2023-11-10
Complex Magnetic Permeability Evaluation of Steel Fibers Using Eddy Current NDE and Inverse Problem Methods
By
Progress In Electromagnetics Research Letters, Vol. 113, 81-90, 2023
Abstract
This paper presents a simple approach for evaluating the complex magnetic permeability of the steel fibers used in concrete according to frequency. The approach utilises the eddy current non-destructive evaluation method, where the electrical impedance is measured using a precision LCR meter and computed using a magneto-harmonic model solved in Py-FEMM software. Initially, the electrical conductivity of the steel fiber is measured using a two-contact DC method. Then, the inverse problem method is applied to identify the complex magnetic permeability. This is achieved by iteratively minimising the difference between the calculated and measured impedances using a simplex optimization algorithm. The proposed approach offers a non-contact, non-destructive, fast, and efficient procedure to evaluate the complex permeability. The obtained results provide valuable insights into evaluating the distribution of steel fibers in concrete.
Citation
Loukmane Gherdaoui, Samir Bensaid, Didier Trichet, Hamza Houassine, and Nacira Saoudi, "Complex Magnetic Permeability Evaluation of Steel Fibers Using Eddy Current NDE and Inverse Problem Methods," Progress In Electromagnetics Research Letters, Vol. 113, 81-90, 2023.
doi:10.2528/PIERL23090804
References

1. Altun, F., T. Haktanir, and K. Ari, "Effects of steel fiber addition on mechanical properties of concrete and RC beams," Construction and Building Materials, Vol. 21, No. 3, 654-661, 2007.
doi:10.1016/j.conbuildmat.2005.12.006        Google Scholar

2. Lee, J. H., "Influence of concrete strength combined with fiber content in the residual flexural strengths of fiber reinforced concrete," Composite Structures, Vol. 168, 216-225, 2017.
doi:10.1016/j.compstruct.2017.01.052        Google Scholar

3. Akkaya, Y., S. P. Shah, and B. Ankenman, "Effect of fiber dispersion on multiple cracking of cement composites," Journal of Engineering Mechanics, Vol. 127, No. 4, 311-316, 2001.
doi:10.1061/(ASCE)0733-9399(2001)127:4(311)        Google Scholar

4. Kang, S. T. and J. K. Kim, "The relation between fiber orientation and tensile behaviour in an ultra high performance fiber reinforced cementitious composites (UHPFRCC)," Journal of Engineering Mechanics, Vol. 127, No. 4, 311-316, 2001.        Google Scholar

5. Abrishambaf, A., J. A. Barros, and V. M. Cunha, "Relation between fibre distribution and postcracking behaviour in steel fibre reinforced self-compacting concrete panels," Cement and Concrete Research, Vol. 51, 57-66, 2013.
doi:10.1016/j.cemconres.2013.04.009        Google Scholar

6. Bordelon, A. C. and J. R. Roesler, "Spatial distribution of synthetic fibers in concrete with X-ray computed tomography," Cement and Concrete Composites, Vol. 53, 35-43, 2014.
doi:10.1016/j.cemconcomp.2014.04.007        Google Scholar

7. Liu, J., C. Li, J. Liu, et al. "Study on 3D spatial distribution of steel fibers in fiber reinforced cementitious composites through micro-CT technique," Construction and Building Materials, Vol. 48, 656-661, 2013.
doi:10.1016/j.conbuildmat.2013.07.052        Google Scholar

8. Fladr, J., P. Bily, and I. Broukalova, "Evaluation of steel fiber distribution in concrete by computeraided image analysis," Compos. Mater. Eng, Vol., Vol. 1, No. 1, 49-70, 2019.        Google Scholar

9. Lataste, J., M. Behloul, and D. Breysse, "Characterisation of fibres distribution in a steel fibre reinforced concrete with electrical resistivity measurements," NDT E International, Vol. 41, No. 8, 638-647, 2008.
doi:10.1016/j.ndteint.2008.03.008        Google Scholar

10. Faifer, M., R. Ottoboni, S. Toscani, et al. "Steel fiber reinforced concrete characterization based on a magnetic probe," 2010 IEEE Instrumentation and Measurement Technology Conference Proceedings, 157-162, 2010.
doi:10.1109/IMTC.2010.5488179        Google Scholar

11. Cavalaro, S. H. P., R. L´opez, J. M. Torrents, et al. "Improved assessment of fibre content and orientation with inductive method in SFRC," Materials and Structures, Vol. 48, 1859-1873, 2015.
doi:10.1617/s11527-014-0279-6        Google Scholar

12. Cavalaro, S. H. P., R. L´opez-Carre˜no, J. M. Torrents, et al. "Assessment of fibre content and 3D profile in cylindrical SFRC specimens," Materials and Structures, Vol. 49, 577-595, 2015.        Google Scholar

13. Torrents, J. M., A. Blanco, P. Pujadas, et al. "Inductive method for assessing the amount and orientation of steel fibers in concrete," Materials and Structures, Vol. 45, 1577-1592, 2012.
doi:10.1617/s11527-012-9858-6        Google Scholar

14. Martin, L. E., A. E. Fouda, R. K. Amineh et al. "New high-definition frequency tool for tubing and multiple casing corrosion detection," Abu Dhabi International Petroleum Exhibition and Conference, SPE, 2017.        Google Scholar

15. Xia, J., Z. Yuanzhou, B. Ji, et al. "An eddy current testing method based on magnetic induction intensity for detecting cracks in steel bridge decks," Journal of Performance of Constructed Facilities, Vol. 37, No. 3, 04023014, 2023.
doi:10.1061/JPCFEV.CFENG-4235        Google Scholar

16. Bowler, N., "Frequency-dependence of relative complex magnetic permeability in steel," AIP Conference Proceedings, Vol. 820, No. 1, 1269-1276, 2006.
doi:10.1063/1.2184670        Google Scholar

17. Tokpanov, Y., V. Lebedev, and W. Pellico, "Measurements of complex magnetic permeability of soft steel at high frequencies," Proceedings of IPAC-2012, 2012.        Google Scholar

18. Abeywickrama, K., T. Daszczynski, Y. Serdyuk, et al. "Determination of complex permeability of silicon steel for use in high-frequency modeling of power transformers," IEEE Transactions on Magnetics, Vol. 44, No. 4, 438-444, 2008.
doi:10.1109/TMAG.2007.914857        Google Scholar

19. Okumura, Y., K. Fujii, T. Nagaya, et al. "Simple permeability measurement of thin ferromagnetic sheets at low frequency using LCR meter," Electrical and Electronic Engineering, Vol. 8, No. 2, 53-58, 2018.        Google Scholar

20. Altair "FEKO overview," [Online] Available: http://www.feko.info/.

21. Chen, Y., X. Wang, H. Chen, et al. "Novel ultra-wide band (10 MHz-26 GHz) permeability measurements for magnetic films," IEEE Transactions on Magnetics, Vol. 54, No. 11, 1-4, 2018.        Google Scholar

22. Radoni´c, V., N. Blaˇz, and L. ˇZivanov, "Measurement of complex permeability using short coaxial line reflection method," Acta Physica Polonica A, Vol. 117, No. 5, 820-824, 2010.
doi:10.12693/APhysPolA.117.820        Google Scholar

23. Kacki, M., M. S. Rylko, J. G. Hayes, et al. "Measurement methods for high-frequency characterizations of permeability, permittivity, and core loss of Mn-Zn ferrite cores," IEEE Transactions on Power Electronics, Vol. 37, No. 12, 15152-15162, 2022.
doi:10.1109/TPEL.2022.3189671        Google Scholar

24. David Meeker (2021) PyFEMM (0.1.3) Available from: https://www.femm.info/wiki/pyFEMM.        Google Scholar

25. Nelder, J. A. and R. Mead, "A simplex method for function minimization," The Computer Journal, Vol. 7, No. 4, 308-313, 1965.
doi:10.1093/comjnl/7.4.308        Google Scholar

26. "FEMM (Version 4.2) [Computer software],", 2021.
doi:10.1093/comjnl/7.4.308        Google Scholar

27. Bensaid, S., "Global inductance computation of a multilayer circular air coil with a wire of rectangular cross section: Case of a uniform current distribution," Progress In Electromagnetics Research M, Vol. 102, 149-158, 2021.
doi:10.2528/PIERM21031704        Google Scholar

28. Bensaid, S., D. Trichet, and J. Fouladgar, "Electrical conductivity identification of composite materials using a 3-D anisotropic shell element model," IEEE Transactions on Magnetics, Vol. 45, No. 3, 1859-1862, 2009.
doi:10.1109/TMAG.2009.2012833        Google Scholar

29. Safer, O. A., S. Bensaid, D. Trichet, et al. "Transverse electrical resistivity evaluation of rod unidirectional carbon fiber-reinforced composite using eddy current method," IEEE Transactions on Magnetics, Vol. 54, No. 3, 1-4, 2018.
doi:10.1109/TMAG.2017.2751962        Google Scholar

30. Rose, J. H., E. Uzal, and J. C. Moulder, "Magnetic permeability and eddy-current measurements,” D. O. Thompson and D. E. Chimenti, (eds.)," Review of Progress in Quantitative Nondestructive Evaluation, Springer, Boston, MA, 1995.        Google Scholar