B. Auld, Acoustic Fields and Waves in Solids, J. Wiley and Sons, vol.1, p.48, 1973.

P. Bania, Beta titanium alloys and their role in the titanium industry of special interest, Journal of Metals, vol.46, pp.1619-1648, 1994.

J. Baruchel, J. Buère, E. Maire, P. Merle, and G. Peix, X-ray tomography in Material Science: General Principles, p.37, 2000.

S. Beucher and C. Lantuéjoul, Use of watersheds in contour detection, International workshop on image processing, p.50, 1979.

A. Bhattacharjee, S. Bhargava, V. Varma, S. Kamat, and A. Gogia, Eect of ? grain size on stress induced martensitic transformation in ? solution treated Ti-10V-2Fe-3Al alloy, Scripta Materialia, vol.53, p.77, 2005.

S. Birosca, J. Buère, F. Garcia-pastor, M. Karadge, L. Babout et al., Three-dimensional characterization of fatigue cracks in Ti-6246 using X-ray tomography and electron backscatter diraction, Acta Materialia, p.5758345847, 2009.

C. Blankenship and E. Starke, The fatigue crack growth behavior of the Al-Cu- Li alloy Weldalite049, Fatigue and Fracture of Engineering Materials and Structures, vol.14, pp.103114-100, 1991.

A. Bosak, M. Krisch, M. Mohr, J. Maultzsch, and C. Thomsen, Elasticity of single-crystalline graphite: Inelastic x-ray scattering study, Physical Review B, vol.75, issue.15, pp.153408-153456, 2007.
DOI : 10.1103/PhysRevB.75.153408

Y. Insa-de-lyon, F. Louchet, C. Marchionni, and J. Verger-gaugry, Experimental (TEM and STEM) investigation and theoretical approach to the fatigue-induced dissolution of ?' precipitates in a 2.5 wt% Al-Li alloy, these.pdf © [M. Herbig], [2011], pp.353366-106, 1987.

J. Buère, E. Ferrié, H. Proudhon, L. , and W. , Three-dimensional visualisation of fatigue cracks in metals using high resolution synchrotron X-ray microtomography, Materials Science and Technology, vol.22, issue.43, pp.10191024-10191068, 2006.

W. Burgers and F. Jacobs, Crystal structure of beta-titanium. Zeitschrift f"ur Kristallographie, pp.299300-77, 1936.

J. C. Chesnutt and F. H. Froes, Eect of ?-phase morphology and distribution on the tensile ductility of a metastable beta titanium alloy, Metallurgical and Materials Transactions A, vol.8, issue.6, pp.10131017-10131047, 1977.

N. Clément, A. Lenain, J. , and P. , Mechanical property optimization via microstructural control of new metastable beta titanium alloys, JOM, vol.14, issue.1, pp.50-78, 2007.
DOI : 10.1007/s11837-007-0010-y

P. Clément, J. Angéli, and A. Pineau, SHORT CRACK BEHAVIOUR IN NODULAR CAST IRON, Fatigue & Fracture of Engineering Materials and Structures, vol.4, issue.4, pp.251-276, 1984.
DOI : 10.1016/0013-7944(79)90081-X

P. Cloetens, Contribution to phase contrast imaging, reconstruction and tomography with hard synchrotron radiation -Principles, implementation and applications, p.52, 1999.

P. Cloetens, W. Ludwig, J. Baruchel, D. V. Dyck, J. Van-landuyt et al., Holotomography: Quantitative phase tomography with micrometer resolution using hard synchrotron radiation x rays, Applied Physics Letters, vol.75, issue.19, pp.29122914-82, 1999.
DOI : 10.1063/1.125225

P. Cloetens, M. Pateyron-salomé, J. Buère, G. Peix, J. Baruchel et al., Observation of microstructure and damage in materials by phase sensitive radiography and tomography, Journal of Applied Physics, vol.81, issue.9, pp.815878-5886, 1997.
DOI : 10.1063/1.364374

E. Collings, Applied Superconductivity, Metallurgy, and Physics of Titanium Alloys, p.74, 1986.
DOI : 10.1007/978-1-4613-2095-1

B. Cox and W. Morris, Monte Carlo simulations of the growth of small fatigue cracks, Engineering Fracture Mechanics, vol.31, issue.4, pp.591610-95, 1988.
DOI : 10.1016/0013-7944(88)90102-6

D. Davidson, K. Chan, R. Mcclung, and S. Hudak, Comprehensive Structural Integrity, volume 4 Cyclic Loading and Fatigue, chapter, Small fatigue cracks, pp.12964-12986, 2003.

]. , I. De-lyon, D. L. Tous-droits-réservés-davidson, K. Chan, and R. C. Mcclung, Cu-bearing high-strength lowalloy steels: The inuence of microstructure on the initiation and growth of small fatigue cracks, these.pdf © [M. Herbig], pp.25402556-25402574, 1996.

S. Dey, E. Lauridsen, W. Ludwig, D. Rowenhorst, F. et al., Study of microstructure evolution of grain boundary alpha phase during beta to alpha transformation in Timetal 21S alloy, Proceedings of Titanium 2007 Science and Technology, pp.467470-75, 2007.

O. Düber, B. Künkler, U. Krupp, H. Christ, and C. Fritzen, Experimental characterization and two-dimensional simulation of short-crack propagation in an austenitic???ferritic duplex steel, International Journal of Fatigue, vol.28, issue.9, pp.983992-89, 2006.
DOI : 10.1016/j.ijfatigue.2005.07.048

T. Duerig and W. , The omega-phase reaction in titanium alloy, Titanium 80 Proceedings of the 4th International Conference on Titanium, p.28, 1980.

T. Duerig, J. Albrecht, D. Richter, and P. Fischer, Formation and reversion of stress induced martensite in Ti-10V-2Fe-3Al, Acta Metallurgica, vol.30, issue.12, pp.21612172-73, 1982.
DOI : 10.1016/0001-6160(82)90137-7

T. Duerig, G. Terlinde, W. , and J. , Phase transformations and tensile properties of Ti-10V-2Fe-3AI, Metallurgical Transactions A, vol.22, issue.12, 1980.
DOI : 10.1007/BF02655118

D. C. Dunand, Processing of Titanium Foams, Advanced Engineering Materials, vol.6, issue.6, pp.369376-369404, 2004.
DOI : 10.1002/adem.200405576

D. Eliezer, E. Tal-gutelmacher, and T. Boellinghaus, Hydrogen embrittlement in hydride-and non hydride-forming systems -microstructural / phase changes and cracking mechanisms, Proceedings of the 11th International Conference on Fracture, p.28, 2005.

J. Fanning, Timetal 21S property data, Beta Titanium Alloys in the 1990's, pp.397410-397439, 1993.

J. Fanning, Properties of TIMETAL 555 (Ti-5Al-5Mo-5V-3Cr-0.6Fe), Journal of Materials Engineering and Performance, vol.14, issue.6, pp.788-817, 2005.
DOI : 10.1361/105994905X75628

C. E. Feltner and C. Laird, Factors inuencing the dislocation structures in fatigued metals, TMS-AIME, vol.242, pp.12531257-12531280, 1968.

E. Ferrié, J. Buère, L. , and W. , 3D characterisation of the nucleation of a short fatigue crack at a pore in a cast Al alloy using high resolution synchrotron microtomography, these.pdf © [M. Herbig], pp.12151220-12151245, 2005.
DOI : 10.1016/j.ijfatigue.2005.07.015

E. Ferrié, J. Buère, W. Ludwig, A. Gravouil, and L. Edwards, Fatigue crack propagation: In situ visualization using X-ray microtomography and 3D simulation using the extended finite element method, Acta Materialia, vol.54, issue.4, p.11111122, 2006.
DOI : 10.1016/j.actamat.2005.10.053

P. Forsyth, A two stage process of fatigue crack growth: Her Majesty's Stationery Oce, Crack Propagation: Proceedings of Craneld Symposium, p.7694, 1962.

S. Fréour, D. Gloaguen, M. François, A. Perronnet, and R. Guillén, Determination of single-crystal elasticity constants in a cubic phase within a multiphase alloy: X-ray diffraction measurements and inverse-scale transition modelling, Journal of Applied Crystallography, vol.38, issue.1, pp.3037-3084, 2005.
DOI : 10.1107/S0021889804023441

V. Gerold and H. Karnthaler, On the origin of planar slip in f.c.c. alloys, Acta Metallurgica, vol.37, issue.8, pp.21772183-21772207, 1989.
DOI : 10.1016/0001-6160(89)90143-0

R. Gordon, R. Bender, and G. Herman, Algebraic Reconstruction Techniques (ART) for three-dimensional electron microscopy and X-ray photography, Journal of Theoretical Biology, vol.29, issue.3, pp.471-510, 1970.
DOI : 10.1016/0022-5193(70)90109-8

G. Gottstein, Physikalische Grundlagen der Materialkunde, p.120, 2007.
DOI : 10.1007/978-3-662-09331-3

J. P. Guigay, M. Langer, R. Boistel, C. , and P. , Mixed contrast transfer and transport of intensity approach for phase retrieval in the Fresnel region, Optics Letters, vol.32, pp.16171619-82, 2007.
URL : https://hal.archives-ouvertes.fr/hal-00443269

G. Haicheng and S. Shujuan, Microstructural eect on fatigue thresholds in ? titanium alloy Ti-10V-2Fe-3Al, Fatigue90, p.76, 1990.

P. Heinl, A. Rottmair, C. Koerner, and R. F. Singer, Cellular Titanium by Selective Electron Beam Melting, Advanced Engineering Materials, vol.14, issue.5, pp.360364-360392, 2007.
DOI : 10.1002/adem.200700025

A. Heinz and P. Neumann, Representation of orientation and disorientation data for cubic, hexagonal, tetragonal and orthorombic crystals, Acta Crystallographica Section A: Foundations of Crystallography, issue.6, pp.47780789-47780829, 1991.

. Dipimage, Quantitative Imaging Group

. Insa-de-lyon, M. Herbig, A. King, P. Reischig, H. Proudhon et al., 3D growth of a short fatigue crack within a polycrystalline microstructure studied using combined diraction and phase contrast X-ray tomography, Acta Materialia, vol.59, issue.57, pp.590601-60, 2011.

R. Hertzberg, Deformation and Fracture Mechanics of Engineering Materials, Journal of Engineering Materials and Technology, vol.99, issue.1, p.24, 1995.
DOI : 10.1115/1.3443416

P. Hirsch and F. Humphreys, Physics of Strength and Plasticity, p.24, 1969.

C. Holzapfel, W. Schäf, M. Marx, H. Veho, and F. Mücklich, Interaction of cracks with precipitates and grain boundaries: Understanding crack growth mechanisms through focused ion beam tomography, Scripta Materialia, vol.56, issue.8, pp.697700-88, 2007.
DOI : 10.1016/j.scriptamat.2006.12.025

R. Honeycombe, Plastic Deformation of Metals, p.85, 1984.

E. Hornbogen and K. Zum-gahr, Microstructure and fatigue crack growth in a ??-Fe-Ni-Al alloy, Acta Metallurgica, vol.24, issue.6, pp.581592-92, 1976.
DOI : 10.1016/0001-6160(76)90104-8

G. Johnson, A. King, M. Honnicke, T. Marrow, L. et al., X-ray diraction contrast tomography: a novel technique for three-dimensional grain mapping of polycrystals. II. the combined case, Journal of Applied Crystallography, vol.41, pp.310318-310344, 2008.

A. C. Kak and M. Slaney, Principles of Computerized Tomographic Imaging, Society of Industrial and Applied Mathematics, vol.37, issue.52, p.80, 2001.

H. S. Kim, S. H. Lim, I. D. Yeo, K. , and W. Y. , Stress-induced martensitic transformation of metastable beta-titanium alloy, Materials Science and Engineering: A, vol.73, pp.449-451322325, 2007.

A. King, M. Herbig, W. Ludwig, P. Reischig, E. Lauridsen et al., Non-destructive analysis of micro texture and grain boundary character from X-ray diraction contrast tomography, Nuclear Instruments and Methods in Physics Research B -Beam Interactions with Materials and Atoms, pp.3-4291, 2010.

U. Krupp, Fatigue crack propagation in metals and alloys: microstructural aspects and modelling concepts, p.100, 2007.
DOI : 10.1002/9783527610686

L. Kubin, Mesoscale Simulations of Dislocations and Plasticity, p.105, 2011.

D. Kuroda, M. Niinomi, M. Morinaga, Y. Kato, Y. et al., Design and mechanical properties of new ?? type titanium alloys for implant materials, these.pdf © [M. Herbig], pp.244249-244296, 1998.
DOI : 10.1016/S0921-5093(97)00808-3

J. Labiche, O. Maton, S. Pascarelli, M. Newton, G. Ferre et al., Invited article: The fast readout low noise camera as a versatile x-ray detector for time resolved dispersive extended x-ray absorption fine structure and diffraction studies of dynamic problems in materials science, chemistry, and catalysis, Review of Scientific Instruments, vol.78, issue.9, pp.91301-91344, 2007.
DOI : 10.1063/1.2783112

C. Laird and G. Smith, Crack propagation in high stress fatigue, Philosophical Magazine, vol.24, issue.77, pp.847-869, 1962.
DOI : 10.1080/14786435808237004

C. Laird and G. Thomas, On fatigue-induced reversion and overaging in dispersion strengthened alloy systems, International Journal of Fracture Mechanics, vol.3, issue.2, pp.8197-8218, 1967.
DOI : 10.1007/BF00182687

M. Langer, Phase Retrieval in the Fresnel Region for Hard X-ray Tomography, p.37, 2008.

M. Langer, P. Cloetens, and F. Peyrin, Regularization of phase retrieval with phase-attenuation duality prior for 3D holotomography, IEEE Transactions on Image Processing, vol.19, pp.24282436-82, 2010.
URL : https://hal.archives-ouvertes.fr/hal-00443306

J. Lankford, The growth of small fatigue cracks in 7075-T6 aluminium. Fatigue of engineering materials and structures, pp.233-253, 1982.

C. Leyens and M. Peters, Titanium and Titanium Alloys -Fundamentals and Applications, p.34, 2003.

S. Li, T. Cui, Y. Hao, Y. , and R. , Fatigue properties of a metastable ??-type titanium alloy with reversible phase transformation, Acta Biomaterialia, vol.4, issue.2, p.305317, 2008.
DOI : 10.1016/j.actbio.2007.09.009

W. Ludwig, J. Buère, S. Savelli, C. , and P. , Study of the interaction of a short fatigue crack with grain boundaries in a cast Al alloy using X-ray microtomography, Acta Materialia, vol.51, issue.3, pp.585595-585620, 2003.
DOI : 10.1016/S1359-6454(02)00320-8
URL : https://hal.archives-ouvertes.fr/hal-00475154

W. Ludwig, A. King, P. Reischig, M. Herbig, E. Lauridsen et al., New opportunities for 3D materials science of polycrystalline materials at the micrometre lengthscale by combined use of X-ray diraction and X-ray imaging, Materials Science and Engineering: A, vol.524, issue.12, pp.6976-7001, 2009.

W. Ludwig, P. Reischig, A. King, M. Herbig, E. Lauridsen et al., Three-dimensional grain mapping by x-ray diffraction contrast tomography and the use of Friedel pairs in diffraction data analysis, Review of Scientific Instruments, vol.80, issue.3, pp.33905-33931, 2009.
DOI : 10.1063/1.3100200
URL : https://hal.archives-ouvertes.fr/hal-00431364

. Insa-de-lyon, P. Tous-droits-réservés-luká², and M. Klesnil, Fatigue damage and dislocation substructure, these.pdf © [M. Herbig], [2011] Proceedings of the 2nd international conference on corrosion fatigue, pp.118132-118155, 1971.

T. Martin and A. Koch, Recent developments in X-ray imaging with micrometer spatial resolution, Journal of Synchrotron Radiation, vol.13, issue.2, pp.172179-172222, 2006.
DOI : 10.1107/S0909049506000550

S. Mayo, P. Miller, S. Wilkins, T. Davis, D. Gao et al., Quantitative X-ray projection microscopy: phase-contrast and multi-spectral imaging, Journal of Microscopy, vol.207, issue.2, pp.7996-98, 2002.
DOI : 10.1046/j.1365-2818.2002.01046.x

J. Mcmillian and R. Pelloux, Fatigue crack propagation under program and random loads, Special Technical Publications 415, p.22, 1967.

K. Miller and E. De-los-rios, Short Fatigue Cracks -European Structural Integrity Society, Publication 13, p.24, 1992.

K. Miller, H. Mohamed, and E. De-los-rios, The behaviour of short fatigue cracks, chapter Fatigue damage accumulation above and below the fatigue limit, pp.491-509, 1986.

R. Mokso, P. Cloetens, E. Maire, W. Ludwig, and J. Buère, Nanoscale zoom tomography with hard x rays using Kirkpatrick-Baez optics, Applied Physics Letters, vol.90, issue.14, pp.144104-106, 2007.
DOI : 10.1063/1.2719653
URL : https://hal.archives-ouvertes.fr/hal-00434198

Y. Murakami, Critical review of phase transformations and heat treatment, Proceedings of the 4th International Conference on Titanium, pp.156-184, 1980.

Y. Nadot, N. Ranganathan, J. Mendez, and A. Béranger, A study of natural cracks initiated on casting defects by crack front marking, Scripta Materialia, vol.37, issue.5, pp.549553-549578, 1997.
DOI : 10.1016/S1359-6462(97)00158-9

S. Nag, Inuence of beta instabilities on the early stages of nucleation and growth of alpha in beta titanium alloys, p.29, 2008.

A. Navarro and E. De-los-rios, Short and long fatigue crack growth: A unified model, Philosophical Magazine A, vol.17, issue.1, pp.15-94, 1988.
DOI : 10.1007/BF02654397

S. Neelakantan, P. R. Del-castilloa, and S. Van-der-zwaaga, Prediction of the martensite start temperature for ?? titanium alloys as a function of composition, Scripta Materialia, vol.60, issue.8, pp.611614-76, 2009.
DOI : 10.1016/j.scriptamat.2008.12.034

P. Neumann, Coarse slip model of fatigue, Acta Metallurgica, vol.17, issue.9, pp.121925-121948, 1969.
DOI : 10.1016/0001-6160(69)90099-6

P. Insa-de-lyon-neumann, H. Fuhlrott, and H. Veho, Experiments concerning brittle, ductile, and environmentally controlled fatigue crack growth, these.pdf © [M. Herbig], [2011] Fatigue Mechanisms Proceedings of an ASTM-NBS-NSF symposium American Siciety ofr Testing and Materials, pp.371395-91, 1978.

P. Neumann, H. Veho, and H. Fuhlrott, ON THE MECHANISMS OF FATIGUE CRACK GROWTH, Part IV, vol.2, pp.13131324-13131328, 1977.
DOI : 10.1016/B978-0-08-022140-3.50090-2

J. Newman, The merging of fatigue and fracture mechanics concepts: a historical perspective, Progress in Aerospace Sciences, pp.347390-347414, 1998.

J. J. Newman, FASTRAN II: A fatigue crack growth structural analysis program, 1992.

J. J. Newman, E. Phillips, and M. Swain, Fatigue-life prediction methodology using small-crack theory, International Journal of Fatigue, vol.21, issue.2, pp.109-129, 1999.
DOI : 10.1016/S0142-1123(98)00058-9

D. Paganin, S. Mayo, T. Gureyev, P. Miller, and S. Wilkins, Simultaneous phase and amplitude extraction from a single defocused image of a homogeneous object, Journal of Microscopy, vol.206, issue.1, pp.3340-82, 2002.
DOI : 10.1046/j.1365-2818.2002.01010.x

P. Paris and F. Erdogan, A Critical Analysis of Crack Propagation Laws, Journal of Basic Engineering, vol.85, issue.4, pp.528-546, 1960.
DOI : 10.1115/1.3656900

S. Pearson, Initiation of fatigue cracks in commercial aluminium alloys and the subsequent propagation of very short cracks, Engineering Fracture Mechanics, vol.7, issue.2, pp.235247-235272, 1975.
DOI : 10.1016/0013-7944(75)90004-1

P. Penning, Minimization of shears for pencil glide in body-centered cubic crystals, Metallurgical Transactions A, vol.5, issue.7, pp.10211026-88, 1976.
DOI : 10.1007/BF02644068

G. Petzow, Metallographic Etching. American Society for Metals, p.34, 1978.

A. Pineau, Short fatigue crack behavior in relation to three-dimensional aspects and crack closure eect, Small fatigue Cracks: 2nd International Conference, p.24, 1986.

S. Pommier, Arching' eect in elastic polycrystals: implications for the variability of fatigue lives. Fatigue and Fracture of Engineering Materials and Structures, pp.331348-331372, 2002.

H. Poulsen, Three-Dimensional X-Ray Diraction Microscopy: Mapping Polycrystals and their Dynamics, p.40, 2004.

. Insa-de-lyon, H. Tous-droits-réservés-proudhon, S. Forest, L. , and W. , Large scale nite element simulations of polycrystalline aggregates: applications to X-ray diraction and imaging for fatigue metal behaviour, Proceedings of the 31st Risø International Symposium of Materials Science, 2010.

Y. Qiao and A. Argon, Cleavage crack-growth-resistance of grain boundaries in polycrystalline Fe???2%Si alloy: experiments and modeling, Mechanics of Materials, vol.35, issue.1-2, pp.129154-94, 2003.
DOI : 10.1016/S0167-6636(02)00194-1

Y. Qiao and A. Argon, Cleavage cracking resistance of high angle grain boundaries in Fe???3%Si alloy, Mechanics of Materials, vol.35, issue.3-6, pp.313331-94, 2003.
DOI : 10.1016/S0167-6636(02)00284-3

Y. Qiao and X. Kong, An energy analysis of the grain boundary behavior in cleavage cracking in Fe???3wt.%Si alloy, Materials Letters, vol.58, issue.25, pp.31563160-94, 2004.
DOI : 10.1016/j.matlet.2004.05.063

K. Ravichandran and X. Li, Fracture mechanical character of small cracks in polycrystalline materials: concept and numerical K calculations, Acta Materialia, vol.48, issue.2, pp.525540-525564, 2000.
DOI : 10.1016/S1359-6454(99)00348-1

K. Ravichandran, R. Ritchie, and Y. Murakami, Small Fatigue Cracks: Mechanics, Mechanisms and Applications, 1999.

C. N. Reid, J. L. Routbort, M. , and R. A. , Elastic constants of Ti???40 at.% Nb at 298 ??K, Journal of Applied Physics, vol.44, issue.3, pp.13981399-13981446, 1973.
DOI : 10.1063/1.1662365

R. Ritchie and J. Lankford, Small Fatigue Cracks, p.24, 1986.

Y. Ro, S. Agnew, and R. Ganglo, Crystallography of Fatigue Crack Propagation in Precipitation-Hardened Al-Cu-Mg/Li, Metallurgical and Materials Transactions A, vol.20, issue.436, pp.38-30423062, 2007.
DOI : 10.1007/s11661-007-9344-x

. Rodrigues, Title unknown, Journal of Pure and Applied Mathematics, vol.5, pp.380440-380479, 1840.

J. Ruppen, P. Bhowal, D. Eylon, and A. Mcevily, On the Process of Subsurface Fatigue Crack Initiation in Ti-6Al-4V, Proceedings of an ASTM-NBS-NSF symposium, p.4768, 1979.
DOI : 10.1520/STP35884S

J. Russ, The Image Processing Handbook, p.45, 2003.

W. Schäf, Über die Wechselwirkung kurzer Ermüdungsrisse mit Korngrenzen: Systematische Experimente mit Focussed Ion Beam Microscope und mikrostruktureller Tomographie, p.20, 2010.

W. Schäf, M. Marx, H. Veho, A. Heckl, and P. Randelzhofer, A 3D-view on the mechanisms of short fatigue cracks interacting with grain boundaries, these.pdf © [M. Herbig], [2011], pp.26-88, 2011.

J. Schijve, Fatigue of Structures and Materials, p.17, 2009.
DOI : 10.1007/978-1-4020-6808-9

B. Sharma and J. Donohue, A refinement of the crystal structure of gallium, Zeitschrift f??r Kristallographie, vol.117, issue.4, pp.293-77, 1962.
DOI : 10.1524/zkri.1962.117.4.293

K. Shiozawa and H. Matsushita, Crack initiation and small fatigue crack growth behaviour of beta Ti-15V-3Cr-3Al-3Sn alloy, Proceedings of the Sixth International Fatigue Congress, pp.301-318, 1996.

S. W. Smith, The Scientist and Engineer's Guide to Digital Signal Processing. California Technical Publishing, p.40, 1997.

J. Spowart, Automated serial sectioning for 3-D analysis of microstructures, Scripta Materialia, vol.55, issue.1, pp.510-535, 2006.
DOI : 10.1016/j.scriptamat.2006.01.019

S. Suresh, Fatigue of Materials, p.21, 2003.
DOI : 10.1017/CBO9780511806575

S. Suresh and R. Ritchie, Propagation of short fatigue cracks, International Metal Reviews, vol.29, pp.44576-44596, 1984.

I. Szanto, On the determination of high-purity alpha-titanium lattice parameters, Acta Technica Academiae Scientarum Hungaricae, vol.13, pp.363372-77, 1955.

K. Tanaka and T. Mura, Fatigue crack growth along planar slip bands, Acta Metallurgica, vol.32, issue.10, pp.17311740-17311763, 1984.
DOI : 10.1016/0001-6160(84)90229-3

B. Taylor and E. Weidmann, Application notes -metallographic preparation of titanium, p.31, 2008.

C. Taylor, T. Zhai, A. Wilkinson, M. , and J. , Inuence of grain orientations on the initiation of fatigue damage in an Al-Li alloy, Journal of Microscopy-Oxford, vol.195, pp.239247-239272, 1999.

G. Terlinde and G. Fischer, Titanium 95, Science and Technology, pp.21772194-21772224, 1996.

H. Veho and P. Neumann, In situ SEM experiments concerning the mechanism of ductile crack growth, Acta Metallurgica, vol.27, pp.915920-915943, 1987.

V. Rao, K. Yu, W. , R. , and R. , Fatigue crack propagation in aluminum-lithium alloy 2090: Part II. small crack behavior, Metallurgical Transactions A, vol.21, issue.3, pp.549561-105, 1988.
DOI : 10.1007/BF02649270

Y. Verreman and B. Nie, Early development of fatigue cracking at manual llet welds, Fatigue and Fracture of Engineering Materials and Structures, vol.19, issue.6, p.669681, 1996.

I. Weiss and S. Semiatin, Thermomechanical processing of beta titanium alloys???an overview, Materials Science and Engineering: A, vol.243, issue.1-2, pp.4665-4694, 1998.
DOI : 10.1016/S0921-5093(97)00783-1

G. Welsch, R. Boyer, C. , and E. W. , Materials properties handbook: titanium alloys, pp.31-76, 1994.

A. Wilkinson, M. Henderson, M. , and J. , Examination of fatigue crack plastic zones using scanning-electron-microscope-based electron diraction techniques, Philosophical Magazine Letters, issue.3, pp.74145151-74145176, 1996.

A. Wilkinson, S. Roberts, H. , and P. , Modelling the threshold conditions for propagation of stage I fatigue cracks, Acta Materialia, vol.46, issue.2, pp.379-400, 1998.
DOI : 10.1016/S1359-6454(97)00290-5

Y. Yang, G. P. Li, G. M. Cheng, Y. L. Li, Y. et al., Multiple deformation mechanisms of Ti, Applied Physics Letters, vol.73, pp.9413-77, 2009.

S. Zaeerer, S. Wright, R. , and D. , Three-dimensional orientation microscopy in a focused ion beam-scanning electron microscope: A new dimension of microstructure characterization, Metallurgical and Materials Transactions A, pp.374-399, 2008.

C. Zappfe and C. Worden, Fractographic registrations of fatigue, Transactions of the American Society for Metals, vol.43, pp.98569-98590, 1951.

T. Zhai, X. Jiang, J. Li, M. Garratt, and G. Bray, The grain boundary geometry for optimum resistance to growth of short fatigue cracks in high strength Al-alloys, International Journal of Fatigue, vol.27, issue.10-12, pp.1202-1222, 2005.
DOI : 10.1016/j.ijfatigue.2005.06.021

T. Zhai, A. Wilkinson, M. , and J. , A crystallographic mechanism for fatigue crack propagation through grain boundaries, Acta Materialia, vol.48, issue.20, pp.4917-93, 2000.
DOI : 10.1016/S1359-6454(00)00214-7

Y. Zhang and L. Edwards, Eect of grain boundaries on the development of plastic deformation ahead of small fatigue cracks, Scripta Metallurgica et Materialia, vol.26, issue.25, pp.19011906-94, 1992.

U. Zwicker, Titan und Titan-Legierungen, p.28, 1974.

M. King, A. Reischig, P. Proudhon, H. Lauridsen, E. M. Marrow et al., INSA de Lyon, tous droits réservés Publications Peer-reviewed Herbig 3D growth of a short fatigue crack within a polycrystalline microstructure studied using combined diraction and phase contrast X-ray tomography, Acta Materialia, vol.59, pp.590-601, 2011.

W. Ludwig, A. King, M. Herbig, P. Reischig, H. Proudhon et al., Characterization of polycrystalline materials by combined use of synchrotron X-ray imaging and diraction techniques, Journal of Metals, issue.12, pp.6222-6250, 2010.

A. King, M. Herbig, W. Ludwig, P. Reischig, E. Lauridsen et al., Non-destructive analysis of micro texture and grain boundary character from X-ray diraction contrast tomography, Nuclear Instruments and Methods in Physics Research B -Beam Interactions with Materials and Atoms, pp.3-4291296, 2010.

W. Ludwig, P. Reischig, A. King, M. Herbig, E. Lauridsen et al., Three-dimensional grain mapping by x-ray diffraction contrast tomography and the use of Friedel pairs in diffraction data analysis, Review of Scientific Instruments, vol.80, issue.3, p.33905, 2009.
DOI : 10.1063/1.3100200
URL : https://hal.archives-ouvertes.fr/hal-00431364

W. Ludwig, A. King, P. Reischig, M. Herbig, E. Lauridsen et al., New opportunities for 3D materials science of polycrystalline materials at the micrometre lengthscale by combined use of X-ray diraction and X-ray imaging, Materials Science and Engineering: A, vol.524, issue.12, p.6976, 2009.

H. Non-peer-reviewed-proudhon, M. Herbig, J. Buère, L. , and W. , Simulation par éléments nis de la déformation de polycristaux à partir d'images de tomographie par contraste de diraction, CSMA 2011, 10e Colloque National en Calcul des Structures, Presqu'île de Giens (Var), 2011.

W. Ludwig, M. Herbig, A. King, P. Reischig, H. Proudhon et al., The grain microstructure of polycrystalline materials as revealed by the combined use of synchrotron X-ray imaging and diraction techniques, Actes des Journées Annuelles de la Société Française de Métallurgie et de Matériaux, 2010.

W. Ludwig, P. Reischig, A. King, M. Herbig, H. Proudhon et al., Thoughts about the optimum data acquisition geometry and time resolution of monochromatic beam X-ray diraction microscopy experiments, Proceedings of the 31st Risø Int. Symposium on Materials Science, 2010.