Design of eddy current-based dielectric constant meter for defect detection in glass fiber reinforced plastics

NDT&E International 74 (2015) 24–32

Contents lists available at ScienceDirect

NDT&E International journal homepage: www.elsevier.com/locate/ndteint

Design of eddy current-based dielectric constant meter for defect detection in glass fiber reinforced plastics Koichi Mizukami n, Yoshihiro Mizutani, Akira Todoroki, Yoshiro Suzuki Tokyo Institute of Technology, Department of Mechanical Sciences and Engineering, 2-12-1-I1-70, Ookayama, Meguro-ku, Tokyo 152-8552, Japan

art ic l e i nf o

a b s t r a c t

Article history: Received 30 January 2015 Received in revised form 24 March 2015 Accepted 24 April 2015 Available online 12 May 2015

This paper presents the design of an eddy current testing probe for inspection of non-conductive glass fiber reinforced plastics. Because the magnetic field contains information pertaining to the permittivity of materials under test, eddy current testing offers the possibility of flaw detection in non-conductive materials through detection of the difference in permittivity between the intact part and the defective part of each material. We analytically investigated the design of a probe suitable for dielectric constant measurements. Experimental studies proved that the proposed probe can detect slit defects and flatbottomed holes located 2 mm away from the surface of the glass fiber reinforced plastic samples. & 2015 Elsevier Ltd. All rights reserved.

Keywords: Composite materials FRP (fiber reinforced) plastic Dielectric Eddy currents Theoretical modeling

1. Introduction Glass fiber reinforced plastics (GFRPs) are low-cost structural materials with high specific strength and stiffness, and are used in many applications, including aircraft, wind power generator blades, small boats and tanks. Defects occur in GFRPs both during the manufacturing process and in service. One GFRP manufacturing method, resin transfer molding (RTM), is increasingly commonly used to mold GFRP products because it offers low equipment costs and excellent moldability of complex shapes and large parts [1]. In RTM, a dry fiber reinforcement called a preform is placed in the mold cavity and a low viscosity resin is then pumped into the mold under pressure until the cavity is filled. In particular, when a large composite structure is molded, nonuniform resin flow can easily occur and dry spots are formed [2]. Because these dry spots can cause strength degradation, they must be detected by nondestructive testing (NDT). When GFRP structures are in service, the common forms of damage that occurs in these structures are fiber breakage and matrix cracking [3]. These forms of damage also lead to deterioration of the material’s strength and must be detected before they exceed a critical level. The surfaces of GFRP structures in service are often given an approximately 0.5 mm thick polyester gel coating to improve weather resistance. Flaws in GFRPs under these gel coatings can be invisible and flaw detection is thus a challenging task.

n

Corresponding author. Tel./fax: þ 81 3 5734 3178. E-mail address: [email protected] (K. Mizukami).

http://dx.doi.org/10.1016/j.ndteint.2015.04.005 0963-8695/& 2015 Elsevier Ltd. All rights reserved.

Many NDT techniques have been developed for GFRP inspection, including ultrasonic, thermography and radiography testing. In addition to these techniques, studies of electromagnetic wavebased methods such as microwave and terahertz imaging have been reported in recent years [4–6]. Although these techniques are useful in many applications, they have certain limitations. Ultrasonic testing requires the use of couplant to enable ultrasound to propagate into the material under test, which increases the time cost of the inspection process [7]. In thermography testing, defect detectability depends on the heating conditions and the surface characteristics of the material under test. For example, nonuniform heating and surface emissivity variation make defect detection more difficult [8]. In radiography testing, the inherent radiation hazards are sometimes problematic. Microwave testing and terahertz imaging require expensive test equipment. Testing methods based on capacitance measurements have also been investigated with the aim of overcoming some of the limitations described above. Yin and Hutchins used co-planar capacitive electrodes to detect the local dielectric properties of GFRPs [9]. Detection of local changes in the dielectric properties in damaged regions has been shown to be effective for inspection of GFRPs with a simple apparatus. Eddy current testing (ET) is a well-established NDT method for defect detection in electrically conductive materials such as metals. In ET, eddy currents are induced in the conductive material under test by the driver coil in accordance with Faraday’s law. Defects in the material cause local changes in eddy current path and the distorted magnetic field produced by the eddy currents cause changes in the output signal of the pickup coil that is used as a magnetic sensor. ET offers the advantages of short-time and

K. Mizukami et al. / NDT&E International 74 (2015) 24–32

non-contact inspection [10]. In addition, the costs of test equipment for ET are relatively low. Although ET is conventionally only applied to electrically conductive materials, ET also has the potential for use in non-conductive material inspection as the magnetic field is dependent on the material’s dielectric constant because of the presence of the displacement current. Heuer proved experimentally that ET can measure the dielectric constants of non-conducting materials at high frequency [11]. Heuer investigated the ET output signals from several non-conductive materials while varying the drive frequency, and showed that dielectric constant causes distinct changes in the signal at frequencies above approximately 9 MHz [11]. Gaebler et al. carried out high frequency ET of curing resin and PMMA with artificial hole defects [12]. The experiments of Gaebler also indicate that sample permittivity is a part of ET response. Thus, ET has potential to be a fast and non-contact method for testing of non-conductive materials that overcomes the limitations of the existing NDT methods. However, configuration of ET probe specialized for permittivity measurement has not yet been studied. In this paper, the design of the test probe for dielectric constant measurement for GFRP defect detection applications is studied. First, an analytical solution for the electromagnetic field during ET of an anisotropic non-conductive material was derived to investigate the output signal’s dependence on the dielectric constant of the material under test. Second, the probe was designed such that the pickup coil has a large fractional change in output voltage with dielectric constant. We studied the influence of probe’s dimensions and the arrangement of the driver and the pickup coil on the detectability of change in the material’s permittivity. Third, a test probe was fabricated on the basis of the proposed probe design and was used for experimental detection of defects in GFRPs. In the experiments, a GFRP specimen containing a slit and specimens with flat-bottomed holes were tested to verify the potential of ET for non-conductive GFRPs.

2. Derivation of analytical solutions to ET problems Analytical solutions for the electromagnetic field in ET of a nonconductive anisotropic medium are derived using the formulation of Dodd and Deeds [13,14]. Dodd and Deeds derived analytical solutions for the vector potential in ET of an electrically conductive isotropic material. In this study, the vector potential in ET of a nonconductive material is derived by assuming that the conductivity of the tested material σ ¼ 0 in the Dodd and Deeds formulation, and this formulation is extended to the case of a material with anisotropic permittivity. Fig. 1 shows the analytical model used to derive analytical solutions for the vector potential. In the analytical model, the driver coil and the pickup coil are placed above the material in (r, θ, z) cylindrical coordinates. The driver coil has n turns and a rectangular cross section (inner radius: r1, outer radius: r2, lift off: l1, height: l2–l1). The pickup coil is a wire loop with radius rp at z¼ lp. The distance between the central axis of the driver coil and that of the pickup coil is L. It is assumed that the

25

material under test is a semi-infinite plate that occupies the region where z o0, and the material has conductivity σ xy in the in-plane direction, conductivity σ z in the z direction, relative permittivity εxy in the in-plane direction and relative permittivity εz in the z direction. This assumption of anisotropy is valid for a woven GFRP and a chopped strand mat GFRP, in which the material properties are considered to be approximately isotropic in the in-plane direction. The differential equation for the vector potential A in cylindrical coordinate when a sinusoidal current density with amplitude i0 and frequency ω is applied to the driver coil is written as [15–17], 0 0 1 0 σ xy 0 ! B B C B ∇ A ¼  μ0 @ i0 A þ @jωμ0 @ 0 0 0 2

0 σ xy 0

1

0 εxy 0

0

11

C! 0C AA A :

εz

ð1Þ where, μ0 and ε0 are the magnetic permeability and the permitpffiffiffiffiffiffiffiffi tivity of a vacuum, respectively, and j ¼  1. Note that the vector potential A in Eq. (1) is expressed in complex form [13,14]. Because axial symmetry is valid for this problem, there is only a θ component of the drive current [13] and therefore of A. The θ component of Eq. (1) gives,   ∂2 Aθ 1 ∂Aθ ∂2 Aθ Aθ þ 2  2 ¼  μ0 i0 þ jωμ0 σ xy  ω2 μ0 ε0 εxy Aθ : þ ∂r 2 r ∂r ∂z r

ð2Þ

The contributions of the conductivity and the permittivity to the vector potential are determined by the ratio of the terms in brackets in Eq. (2). Because ωε0 εxy =σ xy 4 4 1 (ε0 ¼ 8:85  10  12 F/m, εxy ¼ 3  5, σ xy ffi 1  10  13 S/m) is valid for testing of GFRPs at frequencies above 10 MHz, the first term in the brackets can then be negligible and Eq. (2) can be written as follows. ∂2 Aθ 1 ∂Aθ ∂2 Aθ Aθ þ 2  2 ¼  μ0 i0 ω2 μ0 ε0 εxy Aθ : þ ∂r 2 r ∂r ∂z r

ð3Þ

The regions of interest in Fig. 1 in this study are l1 r z r l2 and z r 0. The vector potentials in the regions where l1 r z rl2 and z r 0 are required to calculate the output voltage of the pickup coil and the displacement current in the material under test, respectively. Solutions to Eq. (3) can be given by separation of the variables as Dodd and Deeds derived. Solutions for the regions where l1 r z r l2 and z r0 are written as follows [13]. Z  μ i0 1 1 Iðr 2 ; r 1 ÞJ 1 ðαrÞðF þ GÞdα; ð4Þ Aθ ðr; zÞl r z r l ¼ 0 1 2 2 0 αα20  Aθ ðr; zÞz r 0 ¼ μ0 i0

Z

1 0

 1 eα1 z   α0 l1 I ðr 2 ; r 1 ÞJ 1 ðαr Þ e e  α0 l2 dα: αα0 α0 þ α 1 ð5Þ

where J 1 is a first-order Bessel function, α0 ¼ ðα2  ω2 μ0 ε0 Þ1=2 ;

ð6Þ

α1 ¼ ðα2  ω2 μ0 ε0 εxy Þ1=2 ;

ð7Þ

Z Iðr 2 ; r 1 Þ ¼

αr 2 αr1

xJ 1 ðxÞdx;

F ¼ 2 e  α0 ðl2  zÞ  e  α0 ðz  l1 Þ ;

Fig. 1. Analytical model for derivation of analytical solutions for vector potential.

0 εxy C 2 0 A  ω μ0 ε0 B @ 0 σz 0 0

G¼

α0  α1  α0 z  α0 l1 e ðe e  α0 l2 Þ: α0 þ α1

ð8Þ

ð9Þ ð10Þ

26

K. Mizukami et al. / NDT&E International 74 (2015) 24–32

The voltage induced in the pickup coil is given by 0 1 0 Z Z  ! ! B C ! V out ¼ jω A U d s ¼ jω @ Aθ ðr; zÞl1 r z r l2 A Ud s : C C 0

ð11Þ

where C denotes the line integral along the pickup coil loop. The displacement current density distribution Jd(r,z) in the region where z r0 can be calculated using the following equation. 0 1 0  B C J d ðr; zÞ ¼ @ ω2 εxy ε0 Aθ ðr; zÞz r 0 A: ð12Þ 0 Note that theq integrands ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi in Eqs. (4) and (5) have singularities at α ¼ 0 and α ¼ ω2 μ0 ε0 , respectively, as their denominators become zero. To remove the singularities by variable transformation, double exponential formulas for numerical integration are used in this study [18].

3. Design of probe for relative permittivity sensing 3.1. Effects of the probe dimensions on permittivity measurement We investigated how the probe dimensions affect its performance when sensing the change in the dielectric constant of the material under test on the basis of the work in the previous chapter. The driver coil dimensions determine the spatial distribution of the electromagnetic field. The location and dimensions of the pickup coil are related to the way in which this coil extracts information pertaining to the magnetic field from the displacement current. Because the sensitivity of the probe can be strongly linked to its dimensions, study of the effect of the probe dimensions on the detectability of permittivity change is of major importance. This study aims to improve the rate of change of the pickup coil output with the permittivity of the material under test by modifying the probe dimensions. Improvement of the rate of the change of pickup coil voltage is effective because the oscilloscope used to measure the output voltage has resolution limitations. First, the effect of the distance between the driver coil and the pickup coil, L, was investigated using the analytical solutions derived in the previous chapter. The output voltage of the pickup coil was calculated using the derived analytical solution based on the model shown in Fig. 1. Table 1 shows the input parameters used for the analysis. Effect of L was investigated using parameters in Vout analysis #1 column in Table 1. The rate of change of the pickup coil output from εxy ¼ 1 (which is defined as ΔV out =V out ) was calculated for the cases of L¼ 0 mm, 7 mm, 10 mm and 14 mm. L¼ 0 mm denotes the case of a co-axial probe in which the driver coil and the pickup coil have a common axis, while L Z 7 mm indicates that the pickup coil is adjacent to the driver coil. Fig. 2 shows the relationship between the in-plane relative permittivity εxy and the rate of change of the pickup coil outputΔV out =V out for

L¼0 mm, 7 mm, 10 mm and 14 mm. As shown in Fig. 2, in the case where L¼ 0 mm, the output voltage of the pickup coil increases linearly with the relative permittivity of the tested material. This result indicates that intensity of the magnetic field that penetrates the pickup coil in the co-axial probe increases with relative permittivity. The rate of change of the pickup coil’s output voltage in the case where L Z 7 mm is also proportional to the material’s permittivity. However, the output voltage decreases with permittivity, which indicates that the magnetic field penetrating the pickup coil decreases, in contrast to the co-axial probe case. More importantly, as Fig. 2 shows, the rate of change of the output voltage when L Z7 mm is larger than that of the co-axial probe. In addition, ΔV out =V out becomes more sensitive to change in εxy as L increases, because εxy makes a larger contribution to the vector potential at larger value of r. As Eq. (4) shows, the vector potential in the l1 r z rl2 range is expressed as a sum of the following two components. Z μ i0 1 1 Iðr 2 ; r 1 ÞJ 1 ðαrÞFdα; ð13Þ AF ¼ 0 2 0 αα20 AG ¼

μ0 i0 2

Z

1 0

1 Iðr 2 ; r 1 ÞJ 1 ðαrÞGdα: αα20

AF is independent of the permittivity of the material εxy , while AG is dependent on εxy . When the driver coil is in the air, i.e., when  εxy ¼ 1, we obtain Aθ ðr; zÞl r z r l ¼ AF because AG ¼0. This indi1 2 cates that AF is the vector potential induced by the driver coil, while AG is that induced by the displacement current. Thus, by comparing the amplitudes of AF and AG, the contribution of εxy to the electromagnetic field can be examined. Fig. 3 shows the ratio of the amplitudes of AF and AG along the r direction   of  the analytical model shown in Fig. 1. The calculation of AG =AF  is

Fig. 2. Relationship between in-plane relative permittivity εxy and the rate of change of the pickup coil output, ΔV out =V out , for L ¼ 0 mm, 7 mm, 10 mm, and 14 mm (Vout analysis #1).

Table 1 Input parameters used for investigation of the effect of probe dimensions. Parameter

Vout analysis #1

Vout analysis #2

r1 [mm] r2 [mm] l1 [mm] l2 [mm] ω [rad/s]

3 4 0 5

3 4 0 5, 10, 15, 20

2π  10  106 3 0 0, 7, 10, 14

2π  10  106 3 0 7

rp [mm] lp [mm] L [mm]

ð14Þ

Fig. 3. Ratio of amplitudes of AF and AG along the r direction.

K. Mizukami et al. / NDT&E International 74 (2015) 24–32

based on the input parameters shown in Vout analysis   #1  column  in Table 1, and εxy was set to 3. As Fig. 3 shows, AG =AF  has a larger value at larger values of r, which indicates that the contribution of εxy to the electromagnetic field increases as the distance from the driver coil increases. Therefore, the sensitivity of ΔV out =V out to change in εxy can be enhanced by placing the pickup coil further away from the driver coil in the r direction rather than placing the coils coaxially. Second, the effect of the height of the driver coil was investigated. Input parameters shown in Vout analysis #2 column in Table 1 were used to investigate the effect of the driver coil height. The distance between the driver coil and the pickup coil, L, was set at 7 mm. Because l1 ¼0 mm is assumed, l2 then denotes the driver coil height in this analysis. ΔV out =V out is calculated for l2 ¼ 5 mm, 10 mm, 15 mm and 20 mm. Fig. 4 shows the relationship between the in-plane relative permittivity εxy and the rate of change of the pickup coil output ΔV out =V out for l2 ¼5 mm, 10 mm, 15 mm and 20 mm. As shown in Fig. 4, the sensitivity of ΔV out =V out to εxy improves as the height l2 increases. This originates from the increased of εxy to the vector potential. Fig. 5 shows    contribution  the AG =AF  ratio along the r direction for l2 ¼ 5 mm, 10 mm, 15 mm and 20 mm. As shown in Fig. 5, the contribution of εxy to the vector potential increases as l2 increases. Therefore, larger l2 values can improve the sensitivity of the ΔV out =V out ratio to εxy of the material under test. Based on the analyses above, the distance between the driver coil and the pickup coil, and the driver coil height should be increased to enhance the detectability of the dielectric constant of the material under test. When we compare an axial probe with dimensions of L¼ 0 mm and l2 ¼ 5 mm with a probe with dimensions of L ¼7 mm and l2 ¼20 mm, the sensitivity of ΔV out =V out to

27

εxy for the latter probe is about 80 times larger than that of the former probe although the driver coil radius and the pickup coils are identical for both coils. However, it should be noted that the analyses thus far have calculated the output voltages of the pickup coils while assuming that the permittivity of the entire material under test changes uniformly. A larger distance between the driver coil and the pickup coils, and increased driver coil height do not necessarily produces an optimum probe for local flaw detection. The detectability of local changes in permittivity should be investigated by other methods such as experimental verification and numerical simulation.

3.2. Implementation of differential probe The previous section proved that the sensitivity of the probe to a material’s permittivity change can be improved by appropriate modification of the probe dimensions. However, as Figs. 2 and 4 show, the rate of change to be measured in the pickup coil output is still small. This is attributed to large value of F relative to G in Eqs. (9) and (10). Fig. 6 shows the ratio of the magnitudes of F and G for the integral variable α. To calculate the ratio of |F| to |G|, ω ¼ 2π  10  106 rad=s, l1 ¼ 0 mm, l2 ¼ 15 mm, z ¼ 0 mm are substituted into Eqs. (9) and (10). As Fig. 6 shows, |G| is extremely small when compared to |F|, although only |G| is linked to the permittivity change in the material under test. To improve the probe’s sensitivity to permittivity, we introduce a differential probe. Fig. 7 shows a schematic representation of the differential probe. Subtraction of the output voltages of the two pickup coils is measured. When the two pickup coils are placed at z ¼ 0 and z ¼ l2 as shown in Fig. 7, the subtraction of the outputs of the two pickup coils, V sub , is expressed as follows using the relationship of Fjz ¼ 0 ¼ Fjz ¼ l2 . 0 1 0 Z   B μ0 i0 R 1 1 Iðr ; r ÞJ ðαrÞ Gj C !  V sub ¼ jω @ 2 0 αα2 2 1 1 z ¼ 0  G z ¼ l2 dα A Ud s : C

0

0 ð15Þ

Fig. 4. Relationship between in-plane relative permittivity εxy and the rate of change of the pickup coil output, ΔV out =V out , for l2 ¼ 5 mm, 10 mm, 15 mm and 20 mm (Vout analysis #2).

Fig. 6. Ratio of magnitudes of F and G. α is the variable of integration.

Fig. 5. Ratio of amplitudes of AF and AG along the r direction for l2 ¼5 mm, 10 mm, 15 mm, and 20 mm.

Fig. 7. Schematic representation of differential probe for sensing changes in permittivity.

28

K. Mizukami et al. / NDT&E International 74 (2015) 24–32

Fig. 8. Schematic illustration and photograph of the fabricated TTDR probe.

Fig. 9. Analytical result of relationship between V sub and εxy , assuming that a 1 A, 10 MHz sinusoidal alternating current is applied to the driver coil of the fabricated probe.

Table 2 Input parameters used for analysis of displacement current distribution. Parameter

Jd analysis #1

Jd analysis #2

Jd analysis #3

Jd analysis #4

r1 [mm] r2 [mm] l1 [mm] l2 [mm] f [MHz] εxy

1, 3, 5 r1 þ 1 0 15 10 3

3 r1 þ 1 0 10, 15, 20 10 3

3 r1 þ1 0 15 0.1, 1, 10 3

3 r1 þ1 0 15 10 1, 3, 5

The influence of F can be removed in case of the differential probe and it can improve the detectability of the permittivity change dramatically. Fig. 8 shows a schematic illustration and a photograph of the fabricated probe. We name the probe the TTDR probe (tall transmitter and differential receiver probe) because it has a driver coil with enhanced height based on consideration of the work of the previous section. Fig. 9 shows the analytically calculated relationship between V sub and εxy , assuming that a 1 A, 10 MHz sinusoidal alternating current is applied to the driver coil. As shown in Fig. 9, V sub is proportional to εxy and the sensitivity is improved dramatically compared with the case of single pickup coil. This analytical result is based on the premise that the dimensions of the two pickup coils are absolutely identical and that they are positioned exactly at z ¼ 0 and z ¼ l2 . However, the fabrication of two identical pickup coils such that V sub ¼ 0 in the air is quite difficult. Therefore, it is still significant for the differential probe to introduce a design policy to improve ΔV out =V out in the single pickup coil, similar to the work in the previous section.

Fig. 10. Displacement current distribution for r1 ¼ 1 mm, 3 mm, and 5 mm (Jd analysis #1).

4. Analysis of displacement current distribution In this section, the displacement current distribution induced by the driver coil was investigated. The pickup coil detects changes in the permittivity εxy by detecting the magnetic field caused by the displacement current because of the dependence of the displacement current on the permittivity. This indicates that it is difficult to inspect areas in the material under test with small displacement current intensities. Thus, investigation of the displacement current distribution is as significant as importance of investigating the eddy current distribution in ET on conductive materials. We investigated the influence of four parameters on the displacement current distribution: the driver coil radius r1 (we assume that r2 satisfies r 2  r 1 ¼ 1 mm), the driver coil height l2 (l1 ¼ 0 mm is assumed), the drive frequency f and the relative permittivity of the material under test εxy . Table 2 shows the input parameters used for the analysis of the displacement current distribution Jd(r,z). Jd(r,z) is calculated using Eq. (12). The influence of r1 on the displacement current distribution was investigated using parameters in Jd analysis #1 column in Table 2. Fig. 10 shows the displacement current distributions for r1 ¼ 1 mm, 3 mm and 5 mm. In Fig. 10, a 40 mm  10 mm area of the r-z plane is shown. The color bar indicates the displacement current density normalized with respect to the maximum current density. From Fig. 10, the displacement current becomes more widely distributed in both the r direction and the z direction as r1

K. Mizukami et al. / NDT&E International 74 (2015) 24–32

29

Fig. 11. Displacement current distribution for l2 ¼ 5 mm, 15 mm, and 25 mm (Jd analysis #2).

Fig. 13. Displacement current distribution for εxy ¼ 1; 3, and 5 (Jd analysis #4).

Fig. 12. Displacement current distribution for f¼ 100 kHz, 1 MHz, and 10 MHz (Jd analysis #3).

increases. These results indicate that a driver coil with a larger r1 can inspect the deeper regions in the material under test; however, this also indicates that the spatial resolution of the probe decreases. Thus, there must be a trade-off between the spatial resolution and the inspection of deeper regions. Jd analysis #2 column in Table 2 shows the input parameters used for the analysis of the influence of l2 on the displacement current distribution. Fig. 11 shows the displacement current

distributions for l2 ¼5 mm, 15 mm and 25 mm. As shown in Fig. 11, the displacement current is distributed more widely as l2 increases, as occurred with the increase in r1. However, unlike the increasing r1 case, increase in l2 causes a small expansion of the displacement current distribution area in the z direction. Jd analysis #3 column and Jd analysis #4 column in Table 2 show the input parameters used for the analyses of the influence of f and εxy on the displacement current distribution, respectively. Figs. 12 and 13 show the displacement currents for f ¼100 kHz, 1 MHz, and 10 MHz, and for εxy ¼ 1; 3, and 5, respectively. From Figs. 12 and 13, the drive frequency f and the permittivity εxy both have little effect on the displacement current distribution when f r 10 MHz and εxy r 5. In the case of conventional eddy current testing of electrically conductive materials, the penetration depth of the eddy current is dependent on both the drive frequency and the material properties of the tested material. However, the drive frequency and the material properties do not make a significant difference to the displacement current distribution. Therefore, the displacement current distribution cannot be adjusted by varying the drive frequency, unlike ET of conductive materials. The results shown in Figs. 10–13 indicate that the displacement current distribution can only be altered by varying the dimensions of the driver coil when non-conductive materials are being tested, i.e., probes have their inherent displacement current distributions.

5. Experimental 5.1. Preliminary experiment on specimen with a slit 5.1.1. Material and method As mentioned in Section 3.1, the probe is designed to have larger value of ΔV out =V out of the pickup coil when the permittivity of the entire material is changed. Because the probe design does

30

K. Mizukami et al. / NDT&E International 74 (2015) 24–32

not take its spatial resolution into consideration, the relationship between the defect location and the ET output should also be investigated. For example, when the ET probe with the poor spatial resolution is used, its output signal changes even if the scanning probe does not pass right over the defect. We investigated the spatial resolution of the fabricated probe shown in Fig. 8 by scanning it over the GFRP specimen with a slit. Fig. 14 shows the experimental setup used to test the GFRP specimen with a slit. The specimen is a 1.5 mm thick glass fiber fabric/epoxy laminate. We cut into the GFRP from its edge using a fine cutter and inserted a slit with length of 37 mm and width of approximately 1 mm. The testing probe used in this experiment was the fabricated TTDR probe that was shown in Fig. 8. A 10 V, 10 MHz sinusoidal voltage was applied to the driver coil by an arbitrary waveform generator (National Instruments NI PXI-5421, 16 bit, 100 MS/s). Although a higher drive frequency can theoretically improve the detectability of the permittivity change, 10 MHz was chosen so that the drive frequency did not exceed the coil’s self-resonant frequency. The subtraction of the signals from the two pickup coils V sub was small and of the order of micro-volts

even if a 1 A, 10 MHz AC current is applied, as the results of Fig. 9 show. Therefore, a differential amplification circuit and a high speed bipolar amplifier (NF Corporation HSA4101) were used to amplify V sub by 10,000 times. The amplified V sub was then measured by an oscilloscope (Pico Technology Picoscope5244B, 12 bit, 500 MS/s). The test probe was scanned along the x-axis of the specimen and the amplified V sub was measured at 5 mm intervals. The lift-off of this experiment was approximately 0.3 mm. The root mean square (RMS) value of the measured voltage was calculated from 100,000 samples, and 50 RMS data were averaged for each measurement point.

5.1.2. Results and discussion Fig. 15 shows the experimental results from the ET of the GFRP specimen with the slit. The horizontal axis denotes the location of the center of the driver coil on the x-axis of the specimen. The vertical axis denotes the RMS value of the amplified V sub measured by the oscilloscope. As Fig. 15 shows, the measured voltage increases locally when the center of the driver coil is at x ¼5 mm. This result shows that local changes in the permittivity can be detected by the fabricated probe. More importantly, because the midpoint between the driver coil and the pickup coil is located right over the slit when the driver coil is at x ¼5 mm, it is observed that the measured voltage changes when the midpoint between the driver coil and the pickup coil is located at the defect zone. In addition, local changes in the measured voltage were limited to x¼ 5 mm in Fig. 15, and the signals at x o5 mm and x4 5 mm cannot be distinguished from those from the intact zone. This result indicates that the fabricated probe does not detect defects that are 5 mm away in the scanning direction from the midpoint between the driver coil and the pickup coil. Therefore, the fabricated probe has sufficient spatial resolution for at least 5 mm interval inspection.

Fig. 14. Experimental setup for detection of the slit in the GFRP specimen.

Fig. 15. Results of ET experiment of the GFRP specimen with the slit.

Fig. 17. Experimental setup for ET of the GFRP specimens with flat-bottomed holes.

Fig. 16. GFRP specimens with flat-bottomed holes. (a) Specimen #1 (b) Specimen #2.

K. Mizukami et al. / NDT&E International 74 (2015) 24–32

31

Fig. 18. Results of ET of GFRP specimen #1. (a) Front surface inspection (b) Rear surface inspection.

Fig. 19. Results of ET of GFRP specimen #2. (a) Front surface inspection (b) Rear surface inspection.

5.2. ET on specimens with flat-bottomed holes 5.2.1. Materials and method Fig. 16 shows the GFRP specimens used in the experiments. Specimens are 5 mm thick chopped glass fiber/polyester plates containing flat-bottomed holes. Specimen #1 has flat-bottomed holes with diameters of 10 mm, 8 mm and 6 mm. These flatbottomed holes have a depth of 3 mm (see Fig. 16). Specimen #2 has flat-bottomed holes with diameters of 4 mm, 3 mm and 2 mm, and depths of these holes are again 3 mm like specimen #1. Fig. 17 shows the experimental setup used for ET of GFRP with flat-bottomed holes. The experimental setup and the test conditions were same as those used for the previous experiment on the specimen with a slit. A 10 V, 10 MHz sinusoidal voltage was applied to the driver coil. The difference in output voltage between the two pickup coils was amplified and measured by the oscilloscope. The test probe was scanned along the x-axis of the specimen and the amplified V sub was measured at 5 mm intervals. The RMS value of the measured voltage was calculated from 100,000 samples and 30 RMS data were averaged for each measurement point. This experiment was carried out for two cases: front surface inspection, in which the flat-bottomed holes were located on the side of the probe, and rear surface inspection, in which the flatbottomed holes were located in the opposite side of the probe (see left side of Fig. 17).

5.2.2. Results and discussion Figs. 18 and 19 show the results of ET of GFRP specimens #1 and #2, respectively. The horizontal axis denotes the location of the

center of the driver coil on the x-axis of the specimen. The vertical axis denotes the RMS value of the amplified V sub that was measured by the oscilloscope. As Fig. 18(a) shows, the measured voltage increases locally at the locations of the flat-bottomed holes during front surface inspection of specimen #1. This result indicates that the difference in permittivity between the intact part and the flat-bottomed holes can be detected using the fabricated TTDR probe. The results of the rear surface inspection of specimen #1 in Fig. 18(b) show that the measured voltage increases locally at the locations of the flat-bottomed holes, although the increases in the measured voltage are smaller than those observed during the front surface inspection. The results of Fig. 18(b) show that the fabricated probe can detect flatbottomed holes 2 mm away from the surface. This therefore suggests the possibility that ET can be applied to detection of internal defects in GFRPs coated with 0.5 mm thick gel-coat. The measured voltages in Fig. 18(a) and (b) change linearly along the x-direction because of a gradual change in distance between the probe and the specimen during scanning (known as the lift-off effect). Experimental results for front surface inspection of specimen #2 shown in Fig. 19(a) show that the measured voltage increases locally at flat-bottomed holes ϕ3 and ϕ4. However, the change in the measured voltage at flat-bottomed hole ϕ2 is barely visible because its amplitude cannot be distinguished from that of the intact part. However, there is no noticeable signal change in the results of the rear surface inspection on specimen #2, as shown in Fig. 19(b). This shows that it is difficult for the fabricated probe to detect flat-bottomed holes with diameters of less than 4 mm that are located 2 mm away from the surface.

32

K. Mizukami et al. / NDT&E International 74 (2015) 24–32

6. Conclusions In this study, we investigated the design of ET probe specialized for permittivity measurement and the general possibility to use ET on non-conductive GFRPs. First, we derived analytical solutions to the problem of ET on non-conductive materials by extending the formulation of Dodd and Deeds to non-conductive materials with anisotropic permittivity. It was verified that the spatial vector potential is divided into the vector potential induced by the driver coil and that induced by the displacement current in the material under test. Second, the testing probe was designed with focus on improvement of the fractional change in the pickup coil output with permittivity. Analytical results showed that a larger distance between the driver coil and the pickup coil and a larger driver coil height can enhance the detectability of the permittivity change. To further increase the probe sensitivity, the concept of the differential probe was introduced, and we called the proposed probe the TTDR (tall transmitter and differential receiver) probe. It was also analytically proven that the material properties and the drive frequency have little effect on the displacement current distribution when the drive frequency f o10 MHz, unlike conventional ET on conductive materials, while the dimensions of the probe determine the displacement current distribution. Third, we experimentally investigated the effectiveness of the designed probe for defect detection in GFRPs. The experimental results show that a slit and flat-bottomed holes can be detected by the designed probe. In particular, flat-bottomed holes with diameters of 6 mm located 2 mm away from the GFRP surface can be detected. Therefore, it was experimentally verified that the designed probe can detect both slit defects and subsurface defects. In conclusion, the validity of application of ET to GFRPs was proved. Because ET is a fast non-contact inspection method that uses low-cost equipment, application of ET to GFRP inspection can provide considerable advantages over conventional NDT methods. References [1] McCaffery Timothy R, Zguris Zachary Z, Durant Yvon G. Low cost mold development for prototype parts produced by vacuum assisted resin transfer molding (VARTM). J Compos Mater 2003;37(10):899–912. [2] Markicevic B, Heider D, Advani SG, Walsh Shawn. Stochastic modeling of preform heterogeneity to address dry spots formation in the VARTM Process. Composites Part A 2005;36:851–8.

[3] Tong J. Characteristics of fatigue crack growth in GFRP laminates. Int J Fatigue 2002;24:291–7. [4] Hosoi Atsushi, Yamaguchi Yuhei, Ju Yang, Sato Yasumoto, Kitayama Tsunaji. Detection of delamination in GFRP and CFRP by microwaves with focusing mirror sensor. Mater Sci Forum 2013;750:142–6. [5] Naito Kimiyoshi, Kagawa Yutaka, Utsuno Seishi, Naganuma Tamaki, Kurihara Kanshi. Dielectric properties of eight-harness-stain fabric glass fiber reinforced polyimide matrix composite in the THz frequency range. NDT E Int 2009;42:441–5. [6] Park Je-Woong, Im Kwang-Hee, Hsu David K, Chiou Chien-Ping, Barnard Daniel J. Terahertz ray nondestructive characterizations in FRP composites. Adv Mater Res 2010;123-125:839–42. [7] Naik H Rama Murthy, Jerald J, Mathivanan N Rajesh. Impact damage detection in GFRP laminates through ultrasonic imaging. Adv Mater Res 2012;585:337–41. [8] Montanini Roberto. Quantitative determination of subsurface defects in a reference specimen made of Plexiglas by means of lock-in and pulse phase infrared thermography. Infrared Phys Technol 2010;53:363–71. [9] Yin X, Hutchins DA. Non-destructive evaluation of composite materials using a capacitive imaging technique. Composites: Part B 2012;43:1282–92. [10] Janousek Ladislav, Chen Zhenmao, Yusa Noritaka, Miya Kenzo. Excitation with phase shifted fields-enhancing evaluation of deep cracks in eddy-current testing. NDT E Int 2005;38:508–15. [11] Heuer H, Schulze MH, Meyendorf N. Non-destructive evaluation (NDE) of composites: eddy current techniques. Non-destructive evaluation (NDE) of Polymer matrix composites. Woodhead Publishing; 2013. p. 33–55. [12] Gaebler S, Heuer H, Heinrich G. Measuring and imaging permeability of insulators using high-frequency eddy-current devices. IEEE Trans Inst Meas 2015(99):. [13] Dodd CV, Deeds WE. Analytical solutions to eddy-current probe-coil problems. J Appl Phys 1968;39:2829–38. [14] Luquire JW, Deeds WE, Dodd CV. Alternating current distribution between planar conductor. J Appl Phys 1970;41:3983–91. [15] Pratap SB, Weldon WF. Eddy currents in anisotropic composites applied to pulsed machinery. IEEE Trans Magn 1996;32(2):437–44. [16] Bai Yujie, Zhang Xiaozhang, Jiang Lei, Tang Changliang. 3-D eddy currents analysis in orthotropic materials using truncated region eigenfunction expansion method. Appl Mech Mater 2013;239-240:258–63. [17] Giordano Stefano. Equivalent permittivity tensor in anisotropic random media. J Electrostat 2006;64:655–63. [18] Mori M. Developments in the double exponential formulas for numerical integration. ProcInt Congr Math 1990:1585–94.