Модель переноса импульса при высокоскоростном ударе

Abstract

An analytical mechanical model of the ejection arising from a high-velocity impact of a rigid projectile on a semi-infinite target is constructed, and an estimate is given of the ejection mass and the effect of momentum amplification transmitted to the target upon impact. The effect of the momentum amplification is caused by the ejection of target fragments in the 148 direction opposite to the direction of flight of the projectie. At present, there is a steady interest in the study of this effect. This is due, in particular, to the possible use of the effect for deflecting a potentially dangerous object (asteroid) approaching the Earth by means of an impact spacecraft using the effect of momentum amplification. The model presented in this work is constructed in approximation of plane deformation using the minimum number of parameters of the projectiler and target materials. Equations for the mass of the ejection and the increment of the target momentum are obtained, depending on the depth of penetration of the projectile. The model takes into account the dependence of the emission angle of the ejection fragments on the penetration depth of the projectile. It is shown that the model adequately describes the ejection momentum, the rate of change in the ejection momentum, and the ejection mass depending on the penetration depth of the projectile. The possibility of representing the momentum and mass of the ejection by scaling ratios is checked both for the ratio of the densities of the projectile and the target ptρρ, and for the dynamic parameter 20ttVYγρ= (0V - impact velocity, tY - yield stress of the target), in which the proportionality coefficient depends only on the shape of the projectile. It was found that scaling with respect to the dynamic parameter γ takes place at сγγ>, where 330сγ≈ that, e.g., for aluminum gives the value 02.5 km/scV =.