Theory of diffusional rotation about the common boundary of a bicrystal

Abstract

During the creep of polycrystals, individual grains may undergo shape changes, grain boundary sliding and grain rotation. Theoretical studies have focused on the first two of these processes but only recently has the theory of rotation received detailed attention. Diffusional rotation was analysed by Burton [Phil. Mag. A 82 51 (2002); Phil. Mag. 83 2715 (2003)], for a bicrystal with orthorhombic grains of dimensions X, Y and Z with the common boundary in the yz plane and with Z ≫ X,Y. Rate equations were derived and the stress profile over the common boundary predicted, for cases where grain boundary and lattice diffusion predominate. In this paper, the analyses are extended using numerical methods, to the full two- and three-dimensional cases for boundary and lattice diffusion, respectively. For boundary diffusion, the results for Z/Y ≫ 1 reproduce those obtained by analytical means and this is regarded as a verification of the numerical method. When Z/Y = 1, the rotation rates are shown to be about 30% faster, due to the additional diffusion contribution in the z direction. This contribution increases with decreasing values of Z/Y. The stress patterns at the rotating boundary are derived. For lattice diffusion, the stress pattern at the boundary, the shapes of the vacancy potential contours and the variation of the rotation rate with the ratios X/Y and Z/Y are presented.

Acknowledgement

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

Notes

Email: [email protected]

Additional information

Notes on contributors

B. Burton *

Email: [email protected]