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Measurement of shallow defects using noncontact broadband leaky Lamb wave produced by pulsed laser with ultrasound microphone
NDT&E International 111 (2020) 102224
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Measurement of shallow defects using noncontact broadband leaky Lamb wave produced by pulsed laser with ultrasound microphone Ki Chang Kang, Young Hun Kim, Won Young Choi, Kwan Kyu Park * Department of Mechanical Convergence Engineering, Hanyang University, Seoul, 04736, Republic of Korea
A B S T R A C T
In this study, we propose a convenient noncontact laser ultrasonic system to detect small cracks and estimate the wall-thinning defects of thin plates. The system uses an ultrasound microphone to detect the energy leaked from the broadband Lamb-wave propagation. The broadband characteristics of this wave, produced by a pulsed laser, are used to measure the wavenumber. The cumulative standing-wave energy (CSWE) method that uses a traveling wave is implemented to verify the feasibility of the ultrasound microphone. The excitation energy of the pulsed laser was insufficient compared with that of the continuous-wave contact actuator. Therefore, a modified local wavenumber estimation (LWE) method is proposed, which reconstructs several LWE images at various frequencies. These images are averaged to calculate thicknesses of the plate and defects, by using the wavenumber–thickness relationship. The method has an error of 2.84% and 7.7% for the thickness of the plate and defect area, respectively.
1. Introduction Recently, the demand for noncontact ultrasound techniques has increased; the most widely used method is the guided wave technique [1–6]. In particular, Lamb waves have a great capability and potential for nondestructive testing (NDE) and structural health monitoring (SHM) applications for metallic and composite structures [7]. Further more, they can travel long distances and have good sensitivity to various damages [8,9]. In addition, Lamb waves have a dispersive characteristic so that their velocity changes with the thickness changes [10]. Because of these features, Lamb waves are suitable for detecting shallow defects or thickness variation in the plate structure. They are generally measured by full wavefield techniques, which use a dense dataset measured over its time duration. There are two representative methods for detecting defects by using full wavefield. The first is the extraction of the standing wave from the defect. Sohn et al. applied noncontact laser ultrasonic waves from a pulsed laser to a composite structure and visualized the damage by extracting the standing wave from the defect [11]. In this method, a Laplacian filter and an algorithm are used for standing-wave extraction [12]. The second is the local wave estimation (LWE) method, which uses standing waves instead of traveling waves [13,14]. Based on this principle, the LWE method based on scanning LDVs has been developed. This technique generally uses a contact-type actuator to generate Lamb waves with a specified frequency. The LWE is devised as a frequency–wavenumber domain filtering method. In the early stage of this technology, local wavenumber filtering was applied to
the guided-wave field data to detect damage [15]. To analyze the multimode guided-wave field, the separation of the propagating, con verting, and reflecting modes were studied by using wavenumber filtering [16,17]. Kang et al. measured the thickness of a wall-thinned plate using a mode-tuned interdigital transducer [18]. The LWE methods can analyze the thickness of a specimen by using the estimated wavenumber and the material properties of the specimen. Recently, noncontact LWE methods have been developed and combined with many techniques [19–21]. However, precise defect detection is more difficult compared with the continuous wave (CW) contact type actu ator, owing to insufficient excitation energy. Several noncontact techniques enable full wavefield measurement. The most common techniques are pulsed laser, scanning laser Doppler vibrometer [22–25], and air-coupled transducer [26–30]. The typical method for measuring the full wavefield in a noncontact manner is the laser ultrasonic method that generally generates ultrasound waves using a fixed actuator such as a pulsed laser and measures the ultrasound signal using an LDV. The advantage of the scanning LDV is the long-range, the high spatial resolution and that it can overcome the energy dissipation between media by directly focusing the laser beam. However, despite the advantages of easy defect detection, scanning LDV has some disadvantages. (1) It is difficult to reduce the scanning time, and the signal-to-noise ratio (SNR) is low. (2) In addition, it is complex and expensive because of the use of the galvanometer or F-theta lens. (3) Target specimen must have smooth and reflective surface. The technique using the air-coupled transducer has the advantages of easy setup, higher SNR than LDV, and lower cost. However, to generate or receive a
* Corresponding author. E-mail address: [email protected] (K.K. Park). https://doi.org/10.1016/j.ndteint.2020.102224 Received 27 July 2019; Received in revised form 17 January 2020; Accepted 20 January 2020 Available online 21 January 2020 0963-8695/© 2020 Elsevier Ltd. All rights reserved.
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Nomenclature LWE NDE SHM LDV SNR CW LLW CSWE FFT
local wavenumber estimation nondestructive testing structural health monitoring laser Doppler vibrometer signal-to-noise ratio continuous wave leaky Lamb waves cumulative standing wave energy fast Fourier transform
Lamb wave on the plate-like structure, the mode of the longitudinal waves and Lamb waves should be converted. As a result, a critical angle exists for a specific frequency and mode. In this study, a convenient non-contact full wavefield defect detec tion technique was proposed based on a pulsed laser–ultrasound microphone setup. Several disadvantages of the LDVs can be addressed by replacing them with an ultrasound microphone. In the proposed method, the laser is only employed for the excitation of the Lamb wave; therefore, surface smoothness and reflectivity can be neglected. In addition, this technique measures the overall leaky Lamb waves (LLW) signal near the surface, rather than a Lamb wave signal at a specific mode and frequency. As a result, it is not affected by the angle of the ultrasound microphone and waveguide. To verify the feasibility of this technique, we detected defects using the two abovementioned methods. The standing wave extraction method detects small defects using trav eling Lamb waves, that uses the front of the signal measured. Mean while, the LWE method uses the reflected signal at the edges, similar to the steady-state signals from the contact actuator. However, because the excitation Lamb waves energy of the pulsed laser is insufficient compared with the CW contact actuator, and the receiving sensitivity of the ultrasound microphone is lower than ACT at the optimal angle, the local wavenumber estimation results have low SNR. To overcome this problem, we proposed a modified LWE method by using the broadband characteristics of the Lamb waves signal induced by a pulsed laser. The LWE results are obtained for different frequencies, and their average of is used to calculate the thicknesses of the plate and defect. The remainder of this paper is organized as follows. Section 2 pre sents the noncontact laser ultrasonic system based on pulsed laser and ultrasound microphone, and the two methods for visualizing and measuring the defect. Section 3 presents the experimental results of detecting and measuring shallow defects using each method. Section 4 presents the conclusions, discussions, and future work.
Fig. 1. Principle of noncontact laser ultrasonic defect-detection system.
fabricated to reduce the distance between the aluminum plate and the signal measurement point, and to improve the spatial resolution of the acoustic signal. There are two types of signals measured by the micro phone: LLW and direct acoustic signals. The direct acoustic signal has a velocity of 340 m/s in air, and the Lamb wave of a 1-mm-thick aluminum plate has a velocity of 1000 m/s at 100 kHz. As a result, the LLW signal is received first, and then, the direct acoustic signal is received by the microphone. It is easily confirmed by the result of FEA simulation (COMSOL). After the first LLW are received, as shown in Fig. 2 (a), the Lamb wave signals reflected from the edge of the aluminum plate are received continuously, as shown in Fig. 2 (b). The first received LLW signal is suited for using standing wave energy because it clearly identified reflected waves from defects are present. The LLW signals reflected at the edges are similar to the steady-state signals and are, therefore, suitable for LWE method. 2.2. Methods for visualizing defects Two methods for defect visualization are presented in this paper. The first method is the CSWE method proposed by Sohn et al. [11,12]. This method uses the Laplacian filter and standing-wave extraction. After constructing the ultrasound field, the defect is identified and visualized using a filter that can separate the derived standing wave from the defect. Visualization of defects using the CSWE method shows that the LDV is replaced by an ultrasound microphone in a noncontact laser ul trasonic technique. The second method is the modified LWE method that uses the broadband characteristics of the Lamb waves. This method presents a new algorithm that can replace the CW contact actuator with a pulse laser.
2. Methods
2.2.1. Cumulative standing wave energy The CSWE method consists of four steps, after collecting the 3D measurement matrix in the time–space domain, as shown in Fig. 3 [11].
2.1. Principle for measurement of wavenumber and thickness The noncontact laser ultrasonic system is based on measuring the Lamb wave generated by a laser, using an ultrasonic microphone, and this principle is shown in Fig. 1. The Lamb waves generated from the plate coexist in various modes, but the dominant mode is the A0 mode, which is the lowest order of antisymmetric mode. When the Lamb wave propagates in a system such as an elastic plate existing inside a fluid, energy is leaked from the propagating Lamb wave to the surrounding fluid. These waves in the fluid are called leaky Lamb waves (LLW). In the proposed system, the energy of the Lamb wave leaks into the air. LLW are influenced by the coupling and attenuation with air. To minimize this effect, the distance between the aluminum plate and ultrasound microphone must be minimized. As the diameter of the ultrasound microphone used in this work is 4 cm, it is not suitable for measuring the LLW signal at a specific point. Therefore, a conical waveguide is
Fig. 2. Lamb wave propagation snapshot of (a) first received waves and (b) waves reflected from the edge. 2
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This method starts the signal processing by receiving a 3D data matrix in time–space (t–s) domain.
insufficient energy, the LWE image of a single frequency presents wave-pattern artifacts. In contrast with the contact actuator, a pulsed laser produces Lamb waves with broad bandwidth, and using this characteristic, narrow bandpass filter banks of various frequencies are generated and the LWE method of filtering data according to frequency is implemented. Then, the thickness of each frequency is calculated based on the wavenumber–thickness relationship. The artifacts from the LWE images remain on the corresponding thickness images. As the ar tifacts in these images are uncorrelated, the averaging process removes the artifacts and improves the SNR significantly. Fig. 4 shows an over view of the modified LWE method. Similar to the CSWE method, acquiring the 3D measurement matrix is the first step of the algorithm. After that, signal processing is performed according to the following steps.
1) The 3D measurement matrix is transformed from the time–space domain (t–s) to a 3D data matrix of the frequency–wavenumber (f–k) domain, vT , using 3D FFT. Z ∞ Z ∞ Z ∞ � vT kx ; ky ; ω ¼ VT ðx; y; tÞe iðkx xþky yþωtÞ dxdydt ∞
∞
∞
2) The vT matrix is decomposed into components in each quadrant. � � 1 kx > 0 and ky � 0 1 kx � 0 and ky � 0 ϕ1 ¼ ϕ2 ¼ 0 else 0 else � � 1 kx � 0 and ky � 0 1 kx > 0 and ky � 0 ϕ3 ¼ ϕ4 ¼ 0 else 0 else
1) The steady-state response is calculated using the single-frequency FFT (f is a single frequency of the generated narrow band-pass fre quency filter bank.)
3) Each decomposed component is reconverted to the t–s domain using the inverse 3D FFT. Z ∞ Z ∞ Z ∞ � 1 Vp ðx; y; tÞ ¼ vp kx ; ky ; ω e iðkx xþky yþωtÞ dkx dky dω 2π ∞ ∞ ∞
rðx; yÞ ¼
4 X
V 2p ðx; y; tÞ
p¼1
Z
t
SWEðx; y; τÞdτ
CSWEðx; y; tÞ ¼
j2πftÞ
2) The 2D FFT is used to transform the space domain of the calculated steady-state response into the wavenumber domain. A narrow wavenumber filter bank is created using a Gaussian-shaped wave number domain window ðWK Þ, to derive results for the kc value. 0 �qffiffiffiffiffiffiffiffiffiffiffiffiffiffi �2 1 k2x þ k2y kc C � � B WK kx ; ky ; kc ¼ exp@ A 0:72B2K
4) The SWE and CSWE are calculated. SWEðx; y; tÞ ¼ V 2T ðx; y; tÞ
T 1 X V½x; y; t�expð T t¼0
0
In each step, the wave propagating component proceeding in each quadrant direction is decomposed and the SWE is isolated by extracting the energy of the wave propagating component. The CSWE result up to time point t is visualized by combining the CSWE values from all spatial points.
3) The inverse 2D FFT is used to invert the wavenumber domain of the narrow wavenumber filter bank result to the time domain and en velope it. 4) The maximum wavenumber at each point is calculated.
2.2.2. Modified local wavenumber estimation for using pulsed laser The LWE method typically uses attached actuators [15–18]. The use of continuous excitation has the advantage of providing high SNR, as the energy is supplied and measured continuously, without any delay. The method proposed in this paper is a noncontact method using a pulsed laser, and the generated LLW signal has broadband characteristics. Therefore, the energy generated by the laser at a single frequency is lower than that of the method using an attached actuator. Because of
KLOC ½x; y� ¼ argmaxS½x; y; k� k
5) The estimated thickness at a single frequency is computed based on the calculated dispersion curve. 6) The average of the thickness results is calculated. Unlike the conventional LWE method, the narrow band-pass fre quency filter for a specific frequency is used to convert the broadband signal to a signal for a specific frequency before calculating the steadystate response. In the conventional LWE method, the local wavenumber and thickness are estimated at each frequency. The modified LWE method of the noncontact laser ultrasonic system was revised to use the average of the narrow band-pass frequency filter bank results. 3. Experiment 3.1. Experimental setup Fig. 5 shows the experimental setup used to visualize and measure the defects of the aluminum plate. The Nd:YAG laser (Minilite I, Amplitude, CA, USA) was used as the pulsed excitation source in the experiment. The pulsed laser has a wavelength of 532 nm, pulse dura tion of 7 ns and pulse repetition frequency of 10 Hz. The maximum laser intensity is 27 mJ/pulse, and the intensity used in experiments was 19 mJ/pulse. The diameter of the laser spot was 3 mm, without focusing. The irradiated laser was reflected onto an aluminum plate using a mirror. The commercial ultrasound microphone (CM16/CMPA, Avisoft Bioacoustics, Germany) was used to receive a generated LLW signal,
Fig. 3. Overview of cumulative standing wave energy (CSWE) method. 3
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Fig. 4. Overview of modified local wavenumber estimation method.
Fig. 5. Experiment setup for noncontact laser ultrasonic defect-detection system. 4
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with a frequency range of 2–200 kHz and an approximate sensitivity of 500 mV/Pa. A conical waveguide was fabricated with 3D printers to measure the LLW signals at specific points on the aluminum plate. The length of the waveguide was 7.5 cm, and the diameter of its tip was 1 mm. The waveguide also acted as a link to the microphone and motor ized stage. The measured data were transferred to the PC using an oscilloscope. All specimens used in the experiments were fabricated with various milling areas on a 1.1 mm-thick aluminum plate (T6061). The milling areas contained defects, either circular or linear type. The circular-type defects had diameters of 2 mm, 5 mm, or 3 cm. The linear-type defects had a width of 5.5 cm and height of 3 mm. Two specimens had linear defects, which were single and double. Experiments were conducted by placing the milling side of the specimen downward while the laser and microphone were placed on the top. For detecting the defects, the microphone scanned the defect-free side of the specimen. As a result, the proposed method visualized and measured the defect using the Lamb wave, instead of the progressive acoustic signal.
aluminum plate. As in the previous case, both types of signals were measured. Because of the higher velocity of the LLW signal, the time variation of the LLW signal was smaller than that of the acoustic signal. Linear scanning was performed to investigate whether the measured LLW signal has dispersive characteristics. In addition to inspecting the dispersive characterization by producing a dispersion curve using the data acquired from line scanning, the mode of the Lamb wave was also obtained. Fig. 7 shows a dispersion curve constructed using the line-scanning data obtained by moving 500 steps at intervals of 100 μm and the theoretical dispersion curve of the A0 Lamb wave prepared based on the aluminum material property. As the measured data are those of an LLW signal, an error is caused by the influence of the attenuation with the air; however, it is in a form similar to the theoretical value. The dispersion curve shows that the frequency bandwidth of the Lamb wave signal generated by the laser is broadband. Signals from 40 to 200 kHz are generated, which can be confirmed by the frequency analysis using FFT.
3.2. Experimental results of line scanning
3.3. Experimental results of milled specimens
As mentioned above, the signal measured in the experiment consists of an LLW signal and a direct acoustic signal. Fig. 6 shows the result of the ultrasonic microphone measurement using the proposed method. The SNR of an LLW signal is calculated as � � Asignal SNR ¼ 20 log (1)
To detect and visualize defects in the experiments, the 3D mea surement matrix in the t–s domain was acquired by area scanning. Depending on the specimen size, the spacing of the scanning steps was different. To detect a circular defect with a diameter of 5 mm on the 1.1 mm-thick aluminum plate, an area scanning of 51 � 51 steps was per formed at intervals of 400 μm. For the circular defective specimen with a diameter of 3 cm, an area scanning of 110 � 110 steps was performed. The result images comprised 2601 scanning points and 12100 scanning points. The total scanning times were 2 h and 8 h in the current system, respectively. Because the current system uses a single ultrasound microphone, most of the scanning time was required for mechanical movement and the averaging time. The measured data were averaged by eight repetitions because of mechanical limitations. The results were used to reduce the effects of vibration due to the movement of the ul trasound microphone at the motorized stage. The use of an ultrasound microphone array considerably reduces the scanning time, and it may build a one-shot image. Fig. 8 shows the waveform progression in the 3D measurement matrix data at specific time points. A snapshot of the waveform propa gation after 265 μs of irradiating the laser to the aluminum plate is shown in Fig. 8(a). The first measured LLW signal appears to begin to progress. The waveform propagation snapshot after 271 μs of laser irradiation is shown in Fig. 8(b). The LLW propagating on the aluminum plate is dispersive, which means that the frequency and thickness affect
σnoise
where Asignal is the root mean square amplitude of the LLW signal, and
σ noise is the standard deviation of the noise. The SNR of the progress and
reflected LLW signals were 28 dB and 22 dB, respectively. Fig. 6 (a) shows the acoustic data measured 3.5 cm from the laser spot on the aluminum plate. The measurement time of direct acoustic signal coincides with the time taken for the wave to travel a distance of 11 cm at a speed of 340 m/s, which is the sum of the distance from the laser spot and the length of the waveguide. When passing through the waveguide, both signals travel at 340 m/s in air; however, their veloc ities are different at the distance from the laser spot to the waveguide. Unlike the acoustic signal, the Lamb wave moves two to three times faster than the sound velocity in air, depending on the frequency used; therefore, the LLW signals arrive faster than acoustic signals. Fig. 6 (b) shows the acoustic data measured 6.5 cm from the laser spot on the
Fig. 6. Acoustic data (a) 3.5 cm and (b) 6.5 cm from laser spot.
Fig. 7. Dispersion curve with theoretical value. 5
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extremely shallow defect detection is also possible. Because of the laser spot at the upper center part of the figure, the SWE detected at the side is smaller as shown in Fig. 9 (d). In addition, the SWEs generated from linear defects close to the laser spot have larger energies than those farther away. 3.3.2. Experimental results with modified LWE method The conventional LWE method using contact actuators measures the local wavenumber in the steady-state through continuous excitation at a fixed frequency. Pulsed-laser excitation has insufficient energy and is disadvantageous when generating a steady-state response when compared to continuous excitation in contact actuators. However, as the signal reflected from the edge of the specimen is similar to the steadystate signal, the reflected signal can be used for the LWE method. For the Lamb wave A0 mode, the shallow defect area has a lower velocity than the normal aluminum plate, for the same frequency. The wave number and thickness are estimated using a narrow band-pass frequency filter at a specific frequency. The steady-state response of a 140 kHz narrow band-pass filtered signal is calculated as shown in Fig. 10. The wavelength of the defect area is smaller than the normal area and the steady-state response contains indeterminate parts owing to insufficient energy. Based on the steady-state response, the LWE image result is shown in Fig. 10 (b). As the LWE image is reconstructed from a non-CW Lamb wave, the LWE image results present wave-pattern artifacts. The relationship between thickness and wavenumber is shown in Fig. 10 (c), and is calculated from the theoretical A0 Lamb wave dispersion curve. Based on this relationship, the estimated thickness for the 140 kHz narrow band-pass filtered signal is shown in Fig. 10 (d). The wave-pattern artifacts from the LWE image remain on the image of the thickness, and can be pro cessed through the modified method presented in this paper. LWE results are constructed for eight frequencies from 130 kHz to 165 kHz with 5 kHz spacing, as shown in Fig. 11. Wave-pattern artifacts from each frequency are found to be uncorrelated. The estimated wavenumbers have different values according to the center frequency of the narrow band-pass frequency filter. However, as shown in Fig. 12, the thickness estimation image results are mostly consistent with respect to each frequency. These thickness image results are constructed using the relationship
Fig. 8. Snapshot of propagating leaky Lamb wave and acoustic signal.
the propagation velocity. The defect has a thickness of 550 μm, which is 450 μm thinner than the reference aluminum plate, which causes a difference of 25% in the speed at the same frequency. As a result, the signal reflected from the defect is generated, and the wave propagating at the defect propagates at a velocity lower than that of the uncracked portion. The first arriving signal with clearly visible reflections is used in the CSWE method. Fig. 8 (c) is a waveform propagation snapshot at 317 μs after laser irradiation. An acoustic signal with a larger amplitude than that of the LLW signal arrives with a low velocity. The acoustic signals measured at the surface are geometrically influenced by external de fects, and can create differences in the traveling waves at the defects; however, internal defects do not affect the acoustic signals. 3.3.1. Experimental results with CSWE method The CSWE image created using traveling waves was obtained using the initial value of the measured LLW signal. The CSWE method was performed for various types of milled aluminum plates. The CSWE re sults are shown in Fig. 9. Two circular defect specimens of diameter 2 mm and 5 mm and two linear defect specimens were used. As the signal generated by the pulsed laser was a broadband signal, it was difficult to determine a specific wavelength in a Lamb wave with dispersive char acteristics. The wavelength for the frequency range of the signal measured by the ultrasound microphone was approximately 0.7 cm–1 cm in a 1.1 mm-thick aluminum plate. Circular defects with diameters less than half wavelength were detected by the CSWE method and the CSWE result is shown in Fig. 9 (a). This result indicates that defects of less than half wavelength are detectable. In addition, experiments with linear defects were conducted using the CSWE method. The results of a specimen with a single linear defect and double linear defects are shown in Fig. 9 (c) and (d), respectively. The CSWE due to a slightly more milled area of 2 mm diameter is also observed, which implies that
Fig. 9. Specimen and CSWE results: (a) Circular defect of 2 mm diameter, (b) circular defect of 5 mm diameter, (c) single linear defect, and (d) double linear defect. 6
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Fig. 10. (a) Steady-state response, (b) local wavenumber estimation result, (c) calculated relationship between thickness and wavenumber, (d) thickness estimation result at 140 kHz frequency.
Fig. 11. Local wavenumber estimation image of specimen at (a) 130 kHz, (b) 135 kHz, (c) 140 kHz, (d) 145 kHz, (e) 150 kHz, (f) 155 kHz, (g) 160 kHz, and (h) 165 kHz.
Fig. 12. Thickness estimation image of specimen at (a) 130 kHz, (b) 135 kHz, (c) 140 kHz, (d) 145 kHz, (e) 150 kHz, (f) 155 kHz, (g) 160 kHz, and (h) 165 kHz. 7
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between thickness and wavenumber, for each frequency. The wavepattern artifacts remain on the corresponding thickness images, and the artifacts in these images are uncorrelated. Using the average of the various results, the final thickness estima tion result is obtained, as shown in Fig. 13. The estimated thickness of the aluminum plate is 1.07 with a standard deviation of 0.05 (1σ). And the estimated thickness of the shallow defective area is 0.75 with a standard deviation of 0.04 mm (1σ). Compared to the actual thickness of 1.1 mm and 0.75 mm, the average value has an error of 2.84% and 7.7%, respectively. 4. Discussion The CWSE method, which uses the LLW signal in progress, is not affected significantly by the size of the specimen, as compared to the conventional non-contact method. In contrast, the modified LWE method, which uses the reflected signal, is limited by the size of the specimen, as compared to the signal in progress. For the area scanning process in this experiment, an area of approximately 16 cm2 was scan ned depending on the type of defect. However, this is not attributed to the limitations of the technique but rather to the limitation of scanning time in the current system. As the dimensions of test specimens are 15 cm � 20 cm and the LWE images use the data of signals measured after several reflections from the edge without the amplifier. Lamb waves are a promising method for the inspection of plate-like structure owing to their low attenuation and high sensitivity to various damage. From the measured data, the reflected signal amplitude from 400 to 750 μs is almost constant. Therefore, although this modified LWE method is feasible and available enough, it is not an optimal method for large specimens. In the case of using the ACT, including an ultrasound microphone to generate or detect Lamb waves, different experimental errors were easily noticed within the measured data, and the impedance mismatch is significantly high between air and the specimen medium. It causes a huge energy loss at the interface and makes the changes in the amplitude of the propagating Lamb wave, and efficiency lower. The method pro posed in this paper also detects the propagating Lamb waves by using an ultrasound microphone, which results in experimental errors. The dispersion curve obtained from the measured data (a theoretical value image is presented in Fig. 7) exhibits a few differences between the measured dispersion curve and the theoretical dispersion curve. These experimental errors do not always occur in this manner when using the conventional ACT method. However, unlike the conventional ACT method, there are additional errors in this method because it receives the overall broadband signal generated by the laser without considering the angle adjustment and mode conversion. In addition, the waveguide also has a conical shape with a small tip size to receive the signal at a specific point; however, it is not optimized. Therefore, experimental errors can occur when using waveguide for measurements. These dispersive characteristic errors are related to Fig. 12, which estimates the thickness based on the theoretical value. The theoretical dispersion curve value and the measured data exhibit a 5–10% difference in the values, and the slope also differs. These experimental errors and slope differences result in a consistent increment in the estimated thickness that is calculated using the theoretical value with frequency. However, to improve these errors, the modified LWE method is proposed, and the estimated error in the thickness is reduced to 2.84–7.7%. In addition, optimizing the experiment and applying amplifiers can further reduce the errors.
Fig. 13. Thickness estimation results of modified local wavenumber estima tion method.
the cost and complexity of the conventional laser ultrasonic method employing LDV, by replacing the LDV with an ultrasound microphone. In addition, unlike the conventional LDV and ACT techniques, this method eliminates the need to adjust the angle of the laser and ACT. The LLW signal in progress was used for the CSWE method to detect small defects that are smaller than a half wavelength. The conventional LWE method, which generally employs a contact-type actuator, could also be implemented with the modified version by using the proposed noncontact laser ultrasonic system. The issue of excitation-energy insufficiency in the pulsed laser, as compared to the CW contact actu ator, was solved by using the broadband characteristics of the Lamb waves that were induced by the pulsed laser. The local wavenumber for each frequency was estimated by using a narrow band-pass frequency filter, and the corresponding result for thickness estimation was ob tained. The thickness estimation result was calculated by using the average of the results acquired for each frequency and had an error of approximately 2.84–7.7%, as compared to the thickness of real aluminum. The proposed system was not the optimal method for large plates due to the scanning time. However, it could be conducted when implementing an array of ultrasound microphones that reduces the scanning time. Declaration of competing interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Acknowledgments This research was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (No. 2019R1F1A1062162). This research was supported by the MOTIE (Ministry of Trade, In dustry, and Energy) in Korea, under the Fostering Global Talents for Innovative Growth Program (P0008748, Global Human Resource Development for Innovative Design in Robot and Engineering) and su pervised by the Korea Institute for Advancement of Technology (KIAT).
5. Conclusion This paper proposes a convenient noncontact laser ultrasonic method to detect small cracks and estimate the wall-thinning defects in thin plates. The proposed method was implemented using a pulsed laser and an ultrasound microphone. We addressed several problems, including 8
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References
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Measurement of shallow defects using noncontact broadband leaky Lamb wave produced by pulsed laser with ultrasound microphone Ki Chang Kang, Young Hun Kim, Won Young Choi, Kwan Kyu Park * Department of Mechanical Convergence Engineering, Hanyang University, Seoul, 04736, Republic of Korea
A B S T R A C T
In this study, we propose a convenient noncontact laser ultrasonic system to detect small cracks and estimate the wall-thinning defects of thin plates. The system uses an ultrasound microphone to detect the energy leaked from the broadband Lamb-wave propagation. The broadband characteristics of this wave, produced by a pulsed laser, are used to measure the wavenumber. The cumulative standing-wave energy (CSWE) method that uses a traveling wave is implemented to verify the feasibility of the ultrasound microphone. The excitation energy of the pulsed laser was insufficient compared with that of the continuous-wave contact actuator. Therefore, a modified local wavenumber estimation (LWE) method is proposed, which reconstructs several LWE images at various frequencies. These images are averaged to calculate thicknesses of the plate and defects, by using the wavenumber–thickness relationship. The method has an error of 2.84% and 7.7% for the thickness of the plate and defect area, respectively.
1. Introduction Recently, the demand for noncontact ultrasound techniques has increased; the most widely used method is the guided wave technique [1–6]. In particular, Lamb waves have a great capability and potential for nondestructive testing (NDE) and structural health monitoring (SHM) applications for metallic and composite structures [7]. Further more, they can travel long distances and have good sensitivity to various damages [8,9]. In addition, Lamb waves have a dispersive characteristic so that their velocity changes with the thickness changes [10]. Because of these features, Lamb waves are suitable for detecting shallow defects or thickness variation in the plate structure. They are generally measured by full wavefield techniques, which use a dense dataset measured over its time duration. There are two representative methods for detecting defects by using full wavefield. The first is the extraction of the standing wave from the defect. Sohn et al. applied noncontact laser ultrasonic waves from a pulsed laser to a composite structure and visualized the damage by extracting the standing wave from the defect [11]. In this method, a Laplacian filter and an algorithm are used for standing-wave extraction [12]. The second is the local wave estimation (LWE) method, which uses standing waves instead of traveling waves [13,14]. Based on this principle, the LWE method based on scanning LDVs has been developed. This technique generally uses a contact-type actuator to generate Lamb waves with a specified frequency. The LWE is devised as a frequency–wavenumber domain filtering method. In the early stage of this technology, local wavenumber filtering was applied to
the guided-wave field data to detect damage [15]. To analyze the multimode guided-wave field, the separation of the propagating, con verting, and reflecting modes were studied by using wavenumber filtering [16,17]. Kang et al. measured the thickness of a wall-thinned plate using a mode-tuned interdigital transducer [18]. The LWE methods can analyze the thickness of a specimen by using the estimated wavenumber and the material properties of the specimen. Recently, noncontact LWE methods have been developed and combined with many techniques [19–21]. However, precise defect detection is more difficult compared with the continuous wave (CW) contact type actu ator, owing to insufficient excitation energy. Several noncontact techniques enable full wavefield measurement. The most common techniques are pulsed laser, scanning laser Doppler vibrometer [22–25], and air-coupled transducer [26–30]. The typical method for measuring the full wavefield in a noncontact manner is the laser ultrasonic method that generally generates ultrasound waves using a fixed actuator such as a pulsed laser and measures the ultrasound signal using an LDV. The advantage of the scanning LDV is the long-range, the high spatial resolution and that it can overcome the energy dissipation between media by directly focusing the laser beam. However, despite the advantages of easy defect detection, scanning LDV has some disadvantages. (1) It is difficult to reduce the scanning time, and the signal-to-noise ratio (SNR) is low. (2) In addition, it is complex and expensive because of the use of the galvanometer or F-theta lens. (3) Target specimen must have smooth and reflective surface. The technique using the air-coupled transducer has the advantages of easy setup, higher SNR than LDV, and lower cost. However, to generate or receive a
* Corresponding author. E-mail address: [email protected] (K.K. Park). https://doi.org/10.1016/j.ndteint.2020.102224 Received 27 July 2019; Received in revised form 17 January 2020; Accepted 20 January 2020 Available online 21 January 2020 0963-8695/© 2020 Elsevier Ltd. All rights reserved.
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Nomenclature LWE NDE SHM LDV SNR CW LLW CSWE FFT
local wavenumber estimation nondestructive testing structural health monitoring laser Doppler vibrometer signal-to-noise ratio continuous wave leaky Lamb waves cumulative standing wave energy fast Fourier transform
Lamb wave on the plate-like structure, the mode of the longitudinal waves and Lamb waves should be converted. As a result, a critical angle exists for a specific frequency and mode. In this study, a convenient non-contact full wavefield defect detec tion technique was proposed based on a pulsed laser–ultrasound microphone setup. Several disadvantages of the LDVs can be addressed by replacing them with an ultrasound microphone. In the proposed method, the laser is only employed for the excitation of the Lamb wave; therefore, surface smoothness and reflectivity can be neglected. In addition, this technique measures the overall leaky Lamb waves (LLW) signal near the surface, rather than a Lamb wave signal at a specific mode and frequency. As a result, it is not affected by the angle of the ultrasound microphone and waveguide. To verify the feasibility of this technique, we detected defects using the two abovementioned methods. The standing wave extraction method detects small defects using trav eling Lamb waves, that uses the front of the signal measured. Mean while, the LWE method uses the reflected signal at the edges, similar to the steady-state signals from the contact actuator. However, because the excitation Lamb waves energy of the pulsed laser is insufficient compared with the CW contact actuator, and the receiving sensitivity of the ultrasound microphone is lower than ACT at the optimal angle, the local wavenumber estimation results have low SNR. To overcome this problem, we proposed a modified LWE method by using the broadband characteristics of the Lamb waves signal induced by a pulsed laser. The LWE results are obtained for different frequencies, and their average of is used to calculate the thicknesses of the plate and defect. The remainder of this paper is organized as follows. Section 2 pre sents the noncontact laser ultrasonic system based on pulsed laser and ultrasound microphone, and the two methods for visualizing and measuring the defect. Section 3 presents the experimental results of detecting and measuring shallow defects using each method. Section 4 presents the conclusions, discussions, and future work.
Fig. 1. Principle of noncontact laser ultrasonic defect-detection system.
fabricated to reduce the distance between the aluminum plate and the signal measurement point, and to improve the spatial resolution of the acoustic signal. There are two types of signals measured by the micro phone: LLW and direct acoustic signals. The direct acoustic signal has a velocity of 340 m/s in air, and the Lamb wave of a 1-mm-thick aluminum plate has a velocity of 1000 m/s at 100 kHz. As a result, the LLW signal is received first, and then, the direct acoustic signal is received by the microphone. It is easily confirmed by the result of FEA simulation (COMSOL). After the first LLW are received, as shown in Fig. 2 (a), the Lamb wave signals reflected from the edge of the aluminum plate are received continuously, as shown in Fig. 2 (b). The first received LLW signal is suited for using standing wave energy because it clearly identified reflected waves from defects are present. The LLW signals reflected at the edges are similar to the steady-state signals and are, therefore, suitable for LWE method. 2.2. Methods for visualizing defects Two methods for defect visualization are presented in this paper. The first method is the CSWE method proposed by Sohn et al. [11,12]. This method uses the Laplacian filter and standing-wave extraction. After constructing the ultrasound field, the defect is identified and visualized using a filter that can separate the derived standing wave from the defect. Visualization of defects using the CSWE method shows that the LDV is replaced by an ultrasound microphone in a noncontact laser ul trasonic technique. The second method is the modified LWE method that uses the broadband characteristics of the Lamb waves. This method presents a new algorithm that can replace the CW contact actuator with a pulse laser.
2. Methods
2.2.1. Cumulative standing wave energy The CSWE method consists of four steps, after collecting the 3D measurement matrix in the time–space domain, as shown in Fig. 3 [11].
2.1. Principle for measurement of wavenumber and thickness The noncontact laser ultrasonic system is based on measuring the Lamb wave generated by a laser, using an ultrasonic microphone, and this principle is shown in Fig. 1. The Lamb waves generated from the plate coexist in various modes, but the dominant mode is the A0 mode, which is the lowest order of antisymmetric mode. When the Lamb wave propagates in a system such as an elastic plate existing inside a fluid, energy is leaked from the propagating Lamb wave to the surrounding fluid. These waves in the fluid are called leaky Lamb waves (LLW). In the proposed system, the energy of the Lamb wave leaks into the air. LLW are influenced by the coupling and attenuation with air. To minimize this effect, the distance between the aluminum plate and ultrasound microphone must be minimized. As the diameter of the ultrasound microphone used in this work is 4 cm, it is not suitable for measuring the LLW signal at a specific point. Therefore, a conical waveguide is
Fig. 2. Lamb wave propagation snapshot of (a) first received waves and (b) waves reflected from the edge. 2
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This method starts the signal processing by receiving a 3D data matrix in time–space (t–s) domain.
insufficient energy, the LWE image of a single frequency presents wave-pattern artifacts. In contrast with the contact actuator, a pulsed laser produces Lamb waves with broad bandwidth, and using this characteristic, narrow bandpass filter banks of various frequencies are generated and the LWE method of filtering data according to frequency is implemented. Then, the thickness of each frequency is calculated based on the wavenumber–thickness relationship. The artifacts from the LWE images remain on the corresponding thickness images. As the ar tifacts in these images are uncorrelated, the averaging process removes the artifacts and improves the SNR significantly. Fig. 4 shows an over view of the modified LWE method. Similar to the CSWE method, acquiring the 3D measurement matrix is the first step of the algorithm. After that, signal processing is performed according to the following steps.
1) The 3D measurement matrix is transformed from the time–space domain (t–s) to a 3D data matrix of the frequency–wavenumber (f–k) domain, vT , using 3D FFT. Z ∞ Z ∞ Z ∞ � vT kx ; ky ; ω ¼ VT ðx; y; tÞe iðkx xþky yþωtÞ dxdydt ∞
∞
∞
2) The vT matrix is decomposed into components in each quadrant. � � 1 kx > 0 and ky � 0 1 kx � 0 and ky � 0 ϕ1 ¼ ϕ2 ¼ 0 else 0 else � � 1 kx � 0 and ky � 0 1 kx > 0 and ky � 0 ϕ3 ¼ ϕ4 ¼ 0 else 0 else
1) The steady-state response is calculated using the single-frequency FFT (f is a single frequency of the generated narrow band-pass fre quency filter bank.)
3) Each decomposed component is reconverted to the t–s domain using the inverse 3D FFT. Z ∞ Z ∞ Z ∞ � 1 Vp ðx; y; tÞ ¼ vp kx ; ky ; ω e iðkx xþky yþωtÞ dkx dky dω 2π ∞ ∞ ∞
rðx; yÞ ¼
4 X
V 2p ðx; y; tÞ
p¼1
Z
t
SWEðx; y; τÞdτ
CSWEðx; y; tÞ ¼
j2πftÞ
2) The 2D FFT is used to transform the space domain of the calculated steady-state response into the wavenumber domain. A narrow wavenumber filter bank is created using a Gaussian-shaped wave number domain window ðWK Þ, to derive results for the kc value. 0 �qffiffiffiffiffiffiffiffiffiffiffiffiffiffi �2 1 k2x þ k2y kc C � � B WK kx ; ky ; kc ¼ exp@ A 0:72B2K
4) The SWE and CSWE are calculated. SWEðx; y; tÞ ¼ V 2T ðx; y; tÞ
T 1 X V½x; y; t�expð T t¼0
0
In each step, the wave propagating component proceeding in each quadrant direction is decomposed and the SWE is isolated by extracting the energy of the wave propagating component. The CSWE result up to time point t is visualized by combining the CSWE values from all spatial points.
3) The inverse 2D FFT is used to invert the wavenumber domain of the narrow wavenumber filter bank result to the time domain and en velope it. 4) The maximum wavenumber at each point is calculated.
2.2.2. Modified local wavenumber estimation for using pulsed laser The LWE method typically uses attached actuators [15–18]. The use of continuous excitation has the advantage of providing high SNR, as the energy is supplied and measured continuously, without any delay. The method proposed in this paper is a noncontact method using a pulsed laser, and the generated LLW signal has broadband characteristics. Therefore, the energy generated by the laser at a single frequency is lower than that of the method using an attached actuator. Because of
KLOC ½x; y� ¼ argmaxS½x; y; k� k
5) The estimated thickness at a single frequency is computed based on the calculated dispersion curve. 6) The average of the thickness results is calculated. Unlike the conventional LWE method, the narrow band-pass fre quency filter for a specific frequency is used to convert the broadband signal to a signal for a specific frequency before calculating the steadystate response. In the conventional LWE method, the local wavenumber and thickness are estimated at each frequency. The modified LWE method of the noncontact laser ultrasonic system was revised to use the average of the narrow band-pass frequency filter bank results. 3. Experiment 3.1. Experimental setup Fig. 5 shows the experimental setup used to visualize and measure the defects of the aluminum plate. The Nd:YAG laser (Minilite I, Amplitude, CA, USA) was used as the pulsed excitation source in the experiment. The pulsed laser has a wavelength of 532 nm, pulse dura tion of 7 ns and pulse repetition frequency of 10 Hz. The maximum laser intensity is 27 mJ/pulse, and the intensity used in experiments was 19 mJ/pulse. The diameter of the laser spot was 3 mm, without focusing. The irradiated laser was reflected onto an aluminum plate using a mirror. The commercial ultrasound microphone (CM16/CMPA, Avisoft Bioacoustics, Germany) was used to receive a generated LLW signal,
Fig. 3. Overview of cumulative standing wave energy (CSWE) method. 3
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Fig. 4. Overview of modified local wavenumber estimation method.
Fig. 5. Experiment setup for noncontact laser ultrasonic defect-detection system. 4
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with a frequency range of 2–200 kHz and an approximate sensitivity of 500 mV/Pa. A conical waveguide was fabricated with 3D printers to measure the LLW signals at specific points on the aluminum plate. The length of the waveguide was 7.5 cm, and the diameter of its tip was 1 mm. The waveguide also acted as a link to the microphone and motor ized stage. The measured data were transferred to the PC using an oscilloscope. All specimens used in the experiments were fabricated with various milling areas on a 1.1 mm-thick aluminum plate (T6061). The milling areas contained defects, either circular or linear type. The circular-type defects had diameters of 2 mm, 5 mm, or 3 cm. The linear-type defects had a width of 5.5 cm and height of 3 mm. Two specimens had linear defects, which were single and double. Experiments were conducted by placing the milling side of the specimen downward while the laser and microphone were placed on the top. For detecting the defects, the microphone scanned the defect-free side of the specimen. As a result, the proposed method visualized and measured the defect using the Lamb wave, instead of the progressive acoustic signal.
aluminum plate. As in the previous case, both types of signals were measured. Because of the higher velocity of the LLW signal, the time variation of the LLW signal was smaller than that of the acoustic signal. Linear scanning was performed to investigate whether the measured LLW signal has dispersive characteristics. In addition to inspecting the dispersive characterization by producing a dispersion curve using the data acquired from line scanning, the mode of the Lamb wave was also obtained. Fig. 7 shows a dispersion curve constructed using the line-scanning data obtained by moving 500 steps at intervals of 100 μm and the theoretical dispersion curve of the A0 Lamb wave prepared based on the aluminum material property. As the measured data are those of an LLW signal, an error is caused by the influence of the attenuation with the air; however, it is in a form similar to the theoretical value. The dispersion curve shows that the frequency bandwidth of the Lamb wave signal generated by the laser is broadband. Signals from 40 to 200 kHz are generated, which can be confirmed by the frequency analysis using FFT.
3.2. Experimental results of line scanning
3.3. Experimental results of milled specimens
As mentioned above, the signal measured in the experiment consists of an LLW signal and a direct acoustic signal. Fig. 6 shows the result of the ultrasonic microphone measurement using the proposed method. The SNR of an LLW signal is calculated as � � Asignal SNR ¼ 20 log (1)
To detect and visualize defects in the experiments, the 3D mea surement matrix in the t–s domain was acquired by area scanning. Depending on the specimen size, the spacing of the scanning steps was different. To detect a circular defect with a diameter of 5 mm on the 1.1 mm-thick aluminum plate, an area scanning of 51 � 51 steps was per formed at intervals of 400 μm. For the circular defective specimen with a diameter of 3 cm, an area scanning of 110 � 110 steps was performed. The result images comprised 2601 scanning points and 12100 scanning points. The total scanning times were 2 h and 8 h in the current system, respectively. Because the current system uses a single ultrasound microphone, most of the scanning time was required for mechanical movement and the averaging time. The measured data were averaged by eight repetitions because of mechanical limitations. The results were used to reduce the effects of vibration due to the movement of the ul trasound microphone at the motorized stage. The use of an ultrasound microphone array considerably reduces the scanning time, and it may build a one-shot image. Fig. 8 shows the waveform progression in the 3D measurement matrix data at specific time points. A snapshot of the waveform propa gation after 265 μs of irradiating the laser to the aluminum plate is shown in Fig. 8(a). The first measured LLW signal appears to begin to progress. The waveform propagation snapshot after 271 μs of laser irradiation is shown in Fig. 8(b). The LLW propagating on the aluminum plate is dispersive, which means that the frequency and thickness affect
σnoise
where Asignal is the root mean square amplitude of the LLW signal, and
σ noise is the standard deviation of the noise. The SNR of the progress and
reflected LLW signals were 28 dB and 22 dB, respectively. Fig. 6 (a) shows the acoustic data measured 3.5 cm from the laser spot on the aluminum plate. The measurement time of direct acoustic signal coincides with the time taken for the wave to travel a distance of 11 cm at a speed of 340 m/s, which is the sum of the distance from the laser spot and the length of the waveguide. When passing through the waveguide, both signals travel at 340 m/s in air; however, their veloc ities are different at the distance from the laser spot to the waveguide. Unlike the acoustic signal, the Lamb wave moves two to three times faster than the sound velocity in air, depending on the frequency used; therefore, the LLW signals arrive faster than acoustic signals. Fig. 6 (b) shows the acoustic data measured 6.5 cm from the laser spot on the
Fig. 6. Acoustic data (a) 3.5 cm and (b) 6.5 cm from laser spot.
Fig. 7. Dispersion curve with theoretical value. 5
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extremely shallow defect detection is also possible. Because of the laser spot at the upper center part of the figure, the SWE detected at the side is smaller as shown in Fig. 9 (d). In addition, the SWEs generated from linear defects close to the laser spot have larger energies than those farther away. 3.3.2. Experimental results with modified LWE method The conventional LWE method using contact actuators measures the local wavenumber in the steady-state through continuous excitation at a fixed frequency. Pulsed-laser excitation has insufficient energy and is disadvantageous when generating a steady-state response when compared to continuous excitation in contact actuators. However, as the signal reflected from the edge of the specimen is similar to the steadystate signal, the reflected signal can be used for the LWE method. For the Lamb wave A0 mode, the shallow defect area has a lower velocity than the normal aluminum plate, for the same frequency. The wave number and thickness are estimated using a narrow band-pass frequency filter at a specific frequency. The steady-state response of a 140 kHz narrow band-pass filtered signal is calculated as shown in Fig. 10. The wavelength of the defect area is smaller than the normal area and the steady-state response contains indeterminate parts owing to insufficient energy. Based on the steady-state response, the LWE image result is shown in Fig. 10 (b). As the LWE image is reconstructed from a non-CW Lamb wave, the LWE image results present wave-pattern artifacts. The relationship between thickness and wavenumber is shown in Fig. 10 (c), and is calculated from the theoretical A0 Lamb wave dispersion curve. Based on this relationship, the estimated thickness for the 140 kHz narrow band-pass filtered signal is shown in Fig. 10 (d). The wave-pattern artifacts from the LWE image remain on the image of the thickness, and can be pro cessed through the modified method presented in this paper. LWE results are constructed for eight frequencies from 130 kHz to 165 kHz with 5 kHz spacing, as shown in Fig. 11. Wave-pattern artifacts from each frequency are found to be uncorrelated. The estimated wavenumbers have different values according to the center frequency of the narrow band-pass frequency filter. However, as shown in Fig. 12, the thickness estimation image results are mostly consistent with respect to each frequency. These thickness image results are constructed using the relationship
Fig. 8. Snapshot of propagating leaky Lamb wave and acoustic signal.
the propagation velocity. The defect has a thickness of 550 μm, which is 450 μm thinner than the reference aluminum plate, which causes a difference of 25% in the speed at the same frequency. As a result, the signal reflected from the defect is generated, and the wave propagating at the defect propagates at a velocity lower than that of the uncracked portion. The first arriving signal with clearly visible reflections is used in the CSWE method. Fig. 8 (c) is a waveform propagation snapshot at 317 μs after laser irradiation. An acoustic signal with a larger amplitude than that of the LLW signal arrives with a low velocity. The acoustic signals measured at the surface are geometrically influenced by external de fects, and can create differences in the traveling waves at the defects; however, internal defects do not affect the acoustic signals. 3.3.1. Experimental results with CSWE method The CSWE image created using traveling waves was obtained using the initial value of the measured LLW signal. The CSWE method was performed for various types of milled aluminum plates. The CSWE re sults are shown in Fig. 9. Two circular defect specimens of diameter 2 mm and 5 mm and two linear defect specimens were used. As the signal generated by the pulsed laser was a broadband signal, it was difficult to determine a specific wavelength in a Lamb wave with dispersive char acteristics. The wavelength for the frequency range of the signal measured by the ultrasound microphone was approximately 0.7 cm–1 cm in a 1.1 mm-thick aluminum plate. Circular defects with diameters less than half wavelength were detected by the CSWE method and the CSWE result is shown in Fig. 9 (a). This result indicates that defects of less than half wavelength are detectable. In addition, experiments with linear defects were conducted using the CSWE method. The results of a specimen with a single linear defect and double linear defects are shown in Fig. 9 (c) and (d), respectively. The CSWE due to a slightly more milled area of 2 mm diameter is also observed, which implies that
Fig. 9. Specimen and CSWE results: (a) Circular defect of 2 mm diameter, (b) circular defect of 5 mm diameter, (c) single linear defect, and (d) double linear defect. 6
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Fig. 10. (a) Steady-state response, (b) local wavenumber estimation result, (c) calculated relationship between thickness and wavenumber, (d) thickness estimation result at 140 kHz frequency.
Fig. 11. Local wavenumber estimation image of specimen at (a) 130 kHz, (b) 135 kHz, (c) 140 kHz, (d) 145 kHz, (e) 150 kHz, (f) 155 kHz, (g) 160 kHz, and (h) 165 kHz.
Fig. 12. Thickness estimation image of specimen at (a) 130 kHz, (b) 135 kHz, (c) 140 kHz, (d) 145 kHz, (e) 150 kHz, (f) 155 kHz, (g) 160 kHz, and (h) 165 kHz. 7
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between thickness and wavenumber, for each frequency. The wavepattern artifacts remain on the corresponding thickness images, and the artifacts in these images are uncorrelated. Using the average of the various results, the final thickness estima tion result is obtained, as shown in Fig. 13. The estimated thickness of the aluminum plate is 1.07 with a standard deviation of 0.05 (1σ). And the estimated thickness of the shallow defective area is 0.75 with a standard deviation of 0.04 mm (1σ). Compared to the actual thickness of 1.1 mm and 0.75 mm, the average value has an error of 2.84% and 7.7%, respectively. 4. Discussion The CWSE method, which uses the LLW signal in progress, is not affected significantly by the size of the specimen, as compared to the conventional non-contact method. In contrast, the modified LWE method, which uses the reflected signal, is limited by the size of the specimen, as compared to the signal in progress. For the area scanning process in this experiment, an area of approximately 16 cm2 was scan ned depending on the type of defect. However, this is not attributed to the limitations of the technique but rather to the limitation of scanning time in the current system. As the dimensions of test specimens are 15 cm � 20 cm and the LWE images use the data of signals measured after several reflections from the edge without the amplifier. Lamb waves are a promising method for the inspection of plate-like structure owing to their low attenuation and high sensitivity to various damage. From the measured data, the reflected signal amplitude from 400 to 750 μs is almost constant. Therefore, although this modified LWE method is feasible and available enough, it is not an optimal method for large specimens. In the case of using the ACT, including an ultrasound microphone to generate or detect Lamb waves, different experimental errors were easily noticed within the measured data, and the impedance mismatch is significantly high between air and the specimen medium. It causes a huge energy loss at the interface and makes the changes in the amplitude of the propagating Lamb wave, and efficiency lower. The method pro posed in this paper also detects the propagating Lamb waves by using an ultrasound microphone, which results in experimental errors. The dispersion curve obtained from the measured data (a theoretical value image is presented in Fig. 7) exhibits a few differences between the measured dispersion curve and the theoretical dispersion curve. These experimental errors do not always occur in this manner when using the conventional ACT method. However, unlike the conventional ACT method, there are additional errors in this method because it receives the overall broadband signal generated by the laser without considering the angle adjustment and mode conversion. In addition, the waveguide also has a conical shape with a small tip size to receive the signal at a specific point; however, it is not optimized. Therefore, experimental errors can occur when using waveguide for measurements. These dispersive characteristic errors are related to Fig. 12, which estimates the thickness based on the theoretical value. The theoretical dispersion curve value and the measured data exhibit a 5–10% difference in the values, and the slope also differs. These experimental errors and slope differences result in a consistent increment in the estimated thickness that is calculated using the theoretical value with frequency. However, to improve these errors, the modified LWE method is proposed, and the estimated error in the thickness is reduced to 2.84–7.7%. In addition, optimizing the experiment and applying amplifiers can further reduce the errors.
Fig. 13. Thickness estimation results of modified local wavenumber estima tion method.
the cost and complexity of the conventional laser ultrasonic method employing LDV, by replacing the LDV with an ultrasound microphone. In addition, unlike the conventional LDV and ACT techniques, this method eliminates the need to adjust the angle of the laser and ACT. The LLW signal in progress was used for the CSWE method to detect small defects that are smaller than a half wavelength. The conventional LWE method, which generally employs a contact-type actuator, could also be implemented with the modified version by using the proposed noncontact laser ultrasonic system. The issue of excitation-energy insufficiency in the pulsed laser, as compared to the CW contact actu ator, was solved by using the broadband characteristics of the Lamb waves that were induced by the pulsed laser. The local wavenumber for each frequency was estimated by using a narrow band-pass frequency filter, and the corresponding result for thickness estimation was ob tained. The thickness estimation result was calculated by using the average of the results acquired for each frequency and had an error of approximately 2.84–7.7%, as compared to the thickness of real aluminum. The proposed system was not the optimal method for large plates due to the scanning time. However, it could be conducted when implementing an array of ultrasound microphones that reduces the scanning time. Declaration of competing interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Acknowledgments This research was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (No. 2019R1F1A1062162). This research was supported by the MOTIE (Ministry of Trade, In dustry, and Energy) in Korea, under the Fostering Global Talents for Innovative Growth Program (P0008748, Global Human Resource Development for Innovative Design in Robot and Engineering) and su pervised by the Korea Institute for Advancement of Technology (KIAT).
5. Conclusion This paper proposes a convenient noncontact laser ultrasonic method to detect small cracks and estimate the wall-thinning defects in thin plates. The proposed method was implemented using a pulsed laser and an ultrasound microphone. We addressed several problems, including 8
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