Atomistic-to-continuum description of edge dislocation core: Unification of the Peierls-Nabarro model with linear elasticity

Abstract

Conventional linear elasticity theory predicts the strain fields of a dislocation core to diverge, whereas it is known from atomistic simulations that core strains should remain finite. We present an analytical solution to a generalized, variational Peierls-Nabarro model of edge dislocation displacement fields that features a finite core width and correct isotropic elastic behavior at large distances away from the core. We derive an analytical expression for the dislocation core radius, representing the convergence radius of the linear elasticity far-field expansion. The strain fields are in qualitative agreement with atomistic simulations of $\frac{1}{2}[111](10\overline{1})$ edge dislocations in bcc tungsten and iron. The treatment is based on the multistring Frenkel-Kontorova model that we reformulate as a generalized Peierls-Nabarro model using the principle of least action.