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The effect of the velocity of compact metal projectiles of spherical and cylindrical shapes on the size of craters formed in steel targets of different strength was studied in the velocity range 2–10 km/s by numerical simulation using two different computational techniques. The behavior of the materials of the projectile and target is described using a model of a compressible elastoplastic medium with a constant yield strength. The projectile materials are copper, titanium, and tantalum. The projectile mass and velocity are specified assuming that their kinetic energy is constant. It is found that the dependences of the crater depth on the velocity of projectiles with constant kinetic energy have a maximum and the crater volume decreases monotonically with increasing velocity.

Due to their capability to form high velocity elements, explosive launching devices are used for testing objects of rocket and space technology on anti-meteoric resistance. These devices include shaped charges with a combined hemisphere-cylinder liner. Currently used shaped charges with a hemisphere-cylinder liner can produce compact steel elements with velocities of 6 km/s. Based on numerical simulation in the framework of the two-dimensional axisymmetric problem of continuum mechanics, the possibilities of increasing the velocity of compact metal elements formed by shaped charges with a combined hemisphere-cylinder liner up to 9 … 10 km/s are considered. Simulation has been performed for a 100 mm diameter shaped charge with a copper liner. The stated goal has been achieved by giving the jet-forming hemispherical part of the liner a degressive (decreasing from the top to the base) thickness with a change in its shape from hemispherical to semi-ellipsoid. As a result of calculations, liners geometric parameters have been selected to form compact elements of maximum possible mass with velocities in the range from 5 to 9.5 km/s. For an element with a velocity of about 9.5 km/s, the mass was about 5 g.

Operation of shaped charges with copper hemispherical liners of degressive (decreasing from top to bottom) thickness is experimentally studied. The velocity of the head of generated shaped-charge jets is determined along with how deep they penetrate a type-setting target made of steel disks and the sizes of holes made in the disks. The experimental data on an increase in the velocity and a decrease in the mass of the heads of shaped-charge jets, which occur with an increase in the difference in the thicknesses of the hemispherical liner at the apex and at the base are in good agreement with the results of numerical simulation carried out within the framework of a two-dimensional axisymmetric problem of continuous mechanics. According to the experimental results, the effect of technological manufacturing errors on the operation of these charges becomes stronger, which eliminates or significantly limits the increase in the penetrating action. In one of the versions of liners of degressive thickness, the depth of penetration of a target, which is average in two tests, increases by 7.5% as compared to the liner of constant thickness.

X-ray research of particles formed during the explosion of a shaped charge with steel liner of the combined hemisphere-cylinder shape with a jet-forming part of a degressive (decreasing from top to base) thickness and a cylindrical part is carried out. It was experimentally confirmed that the transition from the constant to the degressive thickness of the hemispherical part of the liners allows to increase the velosity of the head section of the material formed during its compression by the jet flow of the material, which is cut off during the collapse of the cylindrical part of the liner. The velosity of a steel compact non-gradient element recorded in experiments for tested variants of a shaped charge was 7.8 … 8.6 km/s, which, within the permissible experimental errors, corresponds to the results of previously performed numerical calculations and approximately 30% higher than the speed of the corresponding element obtained using constant thickness.

The rotational motion of fluted shaped-charge liners has been studied. It has been shown that the main factors affecting the rotation of a shaped-charge jet are the position of the jet-forming layer and the distribution of the circumferential velocity over the liner cross-section. The proposed method can be used to estimate the average angular velocity of a jet with consideration of the dimensions of the fluted shaped-charge liner and the properties of its material. It is shown that the results are consistent with available experimental data.

Studies of shaped charges with hemispherical liners of degressive thickness (decreasing from the top to the base) were continued based on numerical simulation. The possibility of increasing not only the velocity but also the mass of the head elements of shaped-charge jets to the level provided by conical liners of progressive thickness were analyzed. For this purpose, liners of degressive thickness in the form of a truncated sphere and a semi-ellipsoid slightly elongated along the charge axis were additionally studied.

The paper briefly analyzes a number of published works devoted to cumulative explosion under conditions of the possible development of surface instability of the collapsing liner of a shaped charge. Most studies stated that surface instability was initially initiated by harmonic surface disturbances or disturbances in the parameters of a given load simulating an explosive one. The instability manifested itself in the form of the development of surface disturbances over time; the absence or limited growth was considered as the preservation of the stability of the deformable shell. In addition to the influence of instability on cumulative processes, related jet flows were also investigated. This is the so-called explosive dispersion (dusting), which occurs both under the influence of the interference of shock waves and unloading waves, and in the presence of initial disturbances of the surface shape. The analysis is built within the framework of the phenomenological approach — both the main results of the experiments and their mathematical descriptions were considered, which in most cases were carried out from the positions established in the mechanics of continuous media, as well as with the help of numerical modeling. Based on the results, conclusions were formulated about the reasons and forms of manifestation of surface instability of collapsing metal liners of shaped charges, the nature of the development and parameters of functioning of such charges, as well as about the features and laws of this process.

The paper focuses on experiments carried out to determine the effect of a small-diameter channel, passed by a shaped-charge jet before interacting with an obstacle, on its penetrating action. These experiments were conducted in relation to the study of the features of shaped-charge jet motion through the cavity of an elongated solenoid with electromagnetic stabilization of the jet stretching process. For this purpose, steel sleeves with a channel were installed in front of the shaped charge, which made it possible to simulate the mechanical factors affecting the shaped-charge jet when it moves in the air channel. For the conditions implemented in the experiments, it was found that in the absence of collisions of the shaped-charge jet with the channel walls, the penetration depth decreases insignificantly, i.e. within 5%. In experiments in which there were traces of contact interaction with the shaped-charge jet on the channel surface, a significant decrease in the penetrating action was recorded.

In this paper, we present the results of numerical simulation of explosive formation of a high-speed compact element from copper, steel, and aluminum cumulative liners combining the shape of a hemispherical segment smoothly converting into a cylindrical surface (“hemisphere–cylinder” liners). The problem is solved in a two-dimensional axisymmetric setting considering the limiting parameters of the dynamic stress-strain state causing plastic flow and destruction of the cumulative liner material. The original model of the functioning of cumulative shaped charge, which determines the effect of individual elements of the cumulative liners, including the difference in numerical characteristics of their physicomechanical properties and critical destruction conditions, on the final parameters of the high-speed compact element, was used. The plastic properties of the material and the critical conditions for its destruction were found not to affect the final velocity of the formed high-speed compact element, but they affect its shape, dimensions, and mass.

The influence of the geometric parameters of variable-thickness steel disk workpieces on the wall thickness of cylindrical shell parts with a spherical bottom, which are produced by lead stamping, is experimentally studied. The found laws of changing the dome thickness and the edge thickness of stamped parts allowed us to make recommendations for designing the lead stamping of such parts with a given wall thickness distribution.

Particle flows formed from shaped charges with a combined steel liner consisting of a hemisphere and a cylinder with a hemispherical part of degressive thickness (decreasing from top to bottom) were investigated by flash radiography. It has been found experimentally that the change from a constant to a degressive thickness of the hemispherical part increases the velocity of the head part of the liner jet formed during its compression, which is subsequently separated upon collapse of the cylindrical part. The maximum particle velocity obtained as a result of separation in the experiments was 8.6 km/s.

The formation of high-velocity compact elements of shaped charges with a liner of a combined hemisphere–cylinder shape has been analyzed by numerical simulations of a two-dimensional axisymmetric problem of continuum mechanics. This liner jet generator contains a part of a hemisphere, a truncated sphere or a slightly prolate ellipsoid and a cut-off part in the form of a cylinder. The abstract massive speed characteristics of the formed compact elements depend on changes in the geometric parameters of the combined cumulative liner. Variants combined the cumulative liner with an explosive device to ensure the formation of elements of a gradientless weight from 5 g to 15 g at velocities of 7.5–10 km/s. This simple explosive device can be used to simulate the conditions in the Earth's single and group impact of micrometeorites and space debris objects in rocket and space technology.

The paper considers the possibility of using compact projectiles formed by an explosion to break through strong steel barriers of finite thickness protected by a layer of water. There is no problem in penetrating such barriers by high-gradient and high-speed shaped-charge jet of a small diameter formed by shaped charges with ‘high’ conical liners, however, the diameter of the through hole formed in the steel barrier is fairly small and does not meet the defeat criteria for corresponding barriers. To increase the diameter of a through hole in a steel barrier, shaped charges with ‘low’ conical or flat hemispherical liners (in the form of a meniscus) forming compact projectiles can be used, but the movement of such ‘shock cores’ in the water layer is sharply slowed down, up to a complete stop even before interacting with the main steel barrier. The purpose of the paper is to substantiate the possibilities of eliminating this disadvantage when using compact projectiles. Based on theoretical and experimental studies, the paper offers a technical solution related to the known fact of the formation of a cavern (gas cavity) during the movement of a shaped-charge jet in water, expanding as the jet penetrates in the radial direction. In this case, if a known tandem scheme of shaped charges placed one after the other along the axis of the explosive device is used, the first shaped charge, often called pre-charge, will penetrate the body in the head part of the explosive device to the water layer, then form in the latter a cavern up to the main penetrable barrier and the second shaped charge, often referred to as the primary, will form a compact projectile moving to penetrable barrier in the cavity formed by the penetration of shaped-precharge jet in the water. At the same time, due to selecting the necessary delay time between the pre-charge and main charge explosions as well as the design parameters of the pre-charge, the size of the expanding cavity must exceed the size of the compact projectile, excluding its interaction with water up to the approach to the penetrable steel barrier.

The implementation of ground-based modelling of high-speed interaction between objects when conducting studies of the behaviour of materials and structures under high-intensity exposure to various particles of natural and artificial origin is one of the urgent tasks in the development of spacecrafts nowadays. One of the methods for producing high-speed compact elements (HSCE) for subsequent modelling of meteorite impact is the use of explosive throwing devices in the form of high-explosive anti-tank shell (HEAT) with a combined hemisphere-cylinder lining (HC-lining). The purpose of this study was to carry out calculations and experiments to identify the most effective options for combined HC-facing, providing the formation of metal HSCE of the required mass and velocity. Based on numerical simulation, within the framework of the two-dimensional axisymmetric problem of continuum mechanics, the influence of the radius and thickness of the hemispherical part of the HC-lining on the parameters of the formed HSCE was studied. To increase the velocity of the HSCE, it is proposed to use the hemispherical part of the degressive (decreasing from the top to the base of the hemisphere) thickness. Short-circuit variants with similar HC-linings have been developed, which make possible to form steel compact elements of gram-weightes with speeds in the range of 7.5 … 10 km/s. Comparative experimental studies were carried out with the determination of the parameters of the HSCE by the X-ray method and with the use of electrical contact pin.The implementation of ground-based modelling of high-speed interaction between objects when conducting studies of the behaviour of materials and structures under high-intensity exposure to various particles of natural and artificial origin is one of the urgent tasks in the development of spacecrafts nowadays. One of the methods for producing high-speed compact elements (HSCE) for subsequent modelling of meteorite impact is the use of explosive throwing devices in the form of high-explosive anti-tank shell (HEAT) with a combined hemisphere-cylinder lining (HC-lining). The purpose of this study was to carry out calculations and experiments to identify the most effective options for combined HC-facing, providing the formation of metal HSCE of the required mass and velocity. Based on numerical simulation, within the framework of the two-dimensional axisymmetric problem of continuum mechanics, the influence of the radius and thickness of the hemispherical part of the HC-lining on the parameters of the formed H...

The formation of high-velocity compact elements of shaped charges with a liner of a combined hemisphere-cylinder shape has been analyzed by numerical simulations of a two-dimensional axisymmetric problem of continuum mechanics. The influence of the radius and thickness of the hemispherical portion of the combined liner on the parameters of the compact elements has been studied. It is shown that in implosion of hemispherical liners whose thickness decreases from top to bottom, there is an increase in the velocity of the resulting jet flow. When using a hemispherical portion of variable thickness (to increase the velocity of the compact elements formed), it is necessary to solve two additional problems—to implement timely separation of the head part of the jet flow with increased velocity and increase its mass. For this, it is proposed to use the jet-forming part of the combined liner in the form of a truncated sphere or a slightly elongated ellipsoid of revolution. Combined shaped-charge liners in the form of a truncated ellipsoid of variable thickness were developed, allowing the formation of compact elements having a velocity of 7.5–10 km/s.

This paper deals with electromagnetic actions that allow one to control the shaped-charge effect at different stages of shaped-charge operation. A decrease in penetration of the shaped-charge jet is attained by production of an axial magnetic field in the shaped-charge liner immediately before shot, and production of a magnetic field in the conducting target material that is transverse to the direction of jet propagation. The considerable decrease in the penetration capability of the charge observed in the experiments is attributed to a sharp amplification of the magnetic field in the jet formation region upon liner collapse. The effects accompanying the “field pumping” prevent the normal formation of a shaped-charge jet. A model of magnetic field generation in a conducting medium subjected to high-velocity deformation with particle elongation along the magnetic flux lines is considered. X-ray photographs of shaped-charge jets formed from a “magnetized liner” are given. Theoretical calculations have shown that deformation conditions that can provide for intense magnetic field generation also arise during high-velocity jet penetration into a conducting target across the flux lines of the initial magnetic field previously produced in the target.

Experiments on creating an axial magnetic field in the metallic sheath of a shaped charge immediately before explosion are reported. Under such conditions, the penetrability of the charge is shown to decrease substantially. For instance, the penetration into a steel target is reduced more than twice when the initial field in the sheath is several tenths of a tesla. The most plausible reason for this effect is a drastic rise in the magnetic field (to a level as high as several hundreds of teslas) in the jet formation area, which disturbs the cumulative jet formation process. This pumping effect is presumably related to the magnetic field “freezing” into the deforming conductive material. Such a mechanism shows up when the tensile strain of the sheath’s fragments along the magnetic flux lines is significant. The ability of the deformation mechanism of field generation to disturb greatly the jet formation process upon collapsing the shaped charge sheath is substantiated by calculations.

A method for evaluating the penetrating (piercing) power of shaped charges under the condition when an intense electric current pulse is applied to a shaped charge jet is developed. The buildup of waist-type MHD instability and the volume damage of the jet material are viewed as possible mechanisms behind a reduction of the penetrating power of a shaped charge jet under the current action. With this method, electrodynamic action parameters that provide a significant reduction of the penetrating power of a shaped charge jet are calculated for shaped charges of various penetrability.

From the viewpoint of the model of a uniformly stretching cylindrical incompressible rigid‐plastic conducting rod, the salient features of deformation of metal cumulative jets in a longitudinal low‐frequency magnetic field are considered. The electromagnetic processes proceeding in the jet segments when they enter or leave the region with a magnetic field have been investigated. It is shown that the electromagnetic forces arising as the result of deformation of the jet with the magnetic field that has penetrated into its material should inhibit the development of plastic instability, extending the stretching stage of the jet before it breaks up into separate segments and thus creating prerequisites for increasing its penetrating power capacity. The magnetic‐field parameters that enable one to expect a noticeable manifestation of the stabilizing effect have been estimated.

The effect of preheating of liners on the penetration capability of shaped charges is considered theoretically. It is shown that for a plastically fractured shaped‐charge jet, preheating of the liner generally increases the effective jet length and shaped‐charge jet penetration. Restrictions on the parameters of preheating of shaped‐charge liners due to the possible thermal initiation of the explosive are established. It is noted that excessive weakening of a shaped‐charge jet can lead to transition from plastic to volume fracture with a corresponding decrease in shaped‐charge jet penetration. The ultimate possibilities of the thermal method for increasing the penetration capability of shaped charges are estimated. Calculation results are compared with available experimental data.

The paper reports results of experimental and numerical studies of the disruption of metallic shaped-charge jets by passage of a pulsed electric current through them. Experimental results are presented in the form of x-ray photographs of shaped-charge jets with and without a current and tables of penetration depths in targets. Numerical simulation of the disruption of shaped-charge jets with a current is performed for three possible mechanisms of disruption (development ofMHD instability of shaped-charge jets, volume fracture, and simultaneous development ofMHD instability and volume fracture). Numerical and experimental results are compared.

This paper deals with electromagnetic actions that allow one to control the shaped–charge effect at different stages of shaped–charge operation. A decrease in penetration of the shaped–charge jet is attained by passage of a powerful electric current pulse through it, production of an axial magnetic field in the shaped–charge liner immediately before shot, and production of a magnetic field in the conducting target material that is transverse to the direction of jet propagation. The action on a jet by low–frequency and high–frequency longitudinal magnetic fields and “mild” current action are directed toward increasing the penetration capability of a shaped–charge jet by increasing its ultimate elongation. Results of experimental and theoretical studies of different versions of electromagnetic actions are analyzed, and the associated physical effects are considered.

The results of physicomathematical modeling obtained within the framework of continuum mechanics by numerical solution of the two-dimensional axisymmetric nonstationary problem of the dynamic deformation of a compressed elastoplastic bar of variable section are presented. Dependences of the quantitative characteristics of stretching and breakup of a shaped-charge jet (the coefficients of ultimate and inertial elongation and the number of individual elements formed in breakup) on the jet parameters and the jet material properties are revealed by calculations. The calculated dependences are compared with experimental data for plastically failing jets of copper and niobium, and the character of the dependences is explained from the physical viewpoint.

Production of shear-formed liners for rotating shaped charges is of interest since it causes the jet self-spinning effect, which drastically affects the penetration process. A novel four-part methodology for calculating the performance parameters of such charges is suggested. First, the liner strained state is related to the feed rate and mandrel angular velocity during the shear-forming process. Second, based on the polycrystal plasticity theory, a methodology for determining the liner's plastic anisotropy parameters depending on its strained state is realized. Third, a general dependence of the jet angular velocity on the liner plastic anisotropy parameters is obtained. The fourth part presents the methodology of shaped charge performance calculation with respect to spinning effects. The results of calculations performed according to the suggested methodology are in good agreement with experimental data. Calculations also show that the penetration depth increases 9% to 15% compared to a spinning shaped charge with a drawn liner (i.e., without the self-spinning effect) when the self-spinning jet rotates oppositely to the shaped charge. When they rotate in the same direction, penetration depth decreases critically (more than 50%).

The present paper considers the possibility of using external magnetic fields for the antiterrorist protection of various objects against shaped-charge action by means of their magnetic screening - the creation of a magnetic field in the space ahead of the object being protected from attack.

Summary form only given. In recent years, much attention of researchers working in pulsed energy and high magnetic fields has been focused on searching for new applications of pulsed power and high magnetic fields in the protection against shaped-charge weapon. The present paper considers the possibility of using magnetic fields for the antiterrorist protection of various objects against shaped-charge action by means of their magnetic screening -the creation of a magnetic field in the space ahead of the object being protected from attack. The results of an experimental and numerical investigation of the effect of the magnetic field generated in a shaped-charge liner on the structure of the shaped charge formed and penetration into a target are presented. It is shown that a considerable decrease in the depth of penetration of shaped-charge jets into the target can be achieved at moderate magnetic fields of a few tenths of a tesla. The physical mechanisms involved in the disruption of shaped-charge jets and the possibility of using the detected physical phenomena to produce "magnetic armor" by the creation of a magnetic field ahead of an object subjected to shaped-charge attack are discussed. The results of the experiments and estimates confirm that the "magnetic protection" of objects from shaped-charge warheads is in principle possible.

Summary form given only, as follows. The paper deals with electromagnetic actions that allow one to control the shaped-charge effect at different stages of shaped-charge operation. A decrease in penetration for a shaped-charge jet is attained by passage of a powerful current pulse through it, production of an axial magnetic field in the shaped-charge current liner immediately before shot, and production of a magnetic field in the conducting target material that is transverse to the direction of jet propagation. The action on a jet by low-frequency and high-frequency longitudinal magnetic fields and "mild" current action are directed toward increasing the penetration capability of a shaped-charge jet by increasing its ultimate elongation. Results of experimental and theoretical studies of the shaped-charge jet effect for different versions of electromagnetic actions are presented, and the associated physical effects are considered.

It is established experimentally that generation of an axial magnetic field in the metal liner of a shaped charge immediately before ignition can drastically reduce its penetrability. Possible reasons for this effect are considered.