Vladimir D. Sarychev

Model of formation of inner nanolayers in shear flows of material

We consider a mathematical model for the formation of internal nanocrystal layers in shear flows of material, which is based on the evolution of the Kelvin-Helmholtz instability. The dispersion relation is derived for the linear interaction between finite layers of ideal and viscous fluids. Analysis of the dispersion equation shows that viscosity and thickness of a moving layer play a decisive role in the formation of nanosize waves.

Mathematical model of nanostructure formation in rail steel under high intensive mechanical loading

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.

Temperature distribution produced by pulsed energy fluxes, with evaporation of the target

Thermal processes produced by pulsed energy fluxes are analyzed. The proposed model takes account of evaporation and melting of the target. The corresponding mathematical problem is formulated, with change in the type of boundary conditions. A numerical model is developed, as well as a computational program that does not require a fitting parameter. A formula for the dispersion time of the evaporating material is derived. Numerical values are obtained for the depth of melting as a function of the energy density. Options for parameterization of the experimental data are noted.

Thermocapillary model of formation of surface nanostructure in metals at electron beam treatment

The paper presents the thermocapillary model for the formation of nanostructures in surface layers of materials. It is based on Navier-Stokes hydrodynamic equations, the thermal conductivity equation, the state equation and the boundary conditions. A search for the solutions in the form of a progressive wave has been carried out. The dispersion equation has been obtained and analyzed. The dependence of the instability increment on wavelength has been built. The values of the critical wavelength, at which thermocapillary instability for iron and titanium comes, have been obtained. Value comparison of the calculated wavelengths with cell sizes of crystallization has showed a satisfactory agreement.

Viscous flow analysis of the Kelvin–Helmholtz instability for short waves

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.

Model of formation of droplets during electric arc surfacing of functional coatings

The mathematical model was developed for the initial stage of formation of an electrode metal droplet in the process of arc welding. Its essence lies in the fact that the presence of a temperature gradient in the boundary layer of the molten metal causes thermo-capillary instability, which leads to the formation of electrode metal droplets. A system of equations including Navier-Stokes equations, heat conduction and Maxwell’s equations was solved as well as the boundary conditions for the system electrodes-plasma. Dispersion equation for thermo-capillary waves in the linear approximation for the plane layer was received and analyzed. The values of critical wavelengths, at which thermo-capillary instability appears in the nanometer wavelength range, were found. The parameters at which the mode of a fine-droplet transfer of the material takes place were theoretically defined.

Filtration model of plastic flow

Abstract A filtration model for plastic flow based on the idea of a deformed material considered as a two-phase heterogeneous medium has been suggested. In this approach, the wave displacement is regarded as a shock transition in the medium. One of the phases (the excited one) is responsible for system restructuring, and the other phase (the normal one) is unrelated to structural transformations. The plastic wave is the result of the interaction of these two phases. The governing equations for the filtration model are obtained. They include the laws of momentum and mass conservation, as well as the filtration ratio of the phases.

Biphase Model of Plastic Deformation in Electric Fields

The object of the research is creep deformation proceeding in the conditions of electrostatic field effect. The purpose of the research is to develop the mathematical model of creep under the electrostatic field effect from the positions of representations about the wave nature of plastic deformation process. The theoretical studies of electrostatic field effect being characterized by small (up to ± 1V) potentials on the basis of mass, momentum and energy conservation in two-dimensional formulation were carried out in the process of research. The material being deformed was represented as two phase heterogeneous medium. The first component is excited and being responsible for structure transformation, the second one is unexcited and disconnected with them. For each of the components the laws of mass and momentum conservation were written. For electric fields the Maxwell equations were written. For the first time the two phase filtration model of creep was developed as a result of the research. The model takes into account the inhomogeneity of plastic deformation under electrostatic field effect. The dispersion relation for the waves of plasticity is obtained.

The Interaction Mechanism between Solid and Liquid Metals under Ultrasonic Action

At various structural-scale levels, the interaction between the aluminum alloy DT1 and a liquid eutectoid mixture of gallium and indium under the action of mechanical waves of the ultrasonic range is investigated. It is established that the deep penetration of the eutectoid mixture into the solid metal under ultrasonic action is due to the formation of channels along which the mixture moves. These channels are observed in both the axial and radial directions.

Mathematical model of mass transfer at electron beam treatment

The paper proposes a model of convective mass transfer at electron beam treatment with beams in titanium alloys subjected to electro-explosion alloying by titanium diboride powder. The proposed model is based on the concept that treatment with concentrated flows of energy results in the initiation of vortices in the melted layer. The formation mechanism of these vortices rooted in the idea that the availability of temperature drop leads to the initiation of the thermo-capillary convection. For the melted layer of metal the equations of the convective heat transfer and boundary conditions in terms of the evaporated material are written. The finite element solution of these equations showed that electron-beam treatment results in the formation of multi-vortex structure that in developing captures all new areas of material. It leads to the fact that the strengthening particles are observed at the depth increasing many times the depth of their penetration according to the diffusion mechanism. The distribution...