Generalized Kanzaki force field of extended defects in crystals with applications to the modeling of edge dislocations

Abstract

The Kanzaki forces and their associated multipolar moments are standard ways of representing point defects in an atomistically informed way in the continuum. In this article, the Kanzaki force approach is extended to other crystalline defects. The article shows how the resulting Kanzaki force fields are to be computed for any general extended defect by first computing the relaxed defect's structure and then defining an affine mapping between the said defect structure and the original perfect lattice. This methodology can be employed to compute the Kanzaki force field of any mass-conserving defect, including dislocations, grain and twin boundaries, or cracks. Particular focus is then placed on straight edge dislocation in face-centered cubic (fcc) and body-centered cubic (bcc) pure metals, which are studied along different crystallographic directions. The particular characteristics of these force fields are discussed, drawing a distinction between the slip Kanzaki force field associated with the Volterra disregistry that characterizes the dislocation, and the core Kanzaki force field associated with the specific topology of the dislocation's core. The resulting force fields can be employed to create elastic models of the dislocation that, unlike other regularization procedures, offer a geometrically true representation of the core and the elastic fields in its environs, capturing all three-dimensional effects associated with the core.