[Prédiction de la transition entre oxydation interne et externe des alliages à partir dʼun modèle de Wagner étendu]
Leblond [Oxid. Metals 75 (2011) 93–101] a récemment estimé les conditions régissant la transition entre oxydation interne et externe des alliages en utilisant une variante du modèle de Wagner [Z. Elektrochem. 63 (1959) 772–782] incorporant le rôle possible dʼobstacles à la diffusion joué par les oxydes, via une dépendance heuristique du coefficient de diffusion de lʼoxygène vis-à-vis de leur fraction volumique locale. Mais, du fait de la grossièreté de la formule adoptée, la prédiction de lʼoccurrence de lʼoxydation externe ne pouvait être que qualitative. On obtient ici une formule plus précise grâce à une analogie thermique et des calculs par éléments finis de la réduction de la conductivité générée par des obstacles non conducteurs plus ou moins aplatis. Le modèle de Wagner étendu incorporant cette formule conduit à une prédiction analytique de la fraction « critique » locale dʼoxydes correspondant à la transition entre oxydation interne et externe, dépendant du « facteur de forme » des oxydes. La valeur prédite est en accord acceptable avec celle mesurée par Rapp [Acta Metall. 9 (1961) 730–741] pour le système Ag–In, pour une valeur postulée raisonnable de ce facteur de forme.
Leblond [Oxid. Metals 75 (2011) 93–101] recently estimated the conditions governing the transition from internal to external oxidation of alloys using a variant of Wagnerʼs [Z. Elektrochem. 63 (1959) 772–782] model incorporating the possible role of oxides as diffusion barriers, through a heuristic dependence of the diffusion coefficient of oxygen upon their local volume fraction. But the crudeness of the formula adopted made the prediction of the onset of external oxidation only qualitative. A more accurate formula is derived here by using a thermal analogy and finite element computations of the reduction of the conductivity generated by nonconducting, more or less flat obstacles. The extended Wagner model incorporating this formula leads to a prediction of the “critical” local fraction of oxides corresponding to the transition from internal to external oxidation, depending on the “aspect ratio” of the oxides. The predicted value is in acceptable agreement with that measured by Rapp [Acta Metall. 9 (1961) 730–741] for the Ag–In system, for a reasonable postulated value of this aspect ratio.
Accepté le :
Publié le :
Mot clés : Modèle de Wagner étendu, Obstacles à la diffusion, Oxydation interne, Oxydation externe
@article{CRMECA_2013__341_3_314_0,
author = {Jean-Baptiste Leblond and Mo{\"\i}se Pignol and Didier Huin},
title = {Predicting the transition from internal to external oxidation of alloys using an extended {Wagner} model},
journal = {Comptes Rendus. M\'ecanique},
pages = {314--322},
publisher = {Elsevier},
volume = {341},
number = {3},
year = {2013},
doi = {10.1016/j.crme.2013.01.003},
language = {en},
}
TY - JOUR AU - Jean-Baptiste Leblond AU - Moïse Pignol AU - Didier Huin TI - Predicting the transition from internal to external oxidation of alloys using an extended Wagner model JO - Comptes Rendus. Mécanique PY - 2013 SP - 314 EP - 322 VL - 341 IS - 3 PB - Elsevier DO - 10.1016/j.crme.2013.01.003 LA - en ID - CRMECA_2013__341_3_314_0 ER -
%0 Journal Article %A Jean-Baptiste Leblond %A Moïse Pignol %A Didier Huin %T Predicting the transition from internal to external oxidation of alloys using an extended Wagner model %J Comptes Rendus. Mécanique %D 2013 %P 314-322 %V 341 %N 3 %I Elsevier %R 10.1016/j.crme.2013.01.003 %G en %F CRMECA_2013__341_3_314_0
Jean-Baptiste Leblond; Moïse Pignol; Didier Huin. Predicting the transition from internal to external oxidation of alloys using an extended Wagner model. Comptes Rendus. Mécanique, Volume 341 (2013) no. 3, pp. 314-322. doi : 10.1016/j.crme.2013.01.003. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2013.01.003/
[1] Reaktionstypen bei der Oxydation von Legierungen, Z. Elektrochem., Volume 63 (1959), pp. 772-782 (in German)
[2] On the theory of internal oxidation and sulphation of alloys, Can. Metall. Quart., Volume 8 (1969), pp. 35-38
[3] Limiting cases of subscale formation, Acta Metall., Volume 26 (1978), pp. 1791-1794
[4] Precipitate distribution in subscales, Scr. Metall., Volume 13 (1979), pp. 7-10
[5] The formation of solid solution oxides during internal oxidation, Oxid. Metals, Volume 16 (1981), pp. 159-174
[6] Carburization of high-temperature materials. I. Mathematical model description of the penetration and simultaneous precipitation of a compound of the diffusing element, Werkst. Korros., Volume 37 (1986), pp. 385-390
[7] Internal oxidation, Mater. Sci. Technol., Volume 4 (1988), pp. 1072-1078
[8] Oxidation of multicomponent two-phase alloys, Oxid. Metals, Volume 44 (1995), pp. 211-237
[9] The internal oxidation of two-phase binary alloys under low oxidant pressure, Oxid. Metals, Volume 45 (1996), pp. 51-76
[10] The internal oxidation of two-phase binary alloys beneath an external scale of the less-stable oxide, Oxid. Metals, Volume 47 (1997), pp. 355-380
[11] The effect of supersaturation on the internal oxidation of binary alloys, Oxid. Metals, Volume 49 (1998), pp. 237-260
[12] Modelling of internal oxidation of several elements (S.B. Newcomb; J.A. Little, eds.), Microscopy of Oxidation – 3, The Institute of Metals, London, 1997, pp. 573-586
[13] The formation of two layers in the internal oxidation of binary alloys by two oxidants in the absence of external scales, Oxid. Metals, Volume 51 (1999), pp. 129-158
[14] An approximate analysis of the external oxidation of ternary alloys forming insoluble oxides. I: High oxidant pressures, Oxid. Metals, Volume 56 (2001), pp. 517-536
[15] A note on a nonlinear variant of Wagnerʼs model of internal oxidation, Oxid. Metals, Volume 75 (2011), pp. 93-101
[16] Ternary diffusion and its relationship to oxidation and sulfidation (D.L. Douglass, ed.), Oxidation of Metals and Alloys, American Society of Metals, Metals Park, 1971, pp. 101-114
[17] The transition from internal to external oxidation and the formation of interruption bands in silver–indium alloys, Acta Metall., Volume 9 (1961), pp. 730-741
[18] Numerical simulation of internal oxidation of steels during annealing treatments, Oxid. Metals, Volume 64 (2005), pp. 131-167
[19] An implicit finite element algorithm for the simulation of diffusion with phase changes in solids, Int. J. Numer. Methods Eng., Volume 78 (2009), pp. 1492-1512
[20] Numerical implementation and application of an extended model for diffusion and precipitation of chemical elements in metallic matrices, Oxid. Metals, Volume 73 (2010), pp. 565-589
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