Semi-infinite Targets Research Articles

A Numerical Study on the Oblique Penetration of Spherical-Nosed Rigid Projectiles into Semi-Infinite Metallic Targets

A Numerical Study on the Oblique Penetration of Spherical-Nosed Rigid Projectiles into Semi-Infinite Metallic Targets

Determination of critical ricochet conditions for oblique impact of ogive-nosed projectiles on concrete targets using semi-empirical model

This paper presents a simple and efficient semi-empirical model for predicting the dynamic behaviors of rigid ogive-nosed projectiles after obliquely impacting semi-infinite concrete targets. We consider the normal stress acting on the projectile surface as a result of the target resistance. We also reflect the decrease in normal stress caused by crater formation and the presence of the free surface on the target. The normal stress is formulated as a function of the projectile geometry and the properties of the target material. To verify the proposed semi-empirical model, we establish computational frameworks combining the finite element method and smoothed particle hydrodynamics. These frameworks are confirmed to provide results consistent with the experimental data for the normal impact of projectiles on concrete targets. By comparing the results obtained from the semi-empirical model with the reference results obtained from the computational frameworks, we demonstrate that the semi-empirical model can successfully predict the penetration or ricochet of projectiles following oblique impact. Furthermore, considering the nose sharpness, slenderness, impact velocity, and oblique incidence angle of the projectiles as key parameters, we investigate their effects on the dynamic behaviors of projectiles. The penetration capabilities of projectiles increase with sharper and slenderer geometry, higher impact velocity, and lower incidence angle. In particular, considering various combinations of these parameters, we identify the critical conditions for the incidence angle and impact velocity that lead to the ricochets of projectiles. The minimum incidence angle, at which ricochets occur, increases in proportion to the nose sharpness, slenderness, and impact velocity. The maximum impact velocity, up to which ricochets occur, decreases as the nose sharpness and slenderness increase and the incidence angle decreases.

Study on the Equivalence of Penetration Overloading for Projectile-Borne Components in Nonproportional Penetrators

The reliability assessment of the projectile-borne components in a high-speed penetrator is an important issue in the penetration field. In this study, a scaling model embedded with a deceleration measurement device was used to investigate the overloading situation due to the high cost of the prototype test. The projectile could be scaled, while the deceleration measurement device needs to maintain full scale. Thus, a nonproportional scaling design is proposed to represent the rigid-body deceleration of the prototype projectile. This study, considering the mass of the deceleration measurement device, lays out the design criteria of the scaling model and carries out rigid-body deceleration similarity verification tests of the prototype and the scaling model. In addition, the rigid-body deceleration similarity was examined through model predictions and numerical simulation. These results show that the rigid-body deceleration of the nonproportional scaling model is generally in agreement with that of the prototype for penetrating the semi-infinite concrete target. The deviations of rigid-body deceleration magnitude and duration are 6.76% and −12.1%, respectively. This makes it reasonable and feasible to investigate the overloading situation of prototype projectile through a nonproportional scaling model.

The optimal nose shape of a rigid projectile deeply penetrating into a solid target considering friction

The paper deals with the optimal nose shape of a perfectly rigid axi-symmetric projectile which deeply penetrates into a semi-infinite target accounting for the dry friction between the nose surface and the target. Analytical expressions of the contact stresses at the “projectile-target” interface and of the total resistance force as well as of the final penetration depth are developed for targets described by a locked hydrostat and a linear shear failure-pressure relationship. These analytical expressions are developed using the cylindrical cavity expansion (CCE) and the spherical cavity expansion (SCE) approaches. A comparison of these approaches on the optimization problem solution is performed. The effect of dry friction on the optimal shape of the projectile nose is investigated and two main approaches to solving the problem of shape optimization are studied. Two optimization approaches are compared: the first optimization approach is based on minimizing the resistive force (MRF) acting on the projectile, and the second approach is based on maximizing the penetration depth (MPD). The optimal shapes are compared for a fixed shank radius and evaluations are carried out for different nose lengths and different values of the coefficient of friction. It is shown that friction may have a visible effect on the final penetration depth, although in all cases, the friction effect on the optimal shape of the projectile nose is negligible. The obtained optimal nose shapes are implemented in computational analysis in an own developed code that had been verified with numerous test data to examine whether these shapes actually lead to a minimum resistive force and to a maximal penetration depth. Significant effectiveness of the optimal shape performance is shown for larger radius projectiles having a defined nose length.

Study on the penetration of elliptical cross-section projectiles into concrete targets: theory and experiment

To better understand the penetration mechanism of the elliptical cross-section projectile (ECSP) into semi-infinite concrete target, penetration experiments using three types of ECSPs with different shape ratios (1, 1.25 and 1.61) and with striking velocities ranged from 550 m/s to 1050 m/s were conducted. Penetration depths, penetration trajectory and mass erosion rates of the projectile were obtained after the experiments. The experiment results show that the penetration performance and ballistic stability of the ECSP are equivalent to those of the circular cross-section projectile (CCSP). Based on the theory of complex variable function and conformal transformation, a semi-analytical model which can calculate the cavity boundary stress distribution of elliptical section cavity controlled by the displacement boundary condition was established and the model was validated by comparing the model degenerate solution with Kirsch problem results. Theoretical calculation results show that the radial stress of elliptical section cavity increases progressively from the minor axis to the major axis. In addition, a formula combining with the semi-analytical theoretical model and the local interaction theory was developed. The predicted penetration depths were compared with 30 groups of experiment data with different projectile parameters and striking velocities and coincide quite well with the corresponding experimental data. Finally, the influence of shape ratio and caliber-radius-head (CRH) on the penetration performance of projectile and the application prospect of ECSPs on hypersonic weapon platform were studied.

Damage characteristics of semi-infinite aluminium targets subjected to normal and oblique projectile impact

The present study investigates the ballistic performance of 50 mm thick 7075-T651 aluminum target against 7.62 API projectile. The focus of this study is to understand the dissipation of total energy engendered by the projectile in impacting the plate target at 0 (normal), 30° and 60° obliquities. Further, the penetration mechanisms and local as well as global plastic deformations developed in the target and projectile were explored. The ballistic experiments on the targets were performed by employing a universal gun and the depth of penetration of the projectile in the target was observed. Three-dimensional computational modelling of projectile and target was carried out in ABAQUS/Explicit module. The material response of both projectile and target was described by the Johnson-Cook strength and damage model. The influence of projectile deformation on the impact resistance of targets was also studied. The plastic strain energy dissipation in the target as well as projectile was evaluated using the validated numerical results and discussed in terms of the damage evolution and local as well as global deformation modes developed in the target and projectile during the impact process.

Hydrodynamic simulation of laser-induced shock waves using the Turbulence Problem Solver software package

The problem of irradiation of a semi-infinite bulk metal target by a single laser pulse, being important for many lase technology applications, is considered. The model for simulating the propagation and attenuation of shock waves, occurring when metals are irradiated with single laser pulse, is presented. The paper describes the computational algorithm based on the model and features of its implementation in C++ in a software package Turbulence Problem Solver (TPS) for modeling a wide class of problems described by hyperbolic equations. The problem is modeled using different approaches and the results are compared. The object-oriented polymorphic architecture of the software complex accelerates and facilitates the process of model development and calibration, allowing for flexible configuration and combination of elements of numerical models: Riemann solvers, various types of and reconstructions, and equations of state of matter.

The penetration and ricochet of ogive-nosed rigid projectiles obliquely impacting metallic targets

A large number of 3D numerical simulations were performed in order to follow the trajectory changes of rigid CRH3 ogive-nosed projectiles, impacting semi-infinite metallic targets at various obliquities. These trajectory changes are shown to be related to the threshold ricochet angles of the projectile/target pairs. These threshold angles are the impact obliquities where the projectiles end up moving in a path parallel to the target’s face. They were found to depend on a non-dimensional entity which is equal to the ratio between the target’s resistance to penetration and the dynamic pressure exerted by the projectile upon impact. Good agreement was obtained by comparing simulation results for these trajectory changes with experimental data from several published works. In addition, numerically-based relations were derived for the penetration depths of these ogive-nosed projectiles at oblique impacts, which are shown to agree with the simulation results.

Модель переноса импульса при высокоскоростном ударе

An analytical mechanical model of the ejection arising from a high-velocity impact of a rigid projectile on a semi-infinite target is constructed, and an estimate is given of the ejection mass and the effect of momentum amplification transmitted to the target upon impact. The effect of the momentum amplification is caused by the ejection of target fragments in the 148 direction opposite to the direction of flight of the projectie. At present, there is a steady interest in the study of this effect. This is due, in particular, to the possible use of the effect for deflecting a potentially dangerous object (asteroid) approaching the Earth by means of an impact spacecraft using the effect of momentum amplification. The model presented in this work is constructed in approximation of plane deformation using the minimum number of parameters of the projectiler and target materials. Equations for the mass of the ejection and the increment of the target momentum are obtained, depending on the depth of penetration of the projectile. The model takes into account the dependence of the emission angle of the ejection fragments on the penetration depth of the projectile. It is shown that the model adequately describes the ejection momentum, the rate of change in the ejection momentum, and the ejection mass depending on the penetration depth of the projectile. The possibility of representing the momentum and mass of the ejection by scaling ratios is checked both for the ratio of the densities of the projectile and the target ptρρ, and for the dynamic parameter 20ttVYγρ= (0V - impact velocity, tY - yield stress of the target), in which the proportionality coefficient depends only on the shape of the projectile. It was found that scaling with respect to the dynamic parameter γ takes place at сγγ>, where 330сγ≈ that, e.g., for aluminum gives the value 02.5 km/scV =.

Research on the Shock Response Characteristics of a Threaded Connection Using the Thin-Layer Element Method

Nonlinear factors such as the contact stiffness and friction damping at the threaded interface of a projectile–fuse system significantly affect the dynamic response characteristics. To obtain the dynamic response of the fuse body accurately during penetration, it is necessary to characterize these nonlinear factors reasonably. Because the existing structural dynamics software cannot effectively deal with nonlinear factors, the thin-layer element method was used to represent the nonlinear factors in this study. By combining the thread elastic model with thin-layer element principles, an effective method for determining the material parameters of the thin-layer element was established theoretically, which provided a different method of determining material parameters, not just relying on experiments. The accuracy of the material parameters was verified based on modal experiments with threaded tubes having different specifications. The errors were within 5%, indicating the reliability of the theoretical determination method for the material parameters. In addition, projectile penetration into a semi-infinite concrete target was tested to verify the accuracy of the thin-layer element modeling. Compared with the ‘TIED’ constraint method, the resonant frequency obtained with the thin-layer element method was in better agreement with that of the experimental data. The maximum error decreased from 15.7 to 7.8%, indicating that the thin-layer element method could accurately represent the nonlinear factors. Thus, this study serves as a reference for accurately evaluating the dynamic response of the fuse body of a penetrator.

Theoretical analysis for self-sharpening penetration of tungsten high-entropy alloy into steel target with elevated impact velocities

The “self-sharpening” effect has been observed experimentally in the penetration of tungsten high-entropy alloy (WHEA) into steel targets in previous study. From the microscopic observation of the residual WHEA long-rod projectile (LRP), the multiphase structure at micro-scale of WHEA is the key effects on self-sharpening penetration process. In order to describe the distinctive penetration behavior, the interaction between micro phases is introduced to modify the hydrodynamic penetration model. The yield strengths of WHEA phases are determined based on the solid solution strengthening methods. Combined with the elbow-streamline model, the self-sharpening mechanism is revealed in view of the multi-phase flow dynamics and the flow field in the deformation area of the LRP nose is characterized to depict the shear layer evolution and the shape of the LRP’s nose as well as the determination of the penetration channel. The self-sharpening coefficient considering the reduction of nose radius is proposed and introduced into the penetration model to calculate the depth of penetration and the penetration channel. Results show that the multi-phase interaction at the microscopic level contributes to the inhomogeneous distribution of the WHEA phases. The shear layer evolution separates part of the LRP material from the nose and makes the nose radius decrease more quickly. It is also the reason that WHEA LRPs have a pointed nose compared with the mushroom nose of WHA heavy alloy (WHA) LRPs. The calculated results agree well with the corresponding experimental data of WHA and WHEA LRPs penetrating into semi-infinite medium carbon steel targets with elevated impact velocities. The flow field in the projectile nose was established to describe the self-sharpening penetration process of the tungsten high-entropy alloy. Combined with the solid solution strengthening methods, the flow field of the projectile nose was structured based on the multi-phase flow. The nose radius before separation was set as $$r_\mathrm{b}$$ and after separation is $$r_\mathrm{a}$$ . The shear layer evolution separated part of the material from the nose and made the nose radius decrease more quickly.

Investigation on the penetration of jacketed rods with striking velocities of 0.9–3.3 km/s into semi-infinite targets

In this study, a combined experimental, numerical and theoretical investigation is conducted on the penetration of semi-infinite 4340 steel targets by a homogeneous 93W rod and two types of jacketed rods with striking velocities of 0.9–3.3 km/s. The results show that the jacketed rods produced typical “co-erosion” damage at all test velocities, except for the 93W/1060Al jacketed rod, which switched from an early “bi-erosion” damage to later “co-erosion” damage at a striking velocity of 936 m/s. However, the homogeneous 93W rod always forms a large mushroom head during the penetration process. The damage mechanisms of these two types of jacketed rods differ for striking velocities of 0.9–2.0 km/s, but this difference gradually decreases with increased striking velocity. For velocities of 2.0–3.3 km/s, all three types of projectiles exhibit typical hydrodynamic penetration characteristics, and the damage mechanisms of the two types of jacketed rods are almost identical. For the same initial kinetic energy, the penetration performance of the jacketed rods is distinctly superior to that of the homogeneous 93W rods. Compared with jacket density, jacket strength shows a more significant influence on the damage mechanism and penetration performance of the jacketed rod. Finally, an existing theoretical prediction model of the penetration depth of jacketed rods on semi-infinite targets in the co-erosion mode is modified. It transpires that—in terms of penetration depth—the modified theoretical model is in good agreement with the experimental and numerical observations for 93W/TC4 and 93W/1060Al jacketed rods penetrating semi-infinite 4340 steel targets.

Numerical study on the resistance of rigid projectiles penetrating into semi-infinite concrete targets

A study on the resistance of rigid projectiles penetrating into semi-infinite concrete targets is performed in this paper. Experimental data are analyzed to examine the penetration resistance during various stages of the penetration process. A numerical tool using AUTODYN hydrocode is applied in the study. The numerical results on both deceleration-time history and depth of penetration of projectiles are in good agreement with experimental data, which demonstrate the feasibility of the numerical model in these conditions. Based on the numerical model with a two-staged pre-drilled hole, the rigid projectile penetration in tunneling stage is studied for concrete targets with different strengths in a wide range of impact velocities. The results show that the penetration in tunnel stage can be divided into two different cases in terms of initial impact velocity. In the first case, when the impact velocity is approximately less than 600 m/s, the deceleration depends on initial impact velocity. In the second case, when the impact velocity is greater than 600 m/s, the effect of target inertia becomes apparent, which agrees with commonly used concrete penetration resistance equations based on cavity expansion model. A two-staged pre-drilled hole model was developed and the results show that the depth of entrance stage tends to decrease with the increase of impact velocity. The influence of the inertial term at low velocity range (approximately close to 600 m/s) is inconspicuous. With further increase of the penetration velocity, the effect of the target inertia becomes apparent as proposed by Forrestal. The effect of mass abrasion of projectiles, entrance phase and strain effect of concrete materials on the tendency of deceleration was clarified.

Experimental Study on Dynamic Tensile Properties and Ballistic Performance of Different Armor Materials

Hopkinson bar system was used to test the dynamic tensile properties of high nitrogen steel, 685 armor steel, 603 armor steel and 316 stainless steel by adjusting loading pressure, the strain rate and dynamic tensile strength of different armor materials were obtained. Under the experimental conditions in this paper, the dynamic tensile strength of the high-nitrogen steel is 1883 MPa which is the maximum of the four materials. At the same time, by using 12.7 mm armor-piercing projectiles, the ballistic tests of semi-infinite targets of different armor materials were carried out. Penetration depth of high-nitrogen steel is 25.5 mm which is the smallest of the four materials. The standard penetration depths of armor materials decrease with the increase of dynamic tensile strengths, and tensile strength increases under the test conditions in this paper. Therefore, the material with high dynamic tensile strength should be selected as the ballistic component in armor design.

Fourier two-temperature model to describe ultrafast laser pulses interaction with metals: A novel mathematical technique

Ultrafast thermal phenomena during femtosecond laser pulse heating of solids, first of all of metals, were analytically developed using a new mathematical method based upon the two-temperature model via the Fourier approach. A straightforward but powerful mathematical formalism is proposed to evaluate the spatial and temporal profiles of electron temperature under the irradiation with a single Gaussian femtoseconds laser pulse. An illustrative example was selected: a semi-infinite Gold target under femtosecond laser pulse irradiation. The proposed model can be used to guide and design experimental activities, i.e. parameters optimization before conducting real-time experiments of ultrashort laser pulses - metals interaction.

Model of interaction of a rigid mesh with a deformable target

We present an analytical model of the high-velocity impact interaction of a rigid mesh with a semi-infinite deformable target, which is modeled as a rigid-plastic body. We consider the so-called “normal” impact of the mesh on the target: we assume that at the initial moment and subsequent moments of time the mesh is parallel to the target surface while the mesh velocity vector is perpendicular to this surface. The model reproduces the most interesting case in which the mesh aperture is comparable to or less than the diameter of the strings from which the mesh is woven. The aim of the study was to investigate the dependence of the mesh penetration depth on the impact velocity $$V_{0}$$ and on the geometric parameter of the mesh γ that is equal to the ratio of the string diameter to the mesh period. Two versions of the model are considered: with and without taking into accounts the fragmentation of the ejected material of the target. The results obtained on the basis of the proposed model are compared with the numerical solutions which were obtained using the LS-DYNA package. The example of the penetration of a steel mesh into an aluminum-alloy target with impact velocities of 1–3 km/s is analyzed. It is shown that the model that takes into account fragmentation agrees well with the numerical simulations for the mesh parameter interval $$\gamma_{p} < \gamma < 1$$ , in which the lower boundary decreases with increasing impact velocity: $$\gamma_{p}$$ = 0.49, 0.29, 0.2 for $$V_{0}$$ = 1, 2, 3 km/s, respectively.

Penetration characteristics of a penetrator with triangular cross-section impacting semi-infinite targets

This article examines the characteristics of a penetrator with a triangular cross-section perpendicular impacting a semi-infinite metal target. Experiments and numerical simulations were conducted at an impact velocity of 1600 to 1800 m/s. The model, which was constructed to analyze penetration depth, showed the effect of the nose-shaped structure of the penetrator on penetration characteristics. The model can analyze the penetration characteristics of a penetrator with triangular cross-section that attacks semi-infinite targets. The results obtained by the model are primarily attributed to the self-sharpening characteristics of the penetrator.

Failure analysis of semi-infinite concrete targets subjected to tubular projectiles impact

Improving the penetration efficiency of missiles into concrete is a practical research topic. In this paper, a tubular projectile was designed to enhance penetration diameter on concrete targets. To validate numerical simulation methods, an experiment of an ogive-nosed projectile penetrating a semi-infinite concrete target was reproduced by numerical simulation. Based on the validated numerical model, the penetration progress of a tubular projectile into a semi-infinite concrete target was analyzed. By assessing the penetration tunnel diameter and depth, the effects of key parameters, i.e., the wall thickness (15.0, 30.0, 60.0, 90.0, 120.0 mm) and velocity (400.0, 600.0, 800.0, 1000.0, 1200.0, 1400.0 m/s) of tubular projectile on penetrating concrete targets have been investigated in detail. Furthermore, the penetration performances of flat-nosed projectiles and tubular projectiles on concrete targets with the same mass were compared. The results indicate that with the increase in the wall thickness and velocity of the tubular projectiles, the penetration depth of the projectiles into the concrete target increases gradually, and the increase in the diameter of the tunnel is not obvious. In the case of the wall thickness of the tubular projectile which is greater than or equal to 30.0 mm, the concrete core, near the head of the tubular projectile, is completely fractured and separated from the concrete target. When the flat-nosed projectiles have the same mass and length with tubular projectiles, the diameter of the tunnel caused by the tubular projectile on the concrete targets is always much larger than that caused by the flat-nosed projectiles. The difference of them can be 60.5%. In the condition that the flat-nosed projectiles have the same mass and diameter with tubular projectiles, the depth of the tunnels caused by tubular projectiles in the concrete targets is always much larger than that caused by flat-nosed projectiles. The difference of them can be 95.6%.

Penetration of long rods into semi-infinite metallic targets over wide range of impact velocities

In this paper, the analytical model that describes the penetration process of a long rod into a semi-infinite metallic target over wide range of impact velocities has been presented. In this model, the target strength factor Rtis not considered as a constant but it is a function of penetration velocity whereas, the rod strength factor YP is represented by Hugoniot Elastic Limit (HEL) of its material. The penetration process of the present model consists mainly of primary phase during which the rod front is subjected to erosion and secondary (after-flow) phase. The main equations of the used model are presented, arranged and compiled into a computer program. The program is capable of predicting the time histories of the parameters associated with the penetration process. Autodyn hydrocode package is used herein to simulate the penetration processes of long rods into targets examined by the present analytical model. The hydrocode is fed with the same data used in the model for rods and targets materials. Both the model predictions and the obtained numerical results of Auto dynhydro code, respectively, are compared with the corresponding experimental measurements of other investigators. Good agreement is generally obtained. In addition, representative samples of the model predictions and their corresponding simulation results of Autodyn hydro code are presented with relevant analyses and discussions. The obtained results prove the predictive capabilities of both the present model and Autodyn hydro code, respectively, where each of them could be used as a quick tool for determining the main parameters associated with the studied penetration process.

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.