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Rapid estimation of artificial near-side crack dimensions in aluminium using a GMR-based eddy current sensor
NDT&E International 51 (2012) 94–100
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Rapid estimation of artificial near-side crack dimensions in aluminium using a GMR-based eddy current sensor J.H. Espina-Herna´ndez a,n, E. Ramı´rez-Pacheco a, F. Caleyo b, J.A. Pe´rez-Benitez a, J.M. Hallen b a b
´n No Destructiva Electromagne´tica (LENDE), IPN-ESIME-SEPI, UPALM Edif. Z-4, Zacatenco, Me´xico D.F. 07738, Mexico Laboratorio de Evaluacio ´ rgica, IPN-ESIQIE, UPALM Edif. 7, Zacatenco, Me ´xico D.F. 07738, Mexico Departamento de Ingenierı´a Metalu
a r t i c l e i n f o
a b s t r a c t
Article history: Received 13 March 2012 Received in revised form 27 June 2012 Accepted 28 June 2012 Available online 6 July 2012
This paper presents a method for rapid quantification of long artificial cracks using a GMR-based eddy current sensor. The quantification is achieved simultaneously through a proposed phenomenological relationship between the crack’s dimension and two parameters extracted from the GMR output signal. The results show that the proposed method is valid and advantageous when a quick and reliable estimation of the crack’s dimension is necessary. A criterion taking into consideration the filling factor of the excitation coil is proposed in order to improve the system’s sensitivity. & 2012 Elsevier Ltd. All rights reserved.
Keywords: Eddy current NDE GMR sensor Crack Skin depth Aluminium
1. Introduction Eddy current (EC) testing is one of the most known and widely used non-destructive evaluation (NDE) methods of conducting materials. The most common method to detect the presence of defects in conducting materials using EC is indirect, by registering the coil impedance variation due to the interaction between the applied AC magnetic field and the magnetic moment generated by eddy currents. In the case of registering the coil impedance variation due to the presence of a flaw in the material under test, a double detection unit is mandatory in order to register the variations of the in-phase (resistance) and quadrature (reactance) signals of Z. Usually, an LCR metre [1–3] or a dual phase lock-in amplifier [4–6] is used for such a purpose. An extensive discussion of non-destructive techniques based on EC testing can be found in [7]. Solid-state magnetic sensors (AMR, Hall, and GMR) have been introduced in EC systems as an alternative to detection coils, giving better sensitivity to low frequency signals. Solid-state magnetic sensors register the magnitude of the magnetic field rather than its rate of change. Investigation of the magnetic field response from eddy currents using a Hall sensor has been established, where a correlation between the experimental data
n
Corresponding author. Tel./fax: þ 52 55 57296000 54608x54622. E-mail address: [email protected] (J.H. Espina-Herna´ndez).
0963-8695/$ - see front matter & 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.ndteint.2012.06.009
and a model was achieved [8]. A wavelet-based PCA defect classification and quantification method using pulsed eddy currents utilizing a hybrid probe composed of an excitation coil and a Hall sensor reveals the potential of the proposed method [9], although the defect sizing was not achieved with the samples used in the study. Feature extraction techniques for pulsed eddy current NDT including peak value and peak time, spectral characteristics analysis, PCA projection coefficient and response shape curvature has been proposed [10], but the quantitative analysis was missing. One remaining subject that has not been addressed in case of using solid-state magnetic sensors is the difference in their physical layout. In particular, GMR and AMR sensors are formed by multiple elements connected as Wheastone bridge with flux concentrators, which obliges to consider the symmetry between the sensor and the excitation coil. This case is not applied to the Hall sensors. EC systems using GMR sensors have been proposed in the last years due to the high sensitivity and wide frequency response of this type of sensor. An eddy current testing technique in nonmagnetic metals using a GMR sensor and a pancake-type excitation coil was proposed some years ago [11]. The authors proved the advantages of the proposed method using two different hybrid probes, where the high sensitivity of the GMR sensor is exploited by using excitation coils of just a few turns. They introduced GMR sensors as a viable EC testing system, but they did not establish a correlation between the GMR output voltage
´ndez et al. / NDT&E International 51 (2012) 94–100 J.H. Espina-Herna
and the dimension of the defect, which could help in estimating its dimension. Other authors who have used GMR sensors in EC systems aim at improving the sensitivity in the detection of defects. However, the correlation of the GMR output voltage with a set of defects (having different width, depth, and length) was not considered, see for example [12–14]. An EC system to detect and characterize cracks and holes by artificial neural networks, using the same probe configuration proposed in [11], has been recently presented [15]. The GMR sensor was magnetically biased with the use of an AlNiCo permanent magnet, and the system was able to estimate only the width in the crack case and the diameter in the hole case [15]. The authors in [16]proposed a novel design of rotating magnetic field eddy-current probe for non-destructive evaluation of non-ferromagnetic and ferromagnetic tubes in nuclear power plants and they analysed the influence of the geometrical parameters of the excitation coils and GMR sensor arrays in the sensitivity of the probe but not the detectability of the proposed system and the quantification of defects intended to be detected with such probe. Even though EC testing is a well known and established technique in the industry, there are still a lot of efforts to find efficient models in order to estimate the crack’s dimension and also to find the depth profile of narrow cracks [2,3,17]. These models are advantageous over their predecessors but the computational time still poses a constraint when quick estimation of crack dimensions is a necessity. For instance, the rapid computation method proposed in [2] takes approximately 0.2 s per inversion step to obtain EC crack signals. On the other hand, feature extraction and neural network techniques are advantageous in the classification and quantification of defects but their implementation requires a time effort for training the system and there is also a pay-off concerning computational resources. Industry nowadays demands also fast and reliable methods in order to quickly estimate the defect’s dimension. In this context, the authors have shown the possibility to correlate the GMR output voltage with the crack’s dimension by extracting two parameters from the GMR signal. The EC system uses a hybrid probe composed by a GMR sensor and a hand-made pancake coil [18]. In [18], artificial cracks with three different widths (0.5, 1, and 1.4 mm) and depths of 2, 4, 6, and 8 mm were studied and a relationship between the GMR output voltage and the crack’s depth is proposed, taking into consideration the filling factor of the excitation coil [18]. The present paper proposes a phenomenological method based on experimental results to estimate the depth and width of artificial cracks using a wider set of crack’s dimension. The hybrid probe is constructed by exploiting the asymmetry between the GMR sensor and the excitation coil. In the present study, a criterion relating the sensitivity of the EC probe with the coil’s filling factor is presented, which helps defining the relationship between the inner and outer diameters of the excitation coil. A relationship between the crack’s depth and the parameters extracted from the GMR sensor is proposed for the configuration and geometry of the hybrid probe used in the present study.
2. Experimental set-up Fig. 1 shows the block diagram of the experimental set-up for EC measurements. The Agilent 33220A function generator supplies a sinusoidal voltage signal with a selected amplitude and frequency of 860 mVpp and 20 kHz, respectively. This signal is fed into a dual audio amplifier (LM2879T), which supplies a current (Irms) of 780 mA to the excitation coil. The maximum applied magnetic field is 48 mT at the centre of the excitation coil. The depth of penetration in the aluminium (s 34 MS=m) used in this
95
Fig. 1. Block diagram of the experimental set-up.
Table 1 Geometric parameters of the excitation coil. Inside radius Outside radius Length Number of turns Diameter of the wire Lift-off
0.80 mm 2.60 mm 0.36 mm 20 0.18 mm 0.01 mm
study is approximately 0.6 mm for the applied frequency. The EC probe scans the surface of the aluminium plates along the X direction. A PIC16LF876A is used to control the position of the EC probe. The minimum allowable increment of the XY table along the x-axis was 0.16 mm. A custom LabVIEW program registers the data from the Agilent digital multimeter 34410A via GPIB interface. The output voltage of the sensor was amplified (G ¼10) using an instrumentation amplifier (INA118P) and a low-pass filter, which helps extracting the DC component of the signal proportional to the crack. The active low-pass filter has a cut-off frequency of 10 Hz. The GMR sensing axis is along the X direction and perpendicular to the crack length. All cracks were scanned 10 times and the average values and standard deviations of the extracted parameters were obtained in order to correlate the GMR output signal with the width and depth of the artificial cracks. A GMR sensor type AA002-02 manufactured by NVE was used, with an active area about 100 by 200 mm in the middle of the layout [11]. The lift-off of the active area of the GMR sensor is approximately 0.5 mm. The sensor response was measured in the laboratory. The transfer function of the GMR sensor can be found in [18], and its DC sensitivity was found to be 86 mV=mT for a DC voltage of 5.15 V. The sensor is connected to a set of four nickelmetal hydride batteries with a nominal voltage of 1.2 V each. The hand-made excitation coil has two layers of 10 turns each, and it is placed on the GMR sensor. In this way, the excitation coil is closer to the scanned surface. Table 1 gives the geometric parameters of the excitation coil. The GMR sensor is placed slightly off-centre from the excitation coil. Therefore, a magnetic bias is imposed to the GMR sensor without the use of an external source of magnetic field. This configuration is advantageous since it reduces the size and weight of the EC probe. Fig. 2 shows the distribution of the artificial cracks on the three aluminium plates used in this work. Each plate is designed as a family of cracks with the same nominal widths (w), which are 0.6 mm, 1 mm, and 1.4 mm, and having a set of seven cracks with nominal depths (d) of 0.5, 1, 1.5, 2, 4, 6, and 8 mm. The cracks
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were mechanically machined using cardinal cutting disks with the following specifications: 2.5 1/64 1 in (100 teeth), 6 1/ 32 1 in (150 teeth), and 2 3/64 5/8 in (62 teeth). Table A1 – in Appendix A – gives the actual depths and widths of the artificial cracks. They were measured using a Mitutoyo digital slide caliper, model CD-8 CXW, and a Starrett electronic indicator No-3600 series, respectively. Both devices have a scale resolution of 0.01 mm.
3. Results and discussion Fig. 3 shows typical GMR output signals for the three families of cracks when the sensitivity axis of the GMR sensor is perpendicular to the crack length. It can be seen in Fig. 3 that the amplitude of the peaks depends on the crack depth, and that the distance between peaks is larger for smaller depths. It is worth
Fig. 2. Frontal view of the aluminium plates with the cracks’ nominal depths. The crack’s nominal widths were w1 ¼0.6 mm, w2 ¼ 1 mm, and w3 ¼ 1.4 mm in each of the three plates.
0.33
Output Voltage (V)
0.30 Output Voltage (V)
0.33
d = 8 mm d = 6 mm d = 4 mm d = 2 mm d = 1.5 mm d = 1 mm d = 0.5 mm
w1 = 0.6 mm
noting the presence of an intermediate peak in Fig. 3(b) for the crack with a depth of 0.5 mm, and in Fig. 3(c) for the cracks with depths of 0.5, 1, and 1.5 mm. This is related to the asymmetry of the probe. Experiments in the laboratory showed that, for the case of using the crack having w ¼1.4 mm and d ¼2 mm, the intermediate peak started to emerge in the output signal at an excitation frequency of 8 kHz, and is completely visible at an excitation frequency of 5 kHz. The intermediate peak can be considered as a distortion on the GMR output signal, which limits the sensitivity of the proposed configuration for the accurate estimation of the cracks’ dimensions. Therefore, the excitation frequency should be selected according to the dimensions of the cracks intended to be detected and characterized. It can be seen in Fig. 3 that the intermediate peak appears for wider cracks, which could indicate that, if the intention is to detect very thin cracks, the excitation frequency does not have to be higher than 20 kHz for the aluminium material analysed here. This boundary value for the excitation frequency is closely related to the electrical conductivity of the material under analysis. In order to analyse the probe response and correlate it with the crack depth and width, two parameters were defined and their values extracted from the GMR signal. Fig. 4 shows how the voltage difference between peaks (DV) and the difference in position of the peaks (DX) were defined in order to obtain a direct correlation between the GMR signal and the crack dimensions for cases when the crack is scanned with the GMR sensing axis perpendicular to the crack length. DV is defined as the voltage difference between the maximum and minimum values
0.27
0.24
d = 8 mm d = 6 mm d = 4 mm d = 2 mm d = 1.5 mm d = 1 mm d = 0.5 mm
w2 = 1 mm
0.30
0.27
0.24
0.21
0.21 0
2
4 6 Position (mm)
Output Voltage (V)
0.33
8
10
0
2
4 6 Position (mm)
8
10
d = 8 mm d = 6 mm d = 4 mm d = 2 mm d = 1.5 mm d = 1 mm d = 0.5 mm
w3 = 1.4 mm
0.30 0.27 0.24 0.21
0
2
4
6 8 Position (mm)
10
12
Fig. 3. Typical GMR voltage of cracks for the seven nominal depths for each nominal width: (a) w1 ¼0.6 mm, (b) w2 ¼1 mm, and (c) w3 ¼1.4 mm.
´ndez et al. / NDT&E International 51 (2012) 94–100 J.H. Espina-Herna
DX
w1 = 0.6 mm w2 = 1 mm w3 = 1.4 mm
4.5
4.0
0.30
0.27
DXAVE (mm)
Output voltage (V)
0.33
DV
3.5 A 3.0
0.24
2.5
0.21
0 0
4
8 Position (mm)
12
16
Fig. 4. Definition of DV and DX when the crack is scanned with the GMR sensing axis perpendicular to the crack length.
d = 4 mm w1 = 0.6 mm w2 = 1 mm w3 = 1.4 mm
0.33
Output voltage (V)
97
0.30
0.27
0.24
0.21
0
8 4 Position (mm)
12
Fig. 5. GMR output signals for cracks with the same depth (d ¼4 mm) and width of 0.7, 1, and 1.4 mm. The GMR sensing axis is perpendicular to the crack length.
of the output signal, while DX is defined as the difference in position (expressed in mm) between them. Fig. 5 shows the GMR output signal for three cracks with d ¼4 mm, and w¼0.6 mm, 1 mm, and 1.4 mm. The DV parameter of the GMR voltage in Fig. 5 depends on the depth and width of the cracks and this relationship is observed for all of the studied cracks. It can also be seen that the DX parameter is directly proportional to the crack width. According to these results, a correlation between the GMR voltage and the crack dimensions could be proposed by first estimating the crack width and then the depth. 3.1. The DX parameter Fig. 6 shows the DX parameter as a function of crack depth for the three considered crack widths. The dependence of DX as a function of the crack depth is clearly shown: DX is inversely proportional to the crack depth at relatively small crack depths (than 2 mm), and for depth values greater than 2 mm, DX is almost constant. Therefore, two linear zones in each curve can be distinguished where the point for d ¼2 mm represents the limit between the first zone with a finite slope and a second zone with a slope equal to zero. The DX value related to the crack with w2 ¼1 mm and d¼2 mm (point A in Fig. 6) is greater than the respective values for the cracks with nominal depths of 4, 6, and
2
4 d (mm)
6
8
Fig. 6. The parameter DX as a function of the crack depth for the three studied crack widths.
8 mm. From Table A1, the actual width of this crack is 1.02 mm, and for the other three cracks 0.91, 0.92, and 0.93 mm, respectively. The width difference of 0.1 mm between the first crack and the mean value of the other three cracks influences the DX differences for the same nominal width. It is worth noting the good sensitivity of the DX parameter in order to estimate the actual width of the crack. The two linear zones in Fig. 6 should be analysed separately. DX is very sensitive to the crack depth for cracks with depths smaller than 2 mm, which is advantageous for detecting surface cracks in their early stages. The slope (s) of the curves for the cracks with widths of 0.6 and 1 mm are s¼ 0.5 and s¼ 0.4, respectively. The difference between these slope values is 20%, and in order to be able to correlate the slope with the crack depth, a higher excitation frequency should be used. Note in Fig. 3(b) that the signal related to the crack with a depth of 0.5 mm has the intermediate peak. On the other hand, the slope for the cracks with width of 1.4 mm is much bigger, s¼ 0.9, which is also related to the distortion introduced by the presence of the intermediate peak. Note in Fig. 3(c) that the GMR output signals related to these cracks have the intermediate peak. The presence of the intermediate peak plays a negative role on the DX parameter, which means that the excitation frequency should be increased in order to avoid its presence. In the experimental setting used in this work, a maximum excitation frequency of 20 kHz was used due to the restriction imposed by the dual channel audio amplifier. In the second linear zone, for cracks with depths greater than and equal to 2 mm, DX can be considered as constant for a given width. Fig. 7 shows the experimental values of DX and the corresponding linear function. The crack width can be estimated using the linear fit function given in Fig. 7. In this particular case the DX parameter can be used to estimate the crack’s nominal width. The challenge is how to differentiate, for a given width, between the two linear zones. It has been shown that DX follows a different pattern depending on the depth, but in order to really estimate the widths it is necessary to find a method to distinguish between the two zones. This particular issue is treated in an ongoing investigation. 3.2. The DV parameter The DV parameter is associated with the crack depth. Fig. 8 shows the experimental values of the DV parameter as a function of crack depth for each crack width. At relatively low crack depth, DV increases very rapidly with increase of depth for the smaller
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Experimental data Fit function w = 0.9DX - 1.7
1.4
w (mm)
1.2
1.0
0.8
0.6 2.4
2.6
2.8
3.0 DX (mm)
3.2
3.4
3.6
Fig. 7. DX average values and the corresponding linear function for the second linear zone where DX is considered constant.
DV average values (V)
0.15
w1 = 0.6 mm w2 = 1 mm w3 = 1.4 mm
0.12
3.3. Estimation of crack dimensions
0.09
0.06
0.03 0
2
4 d (mm)
6
8
Fig. 8. The DV parameter as a function of the crack depth for the three studied crack widths.
depths, whereas for values greater than 2 mm, the slope of the curves decreases inversely with depth. This behaviour is expected, since the sensitivity of EC systems is related to the depth of penetration. It is worth noting that the probe arrangement proposed herein is able to detect and differentiate cracks with depths greater than the depth of penetration ( 0:58 mm). The experimental values of DV related to the cracks with w3 ¼1.4 mm for the first three depths (0.5, 1, and 1.5 mm) have similar average values than the same depths for the cracks with w2 ¼1.0 mm. This seems to be related to the fact that, for those particular crack dimensions, the intermediate peak is present in the output signal of the GMR sensor (see Fig. 3(c)). Fig. 9 shows the average values of DV and their respective fit functions for cracks with nominal widths of w1 ¼ 0.6 mm, w2 ¼1 mm, and w3 ¼ 1.4 mm. The fit function was found to be DV ¼ mð1f
ad
Þ
ð1Þ
where m is a fitting parameter expressed in volts, f is the filling factor of the excitation coil, and d is the crack’s nominal depth. In order to guarantee the proper cancellation of the physical units, a ¼ 1 mm1 has been introduced as a dummy constant. The coil filling factor is defined as [19] f¼
dout din din þ dout
where dout and din are the outer and inner coil diameters, respectively. For the excitation coil used in this study, f¼0.533. Eq. (1) was obtained empirically, taking into consideration that one parameter should be related to the coil’s physical dimensions. The advantage of having a relationship like Eq. (1) is the possibility to estimate very quickly the crack’s depth. Fig. 9 shows that (1) fits well the three families of experimental values of DV. By analysing the influence of the coil’s physical dimensions on the sensitivity of the system, the filling factor must follow the condition f r 0:5 in order to obtain the maximum sensitivity for a given geometry, according to the application. This condition imposes the obligation that the coil should be built taking into consideration that dout r3din , a criterion that helps optimize the coil design in order to achieve the best possible sensitivity. Fig. 10 shows the dependence of the fitting parameter m as obtained from the curves presented in Fig. 9 as a function of the crack’s nominal width. It is interesting to note the linear relationship of this parameter with the crack’s nominal width. Therefore, using the fitting parameter m in conjunction with DX can help estimate the crack depth.
ð2Þ
It has been shown previously that the DX parameter can be used to estimate the crack width. At present, due to the distortion introduced by the presence of the intermediate peak in the signal related to the cracks with nominal width of 1.4 mm and depths smaller than 2 mm, it is not possible to give a clear relationship between the crack width and DX. The first linear zone in Fig. 6 should be analysed in detail in order to determine if the slopes of the three curves can be used to estimate the crack width. It was shown in the results presented in Fig. 7, that for cracks with depths greater than or equal to 2 mm, the DX values are almost constant for the three studied families of cracks. Once the crack width is known, the process for estimating the crack depth is straightforward. The DV parameter follows (1), having the filling factor of the excitation coil and a fitting parameter m, which is related to the crack width. Having this in mind, the estimation of the crack depth – once the width is known – goes through the following steps: 1. obtaining the fitting parameter m, using the linear relationship presented in Fig. 10, and 2. having m and the extracted DV parameter from the GMR output signal, the crack depth can be estimated. Eq. (3) is the inverse function of Eq. (1), which helps to obtain the depth of the crack. In this case, the modulus is introduced in the natural logarithm in order to avoid a negative value for the case of cracks with depths equal to 8 mm. In this case, a crack with a depth of 8 mm can be considered as the limit of detection of the system: 1 DV d¼ ln 1 ð3Þ ln f m This procedure is intended to estimate the crack dimension without knowing it a priori. Note that (3) is based on the filling factor of the excitation coil, DV is extracted directly from the GMR output signal, and m can be estimated through its linear relationship with DX. 4. Conclusions A method to quickly estimate the crack’s dimension in aluminium has been proposed based on two extracted parameters from
´ndez et al. / NDT&E International 51 (2012) 94–100 J.H. Espina-Herna
w2 = 1 mm Experimental data Fit function
0.12 DVAVE (V)
0.10 DVAVE (V)
0.14
w1 = 0.6 mm Experimental data Fit function
0.12
0.08 0.06
a = 0.117 f = 0.533
0.04
R2 = 0.993 chi2 = 6.3 x 10-6
99
0.10 0.08 a = 0.127 f = 0.533 R2 = 0.993 chi2 = 7.4 x 10-6
0.06 0.04 0.02
0.02 0
2
4 d (mm)
6
0
2
4 d (mm)
6
8
w3 = 1.4 mm Experimental data Fit function
0.14 0.12 DVAVE (V)
8
0.10 0.08 a = 0.138 f = 0.533 R2 = 0.997 chi2 = 3.4 x 10-6
0.06 0.04 0.02 0
2
4 d (mm)
6
8
Fig. 9. DV average values as a function of the crack depth with their corresponding fit functions for cracks with nominal widths of (a) 0.6 mm, (b) 1 mm, and (c) 1.4 mm.
m Fit Function m = 0.026w + 0.101
0.140 0.135
m (V)
0.130 0.125 0.120 0.115 0.6
0.8
1.0 w (mm)
1.2
1.4
Fig. 10. The fitting parameter m as a function of the crack’s nominal width.
the GMR output voltage. The extracted parameters (DX and DV) from the GMR output signal were analysed. Both parameters depend on the crack depth and width, but DX is more sensitive to the width, whereas DV is more sensitive to the depth. The DX parameter has a double linear behaviour depending on the crack depth. It decreases linearly for cracks smaller than 2 mm, and its value remains almost constant for cracks equal to and greater than 2 mm. This behaviour poses a difficulty in the estimation of the crack width. An empirical function relating the DV parameter and the crack depth is proposed. This function is related to the filling factor of the excitation coil and a fitting parameter, which was found to be linear to the DX parameter for cracks with depths greater than and equal to 2 mm. This expression seems to be general for all depths, but experimental data from defects with
depths smaller than 0.5 mm should be used to validate it. To the knowledge of the authors, there is no evidence that such a function is proposed for the case of using hybrid probes composed of an excitation coil and a GMR sensor. A criterion is proposed, based upon the physical dimensions of the excitation coil, that helps increase the detection sensitivity of the system. The intermediate peak distorts the GMR output signal, and affects the DX and DV parameters extracted from the same signal. In this case, a possible solution is to reduce the depth of penetration of the applied magnetic field. Nonetheless, there will always be a certain crack dimension at which the GMR output signal will present such a distortion, thus imposing the limit of sensitivity on the detection system. The hybrid probe used here is constructed by placing the centres of the coil and the GMR sensor asymmetrically. This relative asymmetry sets the magnetic operation point of the GMR sensor without the need of using a permanent magnet, which is advantageous in the probe design. The study and analysis of cracks with varying orientation with respect to the sensitivity axis of the GMR sensor should be performed in order to generalize the results. The proposed method gives a very small number of parameters for the estimation of cracks’ dimensions, which could be advantageous for real-time applications. Besides, the results presented in this experimental study could help to develop a model in order to study a wider range of cracks’ dimension with different orientations. It is worth noting that these results are valid for the given geometry of the excitation coil used in this study, and they are not applied to other coil shapes like the double-D coil when is used together with a GMR sensor.
Acknowledgements This research was financially supported by Instituto Polite´cnico Nacional (SIP-20110953, SIP-20101027, and ESIQIE-CIDIM). E.R.-P.
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Table A1 Actual crack dimensions related to the nominal widths (w1, w2, w3) and depths (d1, d2, d3, d4, d5, d6, d7). All values are given in mm with their respective standard deviation. Crack
w1
w2
w3
d1 ¼ 0.5 w d2 ¼ 1.0 w d3 ¼ 1.5 w d4 ¼ 2.0 w d5 ¼ 4.0 w d6 ¼ 6.0 w d7 ¼ 8.0 w
0.56 70.02 0.50 70.02 1.02 70.02 0.53 70.02 1.51 7 0.02 0.53 70.03 2.18 7 0.02 0.53 70.02 3.56 7 0.02 0.53 70.03 6.08 70.02 0.55 70.02 7.40 70.02 0.56 70.03
0.537 0.02 1.067 0.02 1.067 0.02 1.007 0.03 1.557 0.02 1.017 0.05 1.967 0.02 1.027 0.05 4.017 0.02 0.917 0.03 5.567 0.02 0.927 0.04 7.647 0.02 0.937 0.04
0.49 70.02 1.38 7 0.06 1.02 70.02 1.33 7 0.02 1.49 7 0.02 1.37 7 0.05 1.95 7 0.02 1.29 7 0.04 4.04 70.02 1.29 7 0.02 6.17 7 0.02 1.28 7 0.02 7.68 7 0.02 1.31 7 0.03
thanks CONACYT-Me´xico and PIFI-IPN for the scholarships. The authors appreciate the recommendations and suggestions from the reviewers and the subject editor.
Appendix A. Actual dimensions of the artificial cracks See Table A1. References [1] Peng Xu, Songling Huang, Wei Zhao. A new differential eddy current testing sensor used for detecting crak extension direction. NDT&E Int 2011;44(4): 339–43. [2] Theodoulidis T, Poulakis N, Dragogias A. Rapid computation of eddy current signals from narrow cracks. NDT&E Int 2010;43(1):13–9. [3] Theodoulidis T. Developments in efficiently modelling eddy current testing of narrow cracks. NDT&E Int 2010;43(7):591–8.
[4] Pattabiraman M, Nagendran R, Janawadkar MP. Rapid flaw depth estimation from SQUID-based eddy current nondestructive evaluation. NDT&E Int 2007;40(4):289–93. [5] Yamada H, Hasegawa T, Ishihara Y, Kiwa T, Tsukuda K. Difference in the detection limits of flaws in the depths of multi-layered and continuous aluminium plates using low-frequency eddy current testing. NDT&E Int 2008;41(2):108–11. [6] Yusa N, Sakai Y, Hashizume H. An eddy current probe suitable to gain information about the depth of near-side flaws much deeper than the depth of penetration. NDT&E Int 2011;44(1):121–30. [7] Garcı´a-Martı´n J, Go´mez-Gil J, Va´zquez-Sa´nchez E. Non-destructive techniques based on eddy current testing. Sensors 2011;11(3):2525–65. [8] Simm A, Theodoulidis T, Poulakis N, Tian GY. Investigation of the magnetic field response from eddy current inspection of defects. Int J Adv Manuf Technol 2011;54(1–4):223–30. [9] Tian GY, Sophian A, Taylor D, Rudlin J. Wavelet-based PCA defect classification and quantification for pulsed eddy current NDT. IEE Proc Sci Meas Technol 2005;152:141–8. [10] Zhou D, Tian GY, Zhang B, Morozov M, Wang H. Optimal features combination for pulsed eddy current NDT. Nondestr Test Eval 2010;25:133–43. [11] Dogaru T, Smith ST. Giant magnetoresistance-based eddy-current sensor. IEEE Trans Magn 2001;37(5):3831–8. [12] Jen-Tzong Jeng, Guan-Shiun Lee, Wen-Chu Liao, Chia-Lun Shu. Depthresolved eddy-current detection with GMR magnetometer. J Magn Magn Mater 2006;304(1):e470–3. [13] Nair NV, Malpudi VR, Jimenez HR, Liu X, Deng Y, Zeng Z, et al. A GMR-based eddy current system for NDE of aircraft structures. IEEE Trans Magn 2006;42(10):3312–4. [14] Cacciola M, Megali M, Pllicano´ D, Morabito FC. A GMR-ECT based embedded solution for applications on PCB inspections. Sensors Actuators A: Phys 2011;167(1):25–33. [15] Postolache O, Geirinhas Ramos H, Lopes Ribeiro A. Detection and characterization of defects using GMR probes and artificial neural networks. Comput Stand Interfaces 2011;33(2):191–200. [16] Xin J, Lei N, Udpa L, Udpa SS. Nondestructive inspection using rotating magnetic field eddy-current probe. IEEE Trans Magn 2011;47(5):1070–3. [17] Theodoulidis T, Haitao Wang, Tian GY. Extension of a model for eddy current inspection of cracks to pulsed excitations. NDT&E Int 2012;47(4):144–9. [18] Ramı´rez-Pacheco E, Espina-Herna´ndez JH, Caleyo F, Hallen JM. Defect detection in aluminium with an eddy currents sensor. In: CERMA 2010 proceeedings of 2010 IEEE conference on electronics, robotics and automotive mechanics. Washington, DC, USA: IEEE Computer Society; Washington. p. 765–70. [19] Mohan SS, del Mar Hershenson M, Boyd SP, Lee TH. Simple accurate expression for planar spiral inductance. IEEE J Solid-State Circuits 1999;34(10): 1419–24.
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NDT&E International journal homepage: www.elsevier.com/locate/ndteint
Rapid estimation of artificial near-side crack dimensions in aluminium using a GMR-based eddy current sensor J.H. Espina-Herna´ndez a,n, E. Ramı´rez-Pacheco a, F. Caleyo b, J.A. Pe´rez-Benitez a, J.M. Hallen b a b
´n No Destructiva Electromagne´tica (LENDE), IPN-ESIME-SEPI, UPALM Edif. Z-4, Zacatenco, Me´xico D.F. 07738, Mexico Laboratorio de Evaluacio ´ rgica, IPN-ESIQIE, UPALM Edif. 7, Zacatenco, Me ´xico D.F. 07738, Mexico Departamento de Ingenierı´a Metalu
a r t i c l e i n f o
a b s t r a c t
Article history: Received 13 March 2012 Received in revised form 27 June 2012 Accepted 28 June 2012 Available online 6 July 2012
This paper presents a method for rapid quantification of long artificial cracks using a GMR-based eddy current sensor. The quantification is achieved simultaneously through a proposed phenomenological relationship between the crack’s dimension and two parameters extracted from the GMR output signal. The results show that the proposed method is valid and advantageous when a quick and reliable estimation of the crack’s dimension is necessary. A criterion taking into consideration the filling factor of the excitation coil is proposed in order to improve the system’s sensitivity. & 2012 Elsevier Ltd. All rights reserved.
Keywords: Eddy current NDE GMR sensor Crack Skin depth Aluminium
1. Introduction Eddy current (EC) testing is one of the most known and widely used non-destructive evaluation (NDE) methods of conducting materials. The most common method to detect the presence of defects in conducting materials using EC is indirect, by registering the coil impedance variation due to the interaction between the applied AC magnetic field and the magnetic moment generated by eddy currents. In the case of registering the coil impedance variation due to the presence of a flaw in the material under test, a double detection unit is mandatory in order to register the variations of the in-phase (resistance) and quadrature (reactance) signals of Z. Usually, an LCR metre [1–3] or a dual phase lock-in amplifier [4–6] is used for such a purpose. An extensive discussion of non-destructive techniques based on EC testing can be found in [7]. Solid-state magnetic sensors (AMR, Hall, and GMR) have been introduced in EC systems as an alternative to detection coils, giving better sensitivity to low frequency signals. Solid-state magnetic sensors register the magnitude of the magnetic field rather than its rate of change. Investigation of the magnetic field response from eddy currents using a Hall sensor has been established, where a correlation between the experimental data
n
Corresponding author. Tel./fax: þ 52 55 57296000 54608x54622. E-mail address: [email protected] (J.H. Espina-Herna´ndez).
0963-8695/$ - see front matter & 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.ndteint.2012.06.009
and a model was achieved [8]. A wavelet-based PCA defect classification and quantification method using pulsed eddy currents utilizing a hybrid probe composed of an excitation coil and a Hall sensor reveals the potential of the proposed method [9], although the defect sizing was not achieved with the samples used in the study. Feature extraction techniques for pulsed eddy current NDT including peak value and peak time, spectral characteristics analysis, PCA projection coefficient and response shape curvature has been proposed [10], but the quantitative analysis was missing. One remaining subject that has not been addressed in case of using solid-state magnetic sensors is the difference in their physical layout. In particular, GMR and AMR sensors are formed by multiple elements connected as Wheastone bridge with flux concentrators, which obliges to consider the symmetry between the sensor and the excitation coil. This case is not applied to the Hall sensors. EC systems using GMR sensors have been proposed in the last years due to the high sensitivity and wide frequency response of this type of sensor. An eddy current testing technique in nonmagnetic metals using a GMR sensor and a pancake-type excitation coil was proposed some years ago [11]. The authors proved the advantages of the proposed method using two different hybrid probes, where the high sensitivity of the GMR sensor is exploited by using excitation coils of just a few turns. They introduced GMR sensors as a viable EC testing system, but they did not establish a correlation between the GMR output voltage
´ndez et al. / NDT&E International 51 (2012) 94–100 J.H. Espina-Herna
and the dimension of the defect, which could help in estimating its dimension. Other authors who have used GMR sensors in EC systems aim at improving the sensitivity in the detection of defects. However, the correlation of the GMR output voltage with a set of defects (having different width, depth, and length) was not considered, see for example [12–14]. An EC system to detect and characterize cracks and holes by artificial neural networks, using the same probe configuration proposed in [11], has been recently presented [15]. The GMR sensor was magnetically biased with the use of an AlNiCo permanent magnet, and the system was able to estimate only the width in the crack case and the diameter in the hole case [15]. The authors in [16]proposed a novel design of rotating magnetic field eddy-current probe for non-destructive evaluation of non-ferromagnetic and ferromagnetic tubes in nuclear power plants and they analysed the influence of the geometrical parameters of the excitation coils and GMR sensor arrays in the sensitivity of the probe but not the detectability of the proposed system and the quantification of defects intended to be detected with such probe. Even though EC testing is a well known and established technique in the industry, there are still a lot of efforts to find efficient models in order to estimate the crack’s dimension and also to find the depth profile of narrow cracks [2,3,17]. These models are advantageous over their predecessors but the computational time still poses a constraint when quick estimation of crack dimensions is a necessity. For instance, the rapid computation method proposed in [2] takes approximately 0.2 s per inversion step to obtain EC crack signals. On the other hand, feature extraction and neural network techniques are advantageous in the classification and quantification of defects but their implementation requires a time effort for training the system and there is also a pay-off concerning computational resources. Industry nowadays demands also fast and reliable methods in order to quickly estimate the defect’s dimension. In this context, the authors have shown the possibility to correlate the GMR output voltage with the crack’s dimension by extracting two parameters from the GMR signal. The EC system uses a hybrid probe composed by a GMR sensor and a hand-made pancake coil [18]. In [18], artificial cracks with three different widths (0.5, 1, and 1.4 mm) and depths of 2, 4, 6, and 8 mm were studied and a relationship between the GMR output voltage and the crack’s depth is proposed, taking into consideration the filling factor of the excitation coil [18]. The present paper proposes a phenomenological method based on experimental results to estimate the depth and width of artificial cracks using a wider set of crack’s dimension. The hybrid probe is constructed by exploiting the asymmetry between the GMR sensor and the excitation coil. In the present study, a criterion relating the sensitivity of the EC probe with the coil’s filling factor is presented, which helps defining the relationship between the inner and outer diameters of the excitation coil. A relationship between the crack’s depth and the parameters extracted from the GMR sensor is proposed for the configuration and geometry of the hybrid probe used in the present study.
2. Experimental set-up Fig. 1 shows the block diagram of the experimental set-up for EC measurements. The Agilent 33220A function generator supplies a sinusoidal voltage signal with a selected amplitude and frequency of 860 mVpp and 20 kHz, respectively. This signal is fed into a dual audio amplifier (LM2879T), which supplies a current (Irms) of 780 mA to the excitation coil. The maximum applied magnetic field is 48 mT at the centre of the excitation coil. The depth of penetration in the aluminium (s 34 MS=m) used in this
95
Fig. 1. Block diagram of the experimental set-up.
Table 1 Geometric parameters of the excitation coil. Inside radius Outside radius Length Number of turns Diameter of the wire Lift-off
0.80 mm 2.60 mm 0.36 mm 20 0.18 mm 0.01 mm
study is approximately 0.6 mm for the applied frequency. The EC probe scans the surface of the aluminium plates along the X direction. A PIC16LF876A is used to control the position of the EC probe. The minimum allowable increment of the XY table along the x-axis was 0.16 mm. A custom LabVIEW program registers the data from the Agilent digital multimeter 34410A via GPIB interface. The output voltage of the sensor was amplified (G ¼10) using an instrumentation amplifier (INA118P) and a low-pass filter, which helps extracting the DC component of the signal proportional to the crack. The active low-pass filter has a cut-off frequency of 10 Hz. The GMR sensing axis is along the X direction and perpendicular to the crack length. All cracks were scanned 10 times and the average values and standard deviations of the extracted parameters were obtained in order to correlate the GMR output signal with the width and depth of the artificial cracks. A GMR sensor type AA002-02 manufactured by NVE was used, with an active area about 100 by 200 mm in the middle of the layout [11]. The lift-off of the active area of the GMR sensor is approximately 0.5 mm. The sensor response was measured in the laboratory. The transfer function of the GMR sensor can be found in [18], and its DC sensitivity was found to be 86 mV=mT for a DC voltage of 5.15 V. The sensor is connected to a set of four nickelmetal hydride batteries with a nominal voltage of 1.2 V each. The hand-made excitation coil has two layers of 10 turns each, and it is placed on the GMR sensor. In this way, the excitation coil is closer to the scanned surface. Table 1 gives the geometric parameters of the excitation coil. The GMR sensor is placed slightly off-centre from the excitation coil. Therefore, a magnetic bias is imposed to the GMR sensor without the use of an external source of magnetic field. This configuration is advantageous since it reduces the size and weight of the EC probe. Fig. 2 shows the distribution of the artificial cracks on the three aluminium plates used in this work. Each plate is designed as a family of cracks with the same nominal widths (w), which are 0.6 mm, 1 mm, and 1.4 mm, and having a set of seven cracks with nominal depths (d) of 0.5, 1, 1.5, 2, 4, 6, and 8 mm. The cracks
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were mechanically machined using cardinal cutting disks with the following specifications: 2.5 1/64 1 in (100 teeth), 6 1/ 32 1 in (150 teeth), and 2 3/64 5/8 in (62 teeth). Table A1 – in Appendix A – gives the actual depths and widths of the artificial cracks. They were measured using a Mitutoyo digital slide caliper, model CD-8 CXW, and a Starrett electronic indicator No-3600 series, respectively. Both devices have a scale resolution of 0.01 mm.
3. Results and discussion Fig. 3 shows typical GMR output signals for the three families of cracks when the sensitivity axis of the GMR sensor is perpendicular to the crack length. It can be seen in Fig. 3 that the amplitude of the peaks depends on the crack depth, and that the distance between peaks is larger for smaller depths. It is worth
Fig. 2. Frontal view of the aluminium plates with the cracks’ nominal depths. The crack’s nominal widths were w1 ¼0.6 mm, w2 ¼ 1 mm, and w3 ¼ 1.4 mm in each of the three plates.
0.33
Output Voltage (V)
0.30 Output Voltage (V)
0.33
d = 8 mm d = 6 mm d = 4 mm d = 2 mm d = 1.5 mm d = 1 mm d = 0.5 mm
w1 = 0.6 mm
noting the presence of an intermediate peak in Fig. 3(b) for the crack with a depth of 0.5 mm, and in Fig. 3(c) for the cracks with depths of 0.5, 1, and 1.5 mm. This is related to the asymmetry of the probe. Experiments in the laboratory showed that, for the case of using the crack having w ¼1.4 mm and d ¼2 mm, the intermediate peak started to emerge in the output signal at an excitation frequency of 8 kHz, and is completely visible at an excitation frequency of 5 kHz. The intermediate peak can be considered as a distortion on the GMR output signal, which limits the sensitivity of the proposed configuration for the accurate estimation of the cracks’ dimensions. Therefore, the excitation frequency should be selected according to the dimensions of the cracks intended to be detected and characterized. It can be seen in Fig. 3 that the intermediate peak appears for wider cracks, which could indicate that, if the intention is to detect very thin cracks, the excitation frequency does not have to be higher than 20 kHz for the aluminium material analysed here. This boundary value for the excitation frequency is closely related to the electrical conductivity of the material under analysis. In order to analyse the probe response and correlate it with the crack depth and width, two parameters were defined and their values extracted from the GMR signal. Fig. 4 shows how the voltage difference between peaks (DV) and the difference in position of the peaks (DX) were defined in order to obtain a direct correlation between the GMR signal and the crack dimensions for cases when the crack is scanned with the GMR sensing axis perpendicular to the crack length. DV is defined as the voltage difference between the maximum and minimum values
0.27
0.24
d = 8 mm d = 6 mm d = 4 mm d = 2 mm d = 1.5 mm d = 1 mm d = 0.5 mm
w2 = 1 mm
0.30
0.27
0.24
0.21
0.21 0
2
4 6 Position (mm)
Output Voltage (V)
0.33
8
10
0
2
4 6 Position (mm)
8
10
d = 8 mm d = 6 mm d = 4 mm d = 2 mm d = 1.5 mm d = 1 mm d = 0.5 mm
w3 = 1.4 mm
0.30 0.27 0.24 0.21
0
2
4
6 8 Position (mm)
10
12
Fig. 3. Typical GMR voltage of cracks for the seven nominal depths for each nominal width: (a) w1 ¼0.6 mm, (b) w2 ¼1 mm, and (c) w3 ¼1.4 mm.
´ndez et al. / NDT&E International 51 (2012) 94–100 J.H. Espina-Herna
DX
w1 = 0.6 mm w2 = 1 mm w3 = 1.4 mm
4.5
4.0
0.30
0.27
DXAVE (mm)
Output voltage (V)
0.33
DV
3.5 A 3.0
0.24
2.5
0.21
0 0
4
8 Position (mm)
12
16
Fig. 4. Definition of DV and DX when the crack is scanned with the GMR sensing axis perpendicular to the crack length.
d = 4 mm w1 = 0.6 mm w2 = 1 mm w3 = 1.4 mm
0.33
Output voltage (V)
97
0.30
0.27
0.24
0.21
0
8 4 Position (mm)
12
Fig. 5. GMR output signals for cracks with the same depth (d ¼4 mm) and width of 0.7, 1, and 1.4 mm. The GMR sensing axis is perpendicular to the crack length.
of the output signal, while DX is defined as the difference in position (expressed in mm) between them. Fig. 5 shows the GMR output signal for three cracks with d ¼4 mm, and w¼0.6 mm, 1 mm, and 1.4 mm. The DV parameter of the GMR voltage in Fig. 5 depends on the depth and width of the cracks and this relationship is observed for all of the studied cracks. It can also be seen that the DX parameter is directly proportional to the crack width. According to these results, a correlation between the GMR voltage and the crack dimensions could be proposed by first estimating the crack width and then the depth. 3.1. The DX parameter Fig. 6 shows the DX parameter as a function of crack depth for the three considered crack widths. The dependence of DX as a function of the crack depth is clearly shown: DX is inversely proportional to the crack depth at relatively small crack depths (than 2 mm), and for depth values greater than 2 mm, DX is almost constant. Therefore, two linear zones in each curve can be distinguished where the point for d ¼2 mm represents the limit between the first zone with a finite slope and a second zone with a slope equal to zero. The DX value related to the crack with w2 ¼1 mm and d¼2 mm (point A in Fig. 6) is greater than the respective values for the cracks with nominal depths of 4, 6, and
2
4 d (mm)
6
8
Fig. 6. The parameter DX as a function of the crack depth for the three studied crack widths.
8 mm. From Table A1, the actual width of this crack is 1.02 mm, and for the other three cracks 0.91, 0.92, and 0.93 mm, respectively. The width difference of 0.1 mm between the first crack and the mean value of the other three cracks influences the DX differences for the same nominal width. It is worth noting the good sensitivity of the DX parameter in order to estimate the actual width of the crack. The two linear zones in Fig. 6 should be analysed separately. DX is very sensitive to the crack depth for cracks with depths smaller than 2 mm, which is advantageous for detecting surface cracks in their early stages. The slope (s) of the curves for the cracks with widths of 0.6 and 1 mm are s¼ 0.5 and s¼ 0.4, respectively. The difference between these slope values is 20%, and in order to be able to correlate the slope with the crack depth, a higher excitation frequency should be used. Note in Fig. 3(b) that the signal related to the crack with a depth of 0.5 mm has the intermediate peak. On the other hand, the slope for the cracks with width of 1.4 mm is much bigger, s¼ 0.9, which is also related to the distortion introduced by the presence of the intermediate peak. Note in Fig. 3(c) that the GMR output signals related to these cracks have the intermediate peak. The presence of the intermediate peak plays a negative role on the DX parameter, which means that the excitation frequency should be increased in order to avoid its presence. In the experimental setting used in this work, a maximum excitation frequency of 20 kHz was used due to the restriction imposed by the dual channel audio amplifier. In the second linear zone, for cracks with depths greater than and equal to 2 mm, DX can be considered as constant for a given width. Fig. 7 shows the experimental values of DX and the corresponding linear function. The crack width can be estimated using the linear fit function given in Fig. 7. In this particular case the DX parameter can be used to estimate the crack’s nominal width. The challenge is how to differentiate, for a given width, between the two linear zones. It has been shown that DX follows a different pattern depending on the depth, but in order to really estimate the widths it is necessary to find a method to distinguish between the two zones. This particular issue is treated in an ongoing investigation. 3.2. The DV parameter The DV parameter is associated with the crack depth. Fig. 8 shows the experimental values of the DV parameter as a function of crack depth for each crack width. At relatively low crack depth, DV increases very rapidly with increase of depth for the smaller
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Experimental data Fit function w = 0.9DX - 1.7
1.4
w (mm)
1.2
1.0
0.8
0.6 2.4
2.6
2.8
3.0 DX (mm)
3.2
3.4
3.6
Fig. 7. DX average values and the corresponding linear function for the second linear zone where DX is considered constant.
DV average values (V)
0.15
w1 = 0.6 mm w2 = 1 mm w3 = 1.4 mm
0.12
3.3. Estimation of crack dimensions
0.09
0.06
0.03 0
2
4 d (mm)
6
8
Fig. 8. The DV parameter as a function of the crack depth for the three studied crack widths.
depths, whereas for values greater than 2 mm, the slope of the curves decreases inversely with depth. This behaviour is expected, since the sensitivity of EC systems is related to the depth of penetration. It is worth noting that the probe arrangement proposed herein is able to detect and differentiate cracks with depths greater than the depth of penetration ( 0:58 mm). The experimental values of DV related to the cracks with w3 ¼1.4 mm for the first three depths (0.5, 1, and 1.5 mm) have similar average values than the same depths for the cracks with w2 ¼1.0 mm. This seems to be related to the fact that, for those particular crack dimensions, the intermediate peak is present in the output signal of the GMR sensor (see Fig. 3(c)). Fig. 9 shows the average values of DV and their respective fit functions for cracks with nominal widths of w1 ¼ 0.6 mm, w2 ¼1 mm, and w3 ¼ 1.4 mm. The fit function was found to be DV ¼ mð1f
ad
Þ
ð1Þ
where m is a fitting parameter expressed in volts, f is the filling factor of the excitation coil, and d is the crack’s nominal depth. In order to guarantee the proper cancellation of the physical units, a ¼ 1 mm1 has been introduced as a dummy constant. The coil filling factor is defined as [19] f¼
dout din din þ dout
where dout and din are the outer and inner coil diameters, respectively. For the excitation coil used in this study, f¼0.533. Eq. (1) was obtained empirically, taking into consideration that one parameter should be related to the coil’s physical dimensions. The advantage of having a relationship like Eq. (1) is the possibility to estimate very quickly the crack’s depth. Fig. 9 shows that (1) fits well the three families of experimental values of DV. By analysing the influence of the coil’s physical dimensions on the sensitivity of the system, the filling factor must follow the condition f r 0:5 in order to obtain the maximum sensitivity for a given geometry, according to the application. This condition imposes the obligation that the coil should be built taking into consideration that dout r3din , a criterion that helps optimize the coil design in order to achieve the best possible sensitivity. Fig. 10 shows the dependence of the fitting parameter m as obtained from the curves presented in Fig. 9 as a function of the crack’s nominal width. It is interesting to note the linear relationship of this parameter with the crack’s nominal width. Therefore, using the fitting parameter m in conjunction with DX can help estimate the crack depth.
ð2Þ
It has been shown previously that the DX parameter can be used to estimate the crack width. At present, due to the distortion introduced by the presence of the intermediate peak in the signal related to the cracks with nominal width of 1.4 mm and depths smaller than 2 mm, it is not possible to give a clear relationship between the crack width and DX. The first linear zone in Fig. 6 should be analysed in detail in order to determine if the slopes of the three curves can be used to estimate the crack width. It was shown in the results presented in Fig. 7, that for cracks with depths greater than or equal to 2 mm, the DX values are almost constant for the three studied families of cracks. Once the crack width is known, the process for estimating the crack depth is straightforward. The DV parameter follows (1), having the filling factor of the excitation coil and a fitting parameter m, which is related to the crack width. Having this in mind, the estimation of the crack depth – once the width is known – goes through the following steps: 1. obtaining the fitting parameter m, using the linear relationship presented in Fig. 10, and 2. having m and the extracted DV parameter from the GMR output signal, the crack depth can be estimated. Eq. (3) is the inverse function of Eq. (1), which helps to obtain the depth of the crack. In this case, the modulus is introduced in the natural logarithm in order to avoid a negative value for the case of cracks with depths equal to 8 mm. In this case, a crack with a depth of 8 mm can be considered as the limit of detection of the system: 1 DV d¼ ln 1 ð3Þ ln f m This procedure is intended to estimate the crack dimension without knowing it a priori. Note that (3) is based on the filling factor of the excitation coil, DV is extracted directly from the GMR output signal, and m can be estimated through its linear relationship with DX. 4. Conclusions A method to quickly estimate the crack’s dimension in aluminium has been proposed based on two extracted parameters from
´ndez et al. / NDT&E International 51 (2012) 94–100 J.H. Espina-Herna
w2 = 1 mm Experimental data Fit function
0.12 DVAVE (V)
0.10 DVAVE (V)
0.14
w1 = 0.6 mm Experimental data Fit function
0.12
0.08 0.06
a = 0.117 f = 0.533
0.04
R2 = 0.993 chi2 = 6.3 x 10-6
99
0.10 0.08 a = 0.127 f = 0.533 R2 = 0.993 chi2 = 7.4 x 10-6
0.06 0.04 0.02
0.02 0
2
4 d (mm)
6
0
2
4 d (mm)
6
8
w3 = 1.4 mm Experimental data Fit function
0.14 0.12 DVAVE (V)
8
0.10 0.08 a = 0.138 f = 0.533 R2 = 0.997 chi2 = 3.4 x 10-6
0.06 0.04 0.02 0
2
4 d (mm)
6
8
Fig. 9. DV average values as a function of the crack depth with their corresponding fit functions for cracks with nominal widths of (a) 0.6 mm, (b) 1 mm, and (c) 1.4 mm.
m Fit Function m = 0.026w + 0.101
0.140 0.135
m (V)
0.130 0.125 0.120 0.115 0.6
0.8
1.0 w (mm)
1.2
1.4
Fig. 10. The fitting parameter m as a function of the crack’s nominal width.
the GMR output voltage. The extracted parameters (DX and DV) from the GMR output signal were analysed. Both parameters depend on the crack depth and width, but DX is more sensitive to the width, whereas DV is more sensitive to the depth. The DX parameter has a double linear behaviour depending on the crack depth. It decreases linearly for cracks smaller than 2 mm, and its value remains almost constant for cracks equal to and greater than 2 mm. This behaviour poses a difficulty in the estimation of the crack width. An empirical function relating the DV parameter and the crack depth is proposed. This function is related to the filling factor of the excitation coil and a fitting parameter, which was found to be linear to the DX parameter for cracks with depths greater than and equal to 2 mm. This expression seems to be general for all depths, but experimental data from defects with
depths smaller than 0.5 mm should be used to validate it. To the knowledge of the authors, there is no evidence that such a function is proposed for the case of using hybrid probes composed of an excitation coil and a GMR sensor. A criterion is proposed, based upon the physical dimensions of the excitation coil, that helps increase the detection sensitivity of the system. The intermediate peak distorts the GMR output signal, and affects the DX and DV parameters extracted from the same signal. In this case, a possible solution is to reduce the depth of penetration of the applied magnetic field. Nonetheless, there will always be a certain crack dimension at which the GMR output signal will present such a distortion, thus imposing the limit of sensitivity on the detection system. The hybrid probe used here is constructed by placing the centres of the coil and the GMR sensor asymmetrically. This relative asymmetry sets the magnetic operation point of the GMR sensor without the need of using a permanent magnet, which is advantageous in the probe design. The study and analysis of cracks with varying orientation with respect to the sensitivity axis of the GMR sensor should be performed in order to generalize the results. The proposed method gives a very small number of parameters for the estimation of cracks’ dimensions, which could be advantageous for real-time applications. Besides, the results presented in this experimental study could help to develop a model in order to study a wider range of cracks’ dimension with different orientations. It is worth noting that these results are valid for the given geometry of the excitation coil used in this study, and they are not applied to other coil shapes like the double-D coil when is used together with a GMR sensor.
Acknowledgements This research was financially supported by Instituto Polite´cnico Nacional (SIP-20110953, SIP-20101027, and ESIQIE-CIDIM). E.R.-P.
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Table A1 Actual crack dimensions related to the nominal widths (w1, w2, w3) and depths (d1, d2, d3, d4, d5, d6, d7). All values are given in mm with their respective standard deviation. Crack
w1
w2
w3
d1 ¼ 0.5 w d2 ¼ 1.0 w d3 ¼ 1.5 w d4 ¼ 2.0 w d5 ¼ 4.0 w d6 ¼ 6.0 w d7 ¼ 8.0 w
0.56 70.02 0.50 70.02 1.02 70.02 0.53 70.02 1.51 7 0.02 0.53 70.03 2.18 7 0.02 0.53 70.02 3.56 7 0.02 0.53 70.03 6.08 70.02 0.55 70.02 7.40 70.02 0.56 70.03
0.537 0.02 1.067 0.02 1.067 0.02 1.007 0.03 1.557 0.02 1.017 0.05 1.967 0.02 1.027 0.05 4.017 0.02 0.917 0.03 5.567 0.02 0.927 0.04 7.647 0.02 0.937 0.04
0.49 70.02 1.38 7 0.06 1.02 70.02 1.33 7 0.02 1.49 7 0.02 1.37 7 0.05 1.95 7 0.02 1.29 7 0.04 4.04 70.02 1.29 7 0.02 6.17 7 0.02 1.28 7 0.02 7.68 7 0.02 1.31 7 0.03
thanks CONACYT-Me´xico and PIFI-IPN for the scholarships. The authors appreciate the recommendations and suggestions from the reviewers and the subject editor.
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