. Ph, M. Destuynder, &. S. Djaoua, and . Lescure, Quelques remarques sur la mécanique de la rupture élastique, Journal de Mécanique Théorique et Appliquée, vol.2, issue.1, pp.113-135, 1983.

H. Dhondt, M. Truchon, and &. A. Pineau, Fatigue crack path behavior under polymodal fatigue. Rapports de l'Institut de recherche de la sidérurgie française IRSID, 1982.

]. T. Dick and &. G. Cailletaud, Fretting modelling with a crystal plasticity model of Ti6Al4V, Computational Materials Science, vol.38, issue.1, pp.113-125, 2006.
DOI : 10.1016/j.commatsci.2006.01.015

URL : https://hal.archives-ouvertes.fr/hal-00133520

T. Dick, S. Basseville, and &. G. Cailletaud, Fatigue modelling in fretting contact with a crystal plasticity model, Proceedings of the 16th International Workshop on Computational Mechanics of Materials -IWCMM-16, pp.36-42, 2008.
DOI : 10.1016/j.commatsci.2007.07.055

URL : https://hal.archives-ouvertes.fr/hal-00312041

M. Dubourg and &. B. Villechaise, Stress intensity factors in a bent crack : a model, European Journal of Mechanics and Solids, vol.11, issue.2, pp.169-179, 1992.

]. E. Eden, W. N. Rose, and &. L. Cunningham, The endurance of metals, Proceedings of the Institute of Mecanical Engineers, pp.839-974, 1911.

L. Edwards and &. H. Zhang, Investigation of small fatigue cracks???I. Plastic deformation associated with small fatigue cracks, Acta Metallurgica et Materialia, vol.42, issue.4, pp.1413-1421, 1994.
DOI : 10.1016/0956-7151(94)90160-0

L. Edwards and &. H. Zhang, Investigation of small fatigue cracks???II. A plasticity based model of small fatigue crack growth, Acta Metallurgica et Materialia, vol.42, issue.4, pp.1423-1431, 1994.
DOI : 10.1016/0956-7151(94)90161-9

F. Erdogan and &. G. Sih, On the Crack Extension in Plates Under Plane Loading and Transverse Shear, Journal of Basic Engineering, vol.85, issue.4, pp.519-527, 1963.
DOI : 10.1115/1.3656897

S. Fadag, &. V. Mall, and . Jain, A finite element analysis of fretting fatigue crack growth behavior in

S. Fouvry, P. Kapsa, and &. L. Vincent, Analysis of sliding behaviour for fretting loadings: determination of transition criteria, Wear, vol.185, issue.1-2, pp.35-46, 1995.
DOI : 10.1016/0043-1648(94)06582-9

S. Fouvry, P. Kapsa, L. Vincent, &. K. Dang, and . Van, Theoretical analysis of fatigue cracking under dry friction for fretting loading conditions, Wear, vol.195, issue.1-2, pp.21-34, 1996.
DOI : 10.1016/0043-1648(95)06741-8

URL : https://hal.archives-ouvertes.fr/hal-00111563

S. Fouvry, Etude quantitatives des dégradations en fretting, 1997.

S. Fouvry, P. Kapsa, F. Sidoroff, and &. L. Vincent, Identification of the characteristic length scale for fatigue cracking in fretting contacts, Le Journal de Physique IV, vol.08, issue.PR8, pp.159-166, 1998.
DOI : 10.1051/jp4:1998820

]. S. Fouvry-00a, P. Fouvry, &. L. Kapsa, and . Vincent, Fretting-Wear and Fretting-Fatigue : Relation through a mapping concept Fretting fatigue : current technology and practices

]. S. Fouvry-00b, P. Fouvry, &. L. Kapsa, and . Vincent, A multiaxial fatigue analysis of fretting contact taking into account the size effect . Fretting fatigue : current technology and practices

]. Goh-06a, D. L. Goh, &. W. Mcdowell, and . Neu, Influence of Microstructure in Partial-Slip Fretting Contacts Based Upon Two-Dimensional Crystal Plasticity Simulations, Journal of Tribology, vol.128, issue.4, pp.735-744, 2006.
DOI : 10.1115/1.2345414

D. L. Goh, &. W. Mcdowell, and . Neu, Plasticity in polycrystalline fretting fatigue contacts, Journal of the Mechanics and Physics of Solids, vol.54, issue.2, pp.340-367, 2006.
DOI : 10.1016/j.jmps.2005.06.009

J. H. Arps, Effect of surface treatments on fretting fatigue of Ti?6Al?4V, International Journal of Fatigue, vol.29, issue.7, pp.1302-1310, 2007.

J. Patrick, &. Golden, J. Michael, and . Shepard, Life prediction of fretting fatigue with advanced surface treatments, The McEvily Symposium : Fatigue and Fracture of Traditional and Advanced Materials, pp.15-22, 2006.

]. H. Gough and &. V. Pollard, The strength of metals under combined alternating stresses, Proceedings of the Institute of Mecanical Engineers, pp.1-103, 1935.
DOI : 10.1243/PIME_PROC_1935_131_008_02

]. H. Gough, H. V. Pollard, and &. W. Clenshaw, Some expriments on the resistance of metals to fatigue under combined stresses, Aeronautical Research Council, Report and Memoranda, issue.2522, p.141, 1951.

D. A. Hills, D. Nowell, and &. A. Sackfield, Mechanics of elastic contacts, 1993.

D. Hills, P. Kelly, D. Dai, and &. A. Korsunsky, Solution of Crack Problems: The Distributed Dislocation Technique, Journal of Applied Mechanics, vol.65, issue.2, 1996.
DOI : 10.1115/1.2789094

X. M. Kong, N. Schluter, and &. W. Dahl, Effect of triaxial stress on mixed-mode fracture, Engineering Fracture Mechanics, vol.52, issue.2, pp.379-388, 1995.
DOI : 10.1016/0013-7944(94)00228-A

U. Krupp, Fatigue crack propagation in metals and alloys, 2007.
DOI : 10.1002/9783527610686

M. Riedler, Simulation of Stage I-Short Crack Propagation in Forged Ti6Al4V, Procedia Engineering, vol.2, pp.1701-1709, 2010.

&. L. Dubourg, S. B. Vincent, and . Lee, A theoretical model for the prediction of initial growth angles and sites of fretting fatigue cracks Evaluation of Theories on Mutiaxial Fatigue With Discriminating Specimens, Tribology International, vol.30, issue.6, pp.391-400, 1980.

S. B. Lee, A Criterion for Fully Reversed Out-of-Phase Torsion and Bending, ASTM STP, vol.853, pp.553-568, 1985.
DOI : 10.1520/STP36242S

J. Lemaitre and &. J. Chaboche, Mécanique des matériaux solides, 1996.

H. G. De-lorenzi, 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

D. Christopher, S. Lykins, &. Mall, and . Vinod-jain, An evaluation of parameters for predicting fretting fatigue crack initiation, International Journal of Fatigue, vol.22, issue.8, pp.703-716, 2000.

]. J. Madge, S. B. Leen, and &. P. Shipway, A combined wear and crack nucleation???propagation methodology for fretting fatigue prediction, International Journal of Fatigue, vol.30, issue.9, pp.1509-1528, 2008.
DOI : 10.1016/j.ijfatigue.2008.01.002

]. L. Méric-91b, P. Méric, &. G. Poubanne, and . 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

R. D. Mindlin, Compliance of Elastic Bodies in Contact, Journal of Applied Mechanics, vol.16, pp.259-268, 1949.
DOI : 10.1007/978-1-4613-8865-4_24

R. D. Mindlin and &. H. Deresiewicz, Elastic Spheres in Contact Under Varying Oblique Forces, Journal of Applied Mechanics, vol.20, pp.327-344, 1953.
DOI : 10.1007/978-1-4613-8865-4_35

]. W. Morris, M. R. James, and &. O. Buck, Growth rate models for short surface cracks in AI 2219-T851, Metallurgical Transactions A, vol.7, issue.1, pp.57-64, 1981.
DOI : 10.1007/BF02648508

N. Moës, J. Dolbow, and &. T. 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

S. Munoz, H. Proudhon, J. Dominguez, and &. S. Fouvry, Prediction of the crack extension under fretting wear loading conditions, International Journal of Fatigue, vol.28, issue.12, pp.1769-1779, 2006.
DOI : 10.1016/j.ijfatigue.2006.01.002

S. Naboulsi and &. S. Mall, Fretting fatigue crack initiation behavior using process volume approach and finite element analysis, Tribology International, vol.36, issue.2, pp.121-131, 2003.
DOI : 10.1016/S0301-679X(02)00139-1

]. A. Navarro and &. R. De-los-rios, Short and long fatigue crack growth: A unified model, Philosophical Magazine A, vol.17, issue.1, pp.15-36, 1988.
DOI : 10.1007/BF02654397

]. H. Proudhon-05a and . Proudhon, Identification des mécanismes de fissuration dans un alliage d'alluminium sollicité en fretting et en fatigue, 2005.

H. Proudhon, S. Fouvry, and &. Buffière, A fretting crack initiation prediction taking into account the surface roughness and the crack nucleation process volume, International Journal of Fatigue, vol.27, issue.5, pp.569-579, 2005.
DOI : 10.1016/j.ijfatigue.2004.09.001

URL : https://hal.archives-ouvertes.fr/hal-00436855

H. Proudhon, J. Buffière, and &. S. Fouvry, Characterisation of fretting fatigue damage using synchrotron X-ray micro-tomography, The Fourth International Symposium on Fretting Fatigue, pp.1106-1113, 2006.
DOI : 10.1016/j.triboint.2006.02.047

URL : https://hal.archives-ouvertes.fr/hal-00436155

H. Proudhon, S. Fouvry, and &. G. Yantio, Determination and prediction of the fretting crack initiation: introduction of the (P, Q, N) representation and definition of a variable process volume, International Journal of Fatigue, vol.28, issue.7, pp.707-713, 2006.
DOI : 10.1016/j.ijfatigue.2005.09.005

URL : https://hal.archives-ouvertes.fr/hal-00333260

H. Proudhon, J. Buffière, and &. S. Fouvry, Three-dimensional study of a fretting crack using synchrotron X-ray micro-tomography, Engineering Fracture Mechanics, vol.74, issue.5, pp.782-793, 2007.
DOI : 10.1016/j.engfracmech.2006.06.019

URL : https://hal.archives-ouvertes.fr/hal-00434185

H. Proudhon and &. S. Basseville, Finite element analysis of fretting crack propagation, Engineering Fracture Mechanics, vol.78, issue.4, pp.685-694, 2011.
DOI : 10.1016/j.engfracmech.2010.11.016

URL : https://hal.archives-ouvertes.fr/hal-00567222

]. M. Rahman, S. Tanimoto, D. Yonekura, and &. R. Murakami, Influence of the substrate bias voltage on fretting fatigue behavior of CrN film

S. Suresh, Fatigue of Materials The Edinburgh Building, 1998.

L. Susmel, R. Tovo, and &. P. Lazzarin, The mean stress effect on the high-cycle fatigue strength from a multiaxial fatigue point of view, International Journal of Fatigue, vol.27, issue.8, pp.928-943, 2003.
DOI : 10.1016/j.ijfatigue.2004.11.012

M. P. Szolwinski and &. T. Farris, Mechanics of fretting fatigue crack formation, Wear, vol.198, issue.1-2, pp.93-107, 1996.
DOI : 10.1016/0043-1648(96)06937-2

M. P. Szolwinski, J. F. Matlik, and &. T. Farris, Effects of HCF loading on fretting fatigue crack nucleation, International Journal of Fatigue, vol.21, issue.7, pp.671-677, 1999.
DOI : 10.1016/S0142-1123(99)00028-6

S. Taira, K. Tanaka, and &. Y. Nakai, A model of crack-tip slip band blocked by grain boundary, Mechanics Research Communications, vol.5, issue.6, pp.375-381, 1978.
DOI : 10.1016/0093-6413(78)90014-9

K. Tanaka, Y. Akiniwa, Y. Nakai, and &. R. Wei, Modelling of small fatigue crack growth interacting with grain boundary, Engineering Fracture Mechanics, vol.24, issue.6, pp.803-819, 1986.
DOI : 10.1016/0013-7944(86)90266-3

H. Tian and &. Saka, Finite element analysis of interface cracking in sliding contacts, Wear, vol.155, issue.1, pp.163-182, 1991.
DOI : 10.1016/0043-1648(92)90116-P

L. Vincent, Y. Berthier, M. Dubourg, and &. M. Godet, Mechanics and materials in fretting, Wear, vol.153, issue.1, pp.135-148, 1992.
DOI : 10.1016/0043-1648(92)90266-B

B. Weber, Fatigue multiaxiale des structures industrielles sous chargement quelconque, 1999.