A computational study of the influence of projectile strength on the performance of long-rod penetrators

Two-dimensional numerical simulations were used to explore the penetration capability of long-rods as a function of their strength. Tungsten alloy rods of varying strengths were ‘shot’ at semi-infinite armor steel targets in the velocity range of 1.4–2.2 km/s. It is found that penetration depths versus penetrator strength curves have a maximum which depends on the impact velocity. This effect which, to our best knowledge, has not been reported previously can be explained, at least qualitatively, by considering the deceleration of the rear part of the rod, as its strength increases. This deceleration can lead to a substantial decrease in the velocity of the rear part of the penetrator with the result that its penetration capability is reduced beyond that of a nondecelerating penetrator. The deceleration is a direct consequence of the elastic waves travelling along the back part of the rod with an amplitude which is equal to the strength of the penetrator material.     

On the optimal performance of long-rod penetrators subjected to transverse accelerations

The paper deals with theoretical considerations on the conception and optimization of long-rod penetrators with regard to bending strain and penetration efficiency. In a first step we describe a method allowing to design long penetrators in such a manner that given values of bending stress and deflection are met if the rods are subjected to lateral forces. On the assumption of a constant lateral acceleration this results in rods with various dimensions; the aspect ratio remarkably does not remain constant. Then these penetrators are examined for maximum penetration efficiency while considering rods of equal energy. For the case studied the procedure results in an optimum velocity of about 2700 m/s. This demonstrates a fundamental difference in comparison to the optimization process with L/D-scaled penetrators where a much lower optimum velocity (2300 m/s) is obtained. In comparison to the reference penetrator (L/D=34, V=1800 m/s) the optimum penetrator — still at constant stress level and at an impact velocity of 2700 m/s — has of course a reduced mass, but also a reduced length and diameter showing an aspect ratio of 40. The perforation power could be increased by some 17%. On the other hand, the linearly scaled penetrator at constant energy only shows an increase of about 7% in penetration capability if the impact velocity reaches its optimum value at 2300 m/s. The optimization procedure of the energy-efficient penetration of constant-stress projectiles leads to an optimal velocity well in the hypervelocity regime. Furthermore, the special design of the penetrators with constant stress level results in a gain of penetration efficiency.     

A computational study of the influence of thermal softening on ballistic penetration in metals

A two-dimensional axisymmetric computational study of the penetration of a tungsten heavy alloy (WHA) rod into a 6061-T6 aluminum target has been performed using a Lagrangian formulation. Adaptive remeshing has been used to alleviate the problem of excessive distortion of elements which occurs during large deformation studies (such as ballistic penetration). Strain hardening, strain-rate hardening and thermal softening in both the penetrator and target materials are taken into full consideration. The computed depth of penetration (DOP), residual penetrator length and maximum crater diameter match very well the experimental results reported by Yadav and Ravichandran (Int. J. Impact Eng., Submitted for publication) for an impact velocity of 1100 m/s. Computer simulations reveal that in the absence of failure mechanisms (such as shear banding), introduction of thermal softening in the penetrator material decreases its depth of penetration in a metal target, when compared to a penetrator material which does not soften thermally. These results are in contrast to the recent work of Rosenberg and Dekel (Int. J. Impact Eng. 21 (1998) 283–296) and a plausible explanation for this discrepancy is presented.     

On relations between geometries of microcontact clusters and their overall properties

Interaction between contacts in a cluster produces major effect on compliance of an interface between contacting surfaces and its thermal/electrical resistance. Several methods have been developed to account for this effect. Probably the easiest one [J.A. Greenwood, Constriction resistance and the real area of contact, Br. J. Appl. Phys. 17 (1966) 1621-1622] operates with Holm’s radius - microstructural parameter having the dimension of length. Being introduced in the context of electrical conductance, this parameter may be used in the compliance problem as well due to cross-property connection between the two properties. The present paper focuses on relating Holm’s radius to cluster geometry. Explicit formulas are derived and illustrated on several examples. The obtained results allow one to estimate the effect of interaction between individual contact spots directly from the cluster image.     

Geometry,mechanical and ballistic properties of ADI material perforated plates

In this paper, austempered ductile iron has been evaluated as an alternative to steel for perforated plates applied in the ballistic protection of military vehicles. The austempering was performed in lower and higher austempering ranges in order to obtain two types of austempered ductile iron: one with a higher strength, and the other with a higher ductility. Perforated plates having two different thicknesses of 7 and 9 mm were mounted in front of basic armour and 12.7 × 99 mm armour – piercing incendiary ammunition was fired from 100 m. It was shown that the austempered ductile iron material austempered at a lower temperature has superior ballistic resistance, providing a full (five out of five armour – piercing incendiary shots stopped) ballistic resistance if combined with 13 mm basic armour plate. The thicker austempered ductile iron perforated plate provides more significant penetrating core damage, and therefore, lower basic plate damage. On the other hand, the thinner austempered ductile iron material perforated plate can be considered optimal due to its lower weight and higher mass effectiveness. In austempered ductile iron material austempered at a higher temperature, besides a lower hardness, bulk retained low-carbon metastable austenite transforms into martensite through strain induced mechanism, causing a partial brittle fracture.     

Analytical relations between effective material properties and microporosity: Application to bone mechanics

This work deals with the problem of reconstruction of microstructural parameters of viscoelastic composite material from measurements of its effective properties. The Stieltjes representation of the effective shear complex modulus of two-component composite material is exploited to recover information about structural parameters. This representation is derived from problem of torsion of a heterogeneous cylinder using asymptotic expansions method. The microstructural information is contained in the spectral measure in this analytical representation. The spectral function can be recovered from the measurements over a range of frequencies. The problem of reconstruction of the spectral measure is very ill-posed. Regularized algorithm is derived to ensure stability of the results. We apply the proposed method to recovery of porosity of cancellous bone from measurements of its effective shear modulus. Bone is modeled as a medium with a microstructure composed of two viscoelastic isotropic or/and transversely isotropic materials, with the components representing trabeculae (elastic component) and bone marrow (viscoelastic component). Porosity is understood as volume fraction of bone marrow. To verify the approach we apply it to analytically and numerically simulated response of a cylinder filled with a composite material with hexagonal microstructure. The proposed method does not use any specific assumptions about the microgeometry of the composite and is applicable to any two-phase composite medium.     

Modeling the effects of yarn material properties and friction on the ballistic impact of a plain-weave fabric

Impact of a rigid sphere onto a high-strength plain-weave Kevlar KM2^® fabric was modeled using LS–DYNA^® focusing on the influence of friction and material properties on ballistic performance. Quasi-static friction was experimentally determined and incorporated into the model. Two clamped edges and two free edges were used as boundary conditions to correlate the model to an experimental test providing yarn–yarn movement. Yarns were modeled as continua with modulus and strength dominating along the length. Parametric studies incorporating different yarn material properties and initial projectile velocities were then performed with the above set of boundary conditions. Results indicate that ballistic performance depends upon friction, elastic modulus and strength of the yarns. While friction improves ballistic performance by maintaining the integrity of the weave pattern, material properties of the yarns have a significant influence on the effect of friction. It is shown that fabrics comprised of yarns characterized by higher stiffness and strength relative to the baseline Kevlar KM2^®, exhibited a stronger influence on ballistic performance. Therefore all three parameters viz., friction, elastic modulus and strength along with other variables (fabric architecture, boundary conditions, and projectile parameters) are needed to examine ballistic performance of high-strength fabric structures.     

A note on the deformation of conical penetrators

Conical penetrators have been shown to give enhanced penetration over flat-ended projectiles up to a certain transition velocity. This transition velocity was found to be associated with a separation of the conical nose from the penetrator body which caused the penetrator to revert to the behaviour of a flat-ended penetrator at higher velocities. An explanation of the marked deformation resistance of the conical noses of these penetrators is presented.     

Aspects of the computational testing of the mechanical properties of microheterogeneous material samples

In this paper we investigate topics related to the numerical simulation of the testing of mechanical responses of samples of microheterogeneous solid material. Consistent with what is produced in dispersion manufacturing methods, the microstructures considered are generated by randomly distributing aggregates of particulate material throughout an otherwise homogeneous matrix material. Therefore, the resulting microstructures are irregular and non‐periodic. A primary problem in testing such materials is the fact that only finite‐sized samples can be tested, leading to no single response, but a distribution of responses. In this work, a technique employing potential energy principles is presented to interpret the results of testing groups of samples. Three‐dimensional numerical examples employing the finite element method are given to illustrate the overall analysis and computational testing process. Copyright © 2001 John Wiley & Sons, Ltd.     

An experimental study on ballistic performance of boron carbide tiles

Boron carbide is an attractive candidate for use as armour material because of its lower density combined with high hardness. The ballistic performance of boron carbide tiles were evaluated using standard Depth of Penetration (DOP) test method against hard steel 7.62 mm armour piercing (AP) projectiles. The effect of variation in thickness of tile and the projectile velocity on the ballistic efficiency of the material was studied. It has been found that the differential efficiency factor (DEF) increases with increase in projectile velocity from 600 to 820 m/s. And an insignificant or marginal increase in efficiency was observed for increase in tile thickness from 5.2 mm up to 7.3 mm. The effect of the type of radial confinement on the residual DOP was also studied. It was found that the steel radial confinement produces lower residual DOP values compared to aluminium alloy and with no radial confinement. Results along with photographs have been presented.     

A numerical study of the cavity expansion process and its application to long-rod penetration mechanics

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.     

On the ballistic performance of metallic materials

The paper presents a ballistic performance index for metallic armour materials in terms of the commonly determined mechanical properties such as strength and modulus. The index is derived using an energy-balance approach, where the kinetic energy of the projectile is assumed to be absorbed by the elastic and the plastic deformation involved in the penetration process as well as the kinetic energy imparted to the target material during deformation. The derivation assumes two distinct stages to exist during the penetration of the projectile. At the striking face of the armour, the material is assumed to flow radially in a constrained deformation region but longitudinally at the rear surface leading to typically observed bulging of the armour without constraint. The index is validated using the available experimental and empirical data obtained in the case of small arm projectiles for an impact velocity of about 800 m/sec. This index is expected to facilitate the development of metallic armour, since the number of the ballistic experiments can be reduced significantly and only the promising materials need to be considered.     

Effect of cold rolling on mechanical properties and ballistic performance of nitrogen-alloyed austenitic steels

In this paper, the effects of different amount of cold rolling on mechanical properties, microstructure and ballistic resistance of nitrogen containing austenitic stainless steel in two different conditions have been presented. The ballistic performance was measured in terms of energy absorption against deformable projectiles. It is found that increased percentage of cold reduction increases the strength and hardness with loss of ductility and decreases the energy absorption of material. The nature of failures and damages of the targets has been studied and also the microstructural characterization has been carried out.     

A numerical investigation into the influence of fabric construction on ballistic performance

The use of high-performance fibres has made it possible to produce lightweight and strong personal body armour. Parallel to the creation and use of new fibres, fabric construction also plays an essential role for performance improvement. In this research, finite element (FE) models were built up and used to predict the response of woven fabrics with different structural parameters, including fabric structure, thread density of the fabric and yarn linear density. The research confirmed that the plain woven fabric exhibits superior energy absorption over other structures in a ballistic event by absorbing 34% more impact energy than the fabric made from 7-end satin weave. This could be explained that the maximum interlacing points in this fabric which help transmit stress to a larger fabric area, enabling more secondary yarns to be involved for energy dissipation. It was found that fabric energy absorption decreases as fabric is made denser, and this phenomenon becomes more pronounced in a multi-ply ballistic system than in a single-ply system. The research results also indicated that the level of yarn crimp in a woven fabric is an effective parameter in influencing the ballistic performance of the fabrics. A low level of yarn crimp would lead to the increase of the fabric tensile modulus and consequently influencing the propagation of the transverse wave. In addition, it was found that for fabrics with the same level of yarn crimp, low yarn linear density and high fabric tightness were desirable for ballistic performance improvement.     

A comparative study on the performance of meshless approximations and their integration

The goal of this research is to study the performance of meshless approximations and their integration. Two diffuse shape functions, namely the moving least-squares and local maximum-entropy function, and a linear triangular interpolation are compared using Gaussian integration and the stabilized conforming nodal integration scheme. The shape functions and integration schemes are tested on two elastic problems, an elasto-plastic problem and the inf-sup test. The elastic computation shows a somewhat lower accuracy for the linear triangular interpolation than for the two diffuse functions with the same number of nodes. However, the computational effort for this interpolation is considerably lower. The accuracy of the calculations in elasto-plasticity depends to great extend on the used integration scheme. All shape functions, and even the linear triangular interpolation, perform very well with the nodal integration scheme and locking-free behavior is shown in the inf-sup test.     

A computational library for multiscale modeling of material failure

We present an open-source software framework called PERMIX for multiscale modeling and simulation of fracture in solids. The framework is an object oriented open-source effort written primarily in Fortran 2003 standard with Fortran/C++ interfaces to a number of other libraries such as LAMMPS, ABAQUS, LS-DYNA and GMSH. Fracture on the continuum level is modeled by the extended finite element method (XFEM). Using several novel or state of the art methods, the piece software handles semi-concurrent multiscale methods as well as concurrent multiscale methods for fracture, coupling two continuum domains or atomistic domains to continuum domains, respectively. The efficiency of our open-source software is shown through several simulations including a 3D crack modeling in clay nanocomposites, a semi-concurrent FE-FE coupling, a 3D Arlequin multiscale example and an MD-XFEM coupling for dynamic crack propagation.     

Dielectric properties of nanoscale multi-component systems: A first principles computational study

A new method has been developed within the framework of density functional theory to aid in the study of the dielectric properties of multi-component systems, with explicit treatment of surface and interface effects. Specially, we have determined the position dependent dielectric constant profiles for Si–SiO₂ and SiO₂-polymer systems. We find that at regions close to surfaces and interfaces, the dielectric constant is enhanced compared to the corresponding bulk values. In interior regions, the dielectric constant approaches the corresponding bulk values. The calculated optical and static dielectric constant values of these systems are in excellent agreement with experimental results, and other more involved computational treatments.