Determination of the critical penetration rate of targets from aluminum and magnesium alloys

The motion of a non-deformable kinetic projectile of cylindrical shape in a continuous homogeneous semi-infinite medium is considered based on the well-known Alekseevsky-Tate model. As a result of solving the differential equation of motion of the impactor, the dependence of its speed on the penetration depth was obtained. The boundary conditions are: before penetrating the target, the speed of the impactor is equal to the critical penetration speed, and after penetrating the thickness of the target, the speed of the impactor is equal to zero. A simple formula for calculating the critical velocity of target penetration Vcr is obtained based on this dependence. This formula does not contain empirical coefficients. Therefore, the calculation of Vcr requires a minimum of information about both the material of the projectile and the target. An improved equation for calculating the resistance of the target material is also proposed. For targets from aluminum and magnesium alloys, critical penetration rates depending on their thickness were theoretically calculated and penetration curves were plotted. Also, the critical penetration velocity for targets from these alloys was determined experimentally during ballistic tests the results of the authors' own research and taken from the literature. A good agreement between the experimental data and theoretical calculations of the critical penetration velocity is observed, with the calculation error not exceeding 4%. With regard to the assessment of the critical thickness of the target, the maximum error will be about 5%, the average – 2,5%. It is assumed that in order to provide the reliable guaranteed protection against a known projectile, it is necessary to overestimate by 4% the calculated value of the critical penetration velocity while designing the protective element. Keywords: equation of motion, impactor, target, critical velocity, aluminum alloys, magnesium alloys.