Spherical Projectile Research Articles

Multiple ballistic impacts on 2024-T4 aluminum alloy by spheres: Experiments and modelling

• First investigation on multiple ballistic impacts of 2024Al-T4 alloy. • Crater parameters exhibit power-law increase with the number of impacts. • Twin-like deformation bands and macro-deformation twins coexist around crater walls. • FEM modelling reveals accumulated shear strain leads to deformation twinning. Multiple ballistic impacts are carried out on a 2024-T4 aluminum alloy by spherical steel projectiles (5-mm diameter) at ∼ 400 m s − 1 , to investigate its dynamic deformation and damage. The ballistic impact process is captured with high-speed photography. Postmortem samples are characterized with optical imaging, three-dimensional laser scanning, microhardness testing and electron backscatter diffraction. With increasing number of impacts, crater diameter increases slightly, but crater depth and crater volume increase significantly, and strain accumulation leads to microhardness increase overall. Crater parameters all follow power-law relations with the number of impacts. Twin-like deformation bands and macroscopic deformation twins are produced by impact as a result of spontaneous dislocation self-pinning under high strain rate, large shear deformation. Under multiple impacts, shear strain accumulation in the arc-shaped region of the crater induces deformation twinning when it exceeds a critical value ( ∼ 1.1 − 1.6 ). It is highly possible that the deformation twins are related to deformation bands, since they both share one set of the { 111 } pole with the initial matrix grain. A finite element method model is optimized to reproduce experimental observations and interpret deformation mechanisms.

Hypervelocity impact tests on a Whipple shield using a flyer plate in the velocity range from 4 km/s to 12 km/s

A Mylar flyer plate, being launched by an electric gun, has been applied to explore the ballistic performance of a 2024 alloy Whipple shield consisting of a 1.0-mm-thick bumper and a 3.2-mm-thick rear wall with a standoff of 70 mm between them. In comparison with a spherical projectile, experimental results show that the polymer plate, having about one-fourth mass of an aluminum sphere, can penetrate the same Whipple at impact velocities of 3 km/s and 5 km/s. The ballistic limit curves (BLCs) of the Whipple are obtained in the velocity range from 3 km/s to 12 km/s using 0.25-mm-thick and 0.5-mm-thick Mylar flyers at normal and/or oblique impacts. Different from spherical projectile, the BLCs obtained by a flyer plate oscillate abruptly with impact velocity. The development of the BLC depends on both the spreading feature of the fragmented bumper sheet and the kinetic energy it carries. In normal impact condition, the BLC turns to go upward at the flyer/bumper shock pressures of 41 GPa, 71 GPa and 121 GPa, exactly corresponding to the occurrence of melting in bumper materials under the interactions among rebounded stress pulses, under the first releasing wave propagating through shock-compressed state, and under direct shock compression, respectively. Among the three melting mechanisms, the shock-induced melting produces the most widely spread debris cloud with the finest fragments.

Analytical study on the pressure caused by two spherical projectiles penetrating a liquid-filled container

When a high-velocity projectile penetrates a liquid-filled container, the projectile transmits its energy to the liquid through different ways; thus, different types of pressure waves can be generated in the liquid. In this study, an analytical model was established to calculate the drag pressure caused by two projectiles penetrating a liquid-filled container. The potential flow theory was used to calculate the pressure wave generated by the projectiles. The cavity was regarded as a wave-barrier and a pressure-release interface to include its influence on the pressure distribution. First, two types of experimental results were used to verify the analytical model. The analytical results were then compared with the results obtained by an experimentally verified numerical model to verify the proposed partition method. The influence of impact time interval on the pressure and specific impulse was also investigated. It was found that due to the shielding of the cavity on the pressure wave, the pressure and impulse at some specific regions were not affected by the impact time interval between two projectiles.

High velocity impact properties of composites reinforced by stitched and unstitched glass woven fabrics

The present research aimed to investigate the effect of stitching angle and stacking sequence of stitched layers on high velocity impact behavior of composites reinforced by glass woven fabrics. To study the effect of stitching angle on ballistic impact behavior, six different angles of (0°), (90°), (45°), (0°,90°), (±45°) and (0°,90°,±45°) were chosen as stitching angles. These stitching angles were applied on eight layers of glass woven fabric. To study the effect of stacking sequence of stitched layers, a different number of layers were stitched together with the angle of 0°. Unstitched and stitched composites were exposed to high velocity impact with 180 m/s using a spherical projectile. The residual velocity of projectile and dimensions of damage area on the composites’ front and back sides were measured. It was found that the sample with the 45° stitching angle had the best behavior against ballistic impact and its energy absorption was significantly higher than the other samples. Stitching also reduces damage area in front and back sides of the composites and inhibits delamination.

Ballistic impact response of an alumina-based granular material: Experimental and numerical analyses

Granular materials can be used as protection to stop ballistic projectiles. Nevertheless, very few studies discuss the mechanisms of kinetic energy dissipation into granulates. An experimental setup using ballistic screens was developed to evaluate the deceleration of rigid spherical projectiles penetrating CRUSHMAT® targets. The method was validated by varying the thickness of the target, measuring residual velocities and checking whether the ballistic screens and samples end surfaces did influence the target's response or not. Based on numerical simulations and a suitable constitutive model for CRUSHMAT®, the experimental method was further validated, the projectile kinetic energy dissipation assessed and the validity of the proposed constitutive model discussed. The use of ballistic screens looked suitable to perform such experimental investigations and the proposed constitutive model for CRUSHMAT® satisfying to simulate its ballistic impact response. Additional analyses should be performed to acquire a better understanding of the CRUSHMAT® structure on its mechanical behaviour.

On the improvement of the ballistic performance of a silicon carbide tile through pre-stress: Experiments and simulations

A pre-stressing technique for improving the ballistic performance of a circular silicon carbide tile has been tested against ø12-mm spherical steel projectile. The confining pre-stress was achieved through a heat-shrunk steel collar and was evaluated through neutron diffraction for the ceramic-collar system. Subsequent ballistic experiments and simulations of the impact event were used to elucidate the mechanisms and benefits of pre-stress on the ballistic response. CT-scans of various specimens, post-impact, show that the pre-stress affects the trajectory of the Hertzian cone and limits the overall damage. Furthermore, simulations qualitatively agreed with the experimental result, showing a reduction in crack propagation and altered paths of damage. Greater confining stress led to higher negative triaxiality, which act to arrest the tensile hoop stresses and corresponding cracks.

Calculation of Transparent Armor Resistance to a High-Speed Impact by a Spherical Projectile

Using the computer-based simulation method within the scope of continuous mechanics, impact interaction with a speed of 3000 m/s between a steel ball and a transparent armor target is calculated (the target has three layers). The face layer of the transparent armor is made of aluminum oxynitride; the middle layer, of hardened glass; and the lower layer, of polycarbonate. The influence of the angle of the projectile approach to the target and thickness of the hardened glass layer on the process of target penetration is studied.

Studies of the Fragmentation of Spherical Aluminum Projectiles on a Heavy Mesh at Velocities of up to 7 km/s

The results of experimental studies and numerical simulation of the fragmentation of aluminum alloy projectiles on a tungsten mesh bumper at impact velocities of up to 7 km/s are presented. The projectiles are accelerated by a two-stage light-gas gun. X-ray photography is used to observe the state of a projectile before its impact on the mesh bumper and the process of its fragmentation. The parameters of the cloud of fragments of the projectile are recorded using a thick witness plate made of AMg6 alloy placed behind the mesh bumper. Numerical simulation is performed by the smoothed particle hydrodynamic (SPH) method. Specific features of the morphology of the cloud of fragments are pointed out, and the velocities of the fragments in different parts of the cloud, as well as the arising cumulative effect, are estimated. The experimental results are compared with the results of numerical simulation.

Sandwich panel with in-plane honeycombs in different Poisson's ratio under low to medium impact loads

Abstract In this study, a series of in-plane hexagonal honeycombs with different Poisson's ratio induced by topological diversity are studied, considering re-entrant, semi-re-entrant and convex cells, respectively. The crushing strength of honeycomb in terms of Poisson's ratio is firstly presented. In the previous research, we have studied the compression performance of honeycomb with different negative Poisson's ratio. In this study, a comparative study on the local impact resistance of different sandwich panels is conducted by considering a spherical projectile with low to medium impact speed. Some critical criteria (i.e. local indentation profile, global deflection, impact force and energy absorption) are adopted to analyze the impact resistance. Finally, an influential mechanism of Poisson's ratio on the local impact resistance of sandwich panel is studied by considering the variation of core strength and post-impact collapse behavior.

Parametric analysis of energy absorption capacity of thin aluminum plates impacted by rigid spherical projectiles

A finite element axisymmetric model has been developed to study the energy absorption capacity of thin Aluminum plates (0.2–20 mm thickness) in terms of the ballistic limit. The Johnson-Cook material model was used to describe the mechanical behavior of the 2024-T3 Aluminum. Numerical results were validated by comparison with experimental tests carried on similar plates using a gas gun with two high-speed cameras to measure impact velocities in the order of 100 m/s to 200 m/s. Plastic work (60%) and friction (10%) dissipate the impact energy, while the remaining energy is absorbed in the plate as elastic and kinetic energy. A parametric analysis was performed for projectile radius and plate thickness to study their influence on the perforation energy. Ballistic curves and energy balances were used to obtain the ballistic limit from numerical simulations. Ballistic limit shows a non-linear relation with plate thickness to projectile diameter ratio, while the mean perforation stress shows a linear relation with plate thickness to projectile diameter ratio. From numerical results, a semi-empirical relation is suggested to estimate mean perforation stress and consequently obtain the ballistic limit for a given plate-projectile configuration.

Impact resistance, flexural and tensile properties of amorphous metallic fiber-reinforced cementitious composites according to fiber length

In this study, we examined the effects of the lengths of amorphous metallic fibers on the flexural and tensile properties and the impact resistance of cementitious composites. Cementitious composites were fabricated following the addition of 1.0 or 2.0 vol% of amorphous metallic fibers (lengths of 15 or 30 mm). After the static flexural and tensile tests, high-velocity impact tests were conducted (impact velocities of 170 and 300 m/s) with a spherical projectile (diameter of 25 mm). Amorphous metallic fibers with lengths of 30 mm inhibited the propagation of fractures based on the absorption and distribution of stress until they fractured without being pulled out, which significantly improved the flexural and tensile properties of cementitious composites; this resulted in better inhibition of scabbing in fibers with lengths of 30 mm compared to fibers with lengths of 15 mm. Meanwhile, the amorphous metallic fibers with lengths of 15 mm were pulled out from the matrix owing to their relatively smaller bonding areas compared with the 30 mm fibers. This caused smaller improvements in flexural and tensile properties as well as impact resistance compared with the 30 mm fibers.

Motion analysis of kinetic impact projectiles for physics education in real context

The article presents a proposal to contextualize the study of movement in introductory courses of university physics, as a contribution to decision making in social situations. For this, the use of kinetic impact projectiles and the actual data provided by official sources are considered. This information is used in an object motion model describing the kinematic characteristics of a spherical projectile (a rubber bullet). For these purposes, a Reynolds number Re ≫ 1 was used, which allows one to apply a nonlinear motion equation to find the velocity and impact energy per unit area of a projectile. The results and analysis of this model can generate an interesting discussion in the classroom about the need to build protocols for the use of kinetic impact projectiles, and the importance of using scientific knowledge in social conflicts.

Damage mechanism of CFRP laminates with different curvatures impacted by ice projectile at high velocity

The spherical ice projectile impacting vertically on Carbon Fiber Reinforced Plastic laminates (CFRP laminates) with different curvatures was developed by using the one-stage light gas gun loading system. The numerical simulation results of the vertical impact of the arched CFRP laminates with different curvatures by SHI were compared with the experimental test results, Scanning Electron Microscopy micro failure mode and the image acquisition of the high speed camera by using ABAQUS/Explicit finite element software. The deformation process and failure mode of arched CFRP laminates with different curvatures and simulated hail ice (SHI)were analyzed, and the reliability of the numerical simulation was verified. By establishing a two-hinged simply supported mechanical physical model of arched laminates, the principal stresses of each layer along the direction of 0° and 90° of fibers in arched laminates were obtained. It would provide technical support for the prediction of fiber failure and delamination damage in the process of impacting on laminates at high velocity.

A resistance force model for spherical projectiles penetrating ballistic gelatin based on cavity expansion theory

To investigate the penetration mechanism of spherical projectiles into soft tissues, ballistic gelatin was used as tissue substitute in ballistic tests. A theoretical motion model was established based on the cavity expansion theory. We first presented a quasi-static cylindrical cavity expansion model for the radial stress at the cavity wall of a cracked-hyperelastic material. The pressure on the cavity surface, PS, was also defined as the energy required to open a unit volume in the medium quasi-statically. Based on this interpretation, we proposed an approximate expression for the dynamic pressure, P, acting on the surface of the cavity by analyzing the energy transformation and conservation. Then, based on the analysis and solutions of the cylindrical cavity expansion model, we obtained a resistance force model for spherical projectiles, which consisted of an inertial term and a rate-dependent strength term. Subsequently, ballistic tests, in which gelatin blocks were penetrated by spherical projectiles of different materials and sizes, were analyzed, and the parameters in the resistance model were identified using the test results obtained from the 3 mm steel projectile. Further, the ability of the motion model to describe the motion of spherical projectiles penetrating ballistic gelatin was verified by comparing the calculated and measured results from projectiles of different materials and sizes. The proposed motion model based on the cavity expansion theory can therefore provide a basis for understanding the interaction of small arms ammunition and soft tissues.

Regolith behavior under asteroid-level gravity conditions: low-velocity impacts into mm- and cm-sized grain targets

Context.In situ observations of small asteroids, such as Itokawa, Ryugu, and Bennu, show that surfaces covered by boulders and coarse terrain are frequent on such bodies. Regolith grain sizes have distributions on approximately mm and cm scales, and the behavior of such large grains in the very low-gravity environments of small body surfaces dictates their morphology and evolution.Aims.In order to support the understanding of natural processes (e.g., the recapturing of impact ejecta) or spacecraft-induced interactions (e.g., the fate of a small lander), we aim to experimentally investigate the response of coarse-grained target surfaces to very-low-speed impacts (below 2 m s−1).Methods.We present the outcome of 86 low-speed impacts of a cm-sized spherical projectile into a bed of simulated regolith, composed of irregular mm- and cm-sized grains. These impacts were performed under vacuum and microgravity conditions. Our results include measurements for the projectile coefficient of restitution and penetration depth, as well as ejecta production, speed, and mass estimation. As part of our data analysis, we compared our data set with impacts performed in similar conditions with fine grain regolith targets to determine the dependence of our measurements on the target grain size.Results.We find that impact outcomes include the frequent occurrence of projectile bouncing and tangential rolling on the target surface upon impact. Ejecta is produced for impact speeds higher than about 12 cm s−1, and ejecta speeds scale with the projectile to target the grain size ratio and the impact speed. Ejected mass estimations indicate that ejecta is increasingly difficult to produce for increasing grain sizes. Coefficients of restitution of rebounding projectiles do not display a dependency on the target grain size, unlike their maximum penetration depth, which can be scaled with the projectile to target grain size ratio. Finally, we compare our experimental measurements to spacecraft data and numerical work on Hayabusa 2’s MASCOT landing on the surface of the asteroid Ryugu.

Numerical study of self-sustained oblique detonation in a non-uniform mixture

Self-sustained oblique detonation behind a spherical projectile formed in a non-uniform H2/O2/Ar mixture was numerically investigated. A hypersonic combustible mixture flow around a 4.76 mm diameter body was modeled to be flowing at 2500 m/s and 100 kPa. The concentration gradient was prescribed applying the Gaussian distribution to hydrogen concentration. Axisymmetric Euler equations including a detailed kinetics of 9 species and 27 elementary reactions were solved with an explicit 2nd-order time integration scheme combined with point implicit method for chemical reaction. Oblique detonation was always obtained when the mixture on the centerline was stoichiometric, as it is for a uniform mixture, and a broader range of equivalence ratio could sustain oblique detonation far from the sphere. Local detonation angle was revealed to reasonably match Chapman-Jouguet analytical solutions with a minor difference attributed to curvature, less reactive composition, and the concentration gradient. Also, a strongly fuel-rich region encountered decoupling of the shock-flame, in which an abrupt deflection of the shock front appeared. These decoupling phenomena can be attributed to a slower kinetics of a less reactive mixture. All of interesting findings in this study will also benefit understanding of various form of detonation in non-uniform mixture taking advantage of the analogy between them.

Model trajectories for a spinning tennis ball: III. The effect of a light wind on ground strokes

Theoretical models are presented for the trajectory of a rotating spherical projectile appropriate to the ground stroke in tennis, the ball being delivered in the presence of a light head wind, tail wind or side wind. The aim of the study is to determine, quantitatively, the amount of movement due to such light winds which are known to be present even in enclosed stadiums. The ball is assumed to be struck without spin (i.e., a ‘flat’ stroke), with top-spin or with under-spin (i.e., ‘slice’), with the ball being hit directly down the court or ‘cross-court’. Forces considered are the drag force, the lift force and gravity. It is found that a very modest wind can move the ball/court impact point by large amounts, of the order of tens of centimeters compared to the no-wind case. For example, a wind of 5 km h−1 (1.39 m s−1) may move the impact point by up to 1 m. The direction of movement of the impact point is, not surprisingly, normally in the direction to which the wind is blowing, although the exact direction depends, in-part, on the spin. An under-spun ball, for example, in the presence of a head wind can have its ‘range’ to the impact point actually increased, and in the presence of a tail wind the range can be decreased, a seemingly anomalous behaviour which at first sight seems surprising. Explanations for this behaviour are given. Actual movements due to the wind are compared with the product of the flight time and wind speed, since this quantity might be expected to provide an upper limit to such wind-induced movements. For a head or tail wind of 5 km h−1 and a 150 km h−1 full-court-length flat ground stroke with a flight time of 0.765 s, this product is 1.06 m and the shift in the impact point is 42.5% of this value, with larger shifts of up to 75% occurring for top-spin shots.

Simplified analysis of curvilinear penetration of free fall sphere projectile in soft soil

Free fall projectiles have been used in offshore engineering to determine in-situ undrained shear strength profiles of near-surface soft soils from accelerations recorded during penetrating. In doing so, however, only the equation of motion in the vertical direction has been formulated with the vertical acceleration by assuming vertical impact and penetration. In this study, the governing equations of curvilinear penetration of a sphere projectile are established with consideration of an angle of impact with soil surface. By treating the penetration process as an initial value problem, an algorithm is proposed for computing the trajectory, velocity and linear acceleration of penetration. The effects of impact angle, impact velocity and soil strength non-homogeneity on the penetration behavior are analyzed using a set of parameters reported in literature. The computed results of the final embedment depth and linear acceleration of sphere are shown to be in reasonably good agreement with published field data. Moreover, a new explicit equation is derived for determining the undrained shear strength of soil based on both vertical and horizontal linear accelerations. The accuracy of the undrained shear strength estimated by assuming vertical penetration is assessed. The impact angle is shown to have important influence on soil strength determination.

Damage propagation and dynamic material properties of aluminosilicate glass

Understanding the damage progression in aluminosilicate glass against impact loading is all-important for the design of a transparent structure. The Edge-on impact (EOI) experiments linked to the ultra-high-speed camera on glass plates are completed to visualize and quantify damage propagation. This followed quasi-static compressive and split-tensile, and dynamic compressive experimentation on aluminosilicate samples to examine failure process, strength, and crack initiation. By incorporating the compression and tensile test data, Johnson-Holmquist ceramic (JH-2) model parameters were estimated for aluminosilicate glass. The compression tests simulated for verification of determined JH-2 constants and finally validated by conducting the EOI simulations on glass plates to the spherical and cylindrical-shaped projectile. The simulated results for damage shape, propagation, and spall effect were collated with experiments and JH-2 model for aluminosilicate glass well predicted the impact/damage response. The high-speed visuals, calculated results, and scan electron microscopic imageries confirmed that damage progression is dependent on the impactor shape.

Experiment and numerical investigation of the aero-thermal demise of pristine and pre-damaged GLARE™ fiber-metal laminates

Since many decades researchers have been interrogating the re-entry physics of lunar objects in the Earth’s atmosphere. A request like ‘demise + re-entry’ in a web search engine gives hundreds if not thousands of studies concerned with the breakup and the disappearance of space flotsam in the Earth’s atmosphere. However, it is hard to comprehend a rational reason why the engineering physics involved in the thermal degradation of spacecraft structures still can be explained with inherent uncertainties. Many derelict satellites and spacecraft are orbiting the Earth. They will gradually enter the Earth’s atmosphere attributed to the gravitational force and may will not survive the aero-thermal load induced by the dense Earth’s atmosphere. This study, therefore, investigated the propensity to aero-thermal demise of a pristine and a pre-damaged spacecraft shielding structure during atmospheric re-entry. The shield was made of a GLAss fiber REinforced aluminum panel, which accommodated five quasi-isotropic S2-glass fiber reinforced FM94-epoxy laminates alternately stacked between six aluminum 2024-T3 alloy sheets. The pre-damage of the shielding system was akin to a damage can be generated by an impact of a micrometeoroid. To impart the pre-damage, a GLAss fiber REinforced aluminum plate was first impacted with a 2 mm diameter stainless steel spherical projectile at 5.49 km/s. The projectile perforated through the plate. Next, the perforated GLAss fiber REinforced aluminum plate was exposed to an air plasma-jet (oxygen dissociated) of a specific enthalpy of 5.4 × 103 kJ/kg at standard air pressure conditions. The high enthalpy plasma thermally degraded the pre-damaged plate, while debris was discharged uprange and downrange out of the plate. The dynamic pressure of the plasma flow exacerbated the debris discharge. The endothermic destruction of a pristine GLAss fiber REinforced aluminum specimen followed several steps: first, layer-after-layer oxidation and melting of the aluminum sheets; next, decomposition and sublimation of epoxy accompanied by thermal and viscous diffusion of molten aluminum and molten glass fibers; finally, the onset of a hole in the pristine specimen. By contrast, the plasma-jet that streamed through the punched hole of the pre-damaged GLAss fiber REinforced aluminum specimen, had thermally decomposed the frontal material layers of the specimen to a large extent in the initial few seconds. The punched hole, however, did not succumb to enlarge after the surface temperature of the GLAss fiber REinforced aluminum specimen reached an asymptote. To reproduce the experimental findings, a new Moving Mesh Front procedure had been developed and implemented in a Lagrangian finite element framework. The numerical analysis considered the temperature-dependent thermal properties of orthotropic S2-glass/FM94-epoxy composites and isotropic aluminum alloys. For a comparable heating condition, the agreement between the predicted and the measured temperatures of the specimen front surface was within 4.4%, while the corresponding agreement was within 6.7% for the rear surface temperature of the test specimen.