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, bcc lattice. The phase field allows direct computation of the lattice incompatibility tensor for both dislocation lines and loops.
Bibliographical noteFunding Information:
We thank A. Acharya, K. Olsen, and J. Rønning for many stimulating discussions. The research of J.V. was supported by the National Science Foundation, Grant No. DMR-1838977. L.A. acknowledges support from the Kavli Institute for Theoretical Physics through the National Science Foundation under Grant No. NSF PHY-1748958.
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