Three-dimensional interdiffusion under stress field in Fe-Ni-Cu alloys

We present the method of solving the mechanochemical transport problem in multicomponent solid solutions, namely, the method of quantitative description of the interdiffusion (ID) under the stress field. We postulate that the velocities appearing in the momentum balance equation should be the drift and diffusion velocity. The energy, momentum, and mass transport are diffusion controlled, and the diffusion fluxes of the components are given by the Nernst-Planck formulas. The diffusion depends on the chemical potential gradient and on the stress that can be induced solely by the diffusion as well as by the boundary conditions. The key results lie in the interpretation of the Navier-Lamé equation for the deformed regular crystal, where the concentrations are not uniform and ID occurs. The presented coupling of the Darken and CALPHAD methods with the momentum balance equation allows for quantitative analysis of the transport processes occurring on entirely different time scales. It is shown that the proposed method is effective for modeling transport processes in Fe-Ni-Cu alloys. We demonstrate the case of ID in a planar plate, and predict slower penetration and accumulation. The experimental results confirm theoretical predictions.