Comptes Rendus
no. 4-5
Generalised continuum modelling of grain size effects in polycrystals
Nicolas M. Cordero1 ; Samuel Forest1  ; Esteban P. Busso1
1 MINES ParisTech, centre des matériaux, CNRS UMR 7633, BP 87, 91003 Evry cedex, France
Comptes Rendus. Mécanique, Volume 340 (2012) no. 4-5, pp. 261-274.

The effect of the dislocation density tensor is introduced into the classical crystal plasticity framework by means of the micromorphic theory of single crystals. A computational homogenisation strategy is presented in order to describe the global and local responses of two-dimensional polycrystalline aggregates for grain sizes ranging from 1 to 200 microns. The model is shown to naturally predict a size-dependent kinematic hardening behaviour which is responsible for the observed strong size effects. The yield stress at a given averaged plastic strain is shown to follow a power law scaling relation for grain sizes larger than a critical one. The field of plastic deformation is also strongly affected by grain size, whereby micron-size grains lead to the formation of intense slip bands crossing several grains.

Publié le :
DOI : 10.1016/j.crme.2012.02.009
Mots clés : Crystal plasticity, Strain gradient plasticity, Micromorphic theory, Kinematic hardening, Dislocation density tensor, Grain boundary, Polycrystalline aggregate, Hall–Petch effect
Nicolas M. Cordero 1 ; Samuel Forest 1 ; Esteban P. Busso 1

1 MINES ParisTech, centre des matériaux, CNRS UMR 7633, BP 87, 91003 Evry cedex, France 
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Nicolas M. Cordero; Samuel Forest; Esteban P. Busso. Generalised continuum modelling of grain size effects in polycrystals. Comptes Rendus. Mécanique, Volume 340 (2012) no. 4-5, pp. 261-274. doi : 10.1016/j.crme.2012.02.009. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2012.02.009/

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