Surface Layer Thermodynamics of Steel Penetrators at High and Very High Sliding Velocities

One of the most difficult problems in the mechanics of kinetic energy projectiles penetrating geological or cementitious target materials is a proper understanding of the frictional properties between the projectile surface and the target. The model developed in this study is limited to a simple definition of the state of the projectile surface as a set of uniformly distributed micro-asperities with the same active height, h = 20 microns, which are subject to fast adiabatic shearing. Although the heat conduction equation has not been solved numerically in this study, a useful approximation of the evolution of temperature in the bulk material was applied. This approximation permitted finding the closed form solution for the homologous bulk temperature, at different sliding conditions. Because evolution of the bulk temperature could be estimated, it also permitted finding the evolution of the coefficient of friction as a function of the sliding velocity. For every definition of the coefficient of friction a substantial decrease of the resistance to sliding at increasing velocities has been found. An open question remains as to the role of the hydrostatic pressure. For example, the experimental data suggest that at constant velocity the coefficient of friction will diminish as a function of pressure as predicted by Eq. (51). Thus, an advantage of the model presented here is that hydrostatic pressure can be taken into consideration in a correct way. Albeit implementation of the friction model in the form of Eq. (51) into numerical codes is rather too early, preliminary trials should be recommended.