Hall sensor array based validation of estimation of crack size in metals using magnetic dipole models

NDT&E International 53 (2013) 18–25

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Hall sensor array based validation of estimation of crack size in metals using magnetic dipole models Minhhuy Le a, Jinyi Lee b,n, Jongwoo Jun c, Jungmin Kim a, Sangman Moh d, Kisu Shin e a

Department of Control and Instrumentation Engineering, Graduate School of Chosun University, Gwangju 501-759, Korea Department of Control, Instrumentation and Robotics Engineering, Chosun University, Gwangju 501-759, Korea c Research Center for Real Time NDT, Chosun University, Gwangju 501-759, Korea d Department of Computer Engineering, Chosun University, Gwangju 501-759, Korea e Department of Weapon Systems, Korea National Defense University, Seoul 412–706, Republic of Korea b

a r t i c l e i n f o

a b s t r a c t

Article history: Received 25 October 2011 Received in revised form 12 July 2012 Accepted 30 August 2012 Available online 7 September 2012

Nondestructive evaluation (NDE) is an important methodology for quantifying cracks in engineering structures. In this paper, we propose a dipole model method (DMM) for NDE. The method is used to simulate an alternating magnetic field around a crack on a paramagnetic metal specimen and to estimate the shape and volume of the crack. This method enables faster and simpler evaluation of crack size than the traditional analytical methods. The DMM performance was verified by comparing the simulation results with the experimental results obtained using an AC-type magnetic camera. & 2012 Elsevier Ltd. All rights reserved.

Keywords: NDE Crack Eddy current Dipole model FEM Magnetic camera

1. Introduction Nondestructive evaluation (NDE) methodology is a very important for inspecting, locating and obtaining quantitative information (size, shape and volume) on defects in heavy industries such as aircraft and automobile manufacturing, power generation and railways. Among the NDE methodologies, are widely used techniques such as ultrasonic testing, radiographic testing, magnetic flux leakage testing (MFLT), eddy current testing (ECT), magnetic particle inspection, and penetrant testing. ECT [1–3] is widely used in the inspection of cracks in paramagnetic metals such as aluminum, titanium and copper and is known to be fast, safe and implementation-friendly method. He et al. [4] proposed a pulsed eddy current (PEC) method for detecting

Abbreviations: NDE, Nondestructive evaluation; DMM, Dipole model method; FEM, Finite element method; MFLT, Magnetic flux leakage testing; ECT, Eddy current testing; PEC, Pulsed eddy current; ECP, Electric current perturbation; ACFM, Alternating current field measurement; GMR, Giant magneto-resistive; ETREE, Extended truncated region eigenfunction expansion; MOI, Magneto-optical eddy current imager; STIC, Sheet-type induced current; RMS, Root-mean-square; HPF, High-pass filter; 1/n RN, Noise reduction algorithm n Corresponding author at: Chosun University Department of Control, Instrumentation and Robotics Engineering, 375 Seosuk-dong, Dong-gu Gwangju 501-759, Republic of Korea. Tel.: þ 82 62 230 7101; fax: þ82 62 230 6858. E-mail address: [email protected] (J. Lee). 0963-8695/$ - see front matter & 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.ndteint.2012.08.012

hidden defects using a rectangular excitation coil and a cylindrical detection coil. Burkhardt et al. [5] proposed an electric current perturbation (ECP) method for detecting and characterizing defects. In this method, differential coil sensors and excitation coil axes are oriented perpendicularly, which reduces lift-off sensitivity, noise and the operating frequency. Rowshandel et al. [6] proposed a method for detecting cracks in track rails using an alternating current field measurement (ACFM) sensor and a scanning robot. The sensor probe precisely scans the rail head with the help of the scanning robot and thereby measures the crack surface length and angle. These are all examples of effective crack detection and evaluation using ECT techniques. These methods use a coil as a detection sensor whose size could not be too small for making an area high spatial resolution sensor. Tian et al. [7,8] proposed PEC methods using small detection sensors those are a giant magneto-resistive (GMR) and a Hall element sensor. However, these methods use a single detection sensor and scan the entire surface of the specimen which can be time-consuming. Magneto-optical sensors that can detect large areas have been used in magneto-optical imaging (MOI) system [9,10]. However, it is difficult to use these sensors to quantify and evaluate cracks because the sensors display the magnetic intensity in black and white color image that is 1 bit of resolution. To overcome these drawbacks, the authors have developed a magnetic camera that comprises sheet-type induced current (STIC) and

M. Le et al. / NDT&E International 53 (2013) 18–25

Nomenclature RMS data using in 1/n RN algorithm [V] DRMS G amplifier gain constant [dB] KH Hall constant [V (A mT)  1] IH Hall input current [A] BRMS RMS magnetic intensity [T] VH Hall output voltage [V] V RMS RMS of Hall output voltage [V] DV RMS  differential RMS of Hall output voltage [V] DV RMS total integrated square value of DV RMS in an area [V] Q optimized function used to find optimum value of magnetic charge factor [V4] mRMS RMS of magnetic charge [Wb/m2]

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magnetic charge factor depends on shape of crack [Wb/m2] x0 maximum magnetic charge factor [Wb/m2] a angle between the tangential line of the profile of a crack. [deg.] b angle between the eddy current and X-axis [1] d skin depth [m] f operating frequency [Hz] m absolute permeability [ ] s electrical conductivity [S/m] F crack profile function [m] ðx0 ,y0 ,z0 Þ location of magnetic charge [m] lc ,wc ,dc length, width and depth of crack [m] Lp peak-to-peak distance (two peaks at crack tips) [m]

x

arrayed Hall sensors [11]. The STIC is able to induce a large area of uniform eddy current in a specimen. The Hall element sensors were arrayed in a 2-D plane with high spatial resolution that can detect cracks at high speed. Several theoretical analyses have also been conducted over the years such as finite element method (FEM) [12–15], analytical modeling of PEC based on time-harmonic problems [16,17], and extended truncated region eigenfunction expansion (ETREE) [18]. These methods produce results that are in have good agreement with the experimental results. However, these methods employ complex equations that lead to long simulation times. We have proposed a dipole model method (DMM) to simulate an alternating magnetic field based on MOI [19]. This method uses simple equations that enable rapid calculations. In this research, we extend the DMM for AC-type magnetic camera, which can model the 3-D distribution of an alternating magnetic field around a crack, and then characterize the crack. A good agreement between the simulation results and experimental results was obtained.

2. AC-type magnetic camera Fig. 1(a) shows the AC-type magnetic camera on an aluminum specimen used in the experiment [11]. The Hall sensor array matrix is arrayed as 1024 Hall sensors (32  32), with an effective area of 24:96  24:96 mm2 and a spatial resolution of 0.78 mm. The STIC consists of two coils, two cores and a copper sheet. When an alternating current is applied to the coils, a current is induced in the copper sheet. If the copper sheet is placed on a specimen, an STIC will be induced in the specimen and distorted due to a crack. This STIC will induce an alternating magnetic field into the normal surface of the Hall sensor array matrix that can be measured. A block diagram of the AC-type magnetic camera is shown in Fig. 1(b). The Hall sensor array matrix obtains an alternating magnetic field from the specimen and converts it to a Hall voltage signal matrix by Eq. (1). The Hall voltages are processed by amplifiers, high-pass-filters (HPFs), root-mean-square (RMS) circuits, a processor and a computer software (Eq. (2)). In addition, the differential voltages of consecutive Hall sensors are used and displayed in the software, as expressed by Eq. (3). Although the HPF was used to reduce noise, there was still noise and unwanted data in the image, as shown in Fig. 2(b). Therefore we integrated the 1/n RN algorithm (Fig. 2(a)) into the software, which obtains the RMS of all the data elements, DRMS . All data elements in the interval [DRMS =n, DRMS =n] will then be initialized to zero, and the other data elements will be cut by the 7DRMS =n value. By using 1/n RN, the image became more clear. as shown in Fig. 2(c)

Fig. 1. AC-type magnetic camera (a) and its block diagram (b).

(here, n¼2). V H ¼ K H IH Bz

ð1Þ

V RMS ¼ GK H IH BRMS

ð2Þ

DV RMS ¼ V RMS ði,j þ1ÞV RMS ði,jÞ

ð3Þ

Here, G, K H , IH and BRMS are the amplifier gain constant, Hall constant, Hall input current and RMS magnetic intensity, respectively (Table 2).

3. Principles of DMM with different crack shapes When an eddy current flow approaches a crack, it will circulate around the tips and the bottom of the crack [19]. In the DMM, the magnetic charge dipoles are assumed to occur along the path of the eddy current flows, which means that they occur on the

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M. Le et al. / NDT&E International 53 (2013) 18–25

Fig. 2. Image processing of AC-type magnetic camera: 1/n RN algorithm (a), image of DV RMS before (b) and after (c) deleting unwanted data and using 1/2 RN.

Fig. 3. Complex-shaped crack. (a) 3D view, (b) section view.

surface and walls of the crack. Thus, the distribution of magnetic charges differs according to the shape of the crack and the direction of the eddy current. Positive and negative magnetic charges occur on the right- and left-hand side of the eddy current, respectively. In addition, the magnetic charges on the walls of the crack are complicated, given that they depend on the shape of the crack. However, the distribution of magnetic charges on the surface of the crack can be expressed by an equation. We suggest that the profile of the crack is a function z0 ¼ Fðy0 Þ, as shown in Fig. 3. Thus, the RMS magnetic charge at point ðy0 ,z0 Þ on the profile surface of the crack can be described by Eq. (4). 0

mRMS ¼ xez =d sinacosb tana sina ¼ pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 þ tan2 a tana ¼ F 0 ðy0 Þ

ðz0 o0Þ

cosb ¼ +ðeddycurrent, XaxisÞ 1

d ¼ pffiffiffiffiffiffiffiffiffiffiffiffi

pf ms

ð4Þ

Here d,f , m, s are the skin depth, frequency of the alternating magnetic field, absolute permeability, and electrical conductivity of the specimen, respectively, where a is the angle between the tangential line at point ðy0 ,z0 Þ of the profile and the y-axis, b is the angle between the eddy current and x-axis, and F 0 is the

differential of function F at point y0 , which is known as the angular coefficient of the tangential line. And, x is a magnetic charge factor that is positive or negative according to the position of point ðy0 ,z0 Þ on the right- or left-hand side of the eddy current flow. In this paper, we present some simple crack shapes: rectangular, triangular, elliptical and stepped, as shown in Fig. 4. The distribution of the magnetic charge factor on the walls of each crack (in the y-axis) is indicated in the each graph. 3.1. Rectangular crack Fig. 4(a) shows the dipole model of the rectangular crack (wc  lc  dc ), the coordinate system and the distribution of the magnetic charge factor. The magnetic charge factor is uniform on the two crack tips, and varies linearly along the two crack walls at distance dc from the tips [19]. The RMS magnetic charge at point ðy0 ,z0 Þ on these surfaces can be calculated by Eq. (5), where xR ðy0 Þ, xL ðy0 Þ and xð 7 lc = 2Þ are the magnetic charge factors on the rightand left-hand side of the wall and at the tips of the crack, respectively. 0

mRMS ¼ xðy0 Þez =d y0 lc =2 þdc xR ðy0 Þ ¼ þ x0 dc

M. Le et al. / NDT&E International 53 (2013) 18–25

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Fig. 4. Dipole model and distribution of magnetic charge factor: (a) rectangular crack, (b) triangle crack, (c) elliptical crack and (d) stepped crack.

The RMS magnetic field at point ðx,y,zÞ (out-of-specimen) can be calculated by Eq. (8).

y0 lc =2 þ dc dc xð 7lc =2Þ ¼ 8 x0

xL ðy0 Þ ¼ x0

ð5Þ

BRMS ¼ x0

i¼0

The RMS magnetic field at point ðx,y,zÞ (out-of-specimen) can be calculated by Eq. (6) [19]. BRMS ¼ x0

Z 1 X ð1Þi i¼0

4p

wc =2 wc =2

1 X 1 X

1 þ x0 4pdc j¼0i¼0 Z

dc

0

dc

Z

þ x0

0

ez =d ðzz0 Þ fðxx0 Þ2 þ ðy þ ð1Þi lc =2Þ2 þ ðzz0 Þ2 g

3=2

dz0 dx0

4p

wc =2

wc =2

Z 1 X 1 X sina 4plc j¼0i¼0

Z

0 dc

0

n

ez =d ðzz0 Þ lc 0 ðxx0 Þ2 þ ðy þ ð1Þi ð2d z þ l2c ÞÞ2 þ ðzz0 Þ2 c

0 ð1Þj lc =2

Z

0

o3=2 dz dx

0

0 ð1Þj ð2dc =lc y0 þ dc Þ

ez =d ðzz0 Þð1Þj 2y0 0

 j

ð1Þ ðlc =2dc Þ

3=2

fðx þ ð1Þi wc =2Þ2 þ ðyy0 Þ2 þ ðzz0 Þ2 g

dz0 dy0

ð8Þ

ð1Þj lc =2

ez =d ðzz0 Þðð1Þj y0 lc =2 þ dc Þ

0



Z

Z 1 X ð1Þi

0

3=2

fðx þ ð1Þi wc =2Þ2 þ ðyy0 Þ2 þ ðzz0 Þ2 g

dz0 dy0

ð6Þ 3.3. Elliptical crack

3.2. Triangular crack Fig. 4(b) shows the dipole model of the triangular crack, the coordinate system and the distribution of the magnetic charge factor. The magnetic charge factor is uniform on the two side surfaces and varies linearly along the two walls of the crack. Thus, the RMS magnetic charge at point ðy0 ,z0 Þ on these surfaces can be calculated by Eq. (7), where xw ðy0 Þ and xð 7 lc =2Þ are the magnetic charge factors on the wall and at the tips of the crack, respectively. 0

Fig. 4(c) shows the dipole model of the elliptical crack, the coordinate system and the distribution of the magnetic charge factor. The magnetic charge factor is constant on the elliptical surface and varies linearly along the two walls of the crack. Thus, the RMS magnetic charge at point ðy0 ,z0 Þ on these surfaces can be calculated by Eq. (9), where xw ðy0 Þ and xs ðy0 Þ are the magnetic charge factors on the wall and the elliptical surface of the crack, respectively. 0

mRMS ¼ xðy0 Þez =d sina 0

tana ¼

2dc y lc z

mRMS ¼ xðy0 Þez =d sina qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 sina ¼ dc = dc þ ðlc =2Þ2

tana sina ¼ pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 þtan2 a

2y0 lc xð 7lc =2Þ ¼ 8 x0

xw ðy0 Þ ¼ 7 x0

xw ðy0 Þ ¼ 7 x0

ð7Þ

xs ðy0 Þ ¼ x0

2y0 lc ð9Þ

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M. Le et al. / NDT&E International 53 (2013) 18–25

The RMS magnetic field at point ðx,y,zÞ (out-of-specimen) can be calculated by Eq. (10). BRMS ¼ x0

Z 1 X ð1Þi i¼0

þ

4p

wc =2

Z

wc =2

0 dc

ez=d ðzz0 Þ dz0 dx0 qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 3=2 1ðz0 =dc Þ2 Þ2 þðzz0 Þ2 g

fðxx0 Þ2 þðy þð1Þi lc=2

Table 1 Size of each crack.

Z 0 Z 0 1 X 1 X 1 pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi j p l 4 c ð1Þ lc =2 ð1Þj dc 1ð2y0 =lc Þ2 j¼0i¼0 ez =d ðzz0 Þð1Þj 2y0 sina 0

n

0

ðx þ ð1Þi wc =2Þ2 þ ðyy0 Þ2 þ ðzz0 Þ2

o3=2 dz dy

0

Stepped cracks can be considered to be a combination of rectangular and triangular cracks. Thus, we can still apply the above theories for these types of cracks. The distribution of the magnetic charge factor is shown in Fig. 4(d).

4.1. Experiment setup and simulation parameters Fig. 5 and Table 1 show the shape and size of the cracks with section views of the rectangular, triangular, elliptical and stepped shapes used in this paper. In the experiment, the cracks were machined at the center of each specimen of aluminum alloy (Al7075) using an electrical discharge machining. The vertical magnetic field intensity is obtained by using the dipole model and then processed in the same manner as in the case of the AC-type magnetic camera. The simulation software was designed by using a Visual Basic 6.0 and a 3-D tool (CW3DGraph 6.0 of Measurement Studio by National Instruments Co.). We integrated some real-world parameters into the software, as shown in Table 2 [19]. The magnetic charge factor x0 needs to be determined with certainty. It can be observed that x0 has a linear relationship with the vertical magnetic field intensity and its value can be obtained by comparing the integrated square of the experimental data with the simulated data (DV RMS total in Eq. (11)). By establishing an optimized function Q (Eq. (12)) which includes data for each crack at each frequency and finding its mimimum value, x0 can be obtained. M X N  X

DV RMS ði,jÞ

2

Length [mm]

Width [mm]

Depth [mm]

Crack angle[deg.]

Volume [mm3]

1 2 3 4 5 6 7 8 9 10

10 10 10 10 10 10 10 10 10 10

0.7 0.7 0.7 0.5 0.5 0.7 0.7 0.7 0.7 0.9

1 2 3 1.5 and 3 1.5 and 3 1 2 3 3 3

90 90 90 90 90 11.3 21.8 30.96 61.9 61.9

7 14 21 11.25 11.25 3.5 7 10.5 16.485 21.195

Table 2 Relation between real condition and simulated parameters.

4. Simulated results and experimental results



Crack no.

ð10Þ

3.4. Stepped cracks

DV RMS total ¼

From the experimental results of the AC-type magnetic camera with the 10 crack sizes specified in Table 1 and the operating parameters in Table 2, we obtain a curve of optimized function Q

Real conditions

Simulated parameters

Values in the paper

Properties of specimen material Lift-off Frequency Hall constant Hall input current Amplifier Spatial resolution of the Hall sensor matrix

Absolute permeability ðmÞ Electrical conductivity ðsÞ z f KH IH G Meshing size of the software

1.2566  10  6 H/m 3.5461  107 S/m 1 mm 5, 10, 20 kHz 1.5 V (A mT)  1 10 mA 103.6 (72 dB) 0.78 mm

ð11Þ

i¼1j¼1

Q¼

X X 

Exp 2  Sim 2 2  DV RMS total

DV RMS total

FreqsCracks

¼

X X 

Exp 2

DV RMS total

2

x0 :P2

2 ð12Þ

FreqsCracks

Here, P is a function of G, KH, IH and integral part of BRMS . M  N is the size of the selected data area (here, 28  28).

Fig. 6. Finding optimized magnetic charge factor by finding minimum optimized function.

Fig. 5. Section view shape of cracks.

M. Le et al. / NDT&E International 53 (2013) 18–25

with magnetic charge factor x0 , as shown in Fig. 6. The optimized magnetic charge factor x0 ¼ 0:0716 Wb/m2.

5. Results and discussion Figs. 7 and 8 show the DV RMS images and section views in the experimental and simulated results at 10 kHz, respectively. The images of the cracks are clear and show good agreement between the simulated and experimental results. The group colored regions in Fig. 7 and the peak values in Fig. 8 appear at the two tips of the cracks because the high eddy current concentration there. Observing the images in Fig. 7, we can distinguish the crack shapes. The rectangular crack appears as two colored group regions balanced at each of the two tips (Nos. 1, 2 and 3). In the images of the stepped crack, these groups are not balanced because of the different depths (Nos. 4 and 5). A large group appears at the center of the triangle crack with a smaller groups at each tip of the crack (Nos. 6, 7 and 8). In the case of the elliptical crack, two groups in the middle are close and connected to each other (Nos. 9 and 10). Furthermore, both the size of the middle colored group in Fig. 7 and the peak values in Fig. 8 differ according to the crack size. In the case of the rectangular (Nos. 1, 2 and 3) and triangular (Nos. 6, 7 and 8) cracks, they increase with the crack depth. In the case of the elliptical cracks (Nos. 9 and 10), they increase with the crack width. Fig. 9(a) and (b) show the relation of the peak-to-peak distance Lp with the crack-angle which is the angle between the specimen

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surface and the tip-side along the crack depth direction [11]. The Lp value (length) in both the experimental and simulated results ranges from 10.4 mm to12.3 mm and increases with the crackangle. In addition, the coefficient angles of the interpolate lines are similar. However, in the experimental result, the coefficient angle exhibits greater variation with respect to frequency than in the simulated result. By using Lp , we can estimate the crack-angle and subsequently the crack shape. Fig. 9(c) and (d) show the relation of the crack volume with the integrated square of DV RMS obtained by Eq. (11) in the experimental and simulated results. This value is proportional to the crack volume. However, in the experimental result, it exhibits greater variation with respect to frequency than in the simulation result. Therefore, the crack volume can be estimated by using this integrated square value. Because of the skin effect, the current density decreases more rapidly when the frequency is higher. Consequently, the effect of the crack depth is less pronounced at higher frequency. Therefore, the Lp value and the integrated square of DV RMS are lower at higher frequencies, as shown in Fig. 9. In addition, all the crack shapes described in this paper are highly dependent on the crack depths. At high frequency, a shallow part of a crack (in the depth direction) has a large effect that is equivalent to the effect of a shallow crack depth. Thus, the crack shape has a small effect at high frequency, indicating that the difference in the measured data between cracks is smaller. Therefore, the data in both the experimental and simulated results in Fig. 9(c) and (d) fit better at a higher operating frequency.

Fig. 7. (a) Experimental and (b) simulated results at 10 kHz.

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M. Le et al. / NDT&E International 53 (2013) 18–25

Fig. 8. Section view of DV RMS QUOTE images located on the center line of each crack in the experimental (a) and simulated (b) results.

Fig. 9. Relation of the peak-to-peak distance (Lp) with the crack-angle, and integrated square values of DV RMS QUOTE with the crack volume in the experimental (a), (c) and simulated (b), (d) results.

6. Conclusions This paper proposed a simulation method using a dipole model for eddy currents in quantitative nondestructive evaluation. This

method was used to obtain the magnetic field distribution around a crack, and was based on modeling the results obtained with an AC-type magnetic camera. Further, it uses simple equations that reduce calculation time and memory. Moreover, real-world

M. Le et al. / NDT&E International 53 (2013) 18–25

parameters can be integrated into the method. Several types of cracks with different section views of rectangular, triangular, elliptical, and stepped shape were used to verify the capability of the method. A good agreement between the simulated and experimental results was obtained. In addition, the crack shapes could be observed in both the experimental and simulated images. The crack shape indicated by the angle between the specimen surface and the tip-side along the crack depth direction, could be estimated quantitatively by the peak-to-peak distance, Lp . Furthermore, the crack volume could be estimated by the integrated square of DV RMS , which has a linear fitting relationship.

Acknowledgment This work was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (No. 20110030110). Also this research was supported by the MKE (The Ministry of Knowledge Economy), Korea, under the ITRC (Information Technology Research Centre) support program supervised by the NIPA (National IT Industry Promotion Agency) (NIPA-2012H0310-12-2008). We are grateful for the support. References [1] Lee J, Jun J, Kim J, Lee Jaesun. An application of a magnetic camera for an NDT system for aging aircraft. J Korean Soc Nondestr Test 2010;30(3):212–24. [2] Kosmas K, Sargentis C, Tsamakis D, Hristoforou E. Non-destructive evaluation of magnetic metallic materials using Hall Sensors. J Mater Technol 2005;161: 359–92.

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