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A Theory of Disclination and Dislocation Fields for Grain Boundary Plasticity

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Generalized Continua as Models for Materials

Part of the book series: Advanced Structured Materials ((STRUCTMAT,volume 22))

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Abstract

A continuum mechanics model is introduced for a core and structure sensitive modeling of grain boundary mediated plasticity. It accounts for long range elastic strain and curvature incompatibilities due to the presence of dislocation and disclination densities. The coupled spatio-temporal evolution of the crystal defects is also accounted for by transport equations. Based on atomistic structures, copper tilt boundaries are modeled with periodic sequences of wedge disclination dipoles. Their self-relaxation by transport leads to grain boundary configurations with lower elastic energies, which are compared to molecular statics values. The characteristic internal length inherent to strain gradient elasticity, which relates the elastic energy weight of couple-stresses to that of stresses, is chosen to retrieve the elastic energy obtained by atomistic simulations. This length is found to be lower than interatomic distances. In agreement with atomistic modeling, couple-stress elasticity is thought to be relevant for the modeling of highly heterogeneous defect microstructures at atomic resolution scales only.

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Notes

  1. 1.

    It is found from Frank’s formula that the separation distance \(\displaystyle l\) between the edge dislocations in a dislocation-made tilt boundary of misorientation \(\displaystyle 46.40^{\circ }\) is \(\displaystyle l = 0.34\,nm\), a distance much too short to be realistic. Such a result supports the view that a consistent description of high-angle tilt boundaries should recourse to disclination dipole walls rather than edge dislocation walls.

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Acknowledgments

The authors benefited of financial support from the ANR (Agence Nationale de la Recherche) under grant ANR-11-JS09-007-01, NanoMec.

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Authors and Affiliations

  1. Laboratoire d’Etude des Microstructures et de Mécanique des Matériaux, Université de Lorraine/CNRS, Ile du Saulcy, 57045 , Metz Cedex, France

    V. Taupin, C. Fressengeas & A. Das

  2. G.W. Woodruff School of Mechanical Engineering, Georgia Institute of Technology/CNRS, 57070 , Metz Cedex, France

    L. Capolungo & M. Upadhyay

Authors
  1. V. Taupin
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  2. L. Capolungo
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  3. C. Fressengeas
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  4. A. Das
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  5. M. Upadhyay
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Corresponding author

Correspondence to V. Taupin .

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Editors and Affiliations

  1. , Lehrstuhl für Technische Mechanik, Otto-von-Guericke-Universität Magdeburg, Universitätsplatz 2, Magdeburg, 39112, Germany

    Holm Altenbach

  2. , Centre des Materiaux CNRS UMR 7633, Mines ParisTech, BP 87, EVRY Cedex, 91003, France

    Samuel Forest

  3. University, Dep. of Theoretical Mechanics, St. Petersburg State Polytechnical, Politekhnicheskaya, 29, St. Petersburg, 195251, Russia

    Anton Krivtsov

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Taupin, V., Capolungo, L., Fressengeas, C., Das, A., Upadhyay, M. (2013). A Theory of Disclination and Dislocation Fields for Grain Boundary Plasticity. In: Altenbach, H., Forest, S., Krivtsov, A. (eds) Generalized Continua as Models for Materials. Advanced Structured Materials, vol 22. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-36394-8_18

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