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Highlights • Cavity dynamics in gelatin was studied. • A motion model of temporary cavity is established in gelatin penetrations of rifle bullets. • The motion model is well consistent with the penetration tests. • The radial movement of cavity is characterized by the behavior of bullet and the characteristic velocity. Abstract In wound ballistics, modeling the penetration-cavitation dynamics will set the basis for evaluating the damaging efficiency of projectiles. In our previous study, a motion model to characterize the behavior of rifle bullets has been established and verified in the gelatin penetration. In order to reveal the cavity production analytically, in combination with parameters obtained from the motion model of rifle bullet, cavity dynamics in gelatin was studied and a motion model of temporary cavity in gelatin penetrations of rifle bullets was proposed and verified by comparison with experimental results in terms of maximum cavity wall radius, radial movement along the penetration trajectory and temporary cavity profiles. It can be concluded that calculated results of the cavity motion model agree well with experiment data for penetration of 7.62 mm and 5.56 mm rifle bullets. And the radial movement of cavity can be characterized by the behavior of bullet and the characteristic velocity. It is significant for the trauma assessment to develop an appropriate cavitation model in gelatin for penetrations of rifle bullet. [ABSTRACT FROM AUTHOR]

• Two field tests on concrete targets subjected to a projectile penetration followed by charge explosion were conducted. • The failure mode and stress waves in concrete were experimentally obtained. • Two-step numerical models based on the Kong-Fang concrete material model and SPG method were developed and validated. • The influences of projectile penetration on destructive effects caused by following charge explosion were clarified. The earth penetration weapons (EPWs) usually penetrate into protective structures firstly, and then detonate the charge to induce high-intensity blast stress waves to cause further damage. Existing investigations on the destructive effect caused by the following charge explosion after penetration of EPWs are very limited. To clarify the combined destructive effect in concrete material caused by an EPW, an experimental and numerical investigation on failure mode and stress wave propagation in concrete target subjected to a projectile penetration followed by charge explosion was conducted in the present study. Firstly, two field tests on high strength fiber-reinforced concrete targets subjected to a projectile penetration followed by charge explosion were conducted, in which the failure and blast waves in concrete targets were comprehensively obtained. Then two-step numerical models based on the Kong-Fang concrete material model and SPG method were developed and validated against the experimental data. Finally, based on the validated numerical models, the influences of projectile penetration on the destructive effect caused by following charge explosion were analyzed. The numerical results demonstrated that the damage caused by projectile penetration has significant influences on the final failure mode and stress wave propagation in concrete targets. The research results can provide an important reference for the design of protective structure against EPWs. [ABSTRACT FROM AUTHOR]

We investigated the ballistic resistance of hot-rolled structural steel plates with a nominal yield stress of 355 MPa in this study. Ballistic tests were conducted with 7.62 mm armor piercing bullets on monolithic and multi-layered configurations both in the as-received (AR) state and in a case-hardened (CH) state. In the CH state we made the surface stronger while preserving a relatively ductile core. This was done to improve the ballistic properties of the plates. Quasi-static uniaxial tension tests and Vickers hardness tests were conducted to calibrate constitutive models for numerical simulations. The ballistic tests revealed that the capacity was highest for a monolithic CH plate, and that case hardening increased the perforation resistance by more than 20%. Plate layering decreased the capacity of the CH plates, while the capacity of the AR plates did not decrease consistently by increasing the number of layers. Finally, we used the hardness measurements to distribute material properties across the thickness of the CH plates. These distributed material properties were used in numerical models. Finite element simulations gave predominantly conservative results within 11% of the experimental values. [ABSTRACT FROM AUTHOR]

A new contact algorithm is implemented for the interaction of peridynamic regime and finite elements for the effective impact fracture analysis. The region that might experience fracture is modeled using peridynamics that is a reformulated theory of continuum mechanics while the impact projectile is modeled by three-dimensional finite elements in order to exploit mutual advantages of the formulations. An inverse isoparametric mapping technique and a node-to-surface contact algorithm are customized and implemented, and a penalty method enforcing displacement constraints is then incorporated for the transient analyses using the explicit time integration. The proposed numerical technique is applied to several examples for verification and validation. Starting with examining the material behavior of a peridynamic bar, rigid-body impact is then studied for the verification of contact-impact procedure. The ballistic perforation of an impactor through a steel plate is investigated numerically. Good agreement between numerical simulations and the analytical model is observed in the analysis of the residual velocities. The physical process of perforation is captured accurately in the simulations using the proposed numerical methodology. [ABSTRACT FROM AUTHOR]

The database for depth of penetration by projectiles into semi-infinite targets is quite extensive. The objective is to use the experimental semi-infinite penetration data to predict finite-thickness target effects. Similitude considerations are used to represent penetration response as a function of a normalized impact velocity, which is the ratio of the penetration pressure to the target strength. Then, a least-squares regression analysis methodology was applied to the normalized experimental data to provide an analytic expression for the normalized depth of penetration as a function of the normalized impact velocity over a very large velocity range, typically a few hundred meters per second to over 3500 m/s. We use the analytic expression, along with some simplifying assumptions, to estimate ballistic limit thickness T 50 and/or the ballistic limit velocity V 50 . If a target is overmatched, i.e., perforated by the projectile, an estimate is also made for the projectile residual velocity and residual length. The experimental data on which the regression fit is based consists of L / D 10 projectiles, so a procedure is also developed to account for different projectile aspect ratios. A series of examples are provided to demonstrate the utility and accuracy of the approach. [ABSTRACT FROM AUTHOR]

• High hardness steel (HHS) sheet with UHMWPE composite backing were tested against a hardened steel core projectile. • The projectile core was eroded by the HHS sheet and stopped in UHMWPE composite. • It is observed that only a core eroded to a certain length and weight by armor system can be defeated. • In numerical modeling core failure strain was determined from the residual weight of cores. • The numerical model can be used to evolve armor design. Thin high hardness steel sheets can be an alternative to expensive ceramic armor systems designed to defeat hardened core projectiles. A thin high hardness steel sheet backed with UHMWPE fiber-reinforced composite was ballistically tested against a 7.62 × 39 mm hardened steel core projectile in a single-stage gas gun. Thin steel sheets of 530 BHN hardness were adhesively bonded with UHMWPE fiber-reinforced composite to fabricate armor plates. Armor plates were able to defeat the projectile showing considerable potential. Tensile strength of steel sheet and UHMWPE-fiber reinforced ply was also determined. A detailed numerical simulation of the impact event was also performed to understand the phenomenon of defeat and penetration in greater detail. The numerical model was calibrated from the recovered projectile's core after the ballistic test. [ABSTRACT FROM AUTHOR]

Abstract: An artificial neural network model has been developed for predicting the perforation limits of spaced aluminium armour (aka Whipple shield) under impact of aluminium projectiles at hypervelocity. The network, utilizing a multilayer perceptron architecture, was trained on data from 769 impact tests, for which it accurately predicted the perforation of the shield rear wall (or lack thereof) 92% of the time. Comparatively, the leading empirical approach was found to accurately predict the outcome of 71% of the impact tests. The network output is an analogue probability of perforation, which is adjusted to a binary “Pass”/”Fail” result via a sigmoid fit that also provides physically plausible confidence bounds (i.e. error bars). Interrogation of the network was performed to identify the input parameters that most heavily correlated with the output prediction. Although the majority of the traditional parameters (i.e. those identified in the empirical ballistic limit equation) were amongst the most influential, some unexpected (and potentially spurious) parameters were also identified. A more widely sampled set of training data incorporating increased diversity in projectile and target materials would likely improve the network internal weighting for material properties and avoid accidental identification of biases in the training exemplars. [Copyright &y& Elsevier]

Abstract: This paper discusses the technique of Digital Speckle Radiography (DSR) and its application to the measurement of the internal flow fields in penetration of sand by long-rod projectiles at velocities up to 200 m/s. Three different rod nose shapes were studied: flat-ended, ogive-2, and hemispherical. Impacts performed on gelatine and concrete gave significantly different displacement fields to sand. Sand, therefore, cannot either be modelled as a fluid or as a conventional solid. Simulations performed using a code written by two of the authors (Bobaru and Promratana) showed that the velocity distribution has a very different appearance to the force distribution. This suggests that processes such as reorganisation, sliding and void filling take place, allowing the grains to move in directions other than the applied force. The resulting velocity distribution bears a strong resemblance to the experimentally measured displacement fields. [Copyright &y& Elsevier]

Abstract: The study of penetrator performance without free-surface effects can require prohibitively large monolithic targets. One alternative to monolithic targets is to use segmented targets made by stacking multiple concrete slabs in series. This paper presents an experimental investigation on the performance of segmented concrete targets. Six experiments were carried out on available small scale segmented and monolithic targets using instrumented projectiles. In all but one experiment using stacked slabs, the gap between slabs remained open. In the final experiment design, grout was inserted between the slabs, and this modification produced a target response that more closely represents that of the monolithic target. The results from this study suggest that further research on segmented targets is justified, to explore in more detail the response of segmented targets and the results of large scale tests when using segmented targets versus monolithic targets. [Copyright &y& Elsevier]

• A simplified 2-DOF motion model was presented and compared with older models. • Penetration experiments were conducted and analyzed using two rifle bullets. • The two bullets showed different tumbling features. • The present model showed the best consistency with the experimental results. • The striking yaw angle plays a decisive role in the yawing motion. Ballistic gelatin is a widely used tissue simulant in terminal ballistics. To investigate the yawing motion of rifle bullets in gelatin, this paper presented a simplified 2-DOF motion model describing the translation and rotation of the bullets. Penetration experiments were conducted using rifle bullets of two different calibers. By comparing with the experimental results, the parameters in the present yawing motion model were estimated and analyzed. The present model can predict the yawing motion of the two rifle bullets in gelatin with much higher accuracy than previous models. The yawing motion of rifle bullets was discussed in detail by making comparisons between calculations of two different rifle bullets and comparisons between calculations with different initial conditions. The striking yaw angle was found to play a decisive role in the growth of the yaw angle and thus to noticeably affect the penetration depth when the bullet tumbles through 90°. [ABSTRACT FROM AUTHOR]

Abstract: This paper examines the penetration and perforation of fibre-reinforced plastic (FRP) laminates struck by rigid projectiles with different nose shapes within a wide range of impact conditions using ABAQUS/Explicit code. It is assumed that the FRP laminate target response can be represented by a velocity dependent forcing function which eliminates discretizing the target as well as the need for a complex contact algorithm. The forcing function is then applied to the surface of the projectiles as boundary conditions in the numerical model. With this combined analytical and computational technique we can obtain the depth of penetration, residual velocity, ballistic limit, transient response in terms of time-histories of displacement/penetration, velocity and deceleration of the projectile. It is shown that the model predictions are in good correlation with available experimental data. [Copyright &y& Elsevier]

Abstract : The Alekseevski–Tate equations are typically used to predict the penetration, penetration velocity, rod velocity, and rod length of long rod penetrators and similar projectiles impacting targets. These nonlinear equations were originally solved numerically and more recently by the exact analytical solution of Walters and Segletes. However, due to the nonlinear nature of the equations, the penetration was obtained implicitly as a function of time, so that an explicit functional dependence of the penetration on material properties was not obtained. The current paper obtains the velocities, length, and penetration as an explicit function of time by employing a perturbation solution of the nondimensional Alekseevski–Tate equations. Simple (algebraic) analytical equations are given. Perturbation solutions of the Alekseevski–Tate equations were first undertaken by Forrestal et al., up to the first–order, and good agreement with the exact solutions was shown for relatively short times. In retrospect, this solution was only valid for penetrators impacting weak targets. The current study obtains a third-order perturbation solution and includes both penetrator and target strength terms, and is applicable for strong targets. The paper compares the exact solution to the perturbation solutions, and a typical comparison between the exact and approximate solutions for a tungsten rod impacting a semi-infinite steel armor target is shown. Also, alternate ways are investigated to normalize the governing equations in order to obtain an optimum perturbation parameter. In most cases, the third-order perturbation solution shows good agreement with the exact solution of the Alekseevski–Tate equations. In addition, simple equations based on the first–order perturbation solution are presented, which are accurate for the perforation of finite thickness (short penetration time) targets. [Copyright &y& Elsevier]

Abstract: Experiments were conducted on aluminum plates of 1mm 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. [Copyright &y& Elsevier]

Abstract: An experimental study has been carried out on the ballistic performance of 95% and 99.5% alumina ceramic tiles backed by metal plates, when subjected to normal impact of hard steel 12.7mm armour piercing (AP) projectiles at velocities ranging from 500 to 830ms−1. Typical damaged targets and broken projectiles are presented. The depth of penetration is measured in all the experiments, and the ballistic efficiency factor of the ceramic plates are determined. Results show that the efficiency factor increases with increase in projectile velocity. With the increase in thickness of the ceramic tile, the ballistic efficiency factor for a given velocity is observed to decrease in the case of 99.5% grade and increase in the case of 95% grade ceramic. The higher purity alumina (99.5%) shows higher ballistic performance when compared with the 95% alumina. The 99.5% alumina exhibited a predominantly transcrystalline fracture while the 95% alumina showed a less defined fracture surface. Experiments on 7.62mm AP shots were also done keeping the () ratio same as in 12.7mm AP experiments and results are presented. [Copyright &y& Elsevier]

This article presents computed results for the responses of ceramic targets, with and without prestress, subjected to projectile impact. Also presented is a computational technique to include prestress. Thin and thick ceramic target configurations are used to understand the effect prestressing has on ballistic performance. For both targets two prestress levels (small and large), and two prestress states (radial and hydrostatic) are investigated. The small prestress is similar in magnitude to values obtained experimentally and the large prestress is approximately the maximum prestress the confinement can produce (determined computationally). The targets are subjected to projectile impact and the resulting ballistic responses are evaluated. In all cases prestressing the ceramic enhanced the ballistic performance, although the effect of the different prestress conditions on the ballistic response was not always obvious. [Copyright &y& Elsevier]

Ballistic impact and penetration in sandwich panels at projectile velocities above the ballistic limit are considered. An analytic model is developed that deals with partition of the energy of absorption, allowing for quantitative estimation of the energy fraction consumed via panel elastic response and the one consumed via irreversible damage. The analysis is based on simultaneous solution of two differential equations describing bending and shear deformation of a sandwich panel and taking into account the energy conservation. The solution technique includes the direct and inverse Hankel transformations and results in practical expressions for elastic response and damage energy fractions. Numerical results are corroborated with experimental data obtained from intermediate-velocity impact tests performed for sandwich panels with FRP composite laminate faces and foam cores. [Copyright &y& Elsevier]