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Scalar potential model of eddy-current interactions with three-dimensional flaws

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Abstract

Magnetic scalar potential theory is applied to a model of eddy-current detection of a surface-breaking flaw in a conductor. A general boundary integral equation for the potential is derived first in a form suitable for numerical solution. The problem is then specialized to a flaw in a perfectly conducting half-space. A solution algorithm based on the boundary element method is outlined and demonstrated by application to a three-dimensional rectangular slot. Methods for accounting for the effects of nonvanishing skin depth are discussed.

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References

  1. W. Lord and R. Palanisamy, in G. Birnbaum and G. Free (eds.),Eddy-Current Characterization of Materials and Structures, ASTM STP 722 (American Society for Testing and Materials, Philadelphia, 1981), p. 5.

    Google Scholar 

  2. W. S. Dunbar,J. Nondestruct. Eval. 5: 9 (1985).

    Google Scholar 

  3. R. E. Beissner,J. Appl. Phys. 60: 352 (1986).

    Google Scholar 

  4. N. Ida, in D. O. Thompson and D. E. Chimenti (eds.),Review of Progress in Quantitative NDE, Vol. 3 (Plenum, New York, 1984), p. 547.

    Google Scholar 

  5. R. E. Beissner, K. A. Bartels, and J. L. Fisher, in D. O. Thompson and D. E. Chimenti (eds.),Review of Progress in Quantitative NDE, Vol. 7 (Plenum, New York, 1988), p. 1753.

    Google Scholar 

  6. M. Burrows, Dissertation (University Microfilms, University of Michigan, Ann Arbor, 1964).

    Google Scholar 

  7. B. A. Auld, F. Meunnemann, and D. K. Winslow,J. Nondestruct. Eval. 2: 1 (1981).

    Google Scholar 

  8. R. E. Beissner, C. M. Teller, G. L. Burkhardt, R. T. Smith, and J. R. Barton, in G. Birnbaum and G. Free, (eds.),Eddy-Current Characterization of Materials and Structures, ASTM STP 722 (American Society for Testing and Materials, Philadelphia, 1981), p. 428.

    Google Scholar 

  9. R. E. Beissner, M. J. Sablik, and C. M. Teller, in D. O. Thompson and D. E. Chimenti (eds.),Review of Progress in Quantitative NDE, Vol. 2 (Plenum, New York, 1983), p. 1237.

    Google Scholar 

  10. D. H. Michael and R. Collins, in D. O. Thompson and D. E. Chimenti (eds.),Review of Progress in Quantitative NDE, Vol. 6 (Plenum, New York, 1987), p. 193.

    Google Scholar 

  11. T. G. Kincaid, in D. O. Thompson and D. E. Chimenti (eds.),Review of Progress in Quantitative NDE, Vol. 1 (Plenum, New York, 1982), p. 355.

    Google Scholar 

  12. P. K. Banerjee and R. Butterfield,Boundary Element Methods in Engineering Science (McGraw-Hill, New York, 1981).

    Google Scholar 

  13. F. J. Rizzo and D. J. Shippy,Int. J. Numer. Methods Eng. 11: 1753 (1977).

    Google Scholar 

  14. B. A. Auld, in G. Birnbaum and G. Free (eds.),Eddy-Current Characterization of Materials and Structures, ASTM STP 722 (American Society for Testing and Materials, Philadelphia, 1981), p. 332.

    Google Scholar 

  15. T. H. Fawzi, M. Taher Ahmed, and P. E. Burke,IEEE Trans. Magn. MAG-21: 1835 (1985).

    Google Scholar 

  16. R. Grimberg, H. Mansir, J. L. Muller, and A. Nicolas,IEEE Trans. Magn. MAG-22: 1272 (1986).

    Google Scholar 

  17. R. E. Beissner,J. Nondestruct. Eval. 7: 000–000 (1988).

    Google Scholar 

  18. F. Meunnemann, B. A. Auld, C. M. Fortunko, and S. A. Padget, in D. O. Thompson and D. E. Chimenti (eds.),Review of Progress in Quantitative NDE, Vol. 2 (Plenum, New York, 1983), p. 1501.

    Google Scholar 

  19. B. A. Auld, S. Jefferies, J. C. Moulder, and J. Gerlitz, in D. O. Thompson and D. E. Chimenti (eds.),Review of Progress in Quantitative NDE, Vol. 5 (Plenum, New York, 1986), p. 383.

    Google Scholar 

  20. J. C. Moulder, P. J. Shull, and T. E. Capobianco, in D. O. Thompson and D. E. Chimenti (eds.),Review of Progress in Quantitative NDE, Vol. 6 (Plenum, New York, 1987), p. 601.

    Google Scholar 

  21. C. V. Dodd and W. E. Deeds,J. Appl. Phys. 39: 2829 (1968).

    Google Scholar 

  22. J. A. Stratton,Electromagnetic Theory (McGraw-Hill, New York, 1941), p. 226 ff.

    Google Scholar 

  23. J. D. Jackson,Classical Electrodynamics (Wiley, New York, 1962), Chap. 1.

    Google Scholar 

  24. A. J. Poggio and E. K. Miller, in R. Mittra (ed.),Computer Techniques for Electromagnetics (Pergamon, New York, 1973), p. 159.

    Google Scholar 

  25. T. A. Cruse,Comput. Struct. 4: 741 (1974).

    Google Scholar 

  26. S. K. Burke,J. Phys. D. 18: 1745 (1985).

    Google Scholar 

  27. G. A. Korn and T. M. Korn,Mathematical Handbook for Scientists and Engineers (McGraw-Hill, New York, 1961), p. 569.

    Google Scholar 

  28. R. E. Beissner and M. J. Sablik,J. Appl. Phys. 56: 448 (1984).

    Google Scholar 

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Beissner, R.E. Scalar potential model of eddy-current interactions with three-dimensional flaws. J Nondestruct Eval 7, 15–24 (1988). https://doi.org/10.1007/BF00565773

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  • DOI: https://doi.org/10.1007/BF00565773

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