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The penetration of rigid projectiles in polycarbonate (PC) targets is explored through deep indentation tests with conical-nosed indenters and ballistic penetration results for armor piercing 7.62 mm projectiles. We found that the resistance to penetration in both sets of experiments is practically the same, which means that the rate sensitivity of PC does not play a significant role in its resistance to penetration. We account for this observation by including the pressure dependence of the elastic constants and the strength of PC in its constitutive equation, which we implemented in numerical simulations. This pressure-dependent constitutive relation resulted in good agreements between simulation results and experimental data for both penetration depths and residual velocities of armor piercing projectiles impacting PC targets.

We evaluate the performance of the OptimalTransportationMeshfree (OTM) method of Li et al. [21], suitably extended to account for seizing contact and fracture, in applications involving terminalballistics. The evaluation takes the form of a conventional Verification and Validation (V&V) analysis. In support of the validation analysis, we have conducted tests concerned with the normal impact of Aluminum alloy 6061-T6 thin plates by S2 tool steel spherical projectile over a range of plate thicknesses of [0.8 mm, 1.6 mm] and a range of impact velocities of [100, 400]m/s. The tests were conducted at Caltech’s GALCIT gas-gun Plate-Impact Facility. We find excellent agreement between measured and computed perforation areas and a ballistic limits over the thickness and velocity ranges considered. Our verification analysis consists of model-on-model comparisons and an assessment of the convergence of the OTM method. Specifically, we find excellent agreement between the incident vs. residual velocities predicted by the OTM method and by the power-law relation of Recht and Ipson [36]. We also find robust linear convergence of the OTM method as measured in terms of residual velocity error vs. number of nodes.

The terminal ballistics of long-rod penetrators is a very complex field of research involving high pressure physics, continuum mechanics, material science and high strain rate phenomena. The research in this field is advanced through experimental data collection, engineering models, and numerical simulations. In the present paper, we summarize some of our recent work which is focused on determining the important material parameters in the interaction of long rods with various targets (both stationary and moving). Our basic goal is to be able to account for various phenomena encountered in the experiments, rather than reproduce the data very accurately. We achieve this goal by using the minimal set of material parameters which is needed in order to highlight the basic features in the interaction. We also show how 3D numerical simulations help to establish a simple model for the complex interaction between a tungsten alloy rod and a moving steel plate.

This article is the acceptance keynote presentation after receiving the Distinguished Scientist Award from the Hypervelocity Impact Society at HVIS 2000, held in Galveston, TX, November 2000. As dictated by precedence, the article highlights some of the significant events and activities in my career. My technical activities and contributions can be divided into nominally three areas: 1) fire/thermal loading; 2) warhead mechanics; and 3) penetration/armor mechanics. A commonality of the areas is that they all deal with characterizing and understanding the response of materials or structures to intense loads. A summary of my research activities and significant findings are presented. Additionally, a brief history of the formation of the Hypervelocity Impact Society is presented.

Summary Some remarks in favour of the start-up of a European Solids Mechanics Conference are first made. A very brief outline of Robins' life is then given, followed by a review of his collected papers. He was born in Bath, England, in 1707 and died at Fort St David, India, in 1751. This should place in time the man with whom the lecture is concerned. Several scientific topics to which he made contributions.—the ballistic pendulum, the whirling machine, air resistance sustained by solid shot and the Magnus effect—are described about the changes in his professional inclinations and personal ambitions with time. There was, and has been since the 1730s, controversy about Robins' work between Continental and English scientists. The author briefly details some of the exchanges on this score and uses it to suggest that 1992 is a year after which greater efforts might be made to attain more objective opinions on the history of European mechanics than hitherto. Some of the difficulties which stand in the way are noted and a few suggestions are made for improving the situation. That workers in mechanics come better to appreciate their subject's history is a theme here explicitly and implicitly advocated.

This research conducts 300 small-scale ammunition experiments using moderate bullet speeds and a variety of bullet configurations in order to understand the relationship between penetration behavior and bullet shape. To maximize the survivability of soldiers and reduce their vulnerability and ballistics wounds, it is very important to understand the penetration physics of bullets. Inside human bodies, tumbling and traveling trajectories are important factors to consider when analyzing human injuries due to ballistics. Therefore, many kinds of bullets and armor have been proposed to minimize or maximize human damage. In this study, to support the development of bullets, 10 bullets with different head angle shapes and different diameters were manufactured and fired at speeds less than 200 m/s towards transparent gelatin blocks, and the damage mechanisms, i.e., temporary cavities and permanent cavities, were studied by taking penetration images using a high speed camera. It was found that the tumbling and rotations of bullets are influenced by kinetic energies and the shapes of bullets, and several empirical relationships are derived. The results suggest that the shapes and the diameters are crucial factors for ballistics wounds.

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.

Small (5.56 mm, 7.62 mm and 9 mm) and medium (12.7 mm) arms rounds were fired at snow-filled 1.5m cubic gabions in a mid-winter condition in Fairbanks, Alaska. The rounds were excavated and penetration by each ammunition type was measured. A distribution and average of penetration depth was determined. All 320 rounds fired were captured within 1.5m after entering the snow barrier. Comparison with published models of ballistics penetration of snow showed mixed results with several matching our data within 10% and all but one within 32%. However, most of these models are simplistic in that they accommodate limited variables and therefore may not be expected to perform well in all settings. We conclude that snow-based ballistics protection structures can be quickly and efficiently erected in suitable environments and with minimal size, can provide reliable protection against small and medium arms fire.

We present a novel methodology to experimentally verify constitutive models and numerical algorithms used in terminal ballistics of small arms ammunition. The methodology comprises of the following elements: identification of material models in a set of independent tests, terminal ballistics testing of conditions covering the most important cases of bullet–target interactions, while providing enough data to assess the scatter of parameters measured in the experiments and to create a measure characterising deviation of modelling results from the experiments. To meet the objectives of this study, 7.62 mm armour-piercing ammunition was used to perforate steel armour plates at ordnance velocity. Several parameters that characterise bullet velocity and path, plate deformation and ductility were measured and used as reference data for the verification of models. Relatively complex and simple constitutive and failure models implemented in the Finite Elements (FE) code LS DYNA were used. Finally, solid Lagrange and hybrid solid/Sooth Particles Hydrodynamics (SPH) discretisation methods with detailed models of the bullet and target are presented and different findings are compared with ballistic test results. The methodology shows a significant efficiency in the assessment of the adequacy of models. In this study, stress triaxiality and strain rate based models were found to give results in good agreement with experimental results, and several physical mechanisms are well predicted.

In the field of ballistics, Johnson-Cook (JC) plasticity and fracture models have provided a good theoretical basis for the prediction of ballistic performance by capturing the essence of ductile metal fracture. Nevertheless, the JC model cannot accurately reproduce the fracture behaviour of some metals. Many Lode parameter-dependent fracture criteria have effectively improved this deficiency, indicating that the fracture loci of these metals are Lode-dependent, even though the flow stress behaviour is stress state dependent, which cannot be well characterized by the JC plasticity model. In this paper, a series of mechanical tests and parallel numerical simulations of ZK61m magnesium alloy were conducted. The results showed that the flow stress behaviour and fracture loci of the alloy were obviously Lode dependent. Therefore, it seems insufficient to evaluate only the necessity of incorporating Lode parameter into a fracture criterion in predicting ballistic performance of ZK61m magnesium alloy, and more investigations on the influence of Lode parameter on the plasticity behaviour of the material should be carried out. In the present work, ballistic tests were conducted on 5 mm thick ZK61m magnesium alloy plates using blunt and ogival nose shaped projectiles with a nominal diameter of 12.68 mm. The targets failed by shear plugging when impacted by blunt-nosed projectiles, but caused a unique failure pattern under the impact of ogival-nosed projectiles. Lode-dependent plasticity model and fracture criterion were adopted. Better prediction accuracy was observed when Lode parameter is considered in both the plasticity model and fracture criterion simultaneously.

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°.

An experimental study and hydrocode simulation was conducted to investigate the correlation between hardness of steel and the ballistic performance of steel-encapsulated SiC armour modules against long rod impact. The armour module design composed of a SiC tile in confinement within 10 mm backing and 5 mm cover plates, which were made of AISI 4340 steel with varying hardnesses between HRC 30 to 50. The armour modules were subjected to normal impact by conical tungsten alloy long rods of 8.3 mm diameter and 115 mm length, at a nominal striking velocity of 1.25 km/s. A witness block of AISI 4340 steel was placed behind the armour module to capture the residual projectile. Failure analysis of the armour modules and the measurement of residual penetration in the witness blocks were applied to characterize ballistic performance of the ceramic armour modules. The different modes of failure of the backing plate and its influence on ballistic performance of the module were verified through visual inspection of test modules and analysis of high speed videos. Hydrocode simulation of the experiments using LS-DYNA was carried out to model the penetration and failure processes that occurred in the armour modules. The Johnson Cook model was applied in simulation of the steel confinement, accounting for the influence of hardness on JC model parameters. Results showed that increasing hardness of the backing enhanced the performance of the module while cover plate hardness had no influence within the range of hardnesses tested. This study paves the way for future studies to further understand the influence of steel hardness on the ballistics performance of steel-encapsulated silicon carbide (SiC) armour modules.

We propose a theoretical interpretation of penetration data, based on partition mechanisms of the impact kinetic energy for different projectile/target combinations of metals and related alloys of interest in terminal ballistics. It is shown how the regime between the upper bound of high-velocity impact, where material strength and failure are still dominating, and the threshold of purely hydrodynamic behavior is characterized by the progressive phase transformations of projectile and target materials. Thermodynamics, impedance matching, and shock dynamics considerations allow quantifying such velocity boundaries for arbitrary impact configurations. We believe that the identification of such transition regime would support the choice of techniques and strategies in the computational modeling of metals upon impact and guide related experiments and their interpretation in such domains for ballistic applications.

A single optical fibre sensor is used to measure the dynamics of an impact. The method consists of sewing the optical fibre onto a woven Kevlar layer and placing it between the shoot pack and backing material. The measurement is accomplished by using the friction between the layer and the optical fibre to relate the optical fibre strain to impact deformation. Tests are done using a backing material of Roma Plastilina No.1 clay, and transparent ballistics gel with independent high-speed imaging. A final calculated BFD average error of 7.75% is presented as well as a timing error of 15.5% between the imaged dynamic BFD and the dynamic BFD determined by the FBG. This method is also tested at the U.S. Army Aberdeen Test Center in Maryland with a final calculated error of 7%.

To investigate the interaction mechanisms between bullets and living tissues, ballistic gelatin is used as the tissue simulant and a theoretical ballistic model is established. The drag force, the lift force and the overturning moment on the bullet are obtained based on the assumption that the pressure on the wetted area is consisted of a dynamic term and a static term. To verify the ballistic model, a non-deforming 7.62 × 39 mm rifle bullet is fired in the gelatin block. Spatial positions and orientations of the bullet are obtained through the reflective mirror system. The calculated displacements of the center of mass agree well with the experimental data. Both the yaw angles and the elevation angles of the bullet coincide well with the corresponding experimental data in the first 250 mm of penetration. As shape parameters of the bullet are integrated in the forces and in the moment in the model, the model is expected to be used in the motion predictions of different bullets.

A series of bare silicon carbide ceramic armour disks were manufactured with high-strength steel containment to induce varying magnitudes of radial pre-stress. The induced radial stresses, ranging from 0 to 900 MPa, were measured via neutron diffraction and verified by comparison with numerical calculations. Four targets of each configuration, referred to as slip-fit, moderate pre-stress, and high pre-stress, were subject to ballistic testing with hemispherical-nose, tungsten heavy alloy long rod projectiles to determine the interface defeat transition velocity. In-situ diagnostics were unsuccessful in aiding the identification of interface defeat, necessitating a reliance on post-mortem assessment. A transition velocity of approx. 1000 m/s was identified for the unstressed target, increasing to approx. 1200 m/s for the pre-stressed configurations. No performance effect was discernible between the moderate (372 MPa) and high (899 MPa) pre-stress configurations, suggesting that an optimal performance may be achieved for lower pre-stress levels (i.e.

For both ethical and practical reasons accurate tissue simulant materials are essential for ballistic testing applications. A wide variety of different materials have been previously adopted for such roles, ranging from gelatin to ballistics soap. However, while often well characterised quasi-statically, there is typically a paucity of information on the high strain-rate response of such materials in the literature. Here, building on previous studies by the authors on other tissue analogues, equation-of-state data for the elastomeric epithelial/muscular simulant material Perma-Gel ® is presented, along with results from a series of ballistic tests designed to illustrate its impact-related behaviour. Comparison of both hydrodynamic and ballistic behaviour to that of comparable epithelial tissues/analogues (Sylgard ® and porcine muscle tissue) has provided an insight into the applicability of both Perma-Gel ® and, more generally, monolithic simulants for ballistic testing purposes. Of particular note was an apparent link between the high strain-rate compressibility (evidenced in the Hugoniot relationship in the U s -u p plane) and subsequent ballistic response of these materials. Overall, work conducted in this study highlighted the importance of fully characterising tissue analogues – with particular emphasis on the requirement to understand the behaviour of such analogues under impact as part of a system as well as individually.

Reasonable simulation of the bench blasting has great significance on designing of rock blasting, and the proper consideration of blasting fragmentation size has strong influence on the simulation accuracy. This paper presents a new approach based on the three dimension Distinct Element Code (3DEC) method (Itasca Consulting Group, Inc. 2003) to model the dynamic cracking and casting process of bench blasting with reasonable consideration of blasting fragmentation size. Firstly, an equivalent blasting load consisting of the stress wave pressure and the detonation gas pressure was introduced into the 3DEC model, and it was applied on the outer boundary of blast-induced crushed zone to guarantee the simulation efficiency. Then, the whole numerical model was divided into discrete blocks by several sets of artificial joints to enable the rock to crack, fragment and cast, and at last form a muck-pile, and the artificial joints were assigned with the same mechanical parameters to rock mass itself to avoid the impact of them on stress wave propagation. Different from general discrete schemes which discretize the model with uniform blocks or random balls, the discrete size adopted in this paper gradually increases with distance from the blast source according to the Harries' model (Harries, 1973). At last, the proposed method was examined and verified by simulation of a blasting crater comparing to the field experiment, and then applied to explore the casting process of bench blasting. The simulated muck-pile profile agrees well with the result predicted by the traditional ballistics theory. The simulation also indicates that the casting distance of bench blasting increases with the bench height ( H) , but decreases with the burden distance ( W) , while the height of muck-pile increases with both the W and H . So the muck-pile profile of bench blasting is more sensitive to the W than H after consideration of rock fragmentation size, and the optimization of blasting designs can be significantly enhanced by utilizing the full capabilities of this approach.

In this study, the penetration behaviour of a Mild Steel Cored (MSC) round, 7.62 mm in diameter and 39 mm in length, commonly known as the AK47 round, was studied since it still forms an important part of the threat spectrum for personnel body armour systems. Likewise, boron carbide strike face materials were selected since this armour material is often the material of choice for ultralightweight body armour systems for protection against this particular threat. The presence of two, relatively soft, intermediate materials (the copper jacket and filler material of the bullet, and a fibre-reinforced polymer cladding layer on the ceramic) between the mild steel core and the boron carbide target was examined using reverse ballistics techniques, flash x-radiography and round recovery measurements. This was supported by selective numerical simulations using the computer code ANSYS-AUTODYN. It was found that stripping of the jacket, from the AK47 MSC rounds, makes a difference to its penetrating ability: the mild steel core is significantly reduced in length, and mass, when the jacket is not present. The magnitude of this effect is much greater than previously reported for high-strength steel-cored rounds and for tungsten carbide-cored rounds. The penetration event appears to be a twostage process: mushrooming of the mild steel core on, or near, the surface of the ceramic, followed by a linear erosion process as the core penetrates the ceramic itself. The second step has not been reported previously for MSC rounds.

The PELE ammunition is characterized by a low-density filling material surrounded by a high-density brittle jacket material. An analytical model describing the fragmentation of this ammunition behind a target plate is presented. This model assumes uniaxial strain in the filling and uses the Ranking–Hugoniot relations to calculate the material state. In addition, shock and rarefaction wave interactions at the target free surface and the filling/target interface are accounted for, as well as the radial rarefaction originating from the jacket outer surface. This allows the calculation of the pressure evolution in the filling and the radial acceleration of the jacket at any axial position along the projectile. This model aims at improving previously published analytical models where the acoustic wave approximation was used and the wave interactions were neglected. Experimental results (Paulus and Schirm, 2006) are used to validate the analytical model for different target materials (aluminum and steel), target thicknesses (3 mm and 8 mm), filling materials (polyethylene and aluminum) and impact velocities (900 m/s to 3000 m/s). A qualitative comparison based on X-ray photographs reveals similar features between the model and the experiments, such as smaller and lighter fragments with a greater radial velocity at the front of the projectile compared to the fragment characteristics at the back of the projectile. A quantitative comparison based on the maximum radial velocity of the fragments shows on average a 20% difference between the analytical and experimental results for all impact conditions considered. Despite this difference, the analytical trend follows more closely the experimental one compared to the acoustic approximation especially at high impact velocities. In addition, the acoustic approximation fails to reproduce the jacket fragmentation pattern since the fragmentation length of the jacket is significantly under-predicted. A numerical simulation is also presented using the ANSYS Autodyn 14.0 software. The results show that the numerical and analytical pressure evolution in the filling and the radial velocity of the jacket are in very good agreement, verifying the uniaxial strain assumption. This agreement (together with the experimental agreement) thus suggests that the Rankine–Hugoniot relations, the wave interactions and the radial rarefaction wave must all be included in the model to adequately describe the fragmentation of the PELE ammunition behind a thin target plate.

The ballistic performance of an ultra-high hardness armour steel (UHA) has been evaluated for a range of thicknesses and obliquities against armour piercing (AP) and fragment simulating projectiles (FSPs). Together with published literature, these results enable the effect of plate hardness on performance against both AP and FSP threats to be characterized over a range of plate hardnesses from ~ 300 to 600 HB. For AP projectiles, a complex relationship was observed that corresponded well with historical phenomenological curves describing the effect of varying projectile and armour failure mechanisms. In the ultra-high hardness regime (> 570 HB), against AP projectiles with core hardnesses of 610–745 HB (i.e. 7.62 mm APM2 and 12.7 mm APM2 projectiles), projectile shatter was demonstrated to be the controlling mechanism of armour performance. Against much softer FSPs (281 HB), where projectile shatter is not a relevant mechanism, the armour performance was found to initially decrease with increasing plate hardness up to ~ 450 HB due to increased susceptibility to adiabatic shear plugging. Above ~ 450 HB the performance was observed to plateau. The observed performance plateau appears to relate to a critical threshold for adiabatic shear failure beyond which further increases in plate hardness will not result in a decrease in performance. A number of common empirical and analytical models were applied to reproduce the experimentally-determined relationship between hardness and penetration resistance, none of which were able to qualitatively or quantitatively reproduce the observed relationships for either projectile class.

Soft-matrix ballistic laminates (such as those composed of fibres of Ultra High Molecular-Weight Polyethylene, e.g. Dyneema® HB26 and Spectra Shield) find extensive use as catching type armour syst ...

Various open-literature experimental findings pertaining to the ballistic behavior of glass are used to construct a simple, physically based, high strain-rate, high-pressure, large-strain constitutive model for this material. The basic components of the model are constructed in such a way that the model is suitable for direct incorporation into standard commercial transient non-linear dynamics finite-element based software packages like ANSYS/Autodyn [ANSYS/Autodyn version 11.0, User documentation, Century Dynamics Inc. a subsidiary of ANSYS Inc.; 2007.] or ABAQUS/Explicit [ABAQUS version 6.7, User documentation, Dessault systems, 2007.]. To validate the material model, a set of finite element analyses of the Edge-on-Impact (EOI) tests is carried out and the results compared with their experimental counterparts obtained in the recent work of Strassburger et al. [Strassburger E, Patel P, McCauley JW, Kovalchick C, Ramesh KT, Templeton DW. High-speed transmission shadowgraphic and dynamic photoelasticity study of stress wave and impact damage propagation in transparent materials and laminates using the edge-on impact method. In: Proceedings of the twenty-third international symposium on ballistics. Spain: April 2007, and Strassburger E, Patel P, McCauley W, Templeton DW. Visualization of wave propagation and impact damage in a polycrystalline transparent ceramic-AlON. In: Proceedings of the twenty-second international symposium on ballistics. Vancouver, Canada: November 2005.]. Overall, a good agreement is found between the computational and the experimental results pertaining to: (a) the front-shapes and propagation velocities of the longitudinal and transverse waves generated in the target during impact; (b) the front-shapes and propagation velocities of the “coherent-damage” zone (a zone surrounding the projectile/target contact surface which consists of numerous micron- and sub-micron-size cracks); and (c) the formation of “crack centers”, i.e. isolated cracks nucleated ahead of the advancing coherent-damage zone front. Relatively minor discrepancies between the computational and the experimental results are attributed to the effects of damage-promoting target-fixturing induced stresses and cutting/grinding-induced flaws located along the narrow faces of the target and the surrounding regions.

Summary Investigations are conducted at ISL on new hypervelocity launchers to fulfill requirements in different fields of ballistics such as launching dynamics, aeroballistics, terminal ballistics, aerothermodynamics, and supersonic combustion studies. One objective considered is to determine the operational conditions to accelerate a 90mm-caliber projectile with a mass of ~1.5kg to a velocity of 3km/s while keeping the acceleration level below 40,000g. This moderate level of acceleration is required to investigate at high velocities models that are fragile because of their design and/or their onboard opto-electronical equipments. A means to fulfill these velocity and acceleration requirements is ram-accelerator technology. This paper presents research conducted at ISL with smooth-bore ram-accelerators in the thermally choked propulsion mode. Therefore, two accelerators in calibers 30 and 90mm respectively, operated within the launch room of the aeroballistic range facility are described. Experimental results are presented describing the two-fold strategy followed to achieve the maximum performance, i.e., optimization of the projectile configuration and optimization of the combustible gas mixtures. To date a maximum velocity of about 1985m/s has been achieved with the 90mm accelerator (projectile mass = 1.34kg, ram-section length 16.2m, injection velocity in the ram-section 1330m/s) and 2380m/s with the 30mm accelerator (projectile mass 68.6g, ram-section length 9m, injection velocity in the ram-section = 1380m/s). Potential applications of ram-accelerators for ballistic studies are discussed and performances compared to those of conventional launchers that are currently used at ISL for ballistic studies. Finally, very first preliminary experiments are presented describing the acceleration of high l/d rods using a ram-accelerator.

© 2015 Elsevier Ltd. All rights reserved. The impact response of an ultrahigh molecular weight polyethylene (UHMWPE) fiber reinforced polymer matrix composite laminate has been investigated. The laminate encapsulated an aluminum alloy sandwich panel whose corrugated core was filled with prismatic alumina inserts. The laminate encased hybrid core target could sustain ceramic prism base impacts by a spherical, 12.7 mm diameter steel projectile with velocities in excess of 2.7 km s-1. This was 150% higher than the ballistic limit of an equal areal density, similarly encapsulated aluminum plate target. By contrast, when the projectile impacted a hybrid core target at the apex of a ceramic prism insert, failure of the UHMWPE laminate on the rear face occurred at a lower impact velocity. High-speed imaging, three-dimensional digital image correlation and x-ray tomography measurements are used to show that upon impact the projectile and the ceramic insert fragment. These fragments then load the UHMWPE laminate on the rear face with a significantly reduced pressure compared to the impact pressure of the projectile on the front surface of the target. The loading area on the inner surface of the rear laminate was highest for a prism base impact and lowest for a prism apex impact. The inability to penetrate the rear laminate of the base impacted samples is consistent with the recent identification of an impact pressure controlled mechanism of progressive penetration in this class of laminate.

The mechanisms of progressive penetration for two ultrahigh molecular weight polyethylene (UHMWPE) reinforced laminates have been investigated. One used an UHMWPE fiber reinforcement while the other utilized molecularly aligned tape. Both materials had similar out of plane compressive strengths, but the fiber system had a 40% higher in plane tensile strength than the tape. Laminated, 6 mm thick plates with a [0°/90°] ply architecture were impacted by a 12.7 mm diameter sphere under conditions that either allowed out of plane plate deflection or eliminated this deflection by rear support of the target. The depth of penetration and the ballistic limit in the rear-supported tests were identical for the two materials, and proceeded by progressive ply failure. However, tests in the edge clamped condition resulted in a substantially higher penetration resistance, especially for the higher tensile strength fiber-reinforced material. Edge clamped testing of a bilayer target, where the front third was composed of the tape material and the remainder comprised fiber reinforced laminate, had the same ballistic limit as a target composed of only the higher ply tensile strength fiber reinforced material. Penetration in both test support conditions was discovered to occur by tensile ply rupture under the projectile, consistent with a recently proposed mechanism for converting out of plane compression to in plane ply tension. Lateral displacement of plies was also observed near the sides of impact craters in both materials, indicating the existence of a second mechanism impeding penetration of the spherical shaped projectile.

The ballistic performance of thick ultra-high molecular weight polyethylene (UHMW-PE) composite was experimentally determined for panel thicknesses ranging from 9 mm to 100 mm against 12.7 mm and 20 mm calibre fragment simulating projectiles (FSPs). Thin panels (∼

Composite laminates made of glass/epoxy with and without nano fillers were subjected to projectile impact. The laminates of different thicknesses were prepared by hand lay-up and compression molding processes. Laminates were made from glass woven roving mats of 610 gsm, epoxy resin and nano clay of 1-5 wt.% of matrix. A piston type gas gun setup was used to impact a spherical nose projectile of diameter 9.5 mm and mass of 7.6 g, on the nanocomposite laminates at impact velocities in the range of their ballistic limit and above. The energy absorbed during penetration and ballistic limit of the nanocomposite laminates were studied both experimentally and analytically. The analytical model also predicts the energy absorbed in various failure modes due to tensile failure of primary fibers, deformation of secondary fibers, delamination and matrix crack. Mechanical properties like tensile modulus, stress-strain function, shear modulus, and strain energy release rate were used as input to the analytical model. Laminates of three, five and eight layers have been considered for the analysis. The effect of clay dispersion in the matrix for different failure modes is discussed. Ballistic limit obtained from the model is validated with experimental results and good agreement is found. � 2014 Elsevier Ltd. All rights reserved.

Classical, one-dimensional theory of hydrodynamic penetration is used as the basis of establishing simplified analytical relationships describing energy, momentum, and power deposition during hypervelocity impact events. A concise overview of the 1-D model is given followed by a select grouping of terms into relationships that offer first-order criteria for making engineering design considerations on relevant applications and assist in the analysis of experimental observations. Momentum, energy, and power deposition are found to be proportional to second, third and fourth power exponents, respectively. These analytical terms are presented for constant velocity gradient, i.e. fixed length, rods as well as linear velocity gradient rods, such as shaped charge jets. The role of penetrator-to-target density ratio is then examined in terms of the backflow, or reverse flow of 1-D penetration. Again, the non-dimensional ratio of penetrator-to-target mass density is used to compare the relative velocity of material flow during penetration. The relationship highlights the role of penetrator materials for achieving desired effects in these hypervelocity, terminal ballistics events. Albeit the relationships are derived on the assumptions for hydrodynamic processes, their generality of form and ease of implementation make them a useful first-order description for engineering insight and application over a broad range of velocities.

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.

Helmet designs have evolved over the last three millennia and the use of helmet may be as old as warfare itself. In 600 B.C. the Greeks in Sparta crafted single-piece helmet from bronze, which provided complete head protection, leaving only narrow slits in front for vision and for ventilation. Later in 250 B.C. the Romans developed several helmet designs, which included the round legionary's helmet and the gladiator's helmet, with broad brim and pierced visor, providing exceptional head, face and neck protection. The use of helmets in battle fields continued until the end of 13th century, which signaled a radical change in the emphasis on head protection. With the invention of gunpowder and the growing effectiveness of firearms over swords and spears, helmets gradually vanished from the battle scenes. The metal helmet that once protected against sword and arrows offers little protection against musket rounds. The United States Civil War provides an excellent illustration—in war soldiers donned cloth hats and caps, with little or no emphasis on head protection. In World War I, the helmet was reintroduced because it protected the head against metal-fragments of exploding artillery shells and indirect fire. The French, owing to General Adrian, were the first to adopt the helmet as standard equipment in early 1915. The British, the Germans, and then the rest of Europe soon followed. In World War I, the German helmet provided the best protection for soldiers. It was manufactured in at least two sizes, and different head contours were accommodated by an adjustable leather lining, which provided comfort and allowed for ventilation. The typical helmet used during that period was a hardened steel shell with an inner liner and weighed about 0.5–1.8 kg. Since then, helmets have been issued to troops in all military conflicts, marking the beginning of the development of modern military helmet. This paper presents the results from experiments and AUTODYN-3D® simulations on the ballistic impact of a KEVLAR® helmet. In the experiment, spherical projectile (~11.9 g), launched from a light gas gun, strikes the helmet with an impact velocity of 205 m/s. The interaction of the projectile with the KEVLAR® helmet is captured using high-speed photography. This helmet-projectile interaction is compared with that obtained from the AUTODYN-3D® simulation. Post-test damage photos from the experiments are also compared with those from the simulations. The response of the helmet from the simulations is consistent with those from the experiments. Also included in this paper are AUTODYN-3D® simulations on two ballistics test standards for KEVLAR® helmets. They are namely the NIJ-STD-0106.01 Type II and the V50 requirement of the US military specification for Personal Armor System Ground Troops (PASGT) Helmet, MIL-H-44099A. For the simulation on MIL-H-44099A, a fragment-simulating projectile (FSP) strikes the helmet with an impact velocity of 610 m/s. The simulation revealed that an impact velocity above 610 m/s is required to perforate the KEVLAR® helmet. For the simulation on NIJ-STD-0106.01 Type II helmet, the projectile is a 9 mm full-jacketed bullet with a striking velocity of 358 m/s. Results from the simulation show that the KEVLAR® helmet is able to defeat a 9 mm full-jacketed bullet traveling at 358 m/s.

The paper describes a series of 2D numerical simulations which followed the cavity expansion process in an elasto- plastic solid. The results from these simulations, in terms of cavity wall motion as a function of the applied pressures inside the cavity, highlighted several issues concerning cavity expansion process and the terminal ballistics of both rigid and eroding long rods. These issues include the form of the relation between the dynamic radial stress on the cavity wall and its velocity, which can be written in a simple, normalized form, at least for the materials we simulated here. Also, the difference between target resistance to the penetration of rigid and eroding-rod penetration, was quantified with a series of simulations in which the pressures in the cavity were applied on an angular section, rather than on its whole surface. Finally, we explored the inherent differences between spherical and cylindrical cavity expansion processes, which can be helpful for analytical models of the penetration of rigid rods with different nose shapes.

The mechanisms of projectile penetration of extruded 6061T6 aluminum alloy sandwich panels with empty and alumina filled, triangular corrugated cores have been experimentally investigated using zero obliquity, 12.7 mm diameter hard steel projectiles whose diameter was about a half that of the core's unit cell width. We find that low momentum impacts are laterally deflected by interactions with the inclined webs of the empty core. Complete penetration occurred by shear-off within the impacted front face sheet, followed by stretching, bending and tensile fracture of the core webs and finally shear-off within the back face sheet. This combination of mechanisms was less effective at dissipating the projectiles kinetic energy than the shear-off (plugging) mechanism of penetration of the equivalent solid aluminum panel. Inserting ballistic grade alumina prisms in the triangular cross section spaces of the corrugated core significantly increased the panel's ballistic resistance compared to the empty panel. The presence of the hard ceramic led to severe plastic deformation and fragmentation of the projectile and comminution and macroscopic fracture of the ceramic. The Al/Al2O3 hybrid panel ballistic limit was reached when pairs of parallel cracks formed in the rear face sheet at core web-face sheet nodes. The separation distance between these cracks was dependent upon the location of the impact with respect to that of the web-face sheet nodes. Nodal impacts resulted in pairs of fractures that were separated by one cell width and a critical velocity below that of the equivalent solid plate. Impacts mid-way between pairs of nodes resulted in back face sheet crack pairs separated by twice the cell width, and a critical velocity higher than the equivalent solid plate. Using X-ray tomography we show this resulted from the formation of oval (not circular) cross section fracture conoids in the ceramics. The conoid angle was about 60° in the extrusion direction but only 30° in the transverse direction. This observation may have interesting consequences for a panel's resistance to a second, close proximity impact.

The ability to destroy the key assets of an enemy is an important goal of an attacking force and requires an agile and adaptable military capability effective against a number of very different threats. In ballistics, this contributes to an interest in moving to higher projectile velocities to benefit from the potential to increase the range of a projectile. It also generates an interest in the study of the benefits of increased kinetic energy that can be delivered to a target. The paper describes the work to produce a projectile design solution under certain constraints but with an impact velocity of about 2 km s −1 , good in-bore and in-flight stability and acceptable retardation at the target. The paper shows that a projectile with these characteristics was achieved with a projectile mass of 8.1 kg. The second phase of the research programme was concerned with building a hollow aluminium carrier shell. The paper describes the research to assess the integrity and stability of the projectile under gun launch conditions, to demonstrate acceptable dispersion and impact yaw at the target and to demonstrate a minimum impact velocity of 2.1 km s −1 .

The Sandia Hypervelocity Launcher (HVL) uses impact techniques on a two-stage light-gas gun to launch flier plates to velocities in excess of 10 km/s. An important problem in designing successful third stage techniques for impact launching fliers to such velocities is detailed understanding of the interior ballistic performance of the third stage. This is crucial for preventing melt and fracture of the flier plates during the extraordinary accelerations that they undergo (accelerations on the order of 10{sup 9} g are typical on the HVL). We seek to optimize HVL launch conditions in order to achieve two major goals: first, to maximize the potential launch velocity for a given flier, and second, to allow different flier configurations. One tool that we can apply in studying HVL performance is the use of multi-dimensional wave propagation codes. We have used such codes, particularly the Sandia Eulerian code CTH, to study a variety of interior ballistics issues related to gun performance and launcher development for almost ten years. Recently this work has culminated in a major contribution to HVL design, namely the capability to launch ``chunk`` fliers. `Me initial phases of design development were solely devoted to CTH computations that studied potential designs, identifiedmore » problems, and posed possible solutions for launching chunk fliers on the HVL. Our computations sufficiently narrowed the design space to the point that systematic experimental progress was possible. Our first experiment resulted in the successful launch of an intact 0.33 gram titanium alloy chunk flier to a velocity of 10.2 km/s. The thickness to diameter ratio of this flier was approximately 0.5.« less

On the occasion of the Distinguished Scientist Award presentation at HVIS 1992, the technical and scientific promotion of the Impact Physics Division at EMI in the field of aeroballistics, free flight dynamics, terminal ballistics and impact physics is described. This development is closely related to the work of the recipients. The activities began in the late fifties when a small pressurized ballistic range with a gas gun was built. The problems to construct a well working facility with observation stations are reported that arose, at those early times, from the lack of experience, money and suitable locations. In the mid-sixties, the experimental possibilities were extended by building a two-stage light gas gun that could also be used as a gun tunnel. These facilities have been the foundation for research in the field of free flight aerodynamics, such as the study of near and far wakes behind a blunt hypersonic body or the study of shock wave boundary layer interactions. In 1972, the division took the first step into terminal ballistics and, because of increasing interest, impact physics became the main research area. The division grew and with it the instrumentation. Today, diverse gas guns, powder guns and two-stage light gas guns are in operation. One topic of main interest during the years has been the penetration of rod shaped projectiles. Here the best-known result may be mentioned, the so-called ‘Hohler-Stilp S-shaped penetration curves’. In addition to this, many other topics have been investigated that can be summarized under the title “penetration mechanics and impact physics”. Based on a well developed launching technique and instrumentation, problems were investigated at low velocities of a few hundred m/s, at ordnance velocities and especially at hypervelocities up to 10 km/s. It has been recognized that dynamic material behavior and microstructural effects play an important role in understanding the interaction of projectiles with targets. Therefore, a VISAR, an electronic raster microscope, a Hopkinson bar and further equipment have been installed. Basing on the work of a period of more than 20 years, EMI has come into contact with national and foreign institutions and has become a partner for many cooperations.

High-speed metal-on-metal sliding experiments have shown unique tribological phenomena. Dominant surface modification occurs in the form of teardrop-shaped craters (gouges). Gouges on rocket sled tracks and electromagnetic (EM) launcher rails are the best known cases of steel-on-steel and aluminum-on-copper sliding damages, respectively. We have shown here that severe gouging is produced during hypervelocity sliding between long rods and target material in reverse ballistics experiments. This is the first reported gouging in a non-planar geometry. Nevertheless, the gouges produced are strikingly similar to those found in planar experiments. In this paper, we also present our analysis of gouges caused in a tungsten-steel system due to hypervelocity sliding. The gouges so produced were examined to establish the underlying tribological and fractographic behavior. We found that gouging provides an efficient mode of material removal and a probable cause for fracture. A numerical simulation of plate target interaction with a long rod possessing a gouge indicates that the gouge can indeed lead to fracture and subsequent performance degradation of the penetrator.

The Walker–Anderson and Ravid–Bodner analytical models for penetration of projectiles in metallic plates are well known in the ballistics community. The Walker–Anderson model uses the centerline momentum balance in the projectile and target to calculate the penetration history into a semi-infinite medium, while the Ravid–Bodner model uses the upper bound theorem of plasticity theory modified to include dynamic effects. The Ravid–Bodner model also includes a rich selection of failure modes suitable for finite-thick metallic targets. In this paper a blended model is presented: momentum balance is used to calculate the semi-infinite portion penetration (before the back of the target plate begins to flow), and the Ravid–Bodner failure modes are used to determine projectile perforation. In addition, the model has been extended to handle multiple plate impact. Numerical simulations show that after target failure the projectile still continues to erode for some microseconds. This time has been estimated and incorporated into the model. Examples are presented for long-rod projectiles against thick and spaced-plate targets backed by a witness pack that is separated from the main target element(s) by an air gap. Agreement with results from numerical simulations is quite good.

New ballistics equations for long rods penetrating both elastic-plastic and brittle materials are proposed which generalize the well-known Alekseevskii-Tate equations. These equations are derived from the basis of the Lagrange-Cauchy integral for equations of nonstationary irrotational motion of ideal fluids, as well as the equations of the dynamics of expansion of a spherical cavity. Their solutions determine both the translational movement of the penetrator and the dynamics of cavity formation in the target. The structure of the equations is sufficiently simple for analysis and solution. The calculations demonstrate good qualitative agreement of the theoretical predictions with the experimental data.

This article examines whether the yield surface of silicon carbide depends on the third invariant of the stress tensor, and how such dependence would affect its performance as an armor material. The JHB ceramic model is augmented by a factor introduced for geomaterials that depends on the third invariant of stress and the tri-axial yield ratio (a material parameter defined as yield in tri-axial extension to yield in tri-axial compression.) The factor scales yield on the compressive meridian for other states of stress. Tests of high-velocity impacts of silicon carbide are selected from the literature, and computations are performed with the augmented model using several values of the tri-axial yield ratio. The sensitivity of the computations to the variation of the tri-axial yield ratio is determined for each test. Compressive plate impacts and ballistic impacts of thin targets show the most sensitivity, and comparison of the computed compressive plate impacts to test results suggests a significant dependence on the third invariant.

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.

Normal and oblique impact on 20 mm thick AA6082-T4 aluminium plates are studied both experimentally and numerically. Two types of small arms bullets were used in the ballistic tests, namely the 7.62 × 63 mm NATO Ball (with a soft lead core) and the 7.62 × 63 mm APM2 (with a hard steel core), fired from a long smooth-bore Mauser rifle. The targets were struck at 0°, 15°, 30°, 45° and 60° obliquity, and the impact velocity was about 830 m/s in all tests. During testing, the initial and residual bullet velocities were measured by various laser-based optical devices, and high-speed video cameras were used to photograph the penetration process. Of special interest is the critical oblique angle at which the penetration process changes from perforation to embedment or ricochet. The results show that the critical oblique angle was less than 60° for both bullet types. A material test programme was also conducted for the AA6082-T4 plate to calibrate a modified Johnson–Cook constitutive relation and the Cockcroft–Latham failure criterion, while material data for the bullets mainly were taken from the literature. 3D non-linear FE simulations with detailed models of the bullets were finally run. Good agreement between the FE simulations and the experimental results for the APM2 bullets was in general obtained, while it was more difficult to get reliable FE results for the soft core Ball bullets.

Whipple shields were first proposed as a means of protecting spacecraft from the impact of micrometeoroids in 1947 [1] and are currently in use as micrometeoroid and orbital debris shields on modern spacecraft. In the intervening years, the function of the thin bumper used to shatter or melt threatening particles has been augmented and enhanced by the use of various types and configurations of intermediate layers of various materials. All shield designs serve to minimize the threat of a spall failure or perforation of the main wall of the spacecraft as a result of the impact of the fragments. With increasing use of Whipple shields, various ballistic limit equations (BLEs) for guiding the design and estimating the performance of shield systems have been developed. Perhaps the best known and most used are the "new" modified Cour-Palais (Christiansen) equations [2]. These equations address the three phases of impact: (1) ballistic ( 7 km/s), where the projectile melts or vaporizes at impact. The performance of Whipple shields and the adequacy of the BLEs have been examined for the first two phases using the results of impact tests obtained from two-stage, light-gas gun test firings. Shield performance and the adequacy of the BLEs has not been evaluated in the melt/vaporization phase until now because of the limitations of launchers used to accelerate projectiles with controlled properties to velocities above 7.5 km/s. A three-stage, light-gas gun, developed at the University of Dayton Research Institute (UDRI) [3], is capable of launching small, aluminum spheres to velocities above 9 km/s. This launcher was used to evaluate the ballistic performance of two Whipple shield systems, various thermal protection system materials, and other spacecraft-related materials to the impact of 1.6-mm- to 2.6-mm-diameter, 2017-T4 aluminum spheres at impact velocities ranging from 8.91 km/s to 9.28 km/s. Test results, details of the shield systems, and nominal ballistic limits for the two Whipple shields are shown in Figures 1 and 2.

Blast mitigation seats have been employed in armored vehicles to protect occupants from injuries caused by improvised explosive devices (IEDs). Currently, there exist no standard experimental evaluation methods that can be used to fully assess the protection capability of a particular seat design. For historical reasons, drop-towers have been used extensively for such purpose, as a repeatable laboratory method with some limitations. In this paper, the authors developed analytical models to study the difference between results obtained from a drop tower test and those from actual blast events. It was found that the selection of the test method had a significant effect on the results. In particular, it was found that the drop-tower methodology can often overestimate the performance of blast mitigation seats, which can result in the fielding of sub-optimal solutions for the protection of occupants.

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.

A new technique using nickel–chromium wire, called the NiCr (Nichrome®) wire technique, has been presented in a first paper describing the technique [1]. This second paper focuses on the results obtained when this new technique is applied to ballistic fabrics. Strain distributions on the layer impacted, as well as in different layers, are presented. An energy balance based on the strains is shown to provide reasonable values for the elastic energy stored by the yarns. Failure times of the first layer as a function of impact velocity are discussed and a simple momentum balance is shown to predict well the deflection history of the fabric. Ultra-high-speed photography and high-speed videos allowed recording of fabric deflection vs. time. The combination of the four diagnostic techniques, including X-rays, delivers a very complete picture of the impact mechanics in fabrics, both for early-time and late-time phenomena.

This is the first of two papers that describe a new technique to measure yarn strains in a fabric subjected to ballistic impact. The main objective of this research was to develop the Nickel–Chromium (NiCr) wire technique, although other diagnostic techniques were used simultaneously (X-rays, high-speed video, and ultra-high-speed photography), to support interpretation of results. The NiCr wire principle, calibration, assumptions and test set-up are thoroughly explained. The NiCr wire is then applied to impact on real targets and the results are analyzed. A few examples of strain measurements are shown. It is shown that the NiCr wire signals are very rich in information and can give, not only the strains, but also reveal if the fabric was perforated and how long it took to fail.

An experimental study was made of the pressures generated by a single hydrodynamic ram event. A generic box type fuel tank simulator was fabricated to study the phenomenon and was capable of containing 3785.4 l of liquid thereby isolating the phases of the event from tank wall reflections, and enable separation of the effects of each phase. Tungsten, steel, and aluminum spherical projectiles were fired into the tank and the result was measured using high-speed pressure transducers, which were located throughout the tank, and compared to the pressure waves and events recorded inside the tank simulator with a high-speed video. It was determined that a high-pressure initial wave is generated at impact and is followed by the more gradual drag pressure around the projectile. The angular distribution of the initial wave and the variation with distance were investigated along with the effect of projectile mass on the drag pressure. This region of pressure decreases in the projectile wake, forming a trailing cavity that remains at a low pressure until the cavity begins to collapse. This results in the largest recorded pressure inside the simulator.

In the first part of the paper [Naik D, Sankaran S, Mobasher B, Rajan SD, Pereira M. Development of reliable modeling methodologies for fan blade-out containment analysis. Part I: experimental studies. Int J Impact Eng, in press], details of the experiments to characterize the behavior of dry fabrics including Kevlar®49, and ballistic tests involving the fabric were presented. In this second part of the paper, we discuss the development and verification of a constitutive model for dry fabrics for use in an explicit finite element program. The developed constitutive model is implemented as a user-defined subroutine in LS-DYNA, a commercial finite element program. It is then used to simulate a suite of ballistic tests [Naik D, Sankaran S, Mobasher B, Rajan SD, Pereira M. Development of reliable modeling methodologies for fan blade-out containment analysis. Part I: experimental studies. Int J Impact Eng, in press] that replicate conditions seen in an engine fan blade out (FBO) event. A qualitative and quantitative comparison of the deformation shape of the fabric containment system and a quantitative comparison of the absorbed energy are carried out. Results indicate that the developed constitutive model provides a very encouraging start in modeling these high-speed events and could provide as Federal Aviation Administration (FAA) desires, an attractive complement to full-scale engine FBO tests.