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Generalized Continua as Models for Materials pp 41–64Cite as

Continuum Modelling of Shear-Coupled Grain Boundary Migration

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

Abstract

The deformation accommodation mechanisms associated to grain boundaries (GBs) significantly affect the mechanical behavior of nano-polycrystals. Among these mechanisms, stress-induced GB migration is now seen to compete or interplay with other intra-granular and GB mechanisms in a wide range of temperatures. A complete micromechanics-based model is here proposed using the concepts of continuum thermodynamics and kinematics to derive a new constitutive model able to describe stress-induced GB migration. Like non diffusive phase-transformations, stress-induced GB migration can be considered on the thermodynamics point of view of conservative nature (diffusionless but thermally activated) until high temperature with respect to melting point. Here, in the framework of continuum micro-mechanics which should be easily implemented in a polycrystalline model, we will first describe the micromechanical framework: the kinematics and the thermodynamics associated with additive mechanisms including plastic deformation in the bulk crystals, GB migration and GB sliding. For the sake of illustration of the present general theory, we will focus on planar bi-crystals and only perfect shear-coupling GB migration situations of [001] symmetric tilt GBs in Cu. Numerical examples and responses of the micromechanical model are given for these bi-crystals considering both isotropic and anisotropic elasticity. These ones are fed by computer-aided MD simulations for which deformation mechanisms are identified.

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Notes

  1. 1.

    LAMMPS Molecular Dynamics Simulator; http///lammps.sandia.gov/.

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Acknowledgments

The authors are grateful to the French “Agence Nationale de la Recherche” under contract agreement ANR-07-BLAN-0186 for financial support.

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Authors and Affiliations

  1. Laboratoire d’Etudes des Microstructures et de Mécanique des Matériaux, LEM3, UMR CNRS 7239, University of Lorraine, 57045, Metz, France

    Stéphane Berbenni

  2. Unité Mixte Internationale Georgia Tech Lorraine-CNRS, UMI CNRS 2958, 57070 , Metz, France

    Stéphane Berbenni

  3. George W. Woodruff School of Mechanical Engineering, Georgia Institute of Technology, 30332-0405, Atlanta 22, GA, USA

    Bhasker Paliwal & Mohammed Cherkaoui

Authors
  1. Stéphane Berbenni
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  2. Bhasker Paliwal
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  3. Mohammed Cherkaoui
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Corresponding author

Correspondence to Stéphane Berbenni .

Editor information

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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Berbenni, S., Paliwal, B., Cherkaoui, M. (2013). Continuum Modelling of Shear-Coupled Grain Boundary Migration. 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_3

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