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Modern Mathematical Methods and High Performance Computing in Science and Technology pp 301–309Cite as

Mechanochemical Corrosion: Modeling and Analytical Benchmarks for Initial Boundary Value Problems with Unknown Boundaries

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Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 171))

Abstract

In this paper various corrosion models are considered. Difficulties of the modeling of stress corrosion of constructional elements and the need for developing closed-form solutions are highlighted. A new analytical solution is presented for the plane problem of the mechanochemical corrosion of an elastic plate with an elliptical hole under uniform remote tension. The rate of corrosion is supposed to be linear with the maximum principal stress at a corresponding point on the hole surface. The solution obtained can serve for the study of the mechanochemical effect on the corrosion damage propagation. It is proved that the stress concentration factor at a noncircular hole can either increase or decrease, or stay invariant during the corrosion process, depending on the relationship between the corrosion kinetics constants and applied stress.

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Acknowledgments

I am very grateful to the organizing committee of the International conference on “Modern Mathematical Methods and High Performance Computing in Science & Technology (M3HPCST-2015)” for the invitation and support for my participation in this conference.

I would like to thank S.M. Khryashchev (specialist in differential calculus [12, 13]) for his helpful advises. This work is partially supported by the Russian Foundation for Basic Research (project No. 16-08-00890).

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Authors and Affiliations

  1. St. Petersburg State University, 7/9 Universitetskaya Nab., 199034, St. Petersburg, Russia

    Yulia Pronina

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  1. Yulia Pronina
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Correspondence to Yulia Pronina .

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Editors and Affiliations

  1. Department of Applied Mathematics, Raj Kumar Goel Institute of Technology, Ghaziabad, Uttar Pradesh, India

    Vinai K. Singh

  2. Department of Mathematics and Statistics, University of Victoria, Victoria, British Columbia, Canada

    H.M. Srivastava

  3. Dipartimento di Matematica, University of Turin, Torino, Italy

    Ezio Venturino

  4. High Performance Computing Center (HLRS), University of Stuttgart, Stuttgart, Baden-Württemberg, Germany

    Michael Resch

  5. Department of Mathematics, Netaji Subhas Institute of Technology, New Delhi, India

    Vijay Gupta

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Pronina, Y. (2016). Mechanochemical Corrosion: Modeling and Analytical Benchmarks for Initial Boundary Value Problems with Unknown Boundaries. In: Singh, V., Srivastava, H., Venturino, E., Resch, M., Gupta, V. (eds) Modern Mathematical Methods and High Performance Computing in Science and Technology. Springer Proceedings in Mathematics & Statistics, vol 171. Springer, Singapore. https://doi.org/10.1007/978-981-10-1454-3_25

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