||Multiphysics Numerical Modeling and Analysis of Photoinductive Imaging of Crack and Field Mapping of Eddy Current Probes
||Department of Electrical Engineering
eddy current testing (ECT)
finite element method (FEM)
multiphysics numerical modeling
nondestructive testing (NDT)
photoinductive imaging (PI)
The photoinductive imaging (PI) method is a novel nondestructive inspection technique for detecting surface-breaking conditions and slight subsurface flaws in electrically conductive test specimens. This new technique dramatically increases the image resolution for practical applications. It is also an ideal field-mapping technique that can provide higher spatial resolution and higher sensitivity to the tangential component of the electromagnetic field without perturbations. However, the PI method is a multiphysics sensing method that combines eddy-current testing (ECT) and thermal-wave methods. It is difficult to solve the analytical solution of the PI method. In addition, conventional experimental results can not be compared to the numerical simulation results of the FEM, which leads to insufficient data for modeling the PI method and analyzing the impact parameters for crack inspection and field mapping of EC probes.
The PI technology requires large amounts of time in order to tune the critical parameters which affect experimental results and improve signals. The inability to reduce the tuning time for parameters makes it impossible to rapidly detect flaws and to distinctly characterize the electromagnetic field distributions of an EC probe using this method. However, previous researchers have not fully analyzed the impact factors of both applications. Therefore, multiphysics numerical modeling of the photoinductive imaging (PI) method was performed with a two-dimensional (2-D) transient finite element method (FEM) to characterize corner cracks at the edge of a specimen with a bolt hole and to map the field for eddy-current (EC) probes above a thin metal film. We present how the FEM can be utilized to model the PI effect and observe the influence of critical factors on the coil probe impedance for a rectangular crack in the Ti-6Al-4V specimen. It was also used to observe how the properties of metal film affect the electric and magnetic field mapping signals of EC probes.
The proposed model shows that the PI method has a higher spatial resolution in the area of the defect in 2-D models as compared to the conventional ECT method. The FEM simulation results for 0.25 mm, 0.50 mm, and 0.75 mm rectangular notches are shown and discussed. The effects of coil current frequency, laser point temperature, and lift-off distance on the PI signal are also examined and analyzed. We demonstrate that the PI effect is a novel sensing method for characterizing the geometric shape of cracks, and that the enhanced output signals of the coil probe can also be obtained given an appropriate quantity of factors.
The applicability of actual thin film materials for mapping the field of EC probe when using PI method was studied. The effects of mapping signals with different excited frequencies of EC coils were examined and analyzed. EM field mapping signals of EC probe coils with tilt angles of 0o, 5o, 10o, 15o, and 20o were also examined with appropriate metal film materials. These simulation results showed that the higher-resolution field-mapping signals of EC probes can be obtained by given a titanium thin film. The resolution of field-mapping signals of EC probes correlated positively with resistivity, heat capacity, and density of thin film and correlated negatively with its thermal conductivity. An improved understanding of distinct field distribution of EC probes enables a better selection of optimal probes without tilted coils for EC inspection.
Abstract (Chinese) i
Abstract (English) iii
List of Tables ix
List of Figures x
Chapter 1: Introduction 1
1.1. Crack inspection 1
1.2. Field mapping of EC robes 4
1.3. Research motivation 9
1.4. Outline of approach and thesis 11
Chapter 2: Differential Formulation of the Governing Equations 13
2.1. Basic theoretical background of photoinductive imaging 13
2.2. Equations of heat transfer by conduction 15
2.3. Equations of quasi-static electromagnetic field 18
2.4. Solution of partial differential equations 22
2.4.1. Coefficient form 22
2.4.2. General form 23
2.4.3. Weak form 25
2.5. Formulation implementation by FEM 27
2.5.1. Heat transfer 27
2.5.2. Quasi-static electromagnetic field 29
Chapter 3: The Processing of FEM Simulation and Analysis 31
3.1. Brief overview of COMSOL 33
3.1.1. Module selection 33
3.1.2. Solver selection 34
3.2. The 2-D model the photoinductive imaging method 35
3.2.1. Crack detection 35
3.2.2. Field mapping of EC probes 39
3.3. The programming process of the scanning mode for the PI method 41
Chapter 4: Simulation Results and Analysis for Crack Detection 45
4.1. The 2-D actual size model of the PI method 45
4.2. Comparison the PI and ECT methods in the 2-D simplified model 48
4.2.1. Spatial resolution 49
4.2.2. Excitation current frequency 50
4.2.3. Laser point temperature for PI method 53
4.2.4. Characterizing different length notches 55
4.2.5. Lift-off distance 57
Chapter 5: Simulation Results and Analysis for Field Mapping of EC Probes
5.1. EC probes with tilted coils in the 2-D simplified model 60
5.2. Effects of the excited frequency 63
5.3. Effects of electrical and thermal properties of thin metal film 65
5.3.1. Electrical properties of the thin film 65
5.3.2. Thermal properties of the thin film 69
5.4. Effects of thin film materials 73
5.5. Effects of thicknesses of the thin film 75
5.6. Comparison of field mapping resolution 77
5.7. Comparison of simplified structural coil and actual structural coil 79
5.8. Comparison of 2-D raster scanning results 79
Chapter 6: Conclusions and Future Work 83
6.1. Crack inspection 83
6.2. Field mapping of EC probes 83
6.3. Future Work 84
Appendix 1: Weak Form of Quasi-Static Electromagnetic Field 86
Appendix 2: Thesis Defense 88
Publication List 97
 J. C. Moulder, N. Nakagawa, K. S. No, Y. P. Lee, and J. F. McClelland, “Photoinductive imaging: a new NDE technique,” Review of Progress in Quantitative NDE edited by D. O. Thompson and D. E. Chimenti (Plenum Press, New York), vol. 8A, pp. 599-611, 1989.
 J. C. Moulder and N. Nakagawa, “Characterizing the performance of eddy current probes using photoinductive field-mapping,” Research in Nondestructive Evaluation, vol. 4, pp. 221-236, 1992.
 M. S. Hughes, J. C. Moulder, M. W. Kubovich, and B. A. Auld, “Mapping eddy current probe fields using the photoinductive effect,” NDT & E International vol. 28, p. 251, 1995.
 N. Nakagawa and J. C. Moulder, “Eddy Current Probe Calibration via the Photoinductive Effect,” NDT & E International, vol. 28, pp. 245-246, 1995.
 C.-C. Tai and J. C. Moulder, “Bolt-Hole Corner Crack Inspection Using the Photoinductive Imaging Method,” Journal of Nondestructive Evaluation, vol. 19, pp. 81-93, 2000.
 B. A. Auld, S. R. Jefferies, and J. C. Moulder, “Eddy-current signal analysis and inversion for semielliptical surface cracks,” Journal of Nondestructive Evaluation, vol. 7, pp. 79-94, 1988.
 B. George, G. E. Donald, and M. Leonard. Recent developments in NDE measurements and standards at NIST. In: Harold B, Leonard M, editors. Nondestructive testing standards-present and future, Philadelphia, PA: American Society for Testing and Materials; pp. 89-125, 1992.
 T. E. Capobianco, F. R. Fickett, and J. C. Moulder. Mapping of Eddy Current Probe Fields. In: Thompson DO, Chimenti DE, editors. Review of Progress in Quantitative Nondestructive Evaluation, vol. 5A, Plenum Press, New York, pp. 705-711, 1985.
 T. E. Capobianco. Field Mapping and Performance Characterization of Commercial Eddy Current Probes. In: Thompson DO, Chimenti DE, editors. Review of Progress in Quantitative Nondestructive Evaluation, vol. 6A, Plenum Press, New York, pp. 687-694, 1987.
 J. C. Moulder and J. H. Rose. “Calibrating an eddy-current-probe using a modulated thermal energy source” U.S. Patent 5019775, May. 28, 1991.
 T. Danielson, “Multi-Parameter eddy current measuring system with parameter compensation technical field,” Kaman Instrumentation Corporation, 1996.
 D. Mirshekar-Syahkai and R. F. Mostafavi, “Effects of probe and inducer on saturation of crack signal in high-sensitivity AC field measurement technique,” IEE Proceedings Science, Measurement & Technology, pp. 193-196, 2001.
 A. Abakar, J.-C. Verite, and R. Cauvin, “Sensitivity analysis of eddy current sensor parameters for non-destructive measurement of zirconium oxide thin film using 3D finite element,” 12th Biennial IEEE Conference on Electromagnetic Field Computation, pp. 426-426, 2006.
 W. Yin, R. Binns, S. J. Dickinson, C. Davis, and A. J. Peyton, “Analysis of the Liftoff Effect of Phase Spectra for Eddy Current Sensors,” IEEE Transactions on Instrumentation and Measurement, vol. 56, pp. 2775-2781, 2007.
 C. V. Dodd and W. E. Deeds, “Analytical Solutions to Eddy-current Probe-coil Problems,” Journal of Applied Physics, vol. 39, no. 6, pp. 2829-2838, 1968.
 H.J. Tsaknakis and E.E. Kriezis, “Field Distribution Due to a Circular Current Loop Placed in an Arbitrary Position above a Conducting Plate,” IEEE Transactions on Geoscience and Remote Sensing,, vol. GE-23, pp.197-207, 1985.
 J. Juillard, B. de Barmon, and G. Berthiau, “Simple analytical three-dimensional eddy-current model,” IEEE Transactions on Magnetics, vol. 36, pp.258-266, 2000.
 T. Theodoulidis, “Analytical model for tilted coils in eddy-current nondestructive inspection,” IEEE Transactions on Magnetics., vol. 41, pp. 2447- 2454, 2005.
 J. C. Aldrin and J. S. Knopp, “Crack Characterization Method with Invariance to Noise Features for Eddy Current Inspection of Fasterner Sites,” J. Nondestr. Eval.¬, vol.25, pp. 165-181, 2006.
 Y. H. Zhang, F. L.Luo, and H. X. Sun, “Impedance Evaluation of a Probe-Coil’s Lift-off and Tilt Effect in Eddy-Current Nondestructive Inspection by 3D Finite Element Modeling,” Proceedings of the 17th World Conference on Nondestructive Testing, 2008.
 C.-C. Tai and Y.-L. Pan, “Multiphysics Modeling and Analysis of the Photoinductive Imaging Effect for Crack Detection,” IEEE Transactions on Instrumentation and Measurement, vol. 59, pp. 425-432, 2010.
 F. I. Al-Naemi, J. P. Hall, and A. J. Moses. “FEM modelling techniques of magnetic flux leakage-type NDT for ferromagnetic plate inspections,” Journal of Magnetism and Magnetic Materials, vol. 304, pp. e790-e793, 2006.
 Y. Li, G. Y. Tian, and S. Ward, “Numerical simulation on magnetic flux leakage evaluation at high speed,” NDT & E International, vol. 39, pp. 367-373, 2006.
 Z. Y. Huang, P. W. Que, and L.Chen, “3D FEM analysis in magnetic flux leakage method,” NDT & E International, vol. 39, pp. 61-67, 2006.
 N. Tsopelas and N. J. Siakavellas, “The effect of the angle of inclination of the exciting coil in electromagnetic-thermal non-destructive inspection,” Proceedings of the 4th International Conference on Non-destructive Testing, 2007.
 L. Madani, N. S. Nasreddine, and Z. L. Fatima, “2D finite element method study of the stimulation induction heating in synchronic thermography NDT,” NDT & E International, vol. 41, pp. 577-581, 2008.
 I. Mukriz, G. Y. Tian, and Y. Li, “3D transient magnetic field mapping for angular slots in aluminium,” Insight - Non-Destructive Testing and Condition Monitoring, vol. 51, pp. 21-24, 2009.
 N. Tsopelas and N. J. Siakavellas, “Electromagnetic-thermal NDT in thin conducting plates,” NDT & E International, vol. 39, pp. 391-399, 2006.
 J. Taine and J.-P. Petit, Heat transfer: New York, N.Y. :Prentice Hall, 1993.
 Heat transfer Module User’s Guide. (COMSOL AB, Stockholm, 2006).
 R. W. Lewis, K. Morgan, H. R. Thomas, and K. N. Seetharamu, The finite element method in heat transfer analysis, John Wiley & Sons, Chichester, 1996.
 D. K. Cheng, Field and wave electromagnetics, 2 ed. (Addison-Wesley, Redwood City, 1989).
 AC/DC Module User’s Guide. (COMSOL AB, Stockholm, 2006).
 J. Jianming, The finite element method in electromagnetics, 2 ed. (John Wiley & Sons, New York, 2002).
 COMSOL Multiphysics User’s Guide. (COMSOL AB, Stockholm, 2006).
 J. N, Reddy, An introduction to the finite element method, 3 rd. (McGraw-Hill, New York, 2006).
 V. N. Kaliakin, Introduction to approximate solution techniques, numerical modelling,and finite element methods. (Marcel Dekker, New York, 2002).
 Peter Monk. Finite Element for Maxwell’s Equations. (Clarendon Press, Oxford, 2003).
 F. Yu and P. B. Nagy, “Dynamic Piezoresistivity Calibration for Eddy Current Nondestructive Residual Stress Measurements,” Journal of Nondestructive Evaluation, vol. 24, pp. 143-151, 2005.
 D. R. Lide, CRC handbook of chemistry and physics. (CRC Press, Boca Raton, 2006).