Penetration of a copper rod into a sandy target

Abstract

This paper presents the results of experimental and theoretical studies of high-velocity penetration of cylindrical copper rods into sand. The hydrodynamic Alekseevskii-Tate theory is modified to determine the penetration depth and wear velocity of the material of the rod penetrating into soil target in the plastic and hydrodynamic stages of penetration. The case where the target material is significantly less strong than the rod (impactor) material is considered.Introduction. The high-velocity penetration of long rods (impactors) into dense media includes two stages of deformation [1-3]: 1) plastic stage, where the decrease in the length of the solid part of the impactor occurs at a rate equal to the velocity of the longitudinal plastic wave C p ; 2) hydrodynamic stage, where the wear velocity of the impactor V − U exceeds the velocity of the longitudinal wave of plastic deformation (V is the velocity of the undeformed tail part of the impactor and U is the penetration velocity).The hydrodynamic stage of high-velocity penetration is adequately described by a modified hydrodynamic Alekseevskii-Tate theory (MHT) [4-8] based on the results of experimental studies of penetration of metal rods into high-strength (mainly metal) targets. However, high-velocity penetration of metal rods into porous soft soil media has been studied insufficiently (see, for example, [9]).One of the key parameters characterizing the high-velocity interaction of an impactor with a target in the hydrodynamic stage of penetration is the coefficient of relative penetration K = h/ΔL [h is the current penetration depth and ΔL is the shortening (wear) of the impactor]. The coefficient K allows one to predict the total wear depth of the impactor in the hydrodynamic stage in the case of stationary penetration. Stationarity is provided by a great (not less than sevenfold) elongation of the impactor (see, for example, [7]). According to the Alekseevskii-Tate model, the quantity K depends on the penetration velocity V 0 . As V 0 increases, the value of K decreases, approaching the asymptotic value given by the well-known Lavrent'ev formula [10] for the case of an ideal incompressible fluid:The objectives of the present work was to experimentally determine the critical velocity V * at which plastic deformation begins, the velocities of hydrodynamic transition V ht , and the velocities of a longitudinal plastic wave in a copper rod during its penetration into sand C p , and to improve the MHT to describe high-velocity penetration taking into account two stages of deformation of the impactor in the case where the target material is significantly less strong than the impactor material.1. Results of Experiments. The cylindrical copper impactors fired from ballistic facilities into soil had diameter d = 1 cm, length L 0 = 8.22 cm, and mass m = 57.5 g. The impactors were made of M1 copper alloy with a conventional yield point in compression σ 0.2 ≈ 290 MPa [11] and density ρ p = 8.9 g/cm 3 . Experimental data were obtained by x-ray photography of the penetra...