M. Reyne, solutions et composites : thermodurcissables et thermoplastiques, JEC publication, 2006.

C. Oudet and M. Polymeres, , 1994.

S. Glass, Glass microspheres produce lower weight SMC, Reinforced Plastics, vol.4, pp.34-41, 1997.

M. Oldenbo, S. P. Fernberg, and L. A. Berglund, Mechanical behaviour of SMC composites with toughening and low density additives, Composites Part A: Applied Science and Manufacturing, vol.34, pp.875-85, 2003.

A. Kraemer, S. Lin, D. Brabandt, T. Böhlke, and G. Lanza, Quality control in the production process of SMC lightweight material, Procedia CIRP, vol.17, pp.772-779, 2014.

J. Collister and A. Allen, Sheet molding compound rheology, vol.14, 1993.

C. F. , Etude des paramètres du procède SMC influant sur la qualité des pièces

Z. Jendli, Analyse et modélisation multi échelles du comportement mécanique sous sollicitations rapides de composites SMC, 2005.

C. Daniel and P. Rozycki, Dimensionnement en dynamique rapide de multimatériaux Utilisés en aéronautique, Mécanique & Industrie, vol.2, pp.23-31, 2001.

P. M. Jacobs and F. Jones, Influence of heterogeneous crosslink density on the thermomechanical and hygrothermal properties of an unsaturated polyester resin: 2. Hygrothermal studies, vol.34, pp.2122-2127, 1993.

Y. S. Yang and L. J. Lee, Microstructure formation in the cure of unsaturated polyester resins, Polymer, vol.29, pp.1793-1800, 1988.

. Durand, Les charges minérales dans les matériaux composites

. Berthelot, Matériaux composites : comportement mécanique et analyse des structures Masson, 1996.

J. Fitoussi, Etude micromécanique de l'influence de l'endommagement à l'interface fibre/matrice sur le comportement des composites organiques à renforts discontinus, 1995.

O. Guiraud, P. Dumont, L. Orgéas, and D. Favier, Rheometry of compression moulded fibrereinforced polymer composites: Rheology, compressibility, and friction forces with mould surfaces, Composites Part A: Applied Science and Manufacturing, vol.42, pp.2107-2126, 2012.

S. Advani and C. Tucker, A numerical simulation of short fiber orientation in compression molding, Polymer Composites, vol.11, pp.164-73, 1990.

M. Shirinbayan, J. Fitoussi, F. Meraghni, B. Surowiec, M. Bocquet et al., High strain rate visco-damageable behavior of Advanced Sheet Molding Compound (A-SMC) under tension, Composites Part B: Engineering, vol.82, pp.30-41, 2015.
URL : https://hal.archives-ouvertes.fr/hal-01196382

M. Shirinbayan, J. Fitoussi, M. Bocquet, F. Meraghni, B. Surowiec et al., Multiscale experimental investigation of the viscous nature of damage in Advanced Sheet Molding Compound (A-SMC) submitted to high strain rates, Composites Part B: Engineering, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01540457

M. Shirinbayan, J. Fitoussi, N. Abbasnezhad, F. Meraghni, B. Surowiec et al., Overall mechanical characterization of a Low Density Sheet Molding Compound (LD-SMC): Multi-scale damage analysis and strain rate effect, Composites Part B, p.2017

B. Esmaeillou, J. Fitoussi, A. Lucas, and A. Tcharkhtchi, Multi-scale experimental analysis of the tension-tension fatigue behavior of a short glass fiber reinforced polyamide composite, Procedia Engineering, vol.10, pp.2117-2139, 2011.

J. Fitoussi, G. Guo, and D. Baptiste, A statistical micromechanical model of anisotropic damage for SMC composites, Composites Science and Technology, vol.58, pp.759-63, 1998.

Z. Jendli, F. Meraghni, J. Fitoussi, and D. Baptiste, Micromechanical analysis of strain rate effect on damage evolution in sheet molding compound composites, Composites Part A: Applied Science and Manufacturing, vol.35, pp.779-85, 2004.

Z. Jendli, F. Meraghni, J. Fitoussi, and D. Baptiste, Multi-scales modeling of dynamic behaviour for discontinuous fibre SMC composites, Composites Science and Technology, vol.69, pp.97-103, 2009.

Z. Jendli, J. Fitoussi, F. Meraghni, and D. Baptiste, Anisotropic strain rate effects on the fibrematrix interface decohesion in sheet moulding compound composites, Composites Science and Technology, vol.65, pp.387-93, 2005.

J. Fitoussi, M. Bocquet, and F. Meraghni, Effect of the matrix behavior on the damage of ethylene-propylene glass fiber reinforced composite subjected to high strain rate tension, Composites Part B: Engineering, vol.45, 2013.
URL : https://hal.archives-ouvertes.fr/hal-00984755

K. Y. Hour and H. Sehitoglu, Damage development in a short fiber reinforced composite, Journal of Composite Materials, vol.27, pp.782-805, 1993.

M. C. Thionnet and A. , Applications et théorie des invariants, Ellipses, vol.2, 2003.

M. F. Arif, F. Meraghni, Y. Chemisky, N. Despringre, and G. Robert, «In situ damage mechanisms investigation of PA66/GF30 composite: Effect of relative humidity, Composites: Part B: Engineering, vol.58, pp.487-495, 2014.

M. Schoßig, A. Znkel, C. Bierögel, and P. Pölt, «ESEM investigations for assessment of damage kinetics of short glass fibre reinforced thermoplastics -Results of in situ tensile tests coupled with acoustic emission analysis, Composites Science and Technology, vol.71, pp.257-265, 2011.

M. Arif, N. Saintier, F. Meraghni, J. Fitoussi, Y. Chemisky et al., «Multiscale fatigue damage characterization in short glass fiber reinforced polyamide-66, Composites Part B: Engineering, vol.61, pp.55-65, 2014.

D. Krajcinovic and S. Mastilovic, Some fundamental issues of damage mechanics, Mechanics of Materials, vol.21, pp.217-247, 1995.

D. Krajcinovic, Selection of damage parameter -Art or science, Mechanics of Materials, vol.28, pp.165-79, 1998.

J. Lemaitre and J. L. Chaboche, Mécanique des matériaux solides. Paris: Donud, 1988.

R. Talreja, Fatigue of composite materials: damage mechanisms and fatigue-life diagrams, Proceedings of the Royal Sociey, vol.1981, pp.461-75

A. , Comportement des matériaux composites a fibres courtes : applications a l'impact basse vitesse'', thèse de l'université Paul Sabatier Toulouse, 2008.

K. Y. Hour and H. Sehitoglu, Damage development in a short fibre composite, Journal of Composite Materials, vol.27, issue.8, pp.782-805, 1993.

M. Shirinbayan, Etude du comportement mécanique et de l'endommagement de divers matériaux composites SMC soumis à des chargements de type dynamique, fatigue et dynamique post-fatigue, 2017.

J. L. Chaboche and F. Gallerneau, An overview of the damage approach of durability modelling at elevated temperature, Fatigue and Fracture of Engineering, vol.24, pp.405-423, 2001.

A. Bussiba, M. Kupiec, S. Ifergane, R. Piat, and T. Böhlke, Damage evolution and fracture events sequence in various composites by acoustic emission technique, Composites Science and Technology, vol.68, pp.1144-55, 2008.

J. M. Ferreira, J. T. Pires, J. D. Costa, O. A. Errajhi, and M. Richardson, Fatigue damage and environment interaction of polyester aluminized glass fiber composites, Composite Structures, vol.78, pp.397-401, 2007.

J. Degrieck and W. Van-paepegem, Fatigue Damage Modelling of Fibre-Reinforced Composite Materials, Review. Applied Mechanics Reviews, vol.54, issue.4, pp.279-300, 2001.

T. Simoes, C. Octavio, J. Valença, H. Costa, D. Dias-da-costa et al., Influence of concrete strength and steel fibre geometry on the fibre/matrix interface, Composites Part B, vol.122, pp.156-164, 2017.

H. Rolland, N. Saintier, P. Wilson, J. Merzeau, and G. Robert, In situ X-ray tomography investigation on damage mechanisms in short glass fibre reinforced thermoplastics: Effects of fibre orientation and relative humidity, Composites Part B, vol.109, pp.170-186, 2017.

S. Mortazavian and A. Fatemi, Effects of fiber orientation and anisotropy on tensile strength and elastic modulus of short fiber reinforced polymer composites, Composites Part B, vol.72, pp.116-129, 2015.

V. Bellenger, A. Tcharkhtchi, and P. Castaing, Thermal and mechanical fatigue of a PA66/glass fibers composite material, International Journal of Fatigue, vol.28, issue.10, pp.1348-52, 2006.

R. Khan, R. Alderliesten, S. Badshah, and R. Benedictus, Effect of stress ratio or mean stress on fatigue delamination growth in composites: critical review, Compos Struct, vol.124, pp.214-241, 2015.

J. Andersons, M. Hojob, and S. Ochiaic, Empirical model for stress ratio effect on fatigue delamination growth rate in composite laminates, Int J Fatigue, vol.26, issue.6, pp.597-604, 2004.

H. Kotik, P. Ipiña, and J. , Frequency effect in short-beam shear fatigue of a glass fiber reinforced polyester composite, International Journal of Fatigue, vol.90, pp.116-124, 2016.

M. Eftekhari and A. Fatemi, On the strengthening effect of increasing cycling frequency on fatigue behavior of some polymers and their composites. Experiments and modeling, International Journal of Fatigue, vol.87, pp.153-166, 2016.

B. Esmaeillou, Approche cinétique du comportement en fatigue du Polyamide 66 renforcé par 30% de fibres de verre, Ecole nationale supérieure d'arts et métiers-ENSAM, 2011.

B. Esmaeillou, P. Ferreira, V. Bellenger, and A. Tcharkhtchi, Fatigue behavior of polyamide 66/glass fiber under various kinds of applied load, Polymer Composites, vol.33, pp.540-547, 2012.
URL : https://hal.archives-ouvertes.fr/hal-01202696

A. Avanzini, G. Donzella, D. Gallina, S. Pandini, and C. Petrogalli, Fatigue behavior and cyclic damage of peek short fiber reinforced composites, Compos Part B: Eng, vol.45, pp.397-406, 2013.

A. Launay, Y. Marco, M. H. Maitournam, I. Raoult, and F. Szmytka, Cyclic behavior of short glass fiber reinforced polyamide for fatigue life prediction of automotive components, Procedia Engineering, vol.2, pp.901-911, 2010.
URL : https://hal.archives-ouvertes.fr/hal-00525612

S. Tamboura, H. Sidhom, H. Baptiste, and J. Fitoussi, Evaluation de la tenue en fatigue du composite SMC R42, Matériaux & Techniques, pp.3-4, 2001.

S. Mortazavian, A. Fatemi, S. R. Mellott, and A. Khosrovaneh, Effect of cycling frequency and self-heating on fatigue behavior of reinforced and unreinforced thermoplastic polymers, Society of Plastics Engineers, vol.2015, pp.2005-2013

M. Shirinbayan, J. Fitoussi, F. Meraghni, B. Surowiec, M. Laribi et al., Coupled effect of loading frequency and amplitude on the fatigue behavior of advanced sheet molding compound (A-SMC), Journal of Reinforced Plastics and Composites, 2016.

M. Poncelet, Multiaxialité, hétérogénéités intrinsèques et structurales des essais d'autoéchauffement et de fatigue à grand nombre de cycles, pp.1-12, 2007.

C. M. Sonsino and E. Moosbrugger, Fatigue design of highly loaded short-glass-fibre reinforced polyamide parts in engine compartments, Int. J. Fatigue, vol.30, pp.1279-1288, 2008.

K. Handa, A. Kato, and I. Narisawa, Fatigue characteristics of a glass-fiber-reinforced polyamide, Journal of Applied Polymer Science, vol.72, pp.1783-93, 1999.

A. J. Dentsoras, E. P. Kouvaritakis, and M. D. Laboratory, Effects of vibration frequency on fatigue crack propagation of a polymer at resonance, Science, vol.50, pp.467-73, 1995.

W. Voigt, Lehrbuch der kristallphysik, teubner, 1910.

A. Reuss, Berechnung des fliessgrenze von mischkristallen auf grund der prastizitätsbedingunug für einkristalle, Zeitschrift für angewandte Mathematik und Mechanik, vol.9, pp.49-58, 1929.

R. Hill, Elastic properties of reinforced solids: Some theoretical principals, J. Mech. Phys. Solids, vol.11, pp.357-372, 1963.

J. Aboudi, Mechanics of Composite Materials, Studies in Applied Mechanics, vol.29, 1991.

R. M. Christensen and K. Lo, Solution for effective shear properties of three phase sphere and cylinder models, See also Corrigendum J. Mech. Phys. Solids, vol.27, p.639, 1979.

M. Berveiller and A. Et-zaoui, Modélisation du comportement mécanique des solides microhétérogènes. Introduction à la mécanique des polymères, Vandoeuvre les Nancy : INPL, pp.225-249, 1995.

Z. Hashin, Analysis of composites materials a survey, J. Apll. Mech, vol.50, pp.481-505, 1983.

M. Bornert, T. Bretheau, and P. Et-gilormini, Homogénéisation en mécanique des matériaux 1, Matériaux aléatoires élastiques et milieux périodiques, p.255, 2001.

T. Kanit, S. Forest, I. Galliet, V. Mounoury, and D. Jeulin, Determination of the size of the representative volume element for random composites: statistical and numerical approach, International Journal of Solids and Structures, vol.40, pp.3647-3679, 2003.

M. Lévesque, Modélisation du comportement mécanique de matériaux composites viscoélastiques non linéaires par une approche d'homogénéisation, 2004.

A. Brini, Modélisation multi-échelles du comportement et du vieillissement des mousses syntactiques immergées, 2004.

G. Duvaut, Analyse fonctionnelle et mécanique des milieux continus, application à l'étude des matériaux composites élastiques à structure périodique, 1976.

P. Suquet and . Plasticité, Université Pierre et Marie Curie Paris 6, 1982.

E. Sanchez-palencia, Boundary layer and edge effect in composite homogenization techniques for composite media, Lecture Note in Physics, p.272, 1986.

C. L. Tucker and E. Liang, Stiffness predictions for unidirectional short-fiber composites: Review and evaluation, Composites Science and Technology, vol.59, pp.655-671, 1999.

F. Praud, G. Chatzigeorgiou, J. Bikard, and F. Meraghni, «Phenomenological multimechanisms constitutive modelling for thermoplastic polymers, implicit implementation and experimental validation, » Mechanics of Materials, vol.114, pp.9-29, 2017.

S. Kari, H. Berger, R. Rodriguez-ramos, and G. , «Computational evaluation of effective material properties of composites reinforced by randomly distributed spherical particles, Composite Structures, vol.77, pp.223-231, 2007.

D. Baptiste, Damage Micromechanics Modelling of Discontinuous Reinforced Composites'. Continuum Damage Mechanics of Materials and Structures, 2002.

F. Desrumaux, Contribution à l'analyse micromécanique du comportement élastique endommageable de composites monolithiques et sandwichs, intégration dans un code de calculs par éléments finis, 2000.

J. Eshelby, The Determination of the Elastic Field of an Ellipsoidal Inclusion and Related Problems, Proc. Roy. Soc. London, A, vol.241, pp.376-396, 1957.

N. Bourgeois, Caractérisation et modélisation microscopique du comportement et de l'endommagement d'un composite à matrice métallique : Al/SiCp, 1994.

T. Mura and P. Cheng, The elastic field outside an ellipsoidal inclusion, Journal of Applied Mechanics, pp.591-594, 1977.

Z. Hashin and S. Shtrikman, «A variational approach to the theory of the elastic behaviourof multiphase materials, Journal of the Mechanics and Physics of Solids, vol.11, pp.127-140, 1963.

A. Zaoui, D. François, and A. Pineau, Comportement Mécanique des Matériaux, 'viscoplasticité, endommagement, mécanique de la rupture, mécanique du contact, 1995.

T. Mori and K. Tanaka, Average stress in matrix and average elastic energy of materials with misfitting inclusions, Acta Metallurgica, vol.21, pp.571-574, 1973.

K. Wakashima, M. Otsuka, and S. Umekawa, «Thermal expansions of heterogeneous solids containing aligned ellipsoidal inclusions, » journal of composite material, vol.8, pp.1391-404, 1974.

Y. Benveniste, «A new approach to the application of Mori-Tanaka's theory in composite materials,» mechanics of materials, vol.16, pp.147-157, 1987.

Y. Takao and T. Chou, Effective longitudinal Young's modulus of misoriented short fiber composite, J. of Applied Meth, vol.49, issue.3, pp.536-540, 1982.

G. P. Tandon and G. Weng, Average stress in the matrix and effective moduli of randomly oriented composites, Comp. Sci. Techno, vol.27, pp.111-132, 1986.

Y. Takao and M. Taya, The effect of variable fiber aspect ratio on the stiffness and thermal expansion coefficients of a short fiber composite, J. Comp. Mat, vol.21, issue.2, pp.140-156, 1987.

T. Mura, Micromechanics of defects in solids, 1987.

H. Lee, «a computationnal approach to the investigation of impact damage evolution in discontinously reinforced fiber composite,» computaionnal mechanics, vol.127, pp.504-512, 2001.

Y. M. Shabana, «Incremental constitutive equation for discontinuously reinforced composites considering reinforcement damage and thermoelastoplasticity, Computational Materials Science, vol.128, pp.31-40, 2003.

Y. Cho, Incremental damage theory of particle or short fiber reinforced composite including reinforcement damage, 1997.

A. Krairi and I. Doghri, «Multi-scale damage model for mechanical High Cycle Fatigue (HCF) of short glass fibre reinforced thermoplastics (SGFRTP),» 5Th Fatigue Design Conference, 2013.

J. Fitoussi, G. Gua, and D. Baptiste, «Determination of a tridimensionnal failure criterion at the fibre/matrix interface of an organic-matric/discontinuous reinforcements composite, Composites Science and Technology, vol.56, pp.755-760, 1996.

F. Meraghni, C. Blakeman, and M. Benzeggagh, «Effect of interfacial decohesion on stiffness reduction in a random discontinuous-fibre composite containing matrix microcracks, Composites Science and Technology, vol.56, pp.541-555, 1996.

N. Despringre, Analyse et modélisation des mécanismes d'endommagement et de déformation en fatigue multiaxiale de matériaux composites : polyamide renforcé par des fibres courtes, Ecole nationale supérieure d'arts et métiers, 2015.

N. Achour, Modélisation Multi-échelles et analyse expérimentale du comportement de composites à matrice thermoplastique renforcées en fibres de verre sous sollicitations dynamiques modérées, Ecole nationale supérieure d'arts et métiers, 2015.

J. T. Fong, Damage in composite materials. ASTM STP 775. American Society for Testing and Materials, pp.243-266, 1982.

I. M. Daniel and A. Charewicz, Fatigue damage mechanisms and residual properties of graphite/epoxy laminates, Eng Fracture Mech, vol.25, issue.5/6, pp.793-808, 1986.

P. M. Barnard, R. J. Butler, and C. Pt, Fatigue scatter of UD glass epoxy, a fact or fiction ?, Composite Structures 3, Proceedings of the third International Conference on Composite Structures, vol.3, pp.69-82, 1985.

W. Hwang and K. S. Han, Cumulative damage models and multi-stress fatigue life prediction, J Composite Mat, vol.20, pp.125-153, 1986.

I. R. Farrow, Damage accumulation and degradation of composite laminates under aircraft service loading: assessment and prediction. Volumes I and II, 1989.

F. Ellyin and D. Kujawski, Fatigue testing and life prediction of fibreglass-reinforced composites, First International Conference on Advanced Composite Materials in Bridges and Structures (ACMBS-I), pp.111-118, 1992.

G. P. Sendeckyj, Life prediction for resin-matrix composite materials, Composite Material Series, vol.4, pp.431-483, 1990.

M. A. Miner, Cumulative damage in fatigue, J. Appl. Mech, vol.12, pp.159-164, 1945.

F. Ellyin and H. El-kadi, A fatigue failure criterion for fiber reinforced composite laminae, Composite Struct, vol.15, pp.61-74, 1990.

A. Plumtree, GX Cheng Paramètre de dommage par fatigue pour les composites renforcés par des fibres unidirectionnelles et hors axe, Int J Fatigue, vol.21, issue.8, pp.849-856, 1999.

T. P. Philippidis and A. P. Vassilopoulos, Fatigue strength prediction under multiaxial stress, J Composite Mat, vol.33, issue.17, pp.1578-1599, 1999.

A. Gagel, B. Fiedler, and K. , SchulteOn modelling the mechanical degradation of fatigue loaded glass-fibre non-crimp fabric reinforced epoxy laminates, Compos Sci Technol, vol.66, pp.657-664, 2006.

A. L. Highsmith and K. L. Reifsnider, Damage in Composite Materials, ASTM STP 775, pp.103-117, 1982.

K. O'brien and . Reifsnider, J. Compos. Mater, vol.15, pp.55-70, 1981.

B. Harris, Fatigue behaviour of polymer-based composites and life prediction methods. AIB-Vinçotte Leerstoel, 2 maart 1995, Belgium, Nationaal Fonds voor Wetenschappelijk Onderzoek, vol.28

J. R. Schaff and D. Bd, Life prediction methodology for composite structures. Part I -Constant amplitude and two-stress level fatigue, J Composite Mat, vol.31, issue.2, pp.128-157, 1997.

W. Van-paepegem and J. Degrieck, A New Coupled Approach of Residual Stiffness and Strength for Fatigue of Fibre-Reinforced Composites, Int. J. Fatigue, vol.24, issue.7, pp.747-762, 2002.

H. F. Nouri, P. Meraghni, and . Lory, Fatigue damage model for injection-molded short glass fibre reinforced thermoplastics, International Journal of Fatigue, vol.31, issue.5, pp.934-942, 2009.
URL : https://hal.archives-ouvertes.fr/pastel-00005669

I. Krairi, Doghri/A thermodynamically-based constitutive model for thermoplastic polymers coupling viscoelasticity, viscoplasticity and ductile damage, International Journal of Plasticity, vol.60, pp.163-181, 2014.

. Tang, ;. C. Lee, and W. Tang, Lee Mécanique des dommages appliquée aux propriétés élastiques des polymers, Eng. Fract. Mech, vol.52, pp.717-729, 1995.

. Miehe, ;. C. Keck, and J. Miehe, Keck Super imposé réponse élastique élastique-viscoélastique-plastoélastique finie avec des dommages dans les polymères caoutchouteux remplis. expériences, modélisation et implémentation algorithmique, J. Mech. Phys. Solids, pp.323-365, 2000.

. Balieu, Mottola Un modèle d'endommagement élastoviscoplastique entièrement couplé à des contraintes finies pour un polymère semi-cristallin chargé de minéraux Int, J. Plast, 2013.

. Ayoub, Charrier Prédiction de la durée de vie des matériaux caoutchouteux sous charge multiaxiale en utilisant une approche de mécanique des dommages continue: effets du chargement et du ratio r, Mech. Mater, vol.52, pp.87-102, 2012.

. Ayoub, Kridli Modèle d'endommagement visco-hyperélastique pour l'adoucissement cyclique des contraintes, l'hystérésis et la déformation permanente du caoutchouc à l'aide de la théorie de l'altération du réseau, Int. J. Plast, 2013.

F. Sidoroff and B. Subagio, Fatigue damage modelling of composite materials from bending tests, Second European Conference on Composite Materials(ECCM-II), vol.4, 1987.

S. Vieillevigne, D. Jeulin, J. Renard, and N. Sicot, Modelling of the fatigue behaviour of an unidirectional glass epoxy composite submitted to fatigue loadings, International Conference on fatigue of composites, pp.424-430, 1997.

W. Hwang and K. S. Han, Cumulative damage models and multi-stress fatigue life prediction, J Composite Mat, vol.20, pp.125-153, 1986.

W. Van-paepegem and J. Degrieck, Simulating Damage and Permanent Strain in Composites Under In-Plane Fatigue Loading, Comput. Struct, vol.83, pp.1930-1942, 2005.

W. Van-paepegem and J. Degrieck, Modelling Damage and Permanent Strain in Fibre-Reinforced Composites Under In-Plane Fatigue Loading, Compos. Sci. Technol, vol.63, issue.5, pp.677-694, 2003.

Z. Khan, F. A. Al-sulaiman, J. K. Farooqi, Y. , and M. , Fatigue Life Predictions in Woven Carbon Fabric/Polyester Composites Based on Modulus Degradation, J. Reinf. Plast. Compos, vol.20, issue.5, pp.377-398, 2001.

C. Wen and S. Yazdani, Anisotropic Damage Model for Woven Fabric Composites During Tension-Tension Fatigue, Compos. Struct, vol.82, issue.1, pp.127-131, 2008.

U. Hansen, Damage Development in Woven Fabric Composites During TensionTension Fatigue, J. Compos. Mater, vol.33, issue.7, pp.614-639, 1999.

L. J. Broutman and S. Sahu, A New Theory to Predict Cumulative Fatigue Damage in Fibreglass Reinforced Plastics, Composite Materials: Testing and Design

. Eds and . Corten, STP, vol.497, pp.170-188

M. Shokrieh and L. Lessard, Multiaxial fatigue behaviour of unidirectional plies based on uniaxial fatigue experiments -1. modelling, International Journal of fatigue, vol.19, pp.201-207, 1997.

J. Halpin, K. Jerina, T. A. , and J. , Characterization of composites for the purpose of reliability evaluation, ASTM STP 521, 1973.

H. T. Hahn and R. Y. Kim, Proof Testing of Composite Materials, J Compos Mat, vol.9, p.297, 1975.

P. C. Chou and R. Croman, Residual strength in fatigue based on the strength-life equal rank assumption, J Compos Mat, vol.12, pp.177-94, 1978.

P. C. Chou and R. Croman, Degradation and sudden death models of fatigue of graphite/epoxy composites, Composite materials: testing and design, vol.674, pp.177-194, 1978.

J. N. Yang and S. Du, An exploratory study into the fatigue of composites under spectrum loading, J Compos Mat, vol.17, pp.511-537, 1983.

J. N. Yang, Fatigue and residual strength degradation for graphite/ epoxy composites under tension-compression cyclic loading, J Compos Mat, vol.12, pp.19-39, 1978.

G. P. Sendeckyj, Life Prediction for Resin-Matrix Composite Materials, Composite Material Series, vol.4, pp.431-483, 1991.

M. M. Shokrieh and L. B. Lessard, Multiaxial fatigue behaviour of unidirectional plies based on uniaxial fatigue experiments. Experimental evaluation, Int J Fatigue, vol.19, issue.3, pp.209-226, 1997.

J. A. Epaarachchi and P. D. Clausen, A new cumulative fatigue damage model for glass fiber reinforced plastic composites under step/discrete loading, Compos A, vol.36, pp.1236-1281, 2005.

M. S. Found and M. Quaresimin, Two-stage fatigue loading of woven carbon fiber reinforced laminates, Fatigue Fract Eng Mater Struct, vol.26, pp.17-26, 2003.

Z. Hashin and A. Rotem, A fatigue criterion for fiber reinforced composite materials, J Composite Mat, vol.7, pp.448-464, 1973.

K. L. Reifsnider and Z. Gao, A micromechanics model for composites under fatigue loading, Int J Fatigue, vol.13, issue.2, pp.149-156, 1991.

J. Fitoussi, N. Bourgeois, G. Guo, and D. Baptiste, Prediction of the anisotropic damaged behavior of composite materials: introduction of multilocal failure criteria in a micro-macro relationship, Computational Materials Science, vol.5, issue.95, pp.61-66, 1996.

K. Derrien, J. Fitoussi, G. Guo, and D. Baptiste, Prediction of the effective480 damage properties and failure properties of nonlinear anisotropic discontinuous reinforced composites, Computer Methods in Applied Mechanics and Engineering, vol.185, issue.2-4, pp.93-107, 2000.

F. Desrumaux, F. Meraghni, and M. L. Benzeggagh, Generalised Mori-Tanaka Scheme to Model Anisotropic Damage Using Numerical Eshelby Tensor, Journal of Composite Materials, vol.35, pp.603-624, 2001.

S. Kammoun, I. Doghri, L. Brassart, and L. Delannay, Micromechanical modeling of the progressive failure in short glass-fiber reinforced thermoplastics -First Pseudo-Grain Damage model, Composites Part A: Applied Science and Manufacturing, vol.73, pp.166-175, 2015.

G. Guo, J. Fitoussi, and D. Baptiste, Modelling of damage behavior of a short fiber reinforced composite structure by the finite element analysis using a micro-macro law, International Journal of Damage Mechanics, vol.6, pp.278-299, 1997.

B. N. Nguyen and M. A. Khaleel, A mechanistic approach to damage in short-510 fiber composites based on micromechanical and continuum damage mechanics descriptions, Composites Science and Technology, vol.64, issue.5, pp.293-301, 2004.

F. Meraghni and M. L. Benzeggagh, Micromechanical modelling of matrix degradation in randomly oriented discontinuous-fibre composites, Composites Science and Technology, vol.55, issue.2, pp.96-104, 1995.

H. K. Lee and S. Simunovic, A damage constitutive model of progressive debonding in aligned discontinuous fiber composites, International Journal of Solids and Structures, vol.38, issue.5, pp.60-63, 2001.

H. Lee and S. Simunovic, Modeling of progressive damage in aligned and randomly oriented discontinuous fiber polymer matrix composites, Composites Part B: Engineering, vol.31, pp.77-86, 2000.

J. W. Ju and H. K. Lee, A micromechanical damage model for effective elastoplastic behavior of ductile matrix composites considering evolutionary complete particle debonding, Computer Methods in Applied Mechanics and Engineering, vol.183, issue.3-4, pp.219-223, 2000.

A. Ben-cheikh-larbi, K. Sai, H. Sidhom, and D. Baptiste, Constitutive Model of Micromechanical Damage to Predict Reduction in Stiffness of a FatigueSMC Composite, Journal of Materials Engineering and Performance, vol.15, issue.5, pp.575-580, 2006.

L. M. Kachanov, On subcritical crack growth, Mechanics Research Communications, vol.3, issue.1, pp.51-54, 1976.

A. Jain, J. Veas, S. Straesser, W. Van-paepegem, I. Verpoest et al., The Master SN curve approach -A hybrid multi-scale fatigue simulation of short fiber reinforced composites, Composites: Part A, 2015.

B. Klimkeit, Y. Nadot, S. Castagnet, C. Martin, C. Dumas et al., Évaluation de la résistance à la fatigue multiaxiale pour les polymères renforcés, Int J Fatigue, vol.33, pp.766-780, 2011.

A. Bernasconi, P. Davoli, A. Basile, and A. Filippi, Effet de l'orientation des fibres sur le comportement à la fatigue d'un polyamide 6 renforcé de fibres de verre, Int J Fatigue, vol.29, pp.199-208, 2007.

A. Zago, GS Springer Fatigue vit des pièces thermoplastiques renforcées de fibres courtes, J Reinf Plast Compos, vol.20, pp.606-620, 2001.

M. De-monte, E. Moosbrugger, and M. , Quaresimin Influence de la température et de l'épaisseur sur le comportement hors axe du polyamide 6.6 chargé de fibres cycliques Compos A, Partie Appl Sci Manuf, pp.1368-13793, 2012.

N. Mf-arif, F. Saintier, J. Meraghni, Y. Fitoussi, G. Chemisky et al., Caractérisation multiscale des dommages par fatigue dans le polyamide 66 renforcé de fibres de verre, Compos B -Eng, vol.61, pp.55-65, 2014.

G. Meneghetti and M. , Quaresimin Évaluation de la résistance à la fatigue d'un composite à fibres courtes basé sur la dissipation thermique spécifique, Compos Part B Eng, pp.217-225, 2010.

L. Jegou, Y. Marco, V. L. Saux, and S. , Calloch Prédiction rapide de la courbe de Wohler à partir des mesures d'accumulation de chaleur sur un plastique renforcé de fibres courtes, Int J Fatigue, vol.47, pp.259-267, 2013.

Y. Benveniste, A new approach to the application of Mori-Tanaka's theory, Mechanics of Materials, vol.6, pp.147-157, 1987.

M. A. Laribi, *. , S. Tamboura, J. Fitoussi, R. Tiébi et al., Fast fatigue life prediction of short fiber reinforced composites using a new hybrid damage approach: Application to SMC, Composites Part B: Engineering, vol.139, pp.155-162, 2018.
URL : https://hal.archives-ouvertes.fr/hal-01826582

A. Fatemi and L. , Yang Cumulative fatigue damage and life prediction theories: a survey of the state of the art for homogeneous materials, Int J Fatigue, vol.20, issue.1, pp.9-34, 1998.

L. Yang and A. , Fatemi Cumulative fatigue damage mechanisms and quantifying parameters: a literature review ASTM, J Test Eval, vol.26, issue.2, pp.89-100, 1998.

N. Post, S. Case, and J. , LeskoModeling the variable amplitude fatigue of composite materials: a review and evaluation of the state of the art for spectrum loading, Int J Fatigue, vol.30, issue.12, pp.2064-2086, 2008.

L. Broutman and S. Sahu, A new theory to predict cumulative fatigue damage in fiberglass reinforced plastics, Composite materials: testing and design, pp.170-88, 1972.

A. Zago, G. Springer, and M. , Quaresimin Cumulative damage of short glass fiber reinforced thermoplastics, J Reinf Plast Compos, vol.20, pp.596-605, 2001.

A. Zago and G. , Springer Fatigue lives of short fiber reinforced thermoplastics parts, J Reinf Plast Compos, vol.20, pp.606-620, 2001.

C. Sonsino and E. , Moosbrugger Fatigue design of highly loaded short-glass-fibre reinforced polyamide parts in engine compartments, Int J Fatigue, vol.30, pp.1279-1288, 2008.

J. Hartmann, E. Moosbrugger, and A. , BüterVariable amplitude loading with components made of short fiber reinforced polyamide 6, Proc Eng, vol.6, pp.2009-2015, 2011.