Mesoscopic modelling of precipitation: A tool for extracting physical parameters of phase transformations in metallic alloys

Alexis Deschamps; Michel Perez

doi:10.1016/j.crhy.2010.07.005

Computational metallurgy and changes of scale / Métallurgie numérique et changements d'échelle

Mesoscopic modelling of precipitation: A tool for extracting physical parameters of phase transformations in metallic alloys

Alexis Deschamps ¹ ; Michel Perez ²

¹ SIMAP, Grenoble INP, UMR CNRS 5266, Université Joseph-Fourier, 1130, rue de la Piscine, BP 75, 38402 St Martin d'Hérès cedex, France
² Université de Lyon, INSA Lyon, MATEIS, UMR CNRS 5510, 7, avenue Jean-Capelle, 69621 Villeurbanne cedex, France

Comptes Rendus. Physique, Volume 11 (2010) no. 3-4, pp. 236-244.

Abstract
Résumé

Classical Nucleation and Growth Theories provide a compelling framework predicting the nucleation and growth of precipitates. When implemented in a class model, such an approach provides the time evolution of the Particle Size Distribution. It is shown in this article that a reversion treatment (instantaneous heating of the microstructure to a temperature high enough to induce some dissolution of the precipitates) can be used to calibrate all physical parameters of the model independently: (i) the solubility limit of alloying element is related to the equilibrium volume fraction; (ii) the interfacial energy is related to the minimum of volume fraction evolution; and (iii) the diffusion constant is related to the kinetics of the precipitate radii evolution.

La Théorie Classique de la Germination/Croissance est un puissant outil pour prédire des cinétiques de précipitation. Implémentée dans un modèle par classes de taille, cette approche permet de prédire l'évolution de la distribution de taille des précipités. Dans cet article, il est montré qu'un traitement de réversion (chauffage à une température qui entraine une dissolution partielle des précipités) peut être utilisé pour déterminer de façon indépendante tous les paramètres physiques du modèle : (i) la limite de solubilité est liée à la fraction volumique précipitée d'équilibre, (ii) l'énergie d'interface est liée au minimum de la fraction volumique précipitée, et (iii) le coefficient de diffusion est lié à la cinétique d'évolution du rayon moyen des précipités.

Published online: 2010-04-01

DOI: 10.1016/j.crhy.2010.07.005

Keywords: Precipitation, Classical Nucleation and Growth theories, Class model
Mot clés : Précipitation, Théorie Classique de la Germination/Croissance, Modèle par classes de taille

Author's affiliations:

Alexis Deschamps ¹; Michel Perez ²

¹ SIMAP, Grenoble INP, UMR CNRS 5266, Université Joseph-Fourier, 1130, rue de la Piscine, BP 75, 38402 St Martin d'Hérès cedex, France
² Université de Lyon, INSA Lyon, MATEIS, UMR CNRS 5510, 7, avenue Jean-Capelle, 69621 Villeurbanne cedex, France

@article{CRPHYS_2010__11_3-4_236_0,
     author = {Alexis Deschamps and Michel Perez},
     title = {Mesoscopic modelling of precipitation: {A} tool for extracting physical parameters of phase transformations in metallic alloys},
     journal = {Comptes Rendus. Physique},
     pages = {236--244},
     publisher = {Elsevier},
     volume = {11},
     number = {3-4},
     year = {2010},
     doi = {10.1016/j.crhy.2010.07.005},
     language = {en},
}

TY  - JOUR
AU  - Alexis Deschamps
AU  - Michel Perez
TI  - Mesoscopic modelling of precipitation: A tool for extracting physical parameters of phase transformations in metallic alloys
JO  - Comptes Rendus. Physique
PY  - 2010
SP  - 236
EP  - 244
VL  - 11
IS  - 3-4
PB  - Elsevier
DO  - 10.1016/j.crhy.2010.07.005
LA  - en
ID  - CRPHYS_2010__11_3-4_236_0
ER  -

%0 Journal Article
%A Alexis Deschamps
%A Michel Perez
%T Mesoscopic modelling of precipitation: A tool for extracting physical parameters of phase transformations in metallic alloys
%J Comptes Rendus. Physique
%D 2010
%P 236-244
%V 11
%N 3-4
%I Elsevier
%R 10.1016/j.crhy.2010.07.005
%G en
%F CRPHYS_2010__11_3-4_236_0

Alexis Deschamps; Michel Perez. Mesoscopic modelling of precipitation: A tool for extracting physical parameters of phase transformations in metallic alloys. Comptes Rendus. Physique, Volume 11 (2010) no. 3-4, pp. 236-244. doi : 10.1016/j.crhy.2010.07.005. https://comptes-rendus.academie-sciences.fr/physique/articles/10.1016/j.crhy.2010.07.005/

References
Cited by

[1] O.H. Bratland; O. Grong; H.R. Shercliff; O.R. Myhr; S. Tjotta Modeling of precipitation reactions in industrial processing, Acta Mater., Volume 45 (1997) no. 1, pp. 1-22

[2] J. Lendvai Precipitation and strengthening in aluminum alloys, Mater. Sci. Forum, Volume 217 (1996), pp. 43-56

[3] H. Zurob; C. Hutchinson; Y. Bréchet; G. Purdy Acta Mater., 50 (2002) no. 3075

[4] T. Gladman The Physical Metallurgy of Microalloyed Steels, The Institute of Materials, London, 2002

[5] M. Hillert Inhibition of grain-growth by 2nd-phase particles, Acta Metall., Volume 36 ( Dec. 1988 ) no. 12, pp. 3177-3181

[6] E. Clouet; L. Laé; T. Epicier; W. Lefebvre; M. Nastar; A. Deschamps Complex precipitation pathways in multi-component alloys, Nature Mater., Volume 5 (2006), pp. 482-488

[7] E. Clouet; M. Nastar; A. Barbu; C. Sigli; G. Martin Precipitation in Al–Zr–Sc alloys: A comparison between kinetic Monte Carlo, cluster dynamics and classical nucleation theory (J.M. Howe; D.E. Laughlin; J.K. Lee; D.J. Srolovitz; U. Dahmen, eds.), Solid–Solid Phase Transformations in Inorganic Materials, TMS, Warrendale, USA, 2005 (ISBN: 978-0-87339-608-0)

[8] R. Wagner; R. Kampmann Homogeneous second phase precipitation, Materials Science and Technology: A Comprehensive Treatment, vol. 5, John Wiley & Sons Inc, 1991, pp. 213-302

[9] R. Kampmann; T. Ebel; M. Haese; R. Wagner A combined cluster-dynamic and deterministic description of decomposition kinetics in binary alloys with a tendency for clustering, Phys. Status Solidi B, Volume 172 (1992) no. 1, pp. 295-308

[10] O.R. Myhr; O. Grong Modelling of non-isothermal transformations in alloys containing a particle distribution, Acta Mater., Volume 48 (2000), pp. 1605-1615

[11] J.D. Robson Modelling the overlap of nucleation, growth and coarsening during precipitation, Acta Mater., Volume 52 (2004), pp. 4669-4676

[12] M. Nicolas; A. Deschamps Characterisation and modelling of precipitate evolution in an Al–Zn–Mg alloy during non-isothermal heat treatments, Acta Mater. (2003), pp. 6077-6094

[13] M. Perez; M. Dumont; D. Acevedo Implementation of the classical nucleation theory for precipitation, Acta Mater., Volume 56 (2008), pp. 2119-2132

[14] P. Maugis; M. Gouné Kinetics of vanadium carbonitride precipitation in steel: A computer model, Acta Mater., Volume 53 (2005), pp. 3359-3367

[15] S. Esmaeili; D.J. Lloyd; W.J. Poole A yield strength model for the Al–Mg–Si–Cu alloy AA6111, Acta Mater., Volume 51 (2003), pp. 2243-2257

[16] M. Perez; C. Sidoroff; A. Vincent; C. Esnouf Microstructure evolution of martensitic 100Cr6 bearing steel during tempering, Acta Mater., Volume 57 (2009), pp. 3170-3181

[17] C. Zener Theory of growth of spherical precipitates from solid solution, J. Appl. Phys., Volume 20 (1949), pp. 950-953

[18] J.W. Gibbs, Green and Co., 1928 On the equilibrium of heterogeneous substances (1876), in: Collected Works

[19] J. Thomson Theoretical considerations on the effect of pressure in lowering the freezing point of water, Trans. Roy. Soc. Edinburgh, Volume 16 (1849), pp. 575-580

[20] J. Thomson On crystallization and liquefaction, as influenced by stresses tending to changes of form of crystals, Proc. Roy. Soc., Volume 11 (1862), pp. 473-481

[21] W. Thomson On the equilibrium of vapour at a curved surface of liquid, Philos. Mag., Volume 42 (1871), pp. 448-452

[22] M. Perez Gibbs–Thomson effect in phase transformations, Scripta Mater., Volume 52 (2005), pp. 709-712

[23] M. Perez; F. Perrard; V. Massardier; X. Kleber; A. Deschamps; H. De Monestrol; P. Pareige; G. Covarel Low temperature solubility of copper in iron: Experimental study using ThermoElectric Power, small angle X-ray scattering and tomographic atom probe, Philos. Mag., Volume 85 (2005) no. 20, pp. 2197-2210

[24] A. Deschamps; C. Genevois; M. Nicolas; F. Perrard; F. Bley Study of precipitation kinetics: Towards non-isothermal and coupled phenomena, in: J.D. Embury Honnorary Symposium, Hamilton, Canada, 2005, Philos. Mag., Volume 85 (2005), pp. 3091-3112

Cited by Sources:

Comments - Policy