volume | PIER Journals

Abstract

This paper deals with an innovative implementation of a semi-analytical modeling method, called the Distributed Points Source Method (DPSM), in the case of an eddy current problem. The DPSM has already shown great potentialities for the versatile and computationally efficient modeling of complex electrostatic, electromagnetic or ultrasonic problems. In this paper, we report a new implementation of the DPSM, called differential DPSM, which shows interesting prospects for the modeling of complex eddy current problems such as met in the non-destructive imaging of metallic parts. In this paper, the used eddy current imaging device is firstly presented. It is composed of an eddy current (EC) inducer and a magneto optical set-up used to translate the magnetic field distribution appearing at the surface of the imaged part, into a recordable optical image. In this study, the device is implemented for the time-harmonics (900 Hz) imaging of a two-layer aluminum based assembly, featuring surface-breaking and buried defects. Then, the basics of the time-harmonics DPSM modeling are recalled, and the differential approach is presented. It is implemented for the modeling of the interactions of the eddy current imaging device with the considered flawed assembly in the same operating conditions as the experimental implementation. The comparison between experimental and computed data obtained for millimetric surface and buried defects is presented in the form of complex magnetic cartographies and Lissajous plots. The obtained results show good agreement and open the way to the modeling of complex EC problems. Furthermore, the low computational complexity of the differential DPSM modelings makes it promising to consider for the solving of EC inverse problems.

1. Udpa, S. and P. Moore, Nondestructive Testing Handbook, 3rd Ed., Vol. 5, Electromagnetic Testing, American Nondestructive Testing Society, 2004.

2. Cacciola, M., F. C. Morabito, D. Polimeni, and M. Versaci, "Fuzzy characterization of flawed metallic plates with eddy current tests," Progress In Electromagnetics Research, Vol. 72, 241-252, 2007.
doi:10.2528/PIER07031301 Google Scholar

3. Libby, H. L., Introduction to Electromagnetic Nondestructive Test Methods, Robert Kriegger Publisher Company, 1979.

4. Yusa, N., H. Huang, and K. Miya, "Numerical evaluation of the ill-posedness of eddy current problems to size real cracks," NDT and E Int., No. 40, 185-191, 2007.
doi:10.1016/j.ndteint.2006.10.012 Google Scholar

5. Premel, D. and A. Baussard, "Eddy current evaluation of 3D flaws in flat conductive materials using a Bayesian approach," Inv. Problems, 1873-1889, 2002.
doi:10.1088/0266-5611/18/6/326 Google Scholar

6. Ida, N., Numerical Modeling for Electromagnetic Non Destructive Evaluation, Chapman & Hall, 1995.

7. Dodd, C. V. and W. E. Deeds, "Analytical solutions to eddy-current probe-coil problems," J. Appl. Phys., Vol. 39, 2829, 1968.
doi:10.1063/1.1656680 Google Scholar

8. Uzal, E., J. C. Moulder, S. Mitra, and J. H. Rose, "Impedance of coil over layered metals with continuously variable conductivity and permeability, theory and experiment, probe-coil problems," J. Appl. Phys., No. 74, 2076, 1970. Google Scholar

9. Mukerji, S. K., M. George, M. B. Ramamurthy, and K. Asaduzzaman, "Eddy currents in laminated rectangular cores," Progress In Electromagnetics Research, Vol. 83, 435-445, 2008.
doi:10.2528/PIER08062101 Google Scholar

10. Burke, S. K., "Impedance of a horizontal coil above a conducting half space," Journal of Physics D: Applied Physics, Vol. 19, 1159-1173, 1986.
doi:10.1088/0022-3727/19/7/006 Google Scholar

11. Le Bihan, Y., "Study on the transformer equivalent circuit of eddy current nondestructive evaluation," NDT and E Int., Vol. 36, No. 5, 297-302, Jul. 1 2003.
doi:10.1016/S0963-8695(03)00003-3 Google Scholar

12. Le Diraison, Y., Imagerie a courants de Foucault pour l’evaluation non-destructive de structures rivetees aeronautiques, Ph.D. Thesis, ´Ecole normale superieure de Cachan-ENS Cachan, 2008.

13. Le Diraison, Y., P.-Y. Joubert, and J. Pinassaud, "3D finite element modeling of an eddy current imager," 7th International Symposium on Electric And Magnetic Fields, 99-100, 2006. Google Scholar

14. Bowler, J. R., "Eddy current calculations using half-space Green’s functions," J. Appl. Phys., Vol. 61, 833-839, 1987.
doi:10.1063/1.338131 Google Scholar

15. Dodd, C. V. and W. E. Deed, "Integral solutions to some eddy current problems," International Journal of Non Destructive Testing, Vol. 1, 29-90, 1969. Google Scholar

16. Albanese, R., G. Rubinacci, and F. Villone, "An integral computation model for crack simulation and detection via eddy currents," J. Comput. Phys., Vol. 152, 736-755, 1999.
doi:10.1006/jcph.1999.6261 Google Scholar

17. Rubinacci, G., A. Tamburrino, S. Ventre, F. Villone, L. Udpa, L. Xuan, and Z. Zeng, "Numerical simulation of magneto-optic eddy current imaging," Electromagnetic Nondestructive Evaluation (VII), 180-188, 2006. Google Scholar

18. Premel, D. and P. Baussard, "Eddy current evaluation of 3D flaws in flat conductive materials using a Bayesian approach," Inv. Problems, 1873-1889, 2002.
doi:10.1088/0266-5611/18/6/326 Google Scholar

19. Rubinacci, G., A. Tamburrino, S. Ventre, P.-Y. Joubert, and J. Pinassaud, "Numerical modeling of phase sensitive eddy current imaging system," Studies in Applied Electromagnetics and Mechanics, Electromagnetic Non-destructive Evaluation (X), Vol. 28, 28-33, 2007. Google Scholar

20. Paillard, S., G. Pichenot, Y. Choua, Y. Le Bihan, M. Lambert, H. Voillaume, and N. Dominguez, "Modelling of flawed riveted structures for EC inspection in aeronautics," Studies in Applied Electromagnetics and Mechanics, Electromagnetic Nondestrucitve Evaluation (XI), Vol. 31, 217-224, IOS Press, 2008. Google Scholar

21. Placko, D., T. Kundu, N. Liebaux, and A. Cruau, Procede universel de modelisation des interactions entre au moins une onde et au moins un objet, la surface de chaque objet definissant une interface entre au moins deux milieux, French patent No. FR2895544B1, Dec. 23, 2005; Patent Application Canada No. CA2634903A1, Dec. 20, 2006; Patent Application Japon No. JP2008546450A1, Dec. 20, 2006; Patent Application USA No. US2010-0010781A1, Dec. 20, 2006.

22. Placko, D. and T. Kundu, DPSM for Modeling Engineering Problems, John Wiley & Sons, Inc., 2007.
doi:10.1002/9780470142400

23. Bore, T., D. Placko, F. Taillade, and M. Himbert, "Capacitive sensor for measuring the filled of post-tensioned ducts. Experimental set-up, modelling and signal processing," IEEE Sensors Journal, Vol. 13, 457-465, 2013.
doi:10.1109/JSEN.2012.2219392 Google Scholar

24. Bore, T., D. Placko, F. Taillade, and P. Sabouroux, "Electromagnetic characterization of grouting materials of bridge post tensioned ducts for NDT using capacitive probe," NDT and E Int., Vol. 60, 110-120, 2013.
doi:10.1016/j.ndteint.2013.07.010 Google Scholar

25. Placko, D. and T. Kundu, Ultrasonic nondestructive evaluation: Engineering and biological material characterization, 143-202, T. Kundu (Ed.), Pub. CRC Press, 2004.

26. Kundu, T., D. Placko, S. Das, and T. Bore, "Modeling of ultrasonics fields by distributed point source method," Ultrasonic and Electromagnetic NDE for Structure and Material Characterization: Engineering and Biomedical Applications, 109-166, CRC Press, 2012. Google Scholar

27. Placko, D., T. Bore, and T. Kundu, "Distributed point source method for imaging in electrostatic and electromagnetic problems," Ultrasonic and Electromagnetic NDE for Structure and Material Characterization: Engineering and Biomedical Applications, 249-295, CRC Press, 2012. Google Scholar

28. Eskandazade, M., T. Kundu, N. Liebeaux, D. Placko, and F. Mobadersani, "Numerical simulation of electromagnetic acoustic transducers using distributed point source method," Ultrasonics, Vol. 50, No. 6, 583-591, 2010.
doi:10.1016/j.ultras.2009.12.003 Google Scholar

29. Joubert, P.-Y., E. Vourc’h, and D. Placko, "Qualitative reconstruction of defects in oriented field eddy current magneto-optical imaging," Proceedings of 14th International IGTE Symposium on Numerical Field Calculation in Electrical Engineering, Graz, Austria, Sep. 19–22, 2010.

30. Bausson, S., V. Thomas, P.-Y. Joubert, L. Blanc-Ferraud, J. Darbon, and G. Aubert, "Regularized inversion of a distributed point source model for the reconstruction of defects in eddy currents imaging," COMPEL, Vol. 30, No. 6, 1777-1791, 2011.
doi:10.1108/03321641111168093 Google Scholar

31. Joubert, P.-Y. and J. Pinassaud, "Linear magneto-optic imager for non-destructive evaluation," Sensors and Actuators A, Vol. 129, 126-130, 2006.
doi:10.1016/j.sna.2005.11.028 Google Scholar

32. Le Diraison, Y., P.-Y. Joubert, and D. Placko, "Characterization of subsurface defects in aeronautical riveted lap-joints using multi-frequency eddy current imaging," NDT and E Int., Vol. 42, No. 2, 133-140, 2009.
doi:10.1016/j.ndteint.2008.10.005 Google Scholar

33. Mook, G., F. Michel, and J. Simonin, "Electromagnetic imaging using probe arrays," 17th World Conference on Nondestructive Testing, WCNDT 2008, Shanghai, China, October 2008.

34. Marchand, B., J. M. Decitre, and O. Casula, "Flexible and array eddy current probes, for fast inspection of complex parts," Review of Quantitative Nondestructive Evaluation, Vol. 29, 313-320, D. O. Thompson, D. E. Chimenti (Eds.), American Institute of Physics, 2010. Google Scholar

35. Novotny, P., P. Saddl, and P. Machac, "A magneto-optic imager for NDT applications," NDT and E Int., Vol. 37, No. 8, 645-649, 2004.
doi:10.1016/j.ndteint.2004.05.002 Google Scholar

36. Office of Aviation Research, , Development of an improved magneto optic/eddy current imager, 20591 Final Report DOT/FAA/AR-97/37, Washington DC, 1998.

37. Le, M., J. Lee, and T. Shoji, "A simulation of magneto-optical eddy current imaging," NDT and E Int., Vol. 44, 783-788, 2011.
doi:10.1016/j.ndteint.2011.07.013 Google Scholar

38. Grechishkin, R., S. Chigirinski, M. Gusev, O. Cugat, and N. Dempsey, Magnetic Imaging Films, Magnetic Nanostructures in Modern Technology, 195-224, Springer, 2008.
doi:10.1007/978-1-4020-6338-1_11

39. Placko, D., T. Bore, and A. Rivolet, "Imaging and detection of cracks in metallic structures with eddy current sensors," SPIE — Smart Structures/NDE Proceedings, San Diego, California, 2013. Google Scholar

Dr. Thierry Bore

Dr. Pierre-Yves Joubert

Dr. Dominique Placko