D. Prémel, J.M. Decitre and G. Pichenot. CEA, LIST, F Gif-sur-Yvette, France

Transcription

1 SIMULATION OF EDDY CURRENT INSPECTION INCLUDING MAGNETIC FIELD SENSOR SUCH AS A GIANT MAGNETO-RESISTANCE OVER PLANAR STRATIFIED MEDIA COMPONENTS WITH EMBEDDED FLAWS D. Préme, J.M. Decitre and G. Pichenot CEA, LIST, F Gif-sur-Yvette, France ABSTRACT. The ECT inspection of a conductive component consists in detecting the perturbation of the induced currents due to a faw. Among new detectors, Giant Magneto-Resistance (GMR) or Giant Magnetic Impedance sensors, which are sensitive to the magnetic fied above the surface of the component, have shown growing interest due to their high performances with respect to cassica bobbin cois. In this communication, we present a numerica mode based on the voume integra approach which aows computing the components of the perturbed magnetic fied due to a given notch embedded in a panar stratified media. Though the inducer may be chosen arbitrary in a ist of potentia exciting cois, rectanguar cois or current fois are very usefu for generating a uniform current fow orientated perpendicuary to the ength of the faw. This paper presents firsty some numerica resuts considering two inds of distinct numerica modes, and then some experimenta resuts wi be presented for different inds of practica appications. This numerica mode resuts in new computation faciities which have been transated into new functionaities in the ast version of the CIVA software. Keywords: Eddy Current Simuation, Voume Integra Method, Dyadic formaism, Giant magnetoresistance sensors PACS: Nm, Tp, Ge. INTRODUCTION The detection and the characterization of faws in conductive structures can be successfuy achieved by using Eddy Current Testing (ECT). By carrying a sinusoida current into one or a set of exciting cois, some eddy currents are induced into the worpiece under test and their interaction with a fawed region within the moc-up resuts in the change of the impedance of the exciting coi. According to the operating frequency, eddy currents are induced in a thin "sin" near the surface of the conductive media, so the EC signa is anayzed in order to ocate and size surface defects. Eddy current probes are mainy based on winding cois. However, due to the fact that the sensitivity of a winding coi is decreasing at ow frequencies, these EC probes based on winding cois revea some imitations for the detection of deep faws. In that case, magnetic sensors are very attractive because they eep a good sensitivity at ow frequencies and thans to their sma size, one can design an EC probe with a higher spatia resoution. The CEA LIST has

2 deveoped some advanced technoogies for the design of EC probes based on Giant Magneto-resistance (GMR) or Giant Magneto Impedance sensors [1]. These deveopments has been done thans to the improvements of eddy current simuation toos which are abe to compute the perturbed magnetic fied above a fawed region embedded in a conductive panar structure. Some specific eddy current modues are integrated into the CIVA software [2] patform dedicated to NDT simuation. The strategy of deveopment is based on the choice of semi-anaytica methods rather than fuy numerica methods (finite eements, finite difference, etc.). In particuar, semi-anaytica modes dedicated to eddy current modeing are based on the voume integra equations and the Green s dyadic formaism. The main advantages of this approach ie in the fact that it is ony necessary to mesh a fawed region because Green s dyads tae into account a the boundary conditions outside the faw, at the infinity and moreover at the panar interfaces. Today, CIVA deas with a arge number of NDT configurations which are of interest in ECT. The aim of this contribution is to describe a numerica mode based on the voume integra approach [4, 5, 6] which aows to compute the faw signa due to a given notch embedded in a panar stratified media. The faw signa resuts from the measurement of oca, punctua vaues of the surface magnetic fied. This signa is obtained by using a tiny inductive sensor or a magnetic fied sensor. The inducer may be chosen arbitrary in a ist of exciting cois [7, 8] avaiabe into CIVA. Aternating Current Fied Measurement (ACFM) techniques [9, 10,11] usuay use for instance rectanguar cois or current fois in order to generate a uniform current fow orientated perpendicuary to the ength of the faw. These new deveopments, transated into new functionaities in the ast version of CIVA aow to conduct some parametric studies such as the ift-off of the magnetic sensor, the tit of the inducer, and other parameters which coud be abe to infuence the sizing of the defect by using one or two components of the magnetic fied. This wor may be used to sove the inverse probem [12]. AN EXAMPLE OF AN ECT CONFIGURATION Figure 1 dispays an exampe of ECT configuration consisting of a stratified sab affected by two faws. Eddy currents in the sab are induced by an exciting coi driven by an aternative current of anguar frequency. Into the CIVA software, this exciting coi may be chosen among cyindrica cois, with a ferrite core or not, or rectanguar cois. In this figure, two rectanguar cois are considered in order to obtain roughy eddy currents mainy orientated in the Y direction. A magnetic sensor is assumed to be abe to provide the three components of the perturbed magnetic fied due to the presence of the defects. The response of the sensor is obtained by taing into account the sensitivity of the sensor, expressed in Vots per Tesa and resuts from the difference between the magnetic fied obtained in the presence of the faw and the magnetic fied obtained when there is no faw. The numerica mode may consider an arbitrary number N of ayers made of materias being inear, isotropic and not magnetic (with the permeabiity of the vacuum denoted by 0. The conductivity of each ayer is constant, except when there is a faw. This one is indeed represented by oca variations of the conductivity r in the th ayer. This paper is organized as foows. In the foowing section, the eddy current modeing probem is soved by using the Voume Integra Method impying a system of two integra equations for which the ernes are based on the Green's dyad formaism. New functionaities are consequenty added to the previous version of the CIVA patform in order to be abe to compute the punctua vaues of each component of the perturbed magnetic fied above the fawed materia. The computation of the e.m.f induced in a

3 receiving pic-up coi was aready avaiabe into the previous version. These ast functionaities aready vaidated are here used for obtaining some numerica vaidation resuts. A numerica resuts used for the numerica vaidation are compared in another section before presenting a rea experiment. Finay, a short concusion is proposed. THE VOLUME INTEGRAL METHOD FIGURE 1. An exampe of ECT configuration. The computation of the perturbed magnetic fied above the pate requires firsty the evauation of the eectrica interna fied in a finite domain surrounding the faw. Each ayer may incude one finite voume containing an object and the tota interna fied in each ayer resuts from the interaction from the primary fied E p r in the ayer due to the driving probe and the perturbation fied due to a set of eementary faws, each one being considered in a singe ayer. The tota eectric fied in each ayer, denoted by E r, is given by: E N p ( ee) r E r j G r, E ' d 0 r faw 1 The contribution is nu if there is no faw in the th ayer ( r ' ). The superscript (ee) means that we compute the components of the eectrica fied due to a unit point source which is a soution of: 2 ( ee) r, G r, Ir G In this ast equation, the observation point r is assumed to be in the ayer whie the ( ee). (2) source point is in the ayer. stands for the Kronecer symbo and I is the unit dyad. 2 According to the quasi-static regime, the wave number in the th ayer is given by 2 = j 0. The Green's dyads satisfy as usuay the appropriated boundary conditions at the infinity in the transverse directions and at the interfaces between two different ayers in the norma direction to the panar surface of the stratified medium. The anaytica expression of the Green's dyad corresponding to a mutiayered panar medium is given in [13]. The tota interna fied in each ayer appears inside and outside the integra. This state integra equation must be soved numericay by the Moment Method (MoM) [14]. Knowing the tota eectrica fied in each ayer, the perturbed magnetic fied can be computed above the pate, in the air region 1, by an observation equation which introduces ( me) the Green's dyadg r,. The superscript (me) means that the components of the magnetic fied are cacuated due to a current dipoe: (1)

4 ( ee) r, G r, ( me) G. (3) The tota perturbed magnetic fied taes into account a the contributions of each ayer : B N ( me) r G r, re d r faw 1 This equation has been impemented into CIVA. In order to vaidate these new deveopments, some other numerica data have been computed by using another numerica code which has been previousy vaidated. Indeed, by using the Faraday-Lorentz aw, the components of the magnetic fied can be estimated by the e.m.f induced in a tiny pic-up coi when the section of the pic-up coi tends towards zero. In this case, the responses of a receiving pic-up tiny coi, orientated aong X, Y or Z, are given by the changes in the mutua impedance and can be obtained via the reciprocity theorem: r I N 1I 2Z r faw 1 p re r E d where E p stands for the primary fied that woud be induced by the receiving coi in the fawed region, in the th ayer, if it was driven by a current I 2, and I 1 is the driving current of the exciting coi. The tota eectrica fied E r in the th ayer comes from the numerica resoution of equation (1). According to the orientation of the pic-up receiving coi, one can obtain an approximation of one component of the magnetic fied. The numerica resuts which can be obtained by these two approaches are compared in order to show the vaidity of these new functionaities. NUMERICAL VALIDATION Figure 2 dispays the overview and the front view of an ECT configuration consisting of a non magnetic sab constituted by four ayers. The thicness of each ayer is fixed at 0.8 mm, the vaues of the conductivities of each ayer expressed in MS/m are given by , 0. 5, 1, The operating frequency is chosen at 100 Hz and two notches are considered. The first one is breaing the surface of the first ayer, its ength is 2 mm, its depth is 0.3 mm and the opening is 0.1 mm. The second faw is embedded at the top of the third ayer, its ength is equa to 4 mm, its depth is 0.5 mm and its opening is aso 0.1 mm. These two faws are differenty orientated: the first one is orientated aong the X axis whie the second one is orientated aong the Y direction. The EC probe is constituted by two exciting rectanguar cois. For each one, the inner width is 4 mm, the inner ength is 8 mm and the height is equa to 0.1 mm. The number of turns is 5 and finay the width of the current foi is 1 mm. The EC probe is scanning aong three ines in the X direction and three vaues of the Y position have been chosen in order to verify the vaidity of the resuts in the two directions of scanning. Figure 3 and 4 show a comparison between the two numerica approaches resuting from the impementation of equations (4) and (5). The rea and the imaginary parts of the B z, B x components are respectivey shown. Three curves are dispayed corresponding to three vaues of the Y position of the probe. These numerica resuts show a good agreement between the two numerica approaches. An experimenta vaidation is achieved in the foowing section. (4) (5)

5 FIGURE 2. An overview (on the eft) and a front view (on the right) of an ECT configuration used for the numerica vaidation. FIGURE 3. Rea and imaginary parts of the B component. z EXPERIMENTAL VALIDATION FIGURE 4. Rea and imaginary parts of the B component. Experimenta data have been obtained from an experimenta set-up which is depicted in Figure 5. Let us consider a non magnetic sab made of Incone 600, the conductivity is assumed to be 1.02 MS/m. The operating frequency is 100 Hz. Eddy currents are induced in the sab by a rectanguar coi which is etched on a fexibe fim. The inner width of the coi is 23 mm, the inner ength is 62 mm and the height is equa to 35 m. The number of turns is 100 and finay the width of the current foi is 7 mm. The x

6 distance from the bottom of the exciting coi to the sab is about 2 mm. A Giant Magneto Resistance sensor (GMR) measures the B x component of the magnetic fied. The EC experimenta signa is obtained by subtracting the response of the probe in the fawed region and the signa without the faw. The distance from the GMR to the target is about 0.1 mm but this vaue can be affected by an uncertainty due to the encapsuation of the sensitive part of the sensor in the chip. The thicness of the sab is 1.55 mm and we consider a first notch for a preiminary procedure denoted by "caibration". Indeed, in most industria appications, due to uncertainties in the experimenta system, the measured EC signa has to be caibrated with respect to a reference configuration. At this stage, we choose a first notch of 10 mm ength, 0.93 mm depth and the opening is 0.1 mm. The EC probe is scanning a ine aong the ength of the defect and finay simuated data and experimenta data are normaized in order to fit the maximum vaue of the magnitude of the EC signa. The shapes of the two signas are compared on Figure 6. In this figure, the rea and the imaginary part of the signas are represented; the same signas are aso dispayed in the impedance pane diagram. As it is expected, the comparison shows a very sma discrepancy between simuated data and experimenta data due to, probaby, oca variations of the ift-off during the movement of the probe. The compex vaue of the normaization constant is fixed for a the foowing resuts of comparison. Figure 7 dispays the EC signas when the probe is scanning perpendicuary to the defect. FIGURE 5. A scheme of the experimenta set-up and an exampe of the EC probe incuding the GMR Sensor. Ony one rectanguar coi is activated for obtaining experimenta data. FIGURE 6. A comparison of the EC signas on the first faw for caibration. In the ast experiment, et us consider two identica faws separated with a gap of 3 mm (See Fig. 8). The ength of each defect is 10 mm, the opening is 0.1 mm and the depth is 0.76 mm. Figure 9.a and 9.b dispay two cartographies of the EC signas coected when the probe is scanning above the fawed region. Figure 10 shows a sice view when the probe is moved aong a ine parae to the X axis.

7 FIGURE 7. A comparison of the EC signas on the first faw when the probe is scanning perpendicuary to the notch. FIGURE 8. The experimenta set-up. (a) Simuated data (b) Experimenta data FIGURE 9. Two cartographies corresponding to the magnitude of the EC signas. CONCLUSION A numerica mode based on the Voume Integra Method (VIM) and the Green's dyadic formaism has been deveoped in order to compute the punctua vaues of the perturbed magnetic fied above a fawed region due to an arbitrary number of faws into a stratified panar structure. The new deveopments have been vaidated by two numerica approaches and some comparison between simuated data and experimenta data confirm the vaidity of the goba modeing approach. These deveopments are avaiabe into the version 10 of CIVA and some new deveopments are today aready engaged upon for considering magnetic materias of constant permeabiity.

8 FIGURE 10. A comparison of the EC signas due to two cose faws when the probe is scanning aong a ine perpendicuary to the notches. REFERENCES 1. B. Marchand, C. Zorni, J.M. Decitre and O. Casua, "Recent Deveopments of Eddy currents probes", ENDE 2009, to be pubished. 2. www-civa.cea.fr. 3. R. F. Mostafavi and D. Mirshear-Syaha, "AC Fieds Around Short Cracs in Metas Induced by Rectanguar Cois", IEEE Transactions on Magnetics, 35, no. 3, (1999), pp J.R. Bower and L.D. Sabbagh and H.A. Sabbagh, "A Theoretica and Computationa Mode of Eddy Current Probes incorporating voume integra and Conjuguate Gradient Methods", IEEE Transactions on Magnetics, 25, no. 3, (1989), pp J.R. Bower and S.A. Jenins and L.D. Sabbagh and H.A. Sabbagh, "Eddy Current Probe Impedance due to a voumetric faw", Journa of Appied Physics, 70, no. 3, (1991), pp J.M. Decitre, D. Préme and M. Lemistre, "3D Modeing of a Magneto-optic imager by a dyadic Green's functions approach", Review of quantitative Nondestructive Evauation, 22, ed. D.O. Thompson and D.E. Chimenti, IOP, (2003), pp T. Theodouidis, G Pichenot, "Integration of tited coi modes in a voume integra method for reaistic simuations of eddy current inspections", Eectromagnetic Non-Destructive Evauation (XI), Studies in Appied Eectromagnetics and Mechanics, A. Tamburrino, Y. Meihov and L. Udpa, Amsterdam, IOS Press, T.P. Theodouidis and E.E. Kriezis, Impedance evauation of rectanguar cois for eddy current testing of panar media, NDTE Internationa, 35, no. 6, (2002), pp M. Ravan, S.H.H. Sadeghi and R. Moini, "Neura networ approach for determination of fatigue crac depth profie in a meta, using aternating current fied measurement data", IET Sci. Measurement Technoogy, 2, no. 1, (2008), pp R. K. Amineh, M. Ravan, S. H. Sadeghi, and R. Moini, "Remova of Probe Liftoff Effects on Crac Detection and Sizing in Metas by the AC Fied Measurement Technique", IEEE Transactions on Magnetics, 44, no. 8, (2008), pp R. K. Amineha,1, M. Ravan, S.H. Sadeghi,, R. Moini, "Using AC fied measurement data at an arbitrary iftoff distance to size ong surface-breaing cracs in ferrous metas", NDT\&E Internationa, 41, (2008), pp D. Préme and A. Baussard, "Eddy current evauation of three-dimensiona faws in fat conductive materias using a Bayesian approach, Inverse probems, 18, no. 6, (2002), pp W.C. Chew, Waves and Fieds in Inhomogeneous Media, IEEE Press, Piscataway (2nd edition), R.F. Harrington, The Method of Moments in Eectromagnetics, Journa of Eectromagnetic Waves and Appications, 1, no. 3, (1987), pp