Micromechanics of diffusional creep

Abstract

In polycrystalline materials at high temperatures and low stresses, creep occurs mostly by the diffusion of vacancies through the grain bodies and over the grain boundaries. A continuum theory of vacancy motion is considered to analyze diffusional creep on a microscopical level. A linear version of such a theory was formulated by Nabarro, Herring, Coble and Lifshitz. We revise this theory from the perspectives of continuum mechanics and present it in a thermodynamically consistent nonlinear form. A certain difficulty, which one has to overcome in this endeavor, is the absence of Lagrangian coordinates in diffusional creep, the major building block of any theory in continuum mechanics. A linearized version of the theory is studied for the case of bulk diffusion. We consider the derivation of macro constitutive equations using the homogenization technique. It is shown that macroequations are nonlocal in time and nonlocality is essential in primary creep. For secondary creep polycrystals behave as a viscoelastic body. For secondary creep, a variational principle is found which determines microfields and macromoduli in stress-strain rate constitutive equations. A two-dimensional honeycomb microstructure and single crystal deformation are studied numerically by a finite element method.