Numerous processes take place in materials under the action of concentrated energy flows. The most important ones include heating together with the temperature misdistribution throughout the depth, probable vaporization on the surface layer, melting to a definite depth, and hydrodynamic flotation; generation of thermo-elastic waves; dissolution of heterogeneous matrix particles; and formation of nanolayers. The heat-based model is presented in an enthalpy statement involving changes in the boundary conditions, which makes it possible to consider melting and vaporization on the material surface. As a result, a linear dependence of penetration depth vs. energy density has been derived. The model of thermo-elastic wave generation is based on the system of equations on the uncoupled one-dimensional problem of dynamic thermo-elasticity for a layer with the finite thickness. This problem was solved analytically by the symbolic method. It has been revealed for the first time that the generated stress pulse comprises tension and compression zones, which are caused by increases and decreases in temperature on the boundary. The dissolution of alloying elements is modeled on the example of a titanium-carbon system in the process of electron beam action. The mathematical model is proposed to describe it, and a procedure is suggested to solve the problem of carbon distribution in titanium carbide and liquid titanium-carbide solution in terms of the state diagram and temperature changes caused by phase transitions. Carbon concentration vs. spatial values were calculated for various points of time at diverse initial temperatures of the cell. The dependence of carbon particle dissolution on initial temperature and radius of the particle were derived. A hydrodynamic model based on the evolution of Kelvin-Helmholtz instability in shear viscous flows has been proposed to specify the formation of nanostructures in materials subjected to the action of concentrated energy flows. It has been pointed out for the first time that, for certain parameters of the problem, that there are two micro- and nanoscale peaks in the relation of the decrement to the wavelength of the interface disturbance.

The reported study discusses the formation of micro- and nanocrystalline surface layers in alloys on the example of Ti-Y and Al-Si-Y systems irradiated by electron beams. The study has established a crystallization mechanism of molten layers in the micro-and nanodimensional range, which involves a variety of hydrodynamic instabilities developing on the plasma–melt interface. As suggested, micro- and nanostructures form due to the combination of thermocapillary, concentration and capillary, evaporation and capillary and thermoelectric instabilities. This mechanism has provided the foundation for a mathematical model to describe the development of structures in focus in the electron beam irradiation. The study has pointed out that thermoelectric field strength E ≥ 10⁶ V/m is attributed to the occurring combination of instabilities in micro- and nanodimensional ranges. A full dispersion equation of perturbations on the melt surface was analyzed.

С единых позиций интерпретируются экспериментально установленные закономерности формирования упрочняющих поверхностных наноструктур при различных внешних энергетических воздействиях (электровзрывном легировании, электронно-пучковой обработке, термомеханическом упрочнении проката по режиму ускоренного охлаждения, интенсивных механических воздействиях при длительной эксплуатации рельсов). Выполнено математическое моделирование формирования наноструктурных образований в результате развития неустойчивостей равновесных состояний в поверхностных слоях (неустойчивости Кельвина–Гельмгольца и Марангони), проанализированы соответствующие дисперсионные уравнения и получены аналитические зависимости декремента (α) от длины волны (λ) в микро- и нанодиапазонах. Отмечено соответствие числовых значений наблюдаемых максимумов зависимости α(λ) экспериментальным значениям параметров наноструктур и дана его физическая интерпретация.

The paper presents the mathematical model of the formation of nanostructures in surface layers of rail steel in conditions of continuous service. A dispersion equation in the nanodimensional range has been analyzed. Critical values of wave length, at which instability occurs, have been defined.

In this paper a mathematical model for the formation of nanostructures in the material under an intensive external action due to the occurrence of Kelvin–Helmholtz instability is provided. The model is based on the linearized Navier–Stokes and Euler equations, kinematic and dynamic boundary conditions. A dispersion equation is obtained and analyzed in the short-wave approximation. It is found that the dependence of the decrement in the wave number has two maxima. The first maximum occurs at the wave number corresponding to the microrange wavelength, and the second maximum takes place at the wave number corresponding to the nanorange. Analytical dependences of the wave number, which account for the maximum decrement of input parameters of the problem (viscosity, density of the material of the first and second layers, relative velocity of layers, and surface tension) are found. A range of the parameters for which the bimodal Kelvin–Helmholtz instability appears is specified.

Experimental observations regarding the formation of strengthening surface nanostructures under various external stimuli (electroexplosive alloying, electron-beam treatment, thermomechanical...