Stability analyses of the mass abrasive projectile high-speed penetrating into concrete target. Part Ⅰ: Engineering model for the mass loss and nose-blunting of ogive-nosed projectiles

The mass loss and nose blunting of a projectile during high-speed deep penetration into concrete target may cause structural destruction and ballistic trajectory instability of the penetrator,obviously reducing the penetration efficiency of penetrator.Provided that the work of friction between projectile and target is totally transformed into the heat to melt penetrator material at its nose surface,an engineering model is established for the mass loss and nose-blunting of the ogive-nosed projectile.A dimensionless formula for the relative mass loss of projectile is obtained by introducing the dimensionless impact function I and geometry function N of the projectile.The critical value V c0of the initial striking velocity is formulated,and the mass loss of projectile tends to increase weakly nonlinearly with I/N when V0〉V c0,whilst the mass loss is proportional to the initial kinetic energy of projectile when V0

Stability analyses of the mass abrasive projectile high-speed penetrating into concrete target. Part Ⅱ: Structural stability analyses

The initial oblique and attacking angles as well as the asymmetrical nose abrasion may lead to bending or even fracture of a projectile,and the penetration efficiency decreases distinctly.The structural stability of a high-speed projectile non-normally penetrating into concrete and the parametric influences involved are analyzed with the mass abrasion taken into account.By considering the symmetrical or asymmetrical nose abrasion as well as the initial oblique and attacking angles,both the axial and the transverse drag forces acting on the projectile are derived.Based on the ideal elastic-plastic yield criterion,an approach is proposed for predicting the limit striking velocity（LSV）that is the highest velocity at which no yielding failure has occurred and the projectile can still maintain its integral structural stability.Furthermore,some particular penetration scenarios are separately discussed in detail.Based on the engineering model for the mass loss and nose-blunting of ogive-nose projectiles established in Part I of this study,the above approach is validated by several high-speed penetration tests.The analysis on parametric influences indicates that the LSV is reduced with an increase in the asymmetrical nose abrasion,thelength-diameter-ratio,and the concrete strength,as well as the oblique and attacking angles.Also,the LSV raises with an increase in the initial caliber-radius-head（CRH）and the dimensionless cartridge thickness of a projectile.