Target Of Finite Thickness Research Articles

Research on mass distribution characteristics of the behind armor debris of the EFP penetrating target

Based on the AUTODYN, a numerical simulation model for EFP warhead penetrating finite thickness target was established, and the mass distribution characteristic of the armor debris behind target was analyzed. The result shows that the whole mass of behind armor debris(BAD) of the EFP with 1790m/s and target with 0° inclination angle increased and the quantity of BAD firstly increased and then decreased as target thickness ranging from 10mm to 70mm. For the experiments with employing the EFP with 1790m/s and 40mm target thickness, the BAD mass initially rose and then to drop off, as well as the quantity of BAD increased over inclination angle increasing from 0° to 60°.According to the results with 0° inclination angle and 40mm target thickness, the quantity of BAD also increased and the mass generally decreased as EFP velocity increasing from 1.2km/s to 2.6km/s. Verifications were conducted by using EFP penetrating into the 40mm thickness target with varying inclination angles. The simulation results correlate with the experimental results reasonably well.

Penetration performance and fragmentation mechanism behind target of tungsten fibre/zirconium-based bulk metallic glass matrix composite rod

A tungsten fibre/zirconium-based bulk metallic glass matrix composite (WF/Zr-MG) is a type of armour piercing material with significant development potential. When it penetrates a finite-thickness target plate, it results in damage different from those generated by W alloys. Therefore, the penetration of 80% WF/Zr-MG by volume fraction (the diameter of the W fibre is 0.3 mm) into a 120-mm-thick 45 steel target plate is investigated experimentally at an impact velocity of 1600 ± 20 m/s. Subsequently, the results are comp rod ared with those of a 91 Walloy (91 W) rod to investigate the penetration performance and damage ability behind the target of composite materials. The damage effects of the 45 steel target plate and after-effect target are analysed. The penetration performance and fragmentation mechanism of the two materials are analysed experimentally and based on theoretical calculations. The experimental results indicate that the WF/Zr-MG rod shows self-sharpening in the nose, a smaller average crater diameter, less kinetic energy loss, and better penetration performance compared with the 91 W rod. The bonding force between the phases of WF/Zr-MG is significantly lower than that of 91 W, and cracks formed easily in the material during the penetration process. Radial stress is released instantaneously after the WF/Zr-MG rod departs from the target; consequently, the WF/Zr-MG rod underwent radial expansion, fracture, and dispersion. The damaged areas of WF/Zr-MG measured 1734 and 1661 cm2, which exhibit fragment diffusion angles of 46.5° and 46.1°, respectively. However, the damaged areas of the W alloy are only 1017 and 1193 cm2, and the corresponding fragment diffusion angles are only 35.3° and 37.8°, respectively. The damage parameters of WF/Zr-MG behind the target are greater than those of the tungsten alloy, which increased its killing capacity behind the target.

Numerical simulation study on collinear EFP from warhead with double layer liners penetrating into target

In order to improve the penetration efficiency of the traditional explosively formed projectile (EFP) warhead, a new warhead with double layer liners formed collinear EFP was designed. In order to get the law of its formation and penetration into different type target, the process of the collinear EFP from warhead with double layer liners forming and penetrating into targets was simulated by using LS-DYNA software. It is obtained that the double layer liners formed two EFPs with different axial velocities under the action of detonation wave, and the velocity of the front EFP is higher than that of the rear EFP, which makes the front EFP and rear EFP separation during the flight, so it can effectively attack the reactive armor. For finite thickness target, the front EFP can effectively penetrate the hole on the target, and the rear EFP will enlarge the hole. For infinite thickness target, the collinear EFP can effectively increase the penetration depth. Compared with the single EFP, the collinear EFP from warhead with double layer liners can increase the penetration depth by 36 %.

Simulation of a Group Impact on a Heterogeneous Target of Finite Thickness

Numerical simulation of the processes of high-speed loading of homogeneous and heteroge- neous targets by single projectiles, as well as by a group of projectiles with the same parameters in mass and momentum, has been carried out. Based on a comparison of the numerical simulation results for loading targets with different sets of projectiles, it is found that a projectile in the form of a ring knocks out the maximum hole in the target in terms of geometric dimensions, while a set of seven small disks removes the maximum mass from the target. The ring impact forms a continuous spall plate, which outruns the cloud of fragments of the destroyed material. Adding more than 5% of ceramics to the aluminum target volume does not allow the projectiles to penetrate through

Advanced mathematical model for temperature distribution induced by a pulsed laser in different target configurations using virtual sources

An advanced mathematical model for temperature distributions in semi-infinite and finite thickness targets using different heating mechanisms induced by a pulsed laser is developed. To overcome the violated boundary conditions occurring at certain absorption mechanism, virtual sources are considered. Solutions of the heat transfer equation for different combinations of target thicknesses and different absorption mechanisms are presented. Through limiting conditions applied on the temperature distribution developed for certain absorption mechanism and thickness target, the results for all other combinations can be obtained. By this means it is not necessary to solve the heat transfer equation from the very beginning. Computations of the derived temperature distributions are carried out on aluminum target. The differences in the computed spatial and temporal distributions are discussed and the appearing discrepancies are explained.

A penetration model for semi-infinite composite targets

A penetration model for composites reinforced with high tenacity fibres like ultra-high molecular weight polyethylene (UHMW-PE) is proposed based on the modified Bernoulli theory typically used for metallic targets. The model describes penetration by tensile failure of the composite material through compression loading in an infinitely thick target and includes consideration for projectile deformation. The predicted projectile velocity and axial interface loads shows good agreement with numerical simulations for a deforming and rigid projectile condition against two grades of UHMW-PE composite. The model can also be used to predict transient projectile velocity and interface loads during the first phase of penetration (which acts over most of the penetration event) for a target of finite thickness. It was shown that transition to bulging occurs upon the arrival of the rarefaction wave, generated from the back of an unsupported target, at the projectile-target interface. The stress relief can lead to a change in penetration mode when the magnitude of release is sufficient to reduce the load at the interface below that of the target strength. This change in mode occurs late in the penetration event, and the model developed in this work is demonstrated to be valid up to this point.

Effects of rockfall on an elastic-plastic member: A novel compliance contact model and dynamic response

The study presents the dynamic structural response of steel member subjected to a localized impact from falling rock blocks in rockfall areas. A novel compliance contact model is derived for the interaction between the elastic-plastic member (the target) and an impacting rock block. Unlike other existing models, the proposed compliance contact model accurately evaluates the material properties of the rock block (considered as a deformable indenter) and of the steel target (considered as an elastic-plastic target of finite thickness). A simplified two degrees of freedom (2-DOF) lumped masses model accounting for nonlinear contact interaction and material nonlinearities is used to describe the dynamics of the phenomenon. The proposed contact law and the 2-DOF model are validated with detailed static and dynamic analyses conducted with finite element software ANSYS. The results are compared and commented in order to be implemented in future civil engineering applications.

Developing a validated hydrocode model for adobe under impact loading

We present hydrocode simulations of penetration and perforation of adobe targets by high-hardness spherical steel projectiles. For the description of adobe we employ the RHT concrete model, which describes strength and failure depending on pressure, Lode angle, and strain rate in combination with a porous equation of state. In order to apply this model to adobe we develop a parameter set partially based on material test data. Other parameters are obtained through engineering assumptions, and their importance is assessed by sensitivity analyses. Ballistic reference experiments are reproduced well by our simulations especially regarding residual velocities of projectiles perforating finite-thickness targets. Therein, we also properly capture the deformation of the projectile and the damage of the target. Simulations of the penetration into semi-infinite targets are in acceptable agreement with the ballistic data. However, a significant influence of target setup and boundary conditions on the resulting penetration depths is discovered. The residual velocities obtained by perforation simulations do not show such sensitivity but considerably depend on the yielding threshold of the projectile. Hence, the latter property of the projectile must be correctly included in the simulation in order to be able to draw conclusions on the ability of the material model and the model parameters to describe the target. As for other building and geological materials, the pore compaction is revealed to be an important form of energy dissipation also for adobe and is hence an essential ingredient for the description of the ballistic performance of this material.

Longitudinal impact of piezoelectric media

We consider the elastodynamic impact problem involving a one-dimensional finite-thickness piezoelectric flyer traveling at initial velocity $$V_0$$ that collides with (and adheres to) a stationary piezoelectric target of finite thickness backed by a semi-infinite non-piezoelectric elastic half-space. We derive expressions for the stress, velocity, and electric displacement in the target at all times after impact. A combined d’Alembert and Laplace transform method is used to derive new numerically based solutions for this class of transient wave propagation problems. A modified Dubner–Abate–Crump (DAC) algorithm is used to invert the analytical Laplace transform domain solutions to the time domain. Unlike many authors who neglect electromechanical coupling in the initially unstressed region ahead of the shock, we consider this effect, which gives rise to the development of a tensile stress wave within the piezoelectric target ahead of the shock. To solve the problem, we derive a new piezoelectric impact boundary condition and apply it to the problem of a finite quartz (Si $$\text {O}_2$$ ) flyer impacting a lead zirconate titanate (PZT-4) target and find that the solutions obtained using the modified DAC algorithm compare well with those obtained using both a finite-difference time-domain method, and the commercial finite element code, COMSOL multiphysics.

A penetration model for metallic targets based on experimental data

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 T50 and/or the ballistic limit velocity V50. 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.

The analytic model of a laser-accelerated plasma target and its stability

A self-consistent kinetic theory of a laser-accelerated plasma target with distributed electron/ion densities is developed. The simplified model assumes that after an initial transition period the bulk of cold ions are uniformly accelerated by the self-consistent electric field generated by hot electrons trapped in combined ponderomotive and electrostatic potentials. Several distinct target regions (non-neutral ion tail, non-neutral electron sheath, and neutral plasma bulk) are identified and analytically described. It is shown analytically that such laser-accelerated finite-thickness target is susceptible to Rayleigh-Taylor (RT) instability. Particle-in-cell simulations of the seeded perturbations of the plasma target reveal that, for ultra-relativistic laser intensities, the growth rate of the RT instability is depressed from the analytic estimates.

Modeling of the destruction of targets during a high-velocity impact

The processes of deformation and destruction of finite-thickness targets during the high-velocity impingement of a group of compact impactors were numerically simulated. Three-dimensional calculations with the use of the finite-element method were performed within the framework of an elastoplastic model of the medium. The final stages of the formation of through holes were simulated using complete destruction criteria. Simple criteria for estimating the mutual influence of the impactors and the character of destruction of the target at various incidence angles and distances between the impactors were obtained.

Numerical analysis of the impact resistance of targets and simple constructions

The problem of the high-velocity interaction of various technogenic bodies with targets and constructions usually consisting of a set of simple targets (layered, screened, and spaced) made of various materials is of special importance in the general problem of highvelocity impact phenomena. It is a scientific basis for solving practical problems concerning the development of double-purpose technologies and permanent advancements in the protection of civil, marine, aviation, and space equipment against penetrating impacts of various technogenic bodies. Complex experimental and numerical investigations into the damages caused to finite-thickness targets by projectiles show that mechanisms of the destruction of targets change significantly with variation in the initial conditions of interaction (increase in the collision velocity of bodies, change in the materials of targets and projectiles, their shape, etc.) [1]. Since a high-velocity impact proceeds very quickly (over a time period of about 10 —4 —10 —7 s) and results in destructive action, experimental information on the dynamics of the entire impact process is primarily obtained by high-speed optical shooting (ordinary and laser), pulsed multiple radiography [2], and recording of pressures and velocities by differential laser interferometry, manganin, capacity, and piezoelectric and electret sensors [3]. In addition, mathematical simulation by modern numerical methods is an important source of information immediately from any zone of active deformation, prefracture and fracture of materials of interacting bodies [4]. Computer simulation of the interaction of projectiles with targets and simple constructions was performed by the numerical finite-element method, which was efficiently applied to various impact problems [5]. The physical‐mathematical model of colliding solids that is used in this work is generally represented by a compressible strong medium whose behavior under extreme impact loads is described by a broadband semiempirical equation of state [6], elastoplastic model, dynamic yield stress, shear modulus, and constants of the kinetic fracture model [7]. The last model describes the local formation, development, and target evolution of microdamages, which continuously change the properties of the materials in contact and induce a relaxation of stresses. The spall‐shear fracture process was simulated based on the concept of a continuous accumulation of damages characterized by the specific volume of cracks [7]. The rate of increase in the specific volume of cracks or pores was specified as a function of acting pressure and the volume of damages attained according to relations obtained in [7, 8]. These relations take into account the possibility of partial or complete closure of microdamages upon change in the sign of tensile stresses and the appearance of compressive stresses [9], which is very important for analysis of the perforation of spaced constructions. Step-by-step analysis of contours of the specific volume of cracks (at different times) at the stage of prefracture of materials makes it possible to locally determine the general developmental tendencies of fracture both qualitatively and quantitatively, as well as its mechanism, the local damage degree of a material, and the behavior of the main spall crack and adiabatic shift due to decrease in the strength of the material that is caused by its adiabatic heating [10]. In addition, the formation and evolution of different fracture mechanisms and their interference are revealed. In particular, analysis of a mechanism of the perforation of plates by deformable projectiles revealed that the formation of a separated disc in the upper and lower halves of a plate occurred through different mechanisms [11].

Laser imprint reduction with a shaping pulse, oscillatory Richtmyer–Meshkov to Rayleigh–Taylor transition and other coherent effects in plastic-foam targets

A substantial reduction of the laser imprint with a short, low-energy “shaping” laser pulse incident upon a foam–plastic sandwich target prior to the main laser pulse has been demonstrated to be possible [Metzler et al., Phys. Plasmas 9, 5050 (2002)]. Nonuniformity of this shaping pulse, however, produces standing sonic waves in the target. Laser-imprinted seeds for the Rayleigh–Taylor (RT) instability growth then emerge from the interaction of these waves with the strong shock wave launched by the drive laser pulse. Such coherent interaction between different waves and modes perturbed at the same wavelength is shown to be important in a variety of situations relevant to the inertial confinement fusion studies. As an example, an oscillatory transition from the classical Richtmyer–Meshkov shock-interface instability development to the RT growth exhibiting a characteristic phase reversal in a target of finite thickness is described. Another example refers to the feedout mechanism of seeding the perturbations that come from the nonuniformities of the rear (inner) surface of the laser target. The coherent interaction between the strong shock wave from the main laser pulse and the rippled rarefaction wave produced by a low-intensity foot of the pulse produces observable effects, such as an extra phase reversal compared to the case of no foot. Some of these predictions are shown to be consistent with our new experimental results obtained in the feedout geometry on the Nike laser facility [S. P. Obenschain et al. Phys. Plasmas 3, 2098 (1996)].

The shaped charge jet interaction with finite thickness targets

The problem of reducing the jet penetration capability upon its interaction with the finite-thickness target, due to the erosion of the front region of the jet having perforated through the target, is considered. The experimental examination and the mathematical modeling of the process were performed; semi-empirical formulas were obtained. The calculation techniques are shown to allow the description of interaction processes with satisfactory accuracy.

A generalized formula for the penetration depth of a deformable projectile

A simple analytical algebraic formula is developed for predicting the penetration depth of a deformable projectile into a semi-infinite target. This formula is a simplified version of more general equations that have been developed to predict the time-dependent penetration process in finite thickness targets. Specifically, the formula generalizes the classical hydrodynamic theory to include dependence on elastic properties of the target and on the yield strengths of both the target and the projectile. Moreover, the formula is limited to the case of long-rod penetration where both the projectile and the target experience significant plastic flow. The limiting values of the location of the elastic–plastic boundary in the target have been determined, and a single empirical constant has been introduced to characterize the transition between these limiting values. A value for this empirical constant has been determined which produces theoretical predictions that are in reasonable agreement with experimental data for moderate to high values of the impact velocity of steel and tungsten projectiles penetrating a steel target.

Penetration of a rigid projectile into a finite thickness elastic–plastic target — comparison between theory and numerical computations

Recently, two different analytical solutions have been developed for penetration of a rigid projectile into an elastic–plastic target of finite thickness. One solution satisfies the balance of linear momentum pointwise in target region, but it satisfies the free-surface boundary conditions only in an integrated sense. The second solution satisfies the balance of linear momentum only along a finite number of instantaneous streamlines, but it satisfies the boundary conditions exactly at each intersection of the streamlines with the boundary. The first solution is valid only for normal penetration whereas the second solution has been generalized for oblique penetration. The main objective of the present paper is to compare the predictions of these two theoretical approaches with a numerical solution obtained using the hydrocode Autodyn2D. By modifying the boundary condition used in the first method it is possible to obtain a reasonably accurate description of the penetration process (including the exit stage) with the computational time reduced from a few hours for Autodyn2D to only a few minutes for the analytical solution.

Constant kinetic energy impacts of scale size kE projectiles at ordnance and hypervelocity

Summary This paper presents scale size firings of tungsten alloy KE penetrators into RHA and ceramic targets at constant impact energy. Experiments were carried out mainly at 1.55 and 2.15 km/s but additional data and hydrocode simulations cover a wider velocity range. Semi-infinite RHA and 100 mm thick RHA targets at normal incidence were used, in addition to 40 mm thick RHA at 60 degrees obliquity. The Al2O3 ceramic target was at normal incidence and used a thick lateral confinement, and an RHA backing to measure residual depth of penetration. Behind armour effects (BAE) measurements were made using the finite thickness targets. The semi-infinite RHA experiments show the expected peak in performance at about 2200 m/s and an analytical equation was in good agreement to experiment. The hypervelocity penetrator eroded slightly less than the ordnance velocity case against finite thickness RHA. The mass efficiency of the ceramic target increased from 1.65 at 1.55 km/s to 1.93 at 2.15 km/s but there was still an improvement of 25 % in penetration at the higher velocity. Simulations of the experiments used the GRIM2D and 3D hydrocode and an Armstrong-Zerilli material model and generally gave good agreement. Penetration simulations with a simplified Johnson-Holmquist ceramic model compare well with experiments at the two velocities. Further simulations indicate an optimum velocity at 2500 m/s. The higher velocity impacts produced more behind armour debris, with the fragment number approximately in proportion to the square of the impact velocity.

Eroded length model for yawed penetrators impacting finite thickness targets at normal and oblique incidence

Summary A simple expression is derived to estimate the residual length of a yawed, long-rod penetrator impacting finite thickness targets at both normal and oblique incidence. The unique feature of this model is a determination of the different penetration path through the plate which is not simply a line-of-sight thickness. The presence of yaw results in a penetration path which is determined by the magnitude and direction of the penetration velocity vector which is dependent upon the penetrator velocity component along that path. Hence, the material thickness penetrated through the finite target is an explicit, and variable, function of the impact geometry, (obliquity and yaw), impact velocity, and relative penetrator and target properties (densities and strengths). The eroded penetrator length is also dependent on both the penetration path angle and on the velocity component along that path and thus becomes an explicit function of these variables. Two simple expressions are derived to determine the eroded penetrator length and implications for deep target penetration degradation due to yaw are discussed.

On the role of nose profile in long-rod penetration

The superiority of depleted uranium on tungsten-alloy penetrators has recently been assigned to the self-sharpening mechanism, at the tip of the DU rods, due to the adiabatic shear failure which this material experiences. The purpose of the work presented here was to further investigate the role of deformed nose profile on the deep penetrations of long rods into semi-infinite targets. This was achieved through a series of 2-D numerical simulations and several perforation experiments where we recovered and examined the residual penetrators. The simulations were performed for rigid tungsten-alloy rods having five different nose shapes with the density and elastic properties of tungsten alloys. For the normal impact experiments we chose three rod materials: a tungsten alloy, a copper and a titanium alloy. The residual rods (after perforation of finite thickness targets) were imaged by flash X-ray and softly recovered using sand boxes. As expected, the nose shapes of these rods were very different from each other.