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Modeling microbiologically influenced corrosion of N-80 carbon steel by fuzzy calculus


To investigate microbiologically influenced corrosion (MIC) risk using fuzzy Iogics, weight loss study of N-80 steel was carried out under three circumstances: (1) abiotic, (2) completely biotic (no biocide), and (3) biotic with almost enough biocide (underlined are fuzzy expressions). The microorganism employed was sulphate-reducing bacteria (SRB). Also, effective concentration of a biocide to kill the bacteria was investigated and recorded. Using fuzzy logics and calculus, it was shown that (fuzzy) probability of risk of MIC in the biotic system without biocide was 60 pct, whereas with almost enough biocide, the risk was 50 pct. Different from being absolute risk values, these risk values showed that fuzzy logics methods had the capability of showing how vulnerable a system could be to MIC.

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Operator minimum, implying that the method uses minimum membership functions from the given fuzz sets.


Operator maximum-minimum, showing that from minimum values of membership functions, maximum values will be selected.

U 1, V 1, and U 2 :

The universal sets that contain variables such as biocide concentration, β, risk of MIC, r, and corrosion rate, C, respectively.

A 1, A 2, B 1, A*1, and A*2 :

Fuzzy sets containing fuzzy values or membership functions for each element of the universal sets.

P :

The fuzzy rule that explains relationships between certain values in a fuzzy manner.

P 1 and P 2 :

Fuzzy rules defined for certain memberships such as biocide concentration or corrosion rate to relate them to risk of MIC.

P* 1 and P* 2 :

Fuzzy observations addressing the member-ships in a fuzzy manner.


  1. M. Setareh and R. Javaherdashti: Werkst. Korr./Mater. Corr., 2003, vol. 54 (4).

  2. Microbially Influenced Corrosion of Materials, E. Heitz, H.-C. Flemming, and W. Sand. eds., Springer-Verlag, Berlin, 1996, ch. 1.

  3. D. Walsh, D. Pope, M. Danford, and T. Huff: J. Mater. (JOM), 1993, vol. 45 (9).

  4. R. Javaherdashti: Anti-Corr. Methods Mater., 1999, vol. 46 (3).

  5. D.H. Pope, T.P. Zintel, H. Aldrich, and D. Duquette: Mater. Performance (MP), 1990, vol. 29 (12).

  6. G. Kobrin: A Practical Manual in Microbiologically-Influenced Corrosion, NACE, Houston, TX, 1993.

    Google Scholar 

  7. R. Javaherdashti: Proc. 7th Middle East Corrosion Conf., NACE International, Bahrain, 1996, vol. 2.

    Google Scholar 

  8. “Microbiologically-influenced Corrosion Testing” ASTM STP 1232, J.R. Kearns and B.J. Little, eds., ASTM, Philadelphia, PA, 1994.

    Google Scholar 

  9. “Microbiologically-influenced Corrosion Testing,” ASTM STP 1232, J.R. Kearns and B.J. Little, eds., ASTM, Philadelphia, PA, 1994, ch. 6.

    Google Scholar 

  10. R. Javaherdashti: Proc. 2nd Int. Conf. Appl. Math., Iran University of Science and Technology, Tehran, Iran, Oct. 2000.

  11. R. Javaherdashti: Anti-Corr. Methods Mater., 2000, vol. 47 (3).

  12. R. Javaherdashti: “Fuzzy Algorithm for Defining Risk of Microbiologically Influenced Corrosion by Sulfate-Reducing Bacteria in a Welded, Cathodically Protected Pipe: A Basic Approach,” 2004, unpublished research.

  13. L.A. Zadeh, K.-S. Fu, K. Tanaka, and M. Shimura: Fuzzy Sets and Their Applications to Cognitive and Decision Process, Academic Press Inc., New York, NY, 1975.

    Google Scholar 

  14. H.J. Zimmerman: Fuzzy Set Theory and Its Applications, 6th printing, Kluwer Academic Press, Dordrecht, 1993.

    Google Scholar 

  15. R. Javaherdashti, Filiz Sarioglu, and Nilufer Aksoz: Int. J. Pressure Vessel Piping, 1997, vol. 73.

  16. J.F.D. Stott, B.S. Skerry, and R.A. King: ASTM STP 970, P.E. Francis and T.S. Lee, eds., ASTM, Philadelphia, PA, 1988, pp. 98–111.

    Google Scholar 

  17. W. Lee and W.G. Characklis: Corrosion, 1993, vol. 49 (3).

  18. J.C. Daniko and C.D. Lundin: Proc. Int. Conf. on Microbiologically Influenced Corrosion, New Orleans, LA, May 8–10, 1995, NACE International, Houston, TX, 1995, pp. 14/1–14/12.

    Google Scholar 

  19. “Standard Recommended Practice for Laboratory Immersion Corrosion Testing of Metals,” ASTM G31-72, 11.2.1, ASTM, Philadelphia, PA, 1989.

  20. “Standard Recommended Practice for Preparing, Cleaning and Evaluating Corrosion Test Specimens,” ASTM 72 5.7.2 G1-72, 11.2.1, ASTM, Philadelphia, PA, 1989.

  21. G.G. Geessey: in A Practical Manual on Microbiologically-Influenced Corrosion, G. Kobrin, ed., NACE, Houston, TX, 1993.

    Google Scholar 

  22. S.C. Dexter and J.P. LaFontain: Corrosion, 1998, vol. 54 (11).

  23. Metals Handbook, vol. 13, Corrosion, 9th ed., ASM, Metals Park, OH, 1987, pp. 41–43, 114–20, and 1031–32.

  24. H.A. Videla: Manual of Biocorrosion, CRC Press, Inc., Boca Raton, FL, USA, 1996, pp. 121–35.

    Google Scholar 

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Javaherdashti, R. Modeling microbiologically influenced corrosion of N-80 carbon steel by fuzzy calculus. Metall Mater Trans A 35, 2051–2056 (2004).

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