M. D. Uchic, M. A. Groeber, D. M. Dimiduk, and J. P. Simmons, 3D microstructural characterization of nickel superalloys via serial-sectioning using a dual beam FIB-SEM, Scripta Materialia, vol.55, issue.1, pp.55-78, 2006.
DOI : 10.1016/j.scriptamat.2006.02.039

E. M. Lauridsen, S. R. Dey, R. W. Fonda, and D. Juul-jensen, Nondestructive approaches for 3-D materials characterization, JOM, vol.36, issue.10, pp.58-98, 2006.
DOI : 10.1007/BF02748494

J. S. Park, P. Revecz, A. Kazimirov, and M. P. Miller, lattice strain of bulk polycrystalline material under cyclic load, Review of Scientific Instruments, vol.78, issue.2, pp.78-023910, 2007.
DOI : 10.1063/1.2670463

J. Oddershede, Determining grain resolved stresses in polycrystalline materials using three-dimensional X-ray diffraction, Journal of Applied Crystallography, vol.52, issue.389, pp.539-549, 2010.
DOI : 10.1107/S0021889810012963/ks5240sup1.pdf

H. Moulinec and P. Suquet, A fast numerical method for computing the linear and nonlinear mechanical properties of composites, C. R. Acad Sci Paris II, pp.318-1417, 1994.

H. Moulinec and P. Suquet, A numerical method for computing the overall response of nonlinear composites with complex microstructure, Computer Methods in Applied Mechanics and Engineering, vol.157, issue.1-2, pp.69-94, 1998.
DOI : 10.1016/S0045-7825(97)00218-1

URL : https://hal.archives-ouvertes.fr/hal-01282728

F. Roters, Overview of constitutive laws, kinematics, homogenization and multiscale methods in crystal plasticity finite-element modeling: Theory, experiments, applications, Acta Materialia, vol.58, issue.4, pp.1152-1211, 2010.
DOI : 10.1016/j.actamat.2009.10.058

J. C. Michel, H. Moulinec, and P. Suquet, A computational method based on augmented Lagrangians and fast Fourier transforms for composites with high contrast, Comput. Model. Eng. Sci, vol.1, pp.79-88, 2000.

J. C. Michel, H. Moulinec, and P. Suquet, A computational scheme for linear and non???linear composites with arbitrary phase contrast, International Journal for Numerical Methods in Engineering, vol.58, issue.12, pp.139-158, 2001.
DOI : 10.1002/nme.275

R. A. Lebensohn, N-site modeling of a 3D viscoplastic polycrystal using Fast Fourier Transform, Acta Materialia, vol.49, issue.14, pp.2723-2737, 2001.
DOI : 10.1016/S1359-6454(01)00172-0

R. A. Lebensohn, Y. Liu, and P. P. Castañeda, On the accuracy of the self-consistent approximation for polycrystals: comparison with full-field numerical simulations, Acta Materialia, vol.52, issue.18, pp.5347-5361, 2004.
DOI : 10.1016/j.actamat.2004.07.040

R. A. Lebensohn, R. Brenner, O. Castelnau, and A. D. Rollett, Orientation image-based micromechanical modelling of subgrain texture evolution in polycrystalline copper, Acta Materialia, vol.56, issue.15, pp.3914-3926, 2008.
DOI : 10.1016/j.actamat.2008.04.016

Y. U. Wang, Y. M. Jin, and A. G. Khachaturyan, Phase field microelasticity theory and modeling of elastically and structurally inhomogeneous solid, Journal of Applied Physics, vol.92, issue.3, pp.1351-1360, 2002.
DOI : 10.1063/1.1492859

D. J. Eyre and G. W. Milton, A fast numerical scheme for computing the response of composites using grid refinement, The European Physical Journal Applied Physics, vol.6, issue.1, pp.41-47, 1999.
DOI : 10.1051/epjap:1999150

S. Brisard and L. Dormieux, FFT-based methods for the mechanics of composites: A general variational framework, Computational Materials Science, vol.49, issue.3, pp.663-671, 2010.
DOI : 10.1016/j.commatsci.2010.06.009

URL : https://hal.archives-ouvertes.fr/hal-00722339

J. Zeman, I. Vondrejc, J. Novak, and I. Marek, Accelerating a FFT-based solver for numerical homogenization of periodic media by conjugate gradients, Journal of Computational Physics, vol.229, issue.21, pp.8065-8071, 2010.
DOI : 10.1016/j.jcp.2010.07.010

F. Willot and Y. P. Pellegrini, Fast Fourier Transform computations and build-up of plastic deformation in 2D, elastic-perfectly plastic, pixelwise disordered porous media, Continuum Models and Discrete Systems, pp.443-450, 2008.
URL : https://hal.archives-ouvertes.fr/cea-00412544

R. J. Asaro and A. Needleman, Overview no. 42 Texture development and strain hardening in rate dependent polycrystals, Acta Metallurgica, vol.33, issue.6, pp.923-953, 1985.
DOI : 10.1016/0001-6160(85)90188-9

R. A. Lebensohn, O. Castelnau, R. Brenner, and P. Gilormini, Study of the antiplane deformation of linear 2-D polycrystals with different microstructures, International Journal of Solids and Structures, vol.42, issue.20, pp.5441-5459, 2005.
DOI : 10.1016/j.ijsolstr.2005.02.051

URL : https://hal.archives-ouvertes.fr/hal-00300102

R. A. Lebensohn, Modeling viscoplastic behavior and heterogeneous intracrystalline deformation of columnar ice polycrystals, Acta Materialia, vol.57, issue.5, pp.1405-1415, 2009.
DOI : 10.1016/j.actamat.2008.10.057

URL : https://hal.archives-ouvertes.fr/insu-00420863

R. A. Lebensohn, M. I. Idiart, P. P. Castañeda, and P. G. Vincent, Dilatational viscoplasticity of polycrystalline solids with intergranular cavities, Philosophical Magazine, vol.335, issue.22
DOI : 10.1016/j.euromechsol.2008.11.003

I. L. Dillamore, P. L. Morris, C. J. Smith, and W. B. Hutchinson, Transition Bands and Recrystallization in Metals, Proc R Soc Lond A 329, pp.405-420, 1972.
DOI : 10.1098/rspa.1972.0120

A. D. Rollett, Stress hot spots in viscoplastic deformation of polycrystals, Modelling and Simulation in Materials Science and Engineering, vol.18, issue.7, pp.74005-74021, 2010.
DOI : 10.1088/0965-0393/18/7/074005

T. Saito and J. I. Toriwaki, New algorithms for euclidean distance transformation of an n-dimensional digitized picture with applications, Pattern Recognition, vol.27, issue.11, pp.1551-1565, 1994.
DOI : 10.1016/0031-3203(94)90133-3

C. Hefferan, Statistics of high purity nickel microstructure from high energy X-ray diffraction microscopy, Comput. Mater. Continua, vol.14, pp.209-219, 2010.

N. Lahellec, J. C. Michel, H. Moulinec, and P. Suquet, Analysis of Inhomogeneous Materials at Large Strains using Fast Fourier Transforms, IUTAM Symposium on Computational Mechanics of Solids Materials, ed. C. Miehe (Dordretcht: Kluwer Academic, pp.247-268, 2001.
DOI : 10.1007/978-94-017-0297-3_22

P. A. Turner and C. N. Tomé, A study of residual stresses in Zircaloy-2 with rod texture, Acta Metallurgica et Materialia, vol.42, issue.12, pp.4143-4153, 1994.
DOI : 10.1016/0956-7151(94)90191-0

J. E. Bozek, A geometric approach to modeling microstructurally small fatigue crack formation: I. Probabilistic simulation of constituent particle cracking in AA 7075-T651, Modelling and Simulation in Materials Science and Engineering, vol.16, issue.6, pp.16-065007, 2008.
DOI : 10.1088/0965-0393/16/6/065007

A. Ricardo, Lebensohn is a Scientist with the Materials Science and Technology Division, Los Alamos National Laboratory, Los Alamos, NM 87544, USA; Anthony D. Rollett is a Professor with the Department of, Materials Science and Engineering