Improvement of nonlocal Peierls-Nabarro models

Abstract

We review the major efforts that improve the accuracy of Peierls-Nabarro (PN) model in predicting core structure and Peierls stress, and recognize that the nonlocal atomic interactions in the core region should be accounted for in calculating the dislocation energy. Although some efforts have been devoted to taking the nonlocal interaction into account, further improvement is needed to simplify the computational complexity and resolve the inconsistency between the continuum model and the discrete nature of the lattice. Here we developed a two-dimensional (2D) and a three-dimensional (3D) nonlocal semi-discrete variational Peierls-Nabarro (SVPN) models by incorporating the nonlocal atomic interactions into the semi-discrete variational Peierls framework. The nonlocal SVPN models are applied to dislocations with extended core in copper and compact core in iron. Molecular dynamics simulations are performed to validate the model predictions. We found that the nonlocal SVPN model (both 2D and 3D) significantly improves the prediction accuracy for dislocation core structure and Peierls stress. Moreover, the results show that the 2D and 3D models give similar predictions of the Peierls stress and dislocation core structure, when the atomic relaxation in the normal direction is allowed in the 2D model to describe the interatomic interactions in the slip plane.