Dislocation nucleation in the phase field crystal model

TL;DR

This paper uses the phase field crystal model to investigate dislocation nucleation in two and three dimensions, revealing how stress, lattice incompatibility, and energy considerations influence nucleation events.

Contribution

It introduces a method to predict dislocation nucleation and Burgers vectors using the phase field crystal model, including a Schmid-like criterion for critical stress prediction.

Findings

Dislocation dipoles nucleate under applied stress, conserving Burgers vectors.

Lattice incompatibility fields serve as sensitive indicators of nucleation sites.

A phase field energy calculation correlates with nucleation events.

Abstract

We use the phase field crystal model to study nucleation of edge dislocations in two dimensions under an applied stress field. A dislocation dipole nucleates under the applied stress, consistent with Burgers vector conservation. The phase field correctly accounts for elastic energy storage prior to nucleation, and for dissipative relaxation during the nucleation event. We show that a lattice incompatibility field is a sensitive diagnostic of the location of the nucleation event, and of the Burgers vector and slip direction of the dislocations that will be nucleated above threshold. A direct calculation of the phase field energy accurately correlates with the nucleation event, as signaled by the lattice incompatibility field. We show that a Schmid-like criterion concerning the resolved stress at the nucleation site correctly predicts the critical nucleation stress. Finally, we present preliminary results for a three-dimensional, body-centered cubic lattice. The phase field allows a direct computation of the lattice incompatibility tensor for both dislocation lines and loops.