Theory of bending of polycrystalline beams by creep at low stress

Abstract

Attempts to extend diffusion creep theory from simple grain geometries to more complex polycrystalline structures generally make the assumptions that the vacancy creation (or annihilation) rate is constant over each grain face and that the volume of each grain is conserved. These assumptions do not permit grain rotation, a common feature of polycrystalline creep, nor is diffusion allowed to occur between individual grains. These two aspects are investigated theoretically in this paper, for the specific case of the grain boundary diffusion controlled bending of a polycrystalline beam consisting of a set of orthorhombic grains of dimensions X, Y and Z, with the Z dimension, parallel to the axis of bending, assumed large such that two-dimensional diffusion predominates. The grains are aligned with continuous boundaries across the beam height. For grains highly elongated along the beam length (X ≫ Y), the derived rotation rate is identical to that for a bicrystal having the same height as the beam. For smaller X, diffusion in boundaries along the beam length make increasing contributions and the rotation rate increases. The novel prediction is made that the non-conservation of grain volume is an inevitable consequence of the grain boundary diffusion controlled deformation of this particular polycrystalline configuration.

Acknowledgement

The author is grateful to the Wingate Foundation for the award of a scholarship.