J. Datsko and C. T. Yang, Correlation of Bendability of Materials With Their Tensile Properties, Journal of Engineering for Industry, vol.82, issue.4, pp.309-314, 1960.
DOI : 10.1115/1.3664236

D. K. Leu, A simplified approach for evaluating bendability and springback in plastic bending of anisotropic sheet metals, Journal of Materials Processing Technology, vol.66, issue.1-3, pp.9-17, 1997.
DOI : 10.1016/S0924-0136(96)02453-3

K. Yamazaki, Y. Mizuyama, M. Oka, and Y. Tokunaga, Influence of microstructure on bendability of ultrahigh-strength steel sheet, Journal of the Japan Society for Technology of Plasticity, vol.36, pp.973-978, 1995.

A. Nilsson, L. Melin, and C. Magnusson, Finite-element simulation of V-die bending: a comparison with experimental results, Journal of Materials Processing Technology, vol.65, issue.1-3, pp.65-52, 1997.
DOI : 10.1016/0924-0136(95)02241-4

X. Li, Y. Yang, Y. Wang, J. Bao, and S. Li, Effect of the material-hardening mode on the springback simulation accuracy of V-free bending, Journal of Materials Processing Technology, vol.123, issue.2, pp.123-209, 2002.
DOI : 10.1016/S0924-0136(02)00055-9

W. Gan and R. H. Wagoner, Die design method for sheet springback, International Journal of Mechanical Sciences, vol.46, issue.7, pp.1097-1113, 2004.
DOI : 10.1016/j.ijmecsci.2004.06.006

P. A. Eggertsen and K. Mattiasson, On constitutive modeling for springback analysis, International Journal of Mechanical Sciences, vol.52, issue.6, pp.804-818, 2010.
DOI : 10.1016/j.ijmecsci.2010.01.008

J. Chakrabarty, W. B. Lee, and K. C. Chan, An analysis of the plane-strain bending of an orthotropic sheet in the elastic/plastic range, Journal of Materials Processing Technology, vol.104, issue.1-2, pp.48-52, 2000.
DOI : 10.1016/S0924-0136(00)00542-2

J. Chakrabarty, W. B. Lee, and K. C. Chan, An exact solution for the elastic/plastic bending of anisotropic sheet metal under conditions of plane strain, International Journal of Mechanical Sciences, vol.43, issue.8, pp.43-1871, 2001.
DOI : 10.1016/S0020-7403(01)00009-1

A. R. Ragab and C. A. Saleh, Evaluation of bendability of sheet metals using void coalescence models, Materials Science and Engineering: A, vol.395, issue.1-2, pp.102-109, 2005.
DOI : 10.1016/j.msea.2004.12.011

K. M. Zhao and J. K. Lee, Finite element analysis of the three-point bending of sheet metals, Journal of Materials Processing Technology, vol.122, issue.1, pp.6-11, 2002.
DOI : 10.1016/S0924-0136(01)01064-0

C. Wang, G. Kinzel, and T. Altan, Mathematical modeling of plane-strain bending of sheet and plate, Journal of Materials Processing Technology, vol.39, issue.3-4, pp.279-304, 1993.
DOI : 10.1016/0924-0136(93)90164-2

R. Hambli, A. Mkaddem, and A. Potiron, Finite element damage modeling in bending processes, Journal of Materials Processing Technology, vol.147, issue.3, pp.302-310, 2004.
DOI : 10.1016/S0924-0136(03)00583-1

S. Thuillier, N. Le-maoût, and P. Y. Manach, Bending Limit Prediction of an Aluminum Thin Sheet, International Journal of Material Forming, vol.3, issue.S1, pp.223-226, 2010.
DOI : 10.1007/s12289-010-0747-7
URL : https://hal.archives-ouvertes.fr/hal-00717159

D. Rèche, T. Sturel, O. Bouaziz, A. Col, and A. , Damage development in low alloy TRIP-aided steels during air-bending, Materials Science and Engineering: A, vol.528, issue.15, pp.5241-5250, 2011.
DOI : 10.1016/j.msea.2011.03.042

A. Dalloz, J. Besson, A. F. Gourgues-lorenzon, T. Sturel, and A. Pineau, Effect of shear cutting on ductility of a dual phase steel, Engineering Fracture Mechanics, vol.76, issue.10, pp.76-1411, 2009.
DOI : 10.1016/j.engfracmech.2008.10.009
URL : https://hal.archives-ouvertes.fr/hal-00399528

. Aramis, Optical 3D deformation analysis software developed by GOM GmbH

Z. Marciniak and J. L. Duncan, Bending. The Mechanics of Sheet Metal Forming, pp.68-99, 1992.

J. L. Chaboche, A review of some plasticity and viscoplasticity constitutive theories, International Journal of Plasticity, vol.24, issue.10, pp.1642-1693, 2008.
DOI : 10.1016/j.ijplas.2008.03.009

R. Hill, A Theory of the Yielding and Plastic Flow of Anisotropic Metals, Proc. Royal Soc, pp.281-297, 1948.
DOI : 10.1098/rspa.1948.0045

F. Barlat, D. J. Lege, and J. C. Brem, A six-component yield function for anisotropic materials, International Journal of Plasticity, vol.7, issue.7, pp.693-712, 1991.
DOI : 10.1016/0749-6419(91)90052-Z

A. P. Karafillis and M. C. Boyce, A general anisotropic yield criterion using bounds and a transformation weighting tensor, Journal of the Mechanics and Physics of Solids, vol.41, issue.12, pp.41-1859, 1993.
DOI : 10.1016/0022-5096(93)90073-O

F. Bron and J. Besson, A yield function for anisotropic materials Application to aluminum alloys, International Journal of Plasticity, vol.20, issue.4-5, pp.937-963, 2004.
DOI : 10.1016/j.ijplas.2003.06.001
URL : https://hal.archives-ouvertes.fr/hal-00165873

P. A. Eggertsen and K. Mattiasson, On the modelling of the bending???unbending behaviour for accurate springback predictions, International Journal of Mechanical Sciences, vol.51, issue.7, pp.547-563, 2009.
DOI : 10.1016/j.ijmecsci.2009.05.007

B. W. Williams, C. H. Simha, N. Abedrabbo, R. Mayer, and M. J. Worswick, Effect of anisotropy, kinematic hardening, and strain-rate sensitivity on the predicted axial crush response of hydroformed aluminium alloy tubes, International Journal of Impact Engineering, vol.37, issue.6, pp.652-661, 2010.
DOI : 10.1016/j.ijimpeng.2009.10.010

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.
DOI : 10.1016/S0749-6419(02)00019-0

J. Yoon, F. Barlat, R. E. Dick, K. Chung, and T. J. Kang, Plane stress yield function for aluminum alloy sheets???part II: FE formulation and its implementation, International Journal of Plasticity, vol.20, issue.3, pp.495-522, 2004.
DOI : 10.1016/S0749-6419(03)00099-8

I. N. Vladimirov, M. P. Pietryga, and S. Reese, Anisotropic finite elastoplasticity with nonlinear kinematic and isotropic hardening and application to sheet metal forming, International Journal of Plasticity, vol.26, issue.5, pp.659-687, 2010.
DOI : 10.1016/j.ijplas.2009.09.008

Y. Shinohara, Y. Madi, and J. Besson, A combined phenomenological model for the representation of anisotropic hardening behavior in high strength steel line pipes, European Journal of Mechanics - A/Solids, vol.29, issue.6, pp.917-927, 2010.
DOI : 10.1016/j.euromechsol.2010.06.003
URL : https://hal.archives-ouvertes.fr/hal-00687352

J. L. Chaboche, Constitutive equations for cyclic plasticity and cyclic viscoplasticity, International Journal of Plasticity, vol.5, issue.3, pp.247-302, 1989.
DOI : 10.1016/0749-6419(89)90015-6

S. Thuillier, N. Le-maoût, and P. Y. Manach, Influence of ductile damage on the bending behaviour of aluminium alloy thin sheets, Materials & Design, vol.32, issue.4, pp.2049-2057, 2011.
DOI : 10.1016/j.matdes.2010.11.050
URL : https://hal.archives-ouvertes.fr/hal-00715779

J. Besson and R. Foerch, Large scale object-oriented finite element code design, Computer Methods in Applied Mechanics and Engineering, vol.142, issue.1-2, pp.165-187, 1997.
DOI : 10.1016/S0045-7825(96)01124-3

B. Moran, M. Ortiz, and C. F. Shih, Formulation of implicit finite element methods for multiplicative finite deformation plasticity, International Journal for Numerical Methods in Engineering, vol.14, issue.3, pp.29-483, 1990.
DOI : 10.1002/nme.1620290304

M. B. Bettaieb, X. Lemoine, L. Duchêne, and A. M. Habraken, Simulation of the bending process of hardening metallic sheets using damage model. Part I: Theoretical development and numerical implementation, Materials Science and Engineering: A, vol.528, issue.1, pp.528-434, 2010.
DOI : 10.1016/j.msea.2010.09.030

K. Gieck, Technical formulary, 1997.

J. Muller, General mechanics formulary, p.147, 2000.

L. Geng and R. H. Wagoner, Role of plastic anisotropy and its evolution on springback, International Journal of Mechanical Sciences, vol.44, issue.1, pp.123-148, 2002.
DOI : 10.1016/S0020-7403(01)00085-6

P. A. Friedman and S. G. Luckey, Failure of Al-Mg-Si alloys in bending, Practical Failure Analysis, ASM Inter, vol.1, pp.33-42, 2002.

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.
DOI : 10.1016/j.engfracmech.2004.07.011

Y. Bai and T. Wierzbicki, Application of extended Mohr???Coulomb criterion to ductile fracture, International Journal of Fracture, vol.37, issue.7, pp.1-20, 2010.
DOI : 10.1007/s10704-009-9422-8

J. Besson and R. Foerch, Large scale object-oriented finite element code design, Computer methods in applied mechanics and engineering 142, pp.165-187, 1997.

J. Besson, L. Devilliers-guerville, and A. Pineau, Modeling of scatter and size effect in ductile fracture: application to thermal embrittlement of duplex stainless steels, Engineering Fracture Mechanics, vol.67, issue.2, pp.169-190, 2000.
DOI : 10.1016/S0013-7944(00)00056-4

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.
DOI : 10.1016/S0749-6419(02)00022-0

J. Besson and C. Guillemer-neel, An extension of the Green and Gurson models to kinematic hardening, Mechanics of Materials, vol.35, issue.1-2, pp.1-18, 2003.
DOI : 10.1016/S0167-6636(02)00169-2

B. Bettaieb, M. Lemoine, X. Duchêne, L. Habraken, and A. M. , Simulation of the bending process of hardening metallic sheets using damage model. Part I: Theoretical development and numerical implementation, Materials Science and Engineering: A, vol.528, issue.1, pp.434-441, 2010.
DOI : 10.1016/j.msea.2010.09.030

B. Bettaieb, M. Lemoine, X. Duchêne, L. Habraken, and A. M. , Simulation of the bending process of hardening metallic sheets using damage model, Part II: Numerical investigations, Materials Science and Engineering A528, pp.442-448, 2010.

P. W. Bridgman, Studies in large plastic flow and fracture: With special emphasis on the effects of hydrostatic pressure, 1952.
DOI : 10.4159/harvard.9780674731349

J. L. Chaboche, Constitutive equations for cyclic plasticity and cyclic viscoplasticity, International Journal of Plasticity, vol.5, issue.3, pp.247-302, 1989.
DOI : 10.1016/0749-6419(89)90015-6

J. L. Chaboche, A review of some plasticity and viscoplasticity constitutive theories, International Journal of Plasticity, vol.24, issue.10, pp.1642-1693, 2008.
DOI : 10.1016/j.ijplas.2008.03.009

P. L. Charpentier, Influence of punch curvature on the stretching limits of sheet steel, Metallurgical Transactions A, vol.12, issue.8, pp.1665-1669, 1975.
DOI : 10.1007/BF02641986

W. Y. Chien, J. Pan, and S. C. Tang, A combined necking and shear localization analysis for aluminum sheets under biaxial stretching conditions, International Journal of Plasticity, vol.20, issue.11, pp.1953-1981, 1981.
DOI : 10.1016/j.ijplas.2003.08.006

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.
DOI : 10.1115/1.3224807

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

A. Dalloz, J. Besson, A. F. Gourgues-lorenzon, and A. Pineau, Effect of shear cutting on ductility of a dual phase steel, Engineering Fracture Mechanics, vol.76, issue.10, pp.1411-1424, 2009.
DOI : 10.1016/j.engfracmech.2008.10.009
URL : https://hal.archives-ouvertes.fr/hal-00399528

D. D. Damborg, Prediction of fracture in bending under tension, Proceeding of the 19 th Riso International Symposium on Material Science: Modelling of Structure and Mechanics from Microscale to Product, pp.235-240, 1998.

P. P. Date, K. Narashima, S. K. Maiti, and U. P. Singh, On the prediction of springback in V-bending of metallic sheets under plane strain condition, Proceeding of the International Conference on Sheet Metal, pp.447-456, 1999.

M. Y. Demeri, The stretch-bend forming of sheet metal, Journal of Applied Metalworking, vol.17, issue.1, pp.3-10, 1981.
DOI : 10.1007/BF02833993

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

P. A. Friedman and S. G. Luckey, Failure of Al-Mg-Si alloys in bending, Practical Failure Analysis, vol.331, issue.337, pp.33-42, 2002.
DOI : 10.1007/BF02715390

W. Gan and R. H. Wagoner, Die design method for sheet springback, International Journal of Mechanical Sciences, vol.46, issue.7, pp.1097-1113, 2004.
DOI : 10.1016/j.ijmecsci.2004.06.006

G. M. Goodwin, Application of Strain Analysis to Sheet Metal Forming Problems in the Press Shop, SAE Technical Paper Series, 1968.
DOI : 10.4271/680093

A. K. Ghosh, A criterion for ductile fracture in sheet under biaxial loading, Metallurgical Transactions A 7A, pp.523-533, 1976.

A. Graf and W. Hosford, Effect of changing strain paths on forming limit diagrams of AL2008-T4, Metallurgical Transactions 24A, pp.2503-2512, 1993.

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.
DOI : 10.1115/1.3443401

A. Hudgins, D. Matlock, J. Speer, J. Fekete, and M. Walp, The susceptibility to shear fracture in bending of advanced high strength sheet steels, Proceedings from Materials Science and Technology (MS&T): Advanced High Strength and Other Specialty Sheet Steel Products for the Automotive Industry, pp.145-157, 2007.

A. Kao, H. Kuhn, O. Richemond, and W. Spitzig, Tensile fracture and fractographic analysis of 1045 spheroidized steel under hydrostatic pressure, Journal of Materials Research, vol.7, issue.01, pp.83-91, 1990.
DOI : 10.1016/0001-6160(81)90185-1

J. H. Kim, J. H. Sung, and R. H. Wagoner, Thermo-mechanical modelling of draw-bend formability tests, International Deep Drawing Research Group, International Conference, pp.503-512, 2009.

S. P. Keeler and W. A. Backofen, Plastic instability and fracture in sheets stretched over rigid punches, Transactions of the American Society for Metals, vol.56, pp.25-48, 1963.

J. V. Laukonis and A. K. Ghosh, Effects of strain path changes on the formability of sheet metals, Metallurgical Transactions 9A, pp.1849-1856, 1978.
DOI : 10.1007/BF02663419

J. Lemaitre, A Continuous Damage Mechanics Model for Ductile Fracture, Journal of Engineering Materials and Technology, vol.107, issue.1, pp.83-89, 1985.
DOI : 10.1115/1.3225775

J. Lemaitre and J. L. Chaboche, Mechanics of Solid Materials, 1990.

M. Luo and T. Wierzbicki, Numerical failure analysis of a stretch-bending test on dual-phase steel sheets using a phenomenological fracture model, International Journal of Solids and Structures, vol.47, issue.22-23, pp.3084-3102, 2010.
DOI : 10.1016/j.ijsolstr.2010.07.010

G. Leroy, J. D. Embury, G. Edwards, and M. F. Ashby, A model of ductile fracture based on the nucleation and growth of voids, Acta Metallurgica, vol.29, issue.8, pp.1509-1522, 1981.
DOI : 10.1016/0001-6160(81)90185-1

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.
DOI : 10.1115/1.3601204

G. Perrin and J. B. Leblond, Analytical study of a hollow sphere made of plastic porous material and subjected to hydrostatic tension-application to some problems in ductile fracture of metals, International Journal of Plasticity, vol.6, issue.6, pp.677-699, 1990.
DOI : 10.1016/0749-6419(90)90039-H

D. Rèche, T. Sturel, O. Bouaziz, A. Col, and A. F. Gourgues-lorenzon, Damage development in low allow TRIP-aided steels during air-bending, 2010.

D. Rèche, J. Besson, T. Sturel, X. Lemoine, and A. F. Gourgues-lorenzon, Analysis of the air-bending test using finite-element simulation: Application to steel sheets, International Journal of Mechanical Sciences, vol.57, issue.1, 2011.
DOI : 10.1016/j.ijmecsci.2012.01.014

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.
DOI : 10.1016/0022-5096(69)90033-7

S. Sriram, C. Wong, M. Huang, and B. Yan, Stretch Bendability of Advanced High Strength Steels, SAE Technical Paper Series, pp.107-115, 2003.
DOI : 10.4271/2003-01-1151

J. Sarkar, T. R. Kutty, K. T. Conlon, D. S. Wilkinson, J. D. Embury et al., Tensile and bending properties of AA5754 aluminum alloys, Materials Science and Engineering: A, vol.316, issue.1-2, pp.52-59, 2001.
DOI : 10.1016/S0921-5093(01)01226-6

J. Steninger and A. Melander, The relation between bendability, tensile properties and particle structure of low-carbon steel, Scandinavian Journal of Metallurgy, vol.11, issue.2, pp.55-71, 1982.

S. Thuillier, L. Maoût, N. Manach, and P. Y. , Bending Limit Prediction of an Aluminum Thin Sheet, International Journal of Material Forming, vol.3, issue.S1, pp.223-226, 2010.
DOI : 10.1007/s12289-010-0747-7
URL : https://hal.archives-ouvertes.fr/hal-00717159

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. Uthaisangsuk, U. Prahl, S. Münstermann, and W. Bleck, Experimental and numerical failure criterion for formability prediction in sheet metal forming, Computational Materials Science, vol.43, issue.1, pp.43-50, 2008.
DOI : 10.1016/j.commatsci.2007.07.036

. General, . For, and K. W. Work-bibliography-andrews, Empirical formulae for the calculation of some transformation temperatures, Journal of the Iron and Steel Institute, vol.203, pp.721-727, 1965.

G. Avramovic-cingara, Y. Ososkov, M. K. Jain, and D. S. Wilkinson, Effect of martensite distribution on damage behaviour in DP600 dual phase steels, Materials Science and Engineering: A, vol.516, issue.1-2, pp.7-16, 2009.
DOI : 10.1016/j.msea.2009.03.055

M. Bach, N. Broll, A. Cornet, and L. Gaide, Diffraction X en traitements thermiques : dosage de l'aust??nite r??siduelle par diffraction des rayons X, Le Journal de Physique IV, vol.06, issue.C4, pp.4-887, 1996.
DOI : 10.1051/jp4:1996485

R. Bahloul, A. Mkaddem, . Dal-santo, . Ph, and A. Potiron, Sheet metal bending optimisation using response surface method, numerical simulation and design of experiments, International Journal of Mechanical Sciences, vol.48, issue.9, pp.991-1003, 2006.
DOI : 10.1016/j.ijmecsci.2006.03.004

D. Q. Bai, D. Chiro, A. Yue, and S. , Stability of Retained Austenite in a Nb Microalloyed Mn-Si TRIP Steel, Materials Science Forum, vol.284, issue.286, pp.284-286, 1998.
DOI : 10.4028/www.scientific.net/MSF.284-286.253

Y. Bai and T. Wierzbicki, Application of extended Mohr???Coulomb criterion to ductile fracture, International Journal of Fracture, vol.37, issue.7, pp.1-20, 2010.
DOI : 10.1007/s10704-009-9422-8

S. C. Baik, S. Kim, Y. S. Jin, and O. Kwon, Effects of alloying elements on mechanical properties and phase transformation of cold rolled TRIP steel sheets, ISIJ International, pp.41-290, 2001.

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.
DOI : 10.1016/j.engfracmech.2004.07.011

L. Barbel, L. Tosal-martinez, and B. De-cooman, Effect of phosphorus on the properties of a cold rolled and intercritically annealed TRIP-aided steel, Int. Conf. on TRIP-Aided high strength ferrous alloys, pp.147-152, 2002.

B. Bettaieb, M. Lemoine, X. Duchêne, L. Habraken, and A. M. , Simulation of the bending process of hardening metallic sheets using damage model. Part II: Numerical investigations, Materials Science and Engineering: A, vol.528, issue.1, pp.442-448, 2010.
DOI : 10.1016/j.msea.2010.09.031

G. Béranger, G. Henry, G. Sanz, J. Lavoisier-besson, and R. Foerch, Le livre de l'acier Large scale object-oriented finite element code design, Computer methods in applied mechanics and engineering, pp.165-187, 1994.

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, Engineering Fracture Mechanics, vol.67, issue.2, pp.169-190, 2000.
DOI : 10.1016/S0013-7944(00)00056-4

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.
DOI : 10.1016/S0749-6419(02)00022-0

J. Besson and C. Guillemer-neel, An extension of the Green and Gurson models to kinematic hardening, Mechanics of Materials, vol.35, issue.1-2, pp.1-18, 2003.
DOI : 10.1016/S0167-6636(02)00169-2

W. Bleck, Using the TRIP effect ?The Dawn of a promising group of cold formable steels, Int. Conf. on TRIP-aided high strength ferrous alloys, p.13, 2002.

M. Bobadilla, Solidification in continuous casting, ArcelorMittal internal document, 2008.

J. Bouquerel, K. Verbeken, and B. C. De-cooman, Microstructure-based model for the static mechanical behaviour of multiphase steels, Acta Materialia, vol.54, issue.6, pp.1443-1456, 2006.
DOI : 10.1016/j.actamat.2005.10.059

P. W. Bridgman, Studies in large plastic flow and fracture: With special emphasis on the effects of hydrostatic pressure, 1952.
DOI : 10.4159/harvard.9780674731349

M. Brunet, F. Sabourin, and S. Mguil-touchal, The prediction of necking and failure in 3D sheet forming analysis using damage variable, Journal de Physique III, vol.6, pp.6-473, 1996.
URL : https://hal.archives-ouvertes.fr/jpa-00254480

J. L. Chaboche, Constitutive equations for cyclic plasticity and cyclic viscoplasticity, International Journal of Plasticity, vol.5, issue.3, pp.247-302, 1989.
DOI : 10.1016/0749-6419(89)90015-6

J. L. Chaboche, A review of some plasticity and viscoplasticity constitutive theories, International Journal of Plasticity, vol.24, issue.10, pp.1642-1693, 2008.
DOI : 10.1016/j.ijplas.2008.03.009

P. L. Charpentier, Influence of punch curvature on the stretching limits of sheet steel, Metallurgical Transactions A, vol.12, issue.8, pp.1665-1669, 1975.
DOI : 10.1007/BF02641986

H. C. Chen, H. Era, and M. Shimizu, Effect of phosphorus on the formation of retained austenite and mechanical properties in Si-containing low-carbon steel sheet, Metallurgical Transactions A, vol.13, issue.3, pp.437-445, 1989.
DOI : 10.1007/BF02653923

L. Cheng, A. Böttger, T. H. De-keijser, and E. J. Mittemeijer, Lattice parameters of iron-carbon and iron-nitrogen martensites and austenites, Scripta Metallurgica et Materialia, vol.24, issue.3, pp.509-514, 1990.
DOI : 10.1016/0956-716X(90)90192-J

C. 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.
DOI : 10.1115/1.3224807

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

A. Col, L'emboutissage des aciers, p.273, 2010.

A. Dalloz, Etude de l'endommagement par découpe des aciers Dual Phase pour application automobile, 2007.

J. Datsko and C. T. Yang, Correlation of Bendability of Materials With Their Tensile Properties, Journal of Engineering for Industry, vol.82, issue.4, pp.309-314, 1960.
DOI : 10.1115/1.3664236

M. Y. Demeri, The stretch-bend forming of sheet metal, Journal of Applied Metalworking, vol.17, issue.1, pp.3-10, 1981.
DOI : 10.1007/BF02833993

D. Meyer, M. Vanderschueren, D. De-cooman, and B. C. , The Influence of the Substitution of Si by Al on the Properties of Cold Rolled C-Mn-Si TRIP Steels., ISIJ International, vol.39, issue.8, pp.813-822, 1999.
DOI : 10.2355/isijinternational.39.813

H. Determe, Cétim, Formation: Influence des caractéristiques de la tôle sur les opérations de pliage, 1998.

M. Didier and M. Bobadilla, Solidification and casting. Microsegregation and macrosegregation, ArcelorMittal internal document, 2008.

G. Falkinger, F. Andrieux, D. Helm, and H. Riedel, Finite-element modelling of Nakajima tests in due consideration of anisotropic ductile damage, 2010.

P. A. Friedman and S. G. Luckey, Failure of Al-Mg-Si alloys in bending, Practical Failure Analysis, vol.331, issue.337, pp.33-42, 2002.
DOI : 10.1007/BF02715390

Q. Furnémont, M. Kempf, P. J. Jacques, M. Göcken, and F. Delannay, On the measurement of the nanohardness of the constitutive phases of TRIP-assisted multiphase steels, Materials Science and Engineering: A, vol.328, issue.1-2, pp.26-32, 2002.
DOI : 10.1016/S0921-5093(01)01689-6

M. F. Gallagher, J. G. Speer, D. K. Matlock, and N. M. Fonstein, Microstructure development in TRIP-sheet steels containing Si, Al and P, Proceedings of the 44 th Mechanical Working and Steel Processing Conference and the 8th International Rolling Conference and International Symposium on Zinc-Coated Steels, pp.153-172, 2002.

W. Gan and R. H. Wagoner, Die design method for sheet springback, International Journal of Mechanical Sciences, vol.46, issue.7, pp.1097-1113, 2004.
DOI : 10.1016/j.ijmecsci.2004.06.006

E. Girault, A. Mertens, P. Jacques, Y. Houbaert, B. Verlinden et al., Comparison of the effects of silicon and aluminium on the tensile behaviour of multiphase TRIP-assisted steels, Scripta Materialia, vol.44, issue.6, pp.885-892, 2001.
DOI : 10.1016/S1359-6462(00)00697-7

G. M. Goodwin, Application of Strain Analysis to Sheet Metal Forming Problems in the Press Shop, SAE Technical Paper Series, p.680093, 1968.
DOI : 10.4271/680093

A. K. Ghosh, A Criterion for ductile fracture in sheets under biaxial loading, Metallurgical Transactions A, vol.15, issue.4, pp.523-533, 1976.
DOI : 10.1007/BF02643968

A. Graf and W. Hosford, Effect of changing strain paths on, Metallurgical Transactions A, vol.12, issue.11, pp.2503-2512, 1993.
DOI : 10.1016/0001-6160(65)90145-8

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, pp.99-101, 1977.

G. N. Haidemenopoulos, G. B. Olson, M. Cohen, and K. Tsuzaki, Transformation plasticity of retained austenite in stage-I tempered martensitic steels, Scripta Metallurgica, vol.23, issue.2, pp.207-212, 1989.
DOI : 10.1016/0036-9748(89)90412-2

S. S. Hecker, M. G. Stout, K. P. Staudhammer, and J. L. Smith, Effects of Strain State and Strain Rate on Deformation-Induced Transformation in 304 Stainless Steel: Part I. Magnetic Measurements and Mechanical Behavior, Metallurgical Transactions A, vol.9, issue.4, pp.619-626, 1982.
DOI : 10.1007/BF02644427

R. Hill, A Theory of the Yielding and Plastic Flow of Anisotropic Metals, Proceedings of the Royal Society of, pp.281-297, 1948.
DOI : 10.1098/rspa.1948.0045

J. Huang, R. P. Hammond, K. Conlon, and W. J. Poole, An experimental study of the ferrite austenite two phase regions in a Fe-C-Mn-Si steel using neutron diffraction, Proc. Int. Conf. on TRIP aided high strength ferrous alloys, p.187, 2002.

P. Jacques, On the physics and mechanics of phase transformations in TRIP-assisted multiphase steels, Thèse de doctorat, 1998.

P. Jacques, Q. Furnemont, T. Pardoen, and F. Delannay, On the role of martensitic transformation on damage and cracking resistance in TRIP-assisted multiphase steels, Acta Materialia, vol.49, issue.1, pp.139-152, 2001.
DOI : 10.1016/S1359-6454(00)00215-9

P. J. Jacques, A. Petein, and P. Harlet, Improvement of mechanical properties through concurrent deformation and transformation : new steels for 21st century, Proc. Int. Conf. on TRIP-Aided high strength ferrous alloys, p.281, 2002.

P. J. Jacques, Q. Furnémont, F. Lani, T. Pardoen, and F. Delannay, Multiscale mechanics of TRIP-assisted multiphase steels: I. Characterization and mechanical testing, Acta Materialia, vol.55, issue.11, pp.3681-3693, 2007.
DOI : 10.1016/j.actamat.2007.02.029

P. Jacques, S. Allain, O. Bouaziz, A. De, A. F. Gourgues et al., On measurement of retained austenite in multiphase TRIP steels ??? results of blind round robin test involving six different techniques, Materials Science and Technology, vol.208, issue.5, pp.567-574, 2009.
DOI : 10.1016/S1044-5803(98)00005-9
URL : https://hal.archives-ouvertes.fr/hal-00413810

A. S. Kao, H. A. Kuhn, O. Richemond, and W. A. Spitzig, Tensile fracture and fractographic analysis of 1045 spheroidized steel under hydrostatic pressure, Journal of Materials Research, vol.7, issue.01, pp.83-91, 1990.
DOI : 10.1016/0001-6160(81)90185-1

S. P. Keeler and W. A. Backofen, Plastic instability and fracture in sheets stretched over rigid punches, Transactions of the American Society for Metals, pp.25-48, 1963.

S. J. Kim, C. G. Lee, I. Choi, and S. Lee, Effects of heat treatment and alloying elements on the microstructures and mechanical properties of 0.15 wt pct C transformation-induced plasticity-aided cold-rolled steel sheets, Metallurgical and Materials Transactions A, vol.203, issue.3, pp.505-514, 2001.
DOI : 10.1007/s11661-001-0067-0

S. J. Kim, C. G. Lee, W. C. Jeong, and I. Park, Microstructure and mechanical properties of the 0, 15%C TRIP-Aided cold rolled steels containing Cu, Ni and Cr Proc. Int. Conf. on TRIP-Aided high strength ferrous alloys, p.165, 2002.

D. Kim, F. Barlat, S. Bouvier, M. Rabahallah, T. Balan et al., Non-quadratic anisotropic potentials based on linear transformation of plastic strain rate, International Journal of Plasticity, vol.23, issue.8, pp.1380-1399, 2007.
DOI : 10.1016/j.ijplas.2007.01.006

J. H. Kim, J. H. Sung, and R. H. Wagoner, Thermo-mechanical modelling of draw-bend formability tests, International conference, International Deep Drawing Research Group, pp.503-512, 2009.

J. H. Ladriere and X. J. He, M??ssbauer study on retained austenite in an Fe???Mn???C dual-phase steel, Materials Science and Engineering, vol.77, pp.133-138, 1986.
DOI : 10.1016/0025-5416(86)90361-7

F. Lani, Q. Furnémont, T. Van-rompaey, F. Delannay, P. J. Jacques et al., Multiscale mechanics of TRIP-assisted multiphase steels: II. Micromechanical modelling, Acta Materialia, vol.55, issue.11, pp.3695-3705, 2007.
DOI : 10.1016/j.actamat.2007.02.015

J. V. Laukonis and A. K. Ghosh, Effects of strain path changes on the formability of sheet metals, Metallurgical Transactions A, vol.l, issue.12, pp.1849-1856, 1978.
DOI : 10.1007/BF02663419

C. G. Lee, S. J. Kim, C. S. Oh, and S. Lee, Effects of Heat Treatment and Si Addition on the Mechanical Properties of 0.1 wt% C TRIP-aided Cold-rolled Steels., ISIJ International, vol.42, issue.10, pp.1162-1168, 2002.
DOI : 10.2355/isijinternational.42.1162

C. G. Lee, S. J. Kim, T. H. Lee, and S. Lee, Effects of volume fraction and stability of retained austenite on formability in a 0.1C???1.5Si???1.5Mn???0.5Cu TRIP-aided cold-rolled steel sheet, Materials Science and Engineering: A, vol.371, issue.1-2, pp.16-23, 2004.
DOI : 10.1016/S0921-5093(03)00035-2

J. Lemaitre, A Continuous Damage Mechanics Model for Ductile Fracture, Journal of Engineering Materials and Technology, vol.107, issue.1, pp.83-89, 1985.
DOI : 10.1115/1.3225775

X. Lemoine, M. B. Bettaieb, and J. Goncalves, Bibliography about bending process in particular formability criteria, ArcelorMittal internal document, pp.1-31, 2009.

M. Lin, G. B. Olson, and M. Cohen, Distributed-activation kinetics of heterogeneous martensitic nucleation, Metallurgical Transactions 23A, pp.2987-2998, 1992.

H. Livatyali, G. L. Kinzel, and T. Altan, Computer aided die design of straight flanging using approximate numerical analysis, Journal of Materials Processing Technology, vol.142, issue.2, pp.532-543, 2003.
DOI : 10.1016/S0924-0136(03)00655-1

J. Mahieu, D. Van-dooren, L. Barbé, and B. C. De-cooman, Influence of Al, Si and P on the kinetics of intercritical annealing of TRIP-aided steels: thermodynamical prediction and experimental verification, Proc. Int. Conf. on TRIP-Aided high strength ferrous alloys, p.159, 2002.
DOI : 10.1002/srin.200200207

J. Maki, J. Mahieu, B. C. De-cooman, and S. Claessens, Galvanisability of silicon free CMnAl TRIP steels, Galvanisability of silicon free CMnAl TRIP steels, pp.125-131, 2003.
DOI : 10.1007/BF02648719

Z. Marciniak and J. L. Duncan, Bending. The mechanics of sheet metal forming, pp.68-99, 1992.

O. Matsumura, Y. Sakuma, and H. Takechi, Enhancement of elongation by retained austenite in intercritical annealed 0, 4C-1.5Si-0.8Mn steel, Transactions of the Iron and steel institute of Japan, pp.570-579, 1987.

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.
DOI : 10.1115/1.3601204

B. Mintz, Hot dip galvanising of transformation induced plasticity and other intercritically annealed steels, International Materials Reviews, vol.77, issue.1, pp.169-197, 2001.
DOI : 10.1016/0036-9748(87)90103-7

J. Muller, Formulaire de mécanique générale, p.147, 2000.

Y. Nagataki, S. Tsuyama, Y. Hosoya, and T. Okita, Effect of microstructure on bendability of ultra-high strength steel sheet, High-strength steels for automotive symposium proceedings, pp.239-244, 1994.

J. Ohlert, W. Bleck, and K. Hulka, Control of microstructure on TRIP steels by niobium, Proc. Int. Conf. on TRIP-Aided High Strength Ferrous Alloys, p.199, 2002.

J. R. Patel and M. Cohen, Criterion for the action of applied stress in the martensitic transformation, Acta Metallurgica, vol.1, issue.5, pp.531-538, 1953.
DOI : 10.1016/0001-6160(53)90083-2

E. V. Pereloma, I. B. Timokhina, and P. D. Hodgson, Transformation behaviour in thermomechanically processed C???Mn???Si TRIP steels with and without Nb, Materials Science and Engineering: A, vol.273, issue.275, pp.273-275, 1999.
DOI : 10.1016/S0921-5093(99)00325-1

A. Pichler and P. Stiaszny, TRIP steel with reduced silicon content, Steel Research, vol.21, issue.11, pp.459-465, 1999.
DOI : 10.1002/srin.199905667

F. B. Pickering, Constitution and properties of steels, Materials science and technology : a comprehensive treatment, pp.272-284, 1992.

P. Poruks, I. Yakubtsov, and J. D. Boyd, Martensite???ferrite interface strength in a low-carbon bainitic steel, Scripta Materialia, vol.54, issue.1, pp.41-45, 2006.
DOI : 10.1016/j.scriptamat.2005.09.012

W. M. Quach, J. G. Teng, and K. F. Chung, Residual stresses in steel sheets due to coiling and uncoiling: a closed-form analytical solution, Engineering Structures, vol.26, issue.9, pp.1249-1259, 2004.
DOI : 10.1016/j.engstruct.2004.04.005

W. M. Quach, J. G. Teng, and K. F. Chung, Residual stresses in press-braked stainless steel sections, I: Coiling and uncoiling of sheets, Journal of Constructional Steel Research, vol.65, issue.8-9, pp.1803-1815, 2009.
DOI : 10.1016/j.jcsr.2009.04.007

D. Rèche, T. Sturel, O. Bouaziz, and A. Gourgues-lorenzon, Damage development in low alloy TRIP-aided steels during air-bending, Materials Science and Engineering: A, vol.528, issue.15, pp.5241-5250, 2011.
DOI : 10.1016/j.msea.2011.03.042

R. C. Reed, T. Akbay, Z. Shen, J. M. Robinson, and J. H. Root, Determination of reaustenitisation kinetics in a Fe???0.4C steel using using dilatometry and neutron diffraction, Materials Science and Engineering: A, vol.256, issue.1-2, pp.152-165, 1998.
DOI : 10.1016/S0921-5093(98)00800-4

N. Ridley, H. Stuart, and L. Zwell, Lattice parameters of Fe-C austenites at room temperature, Trans. Met. Soc. AIME, pp.245-1834, 1969.

J. M. Rigsbee and P. J. Van-der-arend, Laboratory studies of microstructures and structure-property relationships in dual phase steels, Proc. Conf, 1977.

C. S. Roberts, Effect of carbon on the volume fractions and lattice parameters of retained austenite and martensite, Trans. AIME, pp.203-204, 0197.

K. Saanouni and H. Badreddine, Damage Prediction in Sheet Metal Forming, AIP Conference Proceedings, pp.105-110, 2007.
DOI : 10.1063/1.2740796

S. Sriram, C. Wong, M. Huang, and B. Yan, Stretch bendability of advanced high strength steels, SAE technical paper, 1151.

Y. Sakuma, O. Matsumura, and H. Takechi, Mechanical properties and retained austenite in intercritically heat-treated bainite-transformed steel and their variation with Si and Mn additions, Metallurgical Transactions A, vol.1, issue.2, pp.489-498, 1991.
DOI : 10.1016/0036-9748(87)90103-7

Y. Shinohara, Y. Madi, and J. , A combined phenomenological model for the representation of anisotropic hardening behavior in high strength steel line pipes, European Journal of Mechanics - A/Solids, vol.29, issue.6, pp.917-927, 2010.
DOI : 10.1016/j.euromechsol.2010.06.003
URL : https://hal.archives-ouvertes.fr/hal-00687352

G. R. Speich and R. L. Miller, Mechanical properties of ferrite-martensite steels, Proc. Conf. Structure and Properties of Dual Phase Steels, pp.145-182, 1979.

S. Sriram, C. Wong, M. Huang, and B. Yan, Stretch Bendability of Advanced High Strength Steels, SAE Technical Paper Series, pp.107-115, 2003.
DOI : 10.4271/2003-01-1151

A. K. Srivastava, D. Bhattacharjee, G. Jha, N. Gope, and S. B. Singh, Microstructural and mechanical characterization of C???Mn???Al???Si cold-rolled TRIP-aided steel, Materials Science and Engineering: A, vol.445, issue.446, pp.445-446, 2007.
DOI : 10.1016/j.msea.2006.09.101

J. Steninger and A. Melander, The Relation between bendability, tensile properties and particle structure of low-carbon steel, Scandinavian Journal of Metallurgy, vol.11, pp.55-71, 1982.

K. I. Sugimoto, R. Kikuchi, and S. I. Hashimoto, Development of high strength low alloy TRIP-aided steels with annealed martensite matrix, Steel Research, vol.14, issue.6-7, pp.253-258, 2002.
DOI : 10.1002/srin.200200205

M. R. Tharrett and T. B. Stoughton, Stretch-Bend Forming Limits of 1008 AK Steel, SAE Technical Paper Series, pp.1-7, 1157.
DOI : 10.4271/2003-01-1157

S. W. Thompson and P. R. Howell, Factors influencing ferrite/pearlite banding and origin of large pearlite nodules in a hypoeutectoid plate steel, Materials Science and Technology, vol.140, issue.9, pp.777-784, 1992.
DOI : 10.1007/BF02663328

S. Thuillier, L. Maoût, N. Manach, and P. Y. , Influence of ductile damage on the bending behaviour of aluminium alloy thin sheets, Materials & Design, vol.32, issue.4, pp.2049-2057, 2011.
DOI : 10.1016/j.matdes.2010.11.050
URL : https://hal.archives-ouvertes.fr/hal-00715779

S. Traint, A. Pichler, K. Hauzenberger, P. Stiaszny, and E. Werner, Influence of silicon, aluminium, phosphorus and copper on the phase transformations of low alloyed TRIP-steels, Proc. Int. Conf. on TRIP-Aided high strength ferrous alloys, p.121, 2002.
DOI : 10.1002/srin.200200206

I. Tsukatani, S. Hashimoto, and T. Inoue, Effects of Silicon and Manganese Addition on Mechanical Properties of High-strength Hot-rolled Sheet Steel Containing Retained Austenite., ISIJ International, vol.31, issue.9, pp.31-992, 1991.
DOI : 10.2355/isijinternational.31.992

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. Tvergaard, Material failure by void growth to coalescence Advances in Applied Mechanics, pp.83-151, 1989.

C. Vallellano, D. Morales, and F. J. Garcia-lomas, On the study of the effect of metal sheets, Conference Numisheet, 2008.

J. Wu, D. Zhou, L. Zhang, Y. J. Zhou, C. Q. Du et al., A failure criterion for stretch bendability of advanced high strength steels, SAE Technical Paper, pp.2006-2007, 2006.

H. Y. Yan, G. Y. Kai, and M. D. Jian, Transformation behaviour of retained austenite under different deformation modes for low alloyed TRIP-assisted steels, Material Science and Engineering A, pp.441-331, 2006.

V. F. Zackay, E. R. Parker, D. Fahr, and R. Bush, The enhancement of ductility in high strength steels, ASM Transactions Quarterly, vol.60, pp.252-259, 1967.

Z. T. Zhang and S. J. Hu, Stress and residual stress distributions in plane strain bending, International Journal of Mechanical Sciences, vol.40, issue.6, pp.533-543, 1998.
DOI : 10.1016/S0020-7403(97)00075-1