TY - JOUR
T1 - A phase field crystal theory of the kinematics of dislocation lines
AU - Skogvoll, Vidar
AU - Angheluta, Luiza
AU - Skaugen, Audun
AU - Salvalaglio, Marco
AU - Viñals, Jorge
N1 - Publisher Copyright:
© 2022 The Author(s)
PY - 2022/9
Y1 - 2022/9
N2 - We introduce a dislocation density tensor and derive its kinematic evolution law from a phase field description of crystal deformations in three dimensions. The phase field crystal (PFC) model is used to define the lattice distortion, including topological singularities, and the associated configurational stresses. We derive an exact expression for the velocity of dislocation line determined by the phase field evolution, and show that dislocation motion in the PFC is driven by a Peach–Koehler force. As is well known from earlier PFC model studies, the configurational stress is not divergence free for a general field configuration. Therefore, we also present a method (PFCMEq) to constrain the diffusive dynamics to mechanical equilibrium by adding an independent and integrable distortion so that the total resulting stress is divergence free. In the PFCMEq model, the far-field stress agrees very well with the predictions from continuum elasticity, while the near-field stress around the dislocation core is regularized by the smooth nature of the phase-field. We apply this framework to study the rate of shrinkage of an dislocation loop seeded in its glide plane.
AB - We introduce a dislocation density tensor and derive its kinematic evolution law from a phase field description of crystal deformations in three dimensions. The phase field crystal (PFC) model is used to define the lattice distortion, including topological singularities, and the associated configurational stresses. We derive an exact expression for the velocity of dislocation line determined by the phase field evolution, and show that dislocation motion in the PFC is driven by a Peach–Koehler force. As is well known from earlier PFC model studies, the configurational stress is not divergence free for a general field configuration. Therefore, we also present a method (PFCMEq) to constrain the diffusive dynamics to mechanical equilibrium by adding an independent and integrable distortion so that the total resulting stress is divergence free. In the PFCMEq model, the far-field stress agrees very well with the predictions from continuum elasticity, while the near-field stress around the dislocation core is regularized by the smooth nature of the phase-field. We apply this framework to study the rate of shrinkage of an dislocation loop seeded in its glide plane.
KW - Atomistic models
KW - Computational methods
KW - Crystal plasticity
KW - Dislocation dynamics
KW - Phase-field crystal modeling
KW - Structure of solids and liquids
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U2 - 10.1016/j.jmps.2022.104932
DO - 10.1016/j.jmps.2022.104932
M3 - Article
AN - SCOPUS:85132432881
SN - 0022-5096
VL - 166
JO - Journal of the Mechanics and Physics of Solids
JF - Journal of the Mechanics and Physics of Solids
M1 - 104932
ER -