Numerical Analysis of Diffusion-Controlled Internal Corrosion by the Cellular Automata Approach


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The cellular automata method offers a promising approach to describe diffusion and diffusion-controlled precipitation processes at high temperatures. During high temperature exposure, technical components like gas-turbine blades, furnaces, or exhaust systems, are operating in corrosive atmospheres. The resulting material-degradation processes are diffusion‐controlled, and corrosive species penetrate into the material leading to the formation of embrittling precipitates. Cellular automata (CA) represent distributed dynamical systems whose structure is particularly well suited to determine the temporal evolution of the system. In this study, it is shown that the model is able to consider diffusion, nucleation and growth aspects, interdiffusion between scales, and high diffusivity paths like grain boundaries. This has been demonstrated by applying CA to (i) nitrogen diffusion, (ii) internal intergranular oxidation of nickel-based alloy, and (iii) interdiffusion of a binary diffusion couple.



Edited by:

Prof. Eugen Rabkin, Amy Novick-Cohen, Leonid Klinger and Nachum Frage




U. Krupp et al., "Numerical Analysis of Diffusion-Controlled Internal Corrosion by the Cellular Automata Approach", Defect and Diffusion Forum, Vol. 383, pp. 51-58, 2018

Online since:

February 2018




* - Corresponding Author

[1] J. Crank. The Mathematics of Diffusion. Oxford University Press, Oxford, Großbritannien, (1979).

[2] L.S. Darken. Diffusion, Mobility and their Interrelation through Free Energy in BinaryMetallic Systems. Transactions of the Metallurgical Society of AIME, 175(1): 184–201, (1948).

[3] C. Wagner, Zeitschrift für Elektrochemie 63, 1959 (772).

[4] K. Bongartz, R. Schulten, W. J. Quadakkers, H. Nickel, A Finite Difference Model describing Carburization in High-Temperature Alloys, Corrosion 42 (1986), 390.

DOI: 10.5006/1.3584919

[5] H. G. Sockel, H. ‐J. Christ, Penetration of Foreign Elements Connected with Internal Precipitation: A Computer-Based Description and First Experimental Verification, Materials Science and Engineering 87 (1987), 119.

DOI: 10.1016/0025-5416(87)90368-5

[6] Y. Li, J. E. Morral, A Local Equilibrium Model for Internal Oxidation, Acta Materialia 50 (2002), 3683.

DOI: 10.1016/s1359-6454(02)00181-7

[7] G. Zimbitas, W. G. Sloof, Modeling Internal Oxidation of Binary Ni Alloys, Materials Science Forum 696 (2011), 82.

DOI: 10.4028/

[8] U. Krupp, V. B. Trindade, H. -J. Christ, U. Buschmann, W. Wiechert, Oxidation Mechanisms of Cr‐Containing Steels and Ni‐Base Alloys at High Temperatures Part II: Computer‐Based Simulation, Materials and Corrosion 57 (2006) 263.

DOI: 10.1002/maco.200503933

[9] Y. H. Wen, L. Q. Chen, J. A. Hawk, Phase-Field Modeling of Corrosion Kinetics under Dual-Oxidants, Modelling and Simulation in Materials Science and Engineering 20 (2012), 035013.

DOI: 10.1088/0965-0393/20/3/035013

[10] C. Shen, Q. Chen, Y.H. Wen, J.P. Simmons, und Y. Wang. Increasing Length Scale of Quantitative Phase Field Modeling of Concurrent Growth and Coarsening Processes. Scripta Materialia, 50(7): 1029–1034, (2004).

DOI: 10.1016/j.scriptamat.2003.12.027

[11] B. Chopard, M. Droz, Cellular Automata Modelling of Physical Systems, Cambridge University Press (1998).

[12] S. G. R. Brown, N. B. Bruce, A 3-Dimensional Cellular Automaton Model of Free, Dendritic Growth, Scripta Metallurgica et Materialia 32 (1995), 241.

DOI: 10.1016/s0956-716x(99)80044-2

[13] M.F. Zhu, C.P. Hong, A Three Dimensional Modified Cellular Automaton Model for the Prediction of Solidification Microstructures, ISIJ International 42 (2002), 52.

DOI: 10.2355/isijinternational.42.520

[14] J. Kroc: Application of Cellular Automata Simulations to Modelling of Dynamic Recrystallization, Computational Science ICCS 2339 (2002), 773.

DOI: 10.1007/3-540-46043-8_78

[15] S. Kundu, M. Dutta, S. Ganguly, S. Chandra, Prediction of Phase Transformation and Microstructure in Steel using Cellular Automaton Technique, Scripta Materialia 50 (2004), 891.

DOI: 10.1016/j.scriptamat.2003.12.007

[16] G. Guillemot, C.A. Gandin, H. Combeau, Modeling of Macrosegregation and Solidification Grain Structures with a Coupled Cellular Automaton-Finite Element Model, ISIJ International 46(6) (2006), 880.

DOI: 10.2355/isijinternational.46.880

[17] D. Raabe, Cellular Automata in Materials Science with Particular Reference to Recrystallization Simulation, Annual Review of Materials Research 32. 1 (2002), 53.

DOI: 10.1146/annurev.matsci.32.090601.152855

[18] L. Zhou, X. Wei, A Randomwalk-Cellular Automaton Model of Precipitation of Internal Oxides, Scripta Materialia 37 (1997), 1483.

DOI: 10.1016/s1359-6462(97)00300-x

[19] L. Zhou, X. Wei, A Randomwalk-Cellular Automaton Simulation of Internal Oxidation and its Transition to External Oxidation, Scripta Materialia 40 (1999), 365.

DOI: 10.1016/s1359-6462(98)00359-5

[20] K. Jahns, M. Landwehr, J. Wübbelmann, U. Krupp, Numerical Analysis of Internal Oxidation and Nitridation by the Cellular Automata Approach, Oxidation of Metals 79 (2013), 107.

DOI: 10.1007/s11085-012-9334-2

[21] K. Jahns, M. Landwehr, J. Wübbelmann, U. Krupp, Numerical Analysis of High Temperature Internal Corrosion Mechanisms by the Cellular Automata Approach, Materials and Corrosion 65(3) (2014), 305.

DOI: 10.1002/maco.201307179

[22] K. Jahns, K. Balinski, M. Landwehr, J. Wübbelmann, U. Krupp, Prediction of High Temperature Corrosion Phenomena by the Cellular Automata Approach, Materials and Corrosion 68(2) (2017), 125.

DOI: 10.1002/maco.201508777

[23] K. Jahns, K. Balinski, M. Landwehr, J. Wübbelmann, U. Krupp, Modeling of Intergranular Oxidation by the Cellular Automata Approach, Oxidation of Metals (2017), DOI: 10. 1007/s11085-017-9732-6.

DOI: 10.1007/s11085-017-9732-6

[24] D. di Caprio, J. Stafiej, G. Luciano, L. Arurault, 3D Cellular Automata Simulations of Intra and Intergranular Corrosion, Corrosion Science 112 (2016), 438.

DOI: 10.1016/j.corsci.2016.07.028

[25] U. Krupp, Innere Nitrierung von Nickelbasislegierungen, Fortschritt-Berichte VDI, Reihe 5, Nr. 529, (VDI-Verlag, Düsseldorf 1998).

[26] H. Mehrer. Diffusion in Solids: Fundamentals, Methods, Materials, Diffusion-Controlled Processes. Springer, Berlin, Deutschland, (2007).

[27] J. -W. Park und C.J. Altstetter, Metallurgical and Materials Transactions A 18, 43 (1987).

[28] R. C. Weast, Handbook of Chemistry and Physics 56th Edition, CRC Press, (1975).

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