Main Article Content
The paper has two different objectives. The first one is to show that Ampere’s double layer method, which is equivalent to one of the Maxwell equations, leads to the integration of a simple closed form expression, thus avoiding the need to solve complicated partial differential equations. The second aim is to study the case of a zero volume defect in a NDE problem by a perturbation method and the introduction of a double layer. The combination of these two techniques leads to a very fast solution of the problem. A practical example including
Authors who publish with this journal agree to the following terms:
- Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
- Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).
Y. Gotoh, A. Kiya, N. Takahashi, Electromagnetic Inspection of Outer Side Defect on Steel Tube With Steel Support Using 3-D Nonlinear FEM Considering Non-Uniform Permeability and Conductivity, IEEE Transaction on Magnetics, vol. 46, no. 8, pp. 3145-3148, 2010.
R. Hamia, C. Cordier, S. Saez, C. Dolabdjian, Eddy-Current Nondestructive Testing Using an Improved GMR Magnetometer and a Single Wire as Inducer: A FEM Performance Analysis, IEEE Trans. Magn., vol. 46, no. 10, pp. 3731–3737, 2010.
C. V. Dodd, W. E. Deeds, Analytical solutions to eddy-current probe-coil problems, Journal of Applied Physics, vol. 39, no. 6, pp. 2829-2838, 1968.
C. V. Dodd, W. E. Deeds, Integral solutions to some eddy current problems, International Journal of Nondestructive Testing, vol. 1, pp. 29-90, 1969.
L. Bettaieb, H. Kokabi, M. Ploujadoff, A. Sentz and A. Tcharkhtchi, Fatigue and/or crack detection in NDE, Nondestructive Testing and Evaluation, vol. 24, no. 4, pp. 1-12, 2009.
Y. Cha, K. H. Kim, J. Shon, Y. H. Kim, and J. Kim, Surface flaws detection using AC magnetic field sensing by a thin film inductive microsensor," IEEE Trans. Magn., vol. 44, no. 11, pp. 4022–4025, 2008.
C. Cordier, S. Saez, S. Lebargy, and C. Dolabdjian, Accurate steel tube axis alignment in nondestructive evaluation probe, IEEE Trans. Magn., vol. 44, no. 10, pp. 2409–2413, 2008.
Y. Hatsukade, S. Okumo, K. Mori, and S. Tanaka, Eddy-current-based SQUID-NDE for detection of surface flaws on copper tubes, IEEE Trans. Appl. Supercond., vol. 17, no. 2, pp. 780–783, 2007.
S. Hirano, Y. Inada, E. Matsumoto, A. Saito, K. Aizawa, M. Matsuda, S. Kuriki, and S. Ohshima, SQUID nondestructive testing system with vibrating normal pick-up coil, IEEE Trans. Appl. Supercond., vol. 17, no. 2, pp. 788–791, 2007.
K. Tsukada, T. Kiwa, T. Kawata, and Y. Ishihara, Low-frequency eddy current imaging using MR sensor detecting tangential magnetic field components for nondestructive evaluation, IEEE Trans. Magn., vol. 42, no. 10, pp. 3315–3317, 2006.
K. Chomsuwan, S. Yamada, M. Iwahara, H. Wakiwaka, and S. Shoji, "Application of eddy current testing technique for high-density doublelayer printed circuit board inspection," IEEE Trans. Magn., vol. 41, no. 10, pp. 3619–3321, 2005.
N. V. Nair, V. R. Melapudi, H. R. Jimenez, X. Liu, Y. Deng, Z. Zeng, L. Udpa, T. J. Moran, and S. S. Udpa, A GMR-based eddy current system for NDE of aircraft structures, IEEE Trans. Magn., vol. 42, no. 10, pp. 3312–3314, 2006.
W. S. Dunbar, The volume integral method of eddy current modeling, Journal of Nondestructive Evaluation, vol. 5, no. 1, pp. 9-14, 1985.
S. M. Nair, J. H. Rose, Electromagnetic induction (eddy currents) in a conducting half-space in the absence of in homogeneities: a new formalism, Journal of Applied Physics, vol. 68, no. 12, pp. 5995-6009, 1990.
Z. Zeng, L. Udpa, S. S. Udpa, and M. S. C. Chan, Reduced magnetic vector potential formulation in the finite element analysis of eddy current nondestructive testing, IEEE Trans. Magn., vol. 45, no. 3, pp. 964–967, 2009.
J. H. McWhirter, J. J. Oravec, and R. W. Haack, Computation of magnetic fields in three-dimensions based on Fredholm integral equations, IEEE Transaction on Magnetics, vol. 18, n° 2, pp. 373-377, 1982.
T. Morisue, A new formulation of the magnetic vector potential method in 3-D multiply connected regions, IEEE Trans. Magn., vol. 24, no. 1, pp. 90–93, 1988.
O. Biro, K. Preis, and W. Renhart, Finite element analysis of 3D multiply connected eddy current problems, IEEE Trans. Magn., vol. 25, no. 5, pp. 4009–4011, 1989.
Y. Le Bihan, J. Pavo and C. Marchand, Calculation of ECT signal of a minute crack by FEMBIM hybrid method, Eur. Phys. J. Appl. Phys., vol. 28, pp. 355-360, 2004.
A. Ruosi, M. Valentino, G. Pepe, V. Monebhurrn, and D. Lesselier, High T_c SQUIDs and eddy-current NDE/: a comprehensive investigation from real data to modeling, Meas. Sci. Techno. vol. 11, pp. 1639-1648, 2000.
J. Bird, T. A. Lipo, A 3-D magnetic charge finite-element model of an electrodynamic wheel, IEEE Transaction on Magnetics, vol. 44, n° 2, pp. 253-265, 2008.
L. Codecasa, P. Dular, R. Specogna, F. Trevisan, A Perturbation Method for the T-Ω Geometric Eddy-Current Formulation, IEEE Transaction on Magnetics, vol. 46, no. 8, pp. 3045 - 3048, 2010.
M. Ya. Antimorov, A. A. Kolyshkin, R. Vaillancourt, Application of a perturbation method to the solution of eddy current testing problems, IEEE Transaction on Magnetics, vol. 30, no. 3, pp. 1247-1250, 1994.
I. El Nahas, B. Szabados, M. Poloujadoff, R. Findlay, and X. Wu, A three-dimensional electromagnetic field analysis technique utilizing the magnetic charge concept, IEEE Transaction on Magnetics, vol. 23, no. 5, pp. 3853-3859, 1987.
R. L. Stoll, The analysis of eddy currents, Oxford: Clarendon press, 1974.
L. Bettaieb, H. Kokabi, M. Poloujadoff, A. Sentz, and H. J. Krause, Analysis of Some Non Destructive Evaluation Experiments Using Eddy Currents, Research in Nondestructive Evaluation, vol. 20, no. 3, pp. 159-177, 2009.
L. Bettaieb, H. Kokabi, M. Poloujadoff, A. Sentz, V. Moser, and C. Coillot, Comparison Of The Use Of SQUID an Hall Effect Sensors In NDE, Materials Evaluation, vol. 68, no. 5, pp. 535-541, 2010.
J. A. Tegopoulos and E. E. Kriezis, Eddy currents in linear conducting media, studies in electrical and electronics engineering, vol. 16, Amsterdam: Elsevier, 1985.
C. V. Dodd, The use of computer-modeling for eddy current testing, research techniques in nondestructive testing, vol. III, edited by R. S. Sharpe (ed.). London: Academic Press, pp. 429-479, 1977.
P. Leroy, C. Coillot, V. Mosser, A. Roux and G. Chanteur, Use of magnetic concentrator to highly improve the sensitivity of Hall effect sensors, Sensor Letters, vol. 5, no. 1, pp. 162-166, 2007.