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Experimental and analytical research methods of losses of stability of meniscal form liners at their high-speed deformation, i.e., collapse, by products of detonation of explosive have limited opportunities. They are caused by the complicated nature of liner thickness change to control the operated loss of stability --- folding, high-speed deformations of liners, intensive drop of pressure acting on them and some other features. The paper introduces an approach to numerical three-dimensional modeling of collapse of meniscal form liners with variable thickness in the circumferential direction in the area of their periphery, the modeling being carried out by the finite element method in Lagrange coordinate system in LS-DYNA software package. The study also shows the main stages of implementing this approach and describes the key parameters of the materials models used, as well as the type of the final element and mechanism of adaptive updating of the computational grid. By the method of numerical simulation, we found the main regularities of liners collapse and folding of the afterbody of high speed elements formed during the collapse of the liners. The results of numerical calculations are confirmed by experimental data. The studies done are of interest to specialists involved in the analysis of the loss of stability of various structures under dynamic loads, as well as to specialists in the field of explosion and impact physics.
Experimental and analytical research methods of losses of stability of meniscal form liners at their high-speed deformation, i.e., collapse, by products of detonation of explosive have limited opportunities. They are caused by the complicated nature of liner thickness change to control the operated loss of stability --- folding, high-speed deformations of liners, intensive drop of pressure acting on them and some other features. The paper introduces an approach to numerical three-dimensional modeling of collapse of meniscal form liners with variable thickness in the circumferential direction in the area of their periphery, the modeling being carried out by the finite element method in Lagrange coordinate system in LS-DYNA software package. The study also shows the main stages of implementing this approach and describes the key parameters of the materials models used, as well as the type of the final element and mechanism of adaptive updating of the computational grid. By the method of numerical simulation, we found the main regularities of liners collapse and folding of the afterbody of high speed elements formed during the collapse of the liners. The results of numerical calculations are confirmed by experimental data. The studies done are of interest to specialists involved in the analysis of the loss of stability of various structures under dynamic loads, as well as to specialists in the field of explosion and impact physics.
The paper considers a separate issue of the shaped charge functioning, i.e., functioning of a rotating charge under preliminary thermal action on its liner. Estimates of two oppositely directed factors are provided: 1) increase in the shaped-charge jet dynamic plasticity (limit elongation coefficient); 2) increase in the jet susceptibility to centrifugal destruction. These factors are activated by preliminary thermal action on the shaped charge liner in the jet heated in excess of usual parameters. The so-called "thermal" increase in the limit elongation coefficient was estimated using empirical and theoretical dependences of this value on the shaped-charge jet parameters, and on the characteristics of its material. Strength dependence on temperature was accepted as linearly decreasing. Centrifugal factor was estimated based on the law of kinetic moment conservation taking into consideration the gradient nature of stretching and, up to a certain point, the radial thinning of jet elements. The moment of centrifugal and strength forces relationship reaching the critical value was accepted as the beginning of the jet element centrifugal destruction. From this time moment the jet radial extension started. The law of decompaction of its enlarging part was taken from studies previously conducted by the authors. It was demonstrated that the two considered factors acting in the opposite directions in a jet were in compliance with each other ensuring optimal preliminary heating of the liner and penetration effect with a local maximum.
The mathematical model for the subsequent numerical study of the shaped charge liner collapse affected by external surface forces simulating an explosive load is presented. The basic liner was considered as an originally cylindrical compressible elastoplastic shell within the framework of a two-dimensional flat nonstationary problem of continuum mechanics. To ensure the rationality of the modeling and numerical calculation at the initial time the design fragment was discriminated in the liner by central beams. Deformation of the fragment being a part of the shell was taken into account by the boundary conditions of cyclic repeatability in the tangential direction. For numerical solving the well-known Wilkins Lagrangian method was used, which was refined in terms of the relations describing the mechanical behavior of an elastoplastic medium. Additionally, a self-developed grid adjustment procedure was used, excluding the appearance of highly elongated cells in the calculation. The instability of the shell deformation was initiated by harmonic surface perturbations, initially assigned on the outer or inner surfaces. The degree of instability was assessed by the deviation of the disturbed surface (or the boundary of the so-called stream-forming layer) from the cylindrical one. The used finite-difference algorithms are implemented in the form of appropriate calculation programs. A number of computational verification measures was performed proving the viability of the developed mathematical model and the possibility of its further use
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