Dynamic drags acting on moving defects in discrete dispersive media: From dislocation to low-angle grain boundary

Although continuum theory has been widely used to describe the long-range elastic behavior of dislocations, it is limited in its ability to describe mechanical behaviors that occur near dislocation cores. This limit of the continuum theory mainly stems from the discrete nature of the core region, which induces a drag force on the dislocation core during glide. Depending on external conditions, different drag mechanisms are activated that govern the dynamics of dislocations in their own way. This is revealed by the resultant speed of the dislocation. In this work, we develop a theoretical framework that generally describes the dynamic drag on dislocations and, as a result, derive a phenomenological cubic constitutive equation. Furthermore, given that a low-angle grain boundary (LAGB) can be regarded as an array of dislocations, we extend the model to describe the mobility law of LAGBs as a function of misorientation angle. As a result, we prove that both dislocations and LAGBs follow the developed constitutive equation with the same mathematical form despite their different governing drag sources. The suggested model is also supported by molecular dynamics simulations. Therefore, this work has significance for a fundamental understanding of the dynamic drag acting on defects and facilitates a general description of various drag mechanisms.