Atomically informed nonlocal semi-discrete variational Peierls-Nabarro model for planar core dislocations

Guisen Liu,Xi Cheng,Yao Shen,Kaiguo Chen,Jian Wang

doi:10.1038/srep43785

Abstract

Prediction of Peierls stress associated with dislocation glide is of fundamental concern in understanding and designing the plasticity and mechanical properties of crystalline materials. Here, we develop a nonlocal semi-discrete variational Peierls-Nabarro (SVPN) model by incorporating the nonlocal atomic interactions into the semi-discrete variational Peierls framework. The nonlocal kernel is simplified by limiting the nonlocal atomic interaction in the nearest neighbor region, and the nonlocal coefficient is directly computed from the dislocation core structure. Our model is capable of accurately predicting the displacement profile, and the Peierls stress, of planar-extended core dislocations in face-centered cubic structures. Our model could be extended to study more complicated planar-extended core dislocations, such as <110> {111} dislocations in Al-based and Ti-based intermetallic compounds.

Highlights

All these improvements were made under the assumption that the constitutive law and the misfit energy linking the two elastic half-spaces depend only on the disregistry profile at a local site, while ignoring the interactions associated with the large gradient of the nonlinear disregistry in the core region
After introducing the nonlocal energy term in the nonlocal SVPN model, the misfit energy increases, and elastic energy decreases. ∆Emisfit for all the dislocations studied in this work is around 0.034~0.039 μb[2], which is about 30% increase compared with the local SVPN model
All the results presented above indicate that the nonlocal SVPN model can significantly improve the predictions of both core structure and Peierls stress, and with the predictions being in better agreement with MD calculations and with experimental estimations[33]

Summary

Introduction

All these improvements were made under the assumption that the constitutive law and the misfit energy linking the two elastic half-spaces depend only on the disregistry profile at a local site, while ignoring the interactions associated with the large gradient of the nonlinear disregistry in the core region. Miller et al.[20] proposed a nonlocal kernel to consider the nonlocal effects in dislocation core and derived its approximate analytical form in real space. They attributed the nonlocal interactions to a modification of the atomic misfit energy, and the nonlocal coefficients were computed by calibrating the misfit energy against the one obtained by atomistic simulations. This method remarkably improves the prediction of the misfit energy, but the core structure did not change much, and sometimes deviated further away from the atomistic results. The results are validated against MD simulations, and compared with experiments

Methods

Results

Conclusion