High-Velocity Penetration of Porous Material Rods

In this article we study the influence of material porosity on penetrative action of the powder shaped-charge jets formed during the explosive collapse of the liners pressed from metal powder. We employed numerical modeling within a two-dimensional axisym-metric problem of continuum mechanics. It allowed us to research the features of elongated porous projectiles penetration into a steel target in the hydrodynamic mode (interaction velocity is several kilometers per second). We considered the compressible elastic-plastic matter with the Tait’s barotropic equation of state as a target material. The model for the behavior of porous projectile material was based on the assumption that closing of micropores in the porous matter happens at a zero pressure, so it behaves as monolithic. We compared the numerical modeling results with the prediction given by the hydrodynamic theory with the incompressible liquid assumption. We established that penetration depth of porous rods exceeds the value calculated on Lavrentiev’s formula. The analysis of interaction in numerical calculations allows to assume that this deviation is connected with formation of the attached shock wave near a surface of contact with a target in the course of penetration (penetration process for the porous projectile has supersonic character due to essential reduction of sound speed in porous materials). Based on this assumption and considering penetration process, Lavrentiev’s liquid jets collision in this article we offer a simple model of elongated porous projectile penetration. Its mathematical description includes system of equations for the attached shock wave front in the projectile, continuity conditions on the surface of projectile and target contact and Bernoulli’s equation which connects state parameters on a contact surface with the shock wave parameters and with parameters of the target. This model for porous projectile penetration depth allowed us to define the ratio containing the additional multiplier to the original Lavrentiev’s formula. The multiplier depends on material porosity. The output of calculations with this ratio is in compliance with the result of numerical modeling.

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