Abstract

A mathematical model was developed and a mechanism was proposed for the formation of nanoscale structural-phase states by using a rail steel example in the process of long-term operation. It is believed that under intense plastic deformations, the material behaves as a viscous incompressible fluid. To consider sliding of a wheel relative to the rail, a two-layer fluid model was proposed in which the upper layer slides at some speed relative to the lower layer. In this case, the Kelvin–Helmholtz instability develops. For each layer, the Navier—Stoles equations, as well as kinematic and dynamic boundary conditions have been written. In the form of normal perturbation modes to the system obtained, a solution was carried out based on the assumption of the viscous-potential material flow. According to this approximation, it is considered that viscosity effects occur only at the layer interface. A dispersion equation was derived and analyzed using a graphical representation of the functions contained in the analytical solution. We have established the ranges of the material characteristics and parameters of the external impact (the velocity of the layer motion) at which two peaks are observed in the dependence of the perturbation’s growth rate on the wave number. The first (hydrodynamic) maximum is due to the motion of layers relative to each other; the second is associated with the effects of fluid viscosity. Approximate formulas have been obtained for the dependence of the perturbation’s growth rate on the wave number. The approximate formulas for the dependence of the perturbation’s growth rate on the wave number have been derived. The conditions necessary for realization of the only maximum have been found. The viscosity-induced maximum at slip velocities of the order of magnitude of 1 m/s may be observed in the nanoscale wavelength range. Assuming that the white layer in the rails occurring in the process of long-term operation is formed mainly due to the action of intense plastic deformations, we believe that the results obtained provide a more detailed understanding of the mechanism of white layer formation in the rails in the case of their long-term exploitation.

中文翻译：

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轨道长期运行过程中纳米结构层形成模型

摘要

建立了数学模型，并提出了在长期运行过程中以钢轨为例，形成纳米级结构相态的机理。据信，在强烈的塑性变形下，该材料表现为粘性的不可压缩流体。为了考虑车轮相对于轨道的滑动，提出了一个两层流体模型，其中上层相对于下层以一定速度滑动。在这种情况下，Kelvin-Helmholtz不稳定性会发展。对于每一层，已编写了Navier-Stoles方程以及运动学和动态边界条件。以所获得系统的正常扰动模式的形式，基于粘性势能物质流的假设进行了求解。根据这个近似值，认为粘度效应仅在层界面处发生。使用包含在解析解决方案中的函数的图形表示来导出并分析色散方程。我们已经建立了材料特性的范围和外部冲击的参数（层运动的速度）的范围，在该范围内，根据扰动的增长率与波数的关系观察到两个峰值。第一（流体动力学）最大值是由于各层相对于彼此的运动所致；第二个因素与流体粘度的影响有关。对于扰动的增长率对波数的依赖性，已经获得了近似公式。得出了扰动增长率与波数的关系的近似公式。已经找到了实现唯一最大值的必要条件。在纳米级波长范围内可以观察到粘度引起的滑移速度的最大值约为1 m / s。假设长期运行过程中出现的钢轨中的白层主要是由于强烈的塑性变形而形成的，我们相信所获得的结果可以更详细地了解钢轨中的白层形成的机理。在长期剥削的情况下。