Theoretical analysis of projectiles penetrating into rock targets at different velocities

As the impact velocity increases, the penetration mechanism varies from rigid penetration to semi-liquid penetration and fluid penetration, each of which follows a wholly different analytical model. In the semi-liquid penetration stage, the mass loss of the projectile body begins to increase obviously, leading to serious decrease of the penetration efficiency and the penetration depth at the increase of the impact velocity. The intrinsic analytical model of rigid penetration was deducted by analysis of the real deformation and stress states of different damage zones. Based on the proposed relationship between penetration and velocity, we established the equation of penetration depth in account of the projectile mass loss, proposed the hypothesis of fluid and rigid region of fluid penetration under hypervelocity impact and, by adopting the laws of conservation of momentum and Bernoulli equation, presented the formulas for penetration resistance, and deduced the corresponding equations of penetration depth using the relational expression of the projectile mass loss. By comparison of the result of calculation with experimental data of penetration into granite, we proved the reliability of the formulas for the three stages, showing them in good compatibility in penetration depth and mass loss of the projectile with each other, and verifying a full agreement between their variation and experimental results.