Lattice-diffusion-controlled rotation of crystals about a common interface

Abstract

During the high-temperature deformation of polycrystalline materials, the interaction between neighbouring grains gives rise to grain shape changes, grain-boundary sliding and grain rotation. There is debate on whether sliding makes a direct contribution to strain or whether it merely accommodates the shape changes. In principle, it is possible to deduce any direct sliding contribution, by comparing the overall strain with grain strain. Such attempts are often confounded, however, by the existence of grain rotation. In a previous paper, by Burton, rotation occurring by interfacial diffusion was anaIysed. It may also occur by lattice diffusion and this is the subject of the present paper, where a numerical method is used to treat the rotation of a bicrystal configuration. The method is validated by adapting it to solve a related problem, that of lattice diffusion creep, and predictions are shown to agree with known analytical solutions. The rate of rotation is calculated as a function of bending moment, grain dimensions and grain aspect ratio. The steady-state vacancy concentration and diflusion fluxes within the bicrystal are determined. The fluxes at the free surfaces are shown to lead to apparent boundary ‘grooving’ and ‘mounding’ effects at the tensile and compressive ends of the interface. The method can be further adapted to solve the diffusion creep problem for a ‘bamboo’ structure and this has given important new results. It allows diffusion fluxes at the free surfaces to be calculated for the first time and the variation in the creep constant to be determined as a function of the grain aspect ratio. Reported measurements of enhanced grain-boundary grooving may be explained by these results.