On the Decomposition of Motion in the Description of Interdiffusion in a Viscoelastic Body

Abstract

The influence of stresses on diffusion is recognized, along with diffusion’s role in the viscous deformation of solids. The interconnection between interdiffusion and deformations in metallic alloys and steels significantly affects the durability of machine components exposed to harsh conditions with substantial temperature and force. In such instances, diffusion facilitates the transportation of alloying elements from the surface layer, impacting the intensity of corrosion and corrosion cracking. Laws correlating diffusion flows to chemical potential gradients can be related to various diffusion reference frames, determined by the base experiment used or the convenience of establishing the boundary value problem. In the related equations of interdiffusion in a deformable solid, we must consider that diffusion happens in a local material volume transported by the convective velocity, and that diffusion is described in a local diffusion frame of reference moving relative to the material. A decision must be made regarding convective velocity and diffusion reference frame (decomposing the material motion into convective and diffusive parts). Within the linear thermodynamics of irreversible processes, a related system of equations is set for a multicomponent medium, where balance equations for composition variables are considered, and stress and strain tensors are introduced for the medium on the whole. Two diffusion descriptions are considered: one assumes a diffusion reference frame frozen into a local material volume, and the other involves a system of markers, small inert particles, moving relative to the material due to unbalanced diffusion flows. Both methods are employed in basic diffusion pair experiments to determine diffusion coefficients. For each of the diffusion descriptions – “material” and “marker” – within the process coupled with viscoelastic deformation, the thermodynamically resolved relations are derived for two-component and three-component metallic alloys. To compare the associated models, a one-dimensional problem is proposed. The perturbation method is applied, yielding the dependency of the relaxation time spectrum on the perturbation wavelength. The values of the effective interdiffusion coefficients align with the inclined asymptotes of these dependencies, and the effective viscosity coefficients match the horizontal ones. The dependency of these effective coefficients on the diffusion and viscoelastic properties for an austenitic alloy Fe65-Cr20-Ni15 at high temperature is examined. Overall, the marker description of interdiffusion provides more information and it is more convenient for setting boundary value problems with boundary diffusion of components.