PSI - Issue 40

A.M. Ignatova et al. / Procedia Structural Integrity 40 (2022) 185–193

186

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Ignatova A.M. at al. / Structural Integrity Procedia 00 (2022) 000 – 000

1. Introduction The study of the process of fragmentation of the various materials under high velocity impact is one of the tasks in the creation of armor-protective materials, the evaluation of the service life of protection of orbital objects from the exposure to space debris, as well as to ensure safety during the operation of aviation equipment. Currently, the fragmentation of metallic materials has been studied to the greatest extent. At the same time, many new refractory non-metallic and composite materials are promising for use in aviation and space technology as protective ones. According by Lamon (2016), the following main types of destruction are distinguished: brittle fracture with the formation of radial cracks; crushing; plastic penetration; Adiabatic Shear Failure; petal-shaped failure. For refractory non-metallic materials, only the first three of the above types are characteristic. With sufficient kinetic energy of the projectile, a fragment cloud is formed. When describing the results of experimental and analytical studies, the fragment cloud is often considered as a single object with its characteristics, which are, by Barenblatt (1964): propagation velocity (velocity of the leading fragment is often used), burst cone of the fragment cloud, an equivalent area of exposure to the fragment, distribution of fragments by mass and fluence of the fragment cloud. The listed parameters of the fragment cloud do not give an idea of the velocity of individual fragments, the value of which is necessary for predicting and evaluating the reaction of self-multiplication of space debris by Stefanov (2005) (a sequence in which the fragmentation during a collision of two particles leads to the formation of numerous smaller particles, which, colliding with each other, form their fragments of a smaller size, etc.). In addition, the individual velocity of rupture fragments after impact is necessary to evaluate how dangerous they are after dispersion. Various models focused on specific collision cases are used to predict the parameters of fragmentation, including the velocity of fragments. Goncharov et al. (2017) introduced a model for predicting the parameters of the rupture of the target and the shell of the projectile, which introduces a tracking equation:

j j U U   

V V 

(1)

1

 

j

j

t t

where V 1 is the velocity of the contact surface between the projectile and the fixed target at the moment of impact, ρ j , ρ t , is the density of the impactor material and the surface, respectively, U j , U t , is the velocity of the particles of the projectile and target material, respectively. This model has a significant limitation: it is impossible to consider the impact angle and external factors affecting the 'target – projectile system. Kiselev et al. (2009) presents a model describing the collision of two particles, which allows us to determine the dispersion velocity of fragments and predict their number. Thus, the velocity of each fragment m α j at the moment of impact consists of the velocity V, determined from equation (2), and the dispersion v j α from the point of collision.

2 2 1 1 1 2 V M M M M VV cos M V M     V is the total velocity of the two particles after the collision; V 1 is the velocity of the first particle before the collision; V 2 is the velocity of the second particle before the collision; M 1 is the mass of the first particle before the collision; M 2 is the mass of the second particle before the collision; 2 2 2 2 1 2 1 2

(2)

M is the total mass of two particles; φ is the angle of particles collis ion. To calculate v j

α , equation (3) is proposed, which has a particular solution (4) for the case when the velocity of all

fragments is the same.