A Phase Field Model For Dislocation Dynamics

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A phase field model for dislocation climb
Pierre-Antoine Geslin, Benoît Appolaire, and Alphonse Finel
Citation: Applied Physics Letters 104, 011903 (2014); doi: 10.1063/1.4860999
View online: http://dx.doi.org/10.1063/1.4860999
View Table of Contents: http://scitation.aip.org/content/aip/journal/apl/104/1?ver=pdfcov
Published by the AIP Publishing
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APPLIED PHYSICS LETTERS 104, 011903 (2014)

A phase field model for dislocation climb
Pierre-Antoine Geslin,a) Beno^ıt Appolaire, and Alphonse Finel
Laboratoire d’Etude des Microstructures, Onera/CNRS, 29 avenue de la division Leclerc, 92322 Ch^ atillon, France

(Received 24 September 2013; accepted 17 December 2013; published online 7 January 2014)
We propose a phase field method to model consistently dislocation climb by vacancy absorption or emission. It automatically incorporates the exact balance between the vacancy flux and the phase field associated with the dislocation evolution, enforced by the conserved character of the total population of vacancies. One of its major advantage is the natural introduction of a dynamic coefficient controlling the kinetics of vacancy emission/absorption by the dislocation. We also derived a closed-form expression of the climb rate valid from the diffusion-limited to the
C 2014 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4860999] attachment-limited regimes. V

Dislocations are linear defects responsible for plastic deformation in crystalline solids. These defects change glide plane by absorbing point defects (climb). Whereas this climb mechanism is inhibited at low temperature, it becomes an essential part of plastic activity at high-temperature (creep).
Therefore, the analysis of climb dynamics is mandatory to have a better understanding of the creep behavior of metals and alloys.
Kabir et al.1 used a Monte-Carlo method to study dislocation climb in iron. The vacancy concentration and the dislocation density in these simulations are inherently very high because of the limited system size. Climb has also been investigated qualitatively with the phase field crystal technique2 but with the same limitation in system size.
To access more relevant scales, recent works3–5 introduced climb in Dislocation Dynamics (DD) modeling based on vacancy diffusion. The climb rate is obtained by integrating analytically Fick’s equation with strong assumptions.
Especially, each point of the dislocation is assumed to act as a perfect source/sink of vacancies and the elastic interactions between dislocations and vacancies are neglected. This first assumption can be spurious in some cases where the jogs concentration along the line is low and climb becomes limited by point defect emission/absorption.6
Gao et al.7 coupled pipe diffusion theory and DD to investigate climb dynamics in case of low jog concentration, but neglecting bulk diffusion, an essential feature of dislocation climb. Among the previously developed models, none is able to investigate climb behavior influenced by both bulk diffusion and absorption/emission kinetics.
The phase field method seems particularly adapted to the study of dislocation climb because it naturally