Ballistic Behavior Research Articles

Theoretical and finite element approaches to model the phenomenon of high-velocity impact on GFRP plates

New energy-based theoretical models that predict the ballistic behaviour of thin and thick woven composite laminates are presented. These models are formulated for high-velocity impacts, where the boundary conditions do not play a relevant role. This can be assumed as the local structural behaviour is responsible for the ballistic performance. A non-dimensional formulation is used to analyse the influence of material properties and geometrical parameters in the ballistic response of the laminate. The models are physically-based on the energy contribution of different energy-absorption mechanisms. Moreover, a 3D finite element model is also developed by means of  a continuum damage mechanics model that takes into account the different failure mechanisms described in the theoretical models to simulate the performance of the laminate under high-velocity impacts and to validate the hypotheses of the theoretical models.  A comparison between FE and theoretical models is performed by means of energy absorption mechanisms. The predictive capability of the proposed models is verified against experimental results, which were originally conducted in this work. The results obtained show the dependencies between the ballistic response and the non-dimensional physical parameters of the model. Furthermore, the proposed models can be used to see the relative importance of the different energy-absorption mechanisms involved and the comparison of these mechanisms between the theoretical and the FE models can reflect the different roles played by them, depending on the material properties and geometrical characteristics of the laminate. These results highlight the relevance of the in-plane and out-of-plane energy-absorption mechanisms, which rule the penetration process depending on the plate thickness.

Computable criteria for ballisticity of random walks in elliptic random environment

We consider random walks in i.i.d. elliptic random environments which are not uniformly elliptic. We introduce a computable condition in dimension d=2 and a general condition valid for dimensions d≥2 expressed in terms of the exit time from a box, which ensure that local trapping would not inhibit a ballistic behavior of the random walk. An important technical innovation related to our computable condition, is the introduction of a geometrical point of view to classify the way in which the random walk can become trapped, either in an edge, a wedge or a square. Furthermore, we prove that the general condition we introduce is sharp.

Impact response of fiber metal laminates based on aluminum and UHMWPE composite: Numerical simulation

Impact behavior of a novel fiber metal laminate based on ultra-high molecular weight polyethylene fiber composite and aluminum sheets is investigated using a comprehensive finite element modeling procedure. A user-defined material subroutine based on continuum damage mechanics is developed. Cohesive zone model is implemented to simulate the inter-laminar damage. High velocity impact simulations showed similar modes of deformation and failure to that observed in experiments, and provide a good approximation for residual velocity against spherical and conical projectiles. The results show that the lay-up sequence is effective on the ballistic behavior of the target exposed to the spherical projectile; but, has little effect if a conical projectile is used.

An investigation of deformation and failure mechanisms of fiber-reinforced composites in layered composite armor

This paper aims to study the deformation characteristics and failure mechanisms of fiber-reinforced polymer composites used in layered composite armor under ballistic impact. A Kevlar-29/epoxy composite and an ultra-high molecular weight polyethylene (UHMWPE) fiber-reinforced composite backed bilayer ceramic armor were respectively impacted against 7.62 mm APM2 projectiles at several different velocities. The dependence of failure mechanisms on impact velocity was analyzed both experimentally and numerically. Ballistic tests revealed that the Kevlar-29/epoxy composite backed armor displayed a lower perforation velocity than the UHMWPE fiber reinforced composite backed armor. However, under non-perforated impacts, the UHMWPE fiber reinforced composite exhibited a much higher back face deflection (BFD). According to the post-mortem visual and SEM analysis, the failure of the Kevlar-29 fiber was dominated by shear plugging in the front layers and fiber tensile breakage in the rear layers, whereas in the UHMWPE fiber reinforced composite, failure was dominated by shear plugging initiated from the front layers. These results suggest that the UHMWPE panel is more effective in resistant fiber tensile breakage which usually occurs on the back side of the panel. Using the Ls-dyna explicit dynamic finite element (FE) program, the ballistic behavior of a layered armor backed by a hybrid panel with varying mix ratios was studied numerically. The results show that using high tensile resistant fiber in the rear layers can effectively prevent fiber tensile failure and using high shear resistance fiber in the front layers can effectively prevent shear failure. These results are valuable in making the best use of fiber-reinforced composites in advanced armor design.

Effect of projectile nose on high‐velocity impact behavior of fiber metal laminates

AbstractFiber metal laminates (FMLs) are a class of hybrid materials consisting of several thin metal layers bonded by layers of composite material. In the present study, the ballistic limit, absorbed energy, specific perforation energy and failure mechanism of FML 2/1 (Al/GFRE/Al) and FML 3/2 (Al/GFRE/Al/GFRE/Al) are numerically and experimentally studied under the high‐velocity impact loading using a single‐stage light gas gun. In addition, the ballistic behavior of FML 2/1 and FML 3/2 is investigated using three different projectile nose geometries. Numerical simulation of the ballistic tests was performed to determine the residual velocity and the FML panel failure mechanism by using AUTODYN. The results indicated that the highest ballistic limit for FML 2/1 and FML 3/2 was obtained for the conical nosed projectile and the ballistic limit of FML 3/2 was 75.63% higher than FML 2/1. Although the FML 3/2 thickness is ~67% higher than FML 2/1, the specific perforation energy of FML 3/2 is improved by 72.51%, 55.26%, and 89.22% compared to FML 2/1 for blunt, hemispherical, and conical nosed projectiles, respectively.

Non-Gaussian, transiently anomalous, and ergodic self-diffusion of flexible dumbbells in crowded two-dimensional environments: Coupled translational and rotational motions.

We employ Langevin-dynamics simulations to unveil non-Brownian and non-Gaussian center-of-mass self-diffusion of massive flexible dumbbell-shaped particles in crowded two-dimensional solutions. We study the intradumbbell dynamics of the relative motion of the two constituent elastically coupled disks. Our main focus is on effects of the crowding fraction ϕ and of the particle structure on the diffusion characteristics. We evaluate the time-averaged mean-squared displacement (TAMSD), the displacement probability-density function (PDF), and the displacement autocorrelation function (ACF) of the dimers. For the TAMSD at highly crowded conditions of dumbbells, e.g., we observe a transition from the short-time ballistic behavior, via an intermediate subdiffusive regime, to long-time Brownian-like spreading dynamics. The crowded system of dimers exhibits two distinct diffusion regimes distinguished by the scaling exponent of the TAMSD, the dependence of the diffusivity on ϕ, and the features of the displacement-ACF. We attribute these regimes to a crowding-induced transition from viscous to viscoelastic diffusion upon growing ϕ. We also analyze the relative motion in the dimers, finding that larger ϕ suppress their vibrations and yield strongly non-Gaussian PDFs of rotational displacements. For the diffusion coefficients D(ϕ) of translational and rotational motion of the dumbbells an exponential decay with ϕ for weak and a power-law variation D(ϕ)∝(ϕ-ϕ^{★})^{2.4} for strong crowding is found. A comparison of simulation results with theoretical predictions for D(ϕ) is discussed and some relevant experimental systems are overviewed.

Optimum design for the ballistic diode based on graphene field-effect transistors

We investigate the transport behavior of two-terminal graphene ballistic devices with bias voltages up to a few volts suitable for electronics applications. Four graphene devices based ballistic designs, specially fabricated from mechanically exfoliated graphene encapsulated by hexagonal boron nitride, exhibit strong nonlinear I-V characteristic curves at room temperature. A maximum asymmetry ratio of 1.58 is achieved at a current of 60 µA at room temperature through the ballistic behavior is limited by the thermal effect at higher bias. An analytical model using a specular reflection mechanism of particles is demonstrated to simulate the specular reflection of carriers from graphene edges in the ballistic regime. The overall trend of the asymmetry ratio depending on the geometry fits reasonably with the analytical model.

Ballistic impact response of complex concentrated alloys

The performance of complex concentrated alloys (or high entropy alloys) with widely varying microstructure is evaluated by ballistically impacting targets with spheres fired at normal incidence. By changing alloy composition in the Al-Co-Cr-Fe-Ni multi-principal system, the variation in microstructure included single-phase equiaxed grains, single-phase with bimodal grain-size distribution, and eutectic two-phase lamellar microstructure. Rigorous characterization in the form of bulk mechanical testing, scanning electron microscopy, and spatially resolved nano-indentation on initial and ballistically impacted plates was used to connect microstructural details to aspects of ballistic behavior governing performance. Based on the results, it was shown that although the addition of a harder secondary phase improves strength, cracks that initiate and propagate within the harder phase and ultimately across the target plate drastically reduce the ballistic performance of the two-phase material. The single-phase alloy with bimodal grain-size distribution exhibited superior ballistic performance compared to the other high entropy alloys, although none of these materials exceeded the performance of conventional rolled homogeneous armor steel. These results pave the way for development of high-performance concentrated alloys for ballistic applications by appropriate microstructural design.

Numerical investigation on the effect of different face sheet materials and core designs on the ballistic response of sandwich structures under low-velocity impact

In the present article, a detailed numerical deformation and failure analysis of sandwiched structures with different face sheet materials and core design has been carried out. Different face sheets materials ranging from aluminium alloys to composites such as carbon/epoxy and kevlar/epoxy fixed on different types of core were analyzed. Sandwiched structure with aluminium alloy face sheet showed minimum deformation of the impacting point, large impactor recoil and least strain energy absorption. Whereas carbon/epoxy face sheet showed large deformation of the impacting point for all the core designs. Employing the carbon/epoxy face sheet, the impactor recoiled only with square and hexagonal core design while the strain energy absorption was minimum for square and maximum for circular core designs. Kevlar/epoxy face sheet also showed large deformation of the impacting point for all the types of honeycomb core designs. The impactor recoiled very minimally for square core design and there was no recoil for the hexagonal and circular core. Kevlar/epoxy face sheet showed maximum displacement of the impacting point and strain energy absorption for the circular core. Thus, it can be said that sandwiched structure with a carbon/epoxy face sheet appeared to be the best choice in terms of energy absorption during the impact. The present study showed improvement in ballistic behaviour of sandwich structure with composite face sheet as compared to metallic face sheet in terms of energy absorption.

Effect of incorporating Lode angle parameter into a fracture criterion in predicting ballistic impact behavior of double-layered 2024-T351 aluminum alloy plates against blunt projectiles

Recent studies showed that the ductility of some metals was affected by not only stress triaxiality but also Lode angle parameter. However, the majority of impact-related simulations used Lode independent fracture criteria. The necessity of incorporating Lode angle parameter into a fracture criterion in predicting ballistic impact behavior of monolithic 2024-T351 aluminum alloy (AA2024-T351) plates has been previously addressed in the work of Xiao et al. [1]. This paper serves as an extension by considering plates with double-layered configuration and the same total thickness. Ballistic impact tests were performed on 4.82 + 4.82 mm thick double-layered plates. Blunt projectiles with dimensions of Φ 12.66×50.56 mm3 and a nominal mass of 50 g were used, and the impact velocities ranged from 133.4 to 363.8 m/s. According to the experimentally obtained data, ballistic limit velocities (BLVs) were calculated and fracture patterns of post-test plates were analyzed. It was found that for double-layered configurations, the first plate failed by shear plugging and the second plate failed by tensile stretching and global deformation. By replacing monolithic plates with double-layered ones, the BLV increased from 138.4 to 180.1 m/s, a 30% improvement in ballistic resistance. Subsequently, numerical simulations of ballistic impact tests were performed by software ABAQUS/Explicit. Mechanical property of AA2024-T351 was described by Johnson-Cook (JC) plasticity model accompanied with either the Lode independent JC fracture criterion or the Lode dependent modified Mohr-Coulomb (MMC) fracture criterion. The numerical results were compared with those obtained from experiments. It was found that MMC criterion predicted BLVs more accurately than JC criterion. The prediction errors for MMC and JC criteria were respectively 3.3% and 11.4%, with the former being merely one-third of the latter. The overall failure modes of double-layered plates were correctly predicted by both JC and MMC fracture criteria. However, details of the fracture patterns, such as the formation of fragments, the shape and number of ejected plugs, and the initiation and propagation of cracks, were better captured by MMC criterion than by JC criterion. Detailed analysis shows that the stress state governing ballistic impact tests locates in the range where Lode angle parameter is strong enough to induce a significant difference between JC and MMC criteria. Under such stress state, the ductility of AA2024-T351 is correctly predicted by the Lode dependent MMC criterion but is overestimated by the Lode independent JC criterion.

Experimental and numerical analysis of the ballistic response of agglomerated cork and its bio-based sandwich structures

Considering the susceptibility of sandwich structures to impact events and the increasing environmental awareness due to pollution, the present work provides a thorough understanding of the ballistic impact behavior of agglomerated cork and of the resulting green sandwich structures produced with polypropylene (PP) skins reinforced with a flax/basalt intraply hybrid fabric. The effect of density on the agglomerated cork response was evaluated (NL10 ρ = 0.14 g/cm3, NL20 ρ = 0.20 g/cm3 and NL25 ρ = 0.25 g/cm3) and a comparison with commercial polyvinyl(chloride) foams was provided (HP130 ρ = 0.13 g/cm3, HP200 ρ = 0.20 g/cm3 and HP250 ρ = 0.25 g/cm3). The effect of a maleic anhydride coupling agent on the mechanical properties of the skins and of the overall sandwich structures was also investigated. The results highlighted a compromising effect of the weak interface between cork granules and polymeric binder on the impact resistance of the agglomerated cork, but a clear improvement of its performance was observed when embedded as core material between the two skins. Indeed, the two classes of sandwich structures produced with neat PP skins and with the two cores with the same density, i.e. agglomerated cork NL10 and PVC foam HP130, displayed the same ballistic limit of 171 m/s confirming that cork integration in the overall structures allows to approach PVC foam performance. The high-velocity impact response of one agglomerated cork (NL25) and one PVC foam (HP130) was also subjected to finite element analysis employing the CRUSHABLE FOAM model available in ABAQUS obtaining a good fitting with the experimental data.

On impact of cryogenic temperature rolled 6082 Al alloy by dome- and conical-nosed projectiles

The simultaneous improvement in strength and toughness through cryogenic temperature rolling observed in recent studies is of profound interest for designers in defence, automobile and aerospace domains. The present work discusses the effects of different projectile nose shapes – dome and conical – on the ballistic impact behaviour of the 1 mm thick AA 6082 alloy targets, rolled to different cryogenic strains, using the experimental data for impact velocities ranging from 50 to 250 m/s reported in our earlier work. The cryogenic rolling strains were imparted by providing different thickness reductions, namely, 50%, 66.66%, 75% and 80%. The target performance was also analysed using velocity drop approach. The projectile nose shape influenced the ballistic limit strongly for 50% and 75% thickness reductions. Conical-nosed projectiles were found to be better penetrators than the dome-nosed projectiles within the overall tested velocity range of 50–250 m/s. The observations confirmed the dominance of the samples with 66.66% thickness reduction impacted with both dome and conical-nosed projectiles in the average and maximum velocity drops after the ballistic limits, indicating superior performance.

Numerical Simulation and Analysis of Muzzle Flow During a Rarefaction Wave Gun Firing

AbstractRarefaction wave gun can significantly reduce the recoil and the barrel heat without affecting projectile velocity during the launching process. This paper aims to improve the understanding of the muzzle flow characteristics during a rarefaction wave gun firing and clarify the different ballistic behaviors between the rarefaction wave gun and the traditional gun. First, the mathematical models and the numerical methods of the muzzle flow with the interior ballistic process were established. Then, the numerical simulation results were compared with the experimental data to validate the reliability and accuracy. Next, the rarefaction wave propagation behavior was described, and the interior ballistic process of the rarefaction wave gun was compared with that of the traditional gun. Then the development law of the muzzle flow field for the rarefaction wave gun coupled with the interior ballistics process was studied. Finally, the different detailed results of the muzzle flow between the traditional gun and the rarefaction wave gun were investigated. The development processes of the muzzle flow in both guns are generally similar, but the strength of the main flow parameters and the ballistic performances for the rarefaction wave gun are smaller than that for the traditional gun due to the rarefaction wave influence. This paper could provide a valuable reference for the research and design on the rarefaction wave gun.

Misleading Entry Wounds From Atypical Bullet Behavior.

Some pistol bullets exhibit atypical wound ballistic behavior that can result in misleading and misinterpreted entry gunshot wounds. We demonstrate the atypical performance and behavior of these bullets using (1) high-speed videography of projectiles penetrating, perforating, and exiting soft tissue simulants; (2) Doppler radar tracking throughout simulated wound production; (3) downrange witness panels to record postperforation bullet orientation during a secondary impact; (4) laser tracking to assess and compare postperforation bullet deflection; (5) evaluation of "bullet wipe" around entry bullet holes in a victim's clothing; and (6) projectile penetration depth for differentiating primary from secondary gunshot wounds. Truncated cone and certain flat-point full-metal-jacketed pistol bullets in the 3 most common calibers of 9 mm, .40 caliber, and .45 caliber typically perforate the victim with little or no yawing, producing straight wound tracks and continuing to travel nose forward upon exiting. Any secondary gunshot victim downrange sustains a normal-appearing entry wound. Common pistol bullets exiting gunshot victims are typically destabilized and enter a yawing or tumbling flight, resulting in entry wounds that appear as typical, first strike entry wounds when in fact, they are secondary gunshot wounds. However, some bullets retain their nose-forward flight after emerging from a gunshot victim. These secondary but normal-appearing, round-shaped entry wounds may be erroneously identified as direct, primary strikes.

Ballistic performance and energy dissipation characteristics of cylindrical honeycomb sandwich structure

The energy absorption (EA) and ballistic behaviour of the cylindrical sandwich shells, which comprised of honeycomb core (AL-3003 H18) and cylindrical face sheets (AL-1100 H12), were investigated by carrying out experiments and numerical simulations. Two distinct nosed shapes, ogive and hemispherical shape impactor of mass 52.5 gram, length 50.8 mm and diameter 19 mm, were impacted normally at the outer curved surface of the sandwich structure. A compressed air gun was used for experiments and the incidence velocities of both the impactor were kept within the range of 50 -146 m/s. The results in the form of ballistic limit, local and global deformation and the failure modes of the sandwich structure were reproduced through numerical simulations which were carried out through commercially available finite element code Abaqus/Explicit. Johnson cook material model was used for the face sheet whereas for the honeycomb core and the adhesive layers, ductile damage material model was employed. The validated numerical model was further extended to discover the influence of facesheet thickness, side length, curvature and cell wall thickness on the ballistic resistance, deformation, failure mode and EA of the sandwich shell structure. The influence of the face sheet thickness on the performance of the cylindrical sandwich structure was more significant compared to the honeycomb core geometric parameters. However, decreasing the side length, and increasing cell wall thickness and curvature enhanced the EA and ballistic resistance marginally.

Investigation on the ballistic performance of rubber-aluminum (AA7075-T651) laminated plates reinforced with borosilicate glass balls

In this study, the ballistic behavior of protective armor plates (PaP) obtained by curing between high structural strength AA7075-T651 aluminum plates by reinforcing with glass balls of two different rubber mixtures whose damping properties were developed with carbon nanotube and glass bubbles fillers were investigated. A total of six PaPs at 27, 30, and 35 mm heights were prepared using two different matrix damping rubbers. High-strength liner rubber used in air bellows is vulcanized on the front and back surfaces of PaPs. Between the PaPs, Ø15.875 and Ø6.747 mm, borosilicate glass balls were placed in a particular arrangement that coincides with the middle of the matrix rubber and does not have any gaps. Liner rubber cured on the front face has managed to hold the energy by forming a layer like clothing around the bullet cores. Glass balls between PAPs play an essential role in the energy absorption of GB-filled mixtures. In contrast, in MWCNT-filled mixtures, they act as a second damping element. The ballistic performance of PAPs prepared with multiwalled carbon nanotubes was determined to be better than those prepared with Glass Bubbles. Thanks to the superior mechanical properties and high aspect ratio of MWCNTs, the penetration and swelling heights of the matrix damping rubbers prepared to have excellent results compared to glass bubbles. With the increase in the thickness of the PaPs prepared with MWCNTs, the deformation effect of the penetration depth and bulging height created by the bullet on the anterior and posterior surfaces decreased. As the thickness of PaP increased from 27 mm to 35 mm, penetration depth decreased by 38%, and bulging height reduced by 35%. The amount of penetration and swelling increased in PaPs using rubber filled with glass bubbles. As the plate thickness increased, the damping feature decreased and the glass balls were activated, and the bullet was stopped.

Phase transition of an open quantum walk

It has been discovered that open quantum walks diffusively distribute in space, since they were introduced in 2012. Indeed, some limit distributions have been demonstrated and most of them are described by Gaussian distributions. We operate an open quantum walk on [Formula: see text] with parameterized operations in this paper, and study its 1st and 2nd moments so that we find its standard deviation. The standard deviation tells us whether the open quantum walker shows diffusive or ballistic behavior, which results in a phase transition of the walker.

Fractional nonlinear electrical lattice.

We examine the linear and nonlinear modes of a one-dimensional nonlinear electrical lattice, where the usual discrete Laplacian is replaced by a fractional discrete Laplacian. This induces a long-range intersite coupling that, at long distances, decreases as a power law. In the linear regime, we compute both the spectrum of plane waves and the mean-square displacement (MSD) of an initially localized excitation, in closed form in terms of regularized hypergeometric functions and the fractional exponent. The MSD shows ballistic behavior at long times, MSD∼t^{2} for all fractional exponents. When the fractional exponent is decreased from its standard integer value, the bandwidth decreases and the density of states shows a tendency towards degeneracy. In the limit of a vanishing exponent, the system becomes completely degenerate. For the nonlinear regime, we compute numerically the low-lying nonlinear modes, as a function of the fractional exponent. A modulational stability computation shows that, as the fractional exponent decreases, the number of electrical discrete solitons generated also decreases, eventually collapsing into a single soliton.

Numerical and experimental investigations on the effect of target thickness and solution treatment on the ballistic behaviour of AA7075 thick plates

The influence of target thickness and solution treatment on the ballistic behaviour of AA7075 targets has been investigated by both numerical and experimental methods. In numerical simulation, the target thickness was varied from 19 to 26 mm and an Ogive nose shaped projectile of 7.62 mm diameter with inlet velocities ranging between 800–875 m/s was considered. In order to justify the numerical observations, high velocity ballistic experiments were conducted on AA7075-T651 and the solution treated plates of various thicknesses (12, 16, 18, 20, 22 and 25 mm). For this experimental study, a deformable form projectile with dimensions of 7.62 × 51 mm and an inlet velocity of 850 ± 20 m/s was used. Microstructures of ballistic test samples were analysed using an optical microscope. Numerical analysis using ABAQUS predicted the minimum thickness required to resist complete penetration to be 20 mm in the case of AA7075 plates in the T651 condition, while experimental results showed it to be 21 mm. In the case of AA7075 solution treated plates, numerical simulation analysis predicted the minimum required plate thickness to resist complete penetration to be 24 mm, while the experimental results showed it to be 23 mm. Post ballistic microstructure analysis revealed that there was no change in the microstructure in the AA7075-T651 condition plates. Solution treated plates showed deformation of grains nearer to the impact region with the formation of adiabatic shear bands. In the case of the T651 plate, the mode of fracture was brittle, resulting in splinters, whereas it was petalling in the case of the solution-treated plates. The numerically predicted depth of penetration on both targets was reasonably close to experimental results with an average of 4% error.

Ballistic Performance Evaluation of Kevlar-Glass Fibre Hybrid Composite Laminate against Medium Velocity Impact

In this paper, the post ballistic impact behaviour of kevlar-glass fibre hybrid composite laminates was investigated against 9×19 mm projectile. Eight different types of composite laminates with different ratios of kevlar woven fibre to glass fibre were fabricated using hand lay-up with epoxy matrix. Ballistic behaviour like ballistic Limit (V50), energy absorption, specific energy absorption and Back Face Signature (BFS) were studied after bullet impact. The results indicated that as the Percentage of glass fibre is increased there was a linear increment in the ballistic behaviour. Addition of 16% kevlar fabric, composite sample meets the performance requirement of NIJ0101.06 Level III-A. Since the maximum specific energy absorption was observed in Pure Kevlar samples and the adding of glass fibre increases the weight and Areal Density of the sample, further investigations need to be carried out to utilize the potential of glass fibre for ballistic applications.