10.14489/td.2026.08.pp.061-070

2026, 08 August

DOI: 10.14489/td.2026.08.pp.061-070

Sokolov R. F., Muratov K. R., Probotyuk V. V., Shuldikova N. C.
NUMERICAL MODELING OF THE INFLUENCE OF DEFECT DEPTH AND MAGNETIC PERMEABILITY OF THE MATERIAL ON THE DISTRIBUTION OF MAGNETIC FIELD COMPONENTS ON THE SURFACE OF THE INSPECTION OBJECT
(pp. 61-70)

Abstract. The method of magnetic flux scattering (MFL) is widely used for diagnostics of ferromagnetic objects, but its indicative character and nonlinear dependence of the magnetic permeability of the material on the field strength complicate data interpretation. In this paper we propose a method of taking into account the influence of the magnetic permeability of the object on the magnitude of the magnetic scattering field appearing above the defect. The results presented in the paper are obtained by numerical modelling using the finite element method in the Elcut software environment. The studies demonstrate the possibility of using corrective algorithms to determine the depth of defects on the basis of a priori information about the magnetic permeability of the controlled material. The simulation results demonstrate that accounting for the nonlinear dependence μ(H) leads to a significant reduction in the error of determining magnetic induction compared to the linear model (μ = const). The effect is most pronounced for materials with low magnetic permeability: at μok = 25, the maximum error in determining Bτ at the metal-defect boundary reaches 230 %, whereas for μok = 200, it does not exceed 3 %. For materials with μok > 100, the proposed method reduces the error in estimating defect depth by approximately 7 %. The effect is quantitative in nature and requires experimental verification and an expansion of the parameter range to confirm its applicability to real test objects.

Keywords: modelling, finite element method, defect, magnetic permeability, magnetic induction, magnetic flux dissipation method.

+ - About the Authors Click to collapse

R. F. Sokolov (Tyumen Industrial University, Tyumen, Russia, Argumentum-Stroy LLC, Tyumen, Russia) E-mail: Данный адрес e-mail защищен от спам-ботов, Вам необходимо включить Javascript для его просмотра.
K. R. Muratov, V. V. Probotyuk, N. C. Shuldikova (Tyumen Industrial University, Tyumen, Russia) E-mail: Данный адрес e-mail защищен от спам-ботов, Вам необходимо включить Javascript для его просмотра. , Данный адрес e-mail защищен от спам-ботов, Вам необходимо включить Javascript для его просмотра. , Данный адрес e-mail защищен от спам-ботов, Вам необходимо включить Javascript для его просмотра.

+ - References Click to collapse

1. Bolshakova, V. V., Kukin, N. A., & Dymkin, G. Ya. (2014). On the possibility of using magnetic non destructive testing methods for assessing the stress strain state of pipelines. Izvestiya Peterburgskogo universiteta putei soobshcheniya, (38), 92–98. [in Russian language].
2. Slesarev, D. A., & Abakumov, A. A. (2013). Processing and presentation of information in the MFL method of non destructive testing. Defektoskopiya, (9), 3–9. [in Russian language].
3. Kanaikin, V. A. (2009). In line magnetic flaw detection of main pipelines (A. F. Matvienko, Ed.). UrO RAN. [in Russian language].
4. Krotov, L. N. (2004). Reconstruction of the interface between media by the spatial distribution of the magnetic leakage field. II. Statement and method for solving the inverse geometric problem of magnetostatics. Defektoskopiya, (6), 36–44. [in Russian language].
5. Gobov, Yu. L., Nikitin, A. V., & Popov, S. E. (2018). Solution of the inverse geometric problem of magnetostatics for corrosion defects taking into account the nonlinear properties of ferromagnets. Defektoskopiya, (12), 30–34. [in Russian language].
6. Nikitin, A. V., Mikhaylov, A. V., Gobov, Yu. L., & Popov, S. E. (2021). Determination of the surface of defect location and restoration of its geometric parameters by the MFL method with one sided access to the ferromagnetic plate. Diagnostics, Resource and Mechanics of Materials and Structures, 6, 45–53.
7. Pipeline Operators. (2016). Specifications and requirements for in line inspection of pipelines. https://pipelineoperators.org/
8. Nikitin, A. V., Mikhaylov, A. V., Mikhaylov, L. V., et al. (2023). Determination of the boundaries of applicability of the method for solving the inverse geometric problem of magnetostatics by constructing magnetic lines in the defect zone. In Fizicheskie metody nerazrushayushchego kontrolya (Yanusovskie chteniya): Tezisy dokladov XXXIV Ural'skoi konferentsii s mezhdunarodnym uchastiem (pp. 38–39). Ekaterinburg. [in Russian language].
9. Shi, Y., Zhang, C., Li, R., et al. (2015). Theory and application of magnetic flux leakage pipeline detection. Sensors (Basel), 15(12), 31036–31055.
10. Dyakin, V. V., Kudryashova, O. V., & Raevsky, V. Ya. (2018). Scattering field of a plate with a surface defect in a uniform external field. Defektoskopiya, (12), 23–31. [in Russian language].
11. Gobov, Yu. L., Nikitin, A. V., & Popov, S. E. (2018). Solution of the inverse geometric problem of magnetostatics for corrosion defects. Defektoskopiya, (10), 51–57. [in Russian language].
12. Nikitin, A. V., Mikhaylov, A. V., Petrov, A. S., & Popov, S. E. (2021). Method for practical reconstruction of the shape parameters of surface two dimensional defects taking into account the nonlinear properties of ferromagnets. Defektoskopiya, (12), 46–55. [in Russian language].
13. Nikitin, A. V., Gobov, Yu. L., Mikhaylov, A. V., & Mikhaylov, L. V. (2022). Method for solving the inverse geometric problem of magnetostatics for surface defects of a magnetically soft ferromagnet. Defektoskopiya, (12), 24–34. [in Russian language]. https://doi.org/10.31857/S013030822212003X
14. Nikitin, A. V., Mikhaylov, A. V., Mikhaylov, L. V., et al. (2022). Verification of the method for reconstructing the shape of defects in magnetically soft ferromagnets using MFL data. Defektoskopiya, (11), 43–49. [in Russian language]. https://doi.org/10.31857/S0130308222110057
15. Potapov, A. I., Syasko, V. A., Pudovkin, O. P., & Sharanova, D. A. (2016). Analysis of the measurement error of residual thickness of bottoms of cylindrical vertical tanks using MFL technology with the finite element method. Kontrol'. Diagnostika, (11), 10–15. [in Russian language].
16. Markov, A. A., Antipov, A. G., & Karelin, M. V. (2018). Assessment of the reliability of automatic recognition of signals from structural elements of the railway track by the magnetodynamic method. Kontrol'. Diagnostika, (3), 16–27. [in Russian language].
17. Nikitin, A. V., Mikhaylov, L. V., Mikhaylov, A. V., et al. (2024). Reconstruction of the defect shape of a ferromagnetic plate by solving the inverse problem of magnetostatics and a series of direct problems. Defektoskopiya, (9), 67–72. [in Russian language].
18. Dyakin, V. V., Kudryashova, O. V., & Raevsky, V. Ya. (2023). On the solution of a magnetostatics problem for a pipe with a defect on the inner surface. Defektoskopiya, (2), 35–46. [in Russian language].
19. Zatsepin, N. N., & Shcherbinin, V. E. (1966). On the calculation of the magnetostatic field of surface defects. Part 1. Topography of the fields of defect models. Defektoskopiya, (5), 50–59. [in Russian language].
20. Neradovsky, D. F., Probotyuk, V. V., & Zainutdinova, Z. R. (2017). Assessment of uniaxial stresses of a ferromagnet in the Takagi model by the method of higher harmonics of magnetization. Estestvennye i tekhnicheskie nauki, (5), 112–125. [in Russian language].
21. Reutov, Yu. Ya., Gobov, Yu. L., & Loskutov, V. E. (2002). On the possibilities of using the ELCUT program in flaw detection calculations. Defektoskopiya, (6), 34–40. [in Russian language].

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