OBRABOTKAMETALLOV TECHNOLOGY Vol. 24 No. 3 2022 Following the same phenomenological model as for the vapor pressure, the heat loss due to evaporation has the form: 0 0 82 , - ( ( ) ) , . , ( ) , h T M s p T C S m h h T m c p T h T c dT T (7) where enthalpy rate per surface unit area Sυ is obtained from the product of vapor mass fl ow per unit surface area mυ and the sum of the specifi c enthalpy h(T) and the latent heat of vaporization hυ per unit mass. Th,0 is the initial temperature of the specifi c enthalpy, and the constant 2 / ( ) M C M R contains a molar mass of M and molar gas constant R, cs is the so-called sticking constant, which takes on a value close to 1 for metals [19, 20]. The plasma arc pressure force is taken into account as follows [21]: 2 2 2 0 0 2 2 2 ( ) ( ) exp ( ) ( ) . pl pl pl I a p x, y , p x, y k I x x y y R f n (8) The radiation is modeled by the Stefan-Boltzmann equation: 4 0 ( ) , rad B s T T (9) where σB is Boltzmann constant, ε is material emissivity, T0 is ambient temperature. The Smoothed Particle Hydrodynamics (SPH) method was used to solve this mathematical model and a series of numerical experiments were carried out to determine the basic regularities of the formation of deposited beads and the transfer of the fi ller material, the dependence of the geometrical characteristics of the deposited beads on the infl uence of the vapor pressure forces, the direction of the heat sources and the azimuthal angle of the heat sources. The variants of the electron-beam deposition process were analyzed at the location of the deposition velocity vector in the plane of the electron beams (Fig. 1, a) and perpendicular to this plane (Fig. 1, b). The following geometrical characteristics of the simulated system and preliminary process parameters were used in the calculations (Table 1). The austenitic chromium-nickel steel 04Cr18Ni10 was considered as a fi ller and a substrate material in the simulation (thermal physical characteristics are presented in Table 2). Numerical realization was performed on a 2×300 sas 15k multiprocessor IBM computer (4xIntel Xeon E7520, 64 GB) using MPI multithreading capabilities of the LAMMPS package. a b Fig. 1. Variants of the relative position of the deposition velocity vector and the action plane of the electron beams: a – the deposition velocity vector lies in the action plane of the electron beams; b – the deposition velocity vector is perpendicular to the action plane of the electron beams
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