Dislocation core field. I. Modeling in anisotropic linear elasticity theory

Abstract

Aside from the Volterra field, dislocations create a core field, which can be modeled in linear anisotropic elasticity theory with force and dislocation dipoles. We derive an expression of the elastic energy of a dislocation taking full account of its core field and show that no cross term exists between the Volterra and the core fields. We also obtain the contribution of the core field to the dislocation interaction energy with an external stress, thus showing that dislocation can interact with a pressure. The additional force that derives from this core field contribution is proportional to the gradient of the applied stress. Such a supplementary force on dislocations may be important in high stress gradient regions, such as close to a crack tip or in a dislocation pile-up.

Line tension of a dislocation moving through an anisotropic crystal

“…6 By considering differences in energy between two similar dislocation configurations, within a sufficiently large crystal the difference in linear elastic strain and kinetic energy will always dominate because it scales logarithmically with the crystal radius, R. We hence neglect effects associated with the dislocation core, not only for simplicity but also assuming that the cores remain similar across two configurations and their effects on the line tension is therefore subleading. For additional details on the energetics of the dislocation core, we refer to, e.g., [35][36][37][38]. 7 A second suite of computations of (2.14) was performed within Mathematica for validation purposes.…”

Dislocation core field.II. Screw dislocation in iron

“…the term n = 1, is completely controlled by the first moments M ij of the line force distribution. Knowing this second rank tensor M ij , one can not only predict the elastic displacement and stress associated with the core field 9 , but also the contribution of the core field to the elastic energy and to the dislocation interaction with an external stress field 10 . It is thus important to know the value of the first moment tensor M ij , and we will see how it can be deduced from ab initio calculations.…”

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

“…Thus, the multipolar moments could be envisioned to effect a correction on the classical Volterra dislocation. The first order correction, the dipolar moments, has been the subject of investigation in the past by Clouet and collaborators [68,69] in the context of screw dislocations and was achieved by energetic methods [70]. Previous works [71][72][73] also attempted to model the core as a set of "line force" dipolar arrangements using atomistic calculation methods reliant on the core's energy.…”

“…These forces have been shown to not generally be in mechanical equilibrium. However, the elastic energy to harmonic order associated with core should be the same as that of Clouet's [68,69] and Hirth and coworkers' [71,72] accounts, since it comprises all non-Volterra effects too. Thus, contrary to these works, the dipolar and higher order multipolar moments we compute here do not necessitate that the core be in mechanical equilibrium; given that individual dislocations are known not to be in mechanical equilibrium [21,74,75], making such an assumption regardless will inevitably lead to a description of the core fields that is not comparable to the one discussed here.…”