Abstract
A method is presented to evaluate flaw signals in eddy current NDE using the finite element technique. The analysis of the electromagnetic field is based on a three-dimensional finite element scheme that computes directly the electromagnetic field distortions due to defects. This direct field-distortion calculation together with an accurate unflawed field calculation provides accurate total field values in general three-dimensional geometries. The paper shows that the application of the reaction concept and the reciprocity theory allows computations of the probe responses by performing integrals over the flaw region only, even if the analysis is performed by a finite element scheme. Two benchmark problems—a plate with rectangular slot scanned by a differential probe and a tube with axial and circumferential slots scanned by an absolute probe—have been solved to demonstrate the validity and the efficiency of the method. The calculated probe responses show good agreement with the measured trajectories. In order to reach better quantitative agreement, a calibration algorithm that adjusts the parameters of the cylindrical coil model and the lift-off within the range of the geometrical tolerances has been developed.
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References
B. A. Auld and M. Riaziat, Spatial frequency analysis and matched filtering in electromagnetic nondestructive evaluation,J. Appl. Phys. 54(6):3509–3517 (1983).
B. A. Auld, J. C. Moulder, S. Jefferies, P. J. Shull, S. Ayter, and J. Kenney, Eddy Current Reflection Probes: Theory and Experiment,Res. Nondestr. Eval. 1:1–11 (1989).
H. A. Sabbagh and L. D. Sabbagh, An eddy current model for three-dimensional inversion,IEEE Trans. Magn. 22(4):282–291 (1986).
J. R. Bowler, Three dimensional eddy current probe-flaw calculation using volume elements,Electrosoft 2(2/3):142–156 (1991).
J. Pavo and K. Miya, Crack shape reconstruction by inverting eddy current field data,IEEE Trans. Magn. 30(9) (in press).
N. Ida, K. Betzold, and W. Lord, Finite element modeling of absolute eddy current probe signals,J. Nondestr. Eval. 3(3): 147–154 (1982).
N. Ida, H. Hoshikawa, and W. Lord, Finite element prediction of differential eddy current probe signals from Fe3O4 deposits in PWR steam generators,NDT Int. 18(6):331–338 (1985).
N. Ida and W. Lord, A finite element model for three-dimensional eddy current NDT phenomena,IEEE Trans. Magn. 21 (6):2635–2643 (1985).
Y. Sun, H. Lin, Y. K. Shin, Z. You, S. Nath, and W. Lord, 3-D finite element modeling of remote field eddy current effect,Rev. Prog. Quant. Nondestr. Eval. 9:319–326 (1990).
Z. Badics, H. Komatsu, H. Mototsuji, K. Aoki, F. Nakayasu, and K. Miya, Numerical simulation of probe-crack interaction of three-dimensional NDE models,Int. J. Appl. Electromagn. Mater. 4:357–362 (1994).
Z. Badics, Y. Matsumoto, K. Aoki, F. Nakayasu, M. Uesaka, and K. Miya, An effective 3D finite element scheme for computing electromagnetic field distortions due to defects in eddy current non-destructive evaluation,IEEE Trans. Magn. (submitted).
R. F. Harrington,Time Harmonic Electromagnetic Fields (McGill-Hill, New York, 1961).
O. Biro and K. Preis, On the use of the magnetic vector potential in the finite element analysis of three-dimensional eddy currents,IEEE Trans. Magn. 25(4):3145–3159 (1989).
L. R. Turner,TEAM Workshop Problems (ANL, April 1988).
T. Takagi, M. Hashimoto, T. Sugiura, S. Norimatsu, S. Arita, and K. Miya, 3D simulation of eddy current testing of a block with a crack, inRev. Prog. Quant. Nondestr. Eval. (Vol. 9): D. O. Thomson and D. E. Chimenti, eds. (Plenum Press, New York, 1990), pp. 327–334.
J. C. Verite, A coil over a crack. (Results for benchmark problem 8 of TEAM Workshop),COMPEL—Int. J. Comput. Math. Electr. Electron. Eng. 9(3):155–167 (1990).
C. V. Dodd and W. E. Deeds, Analytical solutions to eddy current probe-coil problems,J. Appl. Phys. 39:2829–2838 (1968).
Z. Badics, H. Komatsu, Y. Matsumoto, K. Aoki, F. Nakayasu, and K. Miya, A Finite Element Solution of TEAM Problem 15, ASIAN TEAM Workshop, Seoul National University, Seoul, Korea (Chairman: Song-yop Hahn) (June 25, 1994).
S. K. Burke, A benchmark problem for computation of ΔZ in eddy current nondestructive evaluation (NDE),J. Nondestr. Eval. 7(1/2):35–41 (1988).
J. C. Moulder, J. C. Gerlitz, B. A. Auld, M. Riaziat, S. Jeffries, and G. McFetridge, Calibration methods for eddy current measurement systems, inRev. Prog. Quant. Nondestr. Eval. D. O. Thomson and D. E. Chimenti, eds. (Plenum, New York, 1985), pp. 411–420.
Z. Badics, H. Komatsu, Y. Matsumoto, K. Aoki, F. Nakayasu, and K. Miya, Effective 3D finite element modeling of eddy current perturbation due to defects in conducting materials, inProceedings of the International Symposium on Advanced Computational and Design Techniques in Applied Electromagnetic Systems (ISEM-Seoul '94), S-Y. Hahn, ed. (published as a Supplement to theInternational Journal of Applied Electromagnetics in Materials) (Seoul, Korea, June 22–24, 1994).
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Badics, Z., Matsumoto, Y., Aoki, K. et al. Accurate probe-response calculation in eddy current NDE by finite element method. J Nondestruct Eval 14, 181–192 (1995). https://doi.org/10.1007/BF00730888
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DOI: https://doi.org/10.1007/BF00730888