47 3.2.1 Premier et second principe de la thermodynamique, p.47 ,
étudier le comportement cyclique thermomécanique des élastomères. À cette fin, une campagne d'essais a été lancée par PSA en partenariat avec la société TRELLEBORG Une deuxième campagne a aussi été réalisée à Bristol en partenariat avec l'University of the West of England (UWE) pour étudier les effets multiaxiaux. Dans ce cadre, j'ai défini, construit et utilisé un banc d'essai biaxial lors d'un séjour de trois mois sur place. Ce chapitre débute par une présentation des modélisations hyperélastiques. En effet, nous motivons le choix de la modélisation hyperélastique dans la suite de ce mémoire, Puis, nous étudions l'influence de la température sur le comportement stabilisé pour les deux campagnes d'essais. Notons Chapitre 9 ,
169 8.3.1 Description des mécanismes d'endommagement par fatigue, p.175 ,
183 8.6.1 Influence du vieillissement sur la propagation de fissure 184 8.6.2 Influence du vieillissement sur l'amorçage de fissure, p.186 ,
The effect of minimum stress and stress amplitude on the fatigue life of non strain crystallising elastomers, Materials & Design, vol.26, issue.3, pp.239-245, 2005. ,
DOI : 10.1016/j.matdes.2004.02.020
Thermodynamics of elasticity of natural rubber, Transactions of the Faraday Society, vol.59, pp.2493-2502, 1963. ,
DOI : 10.1039/tf9635902493
Sur les solides hyperélastiques à compressibilité induite par l'endommagement. Compte Rendu à l, Académie des Sciences, série II b, vol.324, issue.5, pp.281-288, 1997. ,
DOI : 10.1016/s1251-8069(99)80035-9
Définition d'une nouvelle grandeur prédictive pour la durée de vie en fatigue des matériaux élastomères, Thèse de doctorat, 2006. ,
Prediction of fatigue life improvement in natural rubber using configurational stress, International Journal of Solids and Structures, vol.44, issue.7-8, pp.2079-2092, 2007. ,
DOI : 10.1016/j.ijsolstr.2006.06.046
URL : https://hal.archives-ouvertes.fr/hal-01007193
Equations of state for natural and synthetic rubber-like materials. I. Unaccelerated natural soft rubber, The Journal of Physical Chemistry, vol.46, issue.8, pp.826-840, 1942. ,
DOI : 10.1021/j150422a005
A new unconditionally stable fractional step method for non-linear coupled thermomechanical problems, International Journal for Numerical Methods in Engineering, vol.26, issue.4, pp.737-766, 1992. ,
DOI : 10.1002/nme.1620350408
A priori stability estimates and unconditionally stable product formula algorithms for nonlinear coupled thermoplasticity, International Journal of Plasticity, vol.9, issue.6, pp.749-782, 1993. ,
DOI : 10.1016/0749-6419(93)90036-P
A three-dimensional constitutive model for the large stretch behavior of rubber elastic materials, Journal of the Mechanics and Physics of Solids, vol.41, issue.2, pp.389-412, 1993. ,
DOI : 10.1016/0022-5096(93)90013-6
URL : https://hal.archives-ouvertes.fr/hal-01390807
Effect of ageing on the ability of natural rubber to strain crystallise, Constitutive Models for Rubber III, pp.79-84, 2003. ,
Convexity conditions and existence theorems in nonlinear elasticity, Archive for Rational Mechanics and Analysis, vol.8, issue.4, pp.337-403, 1977. ,
DOI : 10.1007/BF00279992
Discontinuous Equilibrium Solutions and Cavitation in Nonlinear Elasticity, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol.306, issue.1496, pp.557-611, 1982. ,
DOI : 10.1098/rsta.1982.0095
Fatigue Crack Growth Damage in Elastomeric Materials, Fatigue and Fracture Mechanics : 27th Volume, ASTM STP 1296, pp.505-513, 1997. ,
DOI : 10.1520/STP16251S
Efficient numerical integration on the surface of a sphere, Zeitschrift für Angewandte Mathematik und Mechanik, pp.37-49, 1986. ,
Fatigue of Rubber, Rubber Chemistry and Technology, vol.37, issue.5, pp.1341-1364, 1964. ,
DOI : 10.5254/1.3540402
Finite element modeling of heat transfers in viscoelastic materials for large deformations. Numerical Heat Transfer, pp.37-49, 1997. ,
Micromécanisme de propagation de fissure de fatigue dans le caoutchouc naturel (NR) et un caoutchouc synthétique (SBR) Stage de master, École Centrale de Nantes. 5 citations paragraphes 8, 2007. ,
A thermo-viscoelastic model for elastomeric behaviour and its numerical application, Archive of Applied Mechanics (Ingenieur Archiv), vol.71, issue.12, pp.785-801, 2001. ,
DOI : 10.1007/s004190100191
URL : https://hal.archives-ouvertes.fr/hal-01236417
Modelling of a thermo-viscoelastic coupling for large deformations through finite element analysis, International Journal of Heat and Mass Transfer, vol.39, issue.18, pp.3911-3924, 1996. ,
DOI : 10.1016/0017-9310(96)00055-5
Evidence for the stress-thermal rule in an elastomer subjected to simple elongation, The Journal of Chemical Physics, vol.111, issue.15, pp.6965-6969, 1999. ,
DOI : 10.1063/1.479989
Modeling the Thermal State of Tires for Power Loss Calculations, SAE Technical Paper Series, 1981. ,
DOI : 10.4271/810163
A new propagation law for elastomers subjected to 3d arbitrary loadings Cité paragraphe a, Proceedings of the International conference SolMech2006, 2006. ,
Mullins effect and rubber???filler interaction, Journal of Applied Polymer Science, vol.5, issue.15, pp.271-281, 1961. ,
DOI : 10.1002/app.1961.070051504
Dynamic fatigue life of rubber, Industrial and engineering chemistry, vol.12, issue.1, pp.19-23, 1940. ,
Heat aging effects on the material property and the fatigue life of vulcanized natural rubber, and fatigue life prediction equations, Journal of Mechanical Science and Technology, vol.20, issue.10, pp.1229-124228, 2005. ,
DOI : 10.1007/BF02984044
Heat generation in aircraft tires, Computers and Structures, vol.20, pp.1-3, 1985. ,
Sur la résistance à la fatigue des métaux, Thèse de doctorat, 1971. ,
Rise of Temperature on Fast Stretching of Synthetics and Natural Rubbers, Industrial & Engineering Chemistry, vol.34, issue.11, pp.1340-1342, 1942. ,
DOI : 10.1021/ie50395a020
Rise of Temperature on Fast Stretching of Butyl Rubber, The Journal of Chemical Physics, vol.13, issue.1, pp.28-36, 1945. ,
DOI : 10.1063/1.1723964
Tear Strength of Carbon-Black-Filled Compounds, Rubber Chemistry and Technology, vol.69, issue.5, pp.834-850, 1996. ,
DOI : 10.5254/1.3538406
Contribution à l'étude du comportement élastique et de l'endommagement des matériaux élastomères, 1999. ,
On the Development of Volumetric Strain Energy Functions, Journal of Applied Mechanics, vol.67, issue.1, pp.17-20, 2000. ,
DOI : 10.1115/1.321146
Experimental research on the fatigue of natural rubber subjected to multiaxial loading, 7th ICBMFF -International Conference on Biaxial/Multiaxial Fatigue and Fracture, pp.323-328, 2004. ,
Tire Temperature and Rolling Resistance Prediction with Finite Element Analysis, Tire Science and Technology, vol.27, issue.1, pp.2-21, 1999. ,
DOI : 10.2346/1.2135974
Isotropy of Strain Energy Functions Which Depend Only on a Finite Number of Directional Strain Measures, Journal of Applied Mechanics, vol.61, issue.2, pp.284-289, 1994. ,
DOI : 10.1115/1.2901442
Introduction à la physique des polymères, 2002. ,
The Influence of Vacuole Formation on the Response and Failure of Filled Elastomers, Transactions of the Society of Rheology, vol.12, issue.2, pp.315-334, 1968. ,
DOI : 10.1122/1.549111
Engineering with rubber. How to design rubber components, 1992. ,
DOI : 10.3139/9783446428713
Effect of temperature on the ozone cracking of butyl rubbers, Journal of Polymer Science Part A-2: Polymer Physics, vol.5, issue.1, pp.157-164, 1967. ,
DOI : 10.1002/pol.1967.160050113
Internal Rupture of Bonded Rubber Cylinders in Tension, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol.249, issue.1257, pp.195-205, 1959. ,
DOI : 10.1098/rspa.1959.0016
Effect of Temperature and Oxygen on the Strength of Elastomers, Rubber Chemistry and Technology, vol.64, issue.1, pp.96-10720, 1991. ,
DOI : 10.5254/1.3538545
Effect of temperature on ozone cracking of rubbers, Journal of Polymer Science Part A: General Papers, vol.3, issue.4, pp.1473-482, 1965. ,
DOI : 10.1002/pol.1965.100030416
Failure processes in elastomers at or near a rigid spherical inclusion, Journal of Materials Science, vol.17, issue.6, pp.1947-1956, 1984. ,
DOI : 10.1007/BF00550265
A New Constitutive Relation for Rubber, Rubber Chemistry and Technology, vol.69, issue.1, pp.59-61, 1996. ,
DOI : 10.5254/1.3538357
-1,4-Polyisoprene, Rubber Chemistry and Technology, vol.71, issue.4, pp.668-678, 1998. ,
DOI : 10.5254/1.3538496
URL : https://hal.archives-ouvertes.fr/ujm-00440045
Cut growth and fatigue of rubbers. I. The relationship between cut growth and fatigue, Journal of Applied Polymer Science, vol.8, issue.1, pp.455-466, 1964. ,
DOI : 10.1002/app.1964.070080129
Cours De Mécanique Des Milieux Continus, 1973. ,
A description of a property of caoutchouc, or indian rubber. Memoirs of the Literary and Philosophical Society of Manchester, pp.288-295, 1805. ,
Un modèle Élasto-visco-plastique micro-physiquement motivé pour les élastomères chargés -caractérisation en fatigue, 8e COLLOQUE NATIONAL EN CAL- CUL DES STRUCTURES, pp.21-25, 2007. ,
Rupture of rubber. IV. Tear properties of vulcanizates containing carbon black, Journal of Polymer Science, vol.21, issue.98, pp.175-187, 1956. ,
DOI : 10.1002/pol.1956.120219802
Rupture of rubber. III. Determination of tear properties, Journal of Polymer Science, vol.18, issue.88, pp.189-200, 1955. ,
DOI : 10.1002/pol.1955.120188803
Hysteresis Losses in Rolling and Sliding Friction, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol.259, issue.1299, pp.480-207, 1961. ,
DOI : 10.1098/rspa.1961.0004
The friction of hard sliders on lubricated rubber : The importance of deformation losses, Proc. Phys. Soc. 71, pp.989-1001, 1958. ,
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, 1920. ,
DOI : 10.1098/rsta.1921.0006
Non???linear Hysteretic Characterization of Elastomers under Multi???axial Loading Conditions, Tire Science and Technology, vol.30, issue.1, pp.34-44, 2002. ,
DOI : 10.2346/1.2135246
-Polybutadiene, and a 50/50 Blend during Single and Repeated Extension, Rubber Chemistry and Technology, vol.69, issue.5, pp.807-818, 1996. ,
DOI : 10.5254/1.3538404
URL : https://hal.archives-ouvertes.fr/hal-01360284
The Mechanism of Carbon Black Reinforcement of SBR and NR Vulcanizates, Rubber Chemistry and Technology, vol.72, issue.5, pp.946-959, 1999. ,
DOI : 10.5254/1.3538844
Fatigue life analysis and predictions for NR and SBR under variable amplitude and multiaxial loading conditions, International Journal of Fatigue, vol.30, issue.7, 2007. ,
DOI : 10.1016/j.ijfatigue.2007.08.015
Fatigue crack orientation in NR and SBR under variable amplitude and multiaxial loading conditions, Journal of Materials Science, vol.28, issue.6, pp.1783-1794, 2008. ,
DOI : 10.1007/s10853-007-2398-8
A pseudo-elastic model for loading, partial unloading and reloading of particle-reinforced rubber, Zeitschrift fur Angewande Mathematik und Physik, p.608, 1966. ,
On constitutive inequalities for simple materials???I, Journal of the Mechanics and Physics of Solids, vol.16, issue.4, pp.229-242, 1968. ,
DOI : 10.1016/0022-5096(68)90031-8
Analyse thermomécanique par mesure de champs des elastomères, Thèse de doctorat, 2006. ,
Finite thermoelasticity of constrained elastomers subject to biaxial loading, Journal of Elasticity, vol.49, issue.3, pp.189-200, 1997. ,
DOI : 10.1023/A:1007472623454
Decomposition of the Deformation Gradient in Thermoelasticity, Journal of Applied Mechanics, vol.65, issue.2, pp.362-366, 1998. ,
DOI : 10.1115/1.2789063
On Some Thermo-Dynamic Properties of Solids, Philosophical Transactions of the Royal Society of London, vol.149, issue.0, pp.91-131, 1859. ,
DOI : 10.1098/rstl.1859.0005
Experimental Study and Finite Element Simulation of Heat Build-Up in Rubber Compounds with Application to Fracture, Rubber Chemistry and Technology, vol.76, issue.2, pp.386-405, 2003. ,
DOI : 10.5254/1.3547750
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
Beziehungen zwischen elastischen Konstanten und Dehnungsdoppelbrechung hochelastischer Stoffe, Kolloid-Zeitschrift, vol.101, issue.3, pp.248-271, 1942. ,
DOI : 10.1007/BF01793684
Cut growth and fatigue of rubbers. II. Experiments on a noncrystallizing rubber, Journal of Applied Polymer Science, vol.8, issue.2, pp.707-721, 1964. ,
DOI : 10.1002/app.1964.070080212
Fatigue and Fracture of Elastomers, Rubber Chemistry and Technology, vol.68, issue.3, pp.435-460, 1995. ,
DOI : 10.5254/1.3538750
The mechanical fatigue limit for rubber, Journal of Applied Polymer Science, vol.9, 1965. ,
Compressibility induced by damage in carbon black reinforced natural rubber, Constitutive Models for Rubber III, pp.273-281, 2003. ,
URL : https://hal.archives-ouvertes.fr/hal-00164380
Endommagement en fatigue des élastomères, Thèse de doctorat, Ecole Centrale de Nantes. 9 citations paragraphes 8, 2005. ,
Fatigue life of rubber components : 3d damage evolution from x-ray computed microtomography, Constitutive Models for Rubbers V. ECCMR, pp.173-178, 2007. ,
Microstructural Changes in the Crack Tip Region of Carbon-Black-Filled Natural Rubber, Rubber Chemistry and Technology, vol.60, issue.5, 1987. ,
DOI : 10.5254/1.3536164
Extension de l'approche x-fem aux grandes transformations pour la fissuration des milieux hyperélastiques incompressibles, Thèse de doctorat, 2006. ,
Relation betwenn hysteresis and the dynamic crack growth resistance of natural rubber, International Journal of Fracture, vol.9, issue.4, pp.449-462, 1973. ,
Non-Relaxing Crack Growth and Fatigue in a Non-Crystallizing Rubber, Rubber Chemistry and Technology, vol.47, issue.5, pp.1253-1264, 1974. ,
DOI : 10.5254/1.3540497
A physically based method to represent the thermo-mechanical behaviour of elastomers, Acta Mechanica, vol.75, issue.7, pp.1-25, 1997. ,
DOI : 10.1007/BF01178397
Étude du comportement mécanique et des mécanismes d'endommagement des élastomères en fatigue et fissuration par fatigue, Thèse de doctorat, 1991. ,
Decomposition of deformation and representation of the free energy function for isotropic thermoelastic solids, International Journal of Solids and Structures, vol.11, issue.7-8, pp.927-934, 1975. ,
DOI : 10.1016/0020-7683(75)90015-3
Constitutive theories based on the multiplicative decomposition of deformation gradient: Thermoelasticity, elastoplasticity, and biomechanics, Applied Mechanics Reviews, vol.57, issue.2, pp.95-108, 2004. ,
DOI : 10.1115/1.1591000
Tire Rolling Loss Computation with the Finite Element Method, Tire Science and Technology, vol.22, issue.4, pp.206-222, 1994. ,
DOI : 10.2346/1.2139542
Numerical investigation of the deformation characteristics and heat generation in pneumatic aircraft tires, Finite Elements in Analysis and Design, vol.23, issue.2-4, pp.241-263, 1996. ,
DOI : 10.1016/S0168-874X(96)80010-2
Numerical investigation of the deformation characteristics and heat generation in pneumatic aircraft tires, Finite Elements in Analysis and Design, vol.23, issue.2-4, pp.265-290, 1996. ,
DOI : 10.1016/S0168-874X(96)80011-4
Crystallization and Morphology of Rubber, Rubber Chemistry and Technology, vol.68, issue.3, pp.507-539, 1995. ,
DOI : 10.5254/1.3538753
Cristallisation des caoutchoucs chargés et non chargés sous contrainte : Effet sur les chaînes amorphes, Thèse de doctorat, 2006. ,
Ratio on Fatigue of Strain Crystallizing Rubbers, Rubber Chemistry and Technology, vol.76, issue.5, pp.1241-1258, 2003. ,
DOI : 10.5254/1.3547800
Multiaxial fatigue of rubber The University of Toledo. 6 citations paragraphes c, 2001. ,
Multiaxial fatigue of rubber: Part II: experimental observations and life predictions, Fatigue <html_ent glyph="@amp;" ascii="&"/> Fracture of Engineering Materials and Structures, vol.13, issue.6, pp.523-538, 2005. ,
DOI : 10.1177/0014485104039757
Sur la propagation de fissures dans les élastomères, Thèse de doctorat, École Polytechnique. 3 citations paragraphes c, 1998. ,
Heat Generation in Elastomer Compounds: Causes and Effects, Rubber Chemistry and Technology, vol.64, issue.3, pp.481-492, 1991. ,
DOI : 10.5254/1.3538565
Effect of Carbon-Black Loading and Crosslink Density on the Heat Build-Up in Elastomers, Rubber Chemistry and Technology, vol.64, issue.2, pp.269-284, 1991. ,
DOI : 10.5254/1.3538558
Analysis of a thermoviscoelastic model in large strain, Computers & Structures, vol.80, issue.27-30, pp.2085-2098, 2002. ,
DOI : 10.1016/S0045-7949(02)00246-8
URL : https://hal.archives-ouvertes.fr/hal-01236418
Entropic thermoelasticity at finite strains. Aspects of the formulation and numerical implementation, Computer Methods in Applied Mechanics and Engineering, vol.120, issue.3-4, pp.243-269, 1995. ,
DOI : 10.1016/0045-7825(94)00057-T
Cumulative damage in fatigue, Journal of Applied Mechanics, vol.12, pp.159-164, 1945. ,
Rapid stress-induced crystallization in natural rubber, Journal of Polymer Science Part A-2: Polymer Physics, vol.6, issue.10, pp.1689-1703, 1968. ,
DOI : 10.1002/pol.1968.160061001
Modélisation numérique du comportement mécanique de structures en élastomère : de l'élasticité à la thermo-visco-hyperélasticité, Thèse de doctorat, 2000. ,
Self heating and thermal failure of polymers sustaining a compressive cyclic loading, International Journal of Solids and Structures, vol.33, issue.23, pp.3439-3462, 1996. ,
DOI : 10.1016/0020-7683(95)00184-0
Theoretical Model for the Elastic Behavior of Filler-Reinforced Vulcanized Rubbers, Rubber Chemistry and Technology, vol.30, issue.2, pp.555-571, 1957. ,
DOI : 10.5254/1.3542705
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.2117-2120, 2002. ,
DOI : 10.1016/S0032-3861(01)00794-7
Large Deformation Isotropic Elasticity: On the Correlation of Theory and Experiment for Compressible Rubberlike Solids, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol.328, issue.1575, pp.567-583, 1972. ,
DOI : 10.1098/rspa.1972.0096
Large Deformation Isotropic Elasticity - On the Correlation of Theory and Experiment for Incompressible Rubberlike Solids, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol.326, issue.1567, pp.565-584, 1972. ,
DOI : 10.1098/rspa.1972.0026
Non-linear Elastic Deformations, 1984. ,
ON THE THERMOELASTIC MODELING OF RUBBERLIKE SOLIDS, Journal of Thermal Stresses, vol.12, issue.4, pp.533-557, 1992. ,
DOI : 10.5254/1.3538206
Aspects of the phenomenological theory of rubber thermoelasticity, Polymer, vol.28, issue.3, pp.379-385, 1987. ,
DOI : 10.1016/0032-3861(87)90189-3
Comportement en fatigue des élastomères Application aux structures antivibratoires pour l'automobile, Thèse de doctorat, École Centrale de Nantes. Cité paragraphe 8.3, 2005. ,
Crack initiation in natural rubber : experimental database and macroscopic observations, European Conference on Constitutive Models for Rubber III. London, pp.15-17, 2003. ,
URL : https://hal.archives-ouvertes.fr/hal-01004685
Heat generation of filled rubber vulcanizates and its relationship with vulcanizate network structures, European Polymer Journal, vol.36, issue.11, pp.2429-2436, 2000. ,
DOI : 10.1016/S0014-3057(00)00020-3
Thermodynamics of Rubber Elasticity, Journal of Chemical Education, vol.78, issue.2, pp.263-267, 2001. ,
DOI : 10.1021/ed078p263
Analytic stress-strain relationship for isotropic network model of rubber elasticity, 2000. ,
Structures élastomères sous chargement cyclique : comportement , fatigue, durée de vie, Thèse de doctorat, École Polytechnique, Palaiseau. 22 citations paragraphes 1, 2005. ,
Les polymères solides : amorphes, élastomères, semi-cristallins. Cépaduès-éditions, 2002. ,
H NMR Study, Macromolecules, vol.39, issue.24, pp.8356-8368, 2006. ,
DOI : 10.1021/ma0608424
A micromechanically motivated material model for the thermo-viscoelastic material behaviour of rubber-like polymers, International Journal of Plasticity, vol.19, issue.7, pp.909-940, 2003. ,
DOI : 10.1016/S0749-6419(02)00086-4
Theoritical and numerical aspects in the thermo-viscoelastic material behaviour of rubber-like polymer, Mechanics of Time-Dependent Materials, vol.1, issue.4, pp.357-396, 1998. ,
DOI : 10.1023/A:1009795431265
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
The relashionship between unniaxial and equibiaxial fatigue in gum and carbon black filled vulcanizates, 1977. ,
Comportement visco-hyperélastique endommageable d'élastomères SBR et PU : prévision de la durée de vie en fatigue, Thèse de doctorat, 2000. ,
Determination of heat transfer coefficient of rubber to air, Plastics, Rubber and Composites, vol.28, issue.2, pp.65-68, 1999. ,
DOI : 10.1002/app.1963.070070330
Prediction of hysteretic temperature increase in rubber components by finite element analysis, Plastics, Rubber and Composites, vol.14, issue.2, pp.69-73, 1999. ,
DOI : 10.5254/1.3539047
Prévision de la durée de vie en fatigue du NR, sous chargement multiaxial, 2001. ,
Crack initiation and propagation under multiaxial fatigue in a natural rubber, International Journal of Fatigue, vol.28, issue.1, pp.61-72, 2006. ,
DOI : 10.1016/j.ijfatigue.2005.03.006
URL : https://hal.archives-ouvertes.fr/hal-00157190
Mécanique des milieux continus, I et II. Les éditions de l'école polytechnique, Palaiseau. 2 citations paragraphes 2.1 et c, 2002. ,
A New Approach for the Thermomechanical Analysis of Tires by the Finite Element Method, Tire Science and Technology, vol.15, issue.4, pp.261-275, 1987. ,
DOI : 10.2346/1.2148793
Modeling Tire Energy Dissipation for Power Loss Calculations, SAE Technical Paper Series, 1981. ,
DOI : 10.4271/810162
Fatigue sous sollicitations d'amplitude variable. Méthode Rainflow de compatge des cycles, 1993. ,
Chemorheological response of elastomers at elevated temperatures: Experiments and simulations, Journal of the Mechanics and Physics of Solids, vol.53, issue.12, pp.2758-2793, 2005. ,
DOI : 10.1016/j.jmps.2005.07.004
Internal Energy Contribution to the Elasticity of Natural Rubber, Macromolecules, vol.2, issue.4, pp.358-364, 1969. ,
DOI : 10.1021/ma60010a008
Mechanical properties and durability of natural rubber compounds and composites, p.24, 2001. ,
A methodology for test time reduction in rubber part testing, Constitutive Models for Rubber III. ECCMR, pp.27-32, 2003. ,
Bestimmung der wärmeleitfähigkeit von kautschukvulkanisaten in abhängigkeit von der dehnung, Experimentelle Technik der Physik, vol.7, issue.1, pp.1-14, 1959. ,
Rupture of rubber. V. Cut growth in natural rubber vulcanizates, Journal of Polymer Science, vol.31, issue.123, pp.467-480, 1958. ,
DOI : 10.1002/pol.1958.1203112324
Tensile Rupture of Rubber, Rubber Chemistry and Technology, vol.43, issue.2, pp.222-228, 1970. ,
DOI : 10.5254/1.3547249
Strain-induced crystallization of natural rubber as detected real-time by wide-angle X-ray diffraction technique, Polymer, vol.41, issue.14, pp.5423-5429, 2000. ,
DOI : 10.1016/S0032-3861(99)00724-7
New Insights into Structural Development in Natural Rubber during Uniaxial Deformation by In Situ Synchrotron X-ray Diffraction, Macromolecules, vol.35, issue.17, pp.6578-6584, 2002. ,
DOI : 10.1021/ma0205921
An introduction to the terminology used in the carbon black industry, Constitutive Models for Rubber IV. ECCMR, pp.471-476, 2005. ,
Stress-Induced Crystallization around a Crack Tip in Natural Rubber, Macromolecules, vol.35, issue.27, 2002. ,
DOI : 10.1021/ma021106c
Crystallization and Melting Processes in Vulcanized Stretched Natural Rubber, Macromolecules, vol.36, issue.20, pp.7624-7639, 2003. ,
DOI : 10.1021/ma030224c
The elasticity of a network of long-chain molecules. I, Transactions of the Faraday Society, vol.39, pp.36-64, 1943. ,
DOI : 10.1039/tf9433900036
The elasticity of a network of long-chain molecules???II, Trans. Faraday Soc., vol.39, issue.0, pp.241-246, 1943. ,
DOI : 10.1039/TF9433900241
The Non-Linear Field Theories of Mechanics, second edition Edition, 1992. ,
The Strain???Energy Function of a Hyperelastic Material in Terms of the Extension Ratios, Journal of Applied Physics, vol.38, issue.7, pp.2997-3002, 1967. ,
DOI : 10.1063/1.1710039
A network theory for the thermal conductivity of an amorphous polymeric material, Rheologica Acta, vol.221, issue.4, pp.257-266, 1989. ,
DOI : 10.1007/BF01329335
Anisotropic conduction of heat in a flowing polymeric material, Rheologica Acta, vol.29, issue.6, pp.580-587, 1990. ,
DOI : 10.1007/BF01329304
A multiaxial criterion for crack nucleation in rubber, Mechanics Research Communications, vol.33, issue.4, pp.493-498, 2006. ,
DOI : 10.1016/j.mechrescom.2005.06.001
URL : https://hal.archives-ouvertes.fr/hal-01004902
A damage model for the fatigue life of elastomeric materials, Mechanics of Materials, vol.34, issue.8, pp.475-483, 2002. ,
DOI : 10.1016/S0167-6636(02)00175-8
Statistical Theory of Networks of Non???Gaussian Flexible Chains, The Journal of Chemical Physics, vol.20, issue.7, pp.1144-1157, 1952. ,
DOI : 10.1063/1.1700682
A thermomecanical approach to tire power loss modeling, Tire Science and Technology, vol.9, pp.1-4, 1981. ,
DOI : 10.2346/1.2151023
Heat-Aging Effects on the Material Properties and Fatigue Life Prediction of Vulcanized Natural Rubber, e-Journal of Soft Materials, vol.2, 2006. ,
DOI : 10.2324/ejsm.2.7
Heat capacities of linear high polymers, Advances in Polymer Science, vol.7, pp.260-368, 1970. ,
DOI : 10.1007/BFb0051029
Fatigue crack propagation in elastomer compounds : Effects of strain rate, temperature, strain level, and oxidation, Rubber Chemistry and Technology, vol.59, pp.809-825, 1986. ,
Effects of Temperature on Fatigue and Fracture, Rubber Chemistry and Technology, vol.67, issue.1, pp.137-147, 1994. ,
DOI : 10.5254/1.3538660
1 Présentation du comptage Rainflow Le comptage Rainflow (SFMM, 1993) permet d'analyser un signal d'amplitude variable et de reconstituer un signal proche du signal original. Cette méthode est fondée sur l ,
un chargement à amplitude variable, un cycle correspond à une boucle contrainte-déformation fermée Un cycle est défini par exemple par son amplitude et sa moyenne La première opération lors d'un comptage Rainflow est l'extraction des points de rebroussement du signal d'origine. L'algorithme sera appliqué à ce nouveau signal constitué des points de rebroussement . L'extraction d'un cycle utilise quatre points successifs de ce signal, indicés respectivement 1, 2, 3 et 4. Voici l'algorithme portant sur les valeurs des contraintes S : ? si |S 4 ? S 3, |S 3 ? S 2 | et |S 2 ? S 1 | ? |S 3 ? S 2 | (les deux points intermédiaires sont compris entre les deux points extrêmaux, FIG. C.1) ? le cycle représenté par ses valeurs extrêmes S 2 et S 3 est extrait du signal : ? les deux points S 2 et S 3 sont éliminés du signal ,
1 : le premier cycle extrait est le petit cycle (en gris foncé), le deuxième cycle est le grand cycle (en gris clair) Ces cycles correspondent bien à des boucles contrainte-déformation fermées. maximal de déformation. En effet, les éprouvettes ont tendance à casser au plus haut niveau d'accommodation . Nous avons donc préféré réaliser les premières accommodations désignées par "_1", et la dernière par "_2" afin de jouer d'autres signaux entre ces deux parties. Le suffixe "_dephase" désigne l'essai où les deux axes de sollicitation sont déphasés de manière contrôlée, c'est-à-dire non aléatoire. Le signal "SED2" est un signal piste qui peut être joué de deux façons, soit déphasé. Le signal "p2biax" est un deuxième signal piste aléatoire pour chaque axe ,