T. C. , Hales : A proof of the kepler conjecture, Annals of mathematics, vol.162, issue.3, pp.1065-1185, 2005.

B. Champin and B. Gelas, , p.1335, 1984.

M. J. , Donachie : Titanium: a technical guide, 2000.

M. Peters, J. Hemptenmacher, J. Kumpfert, and C. , Leyens : Structure and Properties of Titanium and Titanium Alloys, pp.1-36, 2005.

Y. Combres, Propriétés du titane et de ses alliages, M557), pp.557-558, 1999.

W. Burgers, On the process of transition of the cubic-body-centered modification into the hexagonal-close-packed modification of zirconium, Physica, vol.1, issue.7-12, pp.7-12561, 1934.
DOI : 10.1016/S0031-8914(34)80244-3

D. Eylon, J. R. Newman, and J. Thorne, Titanium and titanium alloy castings, ASM International, Metals Handbook, pp.634-646, 1990.

G. Welsch, R. Boyer, and E. Collings, Materials properties handbook: titanium alloys, 1993.

N. Gey and M. Humbert, Characterization of the variant selection occurring during the ???????????? phase transformations of a cold rolled titanium sheet, Acta Materialia, vol.50, issue.2
DOI : 10.1016/S1359-6454(01)00351-2

, Acta materialia, vol.50, issue.2, pp.277-287, 2002.

D. Bhattacharyya, G. Viswanathan, R. Denkenberger, D. Furrer, and H. L. Fraser, The role of crystallographic and geometrical relationships between ?? and ?? phases in an ??/?? titanium alloy, Acta Materialia, vol.51, issue.16, pp.51-4679, 2003.
DOI : 10.1016/S1359-6454(03)00179-4

M. Humbert, H. Moustahfid, F. Wagner, and M. Philippe, Evaluation of the high temperature texture of the ? phase of a ta6v sample from the individual orientations of grains of the low temperature ? phase. Scripta metallurgica et materialia : Study of the ?-? phase transformations of a ti-64 sheet induced from a high-temperature ? state and a high-temperature ?+ ? state, Metallurgical and Materials Transactions A, pp.377-38251, 1994.

N. Gey and M. Humbert, Specific analysis of ebsd data to study the texture inheritance due to the ? ? ? phase transformation, Journal of Materials Science, vol.38, issue.6, pp.1289-1294, 2003.
DOI : 10.1023/A:1022842712172

H. Ranc, C. Servais, P. Chauvy, S. Debaud, and S. Mischler, Effect of surface structure on frictional behaviour of a tongue/palate tribological system, Tribology International, vol.39, issue.12, pp.1518-1526, 2006.
DOI : 10.1016/j.triboint.2006.01.017

P. Laheurte, W. Elmay, F. Prima, and T. Gloriant, Titane et alliages des matériaux de choix pour les applications médicales. Techniques de l'ingénieur Métaux et alliages, matériaux magnétiques et multimatériaux, base documentaire : TIB357DUO.(ref. article : m4781), 2017.

R. Tricot, Thermomechanical processing of titanium alloys, Sixth World Conference on Titanium. I, pp.23-35, 1988.

S. Neelakantan, P. Rivera-díaz-del-castillo, and S. Van-der-zwaag, Prediction of the martensite start temperature for ?? titanium alloys as a function of composition, Scripta Materialia, vol.60, issue.8, pp.60611-614, 2009.
DOI : 10.1016/j.scriptamat.2008.12.034

G. Lütjering, Influence of processing on microstructure and mechanical properties of (??+??) titanium alloys, Materials Science and Engineering: A, vol.243, issue.1-2, pp.32-45, 1998.
DOI : 10.1016/S0921-5093(97)00778-8

T. Sakai and M. Fine, Plastic deformation of Ti-Al single crystals in prismatic slip, Acta Metallurgica, vol.22, issue.11, pp.1359-1372, 1974.
DOI : 10.1016/0001-6160(74)90036-4

G. Gray, G. Luetjering, and J. Williams, The influence of oxygen on the structure, fracture, and fatigue crack propagation behavior of Ti-8.6 Wt Pct Al, Metallurgical Transactions A, vol.8, issue.1, pp.95-105, 1990.
DOI : 10.1007/BF02644220

X. Feaugas and E. Conforto, Influence de l'hydrog??ne sur les m??canismes de d??formation et d'endommagement des alliages de titane et de zirconium, PlastOx 2007, M??canismes et M??canique des Interactions Plasticit??, Environnement, pp.161-178, 2007.
DOI : 10.1051/ptox/2009012

A. Gavart, Forgeage et matriçage des pièces en titane et en alliages de titane, M690), pp.690-691, 1988.

I. Katzarov, S. Malinov, and W. Sha, Finite element modeling of the morphology of ? + ? phase transformation in ti ? 6al ? 4v alloy. Metallurgical and materials transactions A, pp.1027-1040, 2002.

E. Collings, G. Welsch, and R. Boyer, Materials properties handbook: titanium alloys, 1994.

C. Beauvais, B. Hocheid, and F. Quemper, Rapin : Study of the transformation kinetics of titanium alloy ta6v6e2 under isothermal conditions(transformation kinetics of ti alloy under isothermal conditions in solution treatment as function of temperature), 1970.

G. Lütjering and J. C. Williams, , 2003.

T. Ahmed, Phase transformations during cooling in ??+?? titanium alloys, Materials Science and Engineering: A, vol.243, issue.1-2, pp.206-211, 1998.
DOI : 10.1016/S0921-5093(97)00802-2

R. Castro and L. , Seraphin : Contribution à l'étude métallographique et structurale de l'alliage de titane ta6v. Mémoires scientifiques revue de la métallurgique, pp.1025-1058, 1966.

S. Denis, D. Farias, and A. Simon, Mathematical Model Coupling Phase Transformations and Temperature Evolutions in Steels., ISIJ International, vol.32, issue.3, pp.316-325, 1992.
DOI : 10.2355/isijinternational.32.316

Ø. Grong and H. Shercliff, Microstructural modelling in metals processing, Progress in Materials Science, pp.163-282, 2002.
DOI : 10.1016/S0079-6425(00)00004-9

S. Malinov, Z. Guo, W. Sha, and A. Wilson, Differential scanning calorimetry study and computer modeling of ? ? ? phase transformation in a ti ? 6al ? 4v alloy. Metallurgical and materials transactions A, pp.879-887, 2001.

S. Malinov, P. Markovsky, W. Sha, and Z. Guo, Resistivity study and computer modelling of the isothermal transformation kinetics of ti ? 6al ? 4v and ti ? 6a ? 2sn ? 4zr ? 2mo ? 0.08 ? si alloys, Journal of Alloys and Compounds, issue.1, pp.314181-192, 2001.

C. C. Murgau, R. Pederson, and L. Lindgren, A model for Ti???6Al???4V microstructure evolution for arbitrary temperature changes, Modelling and Simulation in Materials Science and Engineering, vol.20, issue.5, p.55006, 2012.
DOI : 10.1088/0965-0393/20/5/055006

P. N. Banu and S. D. Rani, Beta transus prediction of titanium alloys through integration of artificial neural network and multifactor dimensionality reduction analyses, Materials Discovery, vol.2, pp.16-23, 2015.
DOI : 10.1016/j.md.2016.01.001

Z. Guo, S. Malinov, and W. Sha, Modelling beta transus temperature of titanium alloys using artificial neural network, Computational Materials Science, vol.32, issue.1, pp.1-12, 2005.
DOI : 10.1016/j.commatsci.2004.05.004

R. Boyer, Titanium for aerospace: Rationale and applications, Advanced Performance Materials, pp.349-368, 1995.
DOI : 10.1016/B978-0-08-006564-9.50111-1

R. Boyer, An overview on the use of titanium in the aerospace industry, Materials Science and Engineering: A, vol.213, issue.1-2, pp.103-114404, 1996.
DOI : 10.1016/0921-5093(96)10233-1

P. Ciraud, Verfahren und vorrichtung zur herstellung beliebiger gegenstaende aus beliebigem schmelzbarem material Method and device for making any belongings from any fusible material, btitle, p.722263777, 1973.

E. C. Santos, M. Shiomi, K. Osakada, and T. Laoui, Rapid manufacturing of metal components by laser forming, International Journal of Machine Tools and Manufacture, vol.46, issue.12-13, pp.1459-1468, 2006.
DOI : 10.1016/j.ijmachtools.2005.09.005

C. Hull, Apparatus for production of three-dimensional objects by stereolithography , btitle, US Patent, vol.4, p.575330, 1986.

C. Deckard, Method and apparatus for producing parts by selective sintering, btitle, US Patent, vol.4863, p.538, 1989.

W. Meiners, K. Wissenbach, and A. Gasser, Selective laser sintering at melting temperature, btitle, US Patent, vol.6215, p.93, 2001.

G. N. Levy, The role and future of the Laser Technology in the Additive Manufacturing environment, Physics Procedia, vol.5, pp.65-80, 2010.
DOI : 10.1016/j.phpro.2010.08.123

, An in-depth global study on the advances in additive manufacturing technologies and applications, Annual Worldwide Progress Report, 2010.

J. Kruth, G. Levy, F. Klocke, and T. Childs, Consolidation phenomena in laser and powder-bed based layered manufacturing, CIRP Annals, vol.56, issue.2, pp.730-759, 2007.
DOI : 10.1016/j.cirp.2007.10.004

J. Kruth, P. Mercelis, J. Van-vaerenbergh, L. Froyen, and M. Rombouts, Binding mechanisms in selective laser sintering and selective laser melting, Rapid Prototyping Journal, vol.11, issue.1, pp.26-36, 2005.
DOI : 10.1126/science.1086989

E. Brandl, U. Heckenberger, V. Holzinger, and D. Buchbinder, Additive manufactured AlSi10Mg samples using Selective Laser Melting (SLM): Microstructure, high cycle fatigue, and fracture behavior, Materials & Design, vol.34, pp.159-169, 2012.
DOI : 10.1016/j.matdes.2011.07.067

T. Caffrey, Wohlers Associates, 2015.

A. Simchi, Direct laser sintering of metal powders: Mechanism, kinetics and microstructural features, Materials Science and Engineering: A, vol.428, issue.1-2, pp.148-158, 2006.
DOI : 10.1016/j.msea.2006.04.117

]. A. Bibliographie51, G. Bernard, L. N. Taillandier, C. Carter, P. J. Martin et al., Le prototypage rapide Attallah : The influence of the laser scan strategy on grain structure and cracking behaviour in slm powder-bed fabricated nickel superalloy, Hermes Journal of Alloys and Compounds, vol.615, pp.338-347, 1998.

P. Muller, J. Hascoet, and P. Mognol, Toolpaths for additive manufacturing of functionally graded materials (FGM) parts, Rapid Prototyping Journal, vol.20, issue.6, pp.511-522, 2014.
DOI : 10.1108/13552540510573383

S. H. Huang, P. Liu, A. Mokasdar, and L. Hou, Additive manufacturing and its societal impact: a literature review. The International Journal of Advanced Manufacturing Technology, pp.1-13, 2013.

J. Kruth, B. Vandenbroucke, and V. J. Vaerenbergh, Mercelis : Benchmarking of different sls/slm processes as rapid manufacturing techniques, 2005.

P. Mognol, D. Lepicart, and N. Perry, Rapid prototyping: energy and environment in the spotlight, Rapid Prototyping Journal, vol.12, issue.1, pp.26-34, 2006.
DOI : 10.1016/S0736-5845(99)00017-4

URL : https://hal.archives-ouvertes.fr/hal-00476639

M. Baumers, P. Dickens, C. Tuck, and R. Hague, The cost of additive manufacturing: machine productivity, economies of scale and technology-push, Technological Forecasting and Social Change, vol.102, pp.193-201, 2016.
DOI : 10.1016/j.techfore.2015.02.015

L. Thijs, F. Verhaeghe, T. Craeghs, J. Van-humbeeck, and J. , A study of the microstructural evolution during selective laser melting of Ti???6Al???4V, Acta Materialia, vol.58, issue.9, pp.3303-3312, 2010.
DOI : 10.1016/j.actamat.2010.02.004

N. Hopkinson, R. Hague, and P. Dickens, Rapid manufacturing: an industrial revolution for the digital age, 2006.
DOI : 10.1002/0470033991

R. P. Feynman, , 1987.

F. Royer, Fonctionnement et singularités du procédé de fusion laser sélective: Illustration par application à deux superalliages à base nickel et considérations énergétiques, Thèse de doctorat, 2014.

I. Yadroitsev and I. Smurov, Selective laser melting technology: From the single laser melted track stability to 3D parts of complex shape, Physics Procedia, vol.5, pp.551-560, 2010.
DOI : 10.1016/j.phpro.2010.08.083

I. Yadroitsev, A. Gusarov, I. Yadroitsava, and I. Smurov, Single track formation in selective laser melting of metal powders, Journal of Materials Processing Technology, vol.210, issue.12, pp.1624-1631221, 2006.
DOI : 10.1016/j.jmatprotec.2010.05.010

X. Jin, P. Berger, and T. Graf, Multiple reflections and Fresnel absorption in an actual 3D keyhole during deep penetration laser welding, Journal of Physics D: Applied Physics, vol.39, issue.21, p.394703, 2006.
DOI : 10.1088/0022-3727/39/21/030

N. K. Tolochko, Y. V. Khlopkov, S. E. Mozzharov, M. B. Ignatiev, T. Laoui et al., Absorptance of powder materials suitable for laser sintering, Rapid Prototyping Journal, vol.6, issue.3, pp.155-161, 2000.
DOI : 10.1108/13552540010337029

P. F. Jacobs, Rapid prototyping & manufacturing: fundamentals of stereolithography, Society of Manufacturing Engineers, 1992.

L. Dong, A. Makradi, S. Ahzi, and Y. , Finite Element Analysis of Temperature and Density Distributions in Selective Laser Sintering Process, Materials Science Forum, vol.553, pp.75-80, 2007.
DOI : 10.4028/www.scientific.net/MSF.553.75

URL : https://hal.archives-ouvertes.fr/hal-00592432

K. A. Mumtaz, P. Erasenthiran, and N. Hopkinson, High density selective laser melting of Waspaloy??, Journal of Materials Processing Technology, vol.195, issue.1-3, pp.77-87, 2008.
DOI : 10.1016/j.jmatprotec.2007.04.117

I. Yadroitsev, P. Bertrand, and I. Smurov, Parametric analysis of the selective laser melting process, Applied Surface Science, vol.253, issue.19, pp.8064-8069, 2007.
DOI : 10.1016/j.apsusc.2007.02.088

C. Chan, J. Mazumder, and M. Chen, Effect of surface tension gradient driven convection in a laser melt pool: Three???dimensional perturbation model, Journal of Applied Physics, vol.3, issue.11, pp.6166-6174, 1988.
DOI : 10.1007/BF02645924

C. Chan, J. Mazumder, and M. Chen, A two-dimensional transient model for convection in laser melted pool, Metallurgical Transactions A, vol.14, issue.12, pp.2175-2184, 1984.
DOI : 10.2172/4205348

K. Mills, B. Keene, R. Brooks, and A. Shirali, Marangoni effects in welding, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol.356, issue.1739, pp.911-926, 1998.
DOI : 10.1098/rsta.1998.0196

M. Rombouts, J. Kruth, and L. Froyen, Fundamentals of Selective Laser Melting of alloyed steel powders, CIRP Annals, vol.55, issue.1, pp.187-192, 2006.
DOI : 10.1016/S0007-8506(07)60395-3

P. Langston and A. R. Kennedy, Discrete element modelling of the packing of spheres and its application to the structure of porous metals made by infiltration of packed beds of NaCl beads, Powder Technology, vol.268, pp.210-218, 2014.
DOI : 10.1016/j.powtec.2014.08.018

H. Zhu, J. Fuh, and L. Lu, The influence of powder apparent density on the density in direct laser-sintered metallic parts, International Journal of Machine Tools and Manufacture, vol.47, issue.2, pp.294-298, 2007.
DOI : 10.1016/j.ijmachtools.2006.03.019

. Bibliographie, FRENKEL : Viscous flow of crystalline bodied under the action of surface tension, J. Phys.(USSR), vol.9, pp.385-391, 1945.

A. Spence and R. Crawford, The effect of processing variables on the formation and removal of bubbles in rotationally molded products, Polymer Engineering & Science, vol.6, issue.7, pp.993-1009, 1996.
DOI : 10.1007/BF00367563

A. Simchi, Effects of laser sintering processing parameters on the microstructure and densification of iron powder, Materials Science and Engineering: A, vol.359, issue.1-2, pp.119-128, 2003.
DOI : 10.1016/S0921-5093(03)00341-1

A. Budding and T. Vaneker, New Strategies for Powder Compaction in Powder-based Rapid Prototyping Techniques, Procedia CIRP, vol.6, pp.527-532, 2013.
DOI : 10.1016/j.procir.2013.03.100

URL : https://doi.org/10.1016/j.procir.2013.03.100

G. Shanmugavelayutham and V. Selvarajan, Plasma spheroidization of nickel powders in a plasma reactor, Bulletin of Materials Science, vol.1, issue.5, pp.453-457, 2004.
DOI : 10.1179/pom.2002.45.1.8

N. F. , EN : Iso 3923-1 : Poudres métalliques -détermination de la masse volumique apparente -partie 1: Méthode de l'entonnoir, 2010.

N. F. En, Iso 4490 : Poudres métalliques -détermination du temps d'écoulement au moyen d'un entonnoir calibré, 2008.

W. Beverloo and H. Leniger, The flow of granular solids through orifices, Chemical Engineering Science, vol.15, issue.3-4, pp.260-269, 1961.
DOI : 10.1016/0009-2509(61)85030-6

G. , Roblin : Microscopie. Techniques de l'ingénieur, (ref. article : r6710), 1998.

T. Baudin, Analyse ebsd principe et cartographies d'orientations. Techniques de l'ingénieur Essais métallographiques des métaux et alliages, (ref. article : m4138), 2010.

H. Bunge, Texture analysis in materials science: mathematical methods, 2013.

J. C. Tucker, L. H. Chan, G. S. Rohrer, M. A. Groeber, and A. D. , Rollett : Comparison of grain size distributions in a ni-based superalloy in three and two dimensions using the saltykov method, Scripta Materialia, issue.8, pp.66554-557, 2012.

J. Johanson, A Rolling Theory for Granular Solids, Journal of Applied Mechanics, vol.32, issue.4, 1965.
DOI : 10.1115/1.3627325

V. Katashinskii and M. Shtern, Stressed-strained state of powder being rolled in the densification zone. I. Mathematical model of rolling in the densification zone, Soviet Powder Metallurgy and Metal Ceramics, vol.4, issue.No. 1, pp.882-885, 1983.
DOI : 10.1007/BF00805540

S. Shima and M. Yamada, Compaction of metal powder by rolling Shtern : Stress-strain state of powder being rolled in the densification zone, Powder Metallurgy Powder Metallurgy and Metal Ceramics, vol.27, issue.112, pp.39-44, 1983.

M. Shtern, Plane deformation characteristics of compressible materials, Soviet Powder Metallurgy and Metal Ceramics, vol.21, issue.3, pp.169-175, 1982.

Y. Shanjani and E. Toyserkani, Material spreading and compaction in powder-based solid freeform fabrication methods: mathematical modeling, 19th Annual International Solid Freeform Fabrication Symposium, SFF, pp.399-410, 2008.

A. Gusarov and J. , Modelling of radiation transfer in metallic powders at laser treatment, International Journal of Heat and Mass Transfer, vol.48, issue.16, pp.3423-3434, 2005.
DOI : 10.1016/j.ijheatmasstransfer.2005.01.044

C. Charles and N. Järvstråt, Development of a microstructure model for metal deposition of titanium alloy ti-6al-4v, 2007.

S. Banerjee, G. Dey, D. Srivastava, and S. Ranganathan, Plate-shaped transformation products in zirconium-base alloys, Metallurgical and Materials Transactions A, vol.3, issue.11, pp.2201-2216, 1997.
DOI : 10.1007/BF02811653

M. Glavicic, P. Kobryn, and T. Bieler, A method to determine the orientation of the high-temperature beta phase from measured EBSD data for the low-temperature alpha phase in Ti-6Al-4V, Materials Science and Engineering: A, vol.346, issue.1-2, pp.50-59, 2003.
DOI : 10.1016/S0921-5093(02)00535-X

A. Gusarov, I. Yadroitsev, and P. Bertrand, Model of Radiation and Heat Transfer in Laser-Powder Interaction Zone at Selective Laser Melting, Journal of Heat Transfer, vol.52, issue.7, p.72101, 2009.
DOI : 10.1016/j.jmatprotec.2003.11.051

M. Rombouts, L. Froyen, A. Gusarov, E. H. Bentefour, and C. Glorieux, Photopyroelectric measurement of thermal conductivity of metallic powders, Journal of Applied Physics, vol.45, issue.2, p.24905, 2005.
DOI : 10.1016/S0017-9310(02)00370-8

Y. Chiew and E. Glandt, The effect of structure on the conductivity of a dispersion, Journal of Colloid and Interface Science, vol.94, issue.1, pp.90-104, 1983.
DOI : 10.1016/0021-9797(83)90238-2

P. S. Sheng and V. S. Joshi, Analysis of heat-affected zone formation for laser cutting of stainless steel, Journal of Materials Processing Technology, vol.53, issue.3-4, pp.3-4879, 1995.
DOI : 10.1016/0924-0136(94)01761-O

E. Sartori, Convection coefficient equations for forced air flow over flat surfaces, Solar Energy, vol.80, issue.9, pp.1063-1071, 2006.
DOI : 10.1016/j.solener.2005.11.001

L. Zheng, Y. Liu, S. Sun, and H. Zhang, Selective laser melting of al?8

, Chinese Journal of Aeronautics, vol.28, issue.2, pp.564-569, 2015.

C. C. Murgau, R. Pederson, and L. Lindgren, A model for Ti???6Al???4V microstructure evolution for arbitrary temperature changes, Modelling and Simulation in Materials Science and Engineering, vol.20, issue.5, p.55006, 2012.
DOI : 10.1088/0965-0393/20/5/055006

URL : http://ltu.diva-portal.org/smash/get/diva2:980304/FULLTEXT01