2008 ECT BENCHMARK RESULTS: MODELING WITH CIVA OF 3D FLAWS ...
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2008 ECT BENCHMARK RESULTS: MODELING WITH CIVA OF 3D FLAWS ...

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2008 ECT BENCHMARK RESULTS: MODELING WITH CIVA OF 3D
FLAWS RESPONSES IN PLANAR AND CYLINDRICAL WORK
PIECES


C. Reboud, G. Pichenot D. Prémel and R. Raillon

CEA, LIST, Centre de Saclay, point courrier 120, F-91191 Gif-sur-Yvette cedex, France ;


ABSTRACT. The configurations proposed in the 2008 ECT modeling benchmark session are addressed
in this paper using the eddy current modeling tool embedded into CIVA, which is a multi-technique
simulation platform dedicated to NDT and developed at the French Atomic Energy Commission (CEA).
The theoretical approach used in CIVA for ECT modeling is based on Volume integral Method (VIM)
coupled with the Method of Moments (MoM) and thus leads to fast and accurate calculations in the case
of canonical geometries. Symmetries of the configurations considered in this benchmark are moreover
exploited by using the Dodd and Deed formalism for the field computations. After a presentation of the
semi-analytical model, results obtained in all benchmark cases are discussed and compared with
experimental data.

Keywords: Eddy Current Testing, Tube Inspection, Modeling, Benchmark, Volume Integral Method.
PACS: 81.70.Ex


INTRODUCTION

The CIVA software developed at the French Atomic Energy Commission for processing
and simulating NDT data includes tools for modeling eddy current inspection of a
component in which virtual defects are positioned. This paper presents the results of the
2008 eddy current benchmark ...

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2008 ECT BENCHMARK RESULTS: MODELING WITH CIVA OF 3D FLAWS RESPONSES IN PLANAR AND CYLINDRICAL WORK PIECES C. Reboud, G. Pichenot D. Prémel and R. Raillon CEA, LIST, Centre de Saclay, point courrier 120, F-91191 Gif-sur-Yvette cedex, France ; ABSTRACT.The configurations proposed in the 2008 ECT modeling benchmark session are addressed in this paper using the eddy current modeling tool embedded into CIVA, which is a multi-technique simulation platform dedicated to NDT and developed at the French Atomic Energy Commission (CEA). The theoretical approach used in CIVA for ECT modeling is based on Volume integral Method (VIM) coupled with the Method of Moments (MoM) and thus leads to fast and accurate calculations in the case of canonical geometries. Symmetries of the configurations considered in this benchmark are moreover exploited by using the Dodd and Deed formalism for the field computations. After a presentation of the semi-analytical model, results obtained in all benchmark cases are discussed and compared with experimental data.Keywords:Eddy Current Testing, Tube Inspection, Modeling, Benchmark, Volume Integral Method. PACS:81.70.Ex INTRODUCTION The CIVA software developed at the French Atomic Energy Commission for processing and simulating NDT data includes tools for modeling eddy current inspection of a component in which virtual defects are positioned. This paper presents the results of the 2008 eddy current benchmark obtained with the CIVA software. Configurations addressed are internal and external tube inspections with differential probes, as well as a plate inspection with a single air-cored coil. The theoretical approach, which is based on Volume Integral Method and the Green’s dyad formalism [1], is briefly presented in the first part of this paper. The various configurations addressed in the 2008 ECT benchmark modeling session are described in the second part, and the results obtained with CIVA (version 9) are finally discussed. PRESENTATION OF ECT MODELING USING VIM APPROACH The semi-analytical model of ECT tube inspection developed in the CIVA platform is based on the Volume Integral Method [1] using the Green’s dyad formalism. It provides accurate results with small computation times in the case of canonical geometries, and requires very few numerical parameters (cell numbers used to mesh the flaw only) in addition to the geometrical description of the probe, the workpiece and the flaw, which makes it much easier to use than purely numerical models for non-specialists in numerical
analysis. The theoretical approach is presented here in the cylindrical geometry, so that we consider in the next section the ECT at the frequencywof a tube containing a flaw located in a regionW. Green’s Dyad Formalism The interaction between the flaw and the electric field generated by the probe is described with an integral equation, which is derived from Maxwell’s equations and solved numerically using the Method of Moments [2]:
(1)
The unknownJWof this equation is a fictitious current density defined in the volumeWcontaining the flaw and depending on the total electric field. This current density is involved in the calculation of the probe response, which constitutes the last step of the model. The contrast functionf(r) is defined by the equation
(2)
wheres0is the tube conductivity ands(r) is the flaw conductivity. The termJ0in (1) is an excitation term depending on the total primary electric fieldE0(r) emitted by the probe in the regionWincluding the flaw. The dyad links the fictitious current density to the (also fictitious) electric field it creates insideW. Calculation of the Primary Electric Field The resolution of the state equation implies that the excitation termJ0is known. As this term depends on the primary electric fieldE0(r), the first part of the calculation consists in its computation in the volumeWof the flaw, as shown in figure 1. The presence of the flaw is not taken into account at this time. If the probe is made of coils that are centered about the tube axis, thenE0(r) has only one component (the azimuthal one) different from zero and is computed very quickly using Dodd & Deeds solutions [3]. Other probe configurations are modeled in CIVA in the case of the cylindrical geometry: punctual coils with axes that are perpendicular to the tube axis and axial coils that are off-centered [4] with respect to the tube axis. In these cases complete 3D calculations are carried out using Green’s dyads:
(3)
whereJis the current density in the coil,wis the angular frequency of the driving current, -7 m0=4p.the magnetic permeability and is a dyadic Green function linking the10 is current density driving the coil to the electric field inside the volumeWof the flaw.
Flaw (volumeW!
Two coils in differential mode
Infinite and non-magnetic tube
FIGURE 1.Example of ECT of a tube using an axial probe operating in differential mode. Application of the Reciprocity Principle for the Calculation of the Probe Response Once the state equation has been solved, the reciprocity principle [5] is used to determine the ECT signaldU (in V) detected by the probe in the vicinity of the flaw. In the case of a single emitting and receiving coil, the application of this principle gives thatdU corresponds exactly to the effect due to the fictitious source previously introduced inW:
(4)
whereI is the amplitude of its driving current. When the probe has a more complex acquisition operating mode and is made of several coils, the output ECT signal is calculated as a weighted combination of contributions due to single coils. ECT CONFIGURATIONS ADRESSED IN THE 2008 BENCHMARK Three configurations were proposed for the QNDE 2008 Eddy Current benchmark. The first two deal with the inspection of tubes using an internal or external bobbin coil. The probe is centred along the tube’s axis and operates in differential mode. The different flaws considered are through-wall, external or internal notches, which orientation are longitudinal or circumferential, and an external groove. The third configuration involves an air-cored coil testing a slab affected by parallepipedal notches. The coil axis is perpendicular to the slab. Workpieces considered here are non magnetic (inconel), and all flaws are considered as voids. Experimental data are provided for all the flaws as values of X and Y (Real and Imaginary) parts of the EC signal with respect to the probe position. A complete description of the configurations addressed by this benchmark can be found at the WFNDEC website (World Federation of NDE Centers, http://www.wfndec.org/). Figures 2, 3 and 4 show a general view of the three configurations only.
a) b) FIGURE 2.First ECT configurations addressed in the ECT benchmark session: Tube inspection using an internal bobbin coil. a) One external groove (This flaw n°1 is referred as “GE40”). b) Three 3D Notches (these flaws n° 2, n° 3 and n° 4 are called “ELE6”, “ELI6” and “GI10”).
a) b) FIGURE 3.Second ECT configurations addressed in the ECT benchmark session: Tube inspection using an external bobbin coil. a) One through-wall borehole (called “TFP1”). b) Three 3D Notches (these flaws n° 2, n° 3 and n° 4 are called “ELE6”, “ELI0” and “ET82”).
FIGURE 4.Third ECT configurations addressed in the ECT benchmark session: Slab inspection using an air-cored coil. The 4 flaws are parallelepipedal notches: n°1 is a through-wall notch called “through-wall notch ”, flaws n°2 (called “80 % internal notch”) and n°3 (called “40 % internal notch”) are internal ones (that is they break the slab’s surface on the probe’s side) and flaw n°4 (called “80 % external notch”) is an external one (that is it breaks the slab’s surface on the side opposite the probe). PRESENTATION OF THE BENCHMARK RESULTS The calculations carried out with CIVA for the 3D configurations of the ECT benchmark lasted several minutes. The following figures show the simulated and experimental plots in the complex plane for all the proposed configurations. Then a table gathers all the experimental and simulated values.
Tube inspection with an internal bobbin coil The comparison between simulation and experiment shows an agreement better than 9 % in amplitude and 2° in phase (figure 4).
FIGURE 4.Benchmark result obtained in the case of the tube inspection with an internal bobbin coil. Tube inspection with an external bobbin coil The comparison between simulation and experiment shows an agreement better than 5 % in amplitude and 1° in phase (figure 5), except for the transversal notch (14%
FIGURE 5.Benchmark result obtained in the case of the tube inspection with an external bobbin coil.
in amplitude and 6° in phase). The tube configurations studied here correspond to typical ECT carried out in industry, for which flaw responses are compared to a calibration response. Therefore only relative amplitudes are considered. The flaws used for the calibration are an external groove and a borehole, which are classical shapes used for calibration in nuclear and metallurgic industries, respectively. The shapes of the ECT signals are very well reproduced by the simulation, even in the case of the internal notch noted ELI6, which depth is very small (10 % of the tube thickness). The third benchmark configuration corresponds to an absolute measurement of flaw response signals. Comparison with simulation here is thus not affected by the simulation performed over a calibration flaw. Here experimental data is obtained using an impedance-meter and without any calibration process over a planar specimen inspected with an air-core bobbin in absolute mode. Slab inspection using an air-cored coil The comparison between simulation and experiment shows an agreement better than 6 % in amplitude and 4° in phase (figure 6).
FIGURE 6.Benchmark result obtained in the case of the tube inspection with an air-core coil.
TABLE 1: experimental and simulated results GE40 Internal bobbin ELE6 EL16 GI10 (calibration) Amp Phase Amp Phase Amp Phase Amp Phase (V) (°) (V) (°) (V) (°) (V) (°) Simulated Civa 2.81 142 0.193 -50 85 173 1.70 -172 values Experimental 2.81 142 0.212 -52 86 172 1.61 -172 values Bore hole External bobbin ELE6 ET82 ELE10 (calibration) Amp Phase Amp Phase Amp Phase Amp Phase (V) (°) (V) (°) (V) (°) (V) (°) Simulated Civa 1 10 1.31 14 1.38 -167 1.41 -169 values Experimental 1 10 1.38 14 1.21 -173 1.34 -170 values Through 80% internal 40% internal 80% external Air-core coil wall notch notch notch notch Amp Phase Amp Phase Amp Phase Amp Phase (V) (°) (V) (°) (V) (°) (V) (°) Simulated Civa 11.36 107 4.48 111 2.12 124 1.54 58 values Experimental 11.68 111 4.58 114 2.18 123 1.64 57 values CONCLUSION The comparison between experiment and simulation shows a general good agreement for amplitudes and phases for various types of flaws and probes (external and internal probes, in absolute and differential modes), for planar and cylindrical specimen, made of conductive and nonmagnetic materials. News configurations will be proposed for a benchmark next year. More complex cases may be considered (array of flaws, ferromagnetic tubes, tilted coils).REFERENCES 1. W.C. Chew. Waves and Fields in Inhomogeneous Media,IEEE Press, Piscatawaynd (2 edition), 1995. 2. R.F. Harrington. The Method of Moments in Electromagnetics.Journal of Electromagnetic Waves and Applications, vol. 1 (3), p. 181–200, 1987. 3. C.V. Dodd and W.E. Deeds. Analytical solutions to eddy-current probe-coil problems. Journal of Applied Physics, vol. 39 (6), p. 2829-2838, 1968. 4. C. Reboud, D. Prémel, G. Pichenot, D. Lesselier and B. Bisiaux. Development and validation of a 3D model dedicated to eddy current non destructive testing of tubes by
5.
encircling probes.International Journal of Applied Electromagnetics and Mechanics, vol. 25, p. 313-317, 2007. B.A. Auld and F.G. Muennemann and M. Riaziat. Nondestructive testing, Chapter 2: Quantitative modelling of flaw responses in eddy current testing. vol. 7,Academic Press, London, 1984.