. La-limite-d, ´ elasticité est très faible comparéè a celle des basses températures (mesures de limite d'´ elasticité de Hanriot sur l'AM1 orienté <001>, pp.490-950

. Mpà-a-650°cminer, existe plus (sauf pour <111> avec une limite d'´ ecoulement supérieure d'environ 30 MPa en traction ) Ceci avait déjàdéjàété constaté pour la limite d'´ elasticitéelasticitéà 0 audeì a de 900°C. Enfin, la présence d'un temps de maintien en traction ne modifie pas la courbe d'´ ecrouissage cyclique. En ce qui concerne les modes de déformation, certains auteurs Poubanne, 1989) ´ evoquent l'homogénéité de la déformationdéformationà 950°C. Ceci est dûdûà l'absence de lignes de glissement visibles, masquées par l'oxydation. Mais des essais sous vide (Hanriot, 1993) ont révélé des bandes de glissement bien nettes, 2% par Shah et Duhl sur le PWA1480 (Shah et Duhl Il appara??tappara??t alors que les orientations <001> et <111> peuvent se déformer de façon homogène ou hétérogène. On constate que les basses vitesses de déformation associées aux fortes contraintes sont un des facteurs responsables de l'hétérogénéité de la déformation, 1984.

. Clément, 1991b) a montré, grâcè a des expériences sur des monocristaux orientés <111>, que le glissement cubique est possible aux basses températures dans la phase ? du CMSX-2 (figure 2.8) On voit bien que le glissement cubique est un phénomène thermiquement activé

.. Oxydation-des-superalliagesàsuperalliagesà-base-de-nickel, 110 4.1.1 Mécanismes d'oxydation surfacique -cas, p.118

. Dans-ce-cas, La fissure cro??tcro??t d'abord vers le bas, puis unedeuxì eme branche tendàtendà appara??treappara??tre en haut (figure 6.39, (b)). La fissuration est diffuse et ce phénomène s'accentue au point de rendre la convergence très lente puis impossible après 54 cycles. Il est donc difficile d'estimer la longueur de fissure. De plus, même si la fissure avaitétéavaitété " mesurable " , la vitesse n'aurait probablement pasétépasété la même que pour le calcul de référence en dépit de l

B. Figure, Influence de la perturbation sur le taux de restitution d'´ energié elastique G (avec la méthode de Parks)

E. F. En-faisant-le-calcul, avec le comportementélastiquecomportementélastique anisotrope de l'AM1àAM1à 950°C. Le passage de G ` a K est fait grâcè a l'´ equation B

E. F. En-faisant-le-calcul, avec le comportementélastiquecomportementélastique anisotrope de l'AM1àAM1à 950°C. Le passage de G ` a K est fait grâcè a l'´ equation B

. En-ce-qui-concerne-la-dépendance-du-facteur-d, intensité des contraintes K ` a l'anisotropie du matériau, on constate que K est plus faible si l'on prend en compte l'anisotropie par rapportà rapportà ce qui est donné par la formule de Strawley. Néanmoins, cette formule décrit très bien K dans le cas isotrope

A. M. Alam and L. Et-rémy, Modèle de calcul de durée de vie des matériaux sous chargement de fatigue-fluage et d'oxydation : application aux essais LCF et FMT des superalliages monocristallins AM1 et CMSX4, 2001.

D. L. Anton, Fatigue crack growth in anisotropic superalloy single crystals ´ editeur : Fatigue 84, Proceedings of the 2nd Conference on Fatigue and Fracture Thresholds, pp.1361-1369, 1984.

A. Azhdari, M. Obata, and S. Et-nemat-nasser, Alternative solution methods for crack problems in plane anisotropic elasticity, with examples, International Journal of Solids and Structures, vol.37, issue.44, pp.6433-6478, 2000.
DOI : 10.1016/S0020-7683(99)00137-7

Z. S. Basinski and S. J. Et-basinski, Low amplitude fatigue of copper single crystals???II. Surface observations, Acta Metallurgica, vol.33, issue.7, pp.1307-1317, 1985.
DOI : 10.1016/0001-6160(85)90241-X

Z. S. Basinski and S. J. Et-basinski, Low amplitude fatigue of copper single crystals???III. PSB sections, Acta Metallurgica, vol.33, issue.7, pp.1319-1327, 1985.
DOI : 10.1016/0001-6160(85)90242-1

Z. S. Basinski, R. Pascual, and S. J. Et-basinski, Low amplitude fatigue of copper single crystals???I. The role of the surface in fatigue failure, Acta Metallurgica, vol.31, issue.4, pp.591-602, 1983.
DOI : 10.1016/0001-6160(83)90049-4

G. Baudin and H. Et-polichella, Nouvelle méthode de mesuresélectriquemesuresélectrique de longueur de fissure, La Recherche Aérospatiale, vol.4, pp.195-203, 1978.

J. Bauschinger, ¨ Uber die Veränderung der Elastizitätsgrenze und des Elastizitätmoduls veschiedener Metalle, Civiling N. F, vol.27, pp.289-348, 1881.

T. Belytschko, N. Moës, S. Usui, and C. Et-parimi, Arbitrary discontinuities in finite elements, International Journal for Numerical Methods in Engineering, vol.8, issue.4, pp.993-1013, 2001.
DOI : 10.1002/1097-0207(20010210)50:4<993::AID-NME164>3.0.CO;2-M

URL : https://hal.archives-ouvertes.fr/hal-01005275

F. M. Beremin, A local criterion for cleavage fracture of a nuclear pressure vessel steel, Metallurgical Transactions A, vol.14, issue.11, pp.14-2277, 1983.
DOI : 10.1007/BF02663302

P. Bernède, Effet de l'oxydation sur la fissuration en fatigue-fluage d'un superalliage pour disque de turbines, l'Astroloy, 1994.

J. Besson, C. Berdin, S. Bugat, R. Desmorat, F. Feyel et al., Local Approach to Fracture, 2004.
URL : https://hal.archives-ouvertes.fr/hal-00755207

D. Bettge and W. Et¨osterleet¨-et¨osterle, ???Cube slip??? in near-[111] oriented specimens of a single-crystal nickel-base superalloy, Scripta Materialia, vol.40, issue.4, pp.389-395, 1999.
DOI : 10.1016/S1359-6462(98)00446-1

P. Boubidi, Caractérisation expérimentale et modélisation numérique de la fatiguè a faible nombre de cycles d'un superalliage base Ni monocristallin sous chargement multiaxial, 2000.

P. Boubidi and R. Et-sievert, Experimental and Numerical Investigations of Macrocrack Initiation Under Low-cycle Fatigue Loading at Notches in a Single Crystal Superalloy at High Temperature, pp.127-141, 2002.

J. Bouvard, J. Chaboche, F. Et-feyel, and . Greece, The use of cohesive zone model for coupled fatigue/plasticity crack propagation simulation, European Conference on Fracture 16, 2006.

J. Bouvard, J. Chaboche, F. Gallerneau, and F. Et-feyel, Numerical simulation of crack growth in high pressure components, International Conference on Fracture 11, 2005.

E. P. Busso and F. A. Et-mcclintock, A dislocation mechanics-based crystallographic model of a B2-type intermetallic alloy, International Journal of Plasticity, vol.12, issue.1, pp.1-28, 1996.
DOI : 10.1016/S0749-6419(95)00041-0

E. P. Busso, F. Meissonnier, and N. Et-o-'dowd, Gradient-dependent deformation of two-phase single crystals, Journal of the Mechanics and Physics of Solids, vol.48, issue.11, pp.2333-2361, 2000.
DOI : 10.1016/S0022-5096(00)00006-5

G. Cailletaud, Une approche micromécanique phénoménologique du comportement inélastique des métaux, Thèse d'´ etat, 1987.

J. Cardona, Comportement et durée de vie despì eces multiperforées : application aux aubes de turbine, Thèse de doctorat, 2000.

P. Caron, T. M. Pollock, R. D. Kissinger, R. R. Bowman, K. A. Green et al., High gamma prime solvus new generation nickel-based superalloys for single crystal turbine blade applications, pp.737-746, 2000.

P. Caron and T. Et-kahn, Anisotropie en fluage dans un superalliage monocristallin gamma -gamma, 1986.

C. Carry and J. Et-strudel, Direct observation of slip in FCC single crystals of a nickel base superalloy, Scripta Metallurgica, vol.9, issue.7, pp.731-736, 1975.
DOI : 10.1016/0036-9748(75)90230-6

J. Chaboche, Constitutive equations for cyclic plasticity and cyclic viscoplasticity, International Journal of Plasticity, vol.5, issue.3, pp.247-302, 1989.
DOI : 10.1016/0749-6419(89)90015-6

J. Chaboche and F. Et-gallerneau, An overview of the damage approach of durability modelling at elevated temperature, Fatigue <html_ent glyph="@amp;" ascii="&"/> Fracture of Engineering Materials and Structures, vol.14, issue.6, pp.405-418, 2001.
DOI : 10.1016/0022-5096(72)90015-4

G. Chalant and L. Et-rémy, Model of fatigue crack propagation by damage accumulation at the crack tip, Engineering Fracture Mechanics, vol.18, issue.5, pp.939-952, 1983.
DOI : 10.1016/0013-7944(83)90068-1

A. S. Cheng and C. Laird, FATIGUE LIFE BEHAVIOR OF COPPER SINGLE CRYSTALS. PART I: OBSERVATIONS OF CRACK NUCLEATION, Fatigue & Fracture of Engineering Materials and Structures, vol.251, issue.4, pp.331-341, 1981.
DOI : 10.1016/0025-5416(78)90174-X

G. P. Cherepanov, On crack propagation in solids, International Journal of Solids and Structures, vol.5, issue.8, pp.863-871, 1969.
DOI : 10.1016/0020-7683(69)90051-1

R. Chieragatti, Influence de l'orientation cristallographique sur le comportement en fatigue oligocyclique du Mar-M200 monocristallin, Thèse de doctorat, 1987.

R. Chieragatti and L. Et-rémy, Influence of orientation on the low cycle fatigue of MAR-M 200 single crystals at 650 ??C II: Cyclic stress-strain behaviour, Materials Science and Engineering: A, vol.141, issue.1, pp.11-22, 1991.
DOI : 10.1016/0921-5093(91)90703-P

S. H. Choi and E. Et-krempl, Viscoplasticity theory based on overstress applied to the modeling of cubic single crystals, European Journal of Mechanics A/Solids, vol.8, issue.3, pp.219-233, 1989.

G. Clark and J. Et-knott, Measurement of fatigue cracks in notched specimens by means of theoretical electrical potential calibrations, Journal of the Mechanics and Physics of Solids, vol.23, issue.4-5, pp.265-276, 1975.
DOI : 10.1016/0022-5096(75)90028-9

N. Clément, A. Couret, and D. Et-caillard, study of cube glide in the ?????-phase of a superalloy, Philosophical Magazine A, vol.1, issue.3, pp.669-695, 1991.
DOI : 10.1080/01418618208239909

N. Clément, A. Couret, and D. Et-caillard, study of cube glide in the ?????-phase of a superalloy, Philosophical Magazine A, vol.133, issue.3, pp.697-708, 1991.
DOI : 10.1016/0001-6160(84)90019-1

S. M. Copley and B. H. Et-kear, A dynamic theory of coherent precipitation hardening with application to nickel-base superalloys. Transactions of the, pp.239977-983, 1967.

A. Cuitiño and M. Ortiz, Computational modelling of single crystals, Modelling and Simulation in Materials Science and Engineering, vol.1, issue.3, pp.225-263, 1992.
DOI : 10.1088/0965-0393/1/3/001

A. Cuitiño and M. Ortiz, Three-dimensional crack-tip fields in four-point-bending copper single-crystal specimens, Journal of the Mechanics and Physics of Solids, vol.44, issue.6, pp.863-904, 1996.
DOI : 10.1016/0022-5096(96)00016-6

A. Defresne, Endommagement en fatigue oligocycliquè a 650°C de superalliages monocristallinsàmonocristallinsà base de nickel : influence de l'orientation cristallographique et d'une concentration de contrainte, 1989.

A. Defresne and L. Et-rémy, Fatigue behaviour of CMSX 2 superalloy [001] single crystals at high temperature II: Fatigue crack growth, Materials Science and Engineering: A, vol.129, issue.1, pp.55-64, 1990.
DOI : 10.1016/0921-5093(90)90344-3

H. G. Delorenzi, Energy release rate calculations by the finite element method, Engineering Fracture Mechanics, vol.21, issue.1, pp.129-143, 1985.
DOI : 10.1016/0013-7944(85)90060-8

G. Dhondt, Automatic 3-D mode I crack propagation calculations with finite elements, International Journal for Numerical Methods in Engineering, vol.37, issue.4, pp.739-757, 1998.
DOI : 10.1002/(SICI)1097-0207(19980228)41:4<739::AID-NME309>3.0.CO;2-M

G. Dhondt, Mixed-mode K-calculations in anisotropic materials, Engineering Fracture Mechanics, vol.69, issue.8, pp.909-922, 2002.
DOI : 10.1016/S0013-7944(01)00127-8

W. Elber, Fatigue crack closure under cyclic tension, Engineering Fracture Mechanics, vol.2, pp.37-45, 1970.

W. Elber, The Significance of Fatigue Crack Closure, Damage Tolerance in Aicraft Structures -ASTM STP 486, pp.230-242, 1971.
DOI : 10.1520/STP26680S

J. Engerand, Mécanique de la rupture, Techniques de l'Ingénieur, 2000.

L. Espié, Etude expérimentale et modélisation numérique du comportement mécanique de monocristaux de superalliages, Thèse de doctorat, 1996.

B. Fedelich and B. , A microstructure based constitutive model for the mechanical behavior at high temperatures of nickel-base single crystal superalloys, Computational Materials Science, vol.16, issue.1-4, pp.248-258, 1999.
DOI : 10.1016/S0927-0256(99)00067-1

B. Fedelich, A microstructural model for the monotonic and the cyclic mechanical behavior of single crystals of superalloys at high temperatures, International Journal of Plasticity, vol.18, issue.1, pp.1-49, 2002.
DOI : 10.1016/S0749-6419(00)00045-0

B. Fedelich, R. F. Kubler, E. P. Busso, N. O-'dowd, M. Toulios et al., SOCRAX Report D3.1 -Crystallographic constitutive equations : formulation, calibration and validation of predicted deformation response, 2004.

B. Fedelich, G. Künecke, and A. Et-epishin, Modelling of rafting and its influence in Ni-base superalloys, Proceedings of the 8th Conference on Materials for Advanced Power Engineering,Lì ege, 2006.

J. M. Finney and C. Laird, Strain localization in cyclic deformation of copper single crystals, Philosophical Magazine, vol.3, issue.2, pp.339-366, 1975.
DOI : 10.1080/14786437308217440

J. C. Fisher, Calculation of Diffusion Penetration Curves for Surface and Grain Boundary Diffusion, Journal of Applied Physics, vol.22, issue.1, pp.74-77, 1951.
DOI : 10.1063/1.1699825

N. A. Fleck, Finite element analysis of plasticity-induced crack closure under plane strain conditions, Engineering Fracture Mechanics, vol.25, issue.4, pp.441-449, 1986.
DOI : 10.1016/0013-7944(86)90258-4

N. A. Fleck, J. C. Et-newman-jr, J. C. Newman-jr, and W. Et-elber, Analysis of Crack Closure Under Plane Strain Conditions, Mechanics of Fatigue Crack Closure, ASTMP STP 982, pp.319-341, 1988.
DOI : 10.1520/STP27218S

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

E. Fleury and L. Et-rémy, Low cycle fatigue damage in nickel-base superalloy single crystals at elevated temperature, Materials Science and Engineering: A, vol.167, issue.1-2, pp.23-30, 1993.
DOI : 10.1016/0921-5093(93)90332-9

S. Flouriot, Plasticité en pointe de fissure dans un monocristal : approche théorique , numérique et expérimentale, Thèse de doctorat, 2004.

S. Flouriot, S. Forest, G. Cailletaud, A. Köster, L. Rémy et al., Strain localization at the crack tip in single crystal CT specimens under monotonous loading: 3D Finite Element analyses and application to nickel-base superalloys, International Journal of Fracture, vol.124, issue.1/2, pp.43-77, 2003.
DOI : 10.1023/B:FRAC.0000009300.70477.ba

URL : https://hal.archives-ouvertes.fr/hal-00165951

S. Flouriot, S. Forest, and L. Et-rémy, Strain localization phenomena under cyclic loading: application to fatigue of single crystals, Computational Materials Science, vol.26, pp.61-70, 2003.
DOI : 10.1016/S0927-0256(02)00393-2

S. Forest, Modèles mécaniques de la déformation hétérogène des monocristaux, 1996.

S. Forest, Milieux continus généralisés et matériaux hétérogènes, 2006.

S. Forest, P. Boudibi, and R. Et-sievert, Strain localization patterns at a crack tip in generalized single crystal plasticity, Scripta Materialia, vol.44, issue.6, pp.953-958, 2001.
DOI : 10.1016/S1359-6462(00)00684-9

S. Forest and P. Et-pilvin, Modelling the Cyclic Behaviour of Two-Phase Single Crystal Nickel-Base Superalloys, editeurs : IUTAM Symposium on Micromechanics of Plasticity and Damage of Multiphase Materials, pp.51-58, 1996.
DOI : 10.1007/978-94-009-1756-9_7

R. Forman, V. Kearney, and R. Et-engle, Numerical Analysis of Crack Propagation in Cyclic-Loaded Structures, Journal of Basic Engineering, vol.89, issue.3, pp.459-464, 1967.
DOI : 10.1115/1.3609637

P. J. Forsyth, A two stage process of fatigue crack growth Her Majesty's Stationery Office, Crack propagation : Proceedings of Cranfield Symposium, pp.76-94, 1962.

P. Franciosi, PlasticitéPlasticitéà froid des monocristaux CFC : ´ etude du durcissement latent, Thèse de doctorat, 1978.

P. Franciosi, M. Berveiller, and A. Et-zaoui, Latent hardening in copper and aluminium single crystals, Acta Metallurgica, vol.28, issue.3, pp.273-283, 1980.
DOI : 10.1016/0001-6160(80)90162-5

D. Francois, A. Pineau, and A. Et-zaoui, Comportement mécanique des matériaux : ´ elasticité et plasticité, 1992.

D. Francois, A. Pineau, and A. Et-zaoui, Comportement mécanique des matériaux : viscoplasticité, endommagement, mécanique de la rupture, 1993.

M. Francois, Rôle de l'oxydation dans l'endommagement en fatigue thermique de l'alliage MarM509 pour aubes fines de turbomachines, Conservatoire National des Arts et Métiers, 1989.

F. Gallerneau and J. Et-chaboche, Fatigue Life Prediction of Single Crystals for Turbine Blade Applications, International Journal of Damage Mechanics, vol.8, issue.4, pp.405-427, 1999.
DOI : 10.1177/105678959900800407

A. A. Griffith, The Phenomena of Rupture and Flow in Solids, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol.221, issue.582-593, pp.163-197, 1921.
DOI : 10.1098/rsta.1921.0006

I. Gu and R. O. Et-ritchie, On the Crack-Tip Blunting Model for Fatigue Crack Propagation in Ductile Materials editeurs : Fatigue and Fracture Mechanics : 29th volume -ASTMP STP 1332, 1999.

C. Guerre, Etude des mécanismes d'endommagement d'un systèmebarrì ere thermique déposé sur un superalliage base nickel, Thèse de doctorat, 2002.

F. Hanriot, Comportement du superalliage monocristallin AM1 sous sollicitation cycliques, Thèse de doctorat, 1993.

F. Hanriot, G. Cailletaud, and L. Et-rémy, Mechanical behaviour of a nickelbased superalloy single crystal ´ editeurs : High temperature constitutive modelling -Theory and application, pp.139-150, 1991.

G. Hartman and D. Et-johnson, D-c electric-potential method applied to thermal/mechanical fatigue crack growth, Experimental Mechanics, vol.107, issue.5, pp.106-112, 1987.
DOI : 10.1007/BF02318872

A. Hazotte and J. Et-lacaze, Chemically oriented ????? plate development in a nickel base superalloy, Scripta Metallurgica, vol.23, issue.11, pp.1877-1882, 1989.
DOI : 10.1016/0036-9748(89)90475-4

O. Helgeland, Cyclic hardening and fatigue of copper single crystals, Journal of the Institute of Metals, vol.93, pp.570-575, 1965.

M. B. Henderson and J. W. Et-martin, The influence of crystal orientation on the high temperature fatigue crack growth of a Ni-based single crystal superalloy, Acta Materialia, vol.44, issue.1, pp.111-126, 1996.
DOI : 10.1016/1359-6454(95)00147-9

M. A. Hicks and C. W. Et-brown, A Comparison of Short Crack Growth Behavior in Engineering Alloys, Proceedings of the 2nd Conference on Fatigue and Fracture Thresholds, pp.1337-1347, 1984.

B. Hoinard and G. , ContributionàContributionà l'´ etude de l'anisotropie de l'´ ecrouissagè a 650°C dans les monocristaux de superalliagesàsuperalliagesà base nickel AM3 et CMSX2, Thèse de doctorat, 1992.

J. W. Hutchinson, Singular behaviour at the end of a tensile crack in a hardening material, Journal of the Mechanics and Physics of Solids, vol.16, issue.1, pp.13-31, 1968.
DOI : 10.1016/0022-5096(68)90014-8

G. R. 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.

G. R. Irwin, Plastic zone near a crack and fracture toughness, Proceedings of the Seventh Sagamore Ordnance Materials Conference, pp.63-78, 1960.

B. Jaoul, Etude de la plasticité et application aux métaux, 1965.

H. Johnson, Calibrating the Electric Potential Method for Studying Slow Crack Growth, Material Research and Standards, vol.5, issue.9, pp.442-445, 1965.

J. E. King, SURFACE DAMAGE AND NEAR-THRESHOLD FATIGUE CRACK GROWTH IN A Ni-BASE SUPERALLOY IN VACUUM, Fatigue & Fracture of Engineering Materials and Structures, vol.12, issue.2, pp.177-188, 1982.
DOI : 10.1016/0001-6160(76)90104-8

A. Korner, , (Al, Ti) above the temperature of the maximum in flow stress, Philosophical Magazine Letters, vol.45, issue.3, pp.103-110, 1989.
DOI : 10.1080/09500838808227792

A. Koster, A. M. Alam, and L. Et-rémy, A physical-base model for life prediction of single crystal turbine blades under creep-fatigue loading and thermal transient conditions, 2002.
DOI : 10.1016/S1566-1369(02)80077-2

I. Rémy, L. Et-petit, and J. , Temperature-Fatigue Interaction, pp.203-212

C. Laird, The Influence of Metallurgical Structure on the Mechanisms of Fatigue Crack Propagation, Fatigue Crack Propagation -ASTM STP 415, pp.131-180, 1967.

C. Laird and G. C. Smith, Crack propagation in high stress fatigue, Philosophical Magazine, vol.24, issue.77, pp.847-857, 1962.
DOI : 10.1080/14786435808237004

S. G. Larsson and A. J. Et-carlsson, Influence of non-singular stress terms and specimen geometry on small-scale yielding at crack tips in elastic-plastic materials, Journal of the Mechanics and Physics of Solids, vol.21, issue.4, pp.263-277, 1973.
DOI : 10.1016/0022-5096(73)90024-0

J. Lemaitre, A course on damage mechanics, 1992.

J. Lemaitre and J. Et-chaboche, Mechanics of Solid Materials, 1990.

J. Lemaitre, J. Sermage, and R. Et-desmorat, A two scale damage concept applied to fatigue, International Journal of Fracture, vol.97, issue.1/4, pp.67-81, 1999.
DOI : 10.1023/A:1018641414428

B. A. Lerch and S. D. Et-antolovich, Fatigue crack propagation behavior of a single crystalline superalloy, Metallurgical Transactions A, vol.13, issue.5, pp.2169-2177, 1990.
DOI : 10.1007/BF02647878

K. Levenberg, A method for the solution of certain non-linear problems in least squares, Quarterly of Applied Mathematics, vol.2, issue.2, pp.164-168, 1944.
DOI : 10.1090/qam/10666

V. Levkovitch, Classical and extended crystal-plasticity and its application to fatigue of FCC single crystals, Thèse de doctorat, 2005.

B. Levkovitch, V. Sievert, R. Et-svendsen, and B. , Life analysis of a FCC single crystal and simulation of crack propagation by blunting and re-sharpening, editeur : International Conference on Computational and Experimental Engineering and Sciences, 2003.

V. Levkovitch, R. Sievert, and B. Et-svendsen, Simulation of Fatigue Crack Propagation in Ductile Metals by Blunting and Re-sharpening, International Conference on Fracture 11, 2005.
DOI : 10.1007/s10704-005-6024-y

S. Li and D. Smith, Development of an anisotropic constitutive model for singlecrystal superalloy for combined fatigue and creep loading, International Journal of Mechanical Sciences, issue.10, pp.40937-948, 1998.

H. Liebowitz, Fracture, volume II, 1968.

E. Lorentz, Lois de comportementàcomportementà gradients de variables internes : construction, formulation variationnelle et mise en oeuvre numérique, Thèse de doctorat, 1999.

B. Ma and C. Laird, Overview of fatigue behaviour in copper single crystals -I, 1989.

B. Ma and C. Laird, Overview of fatigue behaviour in copper single crystals - II. Population, size, distribution and growth kinetics of stage I cracks for tests at constant strain amplitude, Acta Metallurgica, vol.37, pp.337-348, 1989.

J. Malpertu, Fatigue mécano-thermique d'un superalliagè a base de nickel, 1987.

N. Marchal, S. Flouriot, S. Forest, and L. Et-rémy, Crack-tip stress???strain fields in single crystal nickel-base superalloys at high temperature under cyclic loading, Computational Materials Science, vol.37, issue.1-2, pp.42-50, 2006.
DOI : 10.1016/j.commatsci.2005.12.014

URL : https://hal.archives-ouvertes.fr/hal-00139144

M. Marx and H. Vehoff, Propagation of microcracks in single crystalline nickelbased superalloys : size effects on the crack opening, Materials Science and Engineering A, pp.387-389511, 2004.

N. Matan, D. C. Cox, C. M. Rae, and R. C. Et-reed, On the kinetics of rafting in CMSX-4 superalloy single crystals, Acta Materialia, vol.47, issue.7, pp.472031-2045, 1999.
DOI : 10.1016/S1359-6454(99)00093-2

F. A. Mcclintock and J. J. Et-gilman, On the Plasticity of the Growth of Fatigue Cracks, pp.65-102, 1963.

R. M. Mcmeeking, Finite deformation analysis of crack-tip opening in elastic-plastic materials and implications for fracture, Journal of the Mechanics and Physics of Solids, vol.25, issue.5, pp.357-381, 1977.
DOI : 10.1016/0022-5096(77)90003-5

F. Meissonnier, E. P. Busso, and N. Et-o-'dowd, Finite element implementation of a generalised non-local rate-dependent crystallographic formulation for finite strains, International Journal of Plasticity, vol.17, issue.4, pp.601-640, 2001.
DOI : 10.1016/S0749-6419(00)00064-4

L. Milne-thomson, Theoretical Hydrodynamics, 1968.

R. V. Miner, T. P. Gabb, J. Gayda, and K. J. Et-hemker, Orientation and temperature dependence of some mechanical properties of the single-crystal nickel-base superalloy, 1986.

J. Moré, The Levenberg-Marquardt algorithm: Implementation and theory, Numerical Analysis Proceedings Lecture Notes in Mathematics, vol.11, pp.105-116, 1977.
DOI : 10.1137/0111030

N. Moës, J. Dolbow, and T. Et-belytschko, A finite element method for crack growth without remeshing, International Journal for Numerical Methods in Engineering, vol.46, issue.1, pp.131-150, 1999.
DOI : 10.1002/(SICI)1097-0207(19990910)46:1<131::AID-NME726>3.3.CO;2-A

H. Mughrabi, The cyclic hardening and saturation behaviour of copper single crystals, Materials Science and Engineering, vol.33, issue.2, pp.207-223, 1978.
DOI : 10.1016/0025-5416(78)90174-X

H. Mughrabi, R. Wang, K. Differt, U. Et-essmann, W. L. Morris et al., Fatigue Crack Initiation by Cyclic Slip Irreversibilities in High-Cycle Fatigue, Quantitative Measurement of Physical Damage -ASTM STP, vol.811, pp.5-45, 1983.
DOI : 10.1520/STP30551S

D. Mukherji, F. Jiao, W. Chen, and R. P. Et-wahi, Deformation behavior and microstructural evolution in IN738LC under creep and tensile loadings, Commission of the European Communities , ´ editeur : High Temperature Materials for Power Engineering, pp.1067-1076, 1990.

L. Méric, Une modélisation mécanique du comportement des monocristaux, Thèse de doctorat, 1991.

L. Méric and G. Et-cailletaud, Single Crystal Modeling for Structural Calculations: Part 2???Finite Element Implementation, Journal of Engineering Materials and Technology, vol.113, issue.1, pp.171-182, 1991.
DOI : 10.1115/1.2903375

L. Méric, P. Poubanne, and G. Et-cailletaud, Single Crystal Modeling for Structural Calculations: Part 1???Model Presentation, Journal of Engineering Materials and Technology, vol.113, issue.1, pp.162-170, 1991.
DOI : 10.1115/1.2903374

F. R. Nabarro, The thermodynamic driving force for rafting in superalloys, Acta Materialia, vol.44, issue.8, 1996.
DOI : 10.1016/1359-6454(95)00423-8

M. Nazmy, J. Denk, R. Baumann, and A. Et-künzler, Environmental effects on tensile and low cycle fatigue behavior of single crystal nickel base superalloys, Scripta Materialia, vol.48, issue.5, pp.519-524, 2003.
DOI : 10.1016/S1359-6462(02)00506-7

M. Nazmy, A. Künzler, J. Denk, and R. Et-baumann, The effect of strain rate on the room temperature tensile properties of single crystal superalloys, Scripta Materialia, vol.47, issue.8, pp.47521-525, 2002.
DOI : 10.1016/S1359-6462(02)00194-X

P. Neumann, New experiments concerning the slip processes at propagating fatigue cracks???I, Acta Metallurgica, vol.22, issue.9, pp.1155-1165, 1974.
DOI : 10.1016/0001-6160(74)90071-6

P. Neumann, The geometry of slip processe at a propagating fatigue crack -II, 1974.

P. Neumann, H. Vehoff, and H. Et-fuhlrott, ON THE MECHANISMS OF FATIGUE CRACK GROWTH, editeur : International Conference on Fracture 4, p.1313, 1977.
DOI : 10.1016/B978-0-08-022140-3.50090-2

D. Nouailhas, Un modèle de viscoplasticité cyclique pour matériaux anisotropesà anisotropesà symétrie cubique. Comptes-Rendus de l'Académie des Sciences -série II, pp.887-890, 1990.

D. Nouailhas and G. Et-cailletaud, Comparaison de divers critères anisotropes pour monocristaux cubiquesàcubiquesà faces centrées. Comptes-Rendus de l'Académie des Sciences -série II, pp.1573-1579, 1992.

B. Nouailhas, D. Et-cailletaud, and G. , Finite element analysis of the mechanical behavior of two-phase single-crystal superalloys, Scripta Materialia, vol.34, issue.4, pp.565-571, 1996.
DOI : 10.1016/1359-6462(95)00547-1

D. Nouailhas and J. Et-culié, Development and Application of a Model for Single Crystal Superalloys, International Conference on High Temperature Constitutive Modeling, 1991.

D. Nouailhas, J. Culié, G. Cailletaud, and L. Et-méric, Finite element analysis of the stress-strain behavior of single crystal tubes, European Journal of Mechanics A/Solids, vol.14, issue.1, pp.137-154, 1995.

D. Nouailhas and S. Et-lhuillier, On the micro-macro modelling of single crystal behavior, Computational Materials Science, vol.9, issue.1-2, pp.177-187, 1997.
DOI : 10.1016/S0927-0256(97)00073-6

D. Nouailhas, D. Pacou, G. Cailletaud, F. Hanriot, L. D. Et-rémy et al., Experimental Study of the Anisotropic Behaviour of the CMSX2 Single Crystal Superalloy under Tension-Torsion Loadings, Advances in multiaxial fatigue -ASTM STP 1191, pp.244-258, 1993.

P. Paris, The Growth of Cracks Due to Variations in Loads, Thèse de doctorat, 1960.

P. Paris, Fatigue, An Interdisciplinary Approach, editeurs : 10th Sagamore Army Materials Research Conference, pp.107-127, 1964.

P. Paris, R. J. Bucci, E. T. Wessel, W. G. Clark, and T. R. Et-mager, Extensive study of low fatigue crack growth rates in A533 and A508 steels. In Stress analysis and growth of cracks -ASTM STP 513, pp.141-176, 1972.

D. Parks, A stiffness derivative finite element technique for determination of crack tip stress intensity factors, International Journal of Fracture, vol.187, issue.4, pp.487-502, 1974.
DOI : 10.1007/BF00155252

S. Pearson, Initiation of fatigue cracks in commercial aluminium alloys and the subsequent propagation of very short cracks, Engineering Fracture Mechanics, vol.7, issue.2, pp.235-247, 1975.
DOI : 10.1016/0013-7944(75)90004-1

T. O. Pedersen, Remeshing in analysis of large plastic deformations, Computers & Structures, vol.67, issue.4, pp.279-288, 1998.
DOI : 10.1016/S0045-7949(98)00005-4

R. M. Pelloux, Mechanisms of formation of ductile fatigue striations, Transactions of the American Society for Metals, vol.62, pp.281-285, 1969.

A. Pfennig, SOCRAX Report D2.4.2 -The characterisation of the short/long crack growth behaviour of the single crystal superalloys AM1 and PWA1483 : Crack growth data and structural observations, 2005.

S. Pommier, Cyclic plasticity and variable amplitude fatigue, International Journal of Fatigue, vol.25, issue.9-11, pp.983-997, 2003.
DOI : 10.1016/S0142-1123(03)00137-3

S. Pommier and M. Et-risbet, Time derivative equations for mode I fatigue crack growth in metals, International Journal of Fatigue, vol.27, issue.10-12, pp.1297-1306, 2005.
DOI : 10.1016/j.ijfatigue.2005.06.034

URL : https://hal.archives-ouvertes.fr/hal-00114052

D. P. Pope and S. S. Et-ezz, AI and nickel-base alloys with high volume fraction of ??', International Materials Reviews, vol.29, issue.1, pp.136-167, 1984.
DOI : 10.1179/imr.1984.29.1.136

P. Poubanne, Etude et modélisation du comportement mécanique d'un superalliage monocristallin pour aube de turbine, Thèse de doctorat, 1989.

B. Prandtl and L. , Anwendungsbeispiele zu einem henckyschen SatzüberSatz¨Satzüber das plastische Gleichgewicht, Zeitschrift für Angewandte Mathematik und Mechanik, pp.401-406, 1923.

P. Reed and I. Sinclair, Fatigue Crack Path Prediction in UDIMET 720 Nickelbased Alloy Single Crystals, Metallurgical and Materials Transactions A, issue.1, pp.31-109, 2000.

R. C. Reed, N. Matan, D. C. Cox, M. A. Rist, and C. M. Et-rae, Creep of CMSX-4 superalloy single crystals: effects of rafting at high temperature, Acta Materialia, vol.47, issue.12, pp.473367-3381, 1999.
DOI : 10.1016/S1359-6454(99)00217-7

J. Reuchet, Fatiguè a haute température d'un superalliage moulé : interaction fatigue-oxydation, Thèse de doctorat, 1981.

J. Reuchet and L. Et-rémy, Fatigue oxidation interaction in a superalloy???application to life prediction in high temperature low cycle fatigue, Metallurgical Transactions A, vol.12, issue.1, pp.141-149, 1983.
DOI : 10.1007/BF02643747

F. Reza¨?reza¨?-aria, Fatigue thermique et fatigue anisotherme d'un superalliagè a base de cobalt. Etude métallographique de l'endommagement et modélisation, 1986.

F. Reza¨?reza¨?-aria and L. Et-rémy, An oxidation fatigue interaction damage model for thermal fatigue crack growth, Engineering Fracture Mechanics, vol.34, issue.2, pp.283-294, 1989.
DOI : 10.1016/0013-7944(89)90143-4

J. R. Rice, Mechanics of Crack Tip Deformation and Extension by Fatigue, Fatigue Crack Propagation -ASTM STP 415, pp.247-309, 1967.

J. R. Rice, A Path Independent Integral and the Approximate Analysis of Strain Concentration by Notches and Cracks, Journal of Applied Mechanics, vol.35, issue.2, pp.379-386, 1968.
DOI : 10.1115/1.3601206

J. R. Rice, Limitations to the small scale yielding approximation for crack tip plasticity, Journal of the Mechanics and Physics of Solids, vol.22, issue.1, pp.17-26, 1974.
DOI : 10.1016/0022-5096(74)90010-6

J. R. Rice, Tensile crack tip fields in elastic-ideally plastic crystals, Mechanics of Materials, vol.6, issue.4, pp.317-335, 1987.
DOI : 10.1016/0167-6636(87)90030-5

J. R. Rice, D. Hawk, and R. J. Et-asaro, Crack tip fields in ductile crystals, International Journal of Fracture, vol.22, issue.4, pp.301-321, 1990.
DOI : 10.1007/BF01185954

J. R. Rice and G. F. Et-rosengren, Plane strain deformation near a crack tip in a power-law hardening material, Journal of the Mechanics and Physics of Solids, vol.16, issue.1, pp.1-12, 1968.
DOI : 10.1016/0022-5096(68)90013-6

H. Riedel, Fracture at high temperatures, Materials Research and Engineering, 1987.
DOI : 10.1007/978-3-642-82961-1

H. Riedel and J. R. Et-rice, Tensile cracks in creeping solids, Fracture Mechanics : Twelth Conference -ASTM STP 700, pp.112-130, 1980.

R. O. Ritchie and H. J. Et-bathe, On the calibration of the electrical potential technique for monitoring crack growth using finite element methods, International Journal of Fracture, vol.63, issue.1, pp.47-55, 1979.
DOI : 10.1007/BF00115908

R. O. Ritchie and J. Et-lankford, Small Fatigue Cracks. The Metallurgical Society of the American Institute of Mining, Metallurgical and Petroleum Engineers, 1986.

S. Roychowdhury and R. H. Et-dodds, Effect of T-stress on fatigue crack closure in 3-D small-scale yielding, International Journal of Solids and Structures, vol.41, issue.9-10, pp.2581-2606, 2004.
DOI : 10.1016/j.ijsolstr.2003.11.004

D. A. Ryder and S. P. Et-lynch, The effect of environment and frequency on crack nucleation, stage I and stage II crack growth in two aluminium zinc magnesium alloys, 1977.

M. Réger, Amorçage et propagation des fissuresàfissuresà haute température dans un alliagèalliagè a base de nickel, Thèse de doctorat, 1984.

M. Réger and L. Et-rémy, Fatigue oxidation interaction in in 100 superalloy, Metallurgical Transactions A, vol.22, issue.9, pp.2259-2267, 1988.
DOI : 10.1007/BF02645049

L. Rémy, T. Magnin, and J. M. Et-gras, Oxidation effects in high temperature creep and fatigue of engineering alloys, Corrosion-deformation interactions, pp.425-459, 1992.

L. Rémy, H. Bernard, J. Malpertu, and F. Et-reza¨?reza¨?-aria, Fatigue Life Prediction Under Thermal-Mechanical Loading in a Nickel-Base Superalloy, Thermomechanical Fatigue Behavior of Materials -ASTM STP 1186, pp.3-16, 1993.
DOI : 10.1520/STP24246S

F. Sansoz, Propagation des petites fissures de fatigue dans les zones de concentration de contraintes dans le superalliage N18, Thèse de doctorat, 2000.
URL : https://hal.archives-ouvertes.fr/pastel-00000970

F. Sansoz, B. Brethes, and A. Pineau, Propagation of short fatigue cracks from notches in a Ni base superalloy: experiments and modelling, Fatigue <html_ent glyph="@amp;" ascii="&"/> Fracture of Engineering Materials and Structures, vol.33, issue.1, pp.41-53, 2002.
DOI : 10.1016/S0013-7944(98)00016-2

C. M. Sellars and W. J. Et-tegart, La relation entre la résistance et la structure dans la déformationdéformationà chaud, Mémoires scientifiques de la revue de métallurgie, pp.731-746, 1966.

C. M. Sellars and W. J. Et-tegart, Hot workability. International Metallurgical reviews, p.17, 1972.
DOI : 10.1179/095066072790137765

D. Shah, A. Et-cetel, T. M. Pollock, R. D. Kissinger, R. R. Bowman et al., Evaluation of PWA1483 for Large single crystal IGT Blade Applications, Superalloys 2000 (Ninth International Symposium), pp.295-304, 2000.
DOI : 10.7449/2000/Superalloys_2000_295_304

D. Shah, A. D. Et-cetel, R. D. Kissinger, D. J. Deye, D. L. Anton et al., Creep anisotropy in nickel base gamma, gamma prime and gamma/gamma prime superalloys, The Minerals, Metals and Materials Society, p.782, 1996.

D. Shah and D. N. Et-duhl, The effect of orientation, temperature and gamma prime size on the yied strength of a single crystal nickel base superalloy, pp.105-114, 1984.

C. T. Sims, N. S. Stoloff, and W. C. Et-hagel, Superalloys II, 1987.

F. Soniak, Fissuration en fatigue d'un superalliage de la métallurgie des poudres, l'ASTROLOY : Influence de la longueur de fissure et de la température, 1989.

A. E. Staton-bevan, The orientation and temperature dependence of the work hardening rate of single crystals Ni3(Al,Ti), Philosophical Magazine, issue.6, pp.47939-949, 1983.

J. E. Strawley, Wide range stress intensity factor expressions for ASTM E 399 standard fracture toughness specimens, International Journal of Fracture, vol.12, pp.475-476, 1976.

S. Suresh, Fatigue of materials. Solid State Science Series, Cambridge, G.B, vol.2, issue.2, 1998.

S. Suresh and R. O. Et-ritchie, Propagation of short fatigue cracks, International Metals Reviews, vol.29, issue.6, pp.445-476, 1984.

S. Suresh, G. F. Zamiski, and R. O. Et-ritchie, Oxide-Induced Crack Closure: An Explanation for Near-Threshold Corrosion Fatigue Crack Growth Behavior, Metallurgical Transactions A, vol.97, issue.8, pp.1435-1443, 1981.
DOI : 10.1007/BF02643688

U. Tetzlaff and H. Et-mughrabi, Enhancement of the High-Temperature Tensile Creep Strength of Monocrystalline Nickel-Base Superalloys by Pre-rafting in Compression, Superalloys 2000 (Ninth International Symposium), 2000.
DOI : 10.7449/2000/Superalloys_2000_273_282

N. Thompson, N. J. Wadsworth, and N. Et-louat, 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

V. Tvergaard, On fatigue crack growth in ductile materials by crack???tip blunting, Journal of the Mechanics and Physics of Solids, vol.52, issue.9, pp.2149-2166, 2004.
DOI : 10.1016/j.jmps.2004.02.007

V. Tvergaard, Overload effects in fatigue crack growth by crack-tip blunting, International Journal of Fatigue, vol.27, issue.10-12, pp.1389-1397, 2005.
DOI : 10.1016/j.ijfatigue.2005.06.003

V. Tvergaard, Effect of underloads or overloads in fatigue crack growth by crack-tip blunting, Engineering Fracture Mechanics, vol.73, issue.7, pp.869-879, 2006.
DOI : 10.1016/j.engfracmech.2005.10.009

V. Tvergaard and J. W. Et-hutchinson, Crack growth per cycle by blunting and void growth, pp.107-116, 2002.

V. Tvergaard and A. Et-needleman, Analysis of the cup-cone fracture in a round tensile bar, Acta Metallurgica, vol.32, issue.1, pp.157-169, 1984.
DOI : 10.1016/0001-6160(84)90213-X

E. Vasseur, Fatigue anisotherme et microstructures de superalliages colonnaires, 1993.

Y. Verreman and G. Et-espinosa, Comportement des fissures courtes en fatigue, editeurs : La fatigue des matériaux et des structures, pp.333-363, 1997.

F. I. Versnyder and R. W. Et-guard, Directional grain structure for high temperature strength, Transactions of the American Society for Metals, vol.52, p.485, 1960.

F. I. Versnyder and M. E. Shank, The development of columnar grain and single crystal high temperature materials through directional solidification, Materials Science and Engineering, vol.6, issue.4, pp.213-247, 1970.
DOI : 10.1016/0025-5416(70)90050-9

R. Viswanathan and S. T. Et-scheirer, Materials Technology for Advanced Land Based Gas Turbines, Seventh International Conference on Creep and Fatigue at Elevated Temperatures, 2001.

A. New-type-of-microstructural-kissinger, R. D. Deye, D. J. Anton, D. L. Et-cetel, and A. D. , Instability in Superalloys -SRZ, The Minerals, Metals and Materials Society, pp.9-18, 1996.

C. Wang, S. Barter, and Q. Et-liu, A Closure Model to Crack Growth Under Large-Scale Yielding and Through Residual Stress Fields, Journal of Engineering Materials and Technology, vol.125, issue.2, pp.183-190, 2003.
DOI : 10.1115/1.1493804

G. Ward, B. S. Hockenhull, and P. Et-hancock, The effect of cyclic stressing on the oxidation of a low-carbon steel, Metallurgical Transactions, vol.208, issue.6, pp.1451-1455, 1974.
DOI : 10.1007/BF02646632

G. C. Wood, F. H. Stott, D. P. Whittle, Y. Shida, and B. D. Et-bastow, The high-temperature internal oxidation and intergranular oxidation of nickel-chromium alloys, Corrosion Science, vol.23, issue.1, pp.9-25, 1983.
DOI : 10.1016/0010-938X(83)90056-2

N. Yeh and E. Et-krempl, An incremental life prediction law for multiaxial creepfatigue interaction and thermomechanical loading, editeurs : Advances in multiaxial fatigue -ASTM STP 1191, pp.107-119, 1993.

J. L. Yuen, P. Roy, and W. Et-nix, Effect of oxidation kinetics on the near threshold fatigue crack growth behavior of a nickel base superalloy, Metallurgical Transactions A, vol.5, issue.9, pp.1769-1775, 1984.
DOI : 10.1007/BF02666360