, Annexe 2 : micrographies de l'Inconel 625

, Toutes les micrographies sont données dans l'ordre suivant : Coeur ; mi-rayon ; peau. Attention : les échelles ne sont pas les mêmes pour toutes les micrographies

, Croissance de grains 1100°C/10 minutes d'attentes 1100°C/30 minutes d'attentes 1150°C/20 minutes d'attentes

E. P. Degarmo, Materials and processes in manufacturing, 2003.

P. E. Rivera-díaz-del-castillo and M. Huang, « Dislocation annihilation in plastic deformation: I. Multiscale irreversible thermodynamics, Acta Mater, vol.60, pp.2606-2614, 2012.

B. Hutchinson, Nucleation of recrystallisation, vol.27, pp.1471-1475

Y. C. Lin and X. Chen, « A critical review of experimental results and constitutive descriptions for metals and alloys in hot working, Mater. Des, vol.32, issue.4, pp.1733-1759, 2011.

P. Pauskar and R. Shivpuri, Microstructure and Mechanics Interaction in the Modeling of Hot Rolling of Rods, CIRP Ann, vol.48, issue.1, pp.191-194, 1999.

D. L. Preston, D. L. Tonks, and D. C. Wallace, « Model of plastic deformation for extreme loading conditions, J. Appl. Phys, vol.93, issue.1, pp.211-220, 2003.

G. Z. Voyiadjis and A. H. Almasri, « A physically based constitutive model for fcc metals with applications to dynamic hardness, Mech. Mater, vol.40, issue.6, pp.549-563, 2008.

H. Lim, C. C. Battaile, J. D. Carroll, B. L. Boyce, and C. R. Weinberger, « A physically based model of temperature and strain rate dependent yield in BCC metals: Implementation into crystal plasticity, J. Mech. Phys. Solids, vol.74, pp.80-96, 2015.

J. H. Hollomon, « Tensile Deformation, vol.162, pp.268-290, 1945.

D. Fields and W. Backofen, « Determination of strain hardening characteristics by torsion testing, Proc. ASTM, vol.57, pp.1259-1272, 1957.

J. C. Gelin and O. Ghouati, « An inverse method for determining viscoplastic properties of aluminium alloys, J. Mater. Process. Technol, vol.45, pp.435-440, 1994.

S. Diot, « Identification du comportement d'un acier en compression : du quasi-statique au dynamiqueIdentification of a steel compression behaviour: from quasi static approach to dynamic one, Mécanique Ind, vol.4, issue.5, pp.519-524, 2003.

M. and D. Donato, « Flow curve determination by torsion tests using inverse modelling, 2016.

J. Zhou, L. Qi, and G. Chen, « New inverse method for identification of constitutive parameters, Trans. Nonferrous Met. Soc. China, vol.16, issue.1, pp.148-152, 2006.

A. Andrade-campos, S. Thuillier, and P. Pilvin, Teixeira-Dias, « On the determination of material parameters for internal variable thermoelastic-viscoplastic constitutive models », Int. J. Plast, vol.23, issue.8, pp.1349-1379, 2007.

C. F. Gauss, Theoria motus corporum coelestium in sectionibus conicis solem ambientium, vol.7, 1809.

J. M. Ortega and W. C. Rheinboldt, Iterative solution of nonlinear equations in several variables, Philadelphia: Society for Industrial and Applied Mathematics, 2000.

I. Rechenberg, « Cybernetic Solution Path of an Experimental Problem, R. Aircr. Establ. Libr. Transl, 1965.

M. Mitchell, An introduction to genetic algorithms, 1996.

P. Bouchard, J. Gachet, and E. E. Roux, « Ductile damage parameters identification for cold metal forming applications », présenté à The 14th international esaform conference on material forming, pp.47-52, 2011.

E. Roux and P. Bouchard, Kriging metamodel global optimization of clinching joining processes accounting for ductile damage, J. Mater. Process. Technol, vol.213, issue.7, pp.1038-1047, 2013.
URL : https://hal.archives-ouvertes.fr/hal-00805670

X. Yang, Nature-inspired metaheuristic algorithms, 2008.

J. Kennedy and R. Eberhart, « Particle swarm optimization, Proceedings of ICNN'95 -International Conference on Neural Networks, vol.4, pp.1942-1948, 1995.

R. Oftadeh, M. J. Mahjoob, and M. Shariatpanahi, « A novel meta-heuristic optimization algorithm inspired by group hunting of animals: Hunting search », Comput. Math. Appl, vol.60, issue.7, pp.2087-2098, 2010.

M. R. Hestenes and E. Stiefel, « Methods of conjugate gradients for solving linear systems, J. Res. Natl. Bur. Stand, vol.49, issue.6, p.28

J. Nocedal, S. J. Wright, and . Quasi-newton-methods, Numerical Optimization, pp.192-221, 1999.

R. Fletcher, Practical methods of optimization, 1987.

J. Gawad, R. Kuziak, L. Madej, D. Szeliga, and M. Pietrzyk, « Identification of Rheological Parameters on the Basis of Various Types of Compression and Tension Tests, Steel Res. Int, vol.76, issue.2-3, pp.131-137, 2005.

Y. Huang, M. Li, Z. Xiao, H. Liu, and E. S. Wang, « A Dynamic Recrystallization (DRX) Constitutive Model for Elevated Temperature Flow Behavior of Cu-0.5Cr-0.1Zr Alloy, vol.8, pp.45-57, 2019.

M. Pietrzyk and J. Jedrzejewski, « Identification of parameters in the history dependent constitutive model for steels, CIRP Ann.-Manuf. Technol, vol.50, issue.1, pp.161-164, 2001.

D. Sztangret, J. Szeliga, M. Kusiak, and . Pietrzyk, « Application of inverse analysis with metamodelling for identification of metal flow stress, Can. Metall. Q, vol.51, issue.4, pp.440-446, 2012.

D. J. Yu, D. S. Xu, H. Wang, Z. B. Zhao, G. Z. Wei et al., « Refining constitutive relation by integration of finite element simulations and Gleeble experiments, J. Mater. Sci. Technol, vol.35, issue.6, pp.1039-1043, 2019.

E. Kabliman, A. H. Kolody, M. Kommenda, and G. Kronberger, « Prediction of stress-strain curves for aluminium alloys using symbolic regression », présenté à proceedings of the 22nd international esaform conference on material forming, p.180009, 2019.

A. Kawa?ek, H. Dyja, A. M. Ga?kin, K. V. Ozhmegov, and E. S. Sawicki, Physical Modelling of the Plastic Working Processes of Zirconium Alloy Bars and Tubes in Thermomechanical Conditions, vol.59, pp.935-940, 2014.

V. Pidvysotskyy and Z. ?apczy?ski, Characterization of a steel grade on Gleeble simulator », Instytut metalurgii Zelaza, Poland, technical report B0-1613, avr, 2018.

J. Chenot, « Méthodes de calcul en plasticité, p.23, 1991.

R. Ebrahimi and A. Najafizadeh, « A new method for evaluation of friction in bulk metal forming, J. Mater. Process. Technol, vol.152, issue.2, pp.136-143, 2004.

D. Szeliga and M. Pietrzyk, « Identification of Rheological and Tribological Parameters, Metal Forming Science and Practice, pp.227-258, 2002.

A. Hor, F. Morel, J. Lebrun, and G. Germain, « An experimental investigation of the behaviour of steels over large temperature and strain rate ranges », Int. J. Mech. Sci, vol.67, pp.108-122, 2013.

M. Awang, V. H. Mucino, Z. Feng, and S. A. David, Thermo-Mechanical Modeling of Friction Stir Spot Welding (FSSW) Process: Use of an Explicit Adaptive Meshing Scheme », présenté à SAE 2005 World Congress & Exhibition, pp.2005-2006, 2005.

S. Guerdoux and L. Fourment, « A 3D numerical simulation of different phases of friction stir welding, Model. Simul. Mater. Sci. Eng, vol.17, issue.7, p.75001, 2009.

V. Laxmanan and M. C. Flemings, « Deformation of semi-solid Sn-15 pct Pb alloy, Metall. Trans. A, vol.11, pp.1927-1937, 1980.

E. Becker, V. Favier, R. Bigot, P. Cezard, and L. Langlois, « Impact of experimental conditions on material response during forming of steel in semi-solid state, J. Mater. Process. Technol, vol.210, issue.11, pp.1482-1492, 2010.

A. Neag, V. Favier, R. Bigot, and M. Pop, Microstructure and flow behaviour during backward extrusion of semi-solid 7075 aluminium alloy, J. Mater. Process. Technol, vol.212, issue.7, pp.1472-1480

R. De-carvalho and R. A. Valente, Andrade-Campos, « Optimization strategies for non-linear material parameters identification in metal forming problems, Comput. Struct, vol.89, issue.2, pp.246-255, 2011.

A. Hensel and T. Spittel, Kraft und Arbeitsbedarf bildsamer Formgebungsverfahren. Leizig: VEB Deutscher Verlag für Grundstoffindustrie, 1978.

G. Venet, T. Balan, C. Baudouin, and R. Bigot, « Direct usage of the wire drawing process for large strain parameter identification, Int. J. Mater. Form, 2018.

E. S. Puchi-cabrera, J. D. Guérin, J. G. Barbera-sosa, M. Dubar, and L. Dubar, « Incremental constitutive description of SAE 5120 steel deformed under hot-working conditions », Int. J. Mech. Sci, vol.133, pp.619-630, 2017.

M. E. Mehtedi, F. Gabrielli, and E. S. Spigarelli, « Hot workability in process modeling of a bearing steel by using combined constitutive equations and dynamic material model, Mater. Des, vol.53, pp.398-404, 2014.

R. Johnson and W. K. Cook, A constitutive model and data for metals subjected to large strains high strain rates and high temperatures, The 7th International Symposium on Ballistics, 1983.

S. K. Paul, Predicting the flow behavior of metals under different strain rate and temperature through phenomenological modeling, Comput. Mater. Sci, vol.65, pp.91-99

Y. C. Lin and X. Chen, « A combined Johnson-Cook and Zerilli-Armstrong model for hot compressed typical high-strength alloy steel, Comput. Mater. Sci, vol.49, issue.3, pp.628-633, 2010.

H. Shin and J. Kim, « A Phenomenological Constitutive Equation to Describe Various Flow Stress Behaviors of Materials in Wide Strain Rate and Temperature Regimes, J. Eng. Mater. Technol, vol.132, issue.2, p.21009, 2010.

H. Zhang, W. Wen, and H. Cui, « Behaviors of IC10 alloy over a wide range of strain rates and temperatures: Experiments and modeling, Mater. Sci. Eng. A, vol.504, issue.2, pp.99-103, 2009.

A. Hor, « Simulation physique des conditions thermomécaniques de forgeage et d'usinage : caractérisation et modélisation de la rhéologie et de l'endommagement », Arts et Métiers ParisTech, Angers, 2011.

P. Caestecker, « Contribution à l'analyse et au choix de l'identification d'une loi de comportement -Application à la simulation numérique de la coupe, 2003.

B. Davoodi, Etude du comportement quasi-statique et dynamique des matériaux métalliques à haute température -simulation numérique du formage à chaud, 2006.

A. Gavrus, Etude du comportement des matériaux métalliques en dynamique rapide, 2008.

J. Cao and J. Lin, « A study on formulation of objective functions for determining material models, Int. J. Mech. Sci, vol.50, issue.2, pp.193-204, 2008.

J. V. Beck and K. J. Arnold, Parameter estimation in engineering and science, 1977.

R. Forestier, Developement of a parameter identification method by inverse analysis coupled with a 3D finite element model, 2005.
URL : https://hal.archives-ouvertes.fr/pastel-00001362

T. Baudin, « Comportement et endommagement d'aciers sous sollicitations combinées de traction-torsion, ENSMP, 1988.

C. Zhang, M. Bellet, M. Bobadilla, H. Shen, and B. Liu, « Inverse finite element modelling and identification of constitutive parameters of UHS steel based on Gleeble tensile tests at high temperature, Inverse Probl. Sci. Eng, vol.19, issue.4, pp.485-508, 2011.

D. Schmicker, « Experimental identification of flow properties of a S355 structural steel for hot deformation processes, J. Strain Anal. Eng. Des, vol.50, issue.2, pp.75-83, 2015.

D. J. Celentano, M. A. Palacios, E. L. Rojas, M. A. Cruchaga, A. A. Artigas et al., Simulation and experimental validation of multiple-step wire drawing processes, Finite Elem. Anal. Des, vol.45, issue.3, pp.163-180, 2009.

D. Banabic, H. Bunge, K. Pöhlandt, and A. E. Tekkaya, Formability of Metallic Materials : plastic anisotropy, formability testing, forming limits, 2000.

S. Khoddam, P. D. Hodgson, and M. J. Bahramabadi, « An inverse thermal-mechanical analysis of the hot torsion test for calibrating the constitutive parameters, Mater. Des, vol.32, issue.4, pp.1903-1909, 2011.

A. Gavrus, E. Massoni, and J. Chenot, « Thermo-viscoplastic parameter identification formulated as an inverse finite element analysis of the hot torsion test, Steel Res. Int, vol.70, issue.7, pp.259-268, 1999.

P. Cavaliere, E. Cerri, and E. E. Evangelista, « Isothermal forging of AA2618 + 20% Al2O3 by means of hot torsion and hot compression tests, Mater. Sci. Eng. A, pp.857-861, 2004.

A. M. Eleiche, « Torsional strength and ductility of mild steel in quasi-static, dynamic and strainrate-jump loading at different temperatures, J. Mech. Work. Technol, vol.13, issue.1, pp.23-37, 1986.

M. Rastegaev, Neue Methode der homogenen Stauchung von Proben zur Bestimmung der Flie\s sspannung und des Koeffizienten der inneren Reibung (russ.) », Zavod Lab, p.354, 1940.

B. Hopkinson, A Method of Measuring the Pressure Produced in the Detonation of High Explosives or by the Impact of Bullets », Proc. R. Soc. Math. Phys. Eng. Sci, vol.89, pp.411-413, 1914.

L. Meyer and S. Manwaring, « Critical adiabatic shear strength of low alloyed steel under compressive loading, International Conference on Metallurgical Applications of Shock-Wave and High-Strain-Rate Phenomena(EXPLOMET85), pp.657-674, 1985.

J. Peirs, P. Verleysen, J. Degrieck, and F. Coghe, « The use of hat-shaped specimens to study the high strain rate shear behaviour of Ti-6Al-4V », Int. J. Impact Eng, vol.37, issue.6, pp.703-714, 2010.

C. A. Bronkhorst, E. K. Cerreta, Q. Xue, P. J. Maudlin, T. A. Mason et al., « An experimental and numerical study of the localization behavior of tantalum and stainless steel », Int. J. Plast, vol.22, issue.7, pp.1304-1335, 2006.

M. Pietrzyk, J. G. Lenard, and G. M. Dalton, « A study of the plane strain compression test, CIRP Ann.-Manuf. Technol, vol.42, issue.1, pp.331-334, 1993.

B. Kowalski, C. M. Sellars, and M. Pietrzyk, « Identification of rheological parameters on the basis of plane strain compression tests on specimens of various initial dimensions, Comput. Mater. Sci, vol.35, issue.2, pp.92-97, 2006.

M. Graf, T. Henseler, M. Ullmann, R. Kawalla, and U. Prahl, Awiszus, « Study on determination of flow behaviour of 6060-aluminium and AZ31-magnesium thin sheet by means of stacked compression test, IOP Conf. Ser. Mater. Sci. Eng, vol.480, p.12023, 2019.

B. Roebuck, J. D. Lord, M. Brooks, M. S. Loveday, C. M. Sellars et al., Measurement of flow stress in hot axisymmetric compression tests », Mater. High Temp, vol.23, pp.59-83, 2006.

A. Hor, F. Morel, J. Lebrun, and G. Germain, « Modelling, identification and application of phenomenological constitutive laws over a large strain rate and temperature range », Mech. Mater, vol.64, pp.91-110, 2013.

P. L. Charpentier, B. C. Stone, S. C. Ernst, and J. F. Thomas, Characterization and modeling of the high temperature flow behavior of aluminum alloy 2024, vol.17, pp.2227-2237, 1986.

V. Favier and H. V. Atkinson, « Micromechanical modelling of the elastic-viscoplastic response of metallic alloys under rapid compression in the semi-solid state, Acta Mater, vol.59, issue.3, pp.1271-1280, 2011.

V. Kru?i?, M. Arentoft, S. Ma?era, A. Pristov?ek, and T. Rodi?, « A combined approach to determine workpiece-tool-press deflections and tool loads in multistage cold-forging, J. Mater. Process. Technol, vol.211, issue.1, pp.35-42, 2011.

J. Mull, C. Durand, C. Baudouin, R. Bigot, and M. Borsenberger, présenté à PROCEEDINGS OF THE 22ND INTERNATIONAL ESAFORM CONFERENCE ON MATERIAL FORMING: ESAFORM 2019, p.40002, 2019.

S. Leleu, « Contribution à l'évaluation des angles : conception, réalisation et validation d'un plateau pivotant de très haute précision : vers une nouvelle référence angulaire nationale », Ecole nationale supérieure d'Arts et Métiers, 1999.

S. Vajpayee, M. M. Sadek, and S. A. Tobias, « The efficiency and clash load of impact forming machines to the second order of approximation », Int. J. Mach. Tool Des. Res, vol.19, issue.4, pp.237-252, 1979.

F. Jia and F. Xu, « Dynamic analysis of closed high-speed precision press: Modeling, simulation and experiments, Proc. Inst. Mech. Eng. Part C J. Mech. Eng. Sci, vol.228, pp.2383-2401, 2014.

W. F. Savage, Apparatus for studying the effects of rapid thermal cycles and high strain rates on the elevated temperature behavior of materials, J. Appl. Polym. Sci, vol.6, pp.303-315, 1962.

S. Zinn and S. L. Semiatin, Elements of induction heating: design, control, and applications, Metals Park, 1988.

P. Feltham, Grain growth in metals, Acta Metall, vol.5, issue.2, pp.97-105, 1957.

L. Michalski, K. Eckersdorf, J. Kucharski, and J. Mcghee, Temperature Measurement, 1 re éd, 2001.

T. J. Seebeck, Magnetische polarisation der metalle und erze durch temperatur-differenz, p.1895

J. Peltier, « Nouvelles expériences sur la caloricité des courants électrique, Ann Chim Phys, vol.56, pp.371-386, 1834.

D. Szeliga and M. Pietrzyk, « Testing of the inverse software for identification of rheological models of materials subjected to plastic deformation, Arch. Civ. Mech. Eng, vol.7, issue.1, pp.35-52, 2007.

«. Cetim, Test de l'anneau, pp.1-1989

A. T. Male and M. G. Cockcroft, « A Method for the Determination of the Coefficient of Friction of Metals under Conditions of Bulk Plastic Deformation, J Inst Met, vol.93, pp.38-46, 1964.

A. Gavrus, H. Francillette, and D. T. Pham, « An optimal forward extrusion device proposed for numerical and experimental analysis of materials tribological properties corresponding to bulk forming processes, Tribol. Int, vol.47, pp.105-121, 2012.

E. Ghassemali, M. Tan, A. E. Jarfors, and S. C. Lim, « Progressive microforming process: towards the mass production of micro-parts using sheet metal », Int. J. Adv. Manuf. Technol, vol.66, pp.611-621, 2013.

D. Zhang and H. Ou, « Relationship between friction parameters in a Coulomb-Tresca friction model for bulk metal forming, Tribol. Int, vol.95, pp.13-18, 2016.

C. H. Lee and T. Altan, Influence of Flow Stress and Friction Upon Metal Flow in Upset Forging of Rings and Cylinders, J. Eng. Ind, vol.94, issue.3, p.775, 1972.

P. K. Saha and W. R. Wilson, Influence of plastic strain on friction in sheet metal forming, vol.172, pp.167-173, 1994.

R. Grueebler and P. Hora, « Temperature dependent friction modeling for sheet metal forming, Int. J. Mater. Form, vol.2, issue.S1, pp.251-254, 2009.

S. Marie, R. Ducloux, P. Lasne, J. Barlier, and L. Fourment, « Inverse Analysis of Forming Processes based on FORGE environment, vol.611, pp.1494-1502, 2014.

D. Krige, Statistical Approaches to Some Basic Mine Valuation Problems on the Witwatersrand, J. Chem. Metall. Min. Soc. South Afr, vol.52, pp.119-139, 1951.

G. Matheron, Traité de géostatistique appliquée. France: Editions Technip, 1962.

C. Zhang, M. Bellet, M. Bobadilla, H. Shen, and B. Liu, « A Coupled Electrical-Thermal-Mechanical Modeling of Gleeble Tensile Tests for Ultra-High-Strength (UHS) Steel at a High Temperature, Metall. Mater. Trans. A, vol.41, issue.9, pp.2304-2317, 2010.

G. P. Dinda, A. K. Dasgupta, and J. Mazumder, « Laser aided direct metal deposition of Inconel 625 superalloy: Microstructural evolution and thermal stability », Mater. Sci. Eng. A, vol.509, issue.2, pp.98-104, 2009.

J. Mittra, J. S. Dubey, and E. S. Banerjee, « Acoustic emission technique used for detecting early stages of precipitation during aging of Inconel 625, Scr. Mater, vol.49, pp.1209-1214, 2003.

V. Shankar, K. Bhanu-sankara-rao, and S. L. Mannan, « Microstructure and mechanical properties of Inconel 625 superalloy », J. Nucl. Mater, vol.288, issue.2-3, pp.222-232, 2001.

M. Ahmad, J. I. Akhter, M. Shahzad, and M. Akhtar, « Cracking during solidification of diffusion bonded Inconel 625 in the presence of Zircaloy-4 interlayer, J. Alloys Compd, vol.457, issue.2, pp.131-134, 2008.

J. R. Davis, Nickel, cobalt, and their alloys, Materials Park, 2000.

J. W. Brooks, « Forging of superalloys, Mater. Des, vol.21, issue.4, pp.297-303, 2000.

Q. Guo, D. Li, S. Guo, H. Peng, and J. Hu, « The effect of deformation temperature on the microstructure evolution of Inconel 625 superalloy, J. Nucl. Mater, vol.414, issue.3, pp.440-450, 2011.

D. Li, Q. Guo, S. Guo, H. Peng, and Z. Wu, « The microstructure evolution and nucleation mechanisms of dynamic recrystallization in hot-deformed Inconel 625 superalloy, Mater. Des, vol.32, issue.2, pp.696-705, 2011.

H. Y. Wang, J. X. Dong, M. C. Zhang, L. Zheng, Z. H. Yao et al., Effect of Deformation Conditions on Dynamic Recrystallization of As-Cast GH625 Alloy, vol.816, pp.620-627, 2015.

E. I. Galindo-nava and P. E. , Rivera-Díaz-del-Castillo, « Grain size evolution during discontinuous dynamic recrystallization, Scr. Mater, pp.1-4, 2014.

Q. M. Guo, D. F. Li, and S. L. Guo, Microstructural Models of Dynamic Recrystallization in Hot-Deformed Inconel 625 Superalloy », Mater. Manuf. Process, vol.27, pp.990-995, 2012.

M. Zouari, N. Bozzolo, and R. E. Loge, « Mean field modelling of dynamic and post-dynamic recrystallization during hot deformation of Inconel 718 in the absence of ? phase particles, Mater. Sci. Eng. A, vol.655, pp.408-424, 2016.

M. Zouari, R. Logé, and N. Bozzolo, « In Situ Characterization of Inconel 718 Post-Dynamic Recrystallization within a Scanning Electron Microscope », Metals, vol.7, p.476, 2017.

, E04 Committee, « Test Methods for Determining Average Grain Size

M. Avrami, Kinetics of Phase Change. I General Theory », J. Chem. Phys, vol.7, pp.1103-1112, 1939.

M. Avrami, « Kinetics of Phase Change. II Transformation-Time Relations for Random Distribution of Nuclei », J. Chem. Phys, vol.8, issue.2, pp.212-224

M. Avrami and . Granulation, Phase Change, and Microstructure Kinetics of Phase Change. III », J. Chem. Phys, vol.9, issue.2, pp.177-184, 1941.

O. Bylya, A. Reshetov, N. Stefani, M. Rosochowska, and P. Blackwell, « Applicability of JMAK-type model for predicting microstructural evolution in nickel-based superalloys, Procedia Eng, vol.207, pp.1105-1110, 2017.

A. Reshetov, O. Bylya, N. Stefani, M. Rosochowska, P. Blackwell et al., « An Approach to Microstructure Modelling in Nickel Based Superalloys, pp.531-538, 2016.

C. Sommitsch, D. Huber, F. Ingelman-sundberg, S. Mitsche, M. Stockinger et al., « Recrystallization and grain growth in the nickel-based superalloy allvac 718Plus », Int. J. Mater. Res, vol.100, issue.8, pp.1088-1098, 2009.