On the elastic properties of grain boundary dislocations

Abstract

The stress field and the strain energy of a screw grain boundary dislocation (GBD) are evaluated using the image stress solution of Chou ( Physica status solidi (a) 17, 509, 1966). The results show that to a good approximation, a GBD of Burgers vector g can be treated as a crystal dislocation but with a reduced Burgers vector ƒ where ƒ = 1 + 0.21 log α α is the ratio of the elastic constants of the “grain boundary phase” to that of the bulk crystal. The approximation is generally valid for the strain energy of the dislocation, and for stresses with α > 0.5. In addition, it is shown that GBDs in metals remain localised; the stress fields of which are comparable to that of a crystal dislocation. In glassy phase containing ceramics, however, the stress field of a crystal dislocation at the grain boundary can be relaxed significantly. Implications of above findings are discussed.