯穿靶板后的残余速度,S-W和WHM、JZG、F-W模型分别对于较薄靶板、中等厚度靶板和较厚靶板的预测效果较好;而对于尖卵头形弹体,WHM和JBL模型预测效果较好。同时,各模型对于弹道极限预测效果的结论和残余速度一致。分析结论可为坦克、舰船等单、多层金属装甲防护结构设计与计算提供参考和依据。     

Perforation of AA5083-H116 aluminium plates with conical-nose steel projectiles – Calculations

The use of aluminium alloys in lightweight protective structures is increasing. Even so, the number of experimental and computational investigations that give detailed information on such problems is limited. In an earlier paper by some of the authors, perforation experiments were performed with 15–30 mm thick AA5083-H116 aluminium plates and 20 mm diameter, 98 mm long, HRC 53 conical-nose hardened steel projectiles. In all tests, initial and residual velocities of the projectile were measured and the ballistic limit velocity of each target plate was determined. In the present paper, an analytical perforation model based on the cylindrical cavity-expansion theory has been reformulated and used to calculate the ballistic perforation resistance of the aluminium plates. In addition, non-linear finite element simulations have been carried out. The target material was modeled with the Johnson–Cook constitutive relation using 2D axisymmetric elements with adaptive rezoning. To allow ductile hole growth, a pin-hole was introduced in the target. The analytical and numerical results have been compared to the experimental findings, and good agreement was in general obtained. A parametric study was also carried out to identify the importance of the different terms of the Johnson–Cook constitutive relation on the perforation resistance of the target. The results indicate that thermal softening cannot be neglected, so an alternative procedure for identification of the material constants in the power-law constitutive relation used in the cavity-expansion theory has been proposed.     

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.     

Strength and ductility of Weldox 460 E steel at high strain rates, elevated temperatures and various stress triaxialities

Strength and ductility data at high strain rates for Weldox 460 E steel was obtained from tensile tests with axisymmetric specimens. The tests were performed in a Split Hopkinson Tension Bar and the initial temperature was varied between 100 and 500 °C. The combined effect of high strain rate, elevated temperature and stress triaxiality on the behaviour was studied by testing both smooth and pre-notched specimens. It was found that the influence of temperature on the stress-strain behaviour differs at high strain rates compared with quasi-static loading conditions. The true fracture strain depends considerably on the stress triaxiality, which is governed by the notch geometry, while the influence of strain rate and temperature is less clear. Numerical simulations with the explicit finite element code LS-DYNA were performed using a model of elasto-viscoplasticity and ductile damage, which is based on the constitutive relation and fracture criterion of Johnson and Cook. The numerical simulations compare reasonably well with the experiments with respect to strength and ductility for both smooth and notched specimens at elevated temperatures.     

Impact of conical tungsten projectiles on flat silicon carbide targets: Transition from interface defeat to penetration

Normal impact of conical tungsten projectiles on flat silicon carbide targets was studied experimentally and numerically for half apex angles 5° and 5–15°, respectively, and comparisons were made with cylindrical projectiles. A 30 mm powder gun and two 150 kV and four 450 kV X-ray flashes were used in the impact tests. The numerical simulations were run with the Autodyn code in two steps. In the first, the surface loads were determined for different impact velocities under assumed condition of interface defeat. In the second, these surface loads were applied to the targets in order to obtain critical states of damage and failure related to the transition between interface defeat and penetration, and the corresponding critical velocities. In the impact tests, interface defeat occurred below a transition velocity, which was significantly lower for the conical than for the cylindrical projectiles. Above the transition velocity, the initial penetration of conical projectiles differed markedly from that usually observed for cylindrical projectiles. It occurred along a cone-shaped surface crack, qualitatively corresponding to surface failure observed in the simulations. The transition velocity for the conical projectile was found to be close to the critical velocity associated with this surface failure.     

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.     

A study of inclined impact in polymethylmethacrylate plates

The penetration and perforation of a polymethylmethacrylate (PMMA) plate is investigated experimentally and numerically. Two combined failure criteria are used in the numerical analyses: ductile failure with damage evolution and tensile failure. The measured mechanical properties of PMMA are input to the analysis. The determination of the damage evolution parameter in this material is calibrated by simulating and replicating shear localization results obtained in confined PMMA cylinders. The numerical simulation based on these parameters is tested by comparing the numerical trajectory prediction to actual trajectories of inclined impacts of projectiles. The first comparison is qualitative and shows that the numerical simulation predicts ricochet of a projectile impacting at an angle of inclination 30° as reported by Rosenberg et al. (2005) [1]. Additional successful comparison with experimental results of inclined impact of a 0.5″ AP projectile on 3 PMMA plates is reported. The contribution of each failure criterion to the projectile trajectory is studied, showing that the ductile failure criterion enforces a straight trajectory in the initial velocity direction while the tensile failure criterion controls the deflection and ricochet phenomenon. The numerical analyses are further used to study the effect of the angle of inclination on the trajectory and kinetic energy of the projectile. The effect of the projectile mass and impact velocity on the depth of penetration (DOP) was investigated too. It is found that the ricochet phenomenon happens for angles of inclination of 0° < α ≤ 30°. The projectile perforates the plate for 50° ≤α ≤ 90°, thus defining a failure envelope for this experimental configuration. For normal impact (α = 90°) the DOP scales linearly with the projectile's mass and can be fitted by a square polynomial with the impact velocity.     

Observations on shear plug formation in Weldox 460 E steel plates impacted by blunt-nosed projectiles

Shear plug formation in circular Weldox 460 E steel plates impacted by blunt-nosed cylindrical projectiles with striking velocities between 100 and 500 m/s has been investigated. Target thickness and projectile impact velocity were the primary variables, and for each target thickness the ballistic limit curve of the material was precisely determined. The test at an impact velocity just below the ballistic limit for each target thickness was selected for a microscopic examination of shear localisation and fracture. In these tests, the plug was pushed only partway through the target, and the localised shear zones outlining the fracture were easily recognised both in the optical and scanning electron microscope. Clear evidence of adiabatic shear bands and material damage due to void growth was found in several of the target plates. Analytical models available in the literature were compared with the results from the experimental and microscopic studies. Reasonable agreement was found between calculations and experiments.     

Normal and oblique impact of cylindro-conical and cylindrical projectiles on metallic plates

An experimental program has been undertaken to study the phenomenon of both normal and oblique impact of cylindro-conical and cylindrical projectiles on metallic plates, a domain where almost no test data are available. Hard-steel strikers of 12.7 mm nominal diameter and either 60° conical or blunt tips and blunt soft aluminum cylinders of the same diameter were fired at 2024-0 aluminum targets with thickness from 1.78 to 25.4 mm and at both mild steel and medium carbon steel with thickness up to 19.05 mm. Inital velocities ranged from about 20 to 1025 m s⁻¹, achieved with the aid of a pneumatic cannon at low speeds and a powder gun in the upper velocity range. Initial target obliquity was varied from normal to 50°.The primary results obtained involved the measurement of the velocity drop and change in projectile orientation as the result of passage through the target. The target damage, consisting of dishing, petals, plugs and bands separated from the crater, was examined and metallurgical determinations were executed for a selected set of runs. The information obtained should provide a good basis for understanding the mechanisms involved in this type of impact and perforation. It will also serve as a reliable source of data for comparison with the predictions from analytical models of the process which do not currently exist, but will most certainly be developed in the future.     

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.     

Multiple impact penetration of semi-infinite concrete

An experimental study was performed to gather multiple impact, projectile penetration data into concrete. A vertical firing range was developed that consisted of a 30-06 rifle barrel mounted vertically above a steel containment chamber. 0.41 m cubes of an Air Force G mix concrete were suspended in wet sand and positioned in the steel chamber. The concrete targets were subjected to repeated constant velocity impacts from 6.4 mm diameter steel projectiles with an ogive nose shape and a length to diameter ratio of 10. A laser sight was adapted to the rifle to ensure alignment, and a break screen system measured the projectile velocity. After each impact, the projectile penetration and crater formation parameters were recorded. The penetration and crater formation data were consistent with single impact penetration data from previous studies conducted at Sandia National Laboratories. In addition, an analytic/empirical study was conducted to develop a model that predicted the penetration depth of multiple impacts into concrete targets. Using the multiple impact penetration and crater formation data, a single impact penetration model, developed by Forrestal at Sandia National Laboratories, was extended to account for the degradation of the target strength with each subsequent impact. The degradation of the target was determined empirically and included in the model as a strength-modifying factor. The model requires geometry parameters of the ogive nose projectile, projectile velocity, the number of impacts, and target compressive strength to calculate the overall penetration depth of the projectile.     

Effect of distance from the support on the penetration mechanism of clamped circular polycarbonate armor plates

A 1.91-mm thick circular polycarbonate plate of 115 mm diameter was impacted by a spherical steel projectile of 6.98 mm diameter at its center. Subsequent impacts were made at 10, 20, 30, 40, and 50 mm radii of the plate. Dent dimensions for the damaged plate were measured using optical microscope. For a constant projectile velocity of 138 m s⁻¹ which was below the perforation limit of the plate under investigation, a maximum thickness reduction close to the edge support was observed. The experimental work was modeled into explicit finite-element analysis program LSDYNA for simulations. LSDYNA was able to predict the dent depth and reduction in plate thickness at impact points precisely. In this research, the effect of the impact location distance from the supports on the damage mechanism of circular polycarbonate armor plates is investigated. The target plate was subjected to constant velocity projectile impacts starting at the plate midpoint and varying the impact distance from midpoint towards the clamped edge. Failure of plate is predicted close to the constrained boundary under uniform conditions.