Rigid Body Penetration Research Articles

Experimental research on the mechanism of a high-velocity projectile penetrating into a reinforced concrete target

In order to study the high-speed penetration effect of a structural projectile on a reinforced concrete target, tests of structural projectiles with high velocity penetrating into reinforced concrete target were carried out by using a 35mm-caliber ballistic gun as a launching tool, and the penetration velocity of the projectiles ranges from 1030 m/s to 1520 m/s. The test data of the deformation and failure form, remaining length and remaining mass of the projectiles were obtained through detailed measurement of the recovered projectile. The macro-damage of the targets, the penetration depth and crater size of the target bodies were also obtained. Based on the experimental data, the changes of the projectile structure response, penetration of the dimensionless crater depth, and dimensionless crater diameter with penetration velocity were analyzed. According to the deformation and destruction of the projectiles during the penetration process, the penetration depth and penetration mechanism change with penetration velocity were analyzed, and the partition of the penetration velocity was discussed. The results show that, in the penetration velocity ranges from 1030 m/s to 1390 m/s, the heads of the projectiles are eroded, and the degree of erosion increases with the increase in penetration velocity, and the penetration depth increases approximately linearly with the penetration velocity. When the penetration velocity is in the range of 1390−1480 m/s, the heads of the projectiles are severely eroded, and the penetration depth decreases as the penetration velocity increases. When the impact velocity is higher than 1480 m/s, the projectile bodies are severely broken, and the penetration depth decreases sharply as the penetration velocity increases. According to the damage characteristics of the structural projectiles during high-speed penetration, the penetration velocity is divided into rigid body penetration zone, quasi-rigid body penetration zone, eroded body penetration zone and broken body penetration zone, which can provide a reference for the structural design of ground-penetrating projectile.

Similarities in the penetration depth of concrete impacted by rigid projectiles

Similarity can reflect common laws in the mechanism of rigid-body penetration. In this paper, the similarities in rigid-body penetration depth are demonstrated by three non-dimensional but physically meaningful quantities, i.e., $$ \rho_{\text{kinetic}} $$ , $$ I_{ \ln }^{*} $$ and $$ N^{\prime}_{1} $$ . These three quantities represent the non-dimensional areal density of projectile kinetic energy, the effect of nose geometry, and the friction at the interactive cross section between projectile and target respectively. It is shown that experimental data of rigid projectile penetration, from shallow to deep penetration, can be uniquely unified by these three similarity quantities and their relationships. Furthermore, for ogival nose projectiles, their penetration capacities are dominated by $$ \rho_{\text{kinetic}} $$ , which is consisted by non-dimensional effective length $$ L_{\text{eff}} $$ and non-dimensional quantity $$ D_{\text{n}}^{\text{p}} = \frac{{\rho_{\text{p}} v_{0}^{2} }}{AY} $$ which has the same form as Johnson’s damage number. On the sacrifice of minor theoretical accuracy, the non-dimensional penetration depth $$ P/d $$ can be understood as directly controlled by $$ D_{\text{n}}^{\text{p}} $$ , enhanced by projectile effective length $$ L_{\text{eff}} $$ under a multiplication relation, and optimized by projectile nose geometry in the formation of $$ I_{ \ln }^{*} $$ .

SPH simulation of the penetrating object in the wet soil

ABSTRACT In the present study, a Smoothed Particle Hydrodynamic (SPH) method has been developed and used to model the penetration of a rigid body to the soil under a certain force. The soil is considered as a non-Newtonian fluid with a free surface condition. Although the SPH method involves some complexity, it is generally a simple and suitable method for modelling the contact of the rigid body to the soil; the free surface and the movement of the body can easily be implemented by the SPH method. By developing this method, the interaction of soil particles with a rigid body is investigated. The model considered for the soil is Bingham’s model. In this study, the method is developed and validated with the previously available data and then used to model the problem of the rigid body contacting with soil. The purpose of this paper is to develop the SPH method in soil modelling and investigation of the amount of rigid body penetration in the soil. So, the penetration depth of the circular cylinder and rhombic cylinder as the rigid bodies in the collision to the soil are investigated and compared.

On the friction effects on rigid-body penetration in concrete and aluminium-alloy targets

Abstract The friction on the projectile shank is usually excluded in the penetration analysis due to the difficulties to measure the pressure and frictional coefficient. In this article, the frictional force on projectile shank is discussed indirectly through the comparison between experimental data and empirical/analytical formulas of the penetration depth for both concrete and aluminium-alloy targets. It is found that the effect of the frictional force along the projectile shank can be further discussed by the afore comparison and discussion and cannot be ignored because of the relatively large effecting area, especially for deep penetration of concrete and aluminium-alloy targets, where the friction will account for more proportion of penetration resistance.

МОДЕЛИРОВАНИЕ ПРОНИКАНИЯ НЕОСЕСИММЕТРИЧНЫХ ТЕЛ В ГРУНТ ПО ИНЕРЦИИ ПРИ УЧЕТЕ ТРЕНИЯ

The problem of a normal impact and penetration of rigid spatial bodies of a finite mass into a half-space occupied by an elastoplastic soil medium. The penetrated medium is modeled by linearly compressible elastoplastic Grigoryan medium, with the yield strength linearly depending on pressure. The problem is analyzed in a 3D formulation, using software package LS-DYNA. The elastoplastic penetrated medium is analyzed on a fixed Eulerian grid with empty meshes, where the material flows to in the process of deformation. Spatial strikers are modeled by a rigid non-deformable body in a Lagrangian coordinate system. The effect of surface friction during the penetration of strikers of various forms (a round cone, a four-ray star and a pyramidal body) into elastoplastic Grigoryan soil medium is studied. The cross-section of the star-shaped body is generated by two rhombs with the ration of diagonals of 1:2; the base of the pyramid is a rhomb with the ratio of diagonals of 1:3. The analyzed bodies have equal areas of the bases and equal inclinations of the side surface (the angle between the direction of the motion velocity vector of the body and a normal to the side surface). A circular cone with the same base area is considered for comparison.The considered strikers moved with constant velocities and mechanically, in the velocity range of 150 to 600 m/s, corresponding to subsonic and supersonic velocities. The surface friction coefficient is close to the value of the friction coefficient in sandy soils of natural composition. The results are compared with the earlier obtained computational results for a zero friction coefficient. It is found that resistance to penetration and penetration depth can be described using binomial Resale's penetration law with a quadratic velocity. The disagreement between the forces of resistance to penetration of a pyramidal, conical and star-shaped bodies of the same height are within the interval of 10-20%.

Analytical models for penetration mechanics: A Review

A review of analytical penetration models has been conducted and summarized. Models include the Poncelet equation, hydrodynamic theory, modified hydrodynamic theory, Recht-Ipson, Tate-Alekseevskii, cavity expansion, Ravid-Bodner, Walker-Anderson, and similitude modeling. These models describe, depending upon assumptions, rigid-body penetration, eroding penetration, steady-state and transient penetration, and perforation. Model assumptions are highlighted, and examples are provided of model predictions against experimental data. The manuscript has 30 figures, many of which compare model results to experimental data; 59 reference citations are included.

Scale-independent description of the rigid-body penetration of spherical projectiles into semi-infinite adobe targets

In impact experiments, the penetration depth of spherical projectiles into semi-infinite adobe targets has been investigated. In total, 20 tests were performed with steel projectiles of diameters 7.5, 10.0 and 13.5 mm in the velocity regime from 240 to 3230 m/s. In addition, 2 single experiments with aluminum and titanium projectiles were conducted at impact velocities of 830 and 920 m/s, respectively. After an appropriate normalization, all penetration depth vs. velocity data up to impact velocities of around 1500 m/s can be described by one linear curve. This is the velocity regime where projectile fragmentation does not yet occur. The observed linear relation is discussed in the context of a recently published analytical model and shows the scalability of penetration tests also for the considered adobe target material of low strength and low density.

Penetration Of A Coarse Sand Target ByRigid Projectiles

This paper presents a theory for the normal rigid body penetration of particulate media. This theory consists of two separate force regimes divided by a critical velocity at which the transition between the two regimes takes place. Also included in this theory is sliding friction, separated into two different regimes, one for the nose and one for the shank. In order to verify this new penetration theory, a set of laboratory experiments was performed where 7075-T6 Aluminum projectiles were shot into coarse foundry sand. Utilizing the total penetration depth and impact velocity of each projectile in the test, along with known projectile geometry, analyses of the penetration events were completed. The results of these experiments and analyses, which confirm the required use of a friction coefficient on the shank, are reported.

Different Scale Experiments of High Velocity Penetration With Concrete Targets

In this study, two different scale projectile high velocity penetration experiments with concrete targets that had an average compressive strength of 35 MPa were conducted in order to find the velocity limits and nose erosion properties. We conducted the penetration experiments for the small-scale (48 mm diameter, 195 mm long, 2 kg) and the large-scale (144 mm diameter, 680 mm long, 50 kg) ogive-nose projectiles with the hard steel 4340 whose dynamic compression strength is 2.2 GPa. A 100-mm-diameter powder gun was used to launch the five tests of the 2 kg projectiles with striking velocities between 1100 m/s and 1600 m/s and a 320-mm-diameter Davis gun was used to launch the two tests of the 50 kg projectiles with striking velocities 1100 m/s and 1300 m/s. The experimental results showed that the nose material was missing, indicating an apparent eroding process when the striking velocity exceeded 1400 m/s, where the rigid body penetration made a transition into the elastic-plastic hydrodynamics regime and penetration depth begin to decrease when the striking velocity exceeds 1400 m/s. Furthermore, nose changes and mass loss due to nose erosion did not significantly affect the penetrating ability before rigid body penetration made a transition into the hydrodynamic regimes. In addition, nose erosion was analyzed with SEM surface microstructures, and the SEM image showed that the mass loss of projectiles was due to the shear cracks preceded by adiabatic shear bands.

Penetration of self-affine fractal rough rigid bodies into a model elastomer having a linear viscous rheology

The penetration of a rigid body with a randomly rough, self-affine surface in a half space filled with a linearly viscous elastomer is studied numerically using the method of boundary elements. Using Radok's principle of functional equations, it is shown analytically that this problem is closely related to the recently investigated problem of contact of self-affine surfaces with an elastic half space. We show that the penetration velocity occurs to be a power function of the applied force and time, the corresponding exponents depending only on the Hurst exponent. For comparison, the same problem is solved using the method of reduction of dimensionality. Both three-dimensional numerical results and the method of reduction of dimensionality support the analytical predictions provided by general scaling arguments.

Modeling the ballistic response of the 14.5 mm BS41 projectile

This article presents computed results of the U. S. Army Research Laboratory (ARL) 14.5 mm BS41 projectile impacting steel targets with varying impact conditions. The ARL BS41 is a complex projectile that includes a soft metal jacket, lead filler, inert powder and a high-strength tungsten carbide (WC) core. The WC core includes a nominal 6 wt% cobalt binder (WC-.06Co) producing significant ductility in compression but very little in tension. Recent 3D numerical algorithm advancements and a more accurate material model for WC produce computed results that are in good agreement with experimental results. The computed results demonstrate the ability to reproduce several key observations: the stripping of the steel jacket, lead filler and inert powder when impacting thin and thick steel targets; rigid body penetration of the WC core into thin and thick steel targets for normal impact; severe fracture and fragmentation of the core when impacting obliquely; and core fracture due to a yaw angle at impact. The computed results may also explain why the core fractures at low obliquities and shatters at high obliquities. Experimental data are also discussed and compared to the computed results.

Projectile Nose Mass Abrasion of High-Speed Penetration into Concrete

Based on the dynamic spherical cavity expansion theory of concrete and the analysis of experimental data, a mass abrasion model of projectile considering the hardness of aggregates, the relative strength of target and projectile, and the initial impact velocity is constructed in this paper. Furthermore, the effect of mass abrasion on the penetration depth of projectile and the influence of hardness of aggregates and strength of projectile on penetration depth and mass loss are also analyzed. The results show that, for the ogive-nose projectile with the CRH of 3 and aspect ratio of 7 penetrating the concrete of 35 MPa, the “rigid-body penetration” model is available when the initial impact velocity is lower than 800 m/s. However, when the initial impact velocity is higher than 800 m/s, the “deforming/eroding body penetration” model should be adopted. Through theoretical analysis and numerical calculation, the results indicate that the initial impact velocity is the most important factor of mass abrasion. The hardness of aggregates and the strength of projectile are also significant factors. But relatively speaking, the sensitivity of strength of projectile to mass abrasion is higher, which indicates that the effect of projectile material on mass abrasion is more dramatic than the hardness of aggregates.

On the penetration of nonaxisymmetric bodies into a deformable solid medium and their shape optimization

We consider the problem of penetration of rigid pyramidal bodies (impactors) into a strained medium in the case of large speeds of penetration and estimate the depth of the impactor penetration. To this end, we use the two-stage penetration model proposed by Forrestall. We state the shape optimization problem for the penetrating body, which is based on the consideration of a set of bodies of pyramidal external shape with given fixed mass. We study both solid and hollow (shell-shaped) bodies. For the optimization functional we take the penetration depth of the penetrating body, and for the projection variable we take the number of faces of the pyramidal body. We present the results of computations of the penetration depth for different shapes of the impactor and show that, both for shells and solid impactors, the bodies of the shape of a circular cone are optimal. The problems of high-speed penetration of rigid bodies into a deformable medium are nowadays very topical problems [1] which have been studied by Russian and foreign authors [2–8].

Penetration of rigid bodies into loose and layered media

Penetration and motion of rigid bodies in ground media attracts the researchers’ attention because of various problems arising as the technology evolves. In fact, there are two independent directions of studies in this field: (1) the problem of earth excavation when a rigid body of a definite shape slowly moves along a given trajectory in the ground; (2) an impact of a rapidly flying free rigid or deformable body against the ground. In the latter case, to which the proposed studies pertain, it is sometimes of interest to study the medium behavior and the motion of the free body, which moves in the medium after the impact owing to the kinetic energy of itself. In this field, a majority of studies deal with collision and penetration of bodies of various shapes into clay media. An extensive survey of these studies is given in [1]. After this survey appeared, numerous paper dealing with complicated collision conditions have been published [2]. Penetration in loose media has been studied much more rarely. The direct collision with fractured rock was studied in connection with the expected landing of spacecraft on other planets [3, 4]. In this case, the influence of grain dimensions and the density of the filling and vacuum on the penetration was studied for the initial velocities in the range of 1.7–10 m/s. On the other hand, in [5], the results of investigating the penetration of conic bodies in sand at entry velocities of 700–900 m/s are given; these velocities significantly exceed the speed of sound in this medium, which lies in the range of 100–200 m/s for dry sand. Analyzing the experimental results, the author came to the conclusion that it is necessary to use different representations of the drag force in the supersonic and subsonic modes. In the present paper, we do not consider the influence of the grain distribution, sand density, and filling methods on the penetration. But, as follows from the experiments whose results are described in [6] and [7], to represent the results of penetration of rigid bodies at velocities up to several hundreds of meters per second, in addition to the characteristics listed above, it is also required to describe the technology of the experiment preparation, because such media have the property of shape “memory.”

Penetration of rigid bodies into loose and layered media

Penetration of rigid bodies into loose and layered media

Localized interaction models with non-constant friction for rigid penetrating impactors

We suggest approximate penetration models for rigid body penetration that take into account sliding velocity (SV) and pressure dependence of the friction coefficient (FC). It is showed that introducing variable FC in a localized interaction model (LIM) yields a model that belongs to the class of LIM. We developed a general method for determining the depth of penetration (DOP) using the piecewise linear approximation of the impactor’s generatrix. For some classes of SV dependent friction models we obtained analytical formulas for calculating the DOP. Using the experimental data available in the literature, we determined the dependencies of FC vs. pressure and SV. We conducted numerical modeling of penetration of a metal striker into metal and concrete shields employing models with variable and constant FC. Numerical simulations showed that taking into account variable FC strongly effects the DOP when FC changes appreciably for large velocities that are characteristic for the high-speed penetration.

High-velocity impact loading of thick GFRP blocks

In previous depth of penetration experiments with tungsten long rod projectiles was found that the ballistic resistance of a relatively thick - up to the penetrator length - glass fibre reinforced plastic block grows with increasing penetration depth. This penetration behaviour significantly differs from that of other inert armour materials. Until now, no significant difference between unconfined and totally confined GFRP configurations has been found. Newest experiments with up to semi-infinite thick GFRP blocks show a change in the penetration process: For thicknesses significantly higher than the penetrator length the protective power may saturate. During the late penetration phase the shortening and deceleration of the projectile induce a change of penetration mechanism from erosion to rigid body penetration. Additionally, the projectile may break into several individually tumbling parts. Reflected tension waves and, probably, pyrolysis effects may cause increasing precursory damage. These effects together are likely to explain the reduction of the ballistic resistance increase during the late penetration phase. Based on these experimental results the published working hypothesis on the governing mechanism of the GFRP penetration behaviour had to be completed. A new approach based on a hyperbolic tangent function seems to satisfactorily describe the observed thickness dependent phenomena.

A one-dimensional analysis of rigid-body penetration with high-speed friction

A new law for high-speed friction is presented in this paper. This law is based on observations made by several investigators regarding the asymptotic behaviour of sliding friction as the speed is increased. The new frictional effect is incorporated into the equations for rigid-body penetration to develop an analytical penetration theory. The new theory is applied to a series of penetration experiments for several steel projectiles into the same concrete target. The results confirm that the new frictional effect is a very promising addition to the theory of rigid-body penetration.

An investigation of the impact and penetration of solids of revolution into soft earth

The numerical method proposed earlier in [1] is developed to solve problems of the impact and penetration of rigid and deformable bodies of revolution into soft soil, which are described by Grigoryan's model [2]. The effect of the surface Coulomb friction, the bulk compressibility and the shear strength of soft soil on the forces of resistance and contact pressures in the contact zone is analysed. The results of numerical solutions of problems in a coherent formulation are compared with analytical relations and experimental data on the determination of the forces and coefficients of resistance to the penetration of impactors of different shapes into soft soil.

Dynamic X-ray imaging of the penetration of boron carbide

The U.S. Army Research Laboratory has adapted two 1-MeV x-ray pulsers to obtain multiple dynamic, real time x-rays of the impact of 7.62-mm APM2 armor-piercing projectiles on a boron carbide ceramic. The goal was to conduct a high fidelity diagnostic analysis of the impact during the initial transient period and document the penetrator/target interaction. Three conditions ofthe projectile were tested: the full metal jacket projectile; the steel core and lead tip only; and just the steel core. These different conditions allow the observation of the tip breakup mechanism and determination of the average penetration velocity, the time for initiation of rigid body penetration into the ceramic/backing and the ballistic contributions of the projectile components.