Finite Element Simulation of Diffusion and Precipitation with Application to Internal Oxidation of Ni-Xwt%Cr Alloys at 950°C

Abstract:

For the simulation of internal oxidation phenomena, different numerical approaches are proposed in the literature based on 1D finite differences or on explicit time integration schemes which need small time-steps leading to very long computation times. The aim of this paper is to detail a multi-dimentional finite element approach which is coupled with an efficient implicit time integration algorithm. The thermodynamic activities and the total mass fractions are both used as principal nodal variables. The use of finite elements rather than finite differences greatly facilitates the meshing of 2D and 3D bodies. Its implicit time-integration allows using much larger time-steps without any degradation of the results. An application is proposed for the modeling of internal oxidation of chromia for Ni-Xwt%Cr alloys at 950°C by considering the barrier effect of precipitates.

• Periodical: Materials Science Forum (Volumes 783-786)
• Pages: 126-135
• DOI: https://doi.org/10.4028/www.scientific.net/MSF.783-786.126
• Online since: May 2014
• Authors: Eric Feulvarch*
• Keywords: Diffusion, Finite Element, Internal Oxidation, Nickel-Based Alloys, Oxygen Diffusion Coefficient, Precipitation, Simulation

References

[1] Nicolas A., Etude de l´évolution physico-chimique du substrat lors de l'oxydation à haute température des alliages modèle Ni−Cr à faible teneur en chrome et de l'alliage modèle Ni-16Cr−9Fe, PhD thesis, Ecole des Mines de Saint-Etienne, (2012).

DOI: 10.1016/s0151-9107(03)00102-8

[2] Flauder P., Huin D., Leblond J.B., Numerical simulation of internal oxidation of steels during annealing treatments, Oxidation of Metals, 64, 131167, (2005).

DOI: 10.1007/s11085-005-5718-x

[3] Fortunier R., Leblond J.B. and Bergheau J.M., Computer simulation of thermochemical treatments: modelling diffusion and precipitation in metals, J. Shanghai Jiaotong Univ., 5, 303-309, (2000).

[4] Feulvarch E., Bergheau J.M., Leblond J.B., An implicit finite element algorithm for the simulation of diffusion with phase changes in solids, Int. J. Numer. Meth. Engng., 78, 1492-1512, (2009).

DOI: 10.1002/nme.2537

[5] Leblond J.B., Mathematical results for a model of diffusion and precipitation of chemical elements in solid matrices, Nonlinear Anal. B: Real World Applic., 6, 297-322, (2005).

DOI: 10.1016/j.nonrwa.2004.08.010

[6] Bergheau J.M. , Fortunier R., Finite Element Simulation of Heat Transfer, ISTE-Wiley, ISBN 978-1-84821-053-0, (2008).

[7] Feulvarch E., Finite element modeling of interdiffusion phenomena in solid metals, C. R. Mecanique, 340, 695-701, (2012).

DOI: 10.1016/j.crme.2012.10.040

[8] Feulvarch E., Roux J.C., Bergheau J.M., Theoretical Framework of a variational formulation for nonlinear heat transfer with phase changes, Mathematical Problems in Engineering, Vol. 2013, Article ID 257104, 6 pages.

DOI: 10.1155/2013/257104

[9] Knacke O., Kubashewski O., Hesselmann K., Thermochemical Properties of Inorganic Substances, Ed. Heidelberg New York: Springer-Verlag, (1991).

DOI: 10.1007/bf02561491

[10] Wagner C., Reaktionstypen bei der Oxydation von Legierungen. Zeitschrift fur Elektrochemie, 63, 772-782, (1959).

DOI: 10.1002/bbpc.19590630713

[11] Leblond J.B., Pignol M., Huin D., Predicting the transition from internal to external oxidation of alloys using an extended Wagner model, Compte Rendus Mecanique, vol. 341, pp.314-322, (2013).

DOI: 10.1016/j.crme.2013.01.003

[12] Nicolas A., Barnier V., Aublant E., Wolski K., Auger electron spectroscopy analysis of chromium depletion in a model Ni-16Cr-9Fe alloy oxidized at 950oC, Scripta Materialia, Vol. 65, pp.803-806, (2011).

DOI: 10.1016/j.scriptamat.2011.07.036

[13] Goto S., Nomaki K., Koda S., Internal Oxidation of Nickel Alloys Containing a Small Amount of Chromium, Journal of the Japan Institute of Metals, vol. 31, pp.600-606, (1967).

DOI: 10.2320/jinstmet1952.31.4_600

[14] Park J.W., Altstetter C.J., The Diffusion and Solubility of Oxygen in Solid Nickel, Metallurgical Transactions, vol. 18A, pp.43-50, (1987).

DOI: 10.1007/bf02646220

[15] Alcock C.B., Brown P.B., Physicochemical Factors in the Dissolution of Thoria in Solid Nickel, Metal Science, vol. 3, 1, pp.116-120, (1969).

DOI: 10.1179/msc.1969.3.1.116

[16] Zholobov S.P., Malev M.D., Diffusion of Oxygen in a Metal in Electron Bombardment of the Surface, Soviet Physics Technical Physics, vol. 16, p.488, (1971).

[17] Kerr R.A., PhD Thesis of the Ohio State of Columbus University, (1972).

[18] Tsai S. -C., Relation entre l'autodiffusion et le mécanisme de croissance des couches d'oxyde de chrome - Effet de l'yttrium. PhD Thesis of the university of Paris-Sud (in french), (1996).

[19] Kirkaldy J. S., in Oxidation of Metals and Alloys, ed D. L. Douglass (American Society of Metals, Metals Park), p.101, (1971).

[20] Nicolas A., Aublant E., Feulvarch E., Wolski K., The transition from internal to external oxidation of Ni − Xwt. %Cr alloys at 950oC, Defect and Diffusion Forum Vols. 323-325, pp.295-300, (2012).

DOI: 10.4028/www.scientific.net/ddf.323-325.295

[21] ESI Group, Users Manual, (2013).

[22] Leblond J.B., A note on a nonlinear version of Wagner's classical model of internal oxidation, Oxidation of Metals, 75, 93-101, (2011).

DOI: 10.1007/s11085-010-9222-6