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Imaging of contact acoustic nonlinearity using synthetic aperture technique
Ultrasonics 53 (2013) 1349–1354
Contents lists available at SciVerse ScienceDirect
Ultrasonics journal homepage: www.elsevier.com/locate/ultras
Imaging of contact acoustic nonlinearity using synthetic aperture technique Dongseok Yun a, Jongbeom Kim a, Kyung-Young Jhang b,⇑ a b
Graduate School of Mechanical Engineering, Hanyang University, Seoul 133-791, Republic of Korea School of Mechanical Engineering, Hanyang University, Seoul 133-791, Republic of Korea
a r t i c l e
i n f o
Article history: Received 1 December 2012 Received in revised form 31 January 2013 Accepted 2 April 2013 Available online 20 April 2013 Keywords: Contact acoustic nonlinearity (CAN) Contact interface Synthetic aperture focusing technique (SAFT) Short-time Fourier transform (STFT)
a b s t r a c t The angle beam incidence and reflection technique for the evaluation of contact acoustic nonlinearity (CAN) at solid–solid contact interfaces (e.g., closed cracks) has recently been developed to overcome the disadvantage of accessing both the inner and outer surfaces of structures for attaching pulsing and receiving transducers in the through-transmission of normal incidence technique. This paper proposes a technique for B-mode imaging of CAN based on the above reflection technique, which uses the synthetic aperture focusing technique (SAFT) and short-time Fourier transform (STFT) to visualize the distribution of the CAN-induced second harmonic magnitude as well as the nonlinear parameter. In order to verify the usefulness of the proposed method, a solid–solid contact interface was tested and the change of the contact acoustic nonlinearity according to the increasing contact pressure was visualized in images of the second harmonic magnitude and the relative nonlinear parameter. The experimental results showed good agreement with the previously developed theory identifying the dependence of the scattered second harmonics on the contact pressure. This technique can be used for the detection and improvement of the sizing accuracy of closed cracks that are difficult to detect using the conventional linear ultrasonic technique. Ó 2013 Elsevier B.V. All rights reserved.
1. Introduction When an ultrasonic wave is incident to imperfect interfaces, higher harmonic waves are generated in the reflected or transmitted waves due to contact acoustic nonlinearity (CAN) [1–6]. Many researchers have investigated this phenomenon for use in detecting closed cracks, which are hard to detect using conventional linear ultrasonic techniques [7–10]. However, this technique is still limited in practical applications, since the interpretation of the received signal needs a highly experienced expert. That is, further development of the imaging technique is required for easy application. In this paper, we propose a technique for the B-mode imaging of CAN that is based on our previous work, in which the magnitude of the second order harmonic wave generated in the ultrasonic wave reflected by the contact interface was analyzed quantitatively [11]. The ultrasonic imaging technique that uses a phased array has already been commercialized [12–15]. However, this phased array technique is difficult to apply for the imaging of nonlinear ultrasonic characteristics for several reasons: first, the acoustic power transmitted from each small transducer of the phased array probe ⇑ Corresponding author. Address: School of Mechanical Engineering, Hanyang University, Haengdang-dong 17, Seongdong-Gu, Seoul 133-791, Republic of Korea. Tel.: +82 2 2220 0434; fax: +82 2 2299 7207. E-mail address: [email protected] (K.-Y. Jhang). 0041-624X/$ - see front matter Ó 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.ultras.2013.04.002
is too low to activate the acoustic nonlinearity. Nevertheless, in medical applications, the phased array technique is available for the imaging of acoustic nonlinearity because biological soft tissues have much higher nonlinearity, thus a harmonic wave induced by acoustic nonlinearity is observable with comparatively lower acoustic power [16–18]. In applications regarding metallic materials for industrial nondestructive testing (NDT), however, the acoustic nonlinearity is relatively weak, thus a high power input is usually required. Second, in order to produce a high power acoustic wave, a high power electric signal should be supplied to the transducers. Additionally, a high-speed switch (multiplexer) that has the capability to supply a high power electric signal into each of the arrayed transducers is required, but this type of switch has not yet been commercialized. Consequently, the direct implementation of the nonlinear ultrasonic technique into current phased array equipment is difficult at the present time. Our proposed method overcomes this problem by adopting the synthetic aperture focusing technique (SAFT) [19–21], which uses two transducers (a transmitter and receiver pair) that are generally used in the pitch-catch method of ultrasonic NDT and scans them to construct the image. Although this method requires more time to construct the image due to mechanical scanning, a high power electric signal can be supplied into the transducer without a switch and the sensitivity kept high in order to detect the harmonic wave by using a separate transducer as a receiver with a resonant frequency identical to the frequency of the harmonic wave to be
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detected. Furthermore, short-time Fourier transform (STFT) [22,23] was used to acquire the amplitude of the fundamental frequency and the harmonic frequency separately in the time domain for the imaging of CAN. In order to verify the usefulness of the proposed imaging method, a solid–solid interface was constructed using aluminum blocks and was tested by a specially constructed experimental system in which a hydraulic press was employed to control the contact pressure at the contact interface. The variation of the contact acoustic nonlinearity at the contacting interface according to the increase in the contact pressure was visualized in images of the second harmonic magnitude and the relative nonlinear parameter. 2. SAFT for acquiring ultrasonic image The principle for acquiring synthetic aperture ultrasonic images is shown in Fig. 1, where a transducer transmits an ultrasonic wave and all of the transducers receive the wave reflected by a reflector. This procedure is repeated for the number of transducers by sequentially changing the transmitting transducer. Therefore, if the number of transducers is N, then a total of N N signals are acquired. In the figure, (xp, zp) is the image point, (xi, zi) is the position of the transmitting transducer i, (xj, zj) is the position of the receiving transducer j, di is the distance from the transmitter to the image point, and dj is the distance from the image point to the receiver. The echo signal received by each transducer has a time lag that is dependent on the total propagation distance between the transmitter and receiver. Finding the geometric distance from the transmitting transducer to the image point and back to the receiving transducer facilitates the required focusing [19,20]. The total propagation distance of the ultrasonic wave can be expressed as shown in the following equation:
dij ðxp ; zp Þ ¼ di þ dj qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ¼ ðxi xp Þ2 þ ðzi zp Þ2 þ ðxj xp Þ2 þ ðzj zp Þ2
ð1Þ
The corresponding time of flight tij(xp, zp) is:
tij ðxp ; zp Þ ¼
dij ðxp ; zp Þ c
ð2Þ
where c is the wave speed. Then, the amplitude at an image point is acquired as follows:
Iðxp ; zp Þ ¼
N X N X yij tij ðxp ; zp Þ
ð3Þ
j¼1 i¼1
where N is the number of transducers, and yij denotes the signal amplitude obtained when the i -th transducer is the transmitter and the j-th transducer is the receiver. The final image can be reconstructed by repeating the above calculation for all points (pixels) in the imaging area. 3. STFT for acquiring harmonic image In the nonlinear ultrasonic technique using the second harmonic amplitude measurement, the Fourier transform is generally used to measure the magnitude of the second harmonic component from the received signal. The general Fourier transform, however, loses the time information, and thus it is impossible to obtain the position of the reflector. Therefore, we employed the STFT technique to obtain the temporal change of the frequency contents in the signal. Fig. 2a shows the scheme of STFT. Only a portion of the signal overlapped with a fixed-size moving window is Fourier-transformed [21,22]. By moving the window step-bystep, the Fourier transform is repeated to obtain the time–frequency information. The Hanning window function was used in this study with a 3 ls width and a moving time step of 0.1 ls. Fig. 2b shows an example of the STFT result in the spectrogram of a real signal that has a fundamental frequency of 2.5 MHz and a double frequency component at 5 MHz, where the time information corresponds to the center of the moving window. Accordingly, the signal amplitude of the fundamental and harmonic frequency components can be acquired separately in the time-domain. Then, the amplitude at an image point is acquired as follows:
I1 ðxp ; zp Þ ¼
N X N N X N X X Y ij ðf0 ; tij Þ and I2 ðxp ; zp Þ ¼ Y ij ð2f 0 ; tij Þ j¼1 i¼1
ð4Þ
j¼1 i¼1
where Yij is the amplitude of STFT of the signal, and I1 and I2 are the magnitudes of the fundamental frequency f0 and its second harmonic frequency at the imaging point, respectively. Finally, the relative nonlinear parameter b0 [24] is calculated as follows:
b0 ðxp ; zp Þ ¼
I2 ðxp ; zp Þ I21 ðxp ; zp Þ
ð5Þ
4. Experimental procedure
Fig. 1. Basic principle of SAFT: Geometry and method of image construction.
Fig. 3 shows the experimental system to verify the usefulness of the proposed method. A pair of aluminum 6061-T6 blocks placed into contact with an external normal load was used as the test specimen. The imaging area was established at the center of the interfaces as shown in the figure. The bold box indicates the region-of-interest (ROI), and its enlarged diagram is shown in the lower right side. The upper interface was flat, while the lower interface had partial unevenness. Thus, the left side of the ROI had a non-contact interface, whereas the right side had a contact interface. The dimension details and shape of the blocks are shown in Fig. 4. The thickness was 40 mm. The unevenness of the lower block was 1 mm high, and the surface, which made contact with the upper block, was polished using #600 sandpaper.
D. Yun et al. / Ultrasonics 53 (2013) 1349–1354
Fig. 2. Principle of the STFT (a) in the time-domain and (b) result of STFT.
Fig. 3. Schematic diagram of measurement system.
Fig. 4. Dimensions of two aluminum blocks: (a) upper specimen and (b) lower specimen (unit: mm).
Fig. 5. Photograph of jigs applied at the specimen.
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Fig. 6. SAFT images of fundamental and second harmonic frequencies at three different contact pressures, 0 MPa, 20 MPa, and 40 MPa.
Fig. 7. Images of the ratio of nonlinear parameter obtained at (a) 20 MPa and (b) 40 MPa contact pressures to the initial value obtained at no contact pressure.
Hydraulic loading was used to apply a compression load on the contacting interfaces to induce the variations of the contact conditions. The imaging was performed for different loads, and the change in the image according to the variation of the contact pressure was investigated. The load was measured with a load cell attached at the bottom of the specimen. The center of the loading was identical to the center of the unevenness, and the loading area
on the upper specimen was larger than the uneven area, thus the pressure applied on the contact interface was assured to be uniform, and the pressure was calculated as the applied load divided by the area of the contact interface. In order to establish the angle beam incidence and reflection in pitch-catch mode, the transducers were located on the angled sides of the upper specimen as shown in Fig. 3. A similar experimental
D. Yun et al. / Ultrasonics 53 (2013) 1349–1354
set-up is described in other reports for observation of nonlinear acoustic effects at imperfect interfaces [25–27]. The angle of the ultrasonic wave incident to the interface was 45°. By using this set-up, the transducers can be moved without interfering with the external loading, and the path length of the center beam can be made equal regardless of the transmitter position, as shown by the lines of the typical beam path in Fig. 3. This allows omission of a process to compensate for the difference in the attenuation of the signal amplitude due to the difference in the path length. However, this set-up looks different than what was shown in principle, that is, Fig. 1 shows the normal incidence, while Fig. 3 shows the angle incidence. This was because external loading was necessary to apply uniform pressure on the contact interfaces in order to change the contact conditions of the interfaces and to investigate the corresponding variation of CAN, thus the angle incidence and reflection technique was employed to avoid the interference of the transducer with the loading jig. Regardless, the previously described principle of SAFT remained available, except that the transmitter and the receiver were completely separated in our experimental set-up. Fig. 5 shows the jigs to hold the transducer and to maintain a constant pressure between the specimen and the transducer by using springs. In the experiments, a 2.25 MHz longitudinal wave transducer was used as a transmitter, and a 5 MHz longitudinal wave transducer was employed as a receiver. A tone-burst signal of 2.5 MHz was input to the transmitter with a high-power gated amplifier (Ritec, RAM-5000 SNAP). The number of cycles was five. The received signal was monitored with a digital oscilloscope (LECROY WS452). MATLAB was used for the signal processing. We scanned the transducers using a 5 mm step to apply SAFT. The number of transducer scan positions was six for both transmitting and receiving, thus a total of 36 signals were acquired. The experiments were performed after the loading/unloading process was repeated ten times in order to eliminate the hysteresis effect in the contact interfaces [8].
5. Results Fig. 6 shows the results of the fundamental and second harmonic frequency images according to the contact pressure. The dotted box indicates the imaging area. In all of the images, the interface was clearly visualized. Next, the change in the average magnitudes at the non-contact and contact interfaces was evaluated separately. At the non-contact interface, a noticeable change in the magnitudes of the fundamental and second harmonic frequencies was not observed. Conversely, at the contact interface, the magnitude of the fundamental frequency clearly decreased by the increasing contact pressure. This phenomenon results from the contact interfaces closing as the contacting pressure increased, thus the acoustic reflectivity also decreased. However, the magnitude of the second harmonic frequency increased at the beginning of the contact to reach a maximum value, and then decreased because the interface became fully closed. In our experiment, the maximum magnitude of the second harmonic frequency was found at a contact pressure of 20 MPa. These behaviors reflect approximately the nonlinear characteristics of contact interfaces and are in good agreement with the results of our theoretical and experimental study on the harmonic generation of an angle beam incident ultrasonic wave in solid–solid contact interfaces [11]. Consequently, the image of the fundamental frequency magnitude was useful in detecting a non-contact interface such as in the linear ultrasonic technique, while the image of the harmonic frequency magnitude was useful in detecting a contact interface.
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Therefore, if both images are used, both non-contact and contact interfaces can be detected. These characteristics are very attractive for the inspection of cracks with interfaces that are both open and closed. Many stress-corrosive cracks (SCCs) or fatigue cracks have both open and closed portions, but the conventional ultrasonic technique detects only the open portion, which results in underestimation of the actual crack size. Finally, the imaging results of the ratio of nonlinear parameters obtained at 20 and 40 MPa contact pressures to the initial value obtained at no contact pressure are shown in Fig. 7, which was obtained from the image data shown in Fig. 6. According to the increasing contact pressure, the ratio value increased markedly at the contact side, while at the non-contact side the ratio maintained a low without any noticeable change. These tendencies are also in agreement with our prediction. From these results, the usefulness of our imaging method was verified. Currently, the scanning step is coarse and the scanning number is limited, thus the spatial resolution is not high. In order to improve the spatial resolution of the image, scanning parameters such as the scanning step, scanning number, and scanning distance must be considered. 6. Conclusion In this study, we proposed a technique for the B-mode imaging of CAN that uses the synthetic aperture focusing technique (SAFT) and the short-time Fourier transform (STFT) to visualize the distribution of the CAN-induced second harmonic magnitude as well as the nonlinear parameter. The usefulness of the proposed method was verified by experiments for a solid–solid contact interface, where the constructed images of the second harmonic magnitude and the relative nonlinear parameter showed the corresponding change of the contact acoustic nonlinearity according to the increasing contact pressure, which is in good agreement with the theoretical predictions. This technique can be used for the detection and improvement of the sizing accuracy of closed cracks, which are difficult to detect using the conventional linear ultrasonic technique. The proposed technique enables the driving of a high power acoustic wave to activate CAN, and ensures the high sensitivity needed to receive a second harmonic component by using the transmitter and the receiver separately in pitch-catch mode, which is not available in conventional phased array equipment. In this study, the angle incidence and reflection technique were employed to avoid the interference of the transducer with the loading jig; however, the external loading is not necessary in practical applications in order for normal incidence to be available. Moreover, arrayed multiple transducers, each transmitting an acoustic wave with sufficient power to activate CAN and with enough sensitivity to detect the harmonic frequency component, need to be developed for practical applications. Acknowledgement This work was supported by the National Research Foundation of Korea (NRF) – Grant funded by the Korean government (The National Research Foundation of Korea (NRF) – 2008-2003505). References [1] T.H. Lee, K.Y. Jhang, Evaluation of micro crack using nonlinear acoustic effect, JKSNT 28 (2008) 352–357. [2] D. Donskoy, A. Sutin, A. Ekimov, Nonlinear acoustic interaction on contact interfaces and its use for nondestructive testing, NDT E Int. 34 (2001) 231–238. [3] J.Y. Kim, V.A. Yakovlev, S.I. Rokhlin, Surface acoustic wave modulation on a partially closed fatigue crack, J. Acoust. Soc. Am. 115 (2004) 1961–1972.
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[4] S. Hirsekorn, Nonlinear transfer of ultrasound by adhesive joints – a theoretical description, Ultrasonics 39 (2001) 57–68. [5] P.P. Delsanto, S. Hirsekorn, V. Agstini, R. Loparco, A. Koka, Modeling the propagation of ultrasonic waves in the interface region between two bonded elements, Ultrasonics 40 (2002) 605–610. [6] D. Liaptsis, B.W. Drinkwater, R. Thomas, The interaction of oblique incidence ultrasound with rough, partially contacting interfaces, Nondestruct. Test. Eval. 21 (2006) 109–121. [7] J.Y. Kim, A. Baltazar, J.W. Hu, S.I. Rokhlin, Hysteretic linear and nonlinear acoustic responses from pressed interfaces, Int. J. Solid Struct. 43 (2006) 6436– 6452. [8] T.H. Lee, K.Y. Jhang, Experimental investigation of nonlinear acoustic effect at crack, NDT E Int. 42 (2009) 757–764. [9] B.J. Park, T. H Lee, C.S. Kim, K.Y. Jhang, Acoustic nonlinear characteristics of ultrasonic wave reflected at contact interfaces, JKSNT 31 (2011) 40–46. [10] A. Baltazar, S.I. Rokhlin, C. Pecorari, On the relationship between ultrasonic and micromechanical properties of contacting rough surfaces, J. Mech. Phys. Solids 50 (2002) 1397–1416. [11] T.H. Nam, T.H. Lee, C.S. Kim, K.Y. Jhang, N.Y. Kim, Harmonic generation of an obliquely incident ultrasonic wave in solid–solid contact interfaces, Ultrasonics 52 (2012) 778–783. [12] J.M.S. Hutchison, R.D. Selbie, Ultrasonic phased array system, U.S. Patent 4149420, 1979. [13] T.R. Gururaja, Piezoelectric transducers for medical ultrasonic imaging, Proc. IEEE ISAF (1992) 259–265. [14] D. Utrata, R. Clark, Groundwork for rail flaw detection using ultrasonic phased array, Rev. Prog. Q. 22 (2003) 799–805. [15] S.H. Yang, B.S. Yoon, Y.S. Kim, Using phased array ultrasonic technique for the inspection of straddle mount-type low-pressure turbine disc, NDT E Int. 42 (2009) 128–132.
[16] F. Dong, E.L. Madsen, M.C. Macdonald, J.A. Zagzebski, Nonlinearity parameter for tissue-mimicking materials, Ultrasound Med. Biol. 25 (1999) 831–838. [17] K.T. Spencer, J. Bednarz, P.G. Rafter, C. Korcarz, R.M. Lang, Use of harmonic imaging without echocardiographic contrast to improve two-dimensional image quality, Am. J. Cardiol. 82 (1998) 794–799. [18] C. Hohl, T. Schmidt, P. Haage, D. Honnef, M. Blaum, G. Staatz, R.W. Guenther, Phaseinversion tissue harmonic imaging compared with conventional B-mode ultrasound in the evaluation of pancreatic lesions, Eur. Radiol. 14 (2004) 1109–1117. [19] J.A. Jensen, S.I. Nikolov, K.L. Gammelmark, M.H. Pedersen, Synthetic aperture ultrasound imaging, Ultrasonics 44 (2006) e5–e15. [20] Z. Shao, L. Shi, Z. Shao, J. Cai, Design and application of a small size SAFT imaging system for concrete structure, Rev. Sci. Instrum. 82 (2011). [21] M. Spies, H. Rieder, Synthetic aperture focusing of ultrasonic inspection data to enhance the probability of detection of defects in strongly attenuating materials, NDT E Int. 43 (2010) 425–431. [22] D. Beyerbach, H. Nawab, Principal components analysis for the short-time Fourier transform, ICASSP 3 (1991) 1725–1728. [23] F.T.S. Yu, Lu. Guowen, Short-time Fourier transform and wavelet transform with Fourier-domain processing, Appl. Optics 33 (1994) 5262–5270. [24] H.J. Jeong, S.H. Nahm, K.Y. Jhang, Y.H. Nam, A nondestructive method for estimation of the fracture toughness of CrMoV rotor steels based on ultrasonic nonlinearity, Ultrasonics 41 (2003) 543–549. [25] J. Chen, W. Jiang, Y. Shui, Observation of nonlinear acoustic effects at isotropic solid–solid interfaces, J. Acoust. Soc. Am. 109 (2001) 501–507. [26] S.I. Rokhlin, L. Wang, B. Xie, V.A. Yakovlev, L. Adler, Modulated angle beam ultrasonic spectroscopy for evaluation of imperfect interfaces and adhesive bonds, Ultrasonics 42 (2004) 1037–1047. [27] A. Demcenko, R. Akkerman, P.B. Nagy, R. Loendersloot, Non-collinear wave mixing for non-linear ultrasonic detection of physical ageing in PVC, NDT E Int. 49 (2012) 34–39.
Contents lists available at SciVerse ScienceDirect
Ultrasonics journal homepage: www.elsevier.com/locate/ultras
Imaging of contact acoustic nonlinearity using synthetic aperture technique Dongseok Yun a, Jongbeom Kim a, Kyung-Young Jhang b,⇑ a b
Graduate School of Mechanical Engineering, Hanyang University, Seoul 133-791, Republic of Korea School of Mechanical Engineering, Hanyang University, Seoul 133-791, Republic of Korea
a r t i c l e
i n f o
Article history: Received 1 December 2012 Received in revised form 31 January 2013 Accepted 2 April 2013 Available online 20 April 2013 Keywords: Contact acoustic nonlinearity (CAN) Contact interface Synthetic aperture focusing technique (SAFT) Short-time Fourier transform (STFT)
a b s t r a c t The angle beam incidence and reflection technique for the evaluation of contact acoustic nonlinearity (CAN) at solid–solid contact interfaces (e.g., closed cracks) has recently been developed to overcome the disadvantage of accessing both the inner and outer surfaces of structures for attaching pulsing and receiving transducers in the through-transmission of normal incidence technique. This paper proposes a technique for B-mode imaging of CAN based on the above reflection technique, which uses the synthetic aperture focusing technique (SAFT) and short-time Fourier transform (STFT) to visualize the distribution of the CAN-induced second harmonic magnitude as well as the nonlinear parameter. In order to verify the usefulness of the proposed method, a solid–solid contact interface was tested and the change of the contact acoustic nonlinearity according to the increasing contact pressure was visualized in images of the second harmonic magnitude and the relative nonlinear parameter. The experimental results showed good agreement with the previously developed theory identifying the dependence of the scattered second harmonics on the contact pressure. This technique can be used for the detection and improvement of the sizing accuracy of closed cracks that are difficult to detect using the conventional linear ultrasonic technique. Ó 2013 Elsevier B.V. All rights reserved.
1. Introduction When an ultrasonic wave is incident to imperfect interfaces, higher harmonic waves are generated in the reflected or transmitted waves due to contact acoustic nonlinearity (CAN) [1–6]. Many researchers have investigated this phenomenon for use in detecting closed cracks, which are hard to detect using conventional linear ultrasonic techniques [7–10]. However, this technique is still limited in practical applications, since the interpretation of the received signal needs a highly experienced expert. That is, further development of the imaging technique is required for easy application. In this paper, we propose a technique for the B-mode imaging of CAN that is based on our previous work, in which the magnitude of the second order harmonic wave generated in the ultrasonic wave reflected by the contact interface was analyzed quantitatively [11]. The ultrasonic imaging technique that uses a phased array has already been commercialized [12–15]. However, this phased array technique is difficult to apply for the imaging of nonlinear ultrasonic characteristics for several reasons: first, the acoustic power transmitted from each small transducer of the phased array probe ⇑ Corresponding author. Address: School of Mechanical Engineering, Hanyang University, Haengdang-dong 17, Seongdong-Gu, Seoul 133-791, Republic of Korea. Tel.: +82 2 2220 0434; fax: +82 2 2299 7207. E-mail address: [email protected] (K.-Y. Jhang). 0041-624X/$ - see front matter Ó 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.ultras.2013.04.002
is too low to activate the acoustic nonlinearity. Nevertheless, in medical applications, the phased array technique is available for the imaging of acoustic nonlinearity because biological soft tissues have much higher nonlinearity, thus a harmonic wave induced by acoustic nonlinearity is observable with comparatively lower acoustic power [16–18]. In applications regarding metallic materials for industrial nondestructive testing (NDT), however, the acoustic nonlinearity is relatively weak, thus a high power input is usually required. Second, in order to produce a high power acoustic wave, a high power electric signal should be supplied to the transducers. Additionally, a high-speed switch (multiplexer) that has the capability to supply a high power electric signal into each of the arrayed transducers is required, but this type of switch has not yet been commercialized. Consequently, the direct implementation of the nonlinear ultrasonic technique into current phased array equipment is difficult at the present time. Our proposed method overcomes this problem by adopting the synthetic aperture focusing technique (SAFT) [19–21], which uses two transducers (a transmitter and receiver pair) that are generally used in the pitch-catch method of ultrasonic NDT and scans them to construct the image. Although this method requires more time to construct the image due to mechanical scanning, a high power electric signal can be supplied into the transducer without a switch and the sensitivity kept high in order to detect the harmonic wave by using a separate transducer as a receiver with a resonant frequency identical to the frequency of the harmonic wave to be
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detected. Furthermore, short-time Fourier transform (STFT) [22,23] was used to acquire the amplitude of the fundamental frequency and the harmonic frequency separately in the time domain for the imaging of CAN. In order to verify the usefulness of the proposed imaging method, a solid–solid interface was constructed using aluminum blocks and was tested by a specially constructed experimental system in which a hydraulic press was employed to control the contact pressure at the contact interface. The variation of the contact acoustic nonlinearity at the contacting interface according to the increase in the contact pressure was visualized in images of the second harmonic magnitude and the relative nonlinear parameter. 2. SAFT for acquiring ultrasonic image The principle for acquiring synthetic aperture ultrasonic images is shown in Fig. 1, where a transducer transmits an ultrasonic wave and all of the transducers receive the wave reflected by a reflector. This procedure is repeated for the number of transducers by sequentially changing the transmitting transducer. Therefore, if the number of transducers is N, then a total of N N signals are acquired. In the figure, (xp, zp) is the image point, (xi, zi) is the position of the transmitting transducer i, (xj, zj) is the position of the receiving transducer j, di is the distance from the transmitter to the image point, and dj is the distance from the image point to the receiver. The echo signal received by each transducer has a time lag that is dependent on the total propagation distance between the transmitter and receiver. Finding the geometric distance from the transmitting transducer to the image point and back to the receiving transducer facilitates the required focusing [19,20]. The total propagation distance of the ultrasonic wave can be expressed as shown in the following equation:
dij ðxp ; zp Þ ¼ di þ dj qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ¼ ðxi xp Þ2 þ ðzi zp Þ2 þ ðxj xp Þ2 þ ðzj zp Þ2
ð1Þ
The corresponding time of flight tij(xp, zp) is:
tij ðxp ; zp Þ ¼
dij ðxp ; zp Þ c
ð2Þ
where c is the wave speed. Then, the amplitude at an image point is acquired as follows:
Iðxp ; zp Þ ¼
N X N X yij tij ðxp ; zp Þ
ð3Þ
j¼1 i¼1
where N is the number of transducers, and yij denotes the signal amplitude obtained when the i -th transducer is the transmitter and the j-th transducer is the receiver. The final image can be reconstructed by repeating the above calculation for all points (pixels) in the imaging area. 3. STFT for acquiring harmonic image In the nonlinear ultrasonic technique using the second harmonic amplitude measurement, the Fourier transform is generally used to measure the magnitude of the second harmonic component from the received signal. The general Fourier transform, however, loses the time information, and thus it is impossible to obtain the position of the reflector. Therefore, we employed the STFT technique to obtain the temporal change of the frequency contents in the signal. Fig. 2a shows the scheme of STFT. Only a portion of the signal overlapped with a fixed-size moving window is Fourier-transformed [21,22]. By moving the window step-bystep, the Fourier transform is repeated to obtain the time–frequency information. The Hanning window function was used in this study with a 3 ls width and a moving time step of 0.1 ls. Fig. 2b shows an example of the STFT result in the spectrogram of a real signal that has a fundamental frequency of 2.5 MHz and a double frequency component at 5 MHz, where the time information corresponds to the center of the moving window. Accordingly, the signal amplitude of the fundamental and harmonic frequency components can be acquired separately in the time-domain. Then, the amplitude at an image point is acquired as follows:
I1 ðxp ; zp Þ ¼
N X N N X N X X Y ij ðf0 ; tij Þ and I2 ðxp ; zp Þ ¼ Y ij ð2f 0 ; tij Þ j¼1 i¼1
ð4Þ
j¼1 i¼1
where Yij is the amplitude of STFT of the signal, and I1 and I2 are the magnitudes of the fundamental frequency f0 and its second harmonic frequency at the imaging point, respectively. Finally, the relative nonlinear parameter b0 [24] is calculated as follows:
b0 ðxp ; zp Þ ¼
I2 ðxp ; zp Þ I21 ðxp ; zp Þ
ð5Þ
4. Experimental procedure
Fig. 1. Basic principle of SAFT: Geometry and method of image construction.
Fig. 3 shows the experimental system to verify the usefulness of the proposed method. A pair of aluminum 6061-T6 blocks placed into contact with an external normal load was used as the test specimen. The imaging area was established at the center of the interfaces as shown in the figure. The bold box indicates the region-of-interest (ROI), and its enlarged diagram is shown in the lower right side. The upper interface was flat, while the lower interface had partial unevenness. Thus, the left side of the ROI had a non-contact interface, whereas the right side had a contact interface. The dimension details and shape of the blocks are shown in Fig. 4. The thickness was 40 mm. The unevenness of the lower block was 1 mm high, and the surface, which made contact with the upper block, was polished using #600 sandpaper.
D. Yun et al. / Ultrasonics 53 (2013) 1349–1354
Fig. 2. Principle of the STFT (a) in the time-domain and (b) result of STFT.
Fig. 3. Schematic diagram of measurement system.
Fig. 4. Dimensions of two aluminum blocks: (a) upper specimen and (b) lower specimen (unit: mm).
Fig. 5. Photograph of jigs applied at the specimen.
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Fig. 6. SAFT images of fundamental and second harmonic frequencies at three different contact pressures, 0 MPa, 20 MPa, and 40 MPa.
Fig. 7. Images of the ratio of nonlinear parameter obtained at (a) 20 MPa and (b) 40 MPa contact pressures to the initial value obtained at no contact pressure.
Hydraulic loading was used to apply a compression load on the contacting interfaces to induce the variations of the contact conditions. The imaging was performed for different loads, and the change in the image according to the variation of the contact pressure was investigated. The load was measured with a load cell attached at the bottom of the specimen. The center of the loading was identical to the center of the unevenness, and the loading area
on the upper specimen was larger than the uneven area, thus the pressure applied on the contact interface was assured to be uniform, and the pressure was calculated as the applied load divided by the area of the contact interface. In order to establish the angle beam incidence and reflection in pitch-catch mode, the transducers were located on the angled sides of the upper specimen as shown in Fig. 3. A similar experimental
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set-up is described in other reports for observation of nonlinear acoustic effects at imperfect interfaces [25–27]. The angle of the ultrasonic wave incident to the interface was 45°. By using this set-up, the transducers can be moved without interfering with the external loading, and the path length of the center beam can be made equal regardless of the transmitter position, as shown by the lines of the typical beam path in Fig. 3. This allows omission of a process to compensate for the difference in the attenuation of the signal amplitude due to the difference in the path length. However, this set-up looks different than what was shown in principle, that is, Fig. 1 shows the normal incidence, while Fig. 3 shows the angle incidence. This was because external loading was necessary to apply uniform pressure on the contact interfaces in order to change the contact conditions of the interfaces and to investigate the corresponding variation of CAN, thus the angle incidence and reflection technique was employed to avoid the interference of the transducer with the loading jig. Regardless, the previously described principle of SAFT remained available, except that the transmitter and the receiver were completely separated in our experimental set-up. Fig. 5 shows the jigs to hold the transducer and to maintain a constant pressure between the specimen and the transducer by using springs. In the experiments, a 2.25 MHz longitudinal wave transducer was used as a transmitter, and a 5 MHz longitudinal wave transducer was employed as a receiver. A tone-burst signal of 2.5 MHz was input to the transmitter with a high-power gated amplifier (Ritec, RAM-5000 SNAP). The number of cycles was five. The received signal was monitored with a digital oscilloscope (LECROY WS452). MATLAB was used for the signal processing. We scanned the transducers using a 5 mm step to apply SAFT. The number of transducer scan positions was six for both transmitting and receiving, thus a total of 36 signals were acquired. The experiments were performed after the loading/unloading process was repeated ten times in order to eliminate the hysteresis effect in the contact interfaces [8].
5. Results Fig. 6 shows the results of the fundamental and second harmonic frequency images according to the contact pressure. The dotted box indicates the imaging area. In all of the images, the interface was clearly visualized. Next, the change in the average magnitudes at the non-contact and contact interfaces was evaluated separately. At the non-contact interface, a noticeable change in the magnitudes of the fundamental and second harmonic frequencies was not observed. Conversely, at the contact interface, the magnitude of the fundamental frequency clearly decreased by the increasing contact pressure. This phenomenon results from the contact interfaces closing as the contacting pressure increased, thus the acoustic reflectivity also decreased. However, the magnitude of the second harmonic frequency increased at the beginning of the contact to reach a maximum value, and then decreased because the interface became fully closed. In our experiment, the maximum magnitude of the second harmonic frequency was found at a contact pressure of 20 MPa. These behaviors reflect approximately the nonlinear characteristics of contact interfaces and are in good agreement with the results of our theoretical and experimental study on the harmonic generation of an angle beam incident ultrasonic wave in solid–solid contact interfaces [11]. Consequently, the image of the fundamental frequency magnitude was useful in detecting a non-contact interface such as in the linear ultrasonic technique, while the image of the harmonic frequency magnitude was useful in detecting a contact interface.
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Therefore, if both images are used, both non-contact and contact interfaces can be detected. These characteristics are very attractive for the inspection of cracks with interfaces that are both open and closed. Many stress-corrosive cracks (SCCs) or fatigue cracks have both open and closed portions, but the conventional ultrasonic technique detects only the open portion, which results in underestimation of the actual crack size. Finally, the imaging results of the ratio of nonlinear parameters obtained at 20 and 40 MPa contact pressures to the initial value obtained at no contact pressure are shown in Fig. 7, which was obtained from the image data shown in Fig. 6. According to the increasing contact pressure, the ratio value increased markedly at the contact side, while at the non-contact side the ratio maintained a low without any noticeable change. These tendencies are also in agreement with our prediction. From these results, the usefulness of our imaging method was verified. Currently, the scanning step is coarse and the scanning number is limited, thus the spatial resolution is not high. In order to improve the spatial resolution of the image, scanning parameters such as the scanning step, scanning number, and scanning distance must be considered. 6. Conclusion In this study, we proposed a technique for the B-mode imaging of CAN that uses the synthetic aperture focusing technique (SAFT) and the short-time Fourier transform (STFT) to visualize the distribution of the CAN-induced second harmonic magnitude as well as the nonlinear parameter. The usefulness of the proposed method was verified by experiments for a solid–solid contact interface, where the constructed images of the second harmonic magnitude and the relative nonlinear parameter showed the corresponding change of the contact acoustic nonlinearity according to the increasing contact pressure, which is in good agreement with the theoretical predictions. This technique can be used for the detection and improvement of the sizing accuracy of closed cracks, which are difficult to detect using the conventional linear ultrasonic technique. The proposed technique enables the driving of a high power acoustic wave to activate CAN, and ensures the high sensitivity needed to receive a second harmonic component by using the transmitter and the receiver separately in pitch-catch mode, which is not available in conventional phased array equipment. In this study, the angle incidence and reflection technique were employed to avoid the interference of the transducer with the loading jig; however, the external loading is not necessary in practical applications in order for normal incidence to be available. Moreover, arrayed multiple transducers, each transmitting an acoustic wave with sufficient power to activate CAN and with enough sensitivity to detect the harmonic frequency component, need to be developed for practical applications. Acknowledgement This work was supported by the National Research Foundation of Korea (NRF) – Grant funded by the Korean government (The National Research Foundation of Korea (NRF) – 2008-2003505). References [1] T.H. Lee, K.Y. Jhang, Evaluation of micro crack using nonlinear acoustic effect, JKSNT 28 (2008) 352–357. [2] D. Donskoy, A. Sutin, A. Ekimov, Nonlinear acoustic interaction on contact interfaces and its use for nondestructive testing, NDT E Int. 34 (2001) 231–238. [3] J.Y. Kim, V.A. Yakovlev, S.I. Rokhlin, Surface acoustic wave modulation on a partially closed fatigue crack, J. Acoust. Soc. Am. 115 (2004) 1961–1972.
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