Non-singular dislocation continuum theories: Strain gradient elasticity versus Peierls-Nabarro model

TL;DR

This paper compares non-singular dislocation models, showing that strain gradient elasticity provides more realistic and physically plausible core structures than the Peierls-Nabarro model, enhancing understanding of dislocation behavior.

Contribution

It demonstrates that strain gradient elasticity yields more realistic dislocation core shapes and fields compared to the Peierls-Nabarro model, advancing continuum dislocation theories.

Findings

Strain gradient elasticity predicts narrower, more evenly distributed dislocation cores.

Non-singular fields in strain gradient elasticity are more realistic than Peierls-Nabarro.

Dislocation core size and shape are better modeled by strain gradient elasticity.

Abstract

Non-singular dislocation continuum theories are studied. A comparison between Peierls-Nabarro dislocations and straight dislocations in strain gradient elasticity is given. The non-singular displacement fields, non-singular stresses, plastic distortions and dislocation core shapes are analyzed and compared for the two models. The main conclusion of this study is that due to their characteristic properties, the non-singular displacement fields, non-singular stresses and dislocation core shape of screw and edge dislocations obtained in the framework of strain gradient elasticity are more realistic and physical than the corresponding fields of the Peierls-Nabarro model. Strain gradient elasticity of dislocations is a continuum dislocation theory including a weak nonlocality within the dislocation core and predicting the size and shape of the dislocation core. The dislocation core is narrower in the strain gradient elasticity dislocation model than in the Peierls-Nabarro model and more evenly distributed in two dimensions. The present analysis shows that for the modeling of the dislocation core structure the non-singular dislocation fields of strain gradient elasticity are the suitable ones.