Eddy Current Testing

  • Zhenmao ChenEmail author
  • Cherdpong Jomdecha
  • Shejuan Xie
Reference work entry


In various NDT methods, eddy current testing (ECT) technique is widely used for surface and near surface defect inspection, and characterization of electrical conductive materials. This chapter gives brief introduction of theories and applications of advanced ECT, with emphases on the probe design and numerical simulation methods. The chapter moves from short historical and status reviews of the ECT technique, a basic understanding of ECT principles, to state of the art of the testing method in the first section. As bases of ECT numerical simulation methods, theories of electromagnetics related to the advanced ECT are presented in section “Theory of Electromagnetics for ECT Problem.” The topics include basic equations of the low frequency electromagnetic field, skin effect and standard depth of penetration in ECT, and sensitivity and influence factors in ECT inspection. In section “Numerical Methods for Eddy Current Testing,” numerical methods for the three-dimensional ECT problem are described in terms of the A-ϕ, Ar formulations, and FEM and BEM methods. In addition, the equations for calculating ECT signals from the eddy current field are described based on the Biot-Savart’s law and the reciprocity principle at the end of the section. Due to advancement in ECT probe design and optimization, in section “Design and Optimization of ECT Probes,” typical types of ECT probes and magnetic field sensors are introduced. Later, numerical designs of various ECT probes are presented. Furthermore, a phenomenological strategy based on a simplified relationship between the source magnetic field and the induced eddy current is described for evaluation of crack-probe interaction and detectability of ECT probes. At the end of the section, procedures for optimal design of advanced ECT probes for crack detection are given. In section “Applications of Advanced Numerical Analysis for ECT,” progress in forward and inverse numerical techniques and schemes for simulation of ECT problems are explained in detail. Specific numerical approaches are utilized for the ECT signal simulation and crack profile reconstruction by using a deterministic optimization method, an artificial intelligent method, and stochastic optimization methods. The chapter gives good reference for studentsand researchers in the field of ECT and computational electromagnetics.


  1. Achenbach JD (2000) Quantitative nondestructive evaluation. Int J Solids Struct 37:1–27zbMATHCrossRefGoogle Scholar
  2. Atherton DL (1995) Remote field eddy current inspection. IEEE Trans Magn 31(6):4142–4147CrossRefGoogle Scholar
  3. Auld BA, Moulder JC (1999) Review of advances in quantitative eddy current nondestructive evaluation. J Nondestruct Eval 18:3–36CrossRefGoogle Scholar
  4. Burke SK (1986) Impedance of a horizontal coil above a conducting half space. J Phys D Appl Phys 19:1159–1173CrossRefGoogle Scholar
  5. Bowler J (1987) Eddy current calculations using half-space Green’s functions. J Appl Phys 61(3):833–839CrossRefGoogle Scholar
  6. Badics Z, Pavo J, Komatsu H (1998) Fast flaw reconstruction from 3D eddy current data. IEEE Trans Magn 34:2823–2828CrossRefGoogle Scholar
  7. Chari MVK (1974) Finite element solution of the Eddy current problem in magnetic structures. IEEE Trans Power Appar Syst 93(1):62–72CrossRefGoogle Scholar
  8. Chen Z, Aoto K, Miya K (2000) Reconstruction of cracks with physical closure for signal of eddy current testing. IEEE Trans Magn 36:1018–1022CrossRefGoogle Scholar
  9. Cochran A, Carr C (1995) Recent progress in SQUIDs as sensors for electromagnetic NDE. Studi Appl Electromagn Mech 8:75–86Google Scholar
  10. Cecco VS, Drunan GV, Sharp FL (1986) Eddy current manual: volume 1: test method, NUC-CAN-AECL-7523 Rev.1, Atomic Energy of Canada LimitedGoogle Scholar
  11. Chen Z, Miya K (1998a) ECT inversion using a knowledge based forward solver. J Nondestruct Eval 17(3):167–175Google Scholar
  12. Chen Z, Miya K (1998b) A new approach for optimal design of eddy current probes. J Nondestruct Eval 17(3):105–116Google Scholar
  13. Cheng W, Miya K, Chen Z (1999) Reconstruction of cracks with multiple eddy current coils using a database approach. J Nondestruct Eval 18:149–160CrossRefGoogle Scholar
  14. Chen Z, Miya K, Kurokawa M (1997) A distinctive featured optimization approach for ECT probes. Rev Prog Quant Nondestr Eval 16:989–996CrossRefGoogle Scholar
  15. Chen Z, Miya K, Kurokawa M (1999) Rapid prediction of eddy current testing signals using A-ϕ method and database. NDT&E Int 32:29–36CrossRefGoogle Scholar
  16. Chen Z, Rebican M, Miya K, Takagi T (2005) 3D simulation of remote field ECT by using Ar method and a new formula for signal calculation. Res Nondestr Test 16:35–53CrossRefGoogle Scholar
  17. Chen Z, Rebican M, Yusa N, Miya K (2006) Fast simulation of ECT signal due to a conductive crack of arbitrary width. IEEE Trans Magn 42:683–686CrossRefGoogle Scholar
  18. Chen Z, Takashima H, Miya K (2004) A hybrid database approach for simulation of remote field eddy current testing signals. Int J Appl Electromagn Mech 19:219–223CrossRefGoogle Scholar
  19. Chen Z, Xie S, Li Y (eds) (2015) Electromagnetic nondestructive evaluation (XVIII). IOS Press, AmsterdamGoogle Scholar
  20. Chen Z, Xie S, Li W (2011) Reconstruction of stress corrosion crack with multi-frequency ECT signals. Paper presented at the 8th international conference on flow dynamics, Tohoku University, Sendai, 8–12 Oct 2011Google Scholar
  21. Chen H, Xie S, Zhou H, Chen Z (2014) Numerical simulation of magnetic incremental permeability for ferromagnetic material. Int J Appl Electromagn Mech 45:379–386CrossRefGoogle Scholar
  22. Chen Z, Yusa N, Miya K (2008) Enhancements of ECT techniques for quantitative nondestructive testing of key structural components of nuclear power plants. Nucl Eng Des 238(7):1651–1656CrossRefGoogle Scholar
  23. Chen Z, Yusa N, Miya K (2009) Some advances in numerical analysis techniques for quantitative electromagnetic nondestructive evaluation. Nondestr Test Eval 24(1):69–102CrossRefGoogle Scholar
  24. Chen Z, Yusa N, Miya K (2004b) Advanced MFLT for detecting far side defects in a welding part of an austenitic stainless steel plate. Int J Appl Electromagn Mech 19:527–532CrossRefGoogle Scholar
  25. Chen Z, Yusa N, Miya K (2004c) Inversion techniques for eddy current NDE using optimization strategies and a rapid 3D forward simulator. Int J Appl Electromagn Mech 20:179–187CrossRefGoogle Scholar
  26. Chen Z, Yusa N, Miya K (2006b) Reconstruction of natural stress corrosion crack in coolant tubes from eddy current testing signals. Stud Appl Electromagn Mech 26:197–204Google Scholar
  27. Davis J (1996) Nondestructive evaluation and quality control. ASM Int, Materials ParkGoogle Scholar
  28. Dodd CV (1977) The use of computer modelling in Eddy current testing. Res Tech Nondestr Test 2:429–479Google Scholar
  29. Dodd C, Deeds W (1968) Analytical solutions to eddy-current probe-coil problems. J Appl Phys 39:2829–2838CrossRefGoogle Scholar
  30. Demerdash NA, Nehl TW (1978) An evaluation of the methods of finite elements and finite differences in the solution of nonlinear electromagnetic fields in electrical machines. IEEE Trans Power Appar Syst 98(1):74–87CrossRefGoogle Scholar
  31. Forster F (1959) Nondestructive testing handbook, vol 2, 1st edn. Am Soc Nondestr Test, Columbus, pp 36–42Google Scholar
  32. Fuller E (2006) Steam generator integrity assessment guidelines, Rev 2, Report No.101298. Electric Power Research Institute, Palo AltoGoogle Scholar
  33. Fukutomi H, Takagi T, Tani J (1998) Three-dimensional finite element computation of a remote field eddy current technique to non-magnetic tubes. J JSAEM 6:343–349Google Scholar
  34. Hagemaier DK (1985) Eddy-current standard depth of penetration. Mater Eval 10(43):1438–1454Google Scholar
  35. Harvey ED (1995) Eddy current testing: theory and practice, ASNT reference manual. The American Society for Nondestructive Testing, ColumbusGoogle Scholar
  36. Hayt HW (2006) Engineering electromagnetics. McGraw-Hill, New YorkGoogle Scholar
  37. Haus H, Melcher J (1989) Electromagnetic fields and energy. Prentice-Hall, Englewood CliffsGoogle Scholar
  38. Hellier C (2003) Handbook of nondestructive evaluation. Mcgraw-Hill, New YorkGoogle Scholar
  39. Hughes DV (1879) Induction-balance and experimental researches therewith. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 8:50–56CrossRefGoogle Scholar
  40. Huang L, He R, Zeng Z et al (2012) An extended iterative finite element model for simulating eddy current testing of aircraft skin structure. IEEE Trans Magn 48(7):2161–2165CrossRefGoogle Scholar
  41. He Y, Luo F, Pan M (2010) Pulsed eddy current technique for defect detection in aircraft riveted structures. NDT & E Int 43(2):176–181CrossRefGoogle Scholar
  42. Hernandez JH, Pacheco ER, Caleyo F (2012) Rapid estimation of artificial near-side crack dimensions in aluminium using a GMR-based eddy current sensor. NDT&E Int 51(1):94–100CrossRefGoogle Scholar
  43. He DF, Shiwa M, Jia JP (2011) Multi-frequency ECT with AMR sensor. NDT & E Int 44(5):438–441CrossRefGoogle Scholar
  44. Huang H, Sakurai N, Takagi T (2003) Design of an eddy-current array probe for crack sizing in steam generator tubes. NDT&E Int 36:515–522CrossRefGoogle Scholar
  45. Higashi M, Tokuhisa K, Kurokawa M (2008) Development of Eddy current testing technique for PWR Vessel’s dissimilar metal weld. J JSNDI 57(5):232–235Google Scholar
  46. Hashimoto M, Uesaka M, Miya K (1993) Development of magnetic field visualization system using hall device array probe. Sens Mater 4(6):313–321Google Scholar
  47. IAEA Training Course Series (2011) Eddy current testing at level 2: manual for syllabi, IAEA TEC-DOC-628 Rev2. International Atomic Energy Agency, VeinnaGoogle Scholar
  48. Ishibashi K (1995) Eddy current analysis by the boundary integral method. IEEE Trans Magn 31:1500–1503CrossRefGoogle Scholar
  49. JSAEM report (1997) Report on Advanced ECT technique, JSAEM-R-9601Google Scholar
  50. Janousek L, Capova K, Gombarska D et al (2009) Recent Trends and Developments in Eddy Current Non-Destructive Sensing. Czech Republic, ChebGoogle Scholar
  51. Jomdecha C, Cai W, Xie S Chen Z (2018) Analysis of magnetic flux perturbation due to conductivity variation in equivalent stress-corrosion crack. Int J Appl Electromagn Mech 2018, 59. Scholar
  52. Janousek L, Chen Z, Yusa N (2005) Excitation with phase shifted fields-enhancing evaluation of deep cracks in eddy-current testing. NDT&E Int 38:508–515CrossRefGoogle Scholar
  53. Jogschies L, Klaas D, Kruppe R et al (2015) Recent developments of Magnetoresistive sensors for industrial applications. Sensors 15:28665–28689CrossRefGoogle Scholar
  54. Jander A, Smith C, Shneider R et al (2005) Magnetoresistive sensors for nondestructive evaluation. Paper presented at the 12th International Symposium of Nondestructive Evaluation for Health Monitoring and Diagnostics, San Diego, 8–12 Mar 2005Google Scholar
  55. Kojima F (1997) Numerical scheme for reconstruction of crack shape in SG tubing by using FEMBEM hybrid code and inverse analysis. Trans JSME 63:2650–2656CrossRefGoogle Scholar
  56. Kurokawa M (1997) Development of new eddy-current testing probe. Stud Appl Electromagn Mech 12:177–183Google Scholar
  57. Kreutzbruck MV, Krause HJ (2002) HTs squids for the nondestructive evaluation of composite structures. Physica C: Superconduct 368(1–4):70–79Google Scholar
  58. Kosmas K, Sargentis CH, Tsamakis D (2005) Non-destructive evaluation of magnetic metallic materials using hall sensors. Sens Actuators A 161(1–2):359–362Google Scholar
  59. Kim J, Yang G, Udpa L (2010) Classification of pulsed eddy current GMR data on aircraft structures. NDT&E Int 43:141–144CrossRefGoogle Scholar
  60. Li Y, Bei Y, Li D, Chen Z (2016) Gradient-field pulsed Eddy current probes for imaging of hidden corrosion in conductive structures. Sens Actuators A 238:251–265CrossRefGoogle Scholar
  61. Ludwig R, Dai X (1990) Numerical and analytical modeling of pulsed eddy currents in a conducting half-space. IEEE Trans Magn 26:299–307CrossRefGoogle Scholar
  62. Libby HL, Wandling CR (1970) Eddy current multi-parameter test for tube flaws in support region. BNWL-1468Google Scholar
  63. Li W, Xie S, Chen Z (2013) Reconstruction of stress corrosion cracks using signals of pulsed eddy current testing. NDT&E Int 28(2):145–154Google Scholar
  64. MacMaster RC (1963) Nondestructive testing handbook. The Ronald Press, New YorkGoogle Scholar
  65. Miya K (1995) Analytical electromagnetics and electromagnetic structures. Yokendo Press, TokyoGoogle Scholar
  66. Mottl Z (1990) The quantitative relations between true and standard depth of penetration for air-cored probe coils in eddy current testing. NDT&E Int 23:11–18Google Scholar
  67. Martin JG, Gil JG, Sanchez EV (2011) Non-destructive techniques based on Eddy current testing. Sensors 11(3):2525–2565CrossRefGoogle Scholar
  68. Mook G, Hesse O, Uchanin V (2007) Deep penetrating Eddy currents and probes. Mater Test 49:258–264CrossRefGoogle Scholar
  69. Maeda K, Shimone J, Harada Y (1997) Optimization of transmit-receive coils for ECT probe with use of the 3-D FEM code. Electromagnetic nondestructive evaluation. IOS Press, Amsterdam. pp 199–206Google Scholar
  70. National Research Council (1997) Aging of U.S. Air Force aircraft. National Academy Press, Washington, DCGoogle Scholar
  71. Norton SJ, Bowler JR (1993) Theory of eddy current inversion. J Appl Phys 73:501–512CrossRefGoogle Scholar
  72. Popa RC, Miya K, Kurokawa M (1997) Optimized eddy current detection of small cracks in steam generator tubing. J Nondestruct Eval 16(3):161–173Google Scholar
  73. Recommanded Practice NO. SNT-TC-1A (2016) Personnel qualification and certification in nondestructive testing. American Society for Nondestructive Testing, ColumbusGoogle Scholar
  74. Richard W (1996) Rules for In-service Inspection of Nuclear Power Plant Components, ASME boiler and pressure vessel code section XI. The American Society of Mechanical EngineersGoogle Scholar
  75. Ripka P (2003) Advances in fluxgate sensors. Sensors Actuators A 106(1–3):8–14CrossRefGoogle Scholar
  76. Rothwell E, Cloud M (2001) Electromagnetics. CRC Press, Boca RatonCrossRefGoogle Scholar
  77. Rebican M, Chen Z, Yusa N et al (2005) Investigation of numerical precision of 3D RFECT signal simulation. IEEE Trans Magn 41:1968–1971CrossRefGoogle Scholar
  78. Rebican M, Chen Z, Yusa N (2006) Shape reconstruction of multiple cracks from ECT signals by means of a stochastic method. IEEE Trans Magn 42:1079–1082CrossRefGoogle Scholar
  79. Reis D, Lambert M, Lesselier D (2002) Eddy-current evaluation of three-dimensional defects in a metal plate. Inverse Prob 18:1857–1871MathSciNetzbMATHCrossRefGoogle Scholar
  80. Ramos H, Postolache O, Alegria F (2009) Using the skin effect to estimate cracks depths in metallic structures. IEEE Instr & Meas Tech 21(12):1361–1366Google Scholar
  81. Pelkner M, Pohl R, Erthner T (2015) Eddy Current Testing with High-Spatial Resolution Probes Using MR Arrays as Receiver. Paper presented at the 7th International Symposium on NDT in Aerospace, Bremen, 16–18 Nov 2015Google Scholar
  82. Ramos HG, Ribeiro AL (2014) Present and future impact of magnetic in NDE. Procedia Eng 86:406–419CrossRefGoogle Scholar
  83. Postolache O, Ribeiro A, Ramos H (2012) Uniform Eddy current probe based on GMR sensor Array and image processing for NDT. IEEE Int Instr Measur Tech 8443(3):458–463Google Scholar
  84. Ripka P, Vopalensky M, Platil A (2003) AMR magnetometer. J Magn Magn Mater 254:639–641CrossRefGoogle Scholar
  85. Rebican M, Yusa N, Chen Z (2004) Reconstruction of multiple cracks in an ECT round-robin test. Int J Appl Electromagn Mech 19:399–404CrossRefGoogle Scholar
  86. Sabbagh H, Sabbagh L (1986) An eddy-current model for three-dimensional inversion. IEEE Trans Magn 22:282–291CrossRefGoogle Scholar
  87. Tai C (1971) Dyadic green functions in electromagnetic theory. Oxford University Press, OxfordGoogle Scholar
  88. Tumanski S (2007) Induction coil sensors- a review. Meas Sci Technol 18(3):R31–R46CrossRefGoogle Scholar
  89. Thompson DO, Chimenti DE (1992) Review of Progress in quantitative nondestructive evaluation, vol 15A. Plenum Press, New York, pp 781–788CrossRefGoogle Scholar
  90. Takagi T, Huang H, Fukutomi H (1998) Numerical evaluation of correlation between crack size and Eddy current testing signal by a very fast simulator. IEEE Trans Magn 34(5):2581–2584CrossRefGoogle Scholar
  91. Takagi T, Hashimoto H, Fukutomi H (1994) Benchmark models of eddy current testing for steam generator tube: experiment and numerical analysis. Int J Appl Electromag in Materials 4(5):149–162Google Scholar
  92. Tegopoulos JA, Kriezis EE (1985) Eddy current in linear conducting media. Elsevier, AmsterdamGoogle Scholar
  93. Tian GY, Li Y, Mandache C (2009) Study of lift-off invariance for pulsed Eddy-current signals. IEEE Trans Magn 45:184–191CrossRefGoogle Scholar
  94. Tamburrino A, Rubinacci G (2002) A new non-iteration inversion method for electrical resistance tomography. Inverse Prob 18:1809–1829zbMATHCrossRefGoogle Scholar
  95. Takagi T, Uesaka M, Miya K (1997a) Electromagnetic NDE research activities in JSAEM. Stud Appl Electromagn Mech 12:9–16Google Scholar
  96. Takagi T, Uesaka M, Miya K (1997b) Electromagnetic NDE research activities in JSAEM, electromagnetic nondestructive evaluation. IOS Press, Amsterdam. pp 9–16Google Scholar
  97. Udpa S, Moore P (2004) Nondestructive testing handbook: electromagnetic testing, 3rd edn. American Society for Nondestructive Testing, Columbus, OhioGoogle Scholar
  98. Xie S (2012) Quantitative Nondestructive Evaluation of Pipe Wall Thinning Using Pulsed Eddy Current Testing. Dissertation, Tohoku UniversityGoogle Scholar
  99. Xie S, Chen Z, Takagi T et al (2011) Efficient numerical solver for simulation of pulsed Eddy current testing signals. IEEE Trans Magn 47:4582–4591CrossRefGoogle Scholar
  100. Yusa N, Chen Z, Miya K (2000) Quantitative profile evaluation of natural crack in steam generator tube from eddy current signals. Int J Appl Electromagn Mech 12:139–150CrossRefGoogle Scholar
  101. Yusa N, Chen Z, Miya K (2003) Large scale parallel computation for the reconstruction of natural stress corrosion cracks from eddy current testing signals. NDT&E Int 36:449–459CrossRefGoogle Scholar
  102. Yusa N, Chen Z, Miya K (2005) Sizing of stress corrosion cracks in piping of austenitic stainless steel from eddy current NDT signals. Nondestruct Test Eval 20:103–114CrossRefGoogle Scholar
  103. Yusa N, Perrin S, Mizuno K (2007a) Eddy current inspection of closed fatigue and stress corrosion cracks. Meas Sci Technol 18:3403–3408CrossRefGoogle Scholar
  104. Yusa N, Perrin S, Mizuno K (2007b) Numerical modeling of general cracks from the viewpoint of eddy current simulations. NDT&E Int 40:577–583CrossRefGoogle Scholar
  105. Zenglu S, Tsutomu Y, Hideki S (2011) Detection of damage and crack in railhead by using eddy current testing. J Electromagn Anal Appl 3:546–550Google Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.State Key Laboratory for Strength and Vibration of Mechanical Structures Shaanxi ERC for NDT and Structural Integrity Evaluation School of AerospaceXi’an Jiaotong UniversityXianChina

Section editors and affiliations

  • Nathan Ida
    • 1
  • Norbert Meyendorf
    • 2
  1. 1.Department of Electrical and Computer EngineeringUniversity of AkronAkronUSA
  2. 2.Center for Nondestructive EvaluationIowa State UniversityAmesUSA

Personalised recommendations