Two-dimensional model of grain boundary diffusion and oxidation

The grinding of the structure of materials is accompanied by a change in the physical and mechanical properties. This occurs largely due to the accumulation of energy and defects in the structure, which activates the diffusion of impurities contained in the material. The increase in the number of grain boundaries and joints can cause the inelastic behavior of the material, its additional chemical activation. For some metals and alloys this leads to strengthening, while for others it leads to rapid degradation of mechanical properties. Grain boundary diffusion in such materials is the main mechanism of transport of alloying components or harmful impurities, so its study is important. This paper presents a two-dimensional model of grain boundary diffusion in a material with an explicit structure assignment. The model takes into account the presence of chemical transformations that can determine the corrosion mechanisms under operating conditions. For simplicity of calculation the material structure is taken symmetrical and contains two phases: grains and a boundary phase. Diffusion and kinetic parameters of the phases may differ. The model is represented in dimensionless form so that the distances between neighboring grains or the widths of the boundary phase are the same and the grain sizes can vary. Depending on the ratio of phase sizes we can speak about micro- and nanocrystalline structure. The problem was solved numerically using implicit difference scheme and coordinate splitting. Diffusion and kinetic parameters, which are close to the parameters of oxygen grain boundary diffusion in titanium and titanium oxidation, respectively, were taken for the calculations. Integral concentrations reflect the dynamics (kinetics) of oxygen and oxides accumulation over the calculation area. Results showing the role of changes in the oxidation kinetics due to changes in the reaction constants in the phases and the phase size ratio are presented. The model can be useful for assessing the degree of influence of grain boundary diffusion on the oxidation process and the accompanying change in properties, as well as for setting up appropriate experiments.