E. Akman, A. Demir, T. Canel, and T. Sinmazçelik, Laser welding of Ti6Al4V titanium alloys, Journal of Materials Processing Technology, vol.209, issue.8, pp.3705-3713, 2009.
DOI : 10.1016/j.jmatprotec.2008.08.026

B. Armstrong, P. J. , and C. O. Frederick, A mathematical representation of the multiaxial Bauschinger effet, Technical Report RD, p.731, 1966.

M. Asm-aerospace, ASM Aerospace Metals, 2010.

V. Aubin, P. Quaegebeur, and S. Degallaix, Cyclic behaviour of a duplex stainless steel under multiaxial loading: Experiments and modelling, 6th International Conference on Biaxial/Multiaxial Fatigue and Fracture, pp.401-422, 2003.
DOI : 10.1016/S1566-1369(03)80022-5
URL : https://hal.archives-ouvertes.fr/hal-00139378

G. I. Barenblatt and . Barenblatt, The Mathematical Theory of Equilibrium Cracks in Brittle Fracture, Advances in Applied Mechanics, pp.55-129, 1962.
DOI : 10.1016/S0065-2156(08)70121-2

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

. Preuss, Three-dimensional characterization of fatigue cracks in Ti-6346 using X-ray tomography and electron backscatter diffraction, Acta Materialia, pp.5834-5847, 2009.

. Wattrisse, Assessment of Digital Image Correlation Measurement Errors : Methodology and Resultat, Experimental Mechanics, pp.353-370, 2009.

S. Bouvier, N. Benmhenni, W. Tirry, F. Gregory, M. E. Nixon et al., Hardening in relation with microstructure evolution of high purity alpha titanium deformed under monotonic and cyclic shear loading at room temperature, Materials Science, pp.12-21, 2012.

S. Bouvier, H. Gardey, C. Haddadi, and . Teodosiu, Characterization of the strain-induced plastic anisotropy of roller sheets by using Bibliographie -210 sequences of simple shear and uniaxial tensile tests, Journal of Materials Processing Technology, pp.115-126, 2006.

S. Bouvier, H. Haddadi, P. Levée, and C. Teodosiu, Simple shear tests: Experimental techniques and characterization of the plastic anisotropy of rolled sheets at large strains, Journal of Materials Processing Technology, vol.172, issue.1, pp.96-103, 2006.
DOI : 10.1016/j.jmatprotec.2005.09.003

C. L. Briant, Z. F. Wang, and N. Chollocoop, Hydrogen embrittlement of commercial purity titanium, Corrosion Science, vol.44, issue.8, pp.1875-1888, 2002.
DOI : 10.1016/S0010-938X(01)00159-7

P. Bridgman, Studies in Large Plastic Flow and Fracture with Special Emphasis on the Effect of Hydrostatic Pressure, 1964.

F. Bridier, D. L. Mcdowell, P. Villechaise, and J. Mendez, Crystal plasticity modeling of slip activity in Ti6Al4V under high cycle fatigue loading, International Journal of Plasticity, pp.1066-1082, 2009.

F. Bron and J. Besson, A yield function for anisotropic materials; application to aluminium alloys, International Journal of Plasticity, pp.937-063, 2004.
URL : https://hal.archives-ouvertes.fr/hal-00164534

W. G. Bürgers, On the process of transition of the cubic-body-centrered modification into the hexagonal-close-packed modification of zirconium, pp.561-586, 1934.

R. P. Cardoso and J. W. Yoon, Stress integration method for a nonlinear kinematic/isotropic hardening model and its characterization based on polycrystal plasticity, International Journal of Plasticity, vol.25, issue.9, pp.1684-1710, 2009.
DOI : 10.1016/j.ijplas.2008.09.007

O. Castelnau, H. Francillette, B. Bacroix, and R. A. Lebensohn, Texture dependent plastic behavior of Zr 702 at large strain, Journal of Nuclear Materials, vol.297, issue.1, pp.14-26, 2001.
DOI : 10.1016/S0022-3115(01)00589-X

A. Cauchy, Méthode générale pour la résolution des systèmes d'équations simultanées, Compte Rendus de l'Académie des Sciences de Paris, pp.536-538, 1847.

R. Cazes, Soudage par faisceaux à haute énergie: faisceau d'électron et laser, 1994.

J. L. Chaboche, Sur l'utilisation des variables d'état interne pour la description de la viscoplasticité cyclique avec endommagement, Problèmes Non- Linéaires de mécanique, Symposium Franco-Polonais de Rhéologie et mécanique, pp.137-159, 1977.

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

J. L. Chaboche, On some modifications of kinematic hardening to improve the description of ratchetting effects, International Journal of Plasticity, vol.7, issue.7, pp.661-678, 1991.
DOI : 10.1016/0749-6419(91)90050-9

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

N. Chandra, H. Li, C. Shet, and H. Ghonem, Some issues in the application of cohesive zone models for metal???ceramic interfaces, International Journal of Solids and Structures, vol.39, issue.10, pp.2827-2855, 2002.
DOI : 10.1016/S0020-7683(02)00149-X

C. Chauvy, D. R. Chichili, K. T. Ramesh, and K. J. Hemker, Traitements thermomécaniques dans le haut domaine alpha du zircaloy-4 trempé-bêta The high-strain-rate response of alpha titanium : experiments, deformation mechanisms and modeling, Acta Materialia, pp.1025-1043, 1998.

A. Cornec, I. Scheider, and K. H. Schwalbe, On the practical application of the cohesive model, Engineering Fracture Mechanics, vol.70, issue.14, pp.1963-1987, 2003.
DOI : 10.1016/S0013-7944(03)00134-6

J. Crepin, T. Bretheau, D. Caldemaison, and F. Ferrer, Low cycle fatigue behaviour of beta treated zirconium: partial irreversibility of twinning and consequences for damage, Acta Materialia, pp.505-516, 2000.

D. J. Dingley and K. Baba-kishi, Use of electron back scatter diffraction patterns for determination of crystal symettry elements, Scanning Electron Microscopy, pp.383-391, 1986.

L. A. Feldkamp, L. C. Davis, and J. W. Kress, Practical cone-beam algorithm, Journal of the Optical Society of America A, vol.1, issue.6, pp.612-619, 1984.
DOI : 10.1364/JOSAA.1.000612
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.331.8312

P. Follansbee and G. Gray, An analysis at the low temperature, low and high strain-rate deformation of Ti6Al4V, Metallurgical and Materials Transactions A, pp.863-874, 1989.

J. J. Fundenberger, M. J. Philippe, F. Wagner, and C. Esling, Modelling and prediction of mechanical properties for materials with hexagonal symmetry (zinc, titanium and zirconium alloys), Acta Materialia, vol.45, issue.10, pp.4041-4055, 1997.
DOI : 10.1016/S1359-6454(97)00099-2

W. M. Garrison-jr and N. R. Moody, Ductile fracture, Journal of Physics and Chemistry of Solids, vol.48, issue.11, pp.1035-1074, 1987.
DOI : 10.1016/0022-3697(87)90118-1

N. Gey and M. Humbert, Characterization of the variant selection occuring during the ???? ? phase transformations of cold rolled titanium sheet, Acta Materialia, pp.277-288, 2002.

D. E. Goldberg, Genetic Algorithms in Search, Optimization and Machine Learning, 1989.

M. Grediac and F. Hild, Mesures de champs et identification en mécanique des solides, Hermes, 2011.

C. Guillemer, M. Clavel, and G. Cailletaud, Cyclic behavior of extruded magnesium: Experimental, microstructural and numerical approach, International Journal of Plasticity, vol.27, issue.12, pp.2068-2084, 2011.
DOI : 10.1016/j.ijplas.2011.06.002
URL : https://hal.archives-ouvertes.fr/hal-00652975

N. P. Gurao, R. Kapoor, and S. Suwas, Deformation behaviour of commercially pure titanium at extrem strain rates, Acta Materialia, pp.3431-3446, 2011.

A. L. Gurson, Continuum theory of ductile rupture by void nucleation and growth: Part 1: Yield criteria and flow rules for porous ductile media, Journal of Engineering Materials and Technology, pp.2-15, 1977.

. Baruchel, High-resolution three-dimension imaging of flat objects by synchrotron-radiation computed laminography, Applied Physics Letters, 2005.

R. Hill, A Theory of the Yielding and Plastic Flow of Anisotropic Metals, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol.193, issue.1033, pp.281-297, 1948.
DOI : 10.1098/rspa.1948.0045

A. Hillerborg, M. Modéer, and P. E. Petersson, Analysis of crack formation and crack growth in concrete by means of fracture mechanics and finite elements, Cement and Concrete Research, vol.6, issue.6, pp.773-781, 1976.
DOI : 10.1016/0008-8846(76)90007-7

M. Ishiki, T. Kuwabara, and Y. Hayashida, Measurement and analysis of differential work hardening behavior of pure titanium sheet using spline function, International Journal of Material Forming, vol.24, issue.9, pp.193-204, 2011.
DOI : 10.1007/s12289-010-1024-5

I. P. Jones and W. B. Hutchinson, Stress-state dependence of slip in Titanium-6Al-4V and other H.C.P. metals, Acta Metallurgica, vol.29, issue.6, pp.951-968, 1981.
DOI : 10.1016/0001-6160(81)90049-3

A. Kao, H. Kuhn, O. Richmond, 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

A. S. Khan, R. Kazmi, and B. Farrokh, Multiaxial and non-proportional loading responses, anisotropy and modeling of Ti6Al4V titanium alloy over wide ranges of strain rates and temperatures, International Journal of Plasticity, pp.931-950, 2007.

S. Krishna, T. Hassan, I. B. Naceur, K. Saï, and G. Cailletaud, Macro versus micro-scale constitutive models in simulating proportional and nonproportional cyclic and ratcheting responses of stainless steel 304, International Journal of Plasticity, vol.25, issue.10, pp.1910-1949, 2009.
DOI : 10.1016/j.ijplas.2008.12.009
URL : https://hal.archives-ouvertes.fr/hal-00424035

T. Y. Kuo and S. L. Jeng, Porosity reduction in Nd-YAG laser welding of stainless stell and inconel alloy by using a pulsed wave, Journal of Physics D: Applied Physics, pp.722-728, 2005.

D. Kuroda, M. Niinomi, M. Morinaga, Y. Kato, and T. Yashiro, Design and mechanical properties of new alpha-type titanium alloys for implant materials, Materials Science, pp.244-249, 1998.

T. Kuwabara and Y. Horiuchi, Determining sudsequent yield surface of pure titanium sheet by use of abrupt strain path change, International Journal of Material Forming, pp.237-240, 2008.

J. H. Lambert, Photometria, sive de mensura et gradibus luminis, 1760.

W. S. Lee and C. F. Lin, High-temperature deformation behaviour of Ti6Al4V alloy evaluated by high strain-rate compression tests, Journal of Materials Processing Technology, vol.75, issue.1-3, pp.127-136, 1998.
DOI : 10.1016/S0924-0136(97)00302-6

J. Lemaitre, A Continuous Damage Mechanics Model for Ductile Fracture, Journal of Engineering Materials and Technology, vol.107, issue.1, 1984.
DOI : 10.1115/1.3225775

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

E. Maire, C. Bordreuil, L. Babout, and J. C. Boyer, Damage initiation and growth in metals. Comparison between modelling and tomography experiments, Journal of the Mechanics and Physics of Solids, vol.53, issue.11, pp.2411-2434, 2005.
DOI : 10.1016/j.jmps.2005.06.005
URL : https://hal.archives-ouvertes.fr/hal-00436860

E. Maire, T. F. Morgeneyer, C. Landron, J. Adrien, and L. Helfen, Bulk evaluation of ductile damage development using high resolution tomography and laminography, Comptes Rendus Physique, vol.13, issue.3, pp.328-336, 2012.
DOI : 10.1016/j.crhy.2011.12.009
URL : https://hal.archives-ouvertes.fr/hal-00685034

K. Mitsui and M. Takahashi, Electrical Resistivity Change during Continuous Heating in Cu-18at.%Pd Alloys Quenched from Various Temperatures, Scripta Materialia, vol.38, issue.9, pp.1435-1441, 1998.
DOI : 10.1016/S1359-6462(98)00050-5

. Baumbach, Ductile crack initiation and propagation assessed via in-situ synchrotron radiation computed laminography, Scripta Materialia, pp.1010-1013, 2011.
URL : https://hal.archives-ouvertes.fr/hal-00652978

S. Naka, Etude des mécanismes de déformation plastique à basse température de monocristaux de titane alpha, O.N.E.R.A, 1983.

H. Nasiri-abarbekoh, A. Ekrami, and A. A. Ziaei-moayyed, Impact of phase transformation on mechanical properties anisotropy of commercilly pure titanium, Materials and Design, pp.223-227, 2012.

H. Nasiri-abarbekoh, A. Ekrami, and A. A. Ziaei-moayyed, Effects of thickness and texture on mechanical properties anisotropy of commercially pure titanium thin sheets, Materials & Design, vol.44, pp.528-534, 2013.
DOI : 10.1016/j.matdes.2012.08.046

M. E. Nixon, O. Cazacu, and R. A. Lebensohn, Anisotropic response of high-purity alpha-titanium : Experimental characterization and constitutive modeling, International Journal of Plasticity, pp.516-532, 2010.

F. H. Norton, The creep of steel at high temperatures, 1929.

T. Obara, H. Yoshinga, and S. Morozumi, Basal slip system in magnesium, Acta Metallurgica, pp.845-853, 1973.

C. Ouchi, H. Iizumi, and S. Mitao, Effects of ultra-high purification and addition of interstitial elements on properties of pure titanium and titanium alloy, Materials Science and Engineering: A, vol.243, issue.1-2, pp.186-195, 1998.
DOI : 10.1016/S0921-5093(97)00799-5

P. G. Patridge, The crystallography and deformation modes of hexagonal close-packed metals, Metallurgical Reviews, pp.169-194, 1967.

M. P. Pietryga, I. N. Vladimirov, and S. Reese, A finite deformation model for evolving flow anisotropy with distortional hardening including experimental validation, Mechanics of Materials, vol.44, pp.163-173, 2012.
DOI : 10.1016/j.mechmat.2011.07.014

V. Randle and O. Engler, Introduction to Teture Analysis: Macrostructure, Microtexture & Orientation Mapping, 2000.

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

A. Roos, J. L. Chaboche, L. Gélébart, and J. Crépin, Multiscale modelling of titanium aluminides, International Journal of Plasticity, vol.20, issue.4-5, pp.811-830, 2004.
DOI : 10.1016/j.ijplas.2003.08.005
URL : https://hal.archives-ouvertes.fr/hal-00111399

D. Rosenthal, The theory of moving sources of heat and its application to metal treatments, Transaction of the American Societu of Mechanical Engineers, pp.849-866, 1946.

G. Rousselier, The Rousselier Model for Porous Metal Plasticity and Ductile Fracture, in Handbook of Materials Behavior Models, pp.436-445, 2001.
DOI : 10.1016/B978-012443341-0/50049-1

A. A. Salem, R. Kalidindi, and R. D. Doherty, Strain hardening of titanium: role of deformation twinning, Acta Materialia, vol.51, issue.14, pp.4225-4237, 2003.
DOI : 10.1016/S1359-6454(03)00239-8

E. Schmid and W. Boas, Plasticity of cristals woth special reference to metals, 1950.

Y. Song, D. S. Xu, R. Yang, D. Li, W. T. Wu et al., Theorical study of the effects of alloying elements on the strength and modulus of alphatype bio-titanium alloys, Materials Science, pp.269-274, 1999.

Q. Y. Sun and H. C. Gu, Tensile and low-cycle fatigue behavior of commercilly pure titanium and Ti-4Al-2.5Sn alloy at 293 and 77°K, Materials Science, pp.80-86, 2001.

K. Takao and K. Kusukawa, Low-cycle fatigue behavior of commercially pure titanium, Materials Science and Engineering: A, vol.213, issue.1-2, pp.81-85, 1996.
DOI : 10.1016/0921-5093(96)10226-4

E. Tenckhoff and P. L. Rittenhouse, Annealing textures in zircaloy tubing, Journal of Nuclear Materials, vol.35, issue.1, pp.14-23, 1970.
DOI : 10.1016/0022-3115(70)90022-X

D. Bornet, M. Bernard, M. Felberbaum, E. Rappaz, and . Boller, In situ Xray tomography observation of inhomogeneous deformation in semi-solid aluminium alloys, Scripta Materialira, pp.449-452, 2009.

S. Thuillier and P. Y. Manach, Comparaison of the work hardening of metallic sheets using tensile and shear strain path, International Journal of Plasticity, pp.733-751, 2009.

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

J. A. Venables and C. J. Harland, Electron back-scattering patterns???A new technique for obtaining crystallographic information in the scanning electron microscope, Philosophical Magazine, vol.27, issue.5, pp.1193-1200, 1973.
DOI : 10.1088/0022-3735/2/3/305

R. Von-mises, Mechanik der festen Köper im plastisch deformablen Zustand, Göttin. Nachr. Math. Phys ESRF ID ESRF. Retrieved OctoberImaging, vol.19, issue.11http, pp.582-592, 1913.

. Wikipedia-algorithme-génétique, Algorithme génétique Wikipedia Algorithme génétique. Retrieved mars, 2013.

M. Yoo, Slip, twinning, and fracture in hexagonal close-packed metals, Metallurgical and Materials Transaction A, pp.409-418, 1981.
DOI : 10.1007/BF02648537

J. M. Yuan and V. P. Shim, Tensile response of ductile alpha titanium at moderately high strain rates, International Journal of Solids and Structures, pp.213-224, 2002.

S. Zaefferer, A study of active deformation systems in titanium alloys: dependence on alloy composition and correlation with deformation texture, Materials Science and Engineering: A, vol.344, issue.1-2, pp.20-30, 2003.
DOI : 10.1016/S0921-5093(02)00421-5

Z. S. Zhu, J. L. Gu, R. Y. Liu, N. P. Chen, and M. G. Yan, Variant selection and its effect on phase transformation textures in cold rolled titanium sheet, Materials Science and Engineering: A, vol.280, issue.1, pp.199-203, 2000.
DOI : 10.1016/S0921-5093(99)00666-8