M. F. Acken, W. E. Singer, and W. P. Davey, X-Ray Study of Rubber Structure, Industrial & Engineering Chemistry, vol.24, issue.1, pp.54-57, 1932.
DOI : 10.1021/ie50265a015

P. Albouy, G. Guillier, D. Petermann, A. Vieyres, O. Sanseau et al., A stroboscopic X-ray apparatus for the study of the kinetics of strain-induced crystallization in natural rubber, Polymer, vol.53, issue.15, pp.3313-3324, 2012.
DOI : 10.1016/j.polymer.2012.05.042

P. Albouy, J. Marchal, and J. Et-rault, Chain orientation in natural rubber, Part I: The inverse yielding effect, The European Physical Journal E, vol.40, issue.3, pp.247-259, 2005.
DOI : 10.1140/epje/i2004-10145-6

A. Amin, A. Lion, and P. Et-höfer, Effect of temperature history on the mechanical behaviour of a filler-reinforced NR/BR blend: literature review and critical experiments, ZAMM, vol.1, issue.5, pp.90347-369, 2010.
DOI : 10.1002/zamm.200900365

S. Amnuaypornsri, J. Sakdapipanich, S. Toki, B. S. Hsiao, N. Ichikawa et al., Strain-Induced Crystallization of Natural Rubber: Effect of Proteins and Phospholipids, Rubber Chemistry and Technology, vol.81, issue.5, pp.753-766, 2008.
DOI : 10.5254/1.3548230

N. André, G. Cailletaud, and R. Et-piques, Haigh diagram for fatigue crack initiation prediction of natural rubber components, Kautschuk und Gummi Kunststoffe, vol.52, issue.2, pp.120-123, 1999.

G. Andreini, P. Straffi, and S. Et-cotugno, COMPARISON OF SINE VERSUS PULSE WAVEFORM EFFECTS ON FATIGUE CRACK GROWTH BEHAVIOR OF NR, SBR, AND BR COMPOUNDS, Rubber Chemistry and Technology, vol.83, issue.4, pp.391-403, 2010.
DOI : 10.5254/1.3512954

G. Andreini, P. Straffi, S. Cotugno, G. Gallone, and G. Et-polacco, CRACK GROWTH BEHAVIOR OF STYRENE-BUTADIENE RUBBER, NATURAL RUBBER, AND POLYBUTADIENE RUBBER COMPOUNDS: COMPARISON OF PURE-SHEAR VERSUS STRIP TENSILE TEST, Rubber Chemistry and Technology, vol.86, issue.1, pp.132-145, 2013.
DOI : 10.5254/rct.13.88957

E. Andrews, Spherulite Morphology in Thin Films of Natural Rubber, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol.270, issue.1341, pp.232-241, 1341.
DOI : 10.1098/rspa.1962.0214

A. Andriyana, Définition d'une nouvelle grandeur prédictive pour la durée de vie en fatigue des matériaux élastomères, Thèse de doctorat, 2006.

L. Ban, W. Hess, and L. Et-papazian, New Studies of Carbon???Rubber Gel, Rubber Chemistry and Technology, vol.47, issue.4, pp.858-894, 1974.
DOI : 10.5254/1.3540470

N. Bekkedahl and L. Wood, Crystallization of Vulcanized Rubber, Rubber Chemistry and Technology, vol.14, issue.2, pp.347-355, 1941.
DOI : 10.5254/1.3540030

S. Beurrot, Micromécanismes de propagation de fissure de fatigue dans le caoutchouc naturel (NR) et un caoutchouc synthétique (SBR), Thèse de master, 2007.

S. Beurrot, B. Huneau, and E. Et-verron, In situ SEM study of fatigue crack growth mechanism in carbon black-filled natural rubber, Journal of Applied Polymer Science, vol.117, pp.1260-1269, 2010.
URL : https://hal.archives-ouvertes.fr/hal-01387690

S. Beurrot, B. Huneau, and E. Et-verron, Strain-induced crystallization of natural rubber subjected to biaxial loading conditions as revealed by X-ray diffraction éditeurs : Constitutive Models for Rubber VII, pp.23-28, 2011.

S. Beurrot-borgarino, Cristallisation sous contrainte du caoutchouc naturel en fatigue et sous sollicitation multiaxiale, Thèse de doctorat, Ecole Centrale de Nantes. 14 citations pages 63, pp.92-129, 2012.
URL : https://hal.archives-ouvertes.fr/tel-00835499

S. Beurrot-borgarino, B. Huneau, E. Verron, and P. Et-rublon, Strain-induced crystallization of carbon black-filled natural rubber during fatigue measured by in situ synchrotron X-ray diffraction, International Journal of Fatigue, vol.47, issue.41, pp.1-7, 2013.
DOI : 10.1016/j.ijfatigue.2012.07.001

S. Beurrot-borgarino, B. Huneau, E. Verron, P. Rublon, D. Thiaudière et al., In-situ synchrotron X-ray diffraction study of strain induced crystallization of natural rubber during fatigue tests, Plastics, Rubber and Composites, vol.2, issue.7, pp.41290-295, 2012.

H. Bouasse and Z. Et-carrière, Sur les courbes de traction du caoutchouc vulcanis??, Annales de la facult?? des sciences de Toulouse Math??matiques, vol.5, issue.3, pp.257-283, 1903.
DOI : 10.5802/afst.205

K. Bruning, K. Schneider, S. V. Roth, and G. Heinrich, Kinetics of Strain-Induced Crystallization in Natural Rubber Studied by WAXD: Dynamic and Impact Tensile Experiments, Macromolecules, vol.45, issue.19, pp.7914-7919, 2012.
DOI : 10.1021/ma3011476

F. Bueche, Molecular Basis for The Mullins Effect, Rubber Chemistry and Technology, vol.34, issue.2, pp.493-505, 1961.
DOI : 10.5254/1.3540224

F. Bueche, Mullins effect and rubber???filler interaction, Journal of Applied Polymer Science, vol.5, issue.15, pp.259-273, 1962.
DOI : 10.1002/app.1961.070051504

C. Bunn, Molecular Structure and Rubber-Like Elasticity. I. The Crystal Structures of Formula Gutta-Percha, Rubber and Polychloroprene, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol.180, issue.980, pp.40-66, 1942.
DOI : 10.1098/rspa.1942.0024

S. Cadwell, R. Merril, C. Sloman, and F. Et-yost, Dynamic Fatigue Life of Rubber, Rubber Chemistry and Technology, vol.13, issue.2, pp.304-315, 1940.
DOI : 10.5254/1.3539515

N. Candau, L. Chazeau, J. Chenal, C. Gauthier, J. Ferreira et al., Characteristic time of strain induced crystallization of crosslinked natural rubber, Polymer, vol.53, issue.13, pp.532540-2543, 2012.
DOI : 10.1016/j.polymer.2012.04.027

Q. Demassieux, Fissuration en mode III dans les caoutchoucs. Limite d'endurance et propagation, Thèse de master, p.104, 2012.

J. Diani, B. Fayolle, and P. Et-gilormini, A review on the Mullins effect, European Polymer Journal, vol.45, issue.3, pp.601-612, 2009.
DOI : 10.1016/j.eurpolymj.2008.11.017

URL : https://hal.archives-ouvertes.fr/hal-00773015

J. Donnet, Nano and microcomposites of polymers elastomers and their reinforcement, Composites Science and Technology, vol.63, issue.8, pp.1085-1088, 2003.
DOI : 10.1016/S0266-3538(03)00028-9

J. Dumbleton and B. Et-bowles, X-ray determination of crystallinity and orientation in poly(ethylene terephtalate) Journal of Polymer Science Part A-2 : Polymer Physics, pp.951-958, 1966.

D. Dunning and P. Et-pennells, Effect of Strain on Rate of Crystallization of Natural Rubber, Rubber Chemistry and Technology, vol.40, issue.5, pp.1381-1393, 1967.
DOI : 10.5254/1.3539150

A. Einstein, A new determination of molecular dimensions, Annalen der Physik, vol.19, issue.289, pp.289-306, 1906.

P. Flory, Principles of Polymer Chemistry, 1953.

A. Gent, P. Lindley, and ;. A. Thomas, Cut growth and fatigue of rubbers. I. The relationship between cut growth and fatigue, Journal of Applied Polymer Science, vol.8, issue.1, pp.292-300, 1965.
DOI : 10.1002/app.1964.070080129

P. H. Geubelle and W. G. Et-knauss, Finite strains at the tip of a crack in a sheet of hyperelastic material: I. Homogeneous case, Journal of Elasticity, vol.44, issue.2, pp.61-98, 1994.
DOI : 10.1007/BF00115539

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.163-198, 1921.
DOI : 10.1098/rsta.1921.0006

A. Guinier, Théorie et technique de la radiocristallographie. Dunod, p.77, 1964.

E. Guth, Theory of Filler Reinforcement, Journal of Applied Physics, vol.16, issue.1, pp.596-604, 1945.
DOI : 10.1063/1.1707495

E. Guth and O. Et-gold, On the hydrodynamic theory of the viscosity of suspensions, Physical Review, vol.53, issue.24, pp.322-343, 1938.

S. Hainsworth, An environmental scanning electron microscopy investigation of fatigue crack initiation and propagation in elastomers, Polymer Testing, vol.26, issue.1, pp.60-70, 2007.
DOI : 10.1016/j.polymertesting.2006.08.007

R. Harbour, A. Fatemi, and W. V. Et-mars, The Effect of a Dwell Period on Fatigue Crack Growth Rates in Filled SBR and NR, Rubber Chemistry and Technology, vol.80, issue.5, pp.838-853, 2007.
DOI : 10.5254/1.3539420

R. J. Harbour, A. Fatemi, and W. V. Et-mars, Fatigue crack growth of filled rubber under constant and variable amplitude loading conditions. Fatigue and Fracture of Engineering Materials and Structures, pp.640-652, 2007.

J. Harwood, L. Mullins, and A. Et-payne, Stress Softening in Natural Rubber Vulcanizates. Part II. Stress Softening Effects in Pure Gum and Filler Loaded Rubbers, Rubber Chemistry and Technology, vol.39, issue.4, pp.814-822, 1966.
DOI : 10.5254/1.3547145

J. Harwood and A. Et-payne, Stress softening in natural rubber vulcanizates. Part III. Carbon black-filled vulcanizates, Journal of Applied Polymer Science, vol.10, issue.2, pp.1544-1552, 1966.
DOI : 10.1002/app.1966.070100212

F. Hild and S. Et-roux, Digital Image Correlation: from Displacement Measurement to Identification of Elastic Properties - a Review, Strain, vol.334, issue.Srie I, pp.69-80, 2006.
DOI : 10.1111/j.1475-1305.2006.00258.x

URL : https://hal.archives-ouvertes.fr/hal-00013816

F. Hild and S. Et-roux, A software for "finite-element" displacement field measurements by digital image correlation, LMT Cachan. Cité, p.148, 2008.

B. Holownia, Effect of carbon black on the elastic constant of elastomers. Rubber Industry, pp.157-160, 1974.

B. Huneau, STRAIN-INDUCED CRYSTALLIZATION OF NATURAL RUBBER: A REVIEW OF X-RAY DIFFRACTION INVESTIGATIONS, Rubber Chemistry and Technology, vol.84, issue.3, pp.425-452, 2011.
DOI : 10.5254/1.3601131

URL : https://hal.archives-ouvertes.fr/hal-01007326

Y. Ikeda, A. Kato, J. Shimanuki, S. Kohjiya, M. Tosaka et al., WAXD Measurements, Rubber Chemistry and Technology, vol.80, issue.2, pp.251-264, 2007.
DOI : 10.5254/1.3539405

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

S. Kaang, Y. Jin, Y. Huh, W. Lee, and W. Et-im, A test method to measure fatigue crack growth rate of rubbery materials, Polymer Testing, vol.25, issue.3, pp.347-352, 2006.
DOI : 10.1016/j.polymertesting.2005.12.005

J. Katz, R??ntgenspektrographische Untersuchungen am gedehnten Kautschuk und ihre m??gliche Bedeutung f??r das Problem der Dehnungseigenschaften dieser Substanz, Die Naturwissenschaften, vol.25, issue.19, pp.410-416, 1925.
DOI : 10.1007/BF01560952

S. Kim and S. Et-lee, Effect of Crosslink Structures on the Fatigue Crack Growth Behavior of NR Vulcanizates with Various Aging Conditions, Rubber Chemistry and Technology, vol.67, issue.4, pp.649-661, 1994.
DOI : 10.5254/1.3538700

M. Komura, K. Nakajima, T. Nishi, T. Ikehara, and Q. Et-zhaobin, Pulsed NMR Studies on Long-Term Crystallization Behavior and Melting Process of Natural Rubber under Elongation, Rubber Chemistry and Technology, vol.81, issue.1, pp.110-120, 2008.
DOI : 10.5254/1.3548191

G. Lake, Mechanical Fatigue of Rubber, Rubber Chemistry and Technology, vol.45, issue.1, pp.309-328, 1972.
DOI : 10.5254/1.3544709

G. Lake, Fatigue and Fracture of Elastomers, Rubber Chemistry and Technology, vol.68, issue.3, pp.435-460, 1995.
DOI : 10.5254/1.3538750

G. Lake and P. Et-lindley, The mechanical fatigue limit for rubber, Journal of Applied Polymer Science, vol.9, issue.4, pp.1233-1251, 1965.
DOI : 10.1002/app.1965.070090405

L. Cam and J. , Endommagement en fatigue des élastomères, Thèse de doctorat, Ecole Centrale de Nantes. 2 citations pages, pp.32-129, 2005.

L. Cam, J. Huneau, B. Verron, E. Et-gornet, and L. , Mechanism of Fatigue Crack Growth in Carbon Black Filled Natural Rubber, Macromolecules, vol.37, issue.13, pp.5011-5017, 2004.
DOI : 10.1021/ma0495386

URL : https://hal.archives-ouvertes.fr/hal-01492140

J. Leblanc, Rubber???filler interactions and rheological properties in filled compounds, Progress in Polymer Science, vol.27, issue.4, pp.627-687, 2002.
DOI : 10.1016/S0079-6700(01)00040-5

D. Lee and J. Et-donovan, Microstructural Changes in the Crack Tip Region of Carbon-Black-Filled Natural Rubber, Rubber Chemistry and Technology, vol.60, issue.5, pp.910-923, 1987.
DOI : 10.5254/1.3536164

K. Legorju-jago and C. Et-bathias, Fatigue initiation and propagation in natural and synthetic rubbers, International Journal of Fatigue, vol.24, issue.2-4, pp.85-92, 2002.
DOI : 10.1016/S0142-1123(01)00062-7

G. Li and J. L. Et-koenig, A Review of Rubber Oxidation, Rubber Chemistry and Technology, vol.78, issue.3, pp.355-390, 2005.
DOI : 10.5254/1.3547889

P. Lindley, Relation between hysteresis and the dynamic crack growth resistance of natural rubber, International Journal of Fracture, vol.9, issue.2, pp.449-462, 1973.

A. Lion, On the large deformation behaviour of reinforced rubber at different temperatures, Journal of the Mechanics and Physics of Solids, vol.45, issue.11-12, pp.1805-1834, 1997.
DOI : 10.1016/S0022-5096(97)00028-8

J. Long, W. Singer, and W. Davey, Fibering of Rubber - Time Lag and Its Relation to Rubber Structure, Industrial & Engineering Chemistry, vol.26, issue.5, pp.543-547, 1934.
DOI : 10.1021/ie50293a017

J. H. Magill, Crystallization and Morphology of Rubber, Rubber Chemistry and Technology, vol.68, issue.3, pp.507-539, 1995.
DOI : 10.5254/1.3538753

J. Marchal, Cristallisation des caoutchoucs chargés et non chargés sous contrainte : Effet sur les chaînes amorphes, Thèse de doctorat, pp.16-92, 2006.

W. Mars and A. Et-fatemi, A literature survey on fatigue analysis approaches for rubber, International Journal of Fatigue, vol.24, issue.9, pp.949-961, 2002.
DOI : 10.1016/S0142-1123(02)00008-7

W. V. Mars and A. Et-fatemi, Ratio on Fatigue of Strain Crystallizing Rubbers, Rubber Chemistry and Technology, vol.76, issue.5, pp.1241-1258, 2003.
DOI : 10.5254/1.3547800

W. V. Mars and A. Et-fatemi, Factors that Affect the Fatigue Life of Rubber: A Literature Survey, Rubber Chemistry and Technology, vol.77, issue.3, pp.391-412, 2004.
DOI : 10.5254/1.3547831

A. Medalia, Effect of Carbon Black on Dynamic Properties of Rubber Vulcanizates, Rubber Chemistry and Technology, vol.51, issue.3, pp.437-523, 1978.
DOI : 10.5254/1.3535748

Y. Merckel, Experimental characterization and modeling of the mechanical behavior of filled rubbers under cyclic loading conditions, Thèse de doctorat, pp.19-104, 2012.
URL : https://hal.archives-ouvertes.fr/tel-00736624

L. Meunier, G. Chagnon, D. Favier, L. Orgéas, and P. Vacher, Mechanical experimental characterisation and numerical modelling of an unfilled silicone rubber, Polymer Testing, vol.27, issue.6, pp.765-777, 2008.
DOI : 10.1016/j.polymertesting.2008.05.011

J. Mitchell, Rapid stress-induced crystallization in natural rubber, Journal of Polymer Science Part A- Polymer Physics, vol.2, issue.610, pp.1689-1703, 1968.

L. Mullins, Effect of Stretching on the Properties of Rubber, Rubber Chemistry and Technology, vol.21, issue.2, pp.281-300, 1948.
DOI : 10.5254/1.3546914

L. Mullins, Softening of Rubber by Deformation, Rubber Chemistry and Technology, vol.42, issue.1, pp.339-362, 1969.
DOI : 10.5254/1.3539210

S. Murakami, K. Senoo, S. Toki, and S. Et-kohjiya, Structural development of natural rubber during uniaxial stretching by in situ wide angle X-ray diffraction using a synchrotron radiation, Polymer, vol.43, issue.7, pp.432117-2120, 2002.
DOI : 10.1016/S0032-3861(01)00794-7

S. Mzabi, Caractérisation et analyse des mécanismes de fracture en fatigue des élastomères chargés, Thèse de doctorat, pp.34-148, 2010.

S. Mzabi, D. Berghezan, S. Roux, F. Hild, and C. Et-creton, A critical local energy release rate criterion for fatigue fracture of elastomers, Journal of Polymer Science Part B: Polymer Physics, vol.6, issue.92, pp.491518-1524, 2011.
DOI : 10.1002/polb.22338

C. Neogi, A. K. Bhowmick, and S. P. Basu, Fatigue Behaviour of Carbon Black Filled Rubber Vulcanizates at High Temperature and under Swollen Conditions, Journal of Elastomers and Plastics, vol.24, issue.2, pp.96-114, 1992.
DOI : 10.1177/009524439202400203

Y. Nie, B. Wang, G. Huang, L. Qu, P. Zhang et al., Relationship between the material properties and fatigue crack-growth characteristics of natural rubber filled with different carbon blacks, Journal of Applied Polymer Science, vol.71, issue.53, pp.3441-3447, 2010.
DOI : 10.1002/app.32098

L. Nielsen, Simple Theory of Stress Strain Properties of Filled Polymers, Rubber Chemistry and Technology, vol.40, issue.3, pp.801-805, 1967.
DOI : 10.5254/1.3539094

B. Omnes, Modélisation micromécanique du comportement d'élastomères chargés, Thèse de doctorat, p.15, 2007.

I. C. Papadopoulos, A. G. Thomas, and J. J. Et-busfield, Rate transitions in the fatigue crack growth of elastomers, Journal of Applied Polymer Science, vol.51, issue.3, pp.1900-1910, 2008.
DOI : 10.1002/app.28086

S. Poompradub, M. Tosaka, S. Kohjiya, Y. Ikeda, S. Toki et al., Mechanism of strain-induced crystallization in filled and unfilled natural rubber vulcanizates, Journal of Applied Physics, vol.97, issue.10, pp.97103529-103529, 2005.
DOI : 10.1063/1.1900927

J. Ramier, Comportement mécanique d'élastomères chargés Influence de l'adhésion charge-polymère, influence de la morphologie, Thèse de doctorat, Institut National des Sciences Appliquées de Lyon. 2 citations pages, pp.15-16, 2004.

S. Ran, D. Fang, X. Zong, B. S. Hsiao, B. Chu et al., Structural changes during deformation of Kevlar fibers via on-line synchrotron SAXS/WAXD techniques, Polymer, vol.42, issue.4, pp.1601-1612, 2001.
DOI : 10.1016/S0032-3861(00)00460-2

J. Rault, J. Marchal, P. Judeinstein, and P. Et-albouy, H NMR Study, Macromolecules, vol.39, issue.24, pp.398356-8368, 2006.
DOI : 10.1021/ma0608424

J. Rault, J. Marchal, P. Judeinstein, and P. A. Et-albouy, Chain orientation in natural rubber, Part II: 2H-NMR study, The European Physical Journal E, vol.37, issue.3, pp.243-61, 2006.
DOI : 10.1140/epje/i2006-10064-6

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

R. Rivlin and A. Thomas, Rupture of rubber. I. Characteristic energy for tearing, Journal of Polymer Science, vol.10, issue.3, pp.291-318, 1953.
DOI : 10.1002/pol.1953.120100303

J. Rouvière, A. Bennani, D. Pachoutinsky, J. Besson, and S. Et-cantournet, Influence of mechanical and fatigue loading on crystallization of carbon blackfilled natural rubber, Constitutive Models for Rubber V, pp.323-326, 2007.

S. Trabelsi, P. Albouy, and J. Et-rault, Stress-Induced Crystallization Properties of Natural and Synthetic CIS-Polyisoprene, Rubber Chemistry and Technology, vol.77, issue.2, pp.303-316, 2004.
DOI : 10.5254/1.3547825

S. Trabelsi, P. Albouy, and J. Et-rault, Stress-Induced Crystallization around a Crack Tip in Natural Rubber, Macromolecules, vol.35, issue.27, pp.10054-10061, 2002.
DOI : 10.1021/ma021106c

S. Trabelsi, P. Albouy, and J. Et-rault, Crystallization and Melting Processes in Vulcanized Stretched Natural Rubber, Macromolecules, vol.36, issue.20, pp.7624-7639, 2003.
DOI : 10.1021/ma030224c

S. Trabelsi, P. Albouy, and J. Et-rault, Effective Local Deformation in Stretched Filled Rubber, Macromolecules, vol.36, issue.24, pp.369093-9099, 2003.
DOI : 10.1021/ma0303566

E. Verron, Modélisation du comportement des structures et des matériaux elastomères . Mémoire d'habilitation à diriger des recherches, p.18, 2003.

T. Vilgis, Time scales in the reinforcement of elastomers, Polymer, vol.46, issue.12, pp.4223-4229, 2005.
DOI : 10.1016/j.polymer.2005.02.060

N. Yan, H. Xia, Y. Zhan, and G. Et-fei, New Insights into Fatigue Crack Growth in Graphene-Filled Natural Rubber Composites by Microfocus Hard-X-Ray Beamline Radiation, Macromolecular Materials and Engineering, vol.37, issue.1, pp.38-44, 2013.
DOI : 10.1002/mame.201200044

D. Young, Dynamic Property and Fatigue Crack Propagation Research on Tire Sidewall and Model Compounds, Rubber Chemistry and Technology, vol.58, issue.4, pp.785-805, 1985.
DOI : 10.5254/1.3536093

D. Young, Fatigue crack propagation in elastomer compounds : effects of strain rate, temperature, strain level and oxidation, Rubber Chemistry and Technology, vol.59, issue.109, pp.809-825, 1986.

D. Young, Application of Fatigue Methods Based on Fracture Mechanics for Tire Compound Development, Rubber Chemistry and Technology, vol.63, issue.4, pp.567-581, 1990.
DOI : 10.5254/1.3538274