CHAPITRE II : MAGNETO-HYDRO-ENERGETIQUE
II.5. FACTEURS D’INFLUENCES
II.5.4. La décélération de la vitesse de refroidissement
La décélération de la vitesse de croissance induit une augmentation ponctuelle de la température et de la concentration dans la zone interdendritique. Ce phénomène induit alors la refusion thermique et solutale des bras de dendrite.
-81-
II.6. CONCLUSION PARTIELLE
Ce chapitre a permis de présenter les équations de base de la Magnéto-Hydro-Energétique (MHE) qui seront employées par la suite. Les différents nombres adimensionnels utiles à la description et l’analyse des cas traités dans le cadre de ce travail ont été explicités. Seulement l’aspect énergétique de ces équations sous forme d’une énergie de brassage électromagnétique a été abordé, afin de l’adapter aux applications de la solidification des alliages métalliques. Une étude sur les différentes configurations utilisées pour le brassage électromagnétique et leurs influences sur les structures de solidification à été effectuée. Plusieurs techniques de brassage ont montré leur efficacité pour améliorer la structure finale voir le perfectionnement des propriétés physiques des matériaux, notamment la technique du RMF-PSAD (rotating
magnetic field with pulse sequence of alternating direction) sur la diminution des canaux
ségrégés, et la technique de couplage RMF-TMF ((rotating magnetic field-travelling
magnetic field) sur l’affinage de la structure, sans oublier l’effet des forces thermoélectriques
induites par des forts champs magnétiques à courant continu sur la favorisation du processus de transition colonnaires-equiaxes (CET).
-82-
REFERENCES BIBLIOGRAPHIQUES DU CHAPITRE II [1] R. Berton, “Magnéto-hydrodynamique”, Masson, 1991.
[2] R. Moreau, “The fundamental of MHD Related to crystal Growth”, Progress in crystal growth and characterization of materials, (1999), P.161.
[3] R. Moreau, “Magnetohydrodynamics”, Dordrecht, Kluwer Academic Publishers, 1990. [4] Y. Fautrelle, “Fluid flows induced by alternating magnetic fields, Liquid Metal
Magnetohydrodynamics”, Kluwer Academic Publisher, (1989), p. 223-232.
[5] E. Taberlet, Y. Fautrelle : “Turbulent stirring in an experimental induction furnace”, journal of Fluid Mech., Vol. 159, 1985, pp. 409-431.
[6] J. J. Moore, “Continuous Casting”, V.3. Warrendale, (1984).
[7] J. L. Meyer, "Electromagnetic Processes in Aluminium Casthouses and Foundries :
An Overview", in Magnetohydrodynamics in process metallurgy , J. Szekely, The
Minerals, Metals & Materials Society, (1991), p. 127.
[8] G. M. Meseha, "Electromagnetic Stirring Application in Copper Bar Manufacturing", , (1997), p. 60.
[9] P. A. Davidson, "Magnetohydrodynamics in Materials Processing", Annual Rev Fluid Mech. V 31, (1999), p. 273.
[10] Y. Fautrelle, "Analytical and Numerical Aspects of the Electromagnetic Stirring
Induced by Alternating Magnetic Fields", J. Fluid. Mech., V 102, (1981), p. 405.
[11] P. Cremer and A. Alemany, "Aspects Expérimentaux du Brassage Electromagnétique
en Creuset", J. Mécanique appliquée, V 5, (1981), p. 37.
[12] E. Taberlet and Y. Fautrelle, "Turbulent Stirring in an Experimental Induction
Furnace", J. fluid Mech., V159, (1985), p. 409.
[13] R. Krishnamurti, "On the Transition to Turbulent Convection. Part 2. The Transition
to Time-Dependent Flow", J. fluid Mech., V 42, (1970), p. 309.
[14] P. J. Prescot and F. P. Incropera, "The Effect of Turbulence on Solidification of a
Binary Metal Alloy with Electromagnetic Stirring", J. heat transfer, V 117, (1995),
p.716.
[15] E. D. Tarapore and J. W. Evans, "Fluid Velocities in Induction Melting Furnaces: Part
I. Theory and Laboratory Experiments", Met. Trans. B. V7, (1976), p. 343.
[16] S. Cuevas, B. F. Pi cologlou, J. S. Walker, G. Talmage and T. Q. Hua, "Heat Transfer
in Laminar and Turbulent Liquid-Metal MHD Flows in Square Ducts with Thin Conducting or Insulating Walls", Int. J. Eng. Sci., V 35, (1997), p. 505.
[17] P. Lehmann, R. Moreau, D. Camel and R. Bolcato, "Modification of Interdendritic
Convection in Directional Solidification by a Uniform Magnetic Field", Acta Mater.,
-83-
[18] S. N. Tewari, R. Shah and H. Song, "Effect of magnetic field on the microstructure
and macrosegregation in directionally solidified Pb-Sn alloys", Metall Mater. Trans.
A, V25, (1994), p. 1535.
[19] S. Kobayashi, "Effects of an External Magnetic Field on Solute Distribution in
Czochralsko Grown Crystals - A Theoretical Analysis", J. Crystal Growth, V75,
(1986), p. 301.
[20] R. W. Series, "Czochralski Growth of Silicon under an Axial Magnetic Field", J. Crystal Growth, V97, (1989), p. 85.
[21] B. Cantor and A. Vogel, “Dendritic solidification and fluid flow”, J. Crystal Growth, V 41, (1977), p. 109.
[22] S. R. Coriell, G.B. McFadden and R. F. Boisvet, “Effect of forced Couette Flow on
Coupled Convective and Morphological Instabilities during Unidirectional Solidification”, J. Crystal Growth, V 69, (1984), p. 15.
[23] R. Ananth and W. N. Gill, "Dendritic Growth in Microgravity and Forced
Convection", J. Crystal Growth, V 179, (1997), p. 263.
[24] Ch. Charbon, A. Jacot and M. Rappaz, "3D Stochastic Modelling of Equiaxed
Solidification in the Presence of Grain Movement", Acta Metall. Mater., V42, (1994),
p. 3953.
[25] A. Buchholz and S. Engler, "The Inluence of Forced Convection on Solidification
Interfaces", Comp. Mat. Science, V 7, (1996), p. 221.
[26] M. R. Bridge and G. D. Rogers, "Structural Effects and Band Segregate Formation
during the Electromagnetic Stirring of Strand-Cast Steel", Met Trans. B, V 15, (1984),
p. 581.
[27] W. D. Griffiths and D. G. McCartney, "The Effect of Electromagnetic Stirring on
Macrostructure and Macrosegregation in the Aluminium Alloy 7150", mater. Sci. Eng
A. V 222, (1997), p. 140.
[28] D. Brabazon, D. J. Browne and A. J. Carr, "Mechanical Stir Casting of Aluminium
alloys form the Mushy State: Process, Microstructure amd Mechanical Properties",
Mater. Sci. Eng, A V326, (2002), p. 370.
[29] Ch. Vivès, "Electromagnetic refining of aluminium alloys by the CREM process: Part
II. Specific practical problems and their solutions", Met Trans. B, V20, (1989), p. 631.
[30] P. Desnain, F. Durand, Y. Fautrelle, D. Bloch, J. L. Meyer and J. P. Riquet, "Effects of
the Electromagnetic Stirring on the Grain Size of Industrial Aluminium Alloys : Experiments and Theoretical Predictions", in Light Metals 1988, L. G. Boxall, The
-84-
[31] D. A. Currey and C. A. Pickles, "Electromagnetic Stirring of Aluminium-Silicon
Alloys", J. Mater. Sci. V 23, (1988), p. 3756.
[32] W. D. Griffiths and D. G. McCartney, "The Effect of Electromagnetic Stirring During
Solidification on the Structure of Al-Si Alloys", Mater. Sci. Eng. A, V 216, (1996), p.
47.
[33] M. C. Flemings, "Behavior of Metal Alloys in the Semisolid State", Met. Trans. B, V 22, (1991), p. 269.
[34] M. Suéry, C. L. Martin and L. Salvo, "Overview of the Rheological Behaviour of
Globular and Dendritic Slurries", in 4th International conference on semi-solid processing of alloys and composites, The University of Sheffield, England, D. Kürwood et P. Kapranos, 1996), p. 21.
[35] Ch. Vivès, "Elaboration of semisolid alloys by means of new electromagnetic rheocasting processes", Met. Trans. B, V 23, (1992), p. 189.
[36] C. J. Paradies, R. N. Smith and M. E. Glicksman, "The Influence of Convection during
Solidification on Fragmentation of the Mushy Zone of a Model Alloy”, Metall. Mater.
Trans. A. V 28, (1997), p. 875.
[37] T. Sato, W. Kurz and K. lkawa, "Experiments on Dendrite Branch Detachment in the
Succinonitrile-Camphor Alloy", Trans Of the Japan institute of metals, V 28, (1987),
p. 1012.
[38] K. A. Jackson, J. D. Hunt, D. R. Uhlmann and T. P. Seward, "On the Origin of the
Equiaxed Zone in Castings", Transaction of the Metallurgical Society of AIME, V 236
(1966), p. 149.
[39] S. Liu, S.-Z. Lu and A. Hellawell, "Dendritic Array Growth in the System
NH4Cl-H2O and [CH2CN]2-H2O: The Detachment of Dendrite Side Arms Induced by Deceleration", J. Crystal Growth, V 234, (2002), p. 740.
[40] J. P. Gu, C. Beckermann and A. F. Giamei, "Motion and Remelting of Dendrite
Fragments during Directional Solidification of a Nickel-Base Superalloy", Metall.
Mater. Trans. A, V 28, (1997), p. 1533.
[41] A. Hellawell, J. R. Sarazin and R. S. Steube, "Channel Convection in Partly Solidified
Systems", Phil. Trans. R. Soc. Lond. A, V345, (1993), p. 507.
[42] J. Pilling and A. Hellawell, "Mechanical deformation of dendrites by fluid flow", Mater. Trans. A, V 27, (1996), p. 229.
[43] S. Liu, S.-Z. Lu and A. Hellawell, "Mechanism of Dendrite Fragmentation in
Castings", in Light Metals 1997, The Minerals, Metals & Materials Society, (1997), p.
-85-
[44] Q. Han and A. Hellawell, "Primary Particle Melting Rates and Equiaxed Grain
nucleation", Metall. Mater. Trans. B, V 28, (1997), p. 169.
[45] Y. Kishida, K. Takeda, I. "Miyoshino and E. Takeuchi, "Anisotropic Effect of
Magnetohydrodynamics on Metal Solidification", ISIJ Int, V 30, (1990), p. 34.
[46] K. Mazuruk. "Control of melt convection using travelling magnetic fields". Advances in Space Research, 29(4) :541_548, 2002.
[47] S. McFadden and D. J. Browne. "Modelling the columnar to equiaxed transition using
a front tracking method". In Howard Jones, editor, 5th Decennial International
Conference on Solidification Processing, (2007), p. 172.
[48] M. Medina. "Ségrégation par solidification en présence de convection naturelle ou
forcée". Thèse d'état, Institut National Polytechnique de Grenoble, Juin 2000.
[49] S. Yesilyurt, S. Motakef, R. Grugel, and K. Mazuruk. "The effect of the traveling
magnetic field (TMF) on the buoyancy-induced convection in the vertical bridgman growth of semiconductors". Journal of Crystal Growth, V. 263, (2004), p.80-89.
[50] K. Zaidat, N. Mangelinck-Noël, and R. Moreau. “Control of the solidification of al-ni
alloys using a travelling magnetic field: macrosegregation”. In TMS, editor, Modeling
of Casting, Welding and Advanced Solidification Processes-XI, (2006), p.341-347. [51] K. Zaidat, T. Ouled-Khachroum, G. Vian, C. Garnier, N. Mangelinck-Noël, M. D.
Dupouy, and R. Moreau. “Directional solidification of refined Al-3.5wt%Ni under
natural convection and under a forced flow driven by a traveling magnetitc field”.
Journal of Crystal Growth, (2005), V. 275. (2005), e1501_e1505.
[52] I. Grants and G. Gerbeth. “Linear three-dimensional instability of a magnetically
driven rotating flow”. Journal of Fluid Mechanics, V. 463, (2002), p. 229-239.
[53] X. Li, Z.M. Ren, Y. Fautrelle. “Effect of a vertical magnetic field on the dendrite
morphology during Bridgman crystal growth of Al–4.5wt% Cu”. Journal of crystal
growth. V. 290. (2006), p 571-57.
[54] X. Li, Z.M. Ren, Y. Fautrelle. “Effect of an axial high magnetic field on the
microstructure in directionally solidified Pb– Sn eutectic alloy”. Journal of crystal
growth. V. 310. (2008), p 3584-3589.
[55] X. Li, Y. Fautrelle, K. Zaidat, A. Gagnoud, Z. Ren, R. Moreau, Y. Zhang, C. Esling. “Columnar-to-equiaxed transitions in al-based alloys during directional solidification
under a high magnetic field”. Journal of crystal growth. V. 312. (2010), p 267-272.
[56] X. Li, A. Gagnoud, Y. Fautrelle, Z. Ren, R. Moreau, Y. Zhang, C. Esling. “Dendrite
fragmentation and columnar-to-equiaxed transition during directional solidification at lower growth speed under a strong magnetic field”. Acta Materialia. V. 60. (2012), p
-86-
[57] P. Desnain, Y. Fautrelle, J.-L. Meyer, J.-P. Riquet, F. Durand, “Prediction of equiaxed
grain density in multicomponent alloys, stirred electromagnetically”, Acta Met. Mat,
V. 38, (1990), p. 1513-1523.
[58] B. Willers, S. Eckert, P.A. Nikrityk, D. Räbiger, J. Dong, K. Eckert, and G. Gerberth. “Efficient Melt Stirring Using Pulse Sequences of a Rotating Magnetic Field: Part II.
Application to Solidification of Al-Si Alloy”.The Minerals, Metals & Materials Society and ASM International 2008.
[59] D Räbiger, M Leonhardt, S Eckert and G Gerbeth. “Flow control during solidification of SnPb-alloys using timemodulated AC magnetic fields”.IOP Conf. Series: Materials Science and Engineering V. 27, (2011), 012053. doi:10.1088/1757-899X/27/1/012053 [60] J. P. Gu, C. Beckermann and A. F. Giamei, "Motion and Remelting of Dendrite
Fragments during Directional Solidification of a Nickel-Base Superalloy", Metall
Mater Trans. V 28A, (1997), p.1533.
[61] R. Ernst, C. Garnier : « Mesure numérique des caractéristiques d’un circuit oscillant
pour le chauffage à induction », Revue Générale d’Electricité, V 8, (1989), p. 1-8.
[62] J. Jang and A. Hellawell, "Use of NH4Cl-H2O Analogue Castings to Model Aspects of
Continuous Casting. Part 2 : Columnar-Equiaxed Grain Transition and Crystal SedimentationRates", Ironmaking and steelmaking V 18, (1991), p. 275.
-87-