A. , O. Abdel-karim, M. Ohno, and N. , Kinematic hardening model suitable for ratchetting with steady-state, International Journal of Plasticity, vol.16, pp.225-240, 2000.

K. Agbessi, Approches expérimentales et multi-échelles des processus d'amorçage des fissures de fatigue sous chargements complexes, 2013.

. Badji, Texture, misorientation and mechanical anisotropy in a deformed dual phase stainless steel weld joint, Materials Science and Engineering: A, vol.575, pp.94-103, 2013.
DOI : 10.1016/j.msea.2013.03.018

F. Barbe, Etude numérique de la plasticité d'agrégats polycristallins, 2000.

. Barbe, Intergranular and intragranular behavior of polycrystalline aggregates. Part 1: F.E. model, International Journal of Plasticity, vol.17, issue.4, pp.513-536, 2001.
DOI : 10.1016/S0749-6419(00)00061-9

. Bari, . Hassan, S. Bari, and T. Hassan, Anatomy of coupled constitutive models for ratcheting simulation, International Journal of Plasticity, vol.16, issue.3-4, pp.381-409, 2000.
DOI : 10.1016/S0749-6419(99)00059-5

O. Basquin, The exponential law of endurance tests, Proceedings of the ASTM, pp.625-630, 1910.

J. P. Bathias, C. Bathias, J. P. , and B. , La fatigue des matériaux et des structures, 1980.

. Belotteau, Mechanical behavior and crack tip plasticity of a strain aging sensitive steel, Materials Science and Engineering: A, vol.526, issue.1-2, pp.156-165, 2009.
DOI : 10.1016/j.msea.2009.07.013

URL : https://hal.archives-ouvertes.fr/hal-00424031

. Berveiller, . Zaoui, 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. Besnard, Caractérisation et quantification de surfaces par stéréocorrélation pour des essais mécaniques du quasi-statique à la dynamique ultra rapide, 2010.

. Besnard, A space???time approach in digital image correlation: Movie-DIC, Optics and Lasers in Engineering, vol.49, issue.1, pp.71-81, 2011.
DOI : 10.1016/j.optlaseng.2010.08.012

URL : https://hal.archives-ouvertes.fr/hal-00521203

. Bodelot, Experimental study of heterogeneities in strain and temperature fields at the microstructural level of polycrystalline metals through fully-coupled full-field measurements by Digital Image Correlation and Infrared Thermography, Mechanics of Materials, vol.43, issue.11, pp.654-670, 2011.
DOI : 10.1016/j.mechmat.2011.08.006

URL : https://hal.archives-ouvertes.fr/hal-00626385

J. Bower, A. Bower, and K. Johnson, The influence of strain hardening on cumulative plastic deformation in rolling and sliding line contact, Journal of the Mechanics and Physics of Solids, vol.37, issue.4, pp.471-493, 1989.
DOI : 10.1016/0022-5096(89)90025-2

. Bronkhorst, An experimental and numerical study of the localization behavior of tantalum and stainless steel, International Journal of Plasticity, vol.22, issue.7, pp.1304-1335, 2006.
DOI : 10.1016/j.ijplas.2005.10.002

F. Buy, Etude expérimentale et modélisation du comportement plastique du tantale. Prise en compte de la vitesse de déformation et de l'histoire de chargement, 1996.

G. Cailletaud, Une approche micromécanique phénoménologique du comportement inélastique des métaux, 1987.

. Cailletaud, . Pilvin, G. Cailletaud, and P. Pilvin, Utilisation de modèles polycristallins pour le calcul par éléments finis. Revue Européenne des Éléments Finis, pp.3-4515, 1994.

K. Chan, Roles of microstructure in fatigue crack initiation, International Journal of Fatigue, vol.32, issue.9, pp.1428-1447, 2010.
DOI : 10.1016/j.ijfatigue.2009.10.005

A. Chrysochoos, Dissipation et blocage d'énergie lors d'un essai d'écrouissage en traction simple, 1987.

A. Clair, Caractérisation expérimentale des propriétés micromécaniques et micromorphologiques des alliages base nickel contraints par la croissance d'une couche d'oxydes formée dans le milieu primaire d'une centrale nucléaire, 2011.

L. Coffin, A study on the effects of cyclic thermal stresses on a ductile metal, Transactions of the American Society of Mechanical Engineers, vol.76, pp.931-950, 1954.

B. Cottrell, A. Cottrell, and B. Bilby, Dislocation Theory of Yielding and Strain Ageing of Iron, Proc. Phys. Soc. Conf. A, pp.49-62, 1949.
DOI : 10.1088/0370-1298/62/1/308

K. Dang-van-dang-van, Sur la résistance à la fatigue des métaux, Sciences et Techniques de l'Armement, pp.641-722, 1973.

. Dang-van, Criteron for high-cycles failure under multiaxial loading, Biaxial and Multiaxial Fatigue, pp.459-478, 1989.

J. Decker, L. Decker, and D. Jeulin, Simulation 3D de mat??riaux al??atoires polycristallins, Revue de M??tallurgie, vol.97, issue.2, pp.271-275, 2000.
DOI : 10.1051/metal/200097020271

C. Depres, Modélisation physique des stades précurseurs de l'endommagement en fatigue dans l'acier inoxydable austénitique 316L, 2004.

. Depres, A dislocation-based model for low-amplitude fatigue behaviour of face-centred cubic single crystals, Scripta Materialia, vol.58, issue.12, pp.1086-1089, 2008.
DOI : 10.1016/j.scriptamat.2008.02.027

. Diard, Distribution of normal stress at grain boundaries in multicrystals: application to an intergranular damage modeling, Computational Materials Science, vol.25, issue.1-2, pp.73-84, 2002.
DOI : 10.1016/S0927-0256(02)00251-3

. Diard, Evaluation of finite element based analysis of 3D multicrystalline aggregates plasticity, International Journal of Plasticity, vol.21, issue.4, pp.691-722, 2005.
DOI : 10.1016/j.ijplas.2004.05.017

URL : https://hal.archives-ouvertes.fr/hal-00165134

A. Diaz and R. Reed-hill, Evidence for slow strain-rate embrittlement in tantalum due to oxygen, Scripta Metallurgica, vol.13, issue.6, pp.491-496, 1979.
DOI : 10.1016/0036-9748(79)90075-9

B. Doquet, V. Doquet, and G. Bertolino, Local approach to fatigue cracks bifurcation, International Journal of Fatigue, vol.30, issue.5, pp.942-950, 2008.
DOI : 10.1016/j.ijfatigue.2007.06.001

B. Doquet, V. Doquet, and G. Bertolino, A material and environment-dependent criterion for the prediction of fatigue crack paths in metallic structures, Engineering Fracture Mechanics, vol.75, issue.11, pp.3399-3412, 2008.
DOI : 10.1016/j.engfracmech.2007.07.004

URL : https://hal.archives-ouvertes.fr/hal-00315973

P. Doumalin, Microextensométrie Locale par Corrélation d'Images Numériques :Application aux études micromécaniques par microscopie électronique à balayage, 2000.

. Dunne, Experimental and computational studies of low cycle fatigue crack nucleation in a polycrystal, International Journal of Plasticity, vol.23, issue.2, pp.273-295, 2007.
DOI : 10.1016/j.ijplas.2006.07.001

. Dziaszyk, On the characterization of recrystallized fraction using electron backscatter diffraction: A direct comparison to local hardness in an IF steel using nanoindentation, Materials Science and Engineering: A, vol.527, issue.29-30, pp.7854-7864, 2010.
DOI : 10.1016/j.msea.2010.08.063

. Bartali, Surface observation and measurement techniques to study the fatigue damage micromechanisms in a duplex stainless steel, International Journal of Fatigue, vol.31, issue.11-12, pp.2049-2055, 2009.
DOI : 10.1016/j.ijfatigue.2008.11.003

URL : https://hal.archives-ouvertes.fr/hal-00411911

. Elliot, Absence of yield points in iron on strain reversal after aging, and the Bauschinger overshoot, Mechanics of Materials, vol.36, issue.11, pp.1143-1153, 2004.
DOI : 10.1016/j.mechmat.2004.04.001

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

. Essmann, A model of extrusions and intrusions in fatigued metals I. Point-defect production and the growth of extrusions, Philosophical Magazine A, vol.40, issue.2, pp.405-426, 1981.
DOI : 10.1080/01418618108239541

V. Eyraud, Caractérisation par microscopie acoustique en régime impulsionnel de matériaux mis en forme, 2000.

A. Falanga, Influence des éléments interstitiels dans le tantale, 1979.

. Fatemi, . Socie, A. Fatemi, and D. Socie, A CRITICAL PLANE APPROACH TO MULTIAXIAL FATIGUE DAMAGE INCLUDING OUT-OF-PHASE LOADING, Fatigue & Fracture of Engineering Materials and Structures, vol.106, issue.3, pp.149-165, 1988.
DOI : 10.1007/BF00184149

E. Fisher, Effects of hydrogen and UHV annealing on the elastic moduli of tantalum, Scripta Metallurgica, vol.11, issue.8, pp.685-688, 1977.
DOI : 10.1016/0036-9748(77)90139-9

S. Forest, Plasticité cristalline et transition d'échelle : cas du monocristal, pp.1-24, 2004.

S. Forest, Plasticité cristalline et transition d'échelle : cas du polycristal, pp.1-12, 2004.

E. Fleury, Endommagement du superalliage monocristallin AM1 en fatigue isotherme et anisotherme, 1991.

. Fonshteyn, Resistance of tantalum to strain and dislocation interaction with interstitial atoms, Phys. Metals Metallogr, vol.14, p.156, 1969.

S. Forest, Mechanical modelling of heterogeneous deformation of single crystals, 1996.

S. Forest, Modeling slip, kink and shear banding in classical and generalized single crystal plasticity, Acta Materialia, vol.46, issue.9, pp.3265-3281, 1998.
DOI : 10.1016/S1359-6454(98)00012-3

P. Forsyth, Some metallographic observations on the fatigue of metals, Journal Inst. Met, vol.80, p.181, 1951.

P. Forsyth, Exudation of Material from Slip Bands at the Surface of Fatigued Crystals of an Aluminium???Copper Alloy, Nature, vol.171, issue.4343, pp.172-173, 1953.
DOI : 10.1038/171172a0

P. Forsyth, Fatigue damage and crack growth in aluminium alloys, Acta Metallurgica, vol.11, issue.7, pp.703-715, 1963.
DOI : 10.1016/0001-6160(63)90008-7

P. Forsyth, Fatigue behaviour and its dependence on microstructure, 1972.

S. Frénois, Modélisation polycristalline du comportement mécanique du tantale. Application à la mise en forme par hydroformage, 2001.

. Gee, Application of EBSD to the evaluation of plastic deformation in the mechanical testing of WC/Co hardmetal, International Journal of Refractory Metals and Hard Materials, vol.27, issue.2, pp.300-312, 2009.
DOI : 10.1016/j.ijrmhm.2008.09.003

. Gerberich, Low and high cycle fatigue???a continuum supported by AFM observations, Acta Materialia, vol.46, issue.14, pp.5007-5021, 1998.
DOI : 10.1016/S1359-6454(98)00169-4

E. Gilbert, Random Subdivisions of Space into Crystals, The Annals of Mathematical Statistics, vol.33, issue.3, pp.958-972, 1962.
DOI : 10.1214/aoms/1177704464

J. Goodman, Mechanics Applied to Engineering, 1899.

S. Graff, Viscoplastic behavior of Zirconium alloys in the temperature range 20C-400C : characterization and modelling of strain ageing, 2006.

. Graff, Finite element simulations of dynamic strain ageing effects at V-notches and crack tips, Scripta Materialia, vol.52, issue.11, pp.1181-1186, 2005.
DOI : 10.1016/j.scriptamat.2005.02.007

URL : https://hal.archives-ouvertes.fr/hal-00014205

. Grédiac, . Hild, M. Grédiac, and F. Hild, Mesures de champs et identification en mécanique des solides, Hermès Science, 2011.

Y. Guilhem, Etude numérique des champs mécaniques locaux dans les agrégats polycristallins d'acier 316L sous chargement de fatigue, 2011.

. Guilhem, Numerical investigations of the free surface effect in three-dimensional polycrystalline aggregates, Computational Materials Science, vol.70, pp.150-162, 2013.
DOI : 10.1016/j.commatsci.2012.11.052

URL : https://hal.archives-ouvertes.fr/hal-01017647

J. Guillaumain, Etude du comportement du tantale en fatigue à grand nombre de cycles, 2009.

C. Gérard, Mesures de champs et identification de modèles de plasticité cristalline, 2008.

B. Haigh, Report on alternating stress tests of a sample of mild steel received from BASC, Report of the British Association, vol.85, pp.163-170, 1915.

B. Haigh, Experiments on the fatigue of brasses, Journal of the Institute od Metals, vol.18, pp.55-77, 1917.

A. Helstroffer, Etude en fatigue du tantale, 2010.

. Herrera, Design of a novel Mn-based 1, 2011.

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

L. Hochhalter, J. Hochhalter, and D. Littlewood, A geometric approach to modeling microstructurally small fatigue crack formation : II. Physically based modeling of microstructure-dependent slip localization and actuation of the crack nucleation mechanism in AA 1075-t651, Modelling and Simulation in Materials Science and Engineering, p.45004, 2010.

L. Hochhalter, J. Hochhalter, and D. Littlewood, A geometric approach to modeling microstructurally small fatigue crack formation: III. Development of a semi-empirical model for nucleation, Modelling and Simulation in Materials Science and Engineering, vol.19, issue.3, p.35008, 2011.
DOI : 10.1088/0965-0393/19/3/035008

M. Hoge, K. Hoge, and A. Mukherjee, The temperature and strain rate dependence of the flow stress of tantalum, Journal of Materials Science, vol.45, issue.8, pp.1666-1672, 1977.
DOI : 10.1007/BF00542818

K. Hosseini, E. Hosseini, and M. Kazeminezhad, Dislocation structure and strength evolution of heavily deformed tantalum, International Journal of Refractory Metals and Hard Materials, vol.27, issue.3, pp.605-610, 2009.
DOI : 10.1016/j.ijrmhm.2008.09.006

G. Irwin, Analysis of stresses and strains near the end of a crack traversing a plate, Journal of Applied Mechanics, vol.24, pp.361-364, 1957.

H. Jousset, Viscoplasticité et microstructures d'un alliage de titane : effets de la température et de la vitesse de sollicitation, 2008.

A. Juanicotena, Etude théorique et expérimentale du comportement viscoplastique deS matériaux aux grandes déformations et grandes vitesses de déformation. Application à l'acier Mars 190 et au tantale, 1998.

B. Kamaya, Quantification of plastic strain of stainless steel and nickel alloy by electron backscatter diffraction, Acta Materialia, vol.54, issue.2, pp.539-548, 2006.
DOI : 10.1016/j.actamat.2005.08.046

. Keller, Finite element analysis of the free surface effects on the mechanical behavior of thin nickel polycrystals, International Journal of Plasticity, vol.29, pp.155-172, 2012.
DOI : 10.1016/j.ijplas.2011.08.007

C. Kerisit, Analyse de recristallisation statique du tantale déformé à froid pour une modélisation en champ moyen, 2012.

. Knobbe, Initiation and propagation of short fatigue cracks in forged Ti6Al4V, Procedia Engineering, pp.931-940, 2010.
DOI : 10.1016/j.proeng.2010.03.101

. Kobayashi, Effects of grain boundary- and triple junction-character on intergranular fatigue crack nucleation in polycrystalline aluminum, Journal of Materials Science, vol.18, issue.321, pp.3792-3799, 2008.
DOI : 10.1007/s10853-007-2236-z

. Kothari, M. Kothari, and L. Anand, Elasto-viscoplastic constitutive equations for polycrystalline metals: Application to tantalum, Journal of the Mechanics and Physics of Solids, vol.46, issue.1, pp.51-83, 1998.
DOI : 10.1016/S0022-5096(97)00037-9

E. Kröner, Zur plastischen verformung des vielkristalls, Acta Metallurgica, vol.9, issue.2, pp.155-161, 1961.
DOI : 10.1016/0001-6160(61)90060-8

F. Kroupa, Wechselnde Aufspaltung einer Schraubenversetzung in kubisch raumzentrierten Metallen, physica status solidi (b), vol.12, issue.11, pp.391-393, 1963.
DOI : 10.1002/pssb.19630031122

F. Kroupa and U. Krupp, Plastic deformation of BCC metals with special reference to slip geometry. Ecole d'été de Pont-à-Mousson Fatigue crack in Metals and Alloys : Microstructural Aspects and Modelling concepts, 1967.

. Kubin, L. Estrin-]-kubin, and Y. Estrin, The portevin-Le Chatelier effect in deformation with constant stress rate, Acta Metallurgica, vol.33, issue.3, pp.397-407, 1985.
DOI : 10.1016/0001-6160(85)90082-3

. Kubin, . Estrin, L. Kubin, and Y. Estrin, Comment on ???the strain rate sensitivity during serrated yielding???, Scripta Metallurgica, vol.23, issue.5, pp.815-817, 1989.
DOI : 10.1016/0036-9748(89)90537-1

. Kubin, . Estrin, L. Kubin, and Y. Estrin, Evolution of dislocation densities and the critical conditions for the Portevin-Le Ch??telier effect, Acta Metallurgica et Materialia, vol.38, issue.5, pp.38-5697, 1989.
DOI : 10.1016/0956-7151(90)90021-8

. Kubin, Low-temperature plastic deformation of metals and the bifurcation theory, Res. Mechanica, vol.10, pp.25-38, 1984.

. Kuo, Prediction of the orientation spread in an aluminum bicrystal during plane strain compression using a DIC-based Taylor model, Computational Materials Science, vol.42, issue.4, pp.564-569, 2008.
DOI : 10.1016/j.commatsci.2007.09.004

. Lachenmann, R. Schultz-]-lachenmann, and H. Schultz, Inherent lattice hardening and interstitial solution hardening in tantalum, Scripta Metallurgica, vol.4, issue.9, pp.709-714, 1970.
DOI : 10.1016/0036-9748(70)90211-5

L. Lebedkina, T. Lebedkina, and M. Lebyodkin, Effect of deformation geometry on the intermittent plastic flow associated with the Portevin???Le Chatelier effect, Acta Materialia, vol.56, issue.19, pp.5567-5574, 2008.
DOI : 10.1016/j.actamat.2008.07.025

. Lebensohn, 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-00096934

. Lebyodkin, Statistical behaviour and strain localization patterns in the Portevin-Le Chatelier effect, Acta Materialia, vol.44, issue.11, pp.4531-4541, 1996.
DOI : 10.1016/1359-6454(96)00076-6

. Lebyodkin, Kinetics and statistics of jerky flow: experiments and computer simulations, Materials Science and Engineering: A, vol.234, issue.236, pp.115-118, 1997.
DOI : 10.1016/S0921-5093(97)00179-2

. Lebyodkin, Spatio-temporal dynamics of the Portevin???Le Chatelier effect: experiment and modelling, Acta Materialia, vol.48, issue.10, pp.2529-2541, 2000.
DOI : 10.1016/S1359-6454(00)00067-7

T. Lin, Analysis of elastic and plastic strains of a face-centred cubic crystal, Journal of the Mechanics and Physics of Solids, vol.5, issue.2, pp.143-149, 1957.
DOI : 10.1016/0022-5096(57)90058-3

. Llorca, Modeling of the high strain and high strain rate behavior of tantalum -Application to the dynamic expansion of a spherical shell. Shock compression of condensed materials, pp.455-458, 2000.

H. Louche, Analyse par thermographie infrarouge des effets dissipatifs de la localisation dans des aciers, 1999.
URL : https://hal.archives-ouvertes.fr/tel-00259398

W. Lüders, Uber die ausserung der elasticitat an stahlartigen eisenstaben und stahlstaber und uber eine beim biegen solcher stabe beobachtete molecularbewegung, Dinglers Polytech. Journal, vol.155, pp.18-22, 1860.

L. Ma, B. Ma, and C. Laird, Overview of fatigue behavior in copper single crystals (parts 1 to 5). acta metall, pp.325-379, 1989.

R. Madec, Détermination de la loi de comportement pour l, 2003.

. Magnin, Aspects microstructuraux de la deformation cyclique dans les metaux et alliages C.C. et C.F.C. -I. consolidation cyclique, pp.467-482, 1984.
URL : https://hal.archives-ouvertes.fr/jpa-00245220

S. Manson, Behavior of materials under conditions of thermal stress, 1954.

A. Marais, Influence du vieillissement statique sur la transition ductilefragile des aciers au C-Mn, 2012.
URL : https://hal.archives-ouvertes.fr/pastel-00820563

. Marais, Identification of a strain-aging model accounting for luders behaviour in a C-Mn steel, pp.3589-3617, 2012.

. Maudlin, Low-symmetry plastic deformation in BCC tantalum: experimental observations, modeling and simulations, International Journal of Plasticity, vol.19, issue.4, pp.483-515, 2003.
DOI : 10.1016/S0749-6419(01)00061-4

P. Mccormick, Theory of flow localisation due to dynamic strain ageing, Acta Metallurgica, vol.36, issue.12, pp.3061-3067, 1998.
DOI : 10.1016/0001-6160(88)90043-0

D. Mcdowell, Stress state dependence of cyclic ratchetting behavior of two rail steels, International Journal of Plasticity, vol.11, issue.4, pp.397-421, 1995.
DOI : 10.1016/S0749-6419(95)00005-4

H. Mecking and K. U. , Kinetics of flow and strain-hardening, Acta Metallurgica, vol.29, issue.11, pp.1865-1875, 1981.
DOI : 10.1016/0001-6160(81)90112-7

. Mitchell, Work-hardening in niobium single crystals, Philosophical Magazine, vol.209, issue.95, pp.1895-1919, 1963.
DOI : 10.1016/0001-6160(63)90058-0

S. Mitchell, T. Mitchell, and W. Spitzig, Three-stage hardening in tantalum single crystals, Acta Metallurgica, vol.13, issue.11, pp.1169-1179, 1965.
DOI : 10.1016/0001-6160(65)90054-4

. Mordike, B. Rudolph-]-mordike, and G. Rudolph, Three-stage hardening in tantalum deformed in compression, Journal of Materials Science, vol.13, issue.4, pp.332-338, 1967.
DOI : 10.1007/BF00572416

H. Mughrabi, Cyclic Slip Irreversibilities and the Evolution of Fatigue Damage, Metallurgical and Materials Transactions A, vol.39, issue.436, pp.1257-1279, 2008.
DOI : 10.1007/s11661-009-9839-8

. Mughrabi, Cyclic deformation and fatigue behaviour of ?-iron mono-and polycrystals, International Journal of Fracture, vol.44, issue.2, pp.193-220, 1981.
DOI : 10.1007/BF00053520

B. Mughrabi, Fatigue crack initiation by cyclic slip irreversibilities in High-Cycle Fatigue. ASTM STP 811 Plasticité cristalline en présence de grandes déformations et d'endommagement Single crystal modeling for structural calculations. Part. 2 : finite element implementation, Journal of Engineering Materials and Technology, vol.113, pp.171-182, 1983.

F. Nadal, Y. Nakada, and A. Keh, Résistance en fatigue du tantale. Document interne CEA. [Nakada and Keh Solid solution hardening in Fe-N single crystal, Journal of metals, vol.17, p.1055, 1965.

. Nemat-nasser, Microstructure of high-strain, high-strain-rate deformed tantalum, Acta Materialia, vol.46, issue.4, pp.1307-1325, 1998.
DOI : 10.1016/S1359-6454(97)00746-5

. Nemat-nasser, A physically-based constitutive model for bcc crystals with application to polycrystalline tantalum, Journal of the Mechanics and Physics of Solids, vol.46, issue.6, pp.1009-1038, 1998.
DOI : 10.1016/S0022-5096(97)00064-1

M. Norlain, Comportement mécanique du tantale, texture et recristallisation, 1999.

. Pantleon, Orientation inhomogeneities within individual grains in cold-rolled aluminium resolved by electron backscatter diffraction, Materials Science and Engineering: A, vol.483, issue.484, pp.668-671, 2008.
DOI : 10.1016/j.msea.2006.08.139

. Papakyriacou, Cyclic plastic deformation of tantalum and niobium at very high numbers of cycles, Materials Science and Engineering: A, vol.325, issue.1-2, pp.520-524, 2002.
DOI : 10.1016/S0921-5093(01)01446-0

. Papakyriacou, Influence of loading frequency on high cycle fatigue properties of b.c.c. and h.c.p. metals, Materials Science and Engineering: A, vol.308, issue.1-2, pp.143-152, 2001.
DOI : 10.1016/S0921-5093(00)01978-X

E. Paris, P. Paris, and F. Erdogan, A Critical Analysis of Crack Propagation Laws, Journal of Basic Engineering, vol.85, issue.4, pp.528-534, 1963.
DOI : 10.1115/1.3656900

. Paris, A rational analytic theory of fatigue. The Trend in Engineering, pp.9-14, 1961.

T. Paris, Modélisation du comportement mécanique des liaisons soudées hétérogènes Ta/TA6V4 : comportement et critère de rupture, 2008.

. Parisot, Modeling the mechanical behavior of a multicrystalline zinc coating on a hot-dip galvanized steel sheet, Computational Materials Science, vol.19, issue.1-4, pp.189-204, 2000.
DOI : 10.1016/S0927-0256(00)00155-5

. Parisot, Deformation and damage mechanisms of zinc coatings on hot-dip galvanized steel sheets: Part I. Deformation modes, Metallurgical and Materials Transactions A, vol.11, issue.3, pp.797-811, 2004.
DOI : 10.1007/s11661-004-0007-x

URL : https://hal.archives-ouvertes.fr/hal-00172912

. Parisot, Deformation and damage mechanisms of zinc coatings on hot-dip galvanized steel sheets: Part II. Damage modes, Metallurgical and Materials Transactions A, vol.58, issue.3, pp.813-823, 2004.
DOI : 10.1007/s11661-004-0008-9

URL : https://hal.archives-ouvertes.fr/hal-00172907

S. Park, Some aspects of dynamic strain aging in the niobium-oxygen system, 1983.

. Peirce, Material rate dependence and localized deformation in crystalline solids, Acta Metallurgica, vol.31, issue.12, pp.1951-1976, 1983.
DOI : 10.1016/0001-6160(83)90014-7

P. Penning, Mathematics of the portevin-le chatelier effect, Acta Metallurgica, vol.20, issue.10, pp.1169-1175, 1972.
DOI : 10.1016/0001-6160(72)90165-4

P. Pilvin, Approches multiéchelles pour la prévision du comportement inélastique des métaux, 1990.

P. Pilvin, The contribution of micromechanical approaches to the modelling of inelastic behaviour, cailletaud et t. lindley. 4th International Conference on Biaxial/multiaxial Fatigue, pp.311-357, 1994.

C. Pilvin, P. Pilvin, and G. Cailletaud, Intergranular and transgranular hardening in viscoplasticity. in m. zyczkowski, Creep in Structures, vol.4, pp.171-178, 1990.

L. Priester, Joints de grain et plasticité cristalline, 2011.

. Rabbe, Essais de fatigue -Partie 1, pp.2-22, 2000.

A. Racine, Influence de l'orientation des hydrures sur les modes de déformation, d'endommagement et de rupture du Zircaloy-4 hydruré, 2005.

. Rittel, Thermomechanical behavior of single crystalline tantalum in the static and dynamic regime, Mechanics of Materials, vol.41, issue.12, pp.1323-1329, 2009.
DOI : 10.1016/j.mechmat.2009.08.001

. Rogaush, K. Mordike-]-rogaush, and B. Mordike, Asymetry of slip in tantalulm and tantalum alloys, Strength of Metals and Alloys (2nd Conference), p.168, 1970.

K. Saada, G. Saada, and T. Kruml, Removal of plastic instabilities by reversal of the applied stress, Philosophical Magazine, vol.9, issue.1-3, pp.256-271, 2013.
DOI : 10.1080/14786435.2012.702232

N. Saintier, Fatigue multiaxiale dans un élastomère de type NR chargé : mécanismes d'endommagement et critère local d'amorçage de fissure, 2001.

. Saintier, Non-local energy based fatigue life calculation method under multiaxial variable amplitude loadings, International Journal of Fatigue, vol.54, pp.68-83, 2013.
DOI : 10.1016/j.ijfatigue.2012.12.013

URL : https://hal.archives-ouvertes.fr/hal-00875444

S. Schoenfeld, Dynamic behaviour of polycrystalline tantalum, International Journal of Plasticity, vol.14, issue.9, pp.871-890, 1998.
DOI : 10.1016/S0749-6419(98)00034-5

Z. Sestak, B. Sestak, and N. Zarubova, Asymmetry of Slip in Fe-Si Alloy Single Crystals, physica status solidi (b), vol.33, issue.1, pp.239-250, 1965.
DOI : 10.1002/pssb.19650100124

A. Sleeswyk, Slow strain-hardening of ingot iron, Acta Metallurgica, vol.6, issue.9, pp.598-603, 1958.
DOI : 10.1016/0001-6160(58)90101-9

J. Snoek, Effect of small quantities of carbon and nitrogen on the elastic and plastic properties of iron, Physica, vol.8, issue.7, pp.711-733, 1941.
DOI : 10.1016/S0031-8914(41)90517-7

M. Soler, Etude du vieillissement d'un acier à bake-hardening : évolution des propriétés mécaniques de traction -corrélation de la microstructure, 1998.

. Sommer, Influence of temperature and carbon content on the cyclic deformation and fatigue behaviour of ??-iron. Part II: Crack initiation and fatigue life, Acta Materialia, vol.46, issue.5, pp.1537-1546, 1998.
DOI : 10.1016/S1359-6454(97)00363-7

J. Strudel, Interactions between dislocations and impurities, 1984.

S. Suresh and . Sutton, Fatigue of Materials The effect of out-of-plane motion on 2D and 3D digital image correlation measurements, BIBLIOGRAPHIE Optics and Lasers in Engineering, vol.46, pp.746-757, 1998.

E. Szkopiak, Z. Szkopiak, and W. Eliasz, Snoek peaks and their stability in annealed and deformed tantalum, Journal of the Less Common Metals, vol.11, issue.4, pp.273-285, 1966.
DOI : 10.1016/0022-5088(66)90014-2

. Tabourot, Generalised constitutive laws for f.c.c. single crystals, Materials Science and Engineering: A, vol.234, issue.236, pp.234-236639, 1997.
DOI : 10.1016/S0921-5093(97)00353-5

K. Takao, K. Takao, and K. Kusukawa, Low-cycle fatigue behavior of commercially pure titanium, Materials Science and Engineering: A, vol.213, issue.1-2, pp.81-85, 1996.
DOI : 10.1016/0921-5093(96)10226-4

. Takeuchi, Orientation dependence of slip in tantalum single crystals, Acta Metallurgica, vol.20, issue.7, pp.909-915, 1972.
DOI : 10.1016/0001-6160(72)90084-3

. Takeuchi, . Maeda, S. Takeuchi, and K. Maeda, Slip in high purity tantalum between 0.7 and 40 K, Acta Metallurgica, vol.25, issue.12, pp.1485-1490, 1977.
DOI : 10.1016/0001-6160(77)90078-5

G. Taylor, Plastic strain in metals, Journal of the Institute of Metals, vol.62, pp.307-324, 1938.

. Teodosiu, Finite element simulation of the large elastoplastic deformation of multicrystals, 5th MECAMAT Int. Seminar on Large Plastic Deformations : Fundamental Aspects and Applications to Metal Forming, pp.153-168, 1993.

. Thompson, Xi. The origin of fatigue fracture in copper, Philosophical Magazine, vol.65, issue.2, pp.113-126, 1956.
DOI : 10.1080/00018735200101161

URL : https://hal.archives-ouvertes.fr/in2p3-00115430

B. Tomkins, Fatigue crack propagation???an analysis, Philosophical Magazine, vol.5, issue.155, pp.1041-1066, 1968.
DOI : 10.1016/0001-6160(63)90010-5

. Varchon, Mécanismes de relaxation inélastique dans le niobium et le tantale au voisinage de l'ambiante. influence de la teneur en oxygène et de l'écrouissage. Revue Phys, Appl, vol.17, pp.261-271, 1982.

. Vignal, Mapping the 3D-surface strain field of patterned tensile stainless steels using atomic force microscopy, Ultramicroscopy, vol.103, issue.3, pp.183-189, 2005.
DOI : 10.1016/j.ultramic.2004.11.021

. Vignal, Influence of the grain orientation spread on the pitting corrosion resistance of duplex stainless steels using electron backscatter diffraction and critical pitting temperature test at the microscale, Corrosion Science, vol.68, pp.275-278, 2013.
DOI : 10.1016/j.corsci.2012.11.013

. Villechaise, On slip band features and crack initiation in fatigued 316L austenitic stainless steel: Part 1: Analysis by electron back-scattered diffraction and atomic force microscopy, Materials Science and Engineering: A, vol.323, issue.1-2, pp.377-385, 2002.
DOI : 10.1016/S0921-5093(01)01381-8

V. Vitek, Theory of the core structures of dislocations in body centred cubic (BCC) metals. Crystals lattice defects, pp.1-34, 1974.

E. Votava, Effect of purity on the mechanical properties of niobium, Journal of the Less Common Metals, vol.9, issue.6, pp.409-415, 1965.
DOI : 10.1016/0022-5088(65)90124-4

. Wang, Portevin???Le Chatelier (PLC) instabilities and slant fracture in C???Mn steel round tensile specimens, Scripta Materialia, vol.64, issue.5, pp.430-433, 2011.
DOI : 10.1016/j.scriptamat.2010.11.005

URL : https://hal.archives-ouvertes.fr/hal-00579436

W. Wasserbach, Work-hardening and dislocation behaviour of tantalum and tantalum alloys. The minerals, 1996.

. Wilkinson, . Britton, A. Wilkinson, and T. Britton, Strains, planes, and EBSD in materials science, Materials Today, vol.15, issue.9, pp.366-376, 2012.
DOI : 10.1016/S1369-7021(12)70163-3

. Wright, Textural and microstructural gradient effects on the mechanical behavior of tantalum plate. Metallurgical and materials transactions A, pp.1025-1031, 1994.

M. Yoshinaga, H. Yoshinaga, and S. Morozumi, The solute atmosphere round a moving dislocation and its dragging stress, Philosophical Magazine, vol.6, issue.186, pp.1367-1385, 1971.
DOI : 10.1080/14786437108217009

A. Zeghadi, Effet de la morphologie tri-dimensionnelle et de la taille de grain sur le comportement mécanique d'agrégats polycristallins, 2005.

. Zhang, Microstructure-sensitive modeling: Application to fretting contacts, International Journal of Fatigue, vol.31, issue.8-9, pp.1397-1406, 2009.
DOI : 10.1016/j.ijfatigue.2009.03.023

. Zouhal, Elastic-plastic effects during cyclic loading as predicted by the Taylor-Lin model of polycrystal elasto-viscoplasticity, International Journal of Plasticity, vol.12, issue.3, pp.343-360, 1996.
DOI : 10.1016/S0749-6419(96)00011-3

. Fig, A.3 ? Comparaison des méthodes de calcul des déformations rapporté à la méthode infinitésimale de référence, p.210

. Ensuite, espace par translation (figure B.1 (b)). A partir de ces germes, une décomposition de Voronoï (module Qhull) est réalisée (figure B.1 (d)), qui va permettre de délimiter des sous-domaines, qui vont constituer les grains. Enfin, le domaine est maillé d'abord en surface (programme BLSurf) puis en volume (programme GHS3D) ; les conditions périodiques sont appliquées aux " bords libres