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Dislocation nucleation and work hardening in anti-plane constrained shear

Abstract

The paper aims at studying the dislocation nucleation, the corresponding work hardening and the influence of resistance to the dislocation motion within the framework of continuum theory of dislocations. We consider an anti-plane constrained shear problem which admits an analytical solution. The interesting features of this solution are the energy and dissipation thresholds for dislocation nucleation, the Bauschinger translational work hardening, and the size effect.

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References

  1. 1.

    Berdichevsky V.L. and Sedov L.I. (1967). Dynamic theory of continuously distributed dislocations: Its relation to plasticity theory. J. Appl. Math. Mech. (PMM). 31: 989–1006

  2. 2.

    Berdichevsky V.L. (2006). Continuum theory of dislocations revisited. Continuum Mech. Thermodyn. 18: 195–222

  3. 3.

    Berdichevsky V.L. (2006). On thermodynamics of crystal plasticity. Scripta Mat. 54: 711–716

  4. 4.

    Mosolov P.P. and Miasnikov V.P. (1971). Variational methods in the theory of the flow of rigid-viscoplastic media. Moscow University Press, Moscow

  5. 5.

    Leibfried G. (1951). Verteilung von Versetzungen im statischen Gleichgewicht. Z. Phys. 130: 214–226

  6. 6.

    Friedman L.H. and Chrzan D.C. (1998). Continuum analysis of dislocation pile-ups: influence of sources. Phil. Mag. 77: 1185–1204

  7. 7.

    Berdichevsky V.L. (1983). Variational principles of continuum mechanics. Nauka, Moscow

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Author information

Correspondence to V. L. Berdichevsky.

Additional information

The financial support by the DFG (German Science Foundation) within the Collaborative Research Center 526 (project D9) for K.C. Le is gratefully acknowledged

Communicated by L. Truskinovsky

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Berdichevsky, V.L., Le, K.C. Dislocation nucleation and work hardening in anti-plane constrained shear. Continuum Mech. Thermodyn. 18, 455–467 (2007). https://doi.org/10.1007/s00161-006-0039-0

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Keywords

  • Dislocation nucleation
  • Work hardening
  • Size effect
  • Continuum theory of dislocations

Pacs

  • 61.72.Bb
  • 61.72.Lk
  • 62.20.Fe