Diffusional creep and diffusionally accommodated grain rearrangement

Abstract

An analysis is made of the normal tractions acting on grain boundaries in a solid with a perfectly regular hexagonal grain structure deforming via diffusional creep. Restrictions are placed on the allowable diffusion paths solely by requiring that the normal stresses on opposite sides of a grain boundary be identical. It is shown that a model for grain switching recently proposed by Ashby and Verrall is inconsistent with this requirement. The problem of grain boundary diffusional flow is solved by treating grains as elastically rigid, and the solution, which agrees with earlier results in the limit of small strains, provides an explicit description of the equilibrium boundary traction distribution during steady state flow. This solution suggests that grain neighbor switching can occur in single phase materials only when grain boundary migration occurs. In two phase materials it is expected that diffusional creep will give rise to a grain switching process in which a grain of one phase wedges between and separates two grains of the other phase.