The initial stage of transient layer formation between film and substrate during heating by a high-current electron beam

At the present time, the processes of interaction of the concentrated energy fluxes with materials are being widely studied. Of greatest interest in this area are the low-energy high-current electron beams, which are often used to modify the pre-applied coating and to improve the adhesion of the coating-substrate system.
Alongside with such processes as heating, phase formation, mixing, etc., at the moment of interaction between electron beam and target surface, the elastic waves of mechanical perturbations are generated. Experimental study of each process separately is difficult. However, mathematical modeling allows one both to study in details all the stages of processing, to evaluate the role of each arising phenomenon separately, and to reveal the relationship between the processes of interest.
The paper presents a mathematical model of the initial stage of transition layer formation between film and substrate when heated by a high-current electron beam. The system of mass balance equation, heat-transfer equation, and equation of motion is used to describe the interaction between the waves of coating material concentration, heat waves, and stress (strain) waves under the action of electron flux. Governing relations correspond to the theory of generalized thermoelastic diffusion. For numerical solving of the problem, a transition to dimensionless variables is carried out. The developed numerical algorithm is based on an implicit difference scheme.
The examples of coupled problem solution for two coating-substrate systems — Mo(Ni), Ni(Cu) are presented in the paper. It is shown that the interaction between waves of different physical nature leads to a distortion of strain wave. It was demonstrated that the action of momentum is followed by the material redistribution, which occurs due to the presence of strain gradient. For various ratios of material properties (coating-base), the qualitative changes in the distribution of concentration and deformations are observed, while the wave interaction mechanisms are similar.