UDC 531.66 MODEL OF HIGH-SPEED SHOCK INTERACTION WITH COMPATIBLE TYPE

This research aims to the process of interaction of a bullet (fragment) with protective barriers, which are formed by a set of hollow cylinders of a compatible type. Models for determining the depth of penetration of the drummer into an obstacle in the form of a set of hollow cylinders of compatible type are proposed. The results of calculations of the value of the depth of penetration of the bullet into the protective barrier in the form of a set of compatible cylinders. Further research is related to the improvement of the armor protection designs by developing new technical solutions using the latest technologies.

Formulation of the problem. In connection with the ongoing hostilities in eastern Ukraine, the issue of developing the protection of servicemen from bullets and shrapnel remains relevant. Modern research on the interaction of bullets and fragments with protective barriers is based on the search for new types of structures and protective materials. The main focus is on the development of protective structures that would increase the level of protection of servicemen, according to NATO standards, using inexpensive available materials with minimal costs for their production and intended use.
Despite some progress in the investigation of collisions of solids, the known results of theoretical and experimental research do not describe a holistic picture of the interaction of the element of damage and interference. Therefore, in the development of protective structures take into account only certain aspects of impact interaction, which are based on the absorption of kinetic energy of the element of damage [1].
The scientific and technical task remains important study of the process of interaction of bullets (fragments) with protective barriers, at the stages of penetration, breaking and their departure, which will develop new models of protection design for servicemen, which are relevant for the Armed Forces of Ukraine.
Analysis of recent research and publications. The issues of interaction of bullets (fragments) with protective obstacles have long been dealt with and various methods and approaches to calculating the depth of penetration of obstacles have been known. Fundamental results of the study of the phenomenon of impact and determination of the conditions for breaking through obstacles by drummers (bullets, fragments) were obtained in the works of Euler, Jacob de Mar, Noble, J. Reinhart and J. Pearson, Berzin K.A. and others [1].
In [1] the parameters of the multilayer protective structure of combat vehicles based on nonlinear mathematical models are substantiated. In [2] the method of research of complex systems of military purpose is resulted. In [3][4][5][6] the modeling of the dynamics of the reaction of the protective structure to the action of the shock-wave load at the impact of a bullet or a fragment of a projectile is considered. In [7] materials for local and individual armoring are investigated. A study of the use of non-traditional methods of interaction of bullets (fragments) with protective barriers is given in research [8].
The main method of studying the process of impact and punching an obstacle with a bullet (fragment) is a combination of analytical and experimental researches. Analytical research methods are based on mathematical modeling of the stages of interaction of bullets (fragments) with the elements of the protective barrier, followed by appropriate mathematical calculations [1]. Experimental research methods are based on determining the level of protection of protected objects and require complex research in laboratory and landfill conditions. The combination of the results of analytical and experimental research allows us to more fully consider the level of protection of protected objects.
However, studies of the interaction of bullets (fragments) with protective obstacles have not been completed, the processes occurring when hitting bullets (fragments) on the obstacle are not fully studied, and the applied models and methods do not fully take into account the design parameters of protective obstacles.
The purpose of the article is to investigate the process of interaction of a bullets with a protective obstacle in the form of a set of compatible cylinders.
The main material. The use of single cylinders and bonded structures are only two of the possible means of increasing the strength of protective structures [8]. Another possible way to increase the strength of protective structures is a method that consists not of a nozzle of structures in the hot state with tension, but by the formation between the component structures (cylinders) of the gap into which the liquid (gas) is injected under pressure. By placing the cylinders in each other and adjusting the pressure of the liquid (gas) in the free zones between the cylinders, it can be achieved that at the same thickness in the cylinder walls, the pressure in the inner cylinder can be greater than in a single cylinder [9].
For a single cylinder, the ultimate pressure in it can reach half the strength limit of the material. For bonded and compatible cylinders, the maximum pressure is twice as high as for a single cylinder. For compatible cylinders, the limit pressure can be increased by another 25%. If autofretted cylinders are used for compatible cylinders, the limiting pressure in the inner cylinder can be four times higher than for a single cylinder [9].
The prop that occurs in compatible cylinders and in bonded cylinders is not the same thing. The prop in the bonded cylinders, brought to a certain limit, then remains constant for the entire period of operation of the bonded cylinders. Prop in compatible cylinders can be variable.
Consider a structure consisting of two cylinders -the outer (2) and inner (1), with the outer diameter of the inner cylinder, in contrast to the bonded cylinders, is smaller than the inner diameter of the outer cylinder. Fluid is injected under pressure into the gap between the outer and inner cylinders (Fig. 1).
Using the known formula for calculating normal stresses in the tangential direction [9,10]: where р in -is the internal pressure in the cylinder, Pa; р ex -is external pressure on the cylinder, Pa; r in -is the internal radius of the cylinder, m; r o -is the external radius of the cylinder, m; r -is the current radius of the cylinder, m. For compatible cylinders, the following expressions can be written [9]: when r = r in Pressure in the radial direction [9]: (1 ) , 1 on the outer surface Equating the values of stresses to the allowable stress for the cylinder material [], to determine the expression   when r = r in we obtain the formula for determining the maximum allowable internal pressure [9]: If the protective structure consists of two cylinders (outer and one inner), then for the outer cylinder: the maximum allowable pressure will be: For any intermediate cylinder (if the protective structure consists of several cylinders: external and several (i) internal), the maximum allowable internal pressure can be written as: Maximum allowable internal pressure in the inner cylinder with n cylinders [9]: For a compatible design consisting of two cylinders, the value of the internal pressure in the outer cylinder is determined by the equation: The value of the internal pressure in the inner cylinder is determined by the equation: The contact pressure that occurs when passing a bullet in the middle of a cylinder of smaller diameter (than the diameter of the bullet) is determined by the expression [10]: The value of the internal pressure in the outer cylinder is determined by the formula (12): The depth of penetration of the bullet into the cylinder h is determined by the formula: 2019 0, 0066 . 305108 h m   Thus, the obtained value of the depth of penetration of the bullet into the compatible cylinder is less than the depth of penetration of the bullet into the bonded cylinder, which is given in research [8].

MODEL OF HIGH-SPEED SHOCK INTERACTION WITH COMPATIBLE TYPE
In connection with military operations, the issue of developing protection for military personnel against bullets and splinters remains an issue. Modern studies of the interaction of bullets and fragments with protective obstacles are based on the search for new types of structures and materials of protection. The focus is on the development of NATO-compliant protective structures to increase the level of protection for military personnel using low-cost, affordable materials with minimal production and intended use.
Despite some advances in the study of solid-body impact, the known results of theoretical and experimental studies do not describe the overall picture of the interaction of the element of damage and interference. When designing protective structures, only certain aspects of the shock interaction are considered, based on the absorption of the kinetic energy of the element of damage. Therefore, it remains important for the scientific and technical task -to continue the study of the process of interaction of bullets (fragments) with protective obstacles, at the stages of penetration, penetration and their departure, which will allow to develop new models of protection structure of military personnel that are relevant for military use.
The main method of studying the process of striking and punching an obstacle with a bullet (fragment) is a combination of analytical and experimental studies. Analytical methods of research are based on mathematical modeling of stages of interaction of bullets (fragments) with elements of a protective obstacle with the subsequent carrying out of corresponding mathematical calculations. Experimental research methods are based on determining the level of security and require complex research in laboratory and polygonal conditions. The combination of analytical and experimental research results makes it possible to consider the level of security more fully.