TY - JOUR

T1 - Development of mean-field continuum dislocation kinematics with junction reactions using de Rham currents and graph theory

AU - Starkey, Kyle

AU - Hochrainer, Thomas

AU - El-Azab, Anter

N1 - Funding Information:
This research was supported by the National Science Foundation, Division of Civil, Mechanical, and Manufacturing Innovation (CMMI), United States through award number 1663311 at Purdue University. The authors appreciate the useful comments by the referees, which led to improvement of the manuscript.
Publisher Copyright:
© 2021 Elsevier Ltd

PY - 2022/1

Y1 - 2022/1

N2 - 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 α=curlβp and divα=0 for the dislocation density tensor α and the plastic distortion βp. 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.

AB - 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 α=curlβp and divα=0 for the dislocation density tensor α and the plastic distortion βp. 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.

KW - Continuum dislocation dynamics

KW - de Rham currents

KW - Dislocation reactions

KW - Graph theory

UR - http://www.scopus.com/inward/record.url?scp=85118831784&partnerID=8YFLogxK

U2 - 10.1016/j.jmps.2021.104685

DO - 10.1016/j.jmps.2021.104685

M3 - Article

AN - SCOPUS:85118831784

VL - 158

JO - Journal of the Mechanics and Physics of Solids

JF - Journal of the Mechanics and Physics of Solids

SN - 0022-5096

M1 - 104685

ER -