. .. Experimental, 2.4 Crack tip localization and effective SIFs estimation

. .. Results, 3.6 Estimation of friction and contact stresses

, Conclusions on mixed mode I + II experiments

. .. Proposed-approach, 178 7.2 Crack growth predictions for sequential mixed-mode I + II & III experiments

, Conclusions & perspectives for the proposed approach

, Cast3m (castem), 2019.

L. Abanto-bueno, J. Bueno, and J. Lambros, Investigation of crack growth in functionally graded materials using digital image correlation, Eng Fract Mech, vol.69, pp.1695-1711, 2002.

M. Akama, Fatigue crack growth under mixed loading of tensile and in-plane shear modes, QR of RTRI, vol.44, pp.65-71, 2003.

K. Akama, M. Akama, and A. Kiuchi, Long co-planar mode III fatigue crack growth under non-proportional mixed mode loading in rail steel, J rail and rapid transit, vol.226, pp.489-500, 2012.

. Amestoy, Déviation infinitésimale d'une fissure dans une direction arbitraire, C.R.A.S, vol.289, pp.99-102, 1979.

[. Ancellotti, Fluid Pressurization and Entrapment Effects on the SIFs of Cracks produced under lubricated Rolling-Sliding Contact Fatigue, Procedia structural integrity, vol.2, pp.3098-3108, 2017.

P. Arnaud-;-arnaud, Etude expérimentale et numérique de l'usure et de son influence sur les mécanismes de fissuration en fretting et fretting fatigue, 2018.

. Arnaud, A numerical simulation of fretting wear profile taking account of the evolution of third body layer, pp.1475-1488, 2017.

[. Barker, Determining K and related stress-field parameters from displacement fields, Experimental Mechanics, vol.25, pp.399-407, 1985.

Z. P. Bazant and L. F. Estenssoro, Surface singularity and crack propagation, Int J Solids Struct, vol.15, pp.405-426, 1979.

, Rapport d'enquête technique sur le déraillement du train 5941 survenu le 25 février 2006 à Saint Flour (15), 2006.

, Rapport d'enquête technique sur la rupture multiple de rail, franchie en vitesse par des trains le 26 novembre 2013 à Carbonne (31), 2016.

, Rapport d'enquête technique sur les multiples ruptures de rail au passage du train 72049 entre Pons et Jonzac (17) le 13 décembre 2016, 2017.

[. Beretta, Fatigue crack propagation and threshold for shallow micro-cracks under out-of-phase multiaxial loading in a gear steel, Eng Fract Mech, vol.77, pp.1835-1848, 0195.

G. Bertolino and V. Doquet, Derivation of effective stress intensity factors from measured crack face displacements, Eng Fract Mech, vol.76, pp.1574-1588, 2009.

[. Blaysat, Interface debonding characterization by image correlation integrated with Double Cantilever Beam kinematics, 2015.

, Int J Solids Struct, vol.55, pp.79-91

[. Bogdanski, S. Lewicki-;-bogdanski, and P. Lewicki, 3D model of liquid entrapment mechanism for rolling contact fatigue cracks in rails, Wear, vol.265, pp.1356-1362, 2008.

[. Bogdanski, Numerical modelling of a 3d rail rcf 'squat'-type crack under operating load, FFEMS, vol.21, pp.923-935, 1998.

P. Bold and . Bonniot, Mixed mode II and III fatigue crack growth in a rail steel, Int J Fatigue, vol.115, pp.42-52, 1990.

[. Bonniot, Determination of effective stress intensity factors under mixed-mode from digital image correlation fields in presence of contact stresses and plasticity, 2019.
URL : https://hal.archives-ouvertes.fr/hal-02359068

R. Branco and F. V. Antunes, Fatigue crack growth under mixed loading of tensile and in-plane shear modes, Eng Fract Mech, p.75, 2003.

[. Branco, Influence of through-thickness crack shape on plasticity induced crack closure, FFEMS, vol.31, pp.209-220, 2008.

[. Brown, Fatigue at notches subjected to reversed torsion and static axial loads, FFEMS, vol.8, issue.3, pp.243-258, 1985.

B. Biempica, Nonlinear analysis of residual stresses in a rail manufacturing process by FEM, Applied Mathematical Modelling, vol.33, pp.34-53, 2009.

[. Cardoso, Wear numerical assessment for partial slip fretting fatigue conditions, Tribology International, vol.136, pp.508-523, 2019.
URL : https://hal.archives-ouvertes.fr/hal-02102120

. Carlson, R. Kardomateas-;-carlson, and G. Kardomateas, Effects of compressive load excursions on fatigue crack growth, Int J Fatigue, vol.16, pp.141-146, 1994.

[. Christodoulou, Fatigue and fracture behavior of pearlitic Grade 900A steel used in railway applications, Theoretical and Applied Fracture Mechanics, vol.83, pp.51-59, 2016.

P. Dahlin and M. Olsson, The effect of plasticity on incipient mixed-mode fatigue crack growth, FFEMS, vol.26, pp.577-588, 2003.

P. Dahlin and M. Olsson, Reduction of mode I fatigue crack growth rate due to occasional mode II loading, Int J Fatigue, vol.26, pp.1083-1093, 2004.

K. Dang-van, A comprehensive approach for modeling fatigue and fracture of rails, Sciences Technique Armement, p.47, 1973.
URL : https://hal.archives-ouvertes.fr/hal-00525603

[. Van, A comprehensive approach for modeling fatigue and fracture of rails, Eng Fract Mech, vol.76, pp.2626-2636, 2009.
URL : https://hal.archives-ouvertes.fr/hal-00525603

N. Matos, P. Matos, and D. Nowell, On the accurate assessment of crack opening and closing stresses in plasticity-induced fatigue crack closure problems, Eng Fract Mech, vol.74, pp.1579-1601, 2007.

P. De-matos and D. Nowell, The influence of the Poisson's ratio and corner point singularities in three-dimensional plasticity-induced fatigue crack closure: A numerical study, Int J Fatigue, vol.30, pp.1930-1943, 2008.

N. Matos, P. Matos, and D. Nowell, Experimental and numerical investigation of thickness effects in plasticity-induced fatigue crack closure, Int J Fatigue, vol.31, pp.1795-1804, 2009.

[. Decreuse, History effect in fatigue crack growth under mixed-mode loading conditions, Int J Fatigue, vol.31, pp.1733-1741, 2009.
URL : https://hal.archives-ouvertes.fr/hal-00417887

[. Decreuse, A novel approach to model mixed mode plasticity at crack tip and crack growth. Experimental validations using velocity fields from digital image correlation, Int J Fatigue, vol.42, pp.271-283, 2012.
URL : https://hal.archives-ouvertes.fr/hal-01576656

[. Destuynder, Some remarks on elastic fracture mechanics, Journal de mécanique théorique et appliquée, vol.2, pp.113-135, 1983.

[. Donzella, The competitive role of wear and RCF in a rail steel, Eng Fract Mech, vol.72, pp.287-308, 2005.

[. Doquet, Influence of the loading path on fatigue crack growth under mixed-mode loading, Int J Fracture, vol.159, pp.219-232, 2009.
URL : https://hal.archives-ouvertes.fr/hal-00424431

V. Doquet and G. Bertolino, A material and environment-dependent criterion for the prediction of fatigue crack paths in metallic structures, Eng Fract Mech, vol.75, pp.3399-3412, 2008.
URL : https://hal.archives-ouvertes.fr/hal-00315973

B. Doquet, V. Doquet, and G. Bertolino, Local approach to fatigue cracks bifurcation, Int J Fatigue, vol.30, pp.942-950, 2008.

[. Doquet, 3D shear-mode fatigue crack growth in maraging steel and Ti-6Al-4V, Int J Fracture, vol.165, pp.61-76, 2010.
URL : https://hal.archives-ouvertes.fr/hal-00501850

[. Doquet, Plasticity and asperity-induced fatigue crack closure under mixed-mode loading, Int J Fatigue, vol.32, pp.1612-1619, 2010.
URL : https://hal.archives-ouvertes.fr/hal-00497694

[. Doquet, Combined tension and torsion cyclic tests inside a scanning electron microscope, Proc. 4th Int. Conf. Biaxial/multiaxial Fatigue, vol.2, pp.19-26, 1994.

V. Doquet and J. Frelat, Branch crack development from the flank of a fatigue crack propagating in mode II, FFEMS, vol.24, issue.3, pp.207-214, 2001.
URL : https://hal.archives-ouvertes.fr/hal-00111334

P. Doquet, V. Doquet, and S. Pommier, Fatigue crack growth under non-proportional mixed-mode loading in ferritic-pearlitic steel, FFEMS, vol.27, pp.1051-1060, 2004.
URL : https://hal.archives-ouvertes.fr/hal-00111416

[. Dylewski, The tridimensional gradient of microstructure in worn rails -Experimental characterization of plastic deformation accumulated by RCF, pp.50-59, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01993208

. Erdogan, F. Ratwani-;-erdogan, and M. Ratwani, A circumferential crack in a cylindrical shell under torsion, International Journal of Fracture Mechanics, vol.8, pp.87-95, 1972.

. Erdogan, F. Sih-;-erdogan, and G. C. Sih, On the crack extension in plates under plane loading and transverse shear, Basic engineering, vol.85, pp.519-525, 1963.

D. Fletcher and J. Beynon, A simple method of stress intensity factor calculation for inclined fluid-filled surface-breaking cracks under contact rolling, Proc Instn Mech Engrs, vol.213, pp.299-304, 1999.

[. Fletcher, Investigating fluid penetration of rolling contact fatigue cracks in rails using a newly developed full-scale test facility, Proceedings of the Institution of Mechanical Engineers, vol.221, issue.1, pp.35-44, 2007.

[. Fremy, Load path effect on fatigue crack propagation in I + II + III mixed mode conditions -Part 2: Finite element analyses, Int J Fatigue, vol.62, pp.113-118, 2014.
URL : https://hal.archives-ouvertes.fr/hal-01636530

[. Fremy, Load path effect on fatigue crack propagation in I + II + III mixed mode conditions -Part 1: Experimental investigations, Int J Fatigue, vol.62, pp.104-112, 2014.
URL : https://hal.archives-ouvertes.fr/hal-01636545

[. Gray, Roughness-induced crack closure: An explanation for microstructurally sensitive fatigue crack growth, Metallurgical transactions, vol.14, pp.421-433, 1983.

[. Gross, Stress intensity factors for a single-edge-notch tension specimen by boundary collocation of a stress function, p.2395, 1964.

M. Gross, T. S. Gross, and D. A. Mendelsohn, On the effect of crack face contact and friction due to fracture surface roughness in edge cracks subjected to external shear, Eng Fract Mech, vol.31, pp.405-420, 1988.

M. Gross, T. S. Gross, and D. A. Mendelsohn, Mode I stress intensity factors induced by fracture surface roughness under pure mode III loading: Application to the effect of loading modes on stress corrosion crack growth, Metallurgical Transactions A, vol.20, issue.10, pp.1989-1999, 1989.

[. Gross, Fracture Surface Interference in Shear-II. Experimental Measurements of Crack-Tip Displacement Field under Mode-II Loading in 7075-T6 A1, Acta Metallurgica et Materialia, vol.43, pp.901-906, 1995.

[. Hamam, Stress intensity factor gauging by digital image correlation: Application in cyclic fatigue, Strain, pp.181-192, 2006.
URL : https://hal.archives-ouvertes.fr/hal-00322199

[. Hamam, Variable amplitude fatigue crack growth, experimental results and modeling, Int J Fatigue, vol.26, pp.1634-1646, 2007.
URL : https://hal.archives-ouvertes.fr/hal-01636575

[. Harilal, A linear least squares approach for evaluation of crack tip stress field parameters using DIC, Optics and Lasers in Engineering, vol.75, pp.95-102, 2015.

[. Hellier, A practical mixed Mode II/III fatigue test rig, Int J Fatigue, vol.9, pp.95-101, 1987.

[. Hellier, A finite element and fatigue threshold study of shelling in heavy haul rails, Wear, vol.144, pp.289-306, 1991.

[. Hellier, On the mode II fatigue threshold for mild steel, Int J Fract, vol.167, pp.267-272, 2011.

W. Highsmith, S. Highsmith, and G. W. Woodruff, Crack path determination for nonproportional mixed-mode fatigue, 2009.

. Hos, Measurements of strain fields around crack tips under proportional and non-proportional mixed-mode fatigue loading, Int J Fatigue, 2016.

[. Hosdez, Plastic zone evolution during fatigue crack growth: Digital image correlation coupled with finite elements method, Int J Solids Struct, vol.171, pp.92-102, 2019.
URL : https://hal.archives-ouvertes.fr/hal-02309146

P. Hourlier, F. Hourlier, and A. Pineau, Propagation of fatigue cracks under polymodal loading, FFEMS, vol.5, issue.4, pp.287-302, 1982.

, Definitive guidelines on the use of different rail grades, 2009.

S. Jägg and B. Scholtes, Crack-tip residual stresses and crack propagation in cyclically-loaded specimens under different loading modes, Zeitschrift für Metallkunde, vol.96, pp.770-774, 2005.

[. Jessop, 3D characterization of rolling contact fatigue crack networks, Wear, pp.392-400, 2016.

J. Kalker-;-kalker, The computation of three-dimensional rolling contact with dry friction, Int. Journal for Numerical Methods in Engineering, vol.14, pp.1293-1307, 1979.

M. Kaneta and Y. Murakami, Effects of oil hydraulic pressure onsurface crack growth in rolling/sliding contact, Tribology International, vol.20, pp.210-217, 1987.

A. Kapoor-;-kapoor, Wear by plastic ratchetting, WEAR, vol.212, pp.119-130, 1997.

A. P. Kfouri-;-kfouri, A crack in a linear-elastic material under mode II loading, vol.22, pp.445-448, 1999.

[. Kim, C. S. Kim, J. , C. S. , and K. , Fatigue crack growth behavior of rail steel under mode I and mixed mode loadings, Materials Science and Engineering, vol.338, pp.191-201, 2002.

[. Lachambre, Extraction of stress intensity factors for 3D small fatigue cracks using digital volume correlation and X-ray tomography, Int J Fatigue, vol.71, pp.3-10, 2015.
URL : https://hal.archives-ouvertes.fr/hal-01537225

P. Ladevèze, Nonlinear Computationnal Structural Mechanics -New Approaches and Non-Incremental Methods of Calculation, 1999.

[. Larijani, The effect of anisotropy on crack propagation in pearlitic rail steel, WEAR, vol.314, pp.57-68, 2014.

[. Leblond, J. Frelat-;-leblond, and J. Frelat, Crack kinking from an initially closed crack, IJSS, vol.37, pp.1595-1614, 2000.

[. Lemaitre, Mécanique des matériaux solides, 2009.

C. Lemaitre, J. Lemaitre, and J. Chaboche, Mechanics of solid materials, 1994.

T. M. Lenkovs'kyi, Influence of the Friction of Crack Faces on the Cyclic Crack-Growth Resistance of 65G Steel Under Mode II Loading, Materials Science, vol.50, issue.5, pp.682-686, 2015.

. Lin, Characterisation of fatigue crack tip field in the presence of significant plasticity, Theor Appl Fract Mec, p.103, 2019.

[. Llavori, A coupled crack initiation and propagation numerical procedure for combined fretting wear and fretting fatigue lifetime assessment, Theoretical and Applied Fracture Mechanics, vol.101, pp.294-305, 2019.

. Lopez-crespo, The stress intensity of mixed mode cracks determined by digital image correlation, The Journal of Strain Analysis for Engineering Design, vol.43, pp.769-780, 2008.

. Lopez-crespo, Some experimental observations on crack closure and crack-tip plasticity, FFEMS, vol.32, pp.418-429, 2009.

[. Mai, Numerical simulation of rolling contact fatigue crack growth in rails with the rail bending and the frictional contact, Eng Fract Mech, vol.174, pp.196-206, 2017.

[. Maierhofer, Oxide induced crack closure in the near threshold regime: The effect of oxide debris release, Int J. Fatigue, vol.117, pp.21-26, 2018.

[. Maouche, On a new method of evaluation of the inelastic state due to moving contact, WEAR, pp.139-147, 1997.
URL : https://hal.archives-ouvertes.fr/hal-00111576

[. Mathieu, Identication of a crack propagation law by digital image correlation, Int J Fatigue, vol.36, pp.146-154, 2012.

M. , Fatigue crack growth rate of two pearlitic rail steels, Eng Fract Mech, vol.138, pp.63-72, 2015.

[. Merati, On the mixed Mode II/III fatigue threshold behaviour for aluminium alloys 2014-T6 and 7075-T6, FFEMS, vol.35, pp.2-12, 2012.

J. C. Newman, A Crack-Closure Model for Predicting Fatigue Crack Growth under Aircraft Spectrum Loading, 1981.

R. Newman, J. C. Newman, and I. S. Raju, An empirical stress-intensity factor equation for the surface crack, Eng Fract Mech, vol.15, pp.185-192, 1981.

. Nguyen-tajan, T. M. Nguyen-tajan, and C. Unfschilling, On a new method of evaluation of the inelastic state due to moving contact, WCRR World congress of railway research, 2011.

, Train Derailment at Hatfield. Technical report, Office of Rail Regulation, 2006.

P. Paris and F. Erdogan, A critical analysis of crack propagation laws, Basic engineering, vol.85, pp.528-533, 1963.

Y. Park and I. Bernstein, The process of crack initiation and effective grain size for cleavage fracture in pearlitic eutectoid steel, Metallurgical Transactions A, vol.10, pp.1653-1664, 1979.

T. Paul, S. K. Paul, and S. Tarafder, Cyclic plastic deformation response at fatigue crack tips, Int J Pressure Vessels and Piping, vol.101, pp.81-90, 2013.

C. Pinna and V. Doquet, Preferred fatigue crack propagation mode in a M250 maraging steel loaded in shear, FFEMS, vol.22, issue.3, pp.173-183, 1999.
URL : https://hal.archives-ouvertes.fr/hal-00111621

R. Plank and G. Kuhn, Fatigue crack propagation under non-proportional mixed mode loading, Eng Fract Mech, vol.62, pp.203-229, 1999.

J. Pokluda and R. Pippan, Can pure mode III fatigue loading contribute to crack propagation in metallic materials? FFEMS, vol.28, pp.179-185, 2008.

[. Pokluda, Near-threshold behaviour of shear-mode fatigue cracks in metallic materials, FFEMS, vol.37, pp.232-254, 2014.

[. Pokluda, Straightforward comparison of fatigue crack growth under modes II and III, Int J Fatigue, vol.30, pp.1498-1506, 2008.

[. Pokorný, Crack closure in near-threshold fatigue crack propagation in railway axle steel EA4T, Eng Fract Mech, vol.185, pp.2-19, 2017.

S. Pommier and P. Bompard, Bauschinger effect of alloys and plasticityinduced crack closure: a finite element analysis. FFEMS, vol.23, pp.129-139, 2000.
URL : https://hal.archives-ouvertes.fr/hal-01636598

S. Pommier and R. Hamam, Incremental model for fatigue crack growth based on a displacement partitioning hypothesis of mode I elastic-plastic displacement fields. FFEMS, vol.30, pp.582-598, 2007.
URL : https://hal.archives-ouvertes.fr/hal-01636582

[. Pommier, Influence of a negative R ratio on the creep-fatigue behaviour of the N18 nickel base superalloy, FFEMS, vol.20, issue.1, pp.93-107, 1997.
URL : https://hal.archives-ouvertes.fr/hal-01636601

J. Réthoré, A fully integrated noise robust strategy for the identification of constitutive laws from digital images, Int J Numer Meth Eng, vol.84, pp.631-660, 2010.

[. Réthoré, Estimation of mixedmode stress intensity factors using digital image correlation and an interaction integral, Int J Fracture, vol.132, issue.1, pp.65-79, 2005.

[. Réthoré, , 2013.

, Robust identification of elasto-plastic constitutive law parameters from digital images using 3D kinematics, Int J Solids Struct, vol.50, pp.73-85

[. Réthoré, Noise-robust stress intensity factor determination from kinematic field measurements, Eng Fract Mech, vol.75, pp.3763-3781, 2007.

P. Rodesch, Prise en compte de Contraintes Résiduelles dans la fatigue de composants ferroviaires, 2013.

S. Roux and F. Hild, Stress intensity factor measurements from digital image correlation: Post-processing and integrated approaches, Int J Fracture, vol.140, issue.1-4, pp.141-157, 2006.
URL : https://hal.archives-ouvertes.fr/hal-00013818

R. Sander, M. Sander, and H. A. Richard, Finite element analysis of fatigue crack growth with interspersed mode I and mixed mode overloads, Int J Fatigue, vol.27, pp.905-913, 2005.

H. Sehitoglu, Crack opening and closure in fatigue, Eng Fract Mech, vol.21, pp.329-339, 1985.

L. Severstal and L. Severstal, Rails et laminés pour superstructures de chemin de fer, 2009.

S. Simon-;-simon, De la dynamique ferroviaire à l'accommodation microstructurale du rail, 2014.
URL : https://hal.archives-ouvertes.fr/tel-01135274

. Simon, Tribological characterization of rail squat defects, Wear, vol.297, issue.1-2, pp.926-942, 2013.
URL : https://hal.archives-ouvertes.fr/hal-00764214

[. Smith, A stress-strain function for the fatigue of metals, J Mater, vol.5, pp.767-778, 1970.

M. Smith and R. Smith, The formation of spherical wear debris in mode II fatigue cracks, Wear, vol.76, pp.105-128, 1982.

M. C. Smith and R. A. Smith, Toward an understanding of mode II fatigue crack growth, Basic Questions in Fatigue, vol.1, pp.260-280, 1988.

[. Stanzl, Fatigue crack growth under combined mode I and mode II loading, STP1020-EB Fracture Mechanics: Perspectives and Directions (Twentieth Symposium), ASTM STP 1020, pp.479-496, 1989.

S. Suresh and R. Ritchie, A Geometric Model for Fatigue Crack Closure Induced by Fracture Surface Roughness, METALLURGICAL TRANSACTIONS A, vol.13, pp.1627-1631, 1982.

[. Suresh, Oxide-induced crack closure: an explanation for near-threshold corrosion fatigue crack growth behavior, Metallurgical Transactions A, vol.12, pp.1435-1443, 1981.

A. M. Tabatabaei, Fracture and fatigue crack growth characterization of conventional and head hardened railway rail steels, 2014.

[. Tada, The stress analysis of cracks, 1973.

K. Tanaka-;-tanaka, Fatigue crack propagation from a crack inclined to the cyclic tensile axis, Eng Fract Mech, vol.6, pp.493-507, 1974.

G. Tarantino, Shear-mode propagation of short cracks under rolling contact fatigue, 2011.

[. Tarantino, A comparison of Mode III threshold under simple shear and RCF conditions, Eng Fract Mech, vol.78, issue.8, pp.1742-1755, 2011.

[. Tong, Full-field characterization of a fatigue crack: Crack closure revisited, J. R, vol.41, pp.2130-2139, 2018.

[. Tong, A model for sliding mode crack closure part I: theory for pure mode II loading, Eng Fract Mech, vol.52, issue.495, pp.599-611, 1995.

[. Tong, A model for sliding mode crack closure part II: mixed mode I and II loading and application, Eng Fract Mech, vol.52, issue.4, pp.613-623, 1995.

Y. ;. Topper, T. Topper, and M. Yu, The effect of overloads on threshold and crack closure, Int J Fatigue, vol.7, pp.159-164, 1985.

B. Trollé, Simulation multi-échelles de la propagation des fissures de fatigue dans les rails, 2014.

E. Tschegg, Sliding mode crack closure and mode III fatigue crack growth in mild steel, Acta Metallurgica, vol.31, issue.9, pp.1323-1330, 1983.

. Tschegg, E. Tschegg, and S. Stanzl, The significance of sliding mode crack closure on mode iii fatigue crack growth. Basic questions in fatigue, vol.1, pp.214-232, 1988.

E. K. Tschegg, Mode III and Mode I fatigue crack propagation behaviour under torsional loading, Journal of Materials Science, vol.18, issue.6, pp.1604-1614, 1983.

. Vojtek, Experimental evidence of a common local mode II growth mechanism of fatigue cracks loaded in modes II, III and II+III in niobium and titanium, Int J Fatigue, vol.92, pp.470-477, 2002.

[. Vojtek, Near-threshold propagation of mode II and mode III fatigue cracks in ferrite and austenite, Acta Materialia, vol.61, pp.4625-4635, 2013.

[. Vojtek, Progress in understanding of intrinsic resistance to shear-mode fatigue crack growth in metallic materials, Int J Fatigue, vol.89, pp.36-42, 2015.

[. Vojtek, Intrinsic Behaviour of Modes II, III and Mixed Mode II+III Fatigue Cracks in Metallic Materials, 2016.

[. Vojtek, Analysis of fatigue crack propagation under mixed mode II + III in ARMCO iron, Int J Fatigue, vol.76, pp.47-52, 2015.

[. Vojtek, Quantitative dependence of oxide-induced crack closure on air humidity for railway axle steel, Int J. Fatigue, vol.123, pp.213-224, 2019.

[. Vormwald, Crack tip displacement fields measured by digital image correlation for evaluating variable mode-mixity during fatigue crack growth, Int J Fatigue, vol.115, pp.53-66, 2018.

[. Wong, A branch criterion for shallow angled rolling contact fatigue cracks in rails, Wear, vol.191, pp.45-53, 1996.

[. Wong, Fatigue crack growth rates under sequential mixed-mode I and II loading cycles, FFEMS, vol.23, pp.667-674, 2000.

[. Wong, Two measurement techniques for determining effective stress intensity factors, FFEMS, vol.23, pp.659-666, 2000.

[. Yates, Quantifying crack tip displacement fields with DIC, Eng Fract Mech, vol.77, pp.2063-2076, 2010.

[. Yoneyama, Evaluating mixed-mode stress intensity factors from full-field displacement fields obtained by optical methods, Eng Fract Mech, vol.74, p.203, 2007.

[. Zanganeh, Locating the crack tip using displacement field data: A comparative study, Strain, vol.49, pp.102-115, 2013.

[. Zhang, Analysis of the effects of compressive stresses on fatigue crack propagation rate, Int J Fatigue, vol.29, pp.1751-1756, 2007.

X. Zhao, Dynamic wheel/rail contact at singular defects with application to Squats, 2012.

, Conclusions Des trajets de chargement subis par les fissures de type Squats ont été simulés en utilisant une chaine de calcul développée par SNCF. Ces trajets sont de mode I + II + III quasi séquentiels

, Un outil de post-traitement de champs de déplacements a été développé afin de suivre des essais représentatifs du chargement subis par ces fissures. Ni le mode I seul, ni les modes de cisaillement seuls n'ont permis d'expliquer la fissuration dans les rails

, Des essais de mode mixte non-proportionnels I + II ont été effectués, dont le trajet et la vitesse de propagation ont pu être prédits avec des critères simples basés sur les FICs effectifs (loi de type Paris & ?K ef f eq

, Cependant, la détermination de ces FICs effectifs à partir des valeurs nominales s'est révélée complexe. Le challenge pour les applications industrielles n'est donc pas seulement de trouver le critère de bifurcation et la loi de propagation les plus adéquates, mais également de prendre en compte le frottement (lié aux aspérités)

, Afin d'estimer ces FICs effectifs, une approche simplifiée a été proposée et validée sur des essais de mode I + II & III séquentiels

, Cette approche reste cependant à valider par rapport au retour d'expérience de SNCF, et des essais menés sur un rail

, pourrait certainement améliorer les prédictions des FICs effectifs. La prise en compte des effets de fermeture induits par l'oxydation pourrait également s'avérer utile, 2018.

D. Abanto-bueno, J. Lambros, and J. , la chaine de calcul finalisée permettra d'optimiser les intervalles de maintenance, de quantifier l'influence des conditions de circulation (géométrie du rail, raideur de la voie, météo, type de train...) sur la propagation des fissures et de proposer des conditions optimisées, Eng Fract Mech, pp.1695-1711, 2002.

M. Akama, Fatigue crack growth under mixed loading of tensile and in-plane shear modes, QR of RTRI, vol.44, pp.65-71, 2003.

P. Arnaud-;-arnaud, Etude expérimentale et numérique de l'usure et de son influence sur les mécanismes de fissuration en fretting et fretting fatigue, 2018.

P. Arnaud and S. Fouvry, A dynamical FEA fretting wear modeling taking into account the evolution of debris layer, WEAR, vol.412, pp.92-108, 2018.
URL : https://hal.archives-ouvertes.fr/hal-02347642

P. Bold and . Bonniot, Determination of effective Stress Intensity Factors under mixed-mode from DIC fields in presence of contact stresses and plasticity, 1990.

P. Dahlin and M. Olsson, The effect of plasticity on incipient mixed-mode fatigue crack growth, FFEMS, vol.26, pp.577-588, 2003.

[. Fremy, Load path effect on fatigue crack propagation in I + II + III mixed mode conditions -Part 1 : Experimental investigations, Int J Fatigue, vol.62, pp.104-112, 2014.
URL : https://hal.archives-ouvertes.fr/hal-01636545

[. Mai, Numerical simulation of rolling contact fatigue crack growth in rails with the rail bending and the frictional contact, Eng Fract Mech, vol.174, pp.196-206, 2017.

[. Pokorný, Crack closure in near-threshold fatigue crack propagation in railway axle steel EA4T, Eng Fract Mech, vol.185, pp.2-19, 2017.

S. Roux and F. Hild, Stress intensity factor measurements from digital image correlation : Post-processing and integrated approaches, Int J Fracture, vol.140, issue.1-4, pp.141-157, 2006.
URL : https://hal.archives-ouvertes.fr/hal-00013818

[. Tada, The stress analysis of cracks, 1973.

B. Trollé-;-trollé, Simulation multi-échelles de la propagation des fissures de fatigue dans les rails, 2014.

[. Wong, Fatigue crack growth rates under sequential mixed-mode I and II loading cycles, FFEMS, vol.23, pp.667-674, 2000.

[. Yoneyama, Evaluating mixed-mode stress intensity factors from full-field displacement fields obtained by optical methods, Eng Fract Mech, vol.74, pp.1399-1412, 2007.