F. Alexandre, S. Deyber, and A. Pineau, Modelling the optimum grain size on the low cycle fatigue life of a Ni based superalloy in the presence of two possible crack initiation sites, Scripta Materialia, vol.50, issue.1, pp.25-30, 2004.
DOI : 10.1016/j.scriptamat.2003.09.043

O. Bernhardi and R. Mücke, A lifetime prediction procedure for anisotropic materials, Communications in Numerical Methods in Engineering, vol.112, issue.8, pp.519-527, 2000.
DOI : 10.1016/0921-5093(89)90350-X

M. Berveiller and A. Zaoui, An extension of the self-consistent scheme to plastically-flowing polycrystals, Journal of the Mechanics and Physics of Solids, vol.26, issue.5-6, pp.325-344, 1979.
DOI : 10.1016/0022-5096(78)90003-0

G. Cailletaud, A micromechanical approach to inelastic behaviour of metals, International Journal of Plasticity, vol.8, issue.1, pp.55-73, 1992.
DOI : 10.1016/0749-6419(92)90038-E

G. Cailletaud and K. Saï, A polycrystalline model for the description of ratchetting: Effect of intergranular and intragranular hardening, Materials Science and Engineering: A, vol.480, issue.1-2, pp.24-39, 2008.
DOI : 10.1016/j.msea.2007.06.071

URL : https://hal.archives-ouvertes.fr/hal-00280855

L. Chen, W. Wen, and H. Cui, Yielding description for a Ni3Al based intermetallic alloy, Materials & Design, vol.41, pp.192-197, 2012.
DOI : 10.1016/j.matdes.2012.05.004

Z. Chu, J. Yu, X. Sun, H. Guan, and Z. Hu, Tensile property and deformation behavior of a directionally solidified Ni-base superalloy, Materials Science and Engineering: A, vol.527, issue.12, pp.3010-3014, 2010.
DOI : 10.1016/j.msea.2010.01.051

J. Eshelby, The Determination of the Elastic Field of an Ellipsoidal Inclusion, and Related Problems, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol.241, issue.1226, pp.376-396, 1957.
DOI : 10.1098/rspa.1957.0133

A. P. Gordon, R. W. Neu, and D. L. Mcdowell, Effect of pre-exposure on crack initiation life of a directionally solidified Ni-base superalloy, International Journal of Fatigue, vol.31, issue.2, pp.393-401, 2009.
DOI : 10.1016/j.ijfatigue.2008.07.009

A. P. Gordon, M. D. Trexler, R. W. Neu, S. Jr, T. J. Mcdowell et al., Corrosion kinetics of a directionally solidified Ni-base superalloy, Acta Materialia, vol.55, issue.10, pp.3375-3385, 2007.
DOI : 10.1016/j.actamat.2007.01.034

S. Han, S. Li, and D. J. Smith, Comparison of phenomenological and crystallographic models for single crystal nickel base superalloys. I. Analytical identification, Mechanics of Materials, vol.33, issue.5, pp.251-266, 2001.
DOI : 10.1016/S0167-6636(00)00070-3

S. Han, S. Li, and D. J. Smith, Comparison of phenomenological and crystallographic models for single crystal nickel base superalloys. II. Numerical simulations, Mechanics of Materials, vol.33, issue.5, pp.267-282, 2001.
DOI : 10.1016/S0167-6636(00)00071-5

F. Hanriot, G. Cailletaud, and L. Rémy, Mechanical behaviour of a nickel-base superalloy single crystal, Proc. of Int. Symp. High Temperature Constitutive Modeling: Theory and Application, 1991.

T. Hasebe, M. Sakane, and M. Ohnami, Elastic Anisotropy of Directionally Solidified Superalloy, Journal of Engineering Materials and Technology, vol.114, issue.2, pp.141-146, 1992.
DOI : 10.1115/1.2904153

B. Hendrix and L. Yu, Self-consistent elastic properties for transversely isotropic polycrystals, Acta Materialia, vol.46, issue.1, pp.127-135, 1998.
DOI : 10.1016/S1359-6454(97)00261-9

R. Hill, Continuum micro-mechanics of elastoplastic polycrystals, Journal of the Mechanics and Physics of Solids, vol.13, issue.2, pp.89-101, 1965.
DOI : 10.1016/0022-5096(65)90023-2

A. Ibanez, V. Srinivasan, and A. Saxena, Creep deformation and rupture behaviour of directionally solidified GTD 111 superalloy, Fatigue & Fracture of Engineering Materials and Structures, vol.35, issue.12, pp.1010-1020, 2006.
DOI : 10.1243/0309324021514934

G. Kneer, ??ber die Berechnung der Elastizit??tsmoduln vielkristalliner Aggregate mit Textur, physica status solidi (b), vol.32, issue.3, pp.825-838, 1965.
DOI : 10.1007/978-3-642-94719-3

R. Kowalewski and H. Mughrabi, Influence of a plasma-sprayed NiCrAlY coating on the low-cycle fatigue behaviour of a directionally solidified nickel-base superalloy, Materials Science and Engineering: A, vol.247, issue.1-2, pp.295-299, 1998.
DOI : 10.1016/S0921-5093(98)00505-X

E. Kröner, Zur plastischen Verformung des Vielkristalls. Acta Metall, pp.155-161, 1961.

R. Kupkovits and R. Neu, Thermomechanical fatigue of a directionally-solidified Ni-base superalloy: Smooth and cylindrically-notched specimens, International Journal of Fatigue, vol.32, issue.8, pp.1330-1342, 2010.
DOI : 10.1016/j.ijfatigue.2010.02.002

F. Latief, K. Kakehi, H. A. Yeh, and H. Murakami, Influences of ruthenium and crystallographic orientation on creep behavior of aluminized nickel-base single crystal superalloys, Materials Science and Engineering: A, vol.592, pp.143-152, 2014.
DOI : 10.1016/j.msea.2013.10.092

Z. Moore and R. Neu, Creep fatigue of a directionally solidified Ni-base superalloy - smooth and cylindrically notched specimens, Fatigue & Fracture of Engineering Materials & Structures, vol.192, issue.1, pp.17-31, 2011.
DOI : 10.1016/0921-5093(94)91069-3

T. Mura, Micromechanics of Defects in Solids, 1987.

J. Nie, Z. Liu, X. Liu, and Z. Zhuang, Size effects of ????? precipitate on the creep properties of directionally solidified nickel-base super-alloys at middle temperature, Computational Materials Science, vol.46, issue.2, pp.400-406, 2009.
DOI : 10.1016/j.commatsci.2009.03.023

M. Okada, M. Tsutsumi, T. Kitamura, and R. Hohtani, INITIATION AND GROWTH OF SMALL CRACKS IN DIRECTIONALLY SOLIDIFIED MAR-M247 UNDER CREEP-FATIGUE. PART I: EFFECT OF MICROSTRUCTURE, Fatigue & Fracture of Engineering Materials & Structures, vol.21, issue.6, pp.741-750, 1998.
DOI : 10.1046/j.1460-2695.1998.00540.x

W. Österle, D. Bettge, B. Fedelich, and H. Klingelhöffer, Modelling the orientation and direction dependence of the critical resolved shear stress of nickel-base superalloy single crystals, Acta Materialia, vol.48, issue.3, pp.689-700, 2000.
DOI : 10.1016/S1359-6454(99)00404-8

A. Paquin, S. Berbenni, V. Favier, X. Lemoine, and M. Berveiller, Micromechanical modeling of the elastic???viscoplastic behavior of polycrystalline steels, International Journal of Plasticity, vol.17, issue.9, pp.1267-1302, 2001.
DOI : 10.1016/S0749-6419(00)00047-4

P. Pilvin, The contribution of micromechanical approaches to the modelling of inelastic behaviour, Fourth Int. Conf. on Biaxial/Multiaxial Fatigue, pp.31-46, 1994.

S. C. Prasad, K. Rajagopal, and I. Rao, A continuum model for the anisotropic creep of single crystal nickel-based superalloys, Acta Materialia, vol.54, issue.6, pp.1487-1500, 2006.
DOI : 10.1016/j.actamat.2005.11.016

S. C. Prasad, I. Rao, and K. Rajagopal, A continuum model for the creep of single crystal nickel-base superalloys, Acta Materialia, vol.53, issue.3, pp.669-679, 2005.
DOI : 10.1016/j.actamat.2004.10.020

H. Sabar, M. Berveiller, V. Favier, and S. Berbenni, A new class of micro???macro models for elastic???viscoplastic heterogeneous materials, International Journal of Solids and Structures, vol.39, issue.12, pp.3257-3276, 2002.
DOI : 10.1016/S0020-7683(02)00256-1

URL : https://hal.archives-ouvertes.fr/hal-00128381

K. Saï, G. Cailletaud, and S. Forest, Micro-mechanical modeling of the inelastic behavior of directionally solidified materials, Mechanics of Materials, vol.38, issue.3, pp.203-217, 2006.
DOI : 10.1016/j.mechmat.2005.06.007

M. Shenoy, D. Mcdowell, and R. Neu, Transversely isotropic viscoplasticity model for a directionally solidified Ni-base superalloy, International Journal of Plasticity, vol.22, issue.12, pp.2301-2326, 2006.
DOI : 10.1016/j.ijplas.2006.03.003

D. Shi, C. Dong, and X. Yang, Constitutive modeling and failure mechanisms of anisotropic tensile and creep behaviors of nickel-base directionally solidified superalloy, Materials & Design, vol.45, pp.663-673, 2013.
DOI : 10.1016/j.matdes.2012.09.031

D. Shi, C. Dong, X. Yang, L. Zhang, J. Hou et al., Experimental investigations on creep rupture strength and failure mechanism of vacuum brazed joints of a DS superalloy at elevated temperature, Materials Science and Engineering: A, vol.545, pp.162-167, 2012.
DOI : 10.1016/j.msea.2012.02.099

D. Shi, J. Liu, X. Yang, H. Qi, and J. Wang, Experimental investigation on low cycle fatigue and creep???fatigue interaction of DZ125 in different dwell time at elevated temperatures, Materials Science and Engineering: A, vol.528, issue.1, pp.233-238, 2010.
DOI : 10.1016/j.msea.2010.08.089

C. M. Stewart, A. P. Gordon, Y. W. Ma, and R. W. Neu, An anisotropic tertiary creep damage constitutive model for anisotropic materials, International Journal of Pressure Vessels and Piping, vol.88, issue.8-9, pp.356-364, 2011.
DOI : 10.1016/j.ijpvp.2011.06.010

A. Suvorov and G. Dvorak, Rate form of the Eshelby and Hill tensors, International Journal of Solids and Structures, vol.39, issue.21-22, pp.5659-5678, 2002.
DOI : 10.1016/S0020-7683(02)00369-4

E. Transvalor, , 2010.

I. N. Vladimirov, S. Reese, and G. Eggeler, Constitutive modelling of the anisotropic creep behaviour of nickel-base single crystal superalloys, International Journal of Mechanical Sciences, vol.51, issue.4, pp.305-313, 2009.
DOI : 10.1016/j.ijmecsci.2009.02.004

L. Wang, G. Xie, J. Zhang, and L. Lou, On the role of carbides during the recrystallization of a directionally solidified nickel-base superalloy, Scripta Materialia, vol.55, issue.5, pp.457-460, 2006.
DOI : 10.1016/j.scriptamat.2006.05.013

P. Xia, J. Yu, X. Sun, H. Guan, and Z. Hu, Influence of ????? precipitate morphology on the creep property of a directionally solidified nickel-base superalloy, Materials Science and Engineering: A, vol.476, issue.1-2, pp.39-45, 2008.
DOI : 10.1016/j.msea.2007.04.065

M. Yaguchi and E. Busso, On the accuracy of self-consistent elasticity formulations for directionally solidified polycrystal aggregates, International Journal of Solids and Structures, vol.42, issue.3-4, pp.1073-1089, 2005.
DOI : 10.1016/j.ijsolstr.2004.07.009

M. Yaguchi, M. Yamamoto, T. Ogata, and N. Ohno, An anisotropic constitutive model for a directionally solidified superalloy, Key Eng. Mater, pp.340-374, 2007.

M. Yamamoto, T. Kitamura, and T. Ogata, Influence of microscopically distributed inhomogeneity and anisotropy of grains on high-temperature crack propagation properties of directionally solidified superalloy, Engineering Fracture Mechanics, vol.75, issue.3-4, pp.779-789, 2008.
DOI : 10.1016/j.engfracmech.2007.01.015

X. Yang, C. Dong, D. Shi, and L. Zhang, Experimental investigation on both low cycle fatigue and fracture behavior of DZ125 base metal and the brazed joint at elevated temperature, Materials Science and Engineering: A, vol.528, issue.22-23, pp.7005-7011, 2011.
DOI : 10.1016/j.msea.2011.05.085

C. Yuan, J. Guo, H. Yang, and S. Wang, Deformation mechanism for high temperature creep of a directionally solidified nickel-base superalloy, Scripta Materialia, vol.39, issue.7, pp.991-997, 1998.
DOI : 10.1016/S1359-6462(98)00255-3

Y. Zhao, L. Wang, H. Li, T. Yu, and Y. Liu, Effects of recrystallization on the low cycle fatigue behavior of directionally solidified superalloy DZ40M, Rare Metals, vol.27, issue.4, pp.425-428, 2008.
DOI : 10.1016/S1001-0521(08)60156-4