Finite element simulations of coherent diffraction in elastoplastic polycrystalline aggregates

H. Proudhon; N. Vaxelaire; S. Labat; S. Forest; O. Thomas

doi:10.1016/j.crhy.2010.07.009

Computational metallurgy and changes of scale / Métallurgie numérique et changements d'échelle

Finite element simulations of coherent diffraction in elastoplastic polycrystalline aggregates

H. Proudhon ¹; N. Vaxelaire ²; S. Labat ²; S. Forest ¹ ; O. Thomas ²

¹ MINES ParisTech, centre des matériaux, CNRS UMR 7633, BP 87, 91003 Evry cedex, France
² Aix-Marseille University, CNRS, IM2NP, FST, avenue Escadrille-Normandie–Niemen, 13397 Marseille cedex, France

Comptes Rendus. Physique, Computational metallurgy and scale transitions, Volume 11 (2010) no. 3-4, pp. 293-303.

Abstract
Résumé

This work ties some crystal plasticity continuum mechanics computations with the diffraction theory. This allows one to predict coherent X-ray diffraction (CXD) patterns in reciprocal space in a polycrystalline specimen. When the sample deforms elastically, the full displacement field can be used to simulate CXD patterns, but it is no longer possible, as soon as plasticity develops within the considered grains. An approximate elastic displacement field, based on a first order Taylor expansion of the elastic deformation field near the center of the grain, is used to extend the predictions in the plastic regime. It is shown that using such a field leads to more realistic CXD patterns and therefore this approach could be useful to interpret coherent diffraction experiments in the future.

La théorie continue de la plasticité cristalline est utilisée pour prédire les figures de diffraction aux rayons X dans l'espace réciproque d'un polycristal métallique. Lorsque l'échantillon se déforme de manière purement élastique, le champ de déplacement calculé par éléments finis est utilisé pour simuler les figures de diffraction. Ce n'est plus possible dès que la plasticité se développe dans les grains étudiés. C'est la distorsion élastique qui intervient alors pour le calcul de diffraction. Un champ de déplacement approché, basé sur un développement de Taylor au premier ordre autour du centre d'un grain, est utilisé pour la prévision des figures de diffraction dans le régime plastique. On montre que l'usage de ce champ approché à la place du déplacement total conduit à des prévisions significativement différentes et plus réalistes des figures de diffraction. Cette approche peut donc être utile pour l'interprétation des expériences de diffraction cohérente.

Published online: 2010-04-01

DOI: 10.1016/j.crhy.2010.07.009

Keywords: Coherent diffraction, Anisotropic elasticity, Crystal plasticity, Finite element modeling
Mots-clés : Diffraction cohérente, Éasticité anisotrope, Plasticité cristalline, Modélisation par éléments finis

Author's affiliations:

H. Proudhon ¹; N. Vaxelaire ²; S. Labat ²; S. Forest ¹; O. Thomas ²

¹ MINES ParisTech, centre des matériaux, CNRS UMR 7633, BP 87, 91003 Evry cedex, France
² Aix-Marseille University, CNRS, IM2NP, FST, avenue Escadrille-Normandie–Niemen, 13397 Marseille cedex, France

@article{CRPHYS_2010__11_3-4_293_0,
     author = {H. Proudhon and N. Vaxelaire and S. Labat and S. Forest and O. Thomas},
     title = {Finite element simulations of coherent diffraction in elastoplastic polycrystalline aggregates},
     journal = {Comptes Rendus. Physique},
     pages = {293--303},
     publisher = {Elsevier},
     volume = {11},
     number = {3-4},
     year = {2010},
     doi = {10.1016/j.crhy.2010.07.009},
     language = {en},
}

TY  - JOUR
AU  - H. Proudhon
AU  - N. Vaxelaire
AU  - S. Labat
AU  - S. Forest
AU  - O. Thomas
TI  - Finite element simulations of coherent diffraction in elastoplastic polycrystalline aggregates
JO  - Comptes Rendus. Physique
PY  - 2010
SP  - 293
EP  - 303
VL  - 11
IS  - 3-4
PB  - Elsevier
DO  - 10.1016/j.crhy.2010.07.009
LA  - en
ID  - CRPHYS_2010__11_3-4_293_0
ER  -

%0 Journal Article
%A H. Proudhon
%A N. Vaxelaire
%A S. Labat
%A S. Forest
%A O. Thomas
%T Finite element simulations of coherent diffraction in elastoplastic polycrystalline aggregates
%J Comptes Rendus. Physique
%D 2010
%P 293-303
%V 11
%N 3-4
%I Elsevier
%R 10.1016/j.crhy.2010.07.009
%G en
%F CRPHYS_2010__11_3-4_293_0

H. Proudhon; N. Vaxelaire; S. Labat; S. Forest; O. Thomas. Finite element simulations of coherent diffraction in elastoplastic polycrystalline aggregates. Comptes Rendus. Physique, Computational metallurgy and scale transitions, Volume 11 (2010) no. 3-4, pp. 293-303. doi : 10.1016/j.crhy.2010.07.009. https://comptes-rendus.academie-sciences.fr/physique/articles/10.1016/j.crhy.2010.07.009/

References
Cited by

[1] G. Cailletaud; S. Forest; D. Jeulin; F. Feyel; I. Galliet; V. Mounoury; S. Quilici Some elements of microstructural mechanics, Computational Materials Science, Volume 27 (2003) no. 3, pp. 351-374

[2] R. Brenner; R.A. Lebensohn; O. Castelnau Elastic anisotropy and yield surface estimates of polycrystals, International Journal of Solids and Structures, Volume 46 (2009), pp. 3018-3026

[3] E. Héripré; M. Dexet; J. Crépin; L. Gélébart; A. Roos; M. Bornert; D. Caldemaison Coupling between experimental measurements and polycrystal finite element calculations for micromechanical study of metallic materials, International Journal of Plasticity, Volume 23 (2007) no. 9, pp. 1512-1539

[4] A. Zeghadi; F. N'Guyen; S. Forest; A.-F. Gourgues; O. Bouaziz Ensemble averaging stress-strain fields in polycrystalline aggregates with a constrained surface microstructure—Part 1: Anisotropic elastic behaviour, Philosophical Magazine, Volume 87 (2007) no. 8–9, pp. 1401-1424

[5] A. Zeghadi; S. Forest; A.-F. Gourgues; O. Bouaziz Ensemble averaging stress-strain fields in polycrystalline aggregates with a constrained surface microstructure—Part 2: Crystal plasticity, Philosophical Magazine, Volume 87 (2007) no. 8–9, pp. 1425-1446

[6] L. St-Pierre; E. Héripré; M. Dexet; J. Crépin; G. Bertolino; N. Bilger 3D simulations of microstructure and comparison with experimental microstructure coming from OIM analysis, International Journal of Plasticity, Volume 24 (2008), pp. 1516-1532

[7] W. Ludwig; A. King; P. Reischig; M. Herbig; E.M. Lauridsen; S. Schmidt; H. Proudhon; S. Forest; P. Cloetens; S. Rolland du Roscoat; J.Y. Buffière; T.J. Marrow; H.F. Poulsen New opportunities for 3d materials science of polycrystalline materials at the micrometre lengthscale by combined use of X-ray diffraction and X-ray imaging, Materials Science and Engineering A, Volume 524 (2009) no. 1–2, pp. 69-76 (Special topic section: Probing strains and dislocation gradients with diffraction)

[8] F. Eberl; S. Forest; T. Wroblewski; G. Cailletaud; J.-L. Lebrun Finite element calculations of the lattice rotation field of a tensile loaded nickel base alloy multicrystal and comparison to topographical X-ray diffraction measurements, Metallurgical and Materials Transactions A, Volume 33 (2002), pp. 2825-2833

[9] D. Faurie; O. Castelnau; R. Brenner; P.O. Renault; E. Le Bourhis; P. Goudeau In situ diffraction strain analysis of elastically deformed polycrystalline thin films, and micromechanical interpretation, Journal of Applied Crystallography, Volume 42 (2009), pp. 1073-1084

[10] N. Vaxelaire; H. Proudhon; S. Labat; C. Kirchlechner; J. Keckes; V. Jacques; S. Ravy; S. Forest; O. Thomas Methodology for studying strain inhomogeneities in polycrystalline thin films during in situ thermal loading using coherent X-ray diffraction, New Journal of Physics, Volume 12 (2010) no. 3, p. 035018

[11] F. Šiška; S. Forest; P. Gumbsch Simulation of stress-strain heterogeneities in copper thin films: Texture and substrate effects, Computational Materials Science, Volume 39 (2007), pp. 137-141

[12] Filip Šiška; Samuel Forest; Peter Gumbsch; Daniel Weygand Finite element simulations of the cyclic elastoplastic behaviour of copper thin films, Modelling and Simulation in Materials Science and Engineering, Volume 15 (2007) no. 1, p. S217-S238

[13] F. Šiška; D. Weygand; S. Forest; P. Gumbsch Comparison of mechanical behaviour of thin film simulated by discrete dislocation dynamics and continuum crystal plasticity, Computational Materials Science, Volume 45 (2009), pp. 793-799

[14] I.K. Robinson; C.A. Kenney-Benson; I.A. Vartanyants Sources of decoherence in beamline optics, Physica B: Condensed Matter, Volume 336 (2003) no. 1–2, pp. 56-62

[15] F. Livet; F. Bley; J. Mainville; R. Caudron; S.G.J. Mochrie; E. Geissler; G. Dolino; D. Abernathy; G. Grubel; M. Sutton Using direct illumination CCDs as high-resolution area detectors for X-ray scattering, Nuclear Instrument & Methods in Physics Research A, Volume 451 (2000) no. 3, pp. 569-609

[16] J. Mandel Une généralisation de la théorie de la plasticité de W.T. Koiter, Int. J. Solids Structures, Volume 1 (1965), pp. 273-295

[17] J. Mandel Plasticité classique et viscoplasticité, CISM Courses and Lectures, vol. 97, Springer-Verlag, Udine/Berlin, 1971

[18] J. Mandel Equations constitutives et directeurs dans les milieux plastiques et viscoplastiques, Int. J. Solids Structures, Volume 9 (1973), pp. 725-740

[19] C. Teodosiu; F. Sidoroff A theory of finite elastoviscoplasticity of single crystals, Int. J. of Engng. Science, Volume 14 (1976), pp. 165-176

[20] C. Teodosiu Large Plastic Deformation of Crystalline Aggregates, CISM Courses and Lectures, vol. 376, Springer-Verlag, Udine/Berlin, 1997

[21] M. Fivel, S. Forest, Plasticité cristalline et transition d'échelle : cas du monocristal, Techniques de l'Ingénieur, M4016, 2004, 23 pp.

[22] S. Kruch Homogenized and relocalized mechanical fields, Journal of Strain Analysis for Engineering Design, Volume 42 (2007), pp. 215-226

[23] J.R. Neighbours; G.A. Alers Elastic constants of silver and gold, Phys. Rev., Volume 111 (1958) no. 3, pp. 707-712

Cited by Sources:

Comments - Policy