V. Chapitre, Modélisation du comportement en FGNC des alliages d'aluminium de fonderie

S. Tabibian, Contributions to thermomechanical fatigue criteria for lost foam casting aluminium alloys, 2011.

I. H. Mohamed, Etude expérimentale et modélisation de la durée de vie en fatigue d'un alliage d'aluminium de fonderie a356-t6 sous chargement multiaxial, Ecole Nationale, 2015.

H. Kaya, E. Çad?rl?, and M. Gündüz, Dendritic Growth in an Aluminum-Silicon Alloy, Journal of Materials Engineering and Performance, vol.33, issue.7, pp.12-21, 2007.
DOI : 10.1007/s11665-006-9002-2

M. Warmuzek, Aluminum-Silicon Casting Alloys, Atlas of Microfractographs, A. International, 2004.

G. Heiberg and L. Arnberg, Investigation of the microstructure of the Al???Si eutectic in binary aluminium???7 wt% silicon alloys by electron backscatter diffraction (EBSD), Journal of Light Metals, vol.1, issue.1, pp.43-49, 2001.
DOI : 10.1016/S1471-5317(00)00005-5

I. Koutiri, Effet des fortes contraintes hydrostatiques sur la tenue en fatigue des matériaux métalliques, Ph.D. dissertation, ENSAM, 2011.

J. Buffière, S. Savelli, P. Jouneau, E. Maire, and R. Fougères, Experimental study of porosity and its relation to fatigue mechanisms of model, pp.7-7

S. Redik, M. Tauscher, and F. Grün, Mechanisms of fatigue-crack initiation and their impact on fatigue life of AlSi7 die-cast components, MATEC Web of Conferences, p.3003, 2014.
DOI : 10.1051/matecconf/20141203003

I. S. Munoz, Etude de l'influence des défauts de fonderie sur le comportement en fatigue de l'alliage aéronautique a357-t6, 2014.

J. Yi, P. Lee, T. Lindley, and T. Fukui, Statistical modeling of microstructure and defect population effects on the fatigue performance of cast A356-T6 automotive components, Materials Science and Engineering: A, vol.432, issue.1-2, pp.59-68, 2006.
DOI : 10.1016/j.msea.2006.07.003

Q. Wang, D. Apelian, and D. Lados, Fatigue behavior of A356/357 aluminum cast alloys. Part II ??? Effect of microstructural constituents, Journal of Light Metals, vol.1, issue.1, pp.85-97, 2001.
DOI : 10.1016/S1471-5317(00)00009-2

L. Zeng, J. Sakamoto, A. Fujii, and H. Noguchi, Role of eutectic silicon particles in fatigue crack initiation and propagation and fatigue strength characteristics of cast aluminum alloy A356, Engineering Fracture Mechanics, vol.115, pp.1-12, 2014.
DOI : 10.1016/j.engfracmech.2013.11.016

E. Ferrie, Caracterisation et modelisation tridimensionnelles de la propagation de fissures de fatigue dans des alliages d'aluminium modeles, Ph.D. dissertation, L'Institut National des Sciences Appliquees de Lyon, 2006.

S. Dezecot and M. Brochu, Microstructural characterization and high cycle fatigue behavior of investment cast A357 aluminum alloy, International Journal of Fatigue, vol.77, pp.154-159, 2015.
DOI : 10.1016/j.ijfatigue.2015.03.004
URL : https://hal.archives-ouvertes.fr/hal-01160555

Y. Gao, J. Yi, P. Lee, and T. Lindley, A micro-cell model of the effect of microstructure and defects on fatigue resistance in cast aluminum alloys, Acta Materialia, vol.52, issue.19, pp.5435-5449, 2004.
DOI : 10.1016/j.actamat.2004.07.035

A. Marie-louise, J. Ferrando, and J. Niclou, Development of a testing method in high cycle fatigue on a specimen with foundry skin, Recueil des conferences Les congrés du CETIM fatigue design, 2007.

M. J. Caton, J. W. Jones, H. Mayer, S. Stanzl-tschegg, and J. E. Allison, Demonstration of an endurance limit in cast 319 aluminum, Metallurgical and Materials Transactions A, vol.30, issue.1???2, pp.33-41, 2003.
DOI : 10.1007/s11661-003-0206-x

M. Caton, J. Jones, J. Boileau, and J. Allison, The effect of solidification rate on the growth of small fatigue cracks in a cast 319-type aluminum alloy, Metallurgical and Materials Transactions A, vol.6, issue.4, pp.3055-3068, 1999.
DOI : 10.1007/s11661-999-0216-4

T. S. Kitagawa and H. , Applicability of fracture mechanics to very small cracks, ASM Proceedings of 2nd international conference on mechanical Metalspark. Ohio, pp.627-631, 1976.

K. Tanaka, Y. Akiniwa, and M. Wakita, Resistance-Curve Method for Predicting Fatigue Thresholds under Combined Loading, Nano and Engineering Materials and Structures, E. Gdoutos, pp.1217-1218, 2006.
DOI : 10.1007/1-4020-4972-2_604

E. Pessard, D. Bellett, F. Morel, and I. Koutiri, A mechanistic approach to the Kitagawa???Takahashi diagram using a multiaxial probabilistic framework, Engineering Fracture Mechanics, vol.109, issue.0, 2013.
DOI : 10.1016/j.engfracmech.2013.06.001
URL : https://hal.archives-ouvertes.fr/hal-00875771

E. Tschegg, Mode III and Mode I fatigue crack propagation behaviour under torsional loading, Journal of Materials Science, vol.15, issue.6, pp.1604-1614, 1983.
DOI : 10.1007/BF00542053

E. K. Tschegg, Fatigue crack growth in high and low strength steel under torsional loading Theoretical and Applied Fracture Mechanics, pp.157-178, 1985.

A. Niklas, U. Abaunza, A. I. Fernandez-calvo, J. Lacaze, and R. Suarez, Thermal analysis as a microstructure prediction tool for a356 aluminium parts solidified under various cooling conditions, 69th World Foundry Congress (WFC) this paper was published by the Foundry Journal Agency in the Chiny foundry journal, pp.89-9589, 2011.

D. A. Lados, D. Apelian, and J. K. Donald, Fatigue crack growth mechanisms at the microstructure scale in Al???Si???Mg cast alloys: Mechanisms in the near-threshold regime, Acta Materialia, vol.54, issue.6, pp.1475-1486, 2006.
DOI : 10.1016/j.actamat.2005.11.019

Y. Murakami, Effects of small defects and nonmetallic inclusions, 2002.

D. Mcdowell, K. Gall, M. Horstemeyer, and J. Fan, Microstructure-based fatigue modeling of cast A356-T6 alloy, Engineering Fracture Mechanics, vol.70, issue.1, pp.49-80, 2003.
DOI : 10.1016/S0013-7944(02)00021-8

Q. Wang, D. Apelian, and D. Lados, Fatigue behavior of A356-T6 aluminum cast alloys. Part I. Effect of casting defects, Journal of Light Metals, vol.1, issue.1, pp.73-84, 2001.
DOI : 10.1016/S1471-5317(00)00008-0

K. S. Chan, P. Jones, and Q. Wang, Fatigue crack growth and fracture paths in sand cast {B319} and {A356} aluminum alloys Available : http://www.sciencedirect.com/science Cast aluminum alloy for high temperature applications, Materials Science and Engineering : A Paper presented at the 132nd TMS Annual Meeting and Exhibition San Diego Convention Center, pp.18-34, 2003.

M. I. Houria, Y. Nadot, R. Fathallah, M. Roy, and D. M. Maijer, Influence of casting defect and {SDAS} on the multiaxial fatigue behaviour of a356-t6 alloy including mean stress effect, International Journal of Fatigue, issue.0, 2015.

D. A. Lados, D. Apelian, P. E. Jones, and J. F. Major, Microstructural mechanisms controlling fatigue crack growth in Al???Si???Mg cast alloys, the McEvily Symposium : Fatigue and Fracture of Traditional and Advanced Materials, {TMS} 2006, pp.237-245, 2007.
DOI : 10.1016/j.msea.2006.08.130

D. Massinon and V. Constantin, Formation metallurgie et defauts de fonderie, 2002.

B. Barlas, Etude du comportement et de l'endommagement en fatigue d'alliages d'aluminium de fonderie, 2004.
URL : https://hal.archives-ouvertes.fr/tel-00162056

S. Savelli, Identification des mécanisme et approche quantitative de la fatigue d'alliages modèle d'aluminum de moulage, 2000.

M. Brochu, Y. Verreman, F. Ajersch, and D. Bouchard, High cycle fatigue strength of permanent mold and rheocast aluminum 357 alloy, International Journal of Fatigue, vol.32, issue.8, pp.1233-1242, 2010.
DOI : 10.1016/j.ijfatigue.2010.01.001

P. Huter, P. Renhart, S. Oberfrank, M. Schwab, F. Grün et al., High- and low-cycle fatigue influence of silicon, copper, strontium and iron on hypo-eutectic Al???Si???Cu and Al???Si???Mg cast alloys used in cylinder heads, International Journal of Fatigue, vol.82, 2015.
DOI : 10.1016/j.ijfatigue.2015.09.015

G. Nicoletto, G. Anzelotti, and R. Kone?ná, X-ray computed tomography vs. metallography for pore sizing and fatigue of cast Al-alloys, Procedia Engineering, vol.2, issue.1, pp.547-554, 2010.
DOI : 10.1016/j.proeng.2010.03.059

Y. Tijani, A. Heinrietz, T. Bruder, and H. Hanselka, Quantitative evaluation of fatigue life of cast aluminum alloys by non-destructive testing and parameter model, International Journal of Fatigue, vol.57, pp.73-78, 2013.
DOI : 10.1016/j.ijfatigue.2013.05.017

M. Roy, Y. Nadot, C. Nadot-martin, P. Bardin, and D. Maijer, Multiaxial Kitagawa analysis of A356-T6, International Journal of Fatigue, vol.33, issue.6, pp.823-832, 2011.
DOI : 10.1016/j.ijfatigue.2010.12.011

M. Roy, Y. Nadot, D. M. Maijer, and G. Benoit, Multiaxial fatigue behaviour of a356-t6 Fatigue and Fracture of Engineering Materials and Structures, pp.1148-1159, 2012.

M. J. Couper and J. R. Griffiths, EFFECTS OF CRACK CLOSURE AND MEAN STRESS ON THE THRESHOLD STRESS INTENSITY FACTOR FOR FATIGUE OF AN ALUMINIUM CASTING ALLOY,, Fatigue & Fracture of Engineering Materials and Structures, vol.11, issue.6, pp.615-624, 1990.
DOI : 10.1016/0167-8442(84)90015-6

J. Boileau and J. Allison, The effect of solidification time and heat treatment on the fatigue properties of a cast 319 aluminum alloy, Metallurgical and Materials Transactions A, vol.30, issue.1???2, pp.1807-1820, 2003.
DOI : 10.1007/s11661-003-0147-4

R. González, A. González, J. Talamantes-silva, S. Valtierra, R. D. Mercado-solís et al., Fatigue of an aluminium cast alloy used in the manufacture of automotive engine blocks, International Journal of Fatigue, vol.54, issue.0, pp.118-126, 2013.
DOI : 10.1016/j.ijfatigue.2013.03.018

C. Davidson, J. Griffiths, M. Badiali, and A. Zanada, Fatigue properties of a semisolid cast al?7si?0.3 mg?t6 alloy, Met Sci Technol, vol.18, issue.2, pp.27-31, 2000.

C. J. Davidson, J. R. Griffiths, and A. Zanada, Fatigue properties of squeeze, semisolid and gravity diecast al-si-mg alloy, Structural Integrity and Fracture : Proceedings of the International Conference, SIF2004. Australian Fracture Group, pp.79-84, 2004.

M. Brochu, Comportement en fatigue de l'aluminium 357 coulé par gravité et rhéocoulé, 2010.

K. and D. Van, Sur la resistance a la fatigue des metaux Sciences et techniques de l'armement, pp.641-772, 1973.

N. Huyen, L. Flaceliere, and F. Morel, A critical plane fatigue model with coupled meso-plasticity and damage Fatigue and Fracture of Engineering Materials and Structures, pp.12-28, 2008.

Y. Murakami, M. T. Endo52-]-t, and . Nguyen, Quantitative evaluation of fatigue strength of metals containing various small defects or cracks <ce :title>Special Issue : International Conference on Advanced Materials Mechanical Properties '90 (ICAMP '90) </ce :title>. [Online] Available : http://www.sciencedirect.com/science Effet des hétérogénéités microstructurales sur le comportement en fatigue multiaxiale a grand nombre de cycles, Engineering Fracture MechanicsAngers LPMI, vol.17, issue.1, pp.1-150013794483900188, 1983.

I. Papadopoulos, Fatigue Limit of Metals Under Multiaxial Stress Conditions : The Microscopic Approach, Joint Research Centre, ISEI, 1993.

N. E. Frost, Propagation of fatigue cracks in various sheet materials, ARCHIVE: Journal of Mechanical Engineering Science 1959-1982 (vols 1-23), vol.1, issue.2, pp.151-170, 1959.
DOI : 10.1243/JMES_JOUR_1959_001_019_02

N. Kobayashi, The Effects of Notch Depth on the Initiation Propagation and Non-propagation of Fatigue Cracks, Transactions of the Japan Society of Mechanical Engineers, vol.35, issue.277, pp.1856-1863, 1969.
DOI : 10.1299/kikai1938.35.1856

Y. Murakami and M. , The Behaviour of Short Fatigue Cracks, Mechanical Engineering Publications, pp.275-293, 1986.

. Murakami, . Uemura, and M. Natsume, Effect of mean stress on the fatigue strength of high-strength steels containing small defects or nonmetallic inclusions., Transactions of the Japan Society of Mechanical Engineers Series A, vol.56, issue.525, pp.1074-1081, 1990.
DOI : 10.1299/kikaia.56.1074

Y. Murakami and M. Endo, Effects of defects, inclusions and inhomogeneities on fatigue strength, International Journal of Fatigue, vol.16, issue.3, pp.163-182, 1994.
DOI : 10.1016/0142-1123(94)90001-9

M. Endo, The multiaxial fatigue strength of specimens containing small defectsMultiaxial Fatigue and Fracture, ser. European Structural Integrity Society, Biaxial/Multiaxial Fatigue and Fracture 6th International Conference on Biaxial, pp.243-264, 2003.

Y. Nadot and T. Billaudeau, Multiaxial fatigue limit criterion for defective materials, Engineering Fracture Mechanics, vol.73, issue.1, pp.112-133, 2006.
DOI : 10.1016/j.engfracmech.2005.06.005

P. Mu, Y. Nadot, C. Nadot-martin, A. Chabod, I. Serrano-munoz et al., Influence of casting defects on the fatigue behavior of cast aluminum AS7G06-T6, International Journal of Fatigue, vol.63, issue.0, pp.97-109, 2014.
DOI : 10.1016/j.ijfatigue.2014.01.011

R. Smith, On the short crack limitations of fracture mechanics, International Journal of Fracture, vol.10, issue.5, pp.717-720, 1977.
DOI : 10.1007/BF00017308

M. E. Haddad, T. Topper, and K. Smith, Prediction of non propagating cracks, Engineering Fracture Mechanics, vol.11, issue.3, pp.573-584, 1979.
DOI : 10.1016/0013-7944(79)90081-X

I. Koutiri, D. Bellett, F. Morel, and E. Pessard, A probabilistic model for the high cycle fatigue behaviour of cast aluminium alloys subject to complex loads, International Journal of Fatigue, vol.47, issue.0, pp.137-147, 2013.
DOI : 10.1016/j.ijfatigue.2012.08.004
URL : https://hal.archives-ouvertes.fr/hal-00821800

E. Pessard, F. Morel, and A. Morel, The Anisotropic Fatigue Behavior of Forged Steel, Advanced Engineering Materials, vol.74, issue.470, pp.732-735, 2009.
DOI : 10.1002/adem.200900040
URL : https://hal.archives-ouvertes.fr/hal-00805154

E. Pessard, F. Morel, A. Morel, and D. Bellett, Modelling the role of non-metallic inclusions on the anisotropic fatigue behaviour of forged steel, International Journal of Fatigue, vol.33, issue.4, pp.568-577, 2011.
DOI : 10.1016/j.ijfatigue.2010.10.012
URL : https://hal.archives-ouvertes.fr/hal-00805277

E. Pessard, F. Morel, C. Verdu, L. Flacelière, and G. Baudry, Microstructural heterogeneities and fatigue anisotropy of forged steels, Materials Science and Engineering: A, vol.529, issue.0, pp.289-299, 2011.
DOI : 10.1016/j.msea.2011.09.031

J. Fan, D. L. Mcdowell, M. F. Horstemeyer, and K. Gall, Cyclic plasticity at pores and inclusions in cast al?si alloys Available : http://www.sciencedirect.com/ science, Engineering Fracture Mechanics, vol.7071, issue.10, pp.1281-1302, 2003.

J. Charbonnier, Gaz dans les alliages d'aluminium de fonderie, 1991.

A. Pickard, The Application of 3-Dimensional Finite Element Methods to Fracture Mechanics and Fatigue Life Prediction Available : http://books.google.fr/books?id= 3oVGAAAAYAAJ [76] Y. Murakami, Stress intensity factors handbook. 1 (1987), ser. Stress Intensity Factors Handbook, EMAS, Engineering Materials Advisory Services Limited, 1986.

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

L. Ceschini, A. Morri, A. Morri, A. Gamberini, and S. Messieri, Correlation between ultimate tensile strength and solidification microstructure for the sand cast A357 aluminium alloy, Materials & Design, vol.30, issue.10, pp.4525-4531, 2009.
DOI : 10.1016/j.matdes.2009.05.012

H. Gough, H. Pollard, and W. Clenshaw, Some Experiments on the Resistance of Metals to Fatigue Under Combined Stresses, ser. Aeronautical Research Council Reports and Memoranda. H.M. Stationery Office, 1951.

S. B. Jamma, F. Morel, D. Bellett, and V. Le, Etude de l'endommagement en fatigue uniaxiale et multiaxiale des alliages de fonderie -application sur un culasse automobile, 2014.

D. Pinna, The preferred fatigue crack propagation mode in a m250 maraging steel loaded in shear Fatigue and Fracture of Engineering Materials and Structures, pp.173-183, 1999.

B. Skallerud, T. Iveland, and G. Härkegård, Fatigue life assessment of aluminum alloys with casting defects, Engineering Fracture Mechanics, vol.44, issue.6, pp.857-8740013794493901085, 1993.
DOI : 10.1016/0013-7944(93)90108-5

E. Merhy, Propagation de fissure sous chargement thermomécanique cyclique anisotherme : Application au dimensionnement de structures automobiles en alliage d'aluminum (al-si), 2011.

D. A. Lados and D. Apelian, Relationships between microstructure and fatigue crack propagation paths in Al???Si???Mg cast alloys, Conference of Crack Paths. [Online]. Available, pp.821-832, 2008.
DOI : 10.1016/j.engfracmech.2007.01.027

C. Robert, N. Saintier, T. Palin-luc, and F. Morel, Micro-mechanical modelling of high cycle fatigue behaviour of metals under multiaxial loads, Mechanics of Materials, vol.55, issue.0, pp.112-129, 2012.
DOI : 10.1016/j.mechmat.2012.08.006

G. Sachs, Zur Ableitung einer Flie??bedingung, Mitteilungen der deutschen Materialprüfungsanstalten, pp.94-97978, 1929.
DOI : 10.1007/978-3-642-92045-5_12

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

S. Stanzl-tschegg, H. Mughrabi, and B. Schoenbauer, Life time and cyclic slip of copper in the VHCF regime, fatigue Damage of Structural Materials {VI} The Sixth International Conference on Fatigue Damage of Structural Materials. [Online]. Available, pp.2050-2059, 2007.
DOI : 10.1016/j.ijfatigue.2007.03.010

D. Bellett and F. Morel, Influence des fortes contraintes hydrostatiques sur la résistance en fatigue d'un alliage d'aluminium as7g03u, SERAM Centre d'Angers, 2005.

M. Caton, J. Jones, and J. Allison, The influence of heat treatment and solidification time on the behavior of small-fatigue-cracks in a cast aluminum alloy, Materials Science and Engineering: A, vol.314, issue.1-2, pp.81-85, 2001.
DOI : 10.1016/S0921-5093(00)01916-X

T. Mbuya, I. Sinclair, A. Moffat, and P. Reed, Micromechanisms of fatigue crack growth in cast aluminium piston alloys, Damage of Structural Materials {VIII}. [Online]. Available, pp.227-237, 2012.
DOI : 10.1016/j.ijfatigue.2011.10.015

L. Makkonen, R. Rabb, and M. Tikanmäki, Size effect in fatigue based on the extreme value distribution of defects, Materials Science and Engineering: A, vol.594, issue.0, pp.68-71, 2014.
DOI : 10.1016/j.msea.2013.11.045

J. Lemaitre, J. Chaboche, A. Benallal, and R. Desmorat, Mécanique des matériaux solides -3ème édition, ser. Physique. Dunod Available : https, 2009.

C. Geuzaine and J. Remacle, Gmsh: A 3-D finite element mesh generator with built-in pre- and post-processing facilities, International Journal for Numerical Methods in Engineering, vol.69, issue.4, pp.1309-1331, 2009.
DOI : 10.1002/nme.2579

M. El, A. Heinrietz, W. Stets, and P. Voigt, Nicolas Mécanique-matériaux Paris, ENSAM 2013 Detection and influence of shrinkage pores and nonmetallic inclusions on fatigue life of cast aluminum alloys, thèse de doctorat dirigée par Palin-Luc, Thierry et Saintier, pp.5408-5415, 2013.

G. Nicoletto, R. Kone?ná, and S. Fintova, Characterization of microshrinkage casting defects of Al???Si alloys by X-ray computed tomography and metallography, fatigue Design and Material Defects. [Online]. Available, pp.39-46, 2012.
DOI : 10.1016/j.ijfatigue.2012.01.006

E. Pessard, B. Abrivard, F. Morel, F. Abroug, and P. Delhaye, The effect of quenching and defects size on the HCF behaviour of Boron steel, International Journal of Fatigue, vol.68, pp.80-89, 2014.
DOI : 10.1016/j.ijfatigue.2014.06.002
URL : https://hal.archives-ouvertes.fr/hal-01061163

S. Murali, T. S. Arvind, K. S. Raman, and K. Murthy, Fatigue Properties of Sand Cast, Stircast and Extruded Al&ndash;7Si&ndash;0.3Mg Alloy with Trace Additions of Be and Mn, Materials Transactions, JIM, vol.38, issue.1, pp.28-36, 1997.
DOI : 10.2320/matertrans1989.38.28

S. C. Gordon, C. E. Powell, and . Mobley, A fractography atlas of casting alloys, 1992.

I. Koutiri, D. Bellett, F. Morel, L. Augustins, and J. Adrien, High cycle fatigue damage mechanisms in cast aluminium subject to complex loads, International Journal of Fatigue, vol.47, issue.0, pp.44-57, 2013.
DOI : 10.1016/j.ijfatigue.2012.07.008
URL : https://hal.archives-ouvertes.fr/hal-01068555

T. Palinluc and C. Bathias, Essais de fatigue gigacyclique sur huit nuances d'alliage d'aluminium, ENSAM, Tech. Rep, 2010.

H. Ammar, A. Samuel, and F. Samuel, Porosity and the fatigue behavior of hypoeutectic and hypereutectic aluminum???silicon casting alloys, International Journal of Fatigue, vol.30, issue.6, pp.1024-1035, 2008.
DOI : 10.1016/j.ijfatigue.2007.08.012

F. Morel and N. Huyen, Plasticity and damage heterogeneity in fatigue, Theoretical and Applied Fracture Mechanics, pp.98-127, 2008.
DOI : 10.1016/j.tafmec.2007.10.006

D. Dugdale, Yielding of steel sheets containing slits, Journal of the Mechanics and Physics of Solids, vol.8, issue.2, pp.100-104, 1960.
DOI : 10.1016/0022-5096(60)90013-2

L. Froustey and D. , Validité des critéres de fatigue multiaxiale a l'endurance en flexion-torsion, " in Fatigue des structures industrielles. 40 promenade Marx-Dormoy, F-93460 Gournay-sur-Marne, France : IITT International, pp.126-138, 1989.

A. Galtier and J. Séguret, Critère multiaxiaux en fatigue : exploitation en bureau d'étude. proposition d'un nouveau critère, Revue Français de Mécanique, pp.291-299, 1990.

F. Hild, R. Billardon, and D. Marquis, Hétérogénéité des contraintes et rupture des materiaux fragiles Comptes rendus de l'Académie des sciences, Sciences de l'univers, Sciences de la Terre, pp.1293-1298, 1992.

. Isibasi, Fatigue of Metals and Prevention of Fracture, 1967.

J. Liu and H. Zenner, Berechnung der Dauerschwingfestigkeit bei mehrachsiger Beanspruchung ??? Teil 1, Materialwissenschaft und Werkstofftechnik, vol.11, issue.7, pp.240-249, 1993.
DOI : 10.1002/mawe.19930240706

Z. Lui, Fatigue limit of ductile metals under multiaxial loadingMultiaxial Fatigue and Fracture, ser. European Structural Integrity Society, Biaxial/Multiaxial Fatigue and Fracture 6th International Conference on Biaxial, pp.147-164, 2003.

R. Mitchell, A Unified Predictive Technique for the Fatigue Resistance of Cast Ferrous-Based Metals and High Hardness Wrought Steels, SAE Technical Paper Series, 1979.
DOI : 10.4271/790890

F. Morel, T. Palin-luc, and C. Froustey, Comparative study and link between mesoscopic and energetic approaches in high cycle multiaxial fatigue, International Journal of Fatigue, vol.23, issue.4, pp.317-327, 2001.
DOI : 10.1016/S0142-1123(00)00100-6
URL : https://hal.archives-ouvertes.fr/hal-01372757

H. Nordburg and R. Sandstrom, Swedish symposium on non-metallic inclusions in steel, Institutet for Metallforskning (Sweden) " and Uddeholms AB. Hagfors, Sweden : Uddeholms AB, pp.395-428, 1981.

I. V. Papadopoulos, P. Papadopoulos, C. Davoli, M. Gorla, A. Filippini et al., A comparative study of multiaxial high-cycle fatigue criteria for metals, International Journal of Fatigue, vol.19, issue.3, pp.219-235, 1987.
DOI : 10.1016/S0142-1123(96)00064-3

. Peterson, Notch sensitivity, Metal Fatigue, 1959.

G. W. Powell, The fractography of casting alloys, Materials Characterization, vol.33, issue.3, pp.275-293, 1994.
DOI : 10.1016/1044-5803(94)90048-5

D. Taylor, On the use of P-a plots to model the behaviour of short fatigue cracks, International Journal of Fatigue, vol.14, issue.3, pp.163-168, 1992.
DOI : 10.1016/0142-1123(92)90369-N

M. Beretta, SIF and threshold for small cracks at small notches under torsion, Fatigue and Fracture of Engineering Materials and Structures, pp.97-104, 2000.
DOI : 10.1046/j.1460-2695.2000.00260.x

L. Susmel, The theory of critical distances: a review of its applications in fatigue, Engineering Fracture Mechanics, vol.75, issue.7, pp.1706-1724, 2008.
DOI : 10.1016/j.engfracmech.2006.12.004

L. Susmel and D. Taylor, The Theory of Critical Distances as an alternative experimental strategy for the determination of KIc and ??Kth, Engineering Fracture Mechanics, vol.77, issue.9, pp.1492-1501, 2010.
DOI : 10.1016/j.engfracmech.2010.04.016

I. V. Papadopoulos and V. P. Panoskaltsis, Invariant formulation of a gradient dependent multiaxial high-cycle fatigue criterion, Engineering Fracture Mechanics, vol.55, issue.4, pp.513-528, 1996.
DOI : 10.1016/S0013-7944(96)00047-1

F. Morel, A. Morel, and Y. Nadot, Comparison between defects and micro-notches in multiaxial fatigue ??? The size effect and the gradient effect, International Journal of Fatigue, vol.31, issue.2, pp.263-275, 2009.
DOI : 10.1016/j.ijfatigue.2008.09.005
URL : https://hal.archives-ouvertes.fr/hal-00809338

H. Neuber, Theory of Notch Stresses : Principles for Exact Calculation of Strength with Reference to Structural Form and Material. United States Atomic Energy Commission, Office of Technical Information, 1958.

R. Guerchais, N. Saintier, F. Morel, and C. Robert, Micromechanical investigation of the influence of defects in high cycle fatigue, International Journal of Fatigue, vol.67, issue.0, pp.159-172, 2013.
DOI : 10.1016/j.ijfatigue.2014.01.005
URL : https://hal.archives-ouvertes.fr/hal-01084156

J. Petit and A. Zeghloul, Influence de l'environnement et de la microstructure sur la propagation en fatigue des fissures courtes tridimensionnelles, Revue de Physique Appliqu??e, vol.24, issue.9, pp.905-91301989002409090500, 1989.
DOI : 10.1051/rphysap:01989002409090500
URL : https://hal.archives-ouvertes.fr/jpa-00246113

N. Grinberg, The effect of vacuum on fatigue crack growth, International Journal of Fatigue, vol.4, issue.2, pp.83-95, 1982.
DOI : 10.1016/0142-1123(82)90064-0

L. Flacelière, Contribution a la modélisation du dommage en fatigue multiaxiale d'un acier c36 : confrontation à l'expérience, thèse de doctorat dirigée par Dragon, André et Morel, Franck Mécanique des solides, des matériaux, des structures et des surfaces Poitiers, 2004.

J. Benabes, Approche énergétique non locale du calcul de durée de vie de structures en fatigue multiaxiale sous chargements d'amplitude variable : application à une roue de train ferroviaire, 2006.

A. Ismail and G. Abdullah, Stress intensity factors under combined tension and torsion loadings, Indian Journal of Engineering and Materials Sciences, vol.191, pp.5-16, 2012.

G. Sinclair, An investigation of the coaxing effect in fatigue of metals, 1952.

Y. Murakami, Y. Tazunoki, and T. Endo, Existence of the coaxing effect and effects of small artificial holes on fatigue strength of an aluminum alloy and 70-30 brass, Metallurgical Transactions A, vol.45, issue.391, pp.2029-2038, 1984.
DOI : 10.1007/BF02646837

O. Engler and J. Hirsch, Texture control by thermomechanical processing of AA6xxx Al???Mg???Si sheet alloys for automotive applications???a review, Materials Science and Engineering: A, vol.336, issue.1-2, pp.249-262, 2002.
DOI : 10.1016/S0921-5093(01)01968-2

D. L. Galindo, A. R. Colas, J. M. Cabrera, and J. Talamantes-silva, Ebsd texture analysis of an alcumg alloy for different solidification rates, 70th World Foundry Congress 2012, p.2012, 2012.

P. Osmond, Etude du vieillissement à chaud des alliages d'aluminium pour culasses diesel et prise en compte dans le dimensionnement, 2010.

A. Nadot, I. Chabaud, P. Serrano-mura, C. Mu, J. Y. Verdu et al., Influence of defect on the fatigue behaviour of as7g06t6 aeronautical alloy (ideffaar), The 2nd International Symposium on Fatigue Design and Material Defects. SF2M, 2014.

K. Lee, Y. N. Kwon, and S. Lee, Effects of eutectic silicon particles on tensile properties and fracture toughness of A356 aluminum alloys fabricated by low-pressure-casting, casting-forging, and squeeze-casting processes, Journal of Alloys and Compounds, vol.461, issue.1-2, pp.532-541, 2008.
DOI : 10.1016/j.jallcom.2007.07.038

. Fatigue, . Astm, . Special, /. Publi-cation-/, . Stp et al., A rapid method for generation of a Haigh diagram for high cycle fatigue Available : https, pp.626-641, 1999.

E. Ferrié, J. Buffière, W. Ludwig, A. Gravouil, and L. Edwards, Fatigue crack propagation: In situ visualization using X-ray microtomography and 3D simulation using the extended finite element method, Acta Materialia, vol.54, issue.4, pp.1111-1122, 2006.
DOI : 10.1016/j.actamat.2005.10.053

E. Ferrié, J. Buffière, and W. Ludwig, 3D characterisation of the nucleation of a short fatigue crack at a pore in a cast Al alloy using high resolution synchrotron microtomography, Damage of Structural Materials V 5th International Conference on Fatigue Damage of Structural Materials. [Online]. Available, pp.1215-1220, 2005.
DOI : 10.1016/j.ijfatigue.2005.07.015

W. Ludwig, J. Buffière, S. Savelli, and P. Cloetens, Study of the interaction of a short fatigue crack with grain boundaries in a cast Al alloy using X-ray microtomography, Acta Materialia, vol.51, issue.3, pp.585-598, 2003.
DOI : 10.1016/S1359-6454(02)00320-8
URL : https://hal.archives-ouvertes.fr/hal-00475154

J. Chaboche, Time-independent constitutive theories for cyclic plasticity, International Journal of Plasticity, vol.2, issue.2, pp.149-188, 1986.
DOI : 10.1016/0749-6419(86)90010-0

Z. Xu, W. Wen, and T. Zhai, Effects of Pore Position in Depth on Stress/Strain Concentration and Fatigue Crack Initiation, Metallurgical and Materials Transactions A, vol.13, issue.8, pp.2763-2770, 2012.
DOI : 10.1007/s11661-011-0947-x

J. P. Iii, Statistical Inference Using Extreme Order Statistics, The Annals of Statistics, pp.119-1312958083, 1975.
DOI : 10.1214/aos/1176343003

A. Davison, Modelling Excesses over High Thresholds, with an Application, Statistical Extremes and Applications, ser. NATO ASI Series, pp.461-482978, 1984.
DOI : 10.1007/978-94-017-3069-3_34

E. Castillo and A. S. Hadi, Fitting the Generalized Pareto Distribution to Data, Journal of the American Statistical Association, vol.6, issue.3, pp.1609-16202965432, 1997.
DOI : 10.1080/01621459.1997.10473683

D. Bellett, D. Taylor, S. Marco, E. Mazzeo, J. Guillois et al., The fatigue behaviour of three-dimensional stress concentrations, International Journal of Fatigue, vol.27, issue.3, pp.207-221, 2005.
DOI : 10.1016/j.ijfatigue.2004.07.006

Q. Vu, D. Halm, and Y. Nadot, Multiaxial fatigue criterion for complex loading based on stress invariants, International Journal of Fatigue, vol.32, issue.7, pp.1004-1014, 2010.
DOI : 10.1016/j.ijfatigue.2009.11.006