TY - JOUR

T1 - Dynamics of curved dislocation ensembles

AU - Groma, István

AU - Ispánovity, Péter Dusán

AU - Hochrainer, Thomas

N1 - Funding Information:
This work has been supported by the National Research, Development, and Innovation Office of Hungary (PDI and IG, Project No. NKFIH-K-119561) and the ELTE Institutional Excellence Program (TKP2020-IKA-05) supported by the Hungarian Ministry of Human Capacities.
Publisher Copyright:
© 2021 American Physical Society.

PY - 2021/5/3

Y1 - 2021/5/3

N2 - To develop a dislocation-based statistical continuum theory of crystal plasticity is a major challenge of materials science. During the last two decades, such a theory has been developed for the time evolution of a system of parallel edge dislocations. The evolution equations were derived by a systematic coarse graining of the equations of motion of the individual dislocations and later retrieved from a functional of the dislocation densities and the stress potential by applying the standard formalism of phase field theories. It is, however, a long-standing issue if a similar procedure can be established for curved dislocation systems. An important prerequisite for such a theory has recently been established through a density-based kinematic theory of moving curves. In this paper, an approach is presented for a systematic derivation of the dynamics of systems of curved dislocations in a single-slip situation. In order to reduce the complexity of the problem, a dipolelike approximation for the orientation-dependent density variables is applied. This leads to a closed set of kinematic evolution equations of total dislocation density, the geometrically necessary dislocation densities, and the so-called curvature density. The analogy of the resulting equations with the edge dislocation model allows one to generalize the phase field formalism and to obtain a closed set of dynamic evolution equations.

AB - To develop a dislocation-based statistical continuum theory of crystal plasticity is a major challenge of materials science. During the last two decades, such a theory has been developed for the time evolution of a system of parallel edge dislocations. The evolution equations were derived by a systematic coarse graining of the equations of motion of the individual dislocations and later retrieved from a functional of the dislocation densities and the stress potential by applying the standard formalism of phase field theories. It is, however, a long-standing issue if a similar procedure can be established for curved dislocation systems. An important prerequisite for such a theory has recently been established through a density-based kinematic theory of moving curves. In this paper, an approach is presented for a systematic derivation of the dynamics of systems of curved dislocations in a single-slip situation. In order to reduce the complexity of the problem, a dipolelike approximation for the orientation-dependent density variables is applied. This leads to a closed set of kinematic evolution equations of total dislocation density, the geometrically necessary dislocation densities, and the so-called curvature density. The analogy of the resulting equations with the edge dislocation model allows one to generalize the phase field formalism and to obtain a closed set of dynamic evolution equations.

UR - http://www.scopus.com/inward/record.url?scp=85106327207&partnerID=8YFLogxK

U2 - 10.1103/PhysRevB.103.174101

DO - 10.1103/PhysRevB.103.174101

M3 - Article

AN - SCOPUS:85106327207

SN - 2469-9950

VL - 103

JO - Physical Review B

JF - Physical Review B

IS - 17

M1 - 174101

ER -