A phase field crystal theory of the kinematics of dislocation lines

We introduce a dislocation density tensor and derive its kinematic evolution law from phase field description of crystal deformations in three dimensions. The (PFC) model is used to define the lattice distortion, including topological singularities, associated configurational stresses. an exact expression for velocity line determined by evolution, show that motion PFC driven Peach-Koehler force. As well known earlier studies, stress not divergence free general configuration. Therefore, we also present method (PFCMEq) constrain diffusive dynamics mechanical equilibrium adding independent integrable distortion so total resulting free. In PFCMEq model, far-field agrees very with predictions continuum elasticity, while near-field around core regularized smooth nature phase-field. apply this framework study rate shrinkage loop seeded glide plane.