TWO DIMENSIONAL INVERSION OF CRACK SIGNAL IN SURFACE

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1 TWO DIMENSIONAL INVERSION OF CRACK SIGNAL IN SURFACE ELECTROMAGNETIC HELD MEASUREMENT TECHNIQUE S. H. H. Sadeghi Department of Electrical Engineering Amirkabir University of Technology Tehran, Iran D. Mirshekar-Syahkal Department of Electronic Systems Engineering University of Essex Colchester C04 3SQ, UK INTRODUCTION Surface electromagnetic field induced in metals have been successfully exploited for detecting and sizing surface cracks. In the two methods of the surface magnetic field measurement (SMFM) and the induction ac potential-drop (IACPD) reported in [1,2], the surface field is produced by U-shaped wires or rectangular coils carrying high frequency currents. In the SMFM technique, the surface magnetic field is interrogated by a noncontacting magnetic field sensor located in the vicinity of the metal surface whereas in the IACPD technique, a contacting two-legged electric field sensor is used for sampling electric potentials at the metal surface, Figure 1. In both techniques, the surface field is discontinuous at the crack lips. The inducer and the sensors, which can be attached together as part of one probe, as well as other components required for signal detection are shown in Figure 1 [3]. One of the main characteristics of the SMFM and IACPD techniques is simplicity in crack sizing. They do not require calibration or calibration standards. For long cracks, a single scan, normal to the crack lips is usually sufficient for the determination of the crack depth using inversion curves (obtained theoretically). Although one-dimensional interpretation of crack signal is computationally fast (and hence highly suitable for real-time systems), it could lead to grossly wrong results for scans close to the crack ends. The problem becomes especially serious when cracks of small aspect ratios are to be sized. Fatigue cracks have approximately circular or elliptical shapes with a wide range of aspect ratios [4]. This paper quantifies the accuracy of the one-dimensional inversion technique for cracks of small aspect ratios and reports on a two-dimensional approach for inverting the SMFM and IACPD crack signals. In this connection, the one-dimensional method is first described. Then, the errors due to this interpretation for circular-arc cracks are discussed using a set of computer simulated results. Finally, two-dimensional inversion curves for fatigue cracks with circular-arc shape are presented. ONE-DIMENSIONAL CRACK SIZING Typical SMFM and IACPD crack signals are plotted in Figure 2 [2]. These are the signals when the crack is scanned normal to its lips. In both cases, they are discontinuous at the crack lips. To measure the crack depth,d, first, the relative magnitude of the discontinuity should be computed as follows: Review of Progress in Quanlitative Nondestructive Evaluation. Vol. 14 Edited by D.O. Thompson and D.E. Chimenti, Plenum Press, New York,

2 AC Current Source Figure 1 Schematic diagram of inducer, probes, current source, detectors and their interconnections for performing SMFM and IACPD techniques. V2 - VI R = --,;;;. ;; VI where VI and VI are the instrument readings when the probe is just before and just after the crack. The dimensionless value of R is then related to the crack depth through an appropriate (the inversion) curve, Figure 3, obtained theoretically for the probe used in the measurement. The validity of the one-dimensional inversion technique described above, rests on the assumptions that (i) the inducer carries a sufficiently high frequency ac current so that the current skin depth in the metal is negligible; (ii) the crack dimensions are much smaller than the product of the metal relative permeability and the current skin depth; (iii) the probe signal contains no parasitic components due to the probe geometry, the crack opening, the edge effect [5], or due to the mechanicalelectrical noise generated in the scanning process; (iv) the crack aspect ratio is large. While conditions (i) - (iii) are frequently met in practice, condition (iv) may undermine the accuracy of the technique in the case of cracks with small aspect ratios. (1) 276

3 -'" ~ t 1.0.~.9 ]0.8 E z 00.7 (a) ' (mm) 2.0 -; t1.s. ~ 11.0 ~ J O''?w 20 20,(mm) x=omm Figure 2 Typical (a) SMFM and IACPO crack signals when a surface crack is scanned normal to its lips [2]. 40 To study the effect of the crack aspect ratio on the accuracy of the one-dimensional interpretation, the theoretical value of R was computed at a set of points along the crack lips for a number of circular-arc cracks. The details of the theoretical model used for the computer simulations are given elsewhere [2]. Figure 3 (a) and show the computed values of R against the local crack depth, d, for a set of 36 mm (2p = 36 mm) long circular-arc cracks with centre line depths (do) ranging from 3 mm to 18 mm. In this figure, R is represented by R. for the SMFM technique and by Ra for the IACPO technique. With reference to Figure 3, it is clear that as the crack aspect ratio increases, the inversion curve (the graph of R versus d) for the circular crack approaches the one-dimensional inversion curve. To demonstrate the region of validity of the one-dimensional model, the measurement errors associated with Figure 3(a) and are plotted in Figure 4(a) and respectively. From this figure, it is found that the error in the depth measurement increases as the aspect ratio is reduced. Also, for a given aspect ratio, the error becomes high when the one-dimensional model uses the readings around the crack ends. TWO-DIMENSIONAL CRACK SIZING As described above, there is a discontinuity in the crack signal when the probe scans the work-piece normal to the crack lips. The relative magnitude of the discontinuity, R, can be utilized for the measurement of the crack depth. For a crack with finite aspect ratio, the crack length affects the distribution of the electromagnetic field around the crack, and hence, the value of R will change with the crack length for the same local crack depth. It is not therefore feasible to base the crack depth measurement solely on the value of R. The problem can be solved by measuring the crack length prior to the depth measurement. The study of SMFM and IACPD crack signals demonstrates that the crack length can be obtained approximately by scanning along the crack lips [2]. Typical crack signals for a crack with 2p =36 mm and do=5 mm are shown in Figure 5. As can be clearly seen in this figure, the SMFM probe produces strong inflections in the signal at the crack ends. In the case of IACPD technique, on the other hand, the magnitude of the crack signal tends to fall rapidly. 277

4 SO ~ T ~------~ 40 b.1smm 1_62mm 14mm b _5_ P.\1""" o20mm d.= 18mm (a) 5 10 IS 20 d (mm) g,:; 150r ~ r ~------~ SO h= tsmm I z:: 62 mm a -24mm b &Smrn p II\1II 6 9 I-D 15 do= 18mm s 10 d (mm) Figure 3 Relative magnitudes of discontinuities in crack signals associated with (a) the SMFM and the IACPD techniques for a set of 36 mm long circular-arc cracks. Dashed lines represent the one-dimensional inversion curves. 278

5 200r-----~----~------~----~----_, (a) ~ ISO ~ SO h & IS mm 1&62mm _24mm b asmm p =limm Dt=20mm -SO sip (%) 200r-----~------~----~ r----, ISO h -ISmm J.61mra a24mm b-smm p = Ilmm b 19""" sip (%) Figure 4 Measurement errors due to the use of one-dimensional inversion curves for the interpretation of relative magnitudes of crack signals shown in Figure 3; (a) SMFM and IACPD. 279

6 When the crack length is detennined, it is possible to adopt the same approach as that described for the one-dimensional inversion method. In fact, following the measurement of the crack length, the crack depth can be obtained in three stages. First, the magnitude of the discontinuity in the crack signal at any arbitrary point along the crack lips is measured. The measured value is then used to compute the value of R. Finally, the crack depth is obtained using an inversion curve relating the values of R to crack depths. This curve is generated theoretically for a particular crack length and a measurement position at the crack lips. From the above discussion, it is concluded that for accurate sizing of cracks with finite aspect ratio, a two-dimensional scan of the work-piece is required. Data corresponding to a close scan parallel to the crack lips is used to measure the crack length and that corresponding to a nonnal scan is employed to find the crack depth. The process requires access to many inversion curves. However, one can use data along the centre line in order to reduce the computing burden for generating excessive inversion curves as well as to increase the accuracy. The study of circular-arc crack signals [6] demonstrates that both the SMFM and IACPD techniques produce the largest discontinuity in their signals when the crack is scanned along its center line (x=o in Figure 1). Also, it is clear from Figure 3 that R. and R. attain their maximum values when the readings along the centre line are used for the inversion. Therefore, the highest resolution and accuracy in the crack depth measurement are achieved for these readings. In this connection, inversion curves for circular-arc cracks of up to 30 mm long associated with two particular SMRv1 and IACPD probes, are shown in Figure 6 (a) and. These probes share the same inducer with a = 8 mm, b = 5 mm, I = 70 mm and h = 10 mm. The separation between the two legs of the IACPD sensor is II = 21 mm, and the distance between the SMFM sensor and the inducer is Ds = 10.5 mm.. ~.9 "" ~ ~0.8.! E z '~ S x (mm) ;. ').S "" W ~1.0 ~ t.~ -; E 00.5 z y=-2 mm x (mm) 30 so Figure 5 Typical (a) SMFM and IACPD crack signals when a circular-arc crack of 36 mm long and of 5 mm depth is scanned parallel to its lips [2]. 280

7 IS0r ~------~ ~ , ha mm anun bas. 0. E (a) 40 IS0r ~~------~ ~------~. " so hll: lomm 1=70mm 11Nn b.5ram Aall.Omm do (nun) Figure 6 (a) SMFM and IACPD inversion curves for sizing circular-arc cracks using SMFM and IACPD probes as specified. 281

8 CONCLUSIONS The two-dimensional sizing methods in the SMFM and IACPD techniques were investigated. In this connection, computer simulations of signals from long cracks and circular-arc cracks were analyzed. It was shown that in general, the discontinuity in the crack signal can be used to determine the crack depth. For long cracks, it is sufficient to use onedimensional inversion curves in order to measure the crack depth. For cracks with finite length, the use of one-dimensional inversion curves leads to erroneous results, specially when readings in the vicinity of the two ends of the crack are used. In this case, twodimensional inversion curves are required with the value of the crack length as a known parameter. In both SMFM and IACPD techniques, the measurement of the crack length is easily performed by conducting a two-dimensional scan of the crack. The signal so obtained involves features from which the two ends of the crack, and hence, the crack length can be obtained. It was also found that for both the SMFM and IACPD techniques, the highest resolution and the least error in depth measurement are achieved when the discontinuity of the signal at the crack center line is used for the measurement of the crack depth. ACKNOWLEDGEMENT This work was supported by the Science and Engineering Research Council, UK. REFERENCES 1. S. H. H. Sadeghi and D. Mirshekar-Syahkal, IEEE Trans. Magn., Vol. 27, p. 674, S. H. H. Sadeghi and D. Mirshekar-Syahkal, IEEE Trans. Magn., Vol. 28, p. 8, S. H. H. Sadeghi and D. Mirshekar-Syahkal, in: Review of Progress in Quantitative Nondestructive Evaluation, D.O. Thompson and D.E. Chimenti (eds.), Vol. lob, p. 2113, R. Collins, W. D. Dover and D. H. Michael, in: Research Techniques in Nondestructive Testing. R. S. Sharpe (ed.), Vol. 8, p. 211, A. H. Kahn, R. Spal and A. Redman, J. of Appl. Phys., Vol. 64(8), p. 3777, S. H. H. Sadeghi and D. Mirshekar-Syahkal, in: Review of Pro~ress in Quantitative Nondestructive Evaluation, D.O. Thompson and D.E. Chimenti (eds.), Vol. loa, p. 269,

A COMBINED ACFM-SMFM SYSTEM FOR REAL-TIME DETECTION AND. S. H. H. Sadeghi and D. Mirshekar-Syahkal

A COMBINED ACFM-SMFM SYSTEM FOR REAL-TIME DETECTION AND SIZING OF SURFACE CRACKS IN METALS S. H. H. Sadeghi and D. Mirshekar-Syahkal Department of Electronic Systems Engineering University of Essex, Colchester