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  • Development of mean-field continuum dislocation kinematics with junction reactions using de Rham currents and graph theory
Title: Development of mean-field continuum dislocation kinematics with junction reactions using de Rham currents and graph theory
An accurate description of the evolution of dislocation networks is an essential part of discrete and continuum dislocation dynamics models. These networks evolve by motion of the dislocation lines and by forming junctions between these lines via cross slip, annihilation and junction reactions. In this work, we introduce these dislocation reactions into continuum dislocation models using the theory of de Rham currents. We introduce dislocations on each slip system as potentially open lines whose boundaries are associated with junction points and, therefore, still create a network of collectively closed lines that satisfy the classical relations and for the dislocation density tensor and the plastic distortion . To ensure this, we leverage Frank’s second rule at the junction nodes and the concept of virtual dislocation segments. We introduce the junction point density as a new state variable that represents the distribution of junction points within the crystal containing the dislocation network. Adding this information requires knowledge of the global structure of the dislocation network, which we obtain from its representation as a graph. We derive transport relations for the dislocation line density on each slip system in the crystal, which now includes a term that corresponds to the motion of junction points. We also derive the transport relations for junction points, which include source terms that reflect the topology changes of the dislocation network due to junction formation.  more » « less
Award ID(s):
1663311
PAR ID:
10358781
Author(s) / Creator(s):
; ;
Date Published:
Journal Name:
Journal of the mechanics and physics of solids
Volume:
158
ISSN:
0022-5096
Page Range / eLocation ID:
1-25
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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