Mathematical Modeling of the Concentrated Energy Flow Effect on Metallic Materials

Abstract

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.

Effect of applied load on welding stress at different time periods

“…Firstly, simplify and clean up the established models and then mesh them. To ensure the accuracy of the premise and reduce the overall model size, the fine mesh is used near a weld where stress gradients are high, while the area far away from a weld is discretized [14][15][16]. The grid model is grouped and named accordingly.…”

The Finite Element Modulation of Thermostressed State of Coating Formation at Electric Contact Surfacing of “Shaft” Type Parts

“…It was established in the work [19] that gravity surfacing is performed with tangential force, which leads to the tangential stress appearance in the contact zone of the joined metals that requires taking this factor into account in modeling the electrocontact surfacing process. In the works [20,21], the effect of strain rate on the grain size of rolled steel was simulated and the effect of an energy pulse on the structure of the coating material was also investigated. However, the technology proposed in the works under consideration involves the modification of the surface layers without coating, which does not quite coincide with the purpose of this study.…”

Control of the surface electron-beam alloying process by vibration monitoring

“…At the same time, due to the short duration of irradiation and thermal inertia, the heating due to compression and internal friction is most likely not a physical factor that determines the behavior of the substance in such conditions. The primary role, in this case, will be played by the mechanical activation of fast physical and chemical processes in the substance, which are mainly solid phase [13,14].…”