Keywords

1 Introduction

Aluminum and alloy tubes are widely used in power generation, transportation, construction, automobile and aerospace industries due to the advantage of good corrosion resistance, high thermal conductivity, light weight and high strength [1,2,3]. However, most of aluminum tubes suffer from severe environments, such as corrosive medium, time-varying thermal stress and heavy load stress. The longitudinal stress corrosion cracking (SCC) and fatigue corrosion cracking (FCC) are easily appeared and extended in both inner and outer surfaces of the aluminum tube. The SCC and FCC grow and gather rapidly as the complex stress and corrosion, which brings potential security problems [4, 5].

Thus the nondestructive testing (NDT) techniques should be carried out to inspect the crack and evaluate the condition of the aluminum tube regularly [6, 7]. However, in most case the costs of time and NDT operations are expensive using two techniques or multiple scans to test both inner and outer surface of the aluminum tube respectively during the in-service time. Thus it is of prime significance to propose an effective NDT method to detect both inner and outer cracks in a one pass scan.

The magnetic flux leakage (MFL) testing method is usually employed to detect inner and outer defects in the ferromagnetic tube, such as the well-known pipeline pigs. Because there is little leaked magnetic field in the aluminum material, the MFL technique cannot be used for the aluminum tube [8]. In the same way, the conventional magnetic particle (MP) testing method is inapplicable for the aluminum tube. The penetrant testing (PT) is suitable for the surface SCC and FCC. But these coatings and attachments on the aluminum tube should be cleaned deeply, which is time-consuming and difficult in the on-site environment. Besides, the PT is hard to detect the inner-wall crack. The radiographic testing (RT) can identify both surface and subsurface cracks clearly. However, the RT is harmful to human body, which is forbidden in many industrial fields. The ultrasonic testing (UT) is not an effective method for thin surface defects, especially the inner cracks. What’s more, the UT needs coupling agent along with the probe. It is also a challenge to identify both inner and outer cracks using the UT in the aluminum tube [9].

Because of the non-ferromagnetic and high-conductive of the aluminum material, the current field perturbation NDT technique are excellent methods for the detection of surface cracks [10,11,12]. The conventional eddy current testing (ET), alternating current field measurement (ACFM), alternating current potential drop (ACPD) technique methods all belong to the current field perturbation NDT technique. When the surface cracks are present in the aluminum tube, the current field will turns obviously around the surface crack. Especially, the excitation frequency can be composited as multiple signals to penetrate different depth of the conductive material [13]. Bernieri, et al. proposed the multi-frequency ET for the detection and characterization of defects on conductive materials [14]. The frequency of the excitation signal is from direct current (DC) to dozens of MHz [15, 16]. He, Gao, Tian, Li, et al. combined the eddy current field and the thermography technique to identify sub-surface cracks [17,18,19,20]. Ge, et al., given the optimal time-domain feature for detection of non-surface crack using the pulsed ACFM technique [21]. Fan, Tian, et al., proposed the pulsed ET method to test subsurface defects and the wall thickness [22,23,24]. The pulse excitation signal gives more information about defects in frequency domain and time domain. However, these methods cannot distinguish and evaluate both inner and outer cracks effectively on the whole 360° cambered surface in a one pass scan. In our previous work, we proposed the CCFT system to measure outer cracks in pipeline using the external coaxial excitation coil [25]. As the high excitation frequency, the induced current gathers in the thin outer surface of the pipeline, which cannot penetrate the thick wall of the pipe. As a result, the inner-wall cracks cannot be inspected by the high frequency CCFT system. What’s more, due to the corner joints and flanges, the external coaxial excitation coil is not suitable for the inspection of aluminum tubes in service time. The bobbin-type coil ET is a good ways to pass through the aluminum tube for the measurement of the inner defects in many piping systems [26]. In the industrial field, detection and evaluation both inner and outer cracks are heavy works in the long and large number of aluminum tubes [27]. It is significant to inspect all inner and outer surface cracks in the aluminum tube in real time by one scan.

In this paper, all inner and outer cracks in the aluminum tube are inspected by the double frequency CCFT method in a one pass scan. The circumferential current field is induced by a coaxial bobbin coil excited by the double frequency excitation signal which is composed of a low frequency component and a high frequency component. The induced circumferential current field can penetrate the wall of the aluminum tube due to the low frequency component. Meanwhile, it gathers in a skin layer in the inner wall due to the high frequency component. When the crack is present in the inner or outer surface, the circumferential current field turns around at the ends and the bottom of the crack resulting in the distorted space magnetic field which is measured by the multiple magnetic sensor arrays. All inner and outer cracks in the 360° cambered surface can be inspected by the double frequency CCFT method in a one pass scan.

The rest of the paper is organized as follows. Firstly, the FEM model of the double frequency CCFT is present to analyze the distorted electromagnetic field around the crack in Sect. 2. The probe and system of CCFT are developed in Sect. 3. The inner and outer cracks are identified, distinguished and evaluated by the double frequency CCFT system in Sect. 4. Finally, the conclusion and future work are drawn in Sect. 5.

2 Finite Element Method Model

2.1 Simulation Model

As shown in Fig. 1, the FEM model of CCFT probe is set up. In the FEM model, the bobbin coil is set as the excitation module which is coaxial with the aluminum tube. Two longitudinal cracks are produced axially (X direction) on the inner and outer surface of the aluminum tube. The depth of the longitudinal crack is in the radial direction (Y direction). The dimensions of the bobbin coil, aluminum tube and cracks are given in Table 1.

Fig. 1
A F E M model displays the cut section of the C C F T system. It consists of an aluminum tube, an outer crack, and an inner crack. The bubble coil inside the structure is along the X-Y direction.

FEM model of CCFT (Cutaway view)

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Table 1 Dimensions of EFM model
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The bobbin coil is made up of 300 turns copper wires. The excitation signal is loaded on the bobbin coil with the frequency \(f\). In the FEM model, the low and high frequency excitation signals are proposed to inspect the outer and inner cracks respectively. The bobbin coil induces the uniform circumferential current field in the aluminum tube. The penetration depth of the induced circumferential current field is given by skin effect Eq. (1).

$$\delta = \left( {{1 \mathord{\left/ {\vphantom {1 {\pi u_{{\text{r}}} u_{0} \gamma f}}} \right. \kern-0pt} {\pi u_{{\text{r}}} u_{0} \gamma f}}} \right)^{{{1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-0pt} 2}}}$$
(1)

where \(\delta\) is the skin depth, \(u_{{\text{r}}}\) is the relative magnetic permeability, \(u_{0}\) is the vacuum permeability, \(\gamma\) is the conductivity of the aluminium tube.

The parameters of the model are given in Table 2. It has been proven that 2–3 mm is the optimized skin depth to test the surface crack in the aluminum specimen. Thus the 1000 Hz is set as the high frequency component of the excitation signal [28]. To penetrate the wall thickness (9 mm) of the aluminum tube, the 80 Hz is set as the low frequency component of the excitation signal.

Table 2 Parameters of EFM model
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2.2 High Frequency Excitation Signal

In the FEM model, the frequency of the excitation signal is 1000 Hz and the amplitude of the excitation current field is 50 mA. Due to the skin effect, the penetration depth of the induced current field is 2.59 mm. Thus induced current field cannot be affected by the outer crack. As shown in Fig. 2a, the vector field of the induced circumferential current is extracted around the inner crack in the aluminum tube. When the current field is far from the inner crack, the current vector is uniform in the circumferential direction. Due to the material discontinuity of the inner crack, the circumferential current field is perpendicular to the longitudinal crack. The circumferential current turns clockwise at one end of the inner crack and turns counterclockwise at the other end of the inner crack. The current density around the inner crack is shown in Fig. 2b. There are two obvious peaks at the ends of the inner crack. Meanwhile, the current density decreases in the depth direction of the inner crack.

Fig. 2
2 parts. A. A schematic depicts the inner wall of the aluminum tube. The two downward arrows denote the clockwise and anti-clockwise current fields. The tube has an inner longitudinal crack along the X and Y directions. B. A contour plot of current density versus offset angle and X directions. It has two peaks of 2 amperes per square meter at negative 20 and 20 meters. Values are estimated.

Perturbation of the induced circumferential current field caused by the inner crack under the excitation frequency of 1000 Hz. a Vector current field (Internal view inside the aluminium tube). b Current density (Offset angle means the degree in the circumferential direction)

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The perturbation current field makes the space magnetic field distorted. The decrease of the current density produces a trough in the axial magnetic field (Bx). The opposite deflecting direction of the current field produces positive and negative peaks in the radial magnetic field (Bz). In practice, the lift-off of the bobbin coil (distance between the bobbin coil and the inner-wall of the aluminum tube) should be small to improve the current density. Thus the magnetic sensors can be set in the bobbin coil to pick up the distorted space magnetic field.

According to the Lenz's Law, the distortion of outer magnetic field is opposite to the magnetic field in the bobbin coil. Thus the distorted magnetic field around the inner crack can be measured by magnetic sensors in the bobbin coil. The space magnetic field is extracted below the bobbin coil at the lift-off of 5 mm (the distance between the inner wall and the magnetic sensor is 5 mm in radial direction). As shown in Fig. 3a, the Bx is normalized by the detection sensitivity Eq. (2):

$${{SBx = \left( {Bx - Bx_{0} } \right)} \mathord{\left/ {\vphantom {{SBx = \left( {Bx - Bx_{0} } \right)} {Bx}}} \right. \kern-0pt} {Bx}}_{0}$$
(2)
Fig. 3
2 3-D graphs. A plots S B X versus offset angle versus X direction. It has a peak of 5% at negative 0.02 millimeters and two falls with a range between negative 12 and negative 4 at negative 0.04 and 0.02. B plots B Z versus offset angle and X direction. It has a peak of 1.5 cross 10 power negative 5 at 0.02 meters while a fall of negative 1.5 cross power negative 5 at negative 0.02. Values are estimated.

Distorted space magnetic field in the bobbin coil under the excitation frequency of 1000 Hz. a Sensitivity of Bx (SBx). b Bz

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where SBx is the detection sensitivity of the Bx. Bx0 is the background signal when the crack is not present.

As shown in Fig. 3a, the SBx shows a peak at the center of the inner crack. The SBx is mainly caused by the decrease of current field in depth direction of the inner crack. Thus the SBx reflects the crack depth. While, the Bz show positive and negative peaks at the tips of the inner crack, as shown in Fig. 3b. By measuring the distance of peaks (Dp) in the Bz, the length of the inner crack can be calculated.

2.3 Low Frequency Excitation Signal

The excitation frequency of the excitation signal is changed to 80 Hz, while keep the current amplitude same (50 mA). The perturbation characteristic of the circumferential current field around the inner crack is the same with that under the excitation frequency of 1000 Hz. But the current density, SBx and Bz are much weak under 80 Hz than that of 1000 Hz. Here we focus on the perturbation of current field caused by the outer crack. As shown in Fig. 4a, the induced circumferential current field penetrates the wall thickness because the penetration depth is 9.17 mm in aluminum tube at the excitation frequency of 80 Hz. The vector current field deflects around the bottom of the outer crack. As shown in Fig. 4b, the vector current field turns around with different deflecting direction at the end of the outer crack inside the aluminum tube. The current density below the outer crack is extracted in the inner wall of the aluminum tube, as shown in Fig. 4c. The current density shows a deep trough in the axial direction under the outer crack.

Fig. 4
3 parts. a. A cross-sectional view indicates the deflecting current field near the outer longitudinal crack. b. A diagram depicts that the current field turns around the end of the crack. c. A 3-D graph plots current density versus offset angle and X direction. It plots a bell-shaped plane with high values at the center.

Perturbation of current field caused by the outer crack under the excitation frequency of 80 Hz. a Vector current field flows at the bottom of the crack (Cross-sectional view). b Vector current field turns around at the ends of the crack (Perspective drawing from the outside). c Current density

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Comparing Fig. 4c with Fig. 2b, the current density caused by the outer crack under the excitation frequency of 80 Hz is much weaker than that caused by the inner crack under the excitation frequency of 1000 Hz. This is due to the induced current field gathers in the skin layer of the inner-wall at 1000 Hz frequency. Thus the 1000 Hz excitation frequency is suitable for inspection of inner crack. What’s more, the induced current field decays exponentially in the aluminum tube to reach the bottom of the outer crack at the excitation frequency of 80 Hz. Thus the distorted space magnetic field cause by the perturbation of current field is weak than that at the excitation frequency of 1000 Hz. As shown in Fig. 5a, the Bx is normalized by the Eq. (2). There is a weak peak in the SBx at the center of the outer crack, while there are two opposite peaks at the end of the outer crack, as shown in Fig. 5b.

Fig. 5
Two 3-D spectral graphs. a. It plots S B X versus channel and X directions. The peak between 0.2 and 0.8 ranges between negative 0.01 and 0.01 millimeters. b. It plots B Z versus channel and X directions. The peak between 0 and 3 cross 10 power negative 4 ranges at 0.01 millimeters. Values are estimated.

Distorted magnetic field below the outer crack in the bobbin coil under the excitation frequency of 80 Hz. a SBx. b Bz

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Comparing Fig. 3a with Fig. 5a, the amplitude of the SBx caused by the outer crack under the excitation frequency of 80 Hz is much less than that caused by the inner crack under the excitation frequency of 1000 Hz. For the outer crack uder the excitation of 80 Hz, the SBx is mainly caused by the decay depth where the bottom of the outer crack is present. The Bz is mainly affected by the different deflecting direction of the current field at the end of the outer crack. Similarly, the SBx and the Dp reflects the residual wall thickness (RWT) and the length of outer cracks respectively.

3 Testing System

3.1 Probe with Sensor Arrays

The bobbin-type probe is shown in Fig. 6a. The bobbin coil is made up of 300 turns enameled wires whose enameled wire is 0.15 mm. The bobbin coil is installed on a plastic yoke. The diameter of the bobbin coil is 43 mm and the length is 50 mm. As shown in Fig. 6b, there are two tunnel magneto resistance (TMR) chips on one printed circuit board (PCB) for the measurement of Bx and Bz respectively at one location. Several PCBs are installed in the plastic yoke, which is covered by the bobbin coil. According to the detection range of the TMR sensor inside the bobbin coil, 18 PCBs should be employed to cover the 360° inner and outer surface of the aluminum tube. To simplify the testing system, 5 PCBs (Including 5 TMR sensors to measure the Bx and another 5 TMR sensors to measure the Bz) are used to pick up Bx and Bz in the bobbin coil, as shown in Fig. 6c. The lift-off of TMR sensors are 5 mm in the radial direction as the same in the FEM model. The measured magnetic signals are amplified (The Bx is amplified 50 times and the Bz is amplified 100 times) preliminarily by the AD620 chip on the PCB.

Fig. 6
3 parts. a. A 3-D structure of the probe. It consists of T M R sensors in the X and Z directions, a bobbin coil, a plastic yoke, and P C B. b. The top and bottom views of T M R sensors on P C B. c. A photo features a plastic yoke containing 5 P C Bs with A D 620 and T M R sensors in Z and X directions.

Bobbin type probe with sensor arrays. a Structure of probe. b TMR sensors on PCB. c Five PCBs inside the plastic yoke

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3.2 Testing System

As shown in Fig. 7a, the double frequency CCFT system is developed. One signal generator produces a sinusoidal signal with the frequency of 1000 Hz and the other signal generator produces a sinusoidal signal with the frequency of 80 Hz. The two sinusoidal signals are added together by a summator which is made by the OPA134 chip [29]. The synthetic excitation signal is amplified by a power amplifier to keep the current amplitude 50 mA. The bobbin coil is excited by the double frequency synthetic excitation signal. Due to the double frequency components, the induced circumferential current field can penetrate the wall thickness and gathers in the inner thin layer of the aluminum tube at the same time. Thus the circumferential current field can turns around at both inner and outer cracks in the aluminum tube using the bobbin coil with double frequency excitation signals. The TMR magnetic sensor arrays measure the Bx and Bz caused by the perturbation of current field.

Fig. 7
2 parts. a. A block diagram of the double-frequency C C F T system. It includes signal generators A and B, an aluminum tube, a bobbin coil, a probe, sensors, a power amplifier, a summator, an acquisition card, a scanner, P C, and P L C. b. A photo of the setup of the testing system. It consists of a probe, aluminum tube, P C, and power amplifier.

Double frequency CCFT system. a Block diagram. b Photo of testing system

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The response signals from the TMR sensors (Bx and Bz) and their unilateral frequency spectrum are shown in Fig. 8. As shown in the response signal, there are two frequency components in the time domain. As shown in the unilateral frequency spectrum, there are two peaks at the frequency of 1000 Hz and 80 Hz. It shows that the two frequency components are measured by TMR sensors in the response signals.

Fig. 8
Two sets of 2 line graphs are labeled a and b. The response signals B x and B z versus time plot a fluctuating sine wave pattern. The modulus of Y of f versus frequency has the highest peaks around (79.37, 2.994) and (79.37, 0.1638), respectively.

Response signals from TMR sensors and unilateral frequency spectrum. a Bx. b Bz.

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The two excitation signals, response signals are captured by the acquisition card and then transferred to the personal computer (PC). In the computer, the response signals are processed by a software developed by the LabVIEW and MATLAB. Firstly, the high frequency component of the response signal is extracted by the lock-in amplifier module using the 1000 Hz excitation signal. Meanwhile, the low frequency component of the response signal is extracted by the lock-in amplifier module using the 80 Hz excitation signal. Secondly, the low frequency component and high frequency component response signals are calculated by root-mean-square respectively. Thirdly, the Bx signals are normalized by the Eq. (2).

In the end, five SBx signals and five Bz signals with low frequency component are plotted respectively by the interpolation method. In the same way, the five SBx signals and five Bz signals with high frequency component are plotted respectively.

4 Inspection of Inner and Outer Cracks

4.1 Specimen

As shown in Fig. 9, there are four specimens with different size inner and outer longitudinal cracks. The specimens are aluminum tubes whose diameters are the same with the FEM model. Four inner and four outer cracks with different depths are introduced in the No. 1 and No. 2 specimens respectively, as shown in Fig. 9a, b. These cracks are with the same length (30 mm) and width (0.5 mm). Four inner and four outer cracks with different lengths are introduced in the No. 1 and No. 2 specimens respectively, as shown in Fig. 9c, d. These cracks are with the same depth (4 mm) and width (0.5 mm). The distance between the crack in each aluminum tube is 100 mm. The diameters of these cracks are shown in Fig. 9.

Fig. 9
4 schematics present the specimen with a bobbin-type probe. a and b. The crack depths in specimens 1 and 2 are 2, 4, 6, and 8 millimeters. c. Specimen 3 with crack lengths of 10, 20, 30, and 40 millimeters. d. Specimen 4 with crack lengths of 30, 35, 40, and 45 millimeters.

Sizes of inner and outer longitudinal cracks in specimens. a No. 1 specimen with different depth inner cracks. b No. 2 specimen with different depth outer cracks. c No. 3 specimen with different length inner longitudinal cracks. d No. 4 specimen with different length outer longitudinal cracks

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4.2 Inspection of Different Depth Cracks

The CCFT probe is pushed by a scanner to pass through inside the aluminum tube at the constant speed of 5 mm/s. The bobbin coil is excited by the double frequency synthetic excitation signal. Thus there are two frequency components in the induced circumferential current field. The high frequency component gathers in the thin layer inside the aluminum tube. The low frequency component penetrates the wall thickness of the aluminum tube. The perturbation of current field will happen near both inner and outer cracks. The distortion of the space magnetic field can be measured by TMR sensor arrays. The distortion of space magnetic field caused by different depth inner cracks in No. 1 specimen is shown in Fig. 10.

Fig. 10
A set of three 3-D spectral graphs. a. S subscript B x versus channel and X direction. b. B z versus channel and X direction. c. S subscript B x versus channel and X direction. The highest value is noted at 9% at 100 millimeters, 300 millivolts at 100 millimeters, and 3.9% at 100 millimeters, respectively. Values are estimated.figure 10

Distortion of space magnetic field caused by different depth inner cracks. a SBx under at 1000 Hz frequency component. b Bz at the 1000 Hz frequency component. c SBx at the 80 Hz frequency component. d Bz at the 80 Hz frequency component

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As shown in Fig. 10a, c, there are four peaks in the SBx at 1000 and 80 Hz frequency components. Meanwhile, the Bz shows four peaks and troughs at the two frequency components at the same location, as shown in Fig. 10b, d. Comparing Fig. 10a with Fig. 10c, the distortion of magnetic caused by different depth inner cracks at the 1000 Hz frequency component is greater than that at the 80 Hz frequency component. The peak value of the SBx raises up with the growth of crack depth. Similarly, the peak of the Bz caused by each inner crack at the 1000 Hz frequency component is stronger than that at the 80 Hz frequency component, as shown in Fig. 10b, d. The peak of the Bz raises up as the crack depth increases. The Dp keeps the same because of the same length of cracks. The results show that the inner crack can be identified by both the 1000 Hz and 80 Hz frequency components. The distortion of space magnetic field caused by the inner crack at the 1000 Hz frequency component are much stronger than that at the 80 Hz frequency component. The conclusions fit with the results from the FEM model. Thus SBx is a key parameter of inner crack depths, while Dp is a key parameter of inner crack lengths.

Due to the stronger distortion of magnetic field caused by inner cracks at the 1000 Hz frequency component, the SBx in Channel 3 from the Fig. 10a is used to evaluate the depth of the inner crack. The peaks of the SBx (Sp) are given in Table3. The first two cracks are set as the calibration cracks to evaluate the last two cracks by Eq. (3).

$$ED = 66.67Sp - 0.33$$
(3)

where the Sp is the peak value of the SBx, the ED is the evaluated depth of inner crack.

The ED of the last two cracks is shown in Table 3. The absolute errors of the evaluated depth of the last two inner cracks are 0.2 mm and 0.3 mm. Because it is not a linear relationship between the crack depth and the Sp, the evaluated errors will increase for deeper inner cracks. However, when the crack depth varies in a certain rang (Due to the limited wall thickness), the evaluated depth is accurate. The measured errors are negligible in the industrial field. Thus the depth of inner crack is identified and evaluated by the 1000 Hz frequency component.

Table 3 Peak of SBx with different depth inner cracks
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The No. 2 specimen is tested by the CCFT probe with the same parameters. As shown in Fig. 11, the distortion of magnetic field caused by different depth outer cracks are imaged. Due to the limited penetration depth of the induced current field at the excitation frequency of 1000 Hz, the current field cannot flows at the bottom of the outer crack. As a result, there is no obvious distortion in the SBx. Because the penetration depth of the induced current field can reach the deepest outer crack at 1000 Hz frequency component, the current field turns around slightly at the tip of the outer crack. Thus the Bz shows weak peaks at the deepest crack and no obvious distortion in other depth outer cracks.

Fig. 11
Three 3-D spectral graphs. A and B. The S B x versus channel versus x direction graph and the B z versus channel versus x direction graph plot a highly fluctuating plane. C. The S B x versus channel versus x direction plots a plane with sharp peaks.figure 11

Distortion of magnetic field caused by different depth outer cracks. a SBx at the 1000 Hz frequency component. b Bz at the 1000 Hz frequency component. c SBx at the 80 Hz frequency component. d Bz at the 80 Hz frequency component

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Because the induced current field penetrates the wall of the aluminum tube under the excitation frequency of 80 Hz, the current field will flows at the bottom of the crack and turns around at the tip of the outer crack. Thus there are four obvious peaks in the SBx at the 80 Hz frequency component. Meanwhile, the Bz shows four peaks and troughs at the tips of outer cracks. The peak of the SBx increases as the residual wall thickness decreases, as shown in Fig. 11c. Comparing Fig. 11c with Fig. 10a, although the amplitudes of the distortion of magnetic field caused by outer cracks at 80 Hz frequency component are much weaker than that of inner cracks at 1000 Hz frequency component, the signal to noise ratio (SNR) is acceptable in the Fig. 11c, even for the shallow outer crack (Wall thickness is 7 mm). The Dp keeps the same because of the same length of outer cracks. It shows that outer cracks can be identified effectively by the 80 Hz frequency component, but cannot be identified by the 1000 Hz frequency component.

Similarly, the SBx in Channel 3 from the Fig. 11c is extracted to evaluate the residual wall thickness (RWT) of the aluminum tube. The Sp of the outer crack with the RWT is shown in Table 4.

Table 4 Sp with different residual wall thickness
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The first two outer cracks are set as the calibration cracks. The residual wall thickness of last two cracks can be evaluated by Eq. (4).

$$E{\text{R}} = - 1667S{\text{p + 15}}{.17}$$
(4)

where the ER is the evaluated residual wall thickness of the aluminum tube.

The evaluated residual wall thickness of the 6 mm depth outer crack is 3.0 mm, which equals the actual residual wall thickness. However, the evaluated residual wall thickness of the 8 mm depth outer crack is −12.2 mm. It does not accord with the actual residual wall thickness. This is due to the induced current field at the 1000 Hz frequency component has penetrated the residual wall thickness of the deepest outer crack. Thus the distorted current field and magnetic field are different from the first three outer cracks. The Sp of the last crack is much greater than that of the first three outer cracks. Meanwhile, this is a good phenomenon for the evaluation of the aluminum tube with little residual wall thickness, which has a higher risk of leakage. The last outer crack can be set as the trough crack in advance.

In conclusion, the outer crack can only be identified by the 80 Hz frequency component and the inner crack can be identified by the 1000 Hz and 80 Hz frequency components. Thus the outer and inner cracks can be distinguished by the response signals with low and high frequency components. The inner crack depth and the RWT of the outer crack can be evaluated by the peak of the SBx at the 1000 Hz and 80 Hz frequency component respectively. Thus the development of the crack depth in the aluminum tube can be evaluated by periodic detection using the double frequency CCFT method.

4.3 Inspection of Different Length Cracks

The No. 3 specimen is tested by the CCFT probe at the same speed. Because response signals of inner crack are sensitive at the 1000 Hz frequency component, the response signals of different length inner cracks at 1000 Hz frequency component are presented only, as shown in Fig. 12.

Fig. 12
Two 3-D spectral plots. a. It plots S B x versus channel and X direction. The plane has four peaks between 2 and 5% at 100, 250, 350, and 500 millimeters. b. It plots B z versus channel and X direction. The plane has three peaks of 290, 200, and 90 millivolts at 110, 250, and 390 millimeters. Values are estimated.

Distortion of magnetic field caused by different length inner cracks at the 1000 Hz frequency component. a SBx. b Bz

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The SBx shows four obvious peaks in the center of the inner crack, while the Bz shows four peaks and troughs at the tips of the inner crack. The four different length inner cracks are identified by the 1000 Hz frequency component. The Dp of the Bz with different length inner cracks is shown in Table 5.

Table 5 Dp with different length inner cracks
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The Dp is less than the length of the inner crack and the maximum absolute error is 2.8 mm. As a matter of fact, the absolute errors can be eliminated by calibration method. The first two cracks are set as the calibration crack. The length of the last two inner cracks can be estimated by Eq. (5).

$$E{\text{L}} = 1.04D{\text{p}} + 1.04$$
(5)

The estimated length (EL) of the last two cracks is 29.54 mm and 39.73 mm respectively. The absolute errors are 0.46 mm and 0.27 mm. which is negligible in the industrial field.

The No. 4 specimen is tested at the same speed. There are no obvious distorted response signals of the different length outer cracks at the 1000 Hz frequency component. The response signals at 80 Hz frequency component are shown in Fig. 13.

Fig. 13
A set of two 3-D spectral plots. a. The S subscript B x versus channel and X direction graph. It has four peaks between 0.3% and 0.5% at 100, 250, 400, and 550 millimeters. b. The B Z versus channel and X direction graph. It has four peaks between 0 and 10 millivolts at 110, 250, 390, and 520 millimeters. Values are estimated.

Distortion of magnetic field caused by different length outer cracks at the 80 Hz frequency component. a SBx. b Bz

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There are four obvious peaks at the center of the crack. Meanwhile there are four opposite peaks at the same location. The four different length outer cracks are identified by the 80 Hz frequency component. The Dp of the Bz is given in Table 6. The maximum absolute error is 3.8 mm. Similarly, the first two cracks are set as the calibration crack. The length of the last outer cracks can be estimated by Eq. (6).

$$E{\text{L}} = 1.02D{\text{p}} + 3.06$$
(6)
Table 6 Dp with different length outer cracks
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where EL is the estimated length of the crack.

The EL of the last two cracks is shown in Table 4. The absolute error is 0.02 mm and 0.29 mm.

In a word, the length of inner and outer cracks can be estimated by the Dp at the 1000 Hz and 80 Hz frequency component respectively. The extension of inner and outer cracks can be monitored by the periodic detection using the double frequency CCFT method.

5 Conclusions and Further Work

The double frequency CCFT is presented for the detection and evaluation of both inner and outer cracks in the aluminum tube in a one pass scan. The FEM model of the CCFT is set up to analyze the disturbed current field and distorted magnetic field around inner and outer longitudinal cracks with the excitation frequency of 1000 Hz and 80 Hz respectively. The CCFT probe is built with TMR sensor arrays inside the bobbin type excitation coil. The 1000 Hz frequency excitation signal and 80 Hz frequency excitation signal are added together as the synthetic excitation signal to excite the bobbin coil in the probe. The response signals with 1000 Hz and 80Hz frequency components are separated by the lock-in amplifier module in the software. The CCFT system is developed for the inspection of different size inner and outer longitudinal cracks in the aluminum tube. The results show that outer cracks can only be identified by the 80 Hz frequency component, while inner cracks can be identified by the 1000 Hz and 80 Hz frequency component. Thus the outer and inner cracks can be distinguished by the double frequency components. The RWT of outer cracks and inner crack depth can be evaluated by the SBx. The crack length can be measured by the Dp of the Bz. As a result, both the inner and outer cracks can be identified, distinguished and evaluated using the double frequency CCFT method with TMR sensor arrays inside the aluminum tube in a one pass scan. The double frequency CCFT probe and system can be used in the in-service inspection by crawling through the aluminum tube. Further work will focus on the inspection of samples with complex defects, the development of the portable instrument.