On the Derivation of Boundary Conditions for Continuum Dislocation Dynamics

Research output: Contribution to journalArticleResearchpeer-review

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.
Original languageEnglish
Article numberCrystals 2017, 7, 235
Pages (from-to)1-12
Number of pages12
JournalCrystals
Volume7
Issue number235
Early online date30 Jul 2017
DOIs
Publication statusPublished - 30 Jul 2017

Fingerprint

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

Keywords

    ASJC Scopus subject areas

    • Materials Science(all)

    Fields of Expertise

    • Advanced Materials Science

    Cite this

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

    In: Crystals, Vol. 7, No. 235, Crystals 2017, 7, 235, 30.07.2017, p. 1-12.

    Research output: Contribution to journalArticleResearchpeer-review

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    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 Kr{\"o}ner–Nye tensor.",
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