Nonlinear field theory of stress induced diffusion in crystalline solids

Two different mathematical descriptions of the material drift based respectively on the concept of mass- and molar-averaged velocities are presented. In this way two different material derivatives over time are introduced: mass and molar, respectively. The first approach based on the overall mass motion is used mainly in the traditional continuum thermodynamics of deformable solids while the second approach developed here comes back to the constitutive modelling used mainly in the chemical physics. The problem of the stress induced diffusion is situated on the border of the two different approaches developed often separately. In this paper, taking into account the standard balance laws for molar motion, the driving forces for diffusion are determined. The forces obtained for diffusion of chemical components depend not only on gradients of chemical potentials (osmotic force) but also on some additional forces controlling the stress induced diffusion process. The driving forces derived for dislocation field comprise the Peach-Koehler force as well as an additional term resulting from the effect of dislocation movement on the concentration of vacancies.