Stress–diffusion coupling. Application to interstitial diffusion

Abstract

A numerical study of the stress–diffusion coupling theory based on the Cahn–Larché method is presented in the case of interstitial diffusion. Indeed, the interaction between diffusion and stress fields has been widely studied in the past. Most of the studies focused on the effect of chemical stress due to mass transport on diffusion. The majority of the studies have been focusing on the coupling between external mechanical and chemical stresses with diffusion. In this study, the effect of stress/strain on mobility and stress gradient mobility and driving forces are presented, based on the model of Voorhees and Larché. The analytical solutions are detailed, from general equations (interstitial diffusion, elastic material) to a macroscopic model (interstitial diffusion, isotropic elastic material, infinite dilute solution, 2D axisymmetric). Numerical simulations for different samples thickness and β parameter helped to better understand and then experimentally identify the prevailing effect of stress on mobility or diffusion driving forces. These studies demonstrated the impact of constant compressive and tensile stress on diffusion kinetics through the mobility term of the equation, as well as the effects of negative and positive stress gradients via the Nernstian term. The results show that constant compressive stress and negative stress gradient hinder the diffusion. On the contrary, tensile stress and positive stress gradient promote the diffusion. This work also demonstrates the importance of coupling between mobility and Nernstian effect on the diffusion promotion.