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.     

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.     

Ballistic limit for oblique impact of thin sandwich panels and spaced plates

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.     

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.     

Numerical–analytical model of penetration of long elastically deformable projectiles into semi-infinite targets

A new numerical–analytical model of penetration of long axisymmetric elastically deformable projectiles in semi-infinite targets is presented. A background of this model is the integral–differential equation of ballistics for non-deformable projectile. This equation is obtained on the basis of the Lagrange–Cauchy integral for non-stationary irrotational motion of an incompressible fluid, as well as the solutions for the quasi-static spherical cavity expansion problem in an infinite medium. The velocity field in a target is defined by actual projectile shape. The functional dependence of penetration velocity is determined for both elastic and rigid projectiles. The effect of forced elastic longitudinal oscillations on penetration velocity is estimated. An estimate is made for the critical impact velocity at which point the projectile plastically deforms causing irreversible changes in its shape, and also leads to instability of its trajectory in the target. This velocity depends on both elastic and strength characteristics of the projectile and target, their densities and projectile shape. Results from our penetration modeling are compared with existing experimental and calculated data.     

Experimental study of perforation and cracking of water-filled aluminum tubes impacted by steel spheres

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

Yaw impact of rod projectiles

The purpose of this numerical study is to investigate the penetration regimes for L/D 30 tungsten-alloy rod projectiles for cases where the impact yaw angle varies from 0 to 90° and for impact velocities from 1.4 to 2.6 km/s. The target is modeled as a semi-infinite or half-space block of rolled homogeneous armor (RHA) at zero obliquity. For cases of mild interference, the penetration channel is still deep and narrow but may be skewed with respect to the original shot-line. While penetration is degraded the efficiency of the rod projectile remains relatively high. With increasing yaw angle the rod may deform due to transverse loading to the extent such that it contacts and produces gouges on the opposite side of the penetration channel. Additionally, lateral loading may induce angular acceleration to the extent such that the tail of the projectile rotates (in the plane of symmetry) and also contacts the opposite side of the penetration channel. In the next discernible penetration regime, the long-rod deforms under transverse load but the tail does not rotate significantly. It is seen that nearly the entire rod length experiences the lateral load with the result that the original shot-line is significantly altered. The deformed rod, again, has multiple contact or loading points (or regions) and the resultant angular acceleration appears to be insufficient to induce rotation of the projectile tail. Thus, rather than ricochet, the projectile cuts a significant slot into the target. Finally, for very large yaw angles the crater becomes indistinguishable from one produced by a side-on or 90° impact even though the impact yaw angle may be significantly less than 90°.     

Target damage from highly oblique hypervelocity impacts of steel spheres against thin laminated targets

Target hole sizes and geometries were measured for a series of highly oblique hypervelocity impacts of steel spheres against thin laminated targets. The impact velocity was nominally 4.6 km/s for most of the experiments with a few tests conducted at 7.3 km/s. Impact obliquity ranged from 60° to 80° from the normal to the target plane. Projectiles were stainless steel spheres with masses of 222 g, 25 g, and 1 g. Targets were laminated MX-2600 silica phenolic bonded to a 2024-T3 substrate. Target thickness, t, was varied to give thickness to projectile diameter, d, ratios of t/d = 0.6 and 0.3 for each projectile. CTH Eulerian wavecode calculations of selected tests were performed to improve our understanding of the experimental results.     

CAVITY MODELS FOR SOLID AND HOLLOW PROJECTILES

Two analytical models for the crater size generated by long-rod and thick-walled tube projectiles are presented. The first is based on energy; in a steady-state penetration, the kinetic energy loss of a projectile is related to the total energy deposited in the target. This simple approach provides an upper bound for the crater size. The second approach is based on the observation that two mechanisms are involved in cavity growth due to long projectiles: flow of projectile erosion products, which exerts radial stress on the target and opens a cavity, and radial momentum of the target as it flows around the projectile nose (cavitation). This analysis includes the centrifugal force exerted by the projectile, radial momentum of the target, and the strength of the target. Thus, it can estimate the extent of cavity growth due to projectile mushrooming, which cannot be predicted by other analyses. This model is shown to be in good agreement with experimental data.     

A meshless treatment of three-dimensional penetrator targets for parallel computation

 A meshless modeling procedure of three-dimensional targets for penetration analysis on parallel computing systems is described. Buried structures are modeled by arbitrary layers of concrete and geologic materials, and the projectile is modeled by standard finite elements. Penetration resistance of the buried structure is provided by functions derived from principles of dynamic cavity expansion. The resistance functions are influenced by the target material properties and projectile kinematics. Additional capabilities accommodate the varying structural and geometrical characteristics of the target. Coupling between the finite elements and the meshless target model is made by applying resistance loads to elements on the outer surface of the projectile mesh. Penetration experiments verify the approach. In this manner, the target is effectively modeled and the strategy is well suited for parallel processing. The procedure is incorporated into an explicit transient dynamics code, using mesh partitioning for a coarse grain parallel processing paradigm. Message Passing Interface (MPI) is used for all interprocessor communication. Large detailed finite element analyses of projectiles are performed on up to several hundred processors with excellent scalability. The efficiency of the strategy is demonstrated by analyses executed on several types of scalable computing platforms.     

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.     

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.     

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.     

A generalized formula for the penetration depth of a deformable projectile

A simple analytical algebraic formula is developed for predicting the penetration depth of a deformable projectile into a semi-infinite target. This formula is a simplified version of more general equations that have been developed to predict the time-dependent penetration process in finite thickness targets. Specifically, the formula generalizes the classical hydrodynamic theory to include dependence on elastic properties of the target and on the yield strengths of both the target and the projectile. Moreover, the formula is limited to the case of long-rod penetration where both the projectile and the target experience significant plastic flow. The limiting values of the location of the elastic–plastic boundary in the target have been determined, and a single empirical constant has been introduced to characterize the transition between these limiting values. A value for this empirical constant has been determined which produces theoretical predictions that are in reasonable agreement with experimental data for moderate to high values of the impact velocity of steel and tungsten projectiles penetrating a steel target.     

Protection effectiveness of an oblique plate against a long rod

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

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.     

Experimental impacts above 10 km/s

In the proceedings of the last symposium, recent work on a technique for launching small projectiles to hypervelocities above 10 km/s using an inhibited shaped charge was presented [1]. In the interim, experiments have been conducted using the inhibited shaped charge to launch aluminum, nickel, and molybdenum projectiles. This paper presents the results of the impact tests, as well as discusses the shaped charge design modifications for the nickel and molybdenum launchers. Radiographs are presented of the impacting projectiles, as are post test photographs of various targets. The data are unique in that they represent low L/D projectile impacts into both monolithic blocks and spaced plates at velocities above 10 km/s. The aluminum projectiles are being launched at 11.25±0.20 km/s, the molybdenum projectiles at 11.72±0.10 km/s, and the nickel projectiles at 10.81±0.10 km/s.     

Deformation and fracture of a long-rod projectile induced by an oblique moving plate: Experimental tests

The influence of projectile length to diameter ratio (15, 30 and 45), plate thickness (0.5, 1 and 2 projectile diameters), projectile velocity (1500, 2000 and 2500 m/s) and plate velocity (−300 to 300 m/s) on the interaction between long-rod tungsten projectiles and oblique steel plates (obliquity 60°) was studied experimentally in small-scale reverse impact tests. The residual projectiles and their motions were characterised in terms of changes in length, velocity, angular momentum, linear momentum and kinetic energy. The parameters found to have the largest influence on the disturbance of the projectile were the plate velocity, in particular its direction, and the thickness of the plate. In the ranges studied, the influence of length to diameter ratio and of projectile velocity were found to be less important.     

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.