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

In this paper, we document the results of a combined experimental, analytical, and computational research program that investigates the penetration of steel projectiles into limestone targets at oblique angles. We first conducted a series of depth-of-penetration experiments using 20.0 g, 7.11-mm-diameter, 71.12-mm-long, vacuum-arc-remelted (VAR) 4340 ogive-nose steel projectiles. These projectiles were launched with striking velocities between 0.4 and 1.3 km/s using a 20-mm powder gun into 0.5 m square limestone target faces with angles of obliquity of 15° and 30°. Next, we employed the initial conditions obtained from the experiments with a 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 based on the dynamic expansion of a spherical cavity to represent the target. Due to angle of obliquity we developed a new free surface effect model based on the solution of a dynamically expanding spherical cavity in a finite sphere of incompressible Mohr–Coulomb target material to account for the difference in target resistance acting on the top and bottom sides of the projectile. Results from the simulations show the final projectile positions are in good agreement with the positions obtained from post-test castings of the projectile trajectories.     

Effects of density ratio and diameter ratio on critical incident angles of projectiles impacting granular media

The dynamic behavior of projectiles upon impact with granular media was recorded using two high-speed video cameras for capturing different angles. We used steel, brass, tungsten carbide spheres, and alumina ceramic spheres with diameters in the range of 6–20 mm as the projectiles and polystyrene beads (6 mm in diameter) and glass beads (1.7 mm in diameter) as the granular media. Upon impact, the projectiles penetrated the media, rebounded from the media, or were deflected such that their resulting motion was in a horizontal direction. Post-impact motion of the projectiles depended on the impact angles of the projectiles, the density ratio (bulk density/projectile density), and the diameter ratio (granular diameter/projectile diameter) and not on the impact velocity. The post-impact motion of the projectiles did not follow a clear trend in terms of the transient angle; instead, we observed the existence of a transient region. On the basis of the area of the transient regions, an empirical equation was derived for determining the critical angle of projectiles (the angle at which they can penetrate the granular media) as a function of the density ratio and the diameter ratio.     

Effect of thin oblique moving plates on long rod projectiles: A reverse impact study

The geometry and motion of long rod projectiles after penetrating thin obliquely oriented and moving armour plates were studied. Plates moving in their normal directions towards as well as away from the projectile (scalar product of velocities negative and positive, respectively) were considered. The influences of plate velocity and obliquity (angle between the normal of the plate and the axis of the projectile) were investigated through small-scale reverse impact tests with tungsten projectiles of length 30 mm and diameter 2 mm, and with 2 mm-thick steel plates. The obliquity (30°, 60° and 70°) and the plate velocity (300 to −300 m/s) were varied systematically for a projectile velocity of 2000 m/s. The disturbing effect of the plate on the projectile was characterised in terms of changes in length, velocity, angular momentum, linear momentum and kinetic energy. Plates with obliquity 60–70° moving away from the projectiles with velocity 200–300 m/s were found to cause extensive fragmentation of the projectile and to have large disturbing effects in terms of all measures used.     

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.     

Experimental and numerical studies on the behavior of thin aluminum plates subjected to impact by blunt- and hemispherical-nosed projectiles

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

Penetration of concrete targets with ogive-nose steel rods

We conducted depth of penetration experiments in concrete targets with 3.0 caliber-radius-head, steel rod projectiles. The concrete targets with 9.5 mm diameter limestone aggregate had a nominal unconfined compressive strength of 58.4 MPa (8.5 ksi) and density 2320 kg/m³. To explore geometric projectile scales, we conducted two sets of experiments. Projectiles with length-to-diameter ratio of ten were machined from 4340R_c 45 steel, round stock and had diameters and masses of 20.3 mm, 0.478 kg and 30.5 mm, 1.62 kg. Powder guns launched the projectiles to striking velocities between 400 and 1200 m/s. For these experiments, penetration depth increased as striking velocity increased. When depth of penetration data was divided by a length scale determined from our model, the data collapsed on a single curve. Thus, a single dimensionless penetration depth versus striking velocity prediction was in good agreement with the data at two geometric projectile scales for striking velocities between 400 and 1200 m/s. In addition, we conducted experiments with AerMet 100R_c 53 steel projectiles and compared depth of penetration and post-test nose erosion data with results from the 4340R_c 45 steel projectiles.     

3D numerical simulations of sharp nosed projectile impact on ductile targets

Three-dimensional FE model is presented for perforation under normal and oblique impact of sharp nosed projectiles on single and layered ductile targets. Numerical simulations have been carried out to study the behavior of Weldox 460 E steel and 1100-H12 aluminum targets impacted by conical and ogive nosed steel projectiles respectively. Weldox 460 E steel targets of 12 mm thickness in single and double layered combination (2 × 6 mm) and 1100-H12 aluminum targets of 1 mm thickness in single and double layered combination (2 × 0.5 mm) impacted at 0°, 15° and 30° obliquity were considered for simulations. The results of monolithic and layered targets were compared for each angle of impact. Monolithic targets were found to have higher ballistic resistance than that of the layered in-contact targets of equivalent thickness. Failure of both the targets occurred through ductile hole enlargement. However, ogive nosed projectile failed 1 mm thick aluminum target through petal formation and conical nosed projectile failed 12 mm thick steel target through a circular or elliptical hole enclosed by a bulge at rear surface. The explicit algorithm of ABAQUS finite element code was used to carry out the numerical simulations. Various parameters which play critical role in numerical simulation such as element size and its aspect ratio have been studied.     

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.     

Perforation of AA5083-H116 aluminium plates with conical-nose steel projectiles—experimental study

The interest regarding use of aluminium alloys in lightweight protective structures is today increasing. Even so, the number of experimental and computational investigations giving detailed information on such problems is still rather limited. In this paper, perforation experiments have been performed on AA5083-H116 aluminium plates with thicknesses varying between 15 and 30 mm impacted by 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 a digital high-speed camera system was used to photograph the penetration and perforation process. Based on these measurements, impact versus residual velocity curves of the target plates were constructed and the ballistic limit velocity of each target was obtained. An analytical perforation model from the open literature is then used to predict the ballistic limit velocity, and excellent agreement with the experimental data is found. The experimental results are finally compared to similar experiments on steel and concrete targets, and the capacity of the different materials is evaluated in relation to total weight.     

Crater distribution on the rear wall of AL-Whipple shield by hypervelocity impacts of AL-spheres

All spacecraft in low orbit are subject to hypervelocity impact by meteoroids and space debris, which can in turn lead to significant damage and catastrophic failure. In order to simulate and study the hypervelocity impact of space debris on spacecraft through hypervelocity impact on AL-Whipple shield, a two-stage light gas gun was used to launch 2017-T4 aluminum alloy sphere projectiles. The projectile diameters ranged from 2.51 mm to 5.97 mm and impact velocities ranged from 0.69 km/s to 6.98 km/s. The modes of crater distribution on the rear wall of AL-Whipple shield by hypervelocity impact of AL-spheres in different impact velocity ranges were obtained. The characteristics of the crater distribution on the rear wall were analyzed. The forecast equations for crater distribution on the rear wall of AL-Whipple shield by normal hypervelocity impact were derived. The results show that the crater distribution on the rear wall is a circular area. As projectile diameter, impact velocity and shielding spacing increased, the area of crater distribution increased. The critical fragmentation velocity of impact projectile is an important factor affecting the characteristics of the crater distributions on the rear wall.     

Normal impact and perforation of thin plates by hemispherically-tipped projectiles — II. Experimental results

The present investigation is concerned with the measurement of the forces, permanent deflections, strains and plugs produced by rigid projectiles during contact and perforation of thin aluminium and mild steel plates. Tests were generally executed just below and just above the ballistic limit; a few experiments were conducted at much higher velocity. The direct force measurements were performed by means of a special technique using a projectile containing a piezoelectric quartz crystal. Observations were carried out on more than two hundred 2024-0 aluminium plates, 0.51, 1.27 and 3.175 mm thick and 1.22 mm thick mild steel plates. The tests involved the use of hard-steel projectiles of 12.7 and 6.35 mm diameter with three different nose shapes. The residual strains, of the order of 40%, were measured by using a grid method while the strain history in the vicinity of the impact point was determined by a specially designed gage capable of measuring strains up to 100%.     

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 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.     

Direct force measurement in normal and oblique impact of plates by projectiles

An experimental investigation of the forces produced by the penetration and perforation of thin aluminum and steel plates by cylindro-conical and hemispherically-tipped projectiles at 0, 15, 30 and 45° angles of incidence has been performed. Additionally, force histories were recorded for normal impact on Lexan, nylon and ceramic targets by conically-tipped strikers. Similar tests on Kevlar were not successful owing to the generation of voltages by rubbing of fibers that completely overwhelmed the transducer signal. A piezoelectric crystal bonded to the tail of the 12.7 mm diameter, 30 g projectiles followed by an inertial mass and a trailing wire provided the instrumentation. The strikers were propelled by means of a pneumatic gun at velocities ranging from 45 to 170 ms⁻¹. Displacement data obtained from high-speed photography for selected runs allowed curve fits to an analytical function which were compared to the directly recorded force histories.The effects of changes in initial velocity, angle of obliquity and striker tip on the peak force have been analyzed. A simple model has been developed for the perforation of plates by hemispherically-tipped projectiles at oblique incidence, and comparisons have been made with the measured force histories. A model was also devised to predict the peak forces obtained for oblique impact by cylindro-conical projectiles. The peak forces obtained experimentally were found to be relatively independent of the initial projectile velocity for shots where perforation occured. For the tests at speeds below the ballistic limit, the maximum forces were approximately proportional to the initial velocity.     

Perforation experiments on HY-100 steel plates with 4340 Rc 38 and maraging T-250 steel rod projectiles

We conducted perforation experiments with 4340 R_c 38 and maraging T-250 steel, long rod projectiles and HY-100 steel target plates at striking velocities between 80 and 370 m/s. Flat-end rod projectiles with lengths of 89 and 282 mm were machined to nominally 30-mm-diameter so they could be launched from a 30-mm-powder gun without sabots. The target plates were rigidly clamped at a 305-mm-diameter and had nominal thicknesses of 5.3 and 10.5 mm. Four sets of experiments were conducted to show the effects of rod length and plate thickness on the measured ballistic limit and residual velocities. In addition to measuring striking and residual projectile velocities, we obtained framing camera data on the back surfaces of several plates that showed clearly the plate deformation and plug ejection process.     

Micro-craters in aluminum foils: Implications for dust particles from comet Wild 2 on NASA's Stardust spacecraft

Dust impacts on aluminum foils during encounter of comet 81P/Wild 2 by the Stardust spacecraft in January 2004 have been simulated using spherical projectiles of monodispersive polymer, glass, and metals, and polydispersive mineral powders of diverse grain shapes. The encounter speed of the cometary particles was a constant and modest 6.1 km s⁻¹, well within the capabilities of light gas guns, permitting high fidelity experiments to infer dust size, density, and mass from quantitative dimensional analysis of both natural and experimental impact features. Specific interest focused on exceptionally small impactors, all <100 μm and some as small as 1.5 μm. To simulate the compound shape of many Stardust craters required novel, artificial aggregate projectiles of heterogeneous mass distribution. We demonstrate that the dimensional scaling obtained previously for millimeter sized impactors extends to particles as small as 10 μm at 6.1 km s⁻¹, all yielding a constant relationship for spherical soda lime glass projectiles of diameter (Dp) to crater diameter (Dc) in Al1100 of Dc = 4.6 Dp; however, this ratio seems to decrease for projectiles ?10 μm. The overwhelming majority of the Stardust craters are <20 μm in diameter, and substantial challenges remain in quantifying the exact size-frequency distribution of the Wild 2 comet dust. Nevertheless, the current experiments provide improved insights into some of the particles' physical properties.     

Perforation of a thick plate by rigid projectiles

Perforation of a thick plate by rigid projectiles with various geometrical characteristics is studied in the present paper. The rigid projectile is subjected to the resistant force from the surrounding medium, which is formulated by the dynamic cavity expansion theory. Two perforation mechanisms, i.e., the hole enlargement for a sharp projectile nose and the plugging formation for a blunt projectile nose, are considered in the proposed analytical model. Simple and explicit formulae are obtained to predict the ballistic limit and residual velocity for the perforation of thick metallic plates, which agree with available experimental results with satisfactory accuracy.     

刚性弹侵彻有限直径金属厚靶的机理与模型研究

采用统一强度理论,考虑靶板中间主应力效应和靶体侧面自由边界的影响,得到线性硬化靶材在弹塑性阶段和塑性阶段的空腔壁径向应力的表达式,建立线性硬化靶材的统一侵彻模型,求出中低速(v₀≤1000 m/s)刚性弹体侵彻有限直径金属厚靶时侵彻阻力、侵彻深度计算公式,并利用Simpson算法对其进行求解,分析了包括强度准则差异在内的弹道终点效应的一系列影响因素。结果表明:该文计算方法可以更好地描述侵彻过程中弹靶的动态响应,还可以得到一系列基于不同强度准则的侵彻阻力和深度的解析解、对靶材在不同撞击速度下侵彻深度的区间范围进行有效预测;强度参数、弹体撞击速度、靶体半径和弹头形状对有限直径金属厚靶的抗侵彻性能均有较大的影响,其中强度参数值由1减小为0时,侵彻深度增加了22.45%;随着靶弹半径比的减小,侵彻深度不断增大,当靶弹半径比小于等于16时,侵彻深度增大的程度显著,此时靶体边界尺寸对侵彻性能的影响很大,不能继续按照半无限靶体进行计算。