Model of nanostructure formation in rail steel during long term operation

A mathematical model of nanostructural layer formation in the wear process has been developed on the basis of available information on unstable flow of materials which arises under severe plastic deformation. This paper puts forward a model for the formation of nano- and microscale structural elements based on the development of instabilities in shear bands. The model is constructed using a previously proposed filtration model for the flow of material during severe plastic deformation. According to this model, the deformable material is divided into two phases: a mobile phase, and an elastic skeleton. The first phase moves through the skeleton and carries the latter. Ignoring the speed of the second phase, we use equations of motion to derive model equations that coincide with the model of a porous medium. In this paper we consider the instability of a porous layer and a layer of a perfect medium moving relative to the porous layer with constant velocity, the so-called Kelvin–Helmholtz instability. In the approximation of short waves an explicit dependence of the decrement on the wave number for various parameters has been obtained. This parameterization allowed us to obtain the dependence with two maxima, similar to the instability of the Kelvin–Helmholtz viscous layer.