Model of nanostructural layers formation at long-term operation of rails

Abstract

A mathematical model was developed and a mechanism was proposed for the formation of nanoscale structural-phase states on the example of rail steel at long-term operation. It was believed that during intense plastic deformations, the material behaves like a viscous incompressible fluid. In order to take into account the sliding of the wheel relative to the rail, a two-layer fluid model was proposed, the top layer of which slides at a certain speed relative to the first. In this case, the Kelvin-Helmholtz instability develops. For each layer, we have written the Navier-Stokes equations and kinematic and dynamic boundary conditions. Solution of the obtained system in the form of normal perturbation modes was carried out on the basis of assumption of the viscous-potential material flow. In this approximation, it was believed that viscosity effects occur only at the layer interface. A dispersion equation was derived, which was analyzed using a graphical representation of the functions included in the analytical solution. A range of characteristics of the material and parameters of the external influence (the velocity of the layer) was established, at which two peaks are observed in dependence of disturbances growth rate on the wave number. The first (hydrodynamic) maximum is due to the motion of the layers relative to each other; the second is associated with the effects of fluid viscosity. Approximate formulas were obtained for dependence of the growth rate of perturbations on the wave number. Conditions for realization of only one maximum were found. The viscously determined maximum at slip velocities of the order of 1 m/s can be in the nanoscale wavelength range. Assuming that the white layer in the rails during long-term operation is formed mainly due to the action of intense plastic deformations, we believe that the obtained results detail the mechanism of white layers formation in the rails in this case.