T. Petit, J. Besson, C. Ritter, K. Colas, L. Helfen et al., Effect of hardening on toughness captured by stress-based damage nucleation in 6061 aluminum alloy, Acta Materialia, vol.180, pp.349-365, 2019.
URL : https://hal.archives-ouvertes.fr/hal-02307867

T. Petit, J. Besson, C. Ritter, K. Colas, L. Helfen et al., Effect of hardening on toughness captured by stress-based damage nucleation in 6061 aluminum alloy, Acta Materialia, vol.180, pp.349-365, 2019.
URL : https://hal.archives-ouvertes.fr/hal-02307867

D. Dumont, A. Deschamps, and Y. Brechet, On the relationship between microstructure, strength and toughness in AA7050 aluminum alloy, Mater. Sci. Eng. A, vol.356, p.145, 2003.

D. Dumont, A. Deschamps, and Y. Brechet, A model for predicting fracture mode and toughness in 7000 series aluminium alloys, Acta Mater, vol.52, pp.2529-2540, 2004.

D. Dumont, A. Deschamps, Y. Bréchet, C. Sigli, and J. C. Ehrström, Characterisation of precipitation microstructures in aluminium alloys 7040 and 7050 and their relationship to mechanical behaviour, Mater. Sci. Technol, vol.20, pp.567-576, 2004.

N. Ryum, The influence of a precipitate-free zone on the mechanical properties of an Al-Mg-Zn alloy, Acta Metall, vol.16, pp.327-332, 1968.

N. Ryum, Ageing and plastic deformation of an Al-Mg-Zn alloy, Acta Metall, vol.17, pp.90101-90102, 1969.

G. M. Ludtka and D. E. Laughlin, The influence of microstructure and strength on the fracture mode and toughness of 7XXX series aluminum alloys, Metall. Trans. A, vol.13, pp.411-425, 1982.

F. Hannard, T. Pardoen, E. Maire, C. L. Bourlot, R. Mokso et al., Characterization and micromechanical modelling of microstructural heterogeneity effects on ductile fracture of 6xxx aluminium alloys, Acta Mater, vol.103, pp.558-572, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01523721

M. Haas and J. T. Hosson, On the effects of thermomechanical processing on failure mode in precipitation-hardened aluminium alloys, J. Mater. Sci, vol.37, pp.5065-5073, 2002.

S. Morita, H. Toda, A. Takahashi, A. Hoshiyama, T. Kobayashi et al., Effects of quenching rate on mechanical properties of 6061 aluminum alloy, J. Jpn. Inst. Light Met, vol.51, pp.307-312, 2001.

Y. Shen, T. F. Morgeneyer, J. Garnier, L. Allais, L. Helfen et al., Three-dimensional quantitative in situ study of crack initiation and propagation in AA6061 aluminum alloy sheets via synchrotron laminography and finite-element simulations, Acta Mater, vol.61, pp.2571-2582, 2013.
URL : https://hal.archives-ouvertes.fr/hal-00815629

T. Petit, C. Ritter, J. Besson, and T. F. Morgeneyer, Impact of machine stiffness on "pop-in" crack propagation instabilities, Eng. Fract. Mech, vol.202, pp.405-422, 2018.
URL : https://hal.archives-ouvertes.fr/hal-01915471

C. C. Chu and A. Needleman, Void Nucleation Effects in Biaxially Stretched Sheets, J. Eng. Mater. Technol, vol.102, pp.249-256, 1980.

A. Dalloz, J. Besson, A. Gourgues-lorenzon, T. Sturel, and A. Pineau, Effect of shear cutting on ductility of a dual phase steel, vol.76, pp.1411-1424, 2007.
URL : https://hal.archives-ouvertes.fr/hal-00399528

T. F. Morgeneyer, L. Helfen, I. Sinclair, H. Proudhon, F. Xu et al., Ductile crack initiation and propagation assessed via in situ synchrotron radiation-computed laminography, Scr. Mater, vol.65, pp.1010-1013, 2011.
URL : https://hal.archives-ouvertes.fr/hal-00652978

T. F. Morgeneyer, T. Taillandier-thomas, A. Buljac, L. Helfen, and F. Hild, On strain and damage interactions during tearing: 3D in situ measurements and simulations for a ductile alloy (AA2139-T3), J. Mech. Phys. Solids, vol.96, pp.550-571, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01383922

A. Needleman and J. R. Rice, Limits to Ductility Set by Plastic Flow Localization, pp.237-267, 1978.

C. Butcher, Z. Chen, and M. Worswick, A lower bound damage-based finite element simulation of stretch flange forming of Al-Mg alloys, Int. J. Fract, vol.142, p.289, 2007.

T. Petit, J. Besson, C. Ritter, K. Colas, L. Helfen et al., Effect of hardening on toughness captured by stress-based damage nucleation in 6061 aluminum alloy, Acta Materialia, vol.180, pp.349-365, 2019.
URL : https://hal.archives-ouvertes.fr/hal-02307867

S. J. Andersen, H. W. Zandbergen, J. Jansen, C. Traeholt, U. Tundal et al., The crystal structure of the ?? phase in Al-Mg-Si alloys, Acta Mater, vol.46, issue.97, p.493, 1998.

S. J. Andersen, C. D. Marioara, A. Frøseth, R. Vissers, and H. W. Zandbergen, Crystal structure of the orthorhombic U2-Al4Mg4Si4 precipitate in the Al-Mg-Si alloy system and its relation to the ?? and ?? phases, Mater. Sci. Eng. A, vol.390, pp.127-138, 2005.

S. J. Andersen, C. D. Marioara, R. Vissers, A. Frøseth, and H. W. Zandbergen, The structural relation between precipitates in Al-Mg-Si alloys, the Al-matrix and diamond silicon, with emphasis on the trigonal phase U1-MgAl2Si2, Mater. Sci. Eng. A, vol.444, pp.157-169, 2007.

R. Vissers, M. A. Van-huis, J. Jansen, H. W. Zandbergen, C. D. Marioara et al., The crystal structure of the ?? phase in Al-Mg-Si alloys, Acta Mater, vol.55, pp.3815-3823, 2007.

T. Na, H. Park, C. Park, J. Park, and N. Hwang, Misorientation angle analysis near the growth front of abnormally growing grains in 5052 aluminum alloy, Acta Mater, vol.115, pp.224-229, 2016.

K. Buchanan, K. Colas, J. Ribis, A. Lopez, and J. Garnier, Analysis of the metastable precipitates in peakhardness aged Al-Mg-Si(-Cu) alloys with differing Si contents, Acta Mater, vol.132, pp.209-221, 2017.

S. K. Suram and K. Rajan, Calibration of reconstruction parameters in atom probe tomography using a single crystallographic orientation, pp.136-142, 2013.

L. Helfen, T. Baumbach, P. Mikulík, D. Kiel, P. Pernot et al., High-resolution three-dimensional imaging of flat objects by synchrotron-radiation computed laminography, Appl. Phys. Lett, vol.86, p.71915, 2005.

L. Helfen, A. Myagotin, P. Pernot, M. Dimichiel, P. Mikulík et al., Investigation of hybrid pixel detector arrays by synchrotron-radiation imaging, Proc. 7th Int. Workshop Radiat, vol.563, pp.163-166, 2006.

L. Helfen, A. Myagotin, P. Mikulík, P. Pernot, A. Voropaev et al., On the implementation of computed laminography using synchrotron radiation, Rev. Sci. Instrum, vol.82, p.63702, 2011.

A. Myagotin, A. Voropaev, L. Helfen, D. Hänschke, and T. Baumbach, Efficient Volume Reconstruction for Parallel-Beam Computed Laminography by Filtered Backprojection on Multi-Core Clusters, IEEE Trans. Image Process, vol.22, pp.5348-5361, 2013.

M. Vogelgesang, T. Farago, T. F. Morgeneyer, L. Helfen, T. Santos-rolo et al., Real-time image-content-based beamline control for smart 4D X-ray imaging, J. Synchrotron Radiat, vol.23, pp.1254-1263, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01421577

T. Ueda, L. Helfen, and T. F. Morgeneyer, In situ laminography study of three-dimensional individual void shape evolution at crack initiation and comparison with Gurson-Tvergaard-Needleman-type simulations, Acta Mater, vol.78, pp.254-270, 2014.
URL : https://hal.archives-ouvertes.fr/hal-01056836

T. Weitkamp, P. Tafforeau, E. Boller, P. Cloetens, J. P. Valade et al., Parallel-beam imaging at the ESRF beamline ID19: current status and plans for the future, AIP Conf. Proc, vol.1234, pp.83-86, 2010.

F. Xu, L. Helfen, H. Suhonen, D. Elgrabli, S. Bayat et al., Correlative Nanoscale 3D Imaging of Electron Density and Elemental Composition in Extended Objects, PloS ONE, vol.7, issue.11, p.50124, 2012.

Y. Shen, Tensile and fracture behavior of AA6061-T6 aluminum alloys : micromechanical approach, 2012.
URL : https://hal.archives-ouvertes.fr/pastel-00820764

F. Hannard, A. Simar, E. Maire, and T. Pardoen, Quantitative assessment of the impact of second phase particle arrangement on damage and fracture anisotropy, Acta Mater, vol.148, pp.456-466, 2018.
URL : https://hal.archives-ouvertes.fr/hal-01814028

T. Petit, J. Besson, C. Ritter, K. Colas, L. Helfen et al., Effect of hardening on toughness captured by stress-based damage nucleation in 6061 aluminum alloy, Acta Materialia, vol.180, pp.349-365, 2019.
URL : https://hal.archives-ouvertes.fr/hal-02307867

M. W. Zandbergen, Q. Xu, A. Cerezo, and G. D. Smith, Study of precipitation in Al-Mg-Si alloys by Atom Probe Tomography I. Microstructural changes as a function of ageing temperature, Acta Mater, vol.101, pp.136-148, 2015.

W. M. Garrison and N. R. Moody, Ductile fracture, J. Phys. Chem. Solids, vol.48, pp.90118-90119, 1987.

E. Voce, The relationship between stress and strain for homogeneous deformations, J. Inst. Met, vol.74, pp.537-562, 1948.

V. Tvergaard and A. Needleman, Analysis of the cup-cone fracture in a round tensile bar, Acta Metall, vol.32, pp.157-169, 1984.

F. A. Mcclintock, A Criterion for Ductile Fracture by the Growth of Holes, J. Appl. Mech, vol.35, pp.363-371, 1968.

G. Rousselier, Ductile fracture models and their potential in local approach of fracture, Nucl. Eng. Des, vol.105, pp.97-111, 1987.

A. Gurson, Continuum Theory of Ductile Rupture by Void Nucleation and Growth : Part 1-Yield Criteria and Flow Rules for Porous Ductilr Media, J. Eng. Mater. Technol, vol.99, pp.2-15, 1977.

V. Tvergaard, Material Failure by Void Growth to Coalescence, Adv. Appl. Mech, pp.83-151, 1989.

J. Besson, Continuum models of ductile fracture : A review, Int. J. Damage Mech, vol.19, pp.3-52, 2010.
URL : https://hal.archives-ouvertes.fr/hal-00550957

A. Pineau, A. A. Benzerga, and T. Pardoen, Failure of metals I: Brittle and ductile fracture, Acta Mater, vol.107, pp.424-483, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01308255

A. A. Benzerga, J. Leblond, A. Needleman, and V. Tvergaard, Ductile failure modeling, Int. J. Fract, vol.201, pp.29-80, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01668734

P. F. Thomason, Three-dimensional models for the plastic limit-loads at incipient failure of the intervoid matrix in ductile porous solids, Acta Metall, vol.33, issue.85, pp.90201-90210, 1985.

P. F. Thomason, A three-dimensional model for ductile fracture by the growth and coalescence of microvoids, Acta Metall, vol.33, pp.1087-1095, 1985.

A. A. Benzerga, J. Besson, and A. Pineau, Anisotropic ductile fracture: Part II: theory, Acta Mater, vol.52, pp.4639-4650, 2004.
URL : https://hal.archives-ouvertes.fr/hal-00164239

M. E. Torki, C. Tekoglu, J. Leblond, and A. A. Benzerga, Theoretical and numerical analysis of void coalescence in porous ductile solids under arbitrary loadings, Int. J. Plast, vol.91, pp.160-181, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01480131

M. Gologanu, J. Leblond, and J. Devaux, Theoretical models for void coalescence in porous ductile solids. II. Coalescence "in columns, Int. J. Solids Struct, vol.38, pp.355-358, 2001.

F. Hannard, S. Castin, E. Maire, R. Mokso, T. Pardoen et al., Ductilization of aluminium alloy 6056 by friction stir processing, Acta Mater, vol.130, pp.121-136, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01538010

J. A. Walsh, K. V. Jata, and E. A. Starke, The influence of Mn dispersoid content and stress state on ductile fracture of 2134 type Al alloys, Acta Metall, vol.37, p.80001, 1989.

A. S. Argon, J. Im, and R. Safoglu, Cavity formation from inclusions in ductile fracture, Metall. Trans. A, vol.6, p.825, 1975.

F. Prat, J. Besson, M. Grange, and E. Andrieu, Behavior and rupture of hydrided ZIRCALOY-4 tubes and sheets, Metall. Mater. Trans. A, vol.29, pp.1643-1651, 1998.

Z. ,

C. Zhang, J. Thaulow, and . Ødegård, A complete Gurson model approach for ductile fracture, Eng. Fract. Mech, vol.67, pp.155-168, 2000.

J. Besson, L. Devillers-guerville, and A. Pineau, Modeling of scatter and size effect in ductile fracture: application to thermal embrittlement of duplex stainless steels, Eng. Fract. Mech, vol.67, pp.169-190, 2000.

T. Petit, J. Besson, C. Ritter, K. Colas, L. Helfen et al., Effect of hardening on toughness captured by stress-based damage nucleation in 6061 aluminum alloy, Acta Materialia, vol.180, pp.349-365, 2019.
URL : https://hal.archives-ouvertes.fr/hal-02307867

T. J. Hughes, Generalization of selective integration procedures to anisotropic and nonlinear media, Int. J. Numer. Methods Eng, vol.15, pp.1413-1418, 1980.

Y. Shinohara, Y. Madi, and J. Besson, Anisotropic ductile failure of a high-strength line pipe steel, Int. J. Fract, vol.197, pp.127-145, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01295773

J. Eshelby, The determination of the elastic field of an ellipsoidal inclusion, and related problems, Proc. R. Soc. Lond. Ser. Math. Phys. Sci, vol.241, p.376, 1957.

M. Kroon and J. Faleskog, Micromechanics of cleavage fracture initiation in ferritic steels by carbide cracking, J. Mech. Phys. Solids, vol.53, pp.171-196, 2005.

D. François, A. Pineau, and A. Zaoui, Fracture mechanics and damage, vol.2, 2013.

I. Kirman, The relation between microstructure and toughness in 7075 aluminum alloy, Metall. Trans, vol.2, pp.1761-1770, 1971.

G. T. Hahn and A. R. Rosenfield, Metallurgical factors affecting fracture toughness of aluminum alloys, Metall. Trans. A, vol.6, pp.653-668, 1975.