H. Abdesselam, J. Crepin, A. Pineau, A. L. Rouffie, P. Gaborit et al., On the crystallographic, stage I-like, character of fine granular area formation in internal fish-eye fatigue cracks, International Journal of Fatigue, vol.106, pp.132-142, 2018.
URL : https://hal.archives-ouvertes.fr/hal-01633714

M. Achouri, G. Germain, P. Santo, and D. Saidane, Experimental characterization and numerical modeling of micromechanical damage under different stress states, Materials & Design, vol.50, pp.207-222, 2013.
URL : https://hal.archives-ouvertes.fr/hal-01057964

C. S. Ades, Bending Strength of Tubing in the Plastic Range, Journal of the Aeronautical Sciences, vol.24, issue.8, pp.605-610, 1957.

L. Anand and W. A. Spitzig, Initiation of localized shear bands in plane strain, Journal of the Mechanics and Physics of Solids, vol.28, issue.2, pp.113-128, 1980.

D. Antolovich and R. W. Armstrong, Plastic strain localization in metals: origins and consequences, Progress in Materials Science, vol.59, pp.1-160, 2014.

, Aubert&Duval : ML340 very high strength steel for high temperature applications, 2014.

R. Ayer and P. M. Machmeier, Transmission electron microscopy examination of hardening and toughening phenomena in aermet 100, Metallurgical Transactions A, vol.24, issue.9, pp.1943-1955, 1993.

Y. Bai and T. Wierzbicki, A new model of metal plasticity and fracture with pressure and Lode dependence, International Journal of Plasticity, vol.24, issue.6, pp.1071-1096, 2008.

Y. Bai and T. Wierzbicki, A comparative study of three groups of ductile fracture loci in the 3d space, Engineering Fracture Mechanics, vol.135, pp.147-167, 2015.

C. Bao, M. Francois, and L. L. Joncour, A Closer Look at the Diffuse and Localised Necking of A Metallic Thin Sheet: Evolution of the Two Bands Pattern, Strain, vol.52, issue.3, pp.244-260, 2016.

C. Bao, M. François, and L. L. Joncour, Influence of Specimen Geometry on Strain Localization Phenomena in Steel Sheets. Applied Mechanics and Materials, vol.784, pp.514-519, 2015.

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

Y. Bao and T. Wierzbicki, A Comparative Study on Various Ductile Crack Formation Criteria, Journal of Engineering Materials and Technology, vol.126, issue.3, pp.314-324

Y. Bao and T. Wierzbicki, On the cut-off value of negative triaxiality for fracture, Engineering Fracture Mechanics, vol.72, issue.7, pp.1049-1069, 2005.

F. Barlat, J. C. Brem, J. W. Yoon, K. Chung, R. E. Dick et al., Plane stress yield function for aluminum alloy sheets-part 1: theory, International Journal of Plasticity, vol.19, issue.9, pp.1297-1319, 2003.

M. Basaran, Stress state dependent damage modeling with a focus on the lode angle influence, 2011.

M. Beese, M. Luo, Y. Li, Y. Bai, and T. Wierzbicki, Partially coupled anisotropic fracture model for aluminum sheets, Engineering Fracture Mechanics, vol.77, issue.7, pp.1128-1152, 2010.

J. Besson, C. Berdin, S. Bugat, and F. Feyel, Local Approach to Fracture. Presses de l'Ecole des Mines, 2004.
URL : https://hal.archives-ouvertes.fr/hal-00755207

J. Besson, G. Cailletaud, J. L. Chaboche, and S. Forest, Non-linear mechanics of materials, vol.167, 2009.

J. Besson, D. Steglich, and W. Brocks, Modeling of crack growth in round bars and plane strain specimens, International Journal of Solids and Structures, vol.38, pp.8259-8284, 2001.

J. Besson, D. Steglich, and W. Brocks, Modeling of plane strain ductile rupture, International Journal of Plasticity, vol.19, issue.10, pp.1517-1541, 2003.

B. L. Boyce, S. L. Kramer, T. R. Bosiljevac, E. Corona, J. A. Moore et al.,

K. Mattie, T. Pack, S. Wierzbicki, S. Chi, A. Lin et al., The second Sandia Fracture Challenge: predictions of ductile failure under quasi-static and moderate-rate dynamic loading, International Journal of Fracture, vol.198, issue.1-2, pp.5-100, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01305640

B. L. Boyce, S. L. Kramer, H. E. Fang, T. E. Cordova, M. K. Neilsen et al., International Journal of Fracture, vol.186, issue.1-2, pp.5-68, 2014.

P. Bridgman, Studies in large plastic flow and fracture, 1952.

F. Bron, Déchirure ductile des tôles minces en alliage d'aluminium 2024 pour application aéronautique. phdthesis, ´ Ecole Nationale Supérieure des Mines de Paris, 2004.

B. Brozzo, B. Deluca, and R. Rendina, A new method for the prediction of formability limits in metal sheets, sheet metal forming and formability, Proceedings of the 7th biennial conference of the international deep drawing research group, amsterdam, 1972.

M. Brünig, S. Gerke, and V. Hagenbrock, Micro-mechanical studies on the effect of the stress triaxiality and the Lode parameter on ductile damage, International Journal of Plasticity, vol.50, pp.49-65, 2013.

D. Bushnell, Buckling of Shells-Pitfall for Designers, AIAA Journal, vol.19, issue.9, pp.1183-1226, 1981.

T. Børvik, S. Dey, and A. H. Clausen, Perforation resistance of five different highstrength steel plates subjected to small-arms projectiles, International Journal of Impact Engineering, vol.36, issue.7, pp.948-964, 2009.

H. Bühler, L. Gerlach, O. Greven, and W. Bleck, The electrochemical reactivation test (ert) to detect the susceptibility to intergranular corrosion, Corrosion Science, vol.45, issue.10, pp.2325-2336, 2003.

S. Cao, J. M. Gachet, P. Montmitonnet, and P. O. Bouchard, A Lode-dependent enhanced Lemaitre model for ductile fracture prediction at low stress triaxiality, Engineering Fracture Mechanics, vol.124, pp.80-96, 2014.
URL : https://hal.archives-ouvertes.fr/hal-00987142

, Trong Son Cao : Modeling ductile damage for complex loading paths. phdthesis, Ecole Nationale Supérieure des Mines de Paris, 2013.

O. Cazacu, B. Plunkett, and F. Barlat, Orthotropic yield criterion for hexagonal closed packed metals, International Journal of Plasticity, vol.22, issue.7, pp.1171-1194, 2006.

J. L. Chaboche, Anisotropic creep damage in the framework of continuum damage mechanics, Nuclear Engineering and Design, vol.79, issue.3, pp.309-319, 1984.

S. Chocron, B. Erice, and C. E. , Anderson : A new plasticity and failure model for ballistic application, International Journal of Impact Engineering, vol.38, issue.8, pp.755-764, 2011.

M. Choung and S. R. Cho, Study on true stress correction from tensile tests, Journal of Mechanical Science and Technology, vol.22, issue.6, pp.1039-1051, 2008.

C. Chu and A. Needleman, Void Nucleation Effects in Biaxially Stretched Sheets, Journal of Engineering Materials and Technology, vol.102, issue.3, pp.249-256, 1980.

M. G. Cockcroft and D. J. Latham, Ductility and the Workability of Metals, Journal of the Institute of Metals, vol.96, pp.33-39, 1968.

A. Considère, Memoire sur l'emploi du fer et de l'acier dans les constructions, p.1885

L. Coppola, P. Cortese, and . Folgarait, The effect of stress invariants on ductile fracture limit in steels, Engineering Fracture Mechanics, vol.76, issue.9, pp.1288-1302, 2009.

T. Cortese, F. Coppola, F. Campanelli, M. Campana, and . Sasso, Prediction of ductile failure in materials for onshore and offshore pipeline applications, International Journal of Damage Mechanics, vol.23, issue.1, pp.104-123, 2014.

K. Decamp, L. Bauvineau, J. Besson, and A. Pineau, Size and geometry effects on ductile rupture of notched bars in a C-Mn steel: experiments and modelling, International Journal of Fracture, vol.88, issue.1, pp.1-18, 1997.

C. Defaisse, L. Marcin, M. Djouma, J. , J. Besson et al., Procede de caractérisation d'un matériau, 2018.

M. Defaisse, L. Mazì-ere, J. Marcin, and . Besson, Ductile fracture of an ultra-high strength steel under low to moderate stress triaxiality, Engineering Fracture Mechanics, 2018.
URL : https://hal.archives-ouvertes.fr/hal-01780585

D. Delagnes, F. Pettinari-sturmel, M. H. Mathon, R. Danoix, F. Danoix et al., Cementite-free martensitic steels: A new route to develop high strength/high toughness grades by modifying the conventional precipitation sequence during tempering, Acta Materialia, vol.60, issue.16, pp.5877-5888
URL : https://hal.archives-ouvertes.fr/hal-01687325

I. Doghri and R. Billardon, Investigation of localization due to damage in elasto-plastic materials, Mechanics of Materials, vol.19, issue.2-3, pp.129-149, 1995.

D. C. Drucker and W. Prager, Soil mechanics and plastic analysis or limit design, Quarterly of applied mathematics, vol.10, issue.2, pp.157-165, 1952.

M. Dunand and D. Mohr, On the predictive capabilities of the shear modified Gurson and the modified Mohr-Coulomb fracture models over a wide range of stress triaxialities and Lode angles, Journal of the Mechanics and Physics of Solids, vol.59, issue.7, pp.1374-1394, 2011.
URL : https://hal.archives-ouvertes.fr/hal-00620573

B. Erice and F. Gálvez, A coupled elastoplastic-damage constitutive model with Lode angle dependent failure criterion, International Journal of Solids and Structures, vol.51, issue.1, pp.93-110, 2014.

J. Faleskog and I. Barsoum, Tension-torsion fracture experiments-Part I: Experiments and a procedure to evaluate the equivalent plastic strain, International Journal of Solids and Structures, vol.50, pp.4241-4257, 2013.

L. Ferrer, Cryogenic treatment of martensitic steel with mixed hardening, p.151, 2011.

L. Ferrer and P. Heritier, Method for producing martensitic steel with mixed hardening, 2011.

A. Freudenthal and H. Geiringer, The mathematical theories of the inelastic continuum, pp.229-433, 1958.

M. Garrison, Ultra high strength steels for aerospace applications, JOM, vol.42, issue.5, pp.20-24, 1990.

A. Ghahremaninezhad and K. Ravi-chandar, Ductile failure behavior of polycrystalline Al 6061-T6, International Journal of Fracture, vol.174, issue.2, pp.177-202

A. Gilioli, A. Manes, M. Giglio, and T. Wierzbicki, Predicting ballistic impact failure of aluminium 6061-T6 with the rate-independent Bao-Wierzbicki fracture model, International Journal of Impact Engineering, vol.76, pp.207-220, 2015.

M. Graham, T. Zhang, X. Gao, and M. Hayden, Development of a combined tension-torsion experiment for calibration of ductile fracture models under conditions of low triaxiality, International Journal of Mechanical Sciences, vol.54, issue.1, pp.172-181, 2012.

M. Gromada, G. Mishuris, and A. Ochsner, Stress Distribution in the Sample Neck during the Tensile Testing. In Correction Formulae for the Stress Distribution in Round Tensile Specimens at Neck Presence, SpringerBriefs in Applied Sciences and Technology, pp.17-65, 2011.

A. J. Gross and K. Ravi-chandar, On the deformation and failure of Al 6061-T6 at low triaxiality evaluated through in situ microscopy, International Journal of Fracture, vol.200, issue.1, pp.185-208, 2016.

A. J. Gross and K. Ravi-chandar, On the deformation and failure of Al 6061-T6 in plane strain tension evaluated through in situ microscopy, International Journal of Fracture, 2018.

G. Gruben, D. Morin, M. Langseth, and O. S. Hopperstad, Strain localization and ductile fracture in advanced high-strength steel sheets, European Journal of Mechanics -A/Solids, vol.61, pp.315-329, 2017.

G. Gu and D. Mohr, Anisotropic Hosford-Coulomb fracture initiation model: Theory and application, Engineering Fracture Mechanics, vol.147, pp.480-497, 2015.

A. L. Gurson, Continuum Theory of Ductile Rupture by Void Nucleation and Growth: Part I-Yield Criteria and Flow Rules for Porous Ductile Media, Journal of Engineering Materials and Technology, vol.99, issue.1, pp.2-15, 1977.

S. S. Haltom, S. Kyriakides, and K. Ravi-chandar, Ductile failure under combined shear and tension, International Journal of Solids and Structures, vol.50, issue.10, pp.1507-1522, 2013.

J. W. Hancock and A. C. Mackenzie, On the mechanisms of ductile failure in highstrength steels subjected to multi-axial stress-states, Journal of the Mechanics and Physics of Solids, vol.24, issue.2, pp.147-160, 1976.

R. Hill, A theory of the yielding and plastic flow of anisotropic metals, Proceedings of the Royal Society of London.A, vol.193, pp.281-297, 1033.

W. F. , Hosford : A Generalized Isotropic Yield Criterion, Journal of Applied Mechanics, vol.39, issue.2, pp.607-609

J. W. Hutchinson and V. Tvergaard, Shear band formation in plane strain, International Journal of Solids and Structures, vol.17, issue.5, pp.451-470, 1981.

G. Johnson and W. Cook, Fracture characteristics of three metals subjected to various strains, strain rates, temperatures and pressures, Engineering Fracture Mechanics, vol.21, issue.1, pp.31-48, 1985.

M. Kamaya and M. Kawakubo, A procedure for determining the true stress-strain curve over a large range of strains using digital image correlation and finite element analysis, Mechanics of Materials, vol.43, issue.5, pp.243-253, 2011.

J. H. Kim, A. Serpantié, F. Barlat, F. Pierron, and M. G. Lee, Characterization of the post-necking strain hardening behavior using the virtual fields method, International Journal of Solids and Structures, vol.50, issue.24, pp.3829-3842, 2013.

H. Kitahara, R. Ueji, N. Tsuji, and Y. Minamino, Crystallographic features of lath martensite in low-carbon steel, Acta Materialia, vol.54, issue.5, pp.1279-1288, 2006.

P. Ladeveze and J. Lemaitre, Damage effective stress in quasi-unilateral material conditions, Proc. IUTAM Congress, vol.25, 1984.

P. Landau, S. Osovski, A. Venkert, V. Gärtnerová, and D. Rittel, The genesis of adiabatic shear bands, Scientific Reports, vol.6, p.37226, 2016.

W. I. Lankford, S. C. Snyder, and J. A. Bauscher, New criteria for predicting the press performance of deep-drawing sheets, Transaction ASM, vol.42, pp.1196-1232, 1950.

J. D. G-le-roy, G. Embury, M. F. Edwards, and . Ashby, A model of ductile fracture based on the nucleation and growth of voids, Acta Metallurgica, vol.29, issue.8, pp.1509-1522, 1981.

H. Leitner, W. Sha, Z. Guo, and W. Xu, Phase transformations in maraging steels, 2012.

J. Lemaitre, A Continuous Damage Mechanics Model for Ductile Fracture, Journal of Engineering Materials and Technology, vol.107, issue.1, pp.83-89, 1985.

J. Lemaitre, Local approach of fracture, Engineering Fracture Mechanics, vol.25, issue.5, pp.523-537, 1986.

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

K. Levenberg, A method for the solution of certain non-linear problems in least squares, Quarterly of Applied Mathematics, vol.2, issue.2, pp.164-168, 1944.

M. Li, J. Luo, T. Gerlach, and . Wierzbicki, Prediction of shear-induced fracture in sheet metal forming, Journal of Materials Processing Technology, vol.210, issue.14, pp.1858-1869, 2010.

W. Lode, Versuchë uber den Einfluß der mittleren Hauptspannung auf das Fließen der

M. Eisen, . Kupfer, and . Nickel, Zeitschrift fur Physik, vol.36, pp.913-939, 1926.

J. Lorthios, Endommagement des aciers TWIP pour application automobile, 2011.
URL : https://hal.archives-ouvertes.fr/pastel-00689791

H. Lou, S. Huh, K. Lim, and . Pack, New ductile fracture criterion for prediction of fracture forming limit diagrams of sheet metals, International Journal of Solids and Structures, vol.49, issue.25, pp.3605-3615, 2012.

M. Luo, M. Dunand, and D. Mohr, Experiments and modeling of anisotropic aluminum extrusions under multi-axial loading -part ii: Ductile fracture, International Journal of Plasticity, pp.36-58, 2012.

L. Malcher, F. M. Andrade-pires, and J. M. , César de Sá : An assessment of isotropic constitutive models for ductile fracture under high and low stress triaxiality, International Journal of Plasticity, pp.81-115, 2012.

S. Marcadet, Ductile fracture after complex loading histories : experimental investigation and constitutive modeling. Thesis, 2015.

J. Marcadet and D. Mohr, Critical hardening rate model for predicting pathdependent ductile fracture, International Journal of Fracture, vol.200, issue.1-2, pp.77-98, 2016.

F. Maresca, V. G. Kouznetsova, and M. G. Geers, On the role of interlath retained austenite in the deformation of lath martensite. Modelling and Simulation in, Materials Science and Engineering, vol.22, issue.4, p.45011, 2014.

D. Marquardt, An Algorithm for Least-Squares Estimation of Nonlinear Parameters, Journal of the Society for Industrial and Applied Mathematics, vol.11, issue.2, pp.431-441, 1963.

F. A. Mcclintock, A Criterion for Ductile Fracture by the Growth of Holes, Journal of Applied Mechanics, vol.35, issue.2, pp.363-371, 1968.

F. A. Mcclintock, Fracture : an advanced treatise -engineering fundamentals and environmental effects, volume III. Academic presséditionpressédition, 1971.

Y. Mine, K. Hirashita, H. Takashima, M. Matsuda, and K. Takashima, Microtension behaviour of lath martensite structures of carbon steel, Materials Science and Engineering : A, vol.560, pp.535-544, 2013.

G. Mirone, A new model for the elastoplastic characterization and the stress-strain determination on the necking section of a tensile specimen, International Journal of Solids and Structures, vol.41, issue.13, pp.3545-3564, 2004.

G. Mirone and D. Corallo, Stress-strain and ductile fracture characterization of an X100 anisotropic steel: Experiments and modelling, Engineering Fracture Mechanics, vol.102, pp.118-145, 2013.

M. S. Mirza, D. C. Barton, and P. Church, The effect of stress triaxiality and strainrate on the fracture characteristics of ductile metals, Journal of Materials Science, vol.31, issue.2, pp.453-461, 1996.

. R-v-mises, Mechanik der festen körper im plastisch-deformablen zustand, Nachrichten von der Gesellschaft der Wissenschaften zu Göttingen, Mathematisch-Physikalische Klasse, vol.1913, issue.4, pp.582-592, 1913.

D. Mohr and S. J. Marcadet, Micromechanically-motivated phenomenological Hosford-Coulomb model for predicting ductile fracture initiation at low stress triaxialities, International Journal of Solids and Structures, p.000357243900003

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.
URL : https://hal.archives-ouvertes.fr/hal-00658608

T. F. Morgeneyer, L. Helfen, and H. Mubarak, Hild : 3d Digital Volume Correlation of Synchrotron Radiation Laminography Images of Ductile Crack Initiation: An Initial Feasibility Study, Experimental Mechanics, vol.53, issue.4, pp.543-556, 2013.

S. Morito, T. Ohba, A. K. Das, T. Hayashi, and M. Yoshida, Effect of solution carbon and retained austenite films on the development of deformation structures of low-carbon lath martensite, ISIJ International, vol.53, issue.12, pp.2226-2232, 2013.

A. P. , Mouritz : Introduction to aerospace materials, 2012.

M. Murayama, K. Hono, and Y. Katayama, Microstructural evolution in a 17-4 PH stainless steel after aging at 400degC. Metallurgical and Materials Transactions A, vol.30, pp.345-353, 1999.

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.

, NASA : MMPDS-02 : Metallic materials properties development and standardization (MMPDS)

L. Nielsen and V. Tvergaard, Effect of a shear modified Gurson model on damage development in a FSW tensile specimen, International Journal of Solids and Structures, vol.46, issue.3-4, pp.587-601, 2009.

K. L. Nielsen and V. Tvergaard, Ductile shear failure or plug failure of spot welds modelled by modified Gurson model, Engineering Fracture Mechanics, vol.77, issue.7, pp.1031-1047, 2010.

Z. Nishiyama, Martensitic transformation, 2012.

I. Oh, C. C. Chen, and S. Kobayashi, Ductile Fracture in Axisymmetric Extrusion and Drawing-Part 2: Workability in Extrusion and Drawing, Journal of Engineering for Industry, vol.101, issue.1, pp.36-44

G. B. Olson, Ferrium M54 steel: High-strength, high-toughness, scc resistant alloy, 2017.

E. Orowan, Discussion in. In Symposium on Internal Stresses in Metals and Alloys, p.451, 1948.

M. Oyane, Criteria of ductile fracture strain, vol.15, pp.1507-1513, 1972.

A. Pampillo and H. W. Paxton, The effect of reverted austenite on the mechanical properties and toughness of 12 ni and 18 ni (200) maraging steels, Metallurgical Transactions, vol.3, issue.11, pp.2895-2903

J. Papasidero, V. Doquet, and D. Mohr, Ductile fracture of aluminum 2024-T351 under proportional and non-proportional multi-axial loading: Bao-Wierzbicki results revisited, International Journal of Solids and Structures, pp.459-474, 2015.
URL : https://hal.archives-ouvertes.fr/hal-01227222

W. Ramberg and W. R. Osgood, Description of stress-strain curves by three parameters

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.201-217, 1969.

J. R. Rice, The localization of plastic deformation, Theoretical and Applied Mechanics, pp.207-220, 1976.

M. Rodríguez-millán and ´. A. Vaz-romero-et´aet´-et´a, Arias : Failure behavior of 2024-T3 aluminum under tension-torsion conditions, Journal of Mechanical Science and Technology, vol.29, issue.11, pp.4657-4663, 2015.

G. L. Rosa, A. Risitano, and G. Mirone, Postnecking elastoplastic characterization: Degree of approximation in the bridgman method and properties of the flow-stress/truestress ratio, Metallurgical and Materials Transactions A, vol.34, issue.3, pp.615-624, 2003.

W. Rudnicki and J. R. , Rice : Conditions for the localization of deformation in pressuresensitive dilatant materials, Journal of the Mechanics and Physics of Solids, vol.23, issue.6, pp.371-394, 1975.

M. Scales, N. Tardif, and S. Kyriakides, Ductile failure of aluminum alloy tubes under combined torsion and tension, International Journal of Solids and Structures, pp.116-128, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01802248

R. Schnitzer, S. Zinner, and H. Leitner, Modeling of the yield strength of a stainless maraging steel, Scripta Materialia, vol.62, issue.5, pp.286-289, 2010.

J. D. Bibliographie, Seidt : Plastic Deformation and Ductile Fracture of 2024-T351 Aluminum under Various Loading Conditions, 2010.

E. Siebel and S. Schwaigerer, On the mechanics of the tensile test (en allemand). Arch Eisenhuttenwes, pp.145-152, 1948.

H. Sobel and S. Z. Newman, Plastic Buckling of Cylindrical Shells Under Axial Compression, Journal of Pressure Vessel Technology, vol.102, issue.1, pp.40-44, 1980.

C. Soyarslan, H. Richter, and S. Bargmann, Variants of Lemaitre's damage model and their use in formability prediction of metallic materials, Mechanics of Materials, vol.92, pp.58-79, 2016.

W. Szczepi´nskiszczepi´nski, L. Dietrich, and J. Miastkowski, La capacitée limite desélémentsdeséléments de construction, 1970.

B. Tanguy, T. T. Luu, G. Perrin, A. Pineau, and J. Besson, Plastic and damage behaviour of a high strength X100 pipeline steel: Experiments and modelling, International Journal of Pressure Vessels and Piping, vol.85, issue.5, pp.322-335, 2008.
URL : https://hal.archives-ouvertes.fr/hal-00280890

V. Tarigopula, O. S. Hopperstad, M. Langseth, A. H. Clausen, F. Hild et al., A study of large plastic deformations in dual phase steel using digital image correlation and fe analysis, vol.48, pp.181-196, 2008.
URL : https://hal.archives-ouvertes.fr/hal-00326970

C. Teko?-glu, J. W. Hutchinson, and T. Pardoen, On localization and void coalescence as a precursor to ductile fracture, Philosophical Transactions of the Royal Soc. A, vol.373, p.20140121, 2015.

G. Thomas, Retained austenite and tempered martensite embrittlement, Metallurgical Transactions A, vol.9, issue.3, pp.439-450, 1978.

N. Thomas, S. Basu, and A. Benzerga, On fracture loci of ductile materials under non-proportional loading, International Journal of Mechanical Sciences, vol.117, pp.135-151, 2016.

R. L. Thomas, J. R. Scully, and R. P. Gangloff, Internal hydrogen embrittlement of ultrahigh-strength AERMET 100 steel, Metallurgical and Materials Transactions A, vol.34, issue.2, pp.327-344, 2003.

H. Tresca, Mémoires sur l'´ ecoulement des corps solides. Imprimerie impériale, p.1869

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.

K. Viswanathan, G. K. Dey, and V. Sethumadhavan, Effects of austenite reversion during overageing on the mechanical properties of 18 ni 350 maraging steel, Materials Science and Engineering : A, vol.398, issue.1-2, pp.367-372, 2005.

T. Wierzbicki and Y. Bai, Application of extended Mohr-Coulomb criterion to ductile fracture, International Journal of Fracture, vol.161, issue.1, pp.1-20, 2010.

T. Wierzbicki, Y. Bao, Y. W. Lee, and Y. Bai, Calibration and evaluation of seven fracture models, International Journal of Mechanical Sciences, vol.47, issue.4, pp.719-743, 2005.

Y. B. Xu, Y. L. Bai, Q. Xue, and L. T. , Shen : Formation, microstructure and development of the localized shear deformation in low-carbon steels, Acta Materialia, vol.44, issue.5, pp.1917-1926, 1996.

L. Xue, Damage accumulation and fracture initiation in uncracked ductile solids subject to triaxial loading, International Journal of Solids and Structures, vol.16, issue.44, pp.5163-5181, 2007.

L. Xue, Ductile fracture modeling : theory, experimental investigation and numerical verification. Thesis, p.2007

L. Xue and T. Wierzbicki, On the effect of the third invariant of the stress deviator on ductile fracture, 2005.

L. Xue and T. Wierzbicki, Ductile fracture initiation and propagation modeling using damage plasticity theory, Engineering Fracture Mechanics, vol.75, issue.11, pp.3276-3293, 2008.

C. Zener and J. , Hollomon : Effect of Strain Rate Upon Plastic Flow of Steel, Journal of Applied Physics, vol.15, issue.1, pp.22-32

Z. L. Zhang, M. Hauge, J. Odegard, and C. Thaulow, Determining material true stress-strain curve from tensile specimens with rectangular cross-section, International Journal of Solids and Structures, vol.36, issue.23, pp.3497-3516, 1999.

X. Zhuang, Y. Meng, and Z. Zhao, Evaluation of prediction error resulting from using average state variables in the calibration of ductile fracture criterion, International Journal of Damage Mechanics, 2017.

L. Lee and C. S. Ades, Plastic torsional buckling strength of cylinders including the effects of imperfections, J Aeronaut Sci, vol.24, issue.4, pp.241-249, 1957.

C. S. Ades, Bending strength of tubing in the plastic range, J Aeronaut Sci, vol.24, issue.8, pp.605-615, 1957.

C. Defaisse, Ductile fracture of an ultra-high strength steel under low to moderate stress triaxiality, Engineering Fracture Mechanics, 2018.
URL : https://hal.archives-ouvertes.fr/hal-01780585

B. L. Boyce, S. Kramer, H. E. Fang, T. E. Cordova, M. K. Neilsen et al., The sandia fracture challenge: blind round robin predictions of ductile tearing, Int J Fract, vol.186, issue.1, pp.5-68, 2014.

B. L. Boyce, S. Kramer, T. R. Bosiljevac, E. Corona, J. A. Moore et al., The second sandia fracture challenge: predictions of ductile failure under quasi-static and moderate-rate dynamic loading, Int. J. Fract, vol.198, issue.1, pp.5-100, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01305640

F. M. Beremin, Cavity formation from inclusions in ductile fracture of A508 steel, Metal Trans A, vol.12, pp.723-754, 1981.

L. Roy, G. Embury, J. D. Edwards, G. Ashby, and M. F. , A model of ductile fracture based on the nucleation and growth of voids, Acta Metall, vol.29, issue.8, pp.1509-1531, 1981.

J. Gr and C. Wh, Fracture characteristics of three metals subjected to various strains, strain rates, temperatures and pressures, Eng Fract Mech, vol.21, issue.1, pp.31-48, 1985.

W. Lode, Versuche über den Einfluß der mittleren Hauptspannung auf das Fließen der Metalle Eisen, Kupfer und Nickel. Zeitschrift für Physik, vol.36, pp.913-952, 1926.

Y. Bai and T. Wierzbicki, A new model of metal plasticity and fracture with pressure and Lode dependence, Int J Plast, vol.24, issue.6, pp.1071-96, 2008.

M. Dunand and D. Mohr, On the predictive capabilities of the shear modified Gurson and the modified Mohr-Coulomb fracture models over a wide range of stress triaxialities and lode angles, J Mech Phys Solids, vol.59, issue.7, pp.1374-94, 2011.
URL : https://hal.archives-ouvertes.fr/hal-00620573

J. Faleskog and I. Barsoum, Tension-torsion fracture experiments-part i: experiments and a procedure to evaluate the equivalent plastic strain, Int J Solids Struct, vol.50, issue.25, pp.4241-57, 2013.

T. Cao, J. Gachet, P. Montmitonnet, and P. Bouchard, A Lode-dependent enhanced Lemaitre model for ductile fracture prediction at low stress triaxiality, Eng Fract Mech, vol.124, pp.80-96, 2014.
URL : https://hal.archives-ouvertes.fr/hal-00987142

L. Cortese, T. Coppola, F. Campanelli, F. Campana, and M. Sasso, Prediction of ductile failure in materials for onshore and offshore pipeline applications, Int J Damage Mech, vol.23, issue.1

L. Ferrer and P. Heritier, Method for producing martensitic steel with mixed hardening, Patent CA2766779 A1 -Snecma

L. Ferrer, Cryogenic treatment of martensitic steel with mixed hardening, Patent CA2777034 A1 -Snecma <https

S. Morito, T. Ohba, A. K. Das, T. Hayashi, and Y. Mai, Effect of solution carbon and retained austenite films on the development of deformation structures of lowcarbon lath martensite, ISIJ Int, vol.53, issue.12, pp.2226-2258, 2013.

H. Abdesselam, J. Crépin, A. Pineau, A. Rouffie, P. Gaborit et al., On the crystallographic, stage I-like, character of fine granular area formation in internal fish-eye fatigue cracks, Int J Fatigue, vol.106, pp.132-174, 2018.
URL : https://hal.archives-ouvertes.fr/hal-01633714

P. W. Bridgman, Studies in large plastic flow and fracture with a special emphasis on the effects of hydrostatic pressure, 1964.

A. Mackenzie, J. Hancock, and D. Brown, On the influence of state of stress on ductile failure initiation in high strength steels, Eng Fract Mech, vol.9, pp.167-88, 1977.

S. M. Graham, T. Zhang, X. Gao, and M. Hayden, Development of a combined tension-torsion experiment for calibration of ductile fracture models under conditions of low triaxiality, Int J Mech Sci, vol.54, issue.1, pp.172-81, 2012.

S. Haltom, S. Kyriakides, and K. Ravi-chandar, Ductile failure under combined shear and tension, Int J Solids Struct, vol.50, issue.10, pp.1507-1529, 2013.

J. Papasidero, V. Doquet, and D. Mohr, Ductile fracture of aluminum 2024-t351 under proportional and non-proportional multi-axial loading: Bao-wierzbicki results revisited, Int J Solids Struct, 2015.
URL : https://hal.archives-ouvertes.fr/hal-01227222

G. L. Rosa, G. Mirone, and A. Risitano, Effect of stress triaxiality corrected plastic flow on ductile damage evolution in the framework of continuum damage mechanics, Eng Fract Mech, vol.68, issue.4, pp.417-451, 2001.

G. H. Majzoobi, F. Fariba, M. Pipelzadeh, and S. Hardy, A new approach for the correction of stress-strain curves after necking in metals, J Strain Anal Eng Des, vol.50, issue.2, pp.125-162, 2015.

G. Mirone and D. Corallo, Stress-strain and ductile fracture characterization of an 100Â anisotropic steel: experiments and modelling, Eng Fract Mech, vol.102, pp.118-163, 2013.

W. Rekik, O. Ancelet, and C. Gardin, Identification of the gradient of mechanical properties in electron beam welded joints of thick Al6061-T6 plate, Proceedings of the ASME pressure vessels and piping conference, 2016.

O. Ancelet and S. Chapuliot, Tensile characterization of narrow gap bimetallic weld ferritic-austenitic steel with a new measurement system for tensile testing, Proceedings of the asme pressure vessels and piping conference, vol.6, 2016.

W. Hosford, Generalized isotropic yield criterion, J Appl Mech, vol.39, issue.2, pp.607-616, 1972.

P. Bridgman, Studies in large plastic flow and fracture, 1952.

Z. Zhang, M. Hauge, J. Odegard, and C. Thaulow, Determining material true stress-strain curve from tensile specimens with rectangular cross-section, Int J Solids Struct, vol.36, issue.23, pp.3497-516, 1999.

I. Scheider, W. Brocks, and A. Cornec, Procedure for the determination of true stress-strain curves from tensile tests with rectangular cross-section specimens, J Eng Mater Technol, vol.126, issue.1, pp.70-76, 2004.

J. M. Choung and S. R. Cho, Study on true stress correction from tensile tests, J Mech Sci Technol, vol.22, issue.6, pp.1039-51, 2008.

G. Mirone, A new model for the elastoplastic characterization and the stress-strain determination on the necking section of a tensile specimen, Int J Solids Struct, vol.41, issue.13, pp.3545-64, 2004.

B. Audoly and J. W. Hutchinson, Analysis of necking based on a one-dimensional model, J Mech Phys Solids, vol.97, pp.68-91, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01212041

M. Kamaya and M. Kawakubo, A procedure for determining the true stress-strain curve over a large range of strains using digital image correlation and finite element analysis, Mech Mater, vol.43, issue.5, pp.243-53, 2011.

D. Mohr and S. Marcadet, Micromechanically-motivated phenomenological hosford-coulomb model for predicting ductile fracture initiation at low stress triaxialities, Int J Solids Struct, pp.40-55, 2015.

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.6, pp.1079-85, 1985.

V. Tvergaard, Behaviour of porous ductile solids at low stress triaxiality in different modes of deformation, Int J Solids Struct, vol.2015, pp.28-34

K. Danas and P. Ponte-castaneda, A finite-strain model for anisotropic viscoplastic porous media: II -applications, Euro J Mech/A, vol.28, issue.3, pp.402-418, 2009.
URL : https://hal.archives-ouvertes.fr/hal-00526643

T. Wierzbicki, Y. Bao, Y. Lee, and Y. Bai, Calibration and evaluation of seven fracture models, Int J Mech Sci, vol.47, issue.4-5, pp.719-762, 2005.

J. R. Rice and D. M. Tracey, On the ductile enlargement of voids in triaxial stress fields, J Mech Phys Solids, vol.17, issue.3, pp.201-218, 1969.

K. Decamp, L. Bauvineau, J. Besson, and A. Pineau, Size and geometry effects on ductile rupture of notched bars in a C-Mn steel: experiments and modelling, Int J Fract, vol.88, issue.1, pp.1-18, 1997.

Y. Bao and T. Wierzbicki, On fracture locus in the equivalent strain and stress triaxiality space, Int J Mech Sci, vol.46, issue.1, pp.81-98, 2004.

M. Luo, M. Dunand, and D. Mohr, Experiments and modeling of anisotropic aluminum extrusions under multi-axial loading -part II: ductile fracture, Int J Plast, pp.36-58, 2012.

L. Cortese, T. Coppola, F. Campanelli, and G. Broggiato, A J 2 -J 3 approach in plastic and damage description of ductile materials, Int J Damage Mech, vol.25, issue.2, pp.228-50, 2016.

K. Zhang, J. Bai, and D. Francois, Numerical analysis of the influence of the lode parameter on void growth, Int J Solids Struct, vol.38, pp.5847-56, 2001.

K. Nahshon and J. Hutchinson, Modification of the Gurson model for shear failure, Euro J Mech/A, vol.27, issue.1, pp.1-17, 2008.

C. Defaisse, Engineering Fracture Mechanics, 2018.

V. Tvergaard and A. Needleman, Analysis of the cup-cone fracture in a round tensile bar, Acta Metall, vol.32, issue.1, pp.157-69, 1984.

Y. Bai and T. Wierzbicki, A comparative study of three groups of ductile fracture loci in the 3d space, Eng Fract Mech, vol.135, pp.147-67, 2015.

Y. Bai and T. Wierzbicki, Application of extended Mohr-Coulomb criterion to ductile fracture, Int J Fract, vol.161, issue.1, pp.1-20, 2010.

G. Gu and D. Mohr, Anisotropic Hosford-Coulomb fracture initiation model: theory and application, Eng Fract Mech, vol.147, pp.480-97, 2015.

M. Dunand and D. Mohr, Effect of lode parameter on plastic flow localization after proportional loading at low stress triaxialities, J Mech Phys Solids, vol.66, pp.133-53, 2014.

R. Hill, The mathematical theory of plasticity, 1950.

F. Barlat, D. Lege, and J. Brem, A six-component yield function for anisotropic materials, Int J Plast, vol.7, pp.693-712, 1991.

A. Benzerga and J. Besson, Plastic potentials for anisotropic porous solids, Euro J Mech/A, vol.20, issue.3, pp.397-434, 2001.

Y. Shinohara, Y. Madi, and J. Besson, Anisotropic ductile failure of a high-strength line pipe steel, Int J Fract, vol.197, pp.127-172, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01295773

A. Needleman and J. Rice, Limits to ductility set by plastic flow localization, pp.237-67, 1978.

L. Daehli, D. Morin, T. Børvik, and O. Hopperstad, Influence of yield surface curvature on the macroscopic yielding and ductile failure of isotropic porous plastic materials, J Mech Phys Solids, vol.107, pp.253-83, 2017.

O. Cazacu, B. Revil-baudard, N. Chandola, and D. Kondo, New analytical criterion for porous solids with tresca matrix under axisymmetric loadings, Int J Solids Struct, vol.51, pp.861-74, 2014.
URL : https://hal.archives-ouvertes.fr/hal-01667110

A. Benzerga, J. Besson, and A. Pineau, Anisotropic ductile fracture Part I: experiments, Acta Mater, vol.52, pp.4623-4661, 2004.
URL : https://hal.archives-ouvertes.fr/hal-00164227

A. Benzerga, J. Besson, and A. Pineau, Anisotropic ductile fracture Part II: theory, Acta Mater, vol.52, pp.4639-50, 2004.
URL : https://hal.archives-ouvertes.fr/hal-00164239

J. Besson and R. Foerch, Large scale object-oriented finite element code design, Comp Meth Appl Mech Eng, vol.142, pp.165-87, 1997.

F. Sidoroff and A. Dogui, Some issues about anisotropic elastic-plastic models at finite strain, Int J Solids Struct, vol.38, pp.9569-78, 2001.

J. Mediavilla, R. Peerlings, and M. Geers, An integrated continuous-discontinuous approach towards damage engineering in sheet metal forming processes, Eng Fract Mech, vol.73, issue.7, pp.895-916, 2006.

E. Lorentz, J. Besson, and V. Cano, Numerical simulation of ductile fracture with the Rousselier constitutive law, Comp Meth Appl Mech Eng, vol.197, pp.1965-82, 2008.
URL : https://hal.archives-ouvertes.fr/hal-00268315

T. Linse, G. Hütter, and M. Kuna, Simulation of crack propagation using a gradient-enriched ductile damage model based on dilatational strain, Eng Fract Mech, vol.95, pp.13-28, 2012.

M. Kroon and J. Faleskog, A probabilistic model for cleavage fracture with a length scale influence of material parameters and constraint, Int J Fract, vol.118, pp.99-118, 2002.

J. Faleskog, M. Kroon, and H. Öberg, A probabilistic model for cleavage fracture with a length scale -parameter estimation and predictions of stationary crack experiments, Eng Fract Mech, vol.71, issue.1, pp.57-79, 2004.

S. Marcadet and D. Mohr, Critical hardening rate model for predicting path-dependent ductile fracture, Int J Fract, vol.200, pp.77-98, 2016.

B. Tanguy, T. Luu, G. Perrin, A. Pineau, and J. Besson, Plastic and damage behavior of a high strength X100 pipeline steel: experiments and modelling, Int J Press Vess Pip, vol.85, issue.5, pp.322-357, 2008.

Y. Bao and T. Wierzbicki, On the cut-off value of negative triaxiality for fracture, Eng Fract Mech, vol.72, issue.7, pp.1049-69, 2005.

C. Defaisse, Ductile fracture of an ultra-high strength steel under low to moderate stress triaxiality, Engineering Fracture Mechanics, 2018.
URL : https://hal.archives-ouvertes.fr/hal-01780585