G. Fournet and A. , GUINIER : Small-Angle scattering of X-rays, 1955.

P. Achon, Comportement et ténacité d'alliages d'aluminium à haute résistance, Thèse de doctorat, Ecole Nationale Supérieure des Mines de Paris, 1994.

J. Allison, D. Backman, and L. Christodoulou, Integrated computational materials engineering: A new paradigm for the global materials profession, JOM, vol.58, issue.11, pp.25-27, 2006.
DOI : 10.1007/s11837-006-0223-5

A. Asserin-lebert, Etude expérimentale et prévision des mécanismes de rupture des tôles et eds joints soudés bout à bout en alliage d'aluminium 6056, Thèse de doctorat, 2005.

Y. Bao and T. Wierzbicki, On fracture locus in the equivalent strain and stress triaxiality space, International Journal of Mechanical Sciences, vol.46, issue.1, pp.81-98, 2004.
DOI : 10.1016/j.ijmecsci.2004.02.006

A. Benzerga and J. Leblond, Ductile Fracture by Void Growth to Coalescence, Advances in Applied Mechanics, pp.169-305, 2010.
DOI : 10.1016/S0065-2156(10)44003-X

L. K. Berg, J. Gjonnes, V. Hansen, X. Z. Li, M. Knutson-wedel et al., GP-zones in Al???Zn???Mg alloys and their role in artificial aging, Acta Materialia, vol.49, issue.17, pp.3443-3451, 2001.
DOI : 10.1016/S1359-6454(01)00251-8

M. Berveiller, ZAOUI : Modélisation de la déformation plastique des polycristaux, 2012.

B. I. Bjorneklett, O. Grong, O. R. Myhr, and A. O. Kluken, A process model for the heat-affected zone microstructure evolution in Al-Zn-Mg weldments, Metallurgical and Materials Transactions A, vol.148, issue.10, pp.2667-2677, 1999.
DOI : 10.1179/136217197791069911

W. Brocks, S. Hao, and D. Steglich, Micromechanical Modelling of the Damage and Toughness Behaviour of Nodular Cast Iron Materials, Le Journal de Physique IV, vol.06, issue.C6, pp.43-52, 1996.
DOI : 10.1051/jp4:1996605
URL : https://hal.archives-ouvertes.fr/jpa-00254433

F. Bron and J. Besson, Simulation of the ductile tearing for two grades of 2024 aluminum alloy thin sheets, Engineering Fracture Mechanics, vol.73, issue.11, pp.1531-1552, 2006.
DOI : 10.1016/j.engfracmech.2006.01.024
URL : https://hal.archives-ouvertes.fr/hal-00136710

G. Cam and M. Kocak, Microstructural and mechanical characterization of electron beam welded Al-alloy 7020, Journal of Materials Science, vol.4, issue.5, pp.7154-7161, 2007.
DOI : 10.1179/095066098790093135

R. Cazes, Soudage par faisceaux à haute énergie : faisceau d'électrons et laser, 2012.

F. De-geuser and A. Deschamps, Precipitate characterisation in metallic systems by small-angle X-ray or neutron scattering, Comptes Rendus Physique, vol.13, issue.3, 2012.
DOI : 10.1016/j.crhy.2011.12.008
URL : https://hal.archives-ouvertes.fr/hal-00728096

A. Deschamps, Influence de la prédéformation et des traitements thermiques sur la microstructure et les propriétés mécaniques des alliages Al-Zn-Mg-Cu, Thèse de doctorat, 1997.

A. Deschamps, Précipitation durcissante dans les matériaux de structure. Habilitation à diriger les recherches, 2003.

A. Deschamps and Y. Bréchet, Influence of quench and heating rates on the ageing response of an Al???Zn???Mg???(Zr) alloy, Materials Science and Engineering: A, vol.251, issue.1-2, pp.200-207, 1998.
DOI : 10.1016/S0921-5093(98)00615-7

A. Deschamps and Y. Bréchet, Influence of predeformation and agEing of an Al???Zn???Mg alloy???II. Modeling of precipitation kinetics and yield stress, Acta Materialia, vol.47, issue.1, pp.293-305, 1999.
DOI : 10.1016/S1359-6454(98)00296-1

A. Deschamps, F. De, and . Geuser, On the validity of simple precipitate size measurements by small-angle scattering in metallic systems, Journal of Applied Crystallography, vol.39, issue.2, pp.343-352, 2011.
DOI : 10.1007/s11663-007-9104-8
URL : https://hal.archives-ouvertes.fr/hal-00591218

A. Deschamps, S. Ringeval, G. Texier, and L. Delfaut-durut, Quantitative characterization of the microstructure of an electron-beam welded medium strength Al???Zn???Mg alloy, Materials Science and Engineering: A, vol.517, issue.1-2, pp.361-368, 2009.
DOI : 10.1016/j.msea.2009.03.088
URL : https://hal.archives-ouvertes.fr/hal-00436512

A. Deschamps, G. Texier, S. Ringeval, and L. Delfaut-durut, Influence of cooling rate on the precipitation microstructure in a medium strength Al???Zn???Mg alloy, Materials Science and Engineering: A, vol.501, issue.1-2, pp.133-139, 2009.
DOI : 10.1016/j.msea.2008.09.067
URL : https://hal.archives-ouvertes.fr/hal-00436677

H. B. Donato, R. Magnabosco, and C. , Effects of weld strength mismatch on J and CTOD estimation procedure for SE(B) specimens, International Journal of Fracture, vol.77, issue.1, pp.1-20, 2009.
DOI : 10.1007/s10704-009-9377-9

B. Dubost and P. Sainfort, Durcissement par précipitation des alliages d'aluminium, 1991.

D. Dumont, Relations Microstructure / Ténacité dans les alliages aéronautiques de la série 7000, Thèse de doctorat, 2001.

D. Dumont, A. Deschamps, and Y. Bréchet, On the relationship between microstructure, strength and toughness in AA7050 aluminum alloy, Materials Science and Engineering: A, vol.356, issue.1-2, pp.326-336, 2003.
DOI : 10.1016/S0921-5093(03)00145-X

D. Dumont, A. Deschamps, and Y. Bréchet, A model for predicting fracture mode and toughness in 7000 series aluminium alloys, Acta Materialia, vol.52, issue.9, p.25292540, 2004.
DOI : 10.1016/j.actamat.2004.01.044

D. Fionn and P. Nik, Introduction to computational plasticity, 2005.

T. Engdahl, V. Hansen, and P. J. Warren, Investigation of fine scale precipitates in Al???Zn???Mg alloys after various heat treatments, Materials Science and Engineering: A, vol.327, issue.1, pp.59-64, 2002.
DOI : 10.1016/S0921-5093(01)01876-7

D. Fabrègue and T. Pardoen, A constitutive model for elastoplastic solids containing primary and secondary voids, Journal of the Mechanics and Physics of Solids, vol.56, issue.3, pp.719-741, 2008.
DOI : 10.1016/j.jmps.2007.07.008

J. Faleskog, X. Gao, C. Fong, and S. , Cell model for nonlinear fracture analysis -1. micromechanics calibration, International Journal of Fracture, vol.89, issue.4, pp.355-373, 1998.
DOI : 10.1023/A:1007421420901

J. Faleskog, X. Gao, C. Fong, and S. , Cell model for nonlinear fracture analysis -2. fracture-process calibration and verification, International Journal of Fracture, vol.89, pp.375-398, 1998.

X. Fan, D. Jiang, Q. Meng, Z. Lai, and X. Zhang, Characterization of precipitation microstructure and properties of 7150 aluminium alloy, Materials Science and Engineering: A, vol.427, issue.1-2, pp.130-135, 2006.
DOI : 10.1016/j.msea.2006.04.043

E. Felder, Dureté des métaux courants -cas limite rigide -plastique. Techniques de l'Ingénieur, m4155, 2012.

S. Flouriot, S. Lamalle, and S. Clément, Rapport technique, CEA Valduc, 2007.

D. François, Lois de comportement des métaux -élastoplasticité. viscoplasticité. Techniques de l'Ingénieur, m4152, 2012.

G. Fribourg, Couplages entre précipitation et plasticité dans un alliage d'aluminium 7XXX : application à des traitements thermomécaniques de réduction des distorsions dans des composants aéronautiques, Thèse de doctorat, 2009.

G. Fribourg, Y. Bréchet, and A. Deschamps, Microstructure-based modelling of isotropic and kinematic strain hardening in a precipitation-hardened aluminium alloy, Acta Materialia, vol.59, issue.9, pp.3621-3635, 2011.
DOI : 10.1016/j.actamat.2011.02.035
URL : https://hal.archives-ouvertes.fr/hal-00639972

X. Gao, T. Wang, and J. Kim, On ductile fracture initiation toughness: Effects of void volume fraction, void shape and void distribution, International Journal of Solids and Structures, vol.42, issue.18-19, pp.5097-5117, 2005.
DOI : 10.1016/j.ijsolstr.2005.02.028

A. Gaudillère, Etude de la précipitation dans un alliage d'aluminium par calorimétrie différentielle à balayage. Rapport technique, CEA Valduc, 2010.

O. Glatter and O. Kratky, Small Angle X-ray Scattering, 1982.

D. Godard, P. Archambault, E. Aeby-gautier, and G. Lapasset, Precipitation sequences during quenching of the AA 7010 alloy, Acta Materialia, vol.50, issue.9, pp.2319-2329, 2002.
DOI : 10.1016/S1359-6454(02)00063-0

M. Gologanu, J. Leblond, and J. Devaux, Approximate models for ductile metals containing non-spherical voids -case of axisymmetric prolate ellipsoidale cavities, Journal of the Mechanics and Physics of Solids, pp.41-111723, 1993.

A. 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, Structure of Age-Hardened Aluminium-Copper Alloys, Nature, vol.142, issue.3595, pp.569-570, 1938.
DOI : 10.1038/142569b0

A. S. Gullerud, X. Gaoa, R. H. Dodds, J. , and R. Haj-alib, Simulation of ductile crack growth using computational cells: numerical aspects, Engineering Fracture Mechanics, vol.66, issue.1, pp.65-92, 2000.
DOI : 10.1016/S0013-7944(99)00147-2

A. L. Gurson, Continuum theory of ductile rupture by void nucleation and growth : part 1 -yield criteria and flow rules for porous ductile media. Transactions of the ASME, 1977.

G. Honyek, I. Kovacs, J. Lendvai, N. , and T. Ungar, The influence of Mg content on the formation and reversion of Guinier-Preston zones in Al-4.5 at % Zn-x Mg alloys, Journal of Materials Science, vol.4, issue.10, pp.2701-2709, 1981.
DOI : 10.2320/matertrans1960.15.99

H. Jiang and R. G. , Modelling of grain boundary segregation, precipitation and precipitate-free zones of high strength aluminium alloys???I. The model, Acta Materialia, vol.44, issue.5, pp.1857-1864, 1996.
DOI : 10.1016/1359-6454(95)00317-7

H. Jiang and R. G. Faulkner, Modelling of grain boundary segregation, precipitation and precipitate-free zones of high strength aluminium alloys???II. Application of the models, Acta Materialia, vol.44, issue.5, pp.1865-1871, 1996.
DOI : 10.1016/1359-6454(95)00318-5

N. Kamp, A. Sullivan, and J. D. , Modelling of friction stir welding of 7xxx aluminium alloys, Materials Science and Engineering: A, vol.466, issue.1-2, pp.246-255, 2007.
DOI : 10.1016/j.msea.2007.02.070

C. Landron, O. Bouaziz, E. Maire, and J. Adriena, Characterization and modeling of void nucleation by interface decohesion in dual phase steels, Scripta Materialia, vol.63, issue.10, pp.973-976973, 2010.
DOI : 10.1016/j.scriptamat.2010.07.021
URL : https://hal.archives-ouvertes.fr/hal-00523143

M. Lech-gregaa, S. Hawrylkiewicz, M. Richert, and W. Szymanski, Structural parameters of 7020 alloy after heat treatment simulating the welding process, Materials Characterization, vol.46, issue.2-3, pp.251-257, 2001.
DOI : 10.1016/S1044-5803(01)00133-4

J. L. Lemaitre, J. L. Chaboche, A. Benallal, and R. Desmorat, Mécanique des matériaux solides, 2009.

X. Z. Li, V. Hansen, J. Gjonnes, and L. R. , WALLENBERG : HREM study and structure modeling of the ?' phase, the hardening precipitates in commercial Al-Zn-Mg alloys, Acta Materiala, vol.49, pp.2651-2659, 1999.

G. Liu, S. Scudino, R. Li, U. Kühn, J. Sun et al., Coupling effect of primary voids and secondary voids on the ductile fracture of heat-treatable aluminum alloys, Mechanics of Materials, vol.43, issue.10, pp.556-566, 2011.
DOI : 10.1016/j.mechmat.2011.06.014

H. Loffler, I. Kovacs, and J. Lendvai, Decomposition processes in Al-Zn-Mg alloys, Journal of Materials Science, vol.8, issue.8, pp.2215-2240, 1983.
DOI : 10.1007/BF02646567

E. Lointier, Q. Puydt, and S. Flouriot, Caractérisation mécanique de soudures en alliage d'aluminium 7020, 2011.

G. M. Ludtka and D. E. Laughlin, The influence of microstructure and strength on the fracture mode and toughness of 7XXX series aluminum alloys, Metallurgical Transactions A, vol.89, issue.3, pp.411-425, 1982.
DOI : 10.1016/0013-7944(77)90053-4

T. Ma, G. Den, and . Ouden, Softening behaviour of Al???Zn???Mg alloys due to welding, Materials Science and Engineering: A, vol.266, issue.1-2, pp.198-204, 1999.
DOI : 10.1016/S0921-5093(99)00020-9

E. Maire, Local approach to fracture, chapitre 3 : Quantitative measurement of damage, pp.79-108, 2004.

T. Marlaud, Microstructures de précipitation et mécanismes de corrosion feuilletante dans les alliages d'aluminium de la série 7000 à très hautes caractéristiques mécaniques

G. Mathers, The welding of aluminium and its alloys, 2002.

F. Matsuda, A new test specimen for self-restraint solidification crack susceptibility test of electron-beam welding bead, Transactions of JWRI, vol.11, pp.87-94, 1982.

L. F. Mondolfo, Aluminium Alloys : Structure and Properties, Butterworth&Co Ltd, 1976.

T. F. Morgeneyer and J. Besson, Flat to slant ductile fracture transition: Tomography examination and simulations using shear-controlled void nucleation, Scripta Materialia, vol.65, issue.11, pp.1002-1005, 2011.
DOI : 10.1016/j.scriptamat.2011.09.004
URL : https://hal.archives-ouvertes.fr/hal-00658608

K. Nahshon and J. W. Hutchinson, Modification of the Gurson Model for shear failure, European Journal of Mechanics - A/Solids, vol.27, issue.1, pp.1-17, 2008.
DOI : 10.1016/j.euromechsol.2007.08.002

M. Nicolas, Evolution de l'état de précipitation dans un alliage Al-Zn-Mg lors de traitements thermiques anisothermes et dans la zone affectée thermiquement de joints soudés

M. Nicolas and A. Deschamps, Characterisation and modelling of precipitate evolution in an Al???Zn???Mg alloy during non-isothermal heat treatments, Acta Materialia, vol.51, issue.20, pp.6077-6094, 2003.
DOI : 10.1016/S1359-6454(03)00429-4

O. , S. Hirosawa, A. Cerezo, and T. Sato, Atom probe tomography of nanoscale microstructures within precipitate free zones in Al-Zn-Mg(-Ag) alloys, Acta Materialia, vol.58, pp.5714-5723, 2010.

T. Pardoen, Numerical simulation of low stress triaxiality ductile fracture, Computers & Structures, vol.84, issue.26-27, pp.1641-1650, 2006.
DOI : 10.1016/j.compstruc.2006.05.001

T. Pardoen, D. Dumont, A. Deschamps, and Y. , Grain boundary versus transgranular ductile failure, Journal of the Mechanics and Physics of Solids, vol.51, issue.4, pp.637-665, 2003.
DOI : 10.1016/S0022-5096(02)00102-3

T. Pardoen and J. W. Hutchinson, An extended model for void growth and coalescence, Journal of the Mechanics and Physics of Solids, vol.48, issue.12, pp.2467-2512, 2000.
DOI : 10.1016/S0022-5096(00)00019-3

G. Perrin and J. Leblond, Accelerated void growth in porous ductile solids containing two populations of cavities, International Journal of Plasticity, vol.16, issue.1, pp.91-120, 2000.
DOI : 10.1016/S0749-6419(99)00049-2

G. Petton, Mécanismes microscopiques et comportement cyclique de l'alliage d'aluminium 7010, Thèse de doctorat, 1995.

G. D. Preston, The Diffraction of X-Rays by Age-Hardening Aluminium Copper Alloys, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol.167, issue.931, pp.526-538, 1938.
DOI : 10.1098/rspa.1938.0152

M. Radomsky, O. Kabisch, H. Loffler, J. Lendvai, T. Ungar et al., On the decomposition behaviour of Al-4.5 at% Zn-2 to 3 at% Mg alloys during continuous heating, Journal of Materials Science, vol.67, issue.12, pp.2906-2912, 1979.
DOI : 10.1007/BF00611473

M. Raghavan, Microanalysis of precipitate free zones (PFZ) in Al-Zn-Mg and Cu-Ni-Nb alloys, Metallurgical Transactions A, vol.16, issue.6, pp.993-999, 1980.
DOI : 10.1111/j.1365-2818.1975.tb03895.x

J. R. Rice and D. M. Tracey, On the ductile enlargement of voids in triaxial stress fields???, Journal of the Mechanics and Physics of Solids, vol.17, issue.3, pp.2012-2029, 1969.
DOI : 10.1016/0022-5096(69)90033-7

S. P. Ringer and K. Hono, Microstructural Evolution and Age Hardening in Aluminium Alloys, Materials Characterization, vol.44, issue.1-2, pp.101-131, 2000.
DOI : 10.1016/S1044-5803(99)00051-0

A. Simar, Y. Bréchet, B. De, M. , A. Denquin et al., Integrated modeling of friction stir welding of 6xxx series Al alloys: Process, microstructure and properties, Progress in Materials Science, vol.57, issue.1, pp.95-183, 2012.
DOI : 10.1016/j.pmatsci.2011.05.003
URL : https://hal.archives-ouvertes.fr/hal-00664802

A. Simar, Y. Bréchet, B. De, M. , A. Denquin et al., Sequential modeling of local precipitation, strength and strain hardening in friction stir welds of an aluminum alloy 6005A-T6, Acta Materialia, vol.55, issue.18, pp.6133-6143, 2007.
DOI : 10.1016/j.actamat.2007.07.012
URL : https://hal.archives-ouvertes.fr/hal-00204237

D. Steglich, W. Brocks, J. Heerens, and T. Pardoen, Anisotropic ductile fracture of Al 2024 alloys, Engineering Fracture Mechanics, vol.75, issue.12, pp.3692-3706, 2008.
DOI : 10.1016/j.engfracmech.2007.04.008
URL : http://www.hzg.de/imperia/md/content/gkss/zentrale_einrichtungen/bibliothek/journals/2007/Steglich-engfracmech.pdf

K. Stiller, P. J. Warren, V. Hansen, J. Angenete, and J. Gjønnes, Investigation of precipitation in an Al???Zn???Mg alloy after two-step ageing treatment at 100?? and 150??C, Materials Science and Engineering: A, vol.270, issue.1, pp.55-63, 1999.
DOI : 10.1016/S0921-5093(99)00231-2

D. Tabor, The hardness of solids, Reviews of Physics in Technology, vol.1, issue.3, 1970.
DOI : 10.1088/0034-6683/1/3/I01

V. Tvergaard, Influence of voids on shear band instabilities under plane strain conditions, International Journal of Fracture, vol.6, issue.4, pp.389-407, 1981.
DOI : 10.1080/14786445108561065

V. Tvergaard, Effect of yield surface curvature and void nucleation on plastic flow localization, Journal of the Mechanics and Physics of Solids, vol.35, issue.1, pp.43-60, 1987.
DOI : 10.1016/0022-5096(87)90027-5

V. Tvergaard and A. Needleman, Analysis of the cup-cone fracture in a round tensile bar, Acta Metallurgica, vol.32, issue.1, pp.157-169, 1984.
DOI : 10.1016/0001-6160(84)90213-X

V. Christian, Métallurgie de l'aluminium. Techniques de l'Ingénieur, p.663, 2010.

J. C. Werenskiold, A. Deschamps, and Y. Bréchet, Characterization and modeling of precipitation kinetics in an Al???Zn???Mg alloy, Materials Science and Engineering: A, vol.293, issue.1-2, pp.267-274, 2000.
DOI : 10.1016/S0921-5093(00)01247-8