A model of a hard axsymmetric projectile’s high-speed impact with a deformable semi-infinite barrier | Mekhanika | kompozitsionnykh | materialov i konstruktsii

A model of a hard axsymmetric projectile’s high-speed impact with a deformable semi-infinite barrier

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An analytical mechanical model of penetration at a high-speed impact of a rigid cylindrical projectile into a semi-infinite barrier has been constructed. The projectile is characterized by three parameters – linear transverse size, mass and initial speed. Regarding the mechanical properties of the barrier material, the hypothesis of a perfectly hard-plastic body with a condition of incompressibility has been adopted. The material of the barrier is characterized by two parameters – density and the yield strength. The problem is considered in the ax symmetrical dynamic setting. The aim of the work is to obtain acceptable engineering estimates of the following parameters – the depth of the projectile ‘s introduction, the mass of material thrown out of the barrier (in its evaluation, it was assumed that the material risen above the initial level of the undeformed barrier, leaves it and does not participate in further consideration of the movement), the effect of strengthening the momentum caused by the release (ejection) of the barrier fragments in the direction opposite to the projectile’s flight direction. The following method of research is proposed. An ax symmetric field of velocities is being built in three zones. The first is the area of the barrier material “sticking” to the projectile and moving with it, like a solid undeformable body. It is modeled as a segment of the ball. The second velocity field is a fragment of a ball layer adjacent to the first zone. The velocity field in this zone is based on the assumption that the speed  ;UR, in a specially selected local spherical coordinate system, depends only on .That is    ;U R g. The speed  ;RUR is determined from the incompressibility condition. The third zone is a cylindrical zone moving like a solid in the direction opposite to the projectile’s movement. At the boundary of the zones a condition of continuity of normal speed component is supposed. The zone parameters are determined from the minimum power of the internal forces. The equation of motion is replaced by an equation of energy balance – the change of kinetic energy equals the power of internal forces. The assumptions made allowed to define the parameters of zones as a function of the depth of the projectile’s penetration. This allowed building a relatively simple analytical engineering model, which permits to determine the depth of the projectile’s introduction, the mass of the ejection, the strengthening of the pulse. In fact, the result is determined by two non-dimensional parameters.