Unified Analysis for Various Diffusion-controlled Deformation and Fracture Processes

Abstract

This article overviews a unified approach for deriving rate equations for various diffusion-controlled deformation and fracture processes. The basic concept behind the present approach is that the change in the overall free energy of a deforming materials is identified as the total driving force of diffusion. Conventional basic equations on the excess chemical potential of an atom derived by Herring are not directly used in the present analysis. As possible driving forces of diffusion, the changes in surface, grain-boundary and elastic strain energies of the material and the change in the potential energy of an external load are considered. Approximate and exact solutions are derived. The approximate solutions enable us to quickly grasp the physical meanning of the processes and the exact solutions enable us to incorporate effects of various driving forces of diffusion into rate equations in a physically clear manner. Several different diffusion-controlled processes are treated as examples: the Nabarro-Herring creep and Coble creep, grain-boundary sliding, climb of an edge dislocation, growth of a grain-boundary void, shape change of a nearly spherical particle and stress relaxation in a dispersion-hardened material.