On the Derivation of Boundary Conditions for Continuum Dislocation Dynamics

Publikation: Beitrag in einer FachzeitschriftArtikelForschungBegutachtung

Abstract

Continuum dislocation dynamics (CDD) is a single crystal strain gradient plasticity theory
based exclusively on the evolution of the dislocation state. Recently, we derived a constitutive
theory for the average dislocation velocity in CDD in a phase field-type description for an
infinite domain. In the current work, so-called rational thermodynamics is employed to obtain
thermodynamically consistent boundary conditions for the dislocation density variables of CDD.
We find that rational thermodynamics reproduces the bulk constitutive equations as obtained from
irreversible thermodynamics. The boundary conditions we find display strong parallels to the
microscopic traction conditions derived by Gurtin and Needleman (M.E. Gurtin and A. Needleman,
J. Mech. Phys. Solids 53 (2005) 1–31) for strain gradient theories based on the Kröner–Nye tensor
Originalspracheenglisch
AufsatznummerCrystals 2017, 7, 235
Seiten (von - bis)1-12
Seitenumfang12
FachzeitschriftCrystals
Jahrgang7
Ausgabenummer235
Frühes Online-Datum30 Jul 2017
DOIs
PublikationsstatusVeröffentlicht - 30 Jul 2017

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derivation
Boundary conditions
Thermodynamics
boundary conditions
continuums
Constitutive equations
Dislocations (crystals)
thermodynamics
Tensors
Plasticity
Single crystals
gradients
traction
constitutive equations
plastic properties
tensors
single crystals

Schlagwörter

  • continuum dislocation dynamics; strain gradient plasticity; boundary conditions; thermodynamic consistency; micro stresses; micro tractions

ASJC Scopus subject areas

  • !!Materials Science(all)

Fields of Expertise

  • Advanced Materials Science

Dies zitieren

On the Derivation of Boundary Conditions for Continuum Dislocation Dynamics. / Hochrainer, Thomas.

in: Crystals, Jahrgang 7, Nr. 235, Crystals 2017, 7, 235, 30.07.2017, S. 1-12.

Publikation: Beitrag in einer FachzeitschriftArtikelForschungBegutachtung

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AB - Continuum dislocation dynamics (CDD) is a single crystal strain gradient plasticity theory based exclusively on the evolution of the dislocation state. Recently, we derived a constitutive theory for the average dislocation velocity in CDD in a phase field-type description for an infinite domain. In the current work, so-called rational thermodynamics is employed to obtain thermodynamically consistent boundary conditions for the dislocation density variables of CDD. We find that rational thermodynamics reproduces the bulk constitutive equations as obtained from irreversible thermodynamics. The boundary conditions we find display strong parallels to the microscopic traction conditions derived by Gurtin and Needleman (M.E. Gurtin and A. Needleman, J. Mech. Phys. Solids 53 (2005) 1–31) for strain gradient theories based on the Kröner–Nye tensor.

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