### Abstract

A phase-field model of a crystalline material is introduced to develop the necessary theoretical framework to study plastic flow due to dislocation motion. We first obtain the elastic stress from the phase-field crystal free energy under weak distortion and show that it obeys the stress-strain relation of linear elasticity. We focus next on dislocations in a two-dimensional hexagonal lattice. They are composite topological defects in the weakly nonlinear amplitude equation expansion of the phase field, with topological charges given by the standard Burgers vector. This allows us to introduce a formal relation between the dislocation velocity and the evolution of the slowly varying amplitudes of the phase field. Standard dissipative dynamics of the phase-field crystal model is shown to determine the velocity of the dislocations. When the amplitude expansion is valid and under additional simplifications, we find that the dislocation velocity is determined by the Peach-Koehler force. As an application, we compute the defect velocity for a dislocation dipole in two setups, pure glide and pure climb, and compare it with the analytical predictions.

Original language | English (US) |
---|---|

Article number | 054113 |

Journal | Physical Review B |

Volume | 97 |

Issue number | 5 |

DOIs | |

State | Published - Feb 26 2018 |

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### Cite this

*Physical Review B*,

*97*(5), [054113]. https://doi.org/10.1103/PhysRevB.97.054113

**Dislocation dynamics and crystal plasticity in the phase-field crystal model.** / Skaugen, Audun; Angheluta, Luiza; Vinals, Jorge.

Research output: Contribution to journal › Article

*Physical Review B*, vol. 97, no. 5, 054113. https://doi.org/10.1103/PhysRevB.97.054113

}

TY - JOUR

T1 - Dislocation dynamics and crystal plasticity in the phase-field crystal model

AU - Skaugen, Audun

AU - Angheluta, Luiza

AU - Vinals, Jorge

PY - 2018/2/26

Y1 - 2018/2/26

N2 - A phase-field model of a crystalline material is introduced to develop the necessary theoretical framework to study plastic flow due to dislocation motion. We first obtain the elastic stress from the phase-field crystal free energy under weak distortion and show that it obeys the stress-strain relation of linear elasticity. We focus next on dislocations in a two-dimensional hexagonal lattice. They are composite topological defects in the weakly nonlinear amplitude equation expansion of the phase field, with topological charges given by the standard Burgers vector. This allows us to introduce a formal relation between the dislocation velocity and the evolution of the slowly varying amplitudes of the phase field. Standard dissipative dynamics of the phase-field crystal model is shown to determine the velocity of the dislocations. When the amplitude expansion is valid and under additional simplifications, we find that the dislocation velocity is determined by the Peach-Koehler force. As an application, we compute the defect velocity for a dislocation dipole in two setups, pure glide and pure climb, and compare it with the analytical predictions.

AB - A phase-field model of a crystalline material is introduced to develop the necessary theoretical framework to study plastic flow due to dislocation motion. We first obtain the elastic stress from the phase-field crystal free energy under weak distortion and show that it obeys the stress-strain relation of linear elasticity. We focus next on dislocations in a two-dimensional hexagonal lattice. They are composite topological defects in the weakly nonlinear amplitude equation expansion of the phase field, with topological charges given by the standard Burgers vector. This allows us to introduce a formal relation between the dislocation velocity and the evolution of the slowly varying amplitudes of the phase field. Standard dissipative dynamics of the phase-field crystal model is shown to determine the velocity of the dislocations. When the amplitude expansion is valid and under additional simplifications, we find that the dislocation velocity is determined by the Peach-Koehler force. As an application, we compute the defect velocity for a dislocation dipole in two setups, pure glide and pure climb, and compare it with the analytical predictions.

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U2 - 10.1103/PhysRevB.97.054113

DO - 10.1103/PhysRevB.97.054113

M3 - Article

VL - 97

JO - Physical Review B

JF - Physical Review B

SN - 2469-9950

IS - 5

M1 - 054113

ER -