of polymer-composite-, 8) metal- 9) and multilayeredplates 10) were also achieved by the normal incidence of 1. Introduction

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1 Materials Transactions, Vol. 9, No. 1 () pp. 61 to 67 # The Japan Institute of Metals and Investigations of Transmission Coefficients of Longitudinal Waves through Metal Plates Immersed in Air for Uses of Air Coupled Ultrasounds Hideo Nishino 1, Shuichi Masuda 1, Kenichi Yoshida 1, Masakazu Takahashi, Hidekazu Hoshino, Yukio Ogura, Hideaki Kitagawa 3, Junichi Kusumoto 3 and Akihiro Kanaya 3 1 Institute of Technology and Science, The University of Tokushima, Tokushima 77-56, Japan Japan Probe Co., Ltd., Yokohama 3-33, Japan 3 Research Laboratory, Kyusyu Electric Power Co., Inc., Fukuoka 15-5, Japan and experimental investigations of transmission coefficients of longitudinal waves through metal plates immersed in air have been carried out for noncontact and nondestructive testing (NDT) of metal plates. Transmission coefficients through metal plates in water and through polymer plates in air have also been shown for comparisons. relations between the transmission coefficients and the Lamb wave dispersions were described. It was confirmed that the transmission coefficients took high values when the Lamb waves were generated without exception. Quantitative evaluations for the transmission coefficients were investigated for the use of the air-coupled ultrasounds. The experimental verifications were carried out using 1-, 3-, and 5-mm-thick aluminum plates. The experimental results of the transmission coefficients were in fairly good agreement with the theoretical predictions. [doi:1.3/matertrans.mra7] (Received August 13, ; Accepted October 6, ; Published November 1, ) Keywords: nondestructive inspection, ultrasonic testing, air-coupled ultrasound, metal plate, lamb wave 1. Introduction An air-coupled transduction of an ultrasound propagating in a solid material is one of the powerful tools for nondestructive testing (NDT). Because of its noncontacting feature, the air-coupled transduction can be applied to NDT in various environments, high temperature, vacuum and so on, where conventional contacting methods cannot be applied. The air-coupled transduction has also been anticipated to apply to on-line monitoring for a production line because of rapid scanning of samples without contaminations. Comparing the other noncontact methods like laserultrasound and electro magnetic acoustic transduction (EMAT), the method has two main advantages; (1) it is cheaper than the other methods, () it can be easily applied only to exchange from conventional contacting transducers to air-coupled transducers. Two types of air-coupled transducers have been mainly used in the current research field of NDT. There are the piezoelectric composite transducer 1,) and the capacitive transducer. 3,) Recently, the capacitive transducer has been well refined to operate at wider frequency range with flat response due to micro-machined manufacturing. 5,6) The capacitance transducer is mainly consisted in just two parts. One is the front vibrating membrane with thinly coated electrode, and the other is solid conductive back-plate with micro-sized air pockets. The air pockets were manufactured classically by sandblaster, 1) and recently by micro-machining. 5) The membrane and the back-plate are formed as a capacitance transducer. The air-gap between the membrane and the back-plate acts as air spring, so the impedance matching between the transducer and air is very well. In accordance with the transducer mechanism, broadband response could be achieved. By using this broadband response, the broadband impulse source was observed. 7) Defect depths estimation by measuring the transverse resonances of polymer-composite-, ) metal- 9) and multilayeredplates 1) were also achieved by the normal incidence of air-coupled ultrasounds with broadband response. On the other hand, the piezoelectric composite transducer consists of piezoelectric pillars embedded in polymer matrix. This structure reduces the density as well as the acoustic impedance of itself also to reduce the impedance mismatch between the air/solid interface. Quarter-wavelength matching layers and high-gain amplifiers (usually 1 db) having optimized electronics are also employed to improve the insertion losses. Recent improved processes of manufacturing the piezoelectric composite transducers also contribute reasonable efficiencies for air-coupled transductions for metal specimens having high acoustic impedances. The Lamb wave generations and detections using piezoelectric composite transducers were carefully compared with a simulation model using finite-elementary method (FEM). ) Also described in Ref. ) was very sensitive critical-angle alignment for Lamb wave transductions in air. In spite of the recent improvements of air-coupled transductions described above, the great impedance mismatch between air and solid matter still exist as one of the greatest drawbacks of airborne ultrasounds. Therefore, transverseresonances of plate specimens have been utilized as not only normal-incidence for bulk wave generations but also obliqueincidence for the Lamb wave generations. So many applications for the Lamb wave transductions using the airborne ultrasounds were reported. Acoustic anisotropy measurements of various kinds of thin plates, 11) lap-joint qualities of adhesive aluminum plates, 1) plate thickness measurements using the Lamb wave dispersion-relations, 13) moisture-content estimations in polymer materials using the attenuation factors of the A -mode Lamb waves, 1) thickness measurements of Al plates 15) and delamination detections in CFRP plates ) were, respectively, carried out. Very interesting way to use the zero group velocity (but finite phase velocity)

2 6 H. Nishino et al. region of the S 1 -mode Lamb wave was proposed for efficient defect detection in plates. 17) As described before air-coupled transductions of the Lamb wave are much suitable for NDT technique for plate structures, while the great impedance mismatch exists between air/solid interface without exception. Therefore to know about the transmission coefficients of oblique incidence of the longitudinal waves in air through solid plates are of great importance for NDT applications of solid plates. Especially in metal plates comparing to polymer plates, impedance mismatches are extremely high. In this paper, transmission coefficients of metal plates were quantitatively evaluated to investigate the characteristics of the Lamb wave transductions using airborne ultrasounds. and experimental investigations of oblique incidence of longitudinal waves in air through metal plates are not yet demonstrated in detail because of some doubts about the feasibility due to extremely large differences of acoustic impedances until now. calculations of transmission coefficients of aluminum plates immersed in air were presented to compare the experimental results. Extremely large insertion losses were observed in the experiments. It was confirmed that the experimental transmission coefficients agreed with the theoretical predictions.. Transmission Coefficients Reissner first theoretically deduced a transmission coefficient of oblique incidence of longitudinal wave through a plate specimen immersed in liquid in ) It was confirmed that the experimental coefficient through an aluminum plate immersed in water were agreed very well with the calculated estimation. 19 1) Transmission coefficients through a stratified plate,3) and a viscoelastic plate ) were also reported as theoretical expansions of Ref. 1). Needless to say, above-mentioned theories can be applied also for the calculation of transmission coefficients for plate specimens immersed in air. Then the theoretical transmission coefficients of oblique incidence of weakly focused longitudinal waves through a polymer composite material immersed in air were shown along with the experimental outcomes. 5 7) The transmission coefficient T with respect to an incident angle through an isotropic solid plate immersed in liquid or gas was shown in eq. (1). 1) Figure 1 shows a schematic illustration of the actual experimental setup for the measurement of the transmission coefficient T to clarify the relation between the theory and the practice described in the next section. where Tr. air θ T ¼ 5 mm N 3M þ N þ 1 ; Re. x translation Fig. 1 setup for measuring the transmission coefficients of the plates immersed in air using the piezoelectric composite air-coupled transducers as the transmitter (Tr.) and the receiver (Re.). θ ð1þ N ¼ Z l cos l Z sin k ly d þ Z t Z Z ¼ v cos ; sin t sin k ty d ; Z l ¼ 1v l cos l ; M ¼ Z l cos l Z tan k ly d þ Z t sin t Z tan k ty d ; Z t ¼ 1v t cos t ; k ly ¼! cos l ; k ty ¼! cos t ; sin l ¼ v l sin ; v l v t v sin t ¼ v t v sin 9 >= ; ðþ >; respectively, and v, v t, v l,, 1, d, and! are the longitudinal velocity of the liquid or gas, the transverse and the longitudinal wave velocities of the plate material, the densities of the liquid or gas and the plate material, the thickness of the plate and angular frequency, respectively. Following calculations were carried out using material parameters shown in Table 1. Color-scale representationss of transmission coefficients of an aluminum plate immersed in water and in air are shown as functions of both incident angle and fd (frequency thickness) value in Figs. and 3, respectively. The colorscale is depicted in decibels (db), thus db means the total transmission. The dynamic ranges of the representations for water and air are 1 db and db, respectively. This means the transmissions in water are generally much higher Table 1 Material parameters used in the calculations. density (kg/m 3 ) transverse wave velocity (m/s) longitudinal wave velocity (m/s) air water 1 15 polymer aluminum steel than those in air. It was confirmed that the regions having high transmission coefficients in Figs. and 3 coincided very well with the Lamb wave dispersion relations. The incident angles Lamb of the high transmission regions can be

3 and Investigations of Transmission Coefficients of Longitudinal Waves through Metal Plates Immersed in Air 63 Fig. Color-scale representation of transmission coefficients of the aluminum plate immersed in water as functions of both fd value and incident angle. Fig. 3 Color-scale representation of transmission coefficients of the aluminum plate immersed in air as functions of both fd value and incident angle. described as the Snell s law. This phenomenon was called coincidence effect in Ref. 6). Lamb ¼ sin 1 v ; ð3þ v Lamb where v Lamb is the phase velocity of the Lamb wave at appropriate fd value. However, the area of high transmission regions in Fig. was much larger than that in Fig. 3. Figure shows transmission coefficients of normal incidence of longitudinal waves through an aluminum plate

4 6 H. Nishino et al. Transmission coef. (db) in water 1 in air 3 5 fd (MHz-mm) Fig. Transmission coefficient of vertical incidence through the aluminum plate immersed in water and air as a function of fd value. The total transmissions are always occurred when the plate thickness equals an integer multiple of the half wavelength of the longitudinal wave of the plate material. There is no dependence with the immersing materials for polymer at.5 MHz S mode A mode Air/CFRP Air/Al Air/Steel for Al and Steel at 1 MHz Fig. 6 Transmission coefficients of the aluminum, steel and polymer plates immersed in air as a function of incident angle at fd = 1 MHz-mm for the aluminum and steel plates and at fd =.5 MHz-mm for the polymer plate Water/Al Water/Steel 1 S mode 3 at 1 MHz A mode Fig. 5 Transmission coefficients of the aluminum and steel plates immersed in water as a function of incident angle at fd = 1 MHz-mm. 5 6 immersed in water and in air as a function of fd value. The total transmission always occurs without depending on water and air surrounding the plate, when the thickness of the plate equals an integer multiple of a half-wavelength. 5,6) The 6- db-width of the total transmission for air (1: 1 MHzmm) is extremely much narrower than that for water (6:3 1 1 MHz-mm). As shown in Fig., the minimum transmission coefficients for water and air are 15 db and 6 db, respectively. Figure 5 shows the transmission coefficients as a function of incident angle of longitudinal wave through the aluminumand the steel-plates immersed in water at 1 MHz-mm. The transmission coefficients of the aluminum- and the steelplates immersed in air are also shown in Fig. 6. Similar characteristics of the dispersion relation for the polymer plate (see Table 1) are appeared at the half of fd value of the metal plates because the longitudinal and transverse wave velocities of the polymer material are about half of the metal materials. Therefore, the transmission coefficient of the polymer-plate at.5 MHz-mm is also shown in Fig. 6 for a comparison to the metal plates. The first and second peaks in Figs. 5 and 6 are the S and the A modes Lamb waves, respectively. The background levels for airborne ultrasounds (Fig. 6) are much lower than those for underwater ultrasounds (Fig. 5). For example, the transmission coefficients of the polymer, the aluminum (Al) and the steel plates immersed in air at the incident angle are 71, 6 and 95 db, respectively. Relatively about 1 5 db differences between the three plate specimens for almost all the incident angles can be confirmed. The 6-dB-width of all the peaks due to the S - and the A -mode Lamb waves are described in Table. Extremely narrow widths are also confirmed for airborne ultrasound as shown in Table. results of these phenomena have been reported in elsewhere ) from the other point of view. The transmission coefficients for Al-, steel- (at MHz-mm), the polymer-plates (at MHz-mm) immersed in water and in air are shown in Figs. 7 and, respectively. The five modes (A,S,A 1,S 1 and A ) of the Lamb wave are existed at MHz-mm. The characteristics of both the transmission coefficients at MHz-mm for the metal plates and at MHz-mm for the polymer plate are very similar characteristics to those at 1 MHz-mm shown in Figs. 5 and 6 except the number of the Lamb wave modes. Table 6-dB-width at the total transmissions due to the Lamb wave resonances. Al in water steel in water Al in air steel in air polymer in air S mode : : 1 1 : : 1 6 3:1 1 A mode 1: : 1 : 1 1:5 1 :1 1 3

5 and Investigations of Transmission Coefficients of Longitudinal Waves through Metal Plates Immersed in Air Water/Al Water/Steel 1 3 at MHz Fig. 7 Transmission coefficients of the aluminum and steel plates immersed in water as a function of incident angle at fd = MHz-mm. Amplitude (a.u.) Air/CFRP Air/Al Air/Steel for polymer at MHz for Al and Steel at MHz Fig. Transmission coefficients of the aluminum, steel and polymer plates immersed in air as a function of incident angle at fd = MHz-mm for the aluminum and steel plates and at fd = MHz-mm for the polymer plate. 3. Verifications Transmission coefficients through the Al plate immersed in air were experimentally evaluated as a function of incident angle. 1, 3 and 5 mm-thick Al plates were used in the experiments. A schematic illustration of the experimental setup is depicted in Fig. 1. A tone-burst-type pulser/receiver (Japan Probe JPR-1B) was used to generate and detect the longitudinal waves in air. 1-cycle negative rectangular monopole burst pulse was utilized as the source-signals in the pulser/receiver. Piezoelectric composite transducers having a center frequency 33 khz (Japan Probe. K 1 N) and 7 khz (Japan Probe. K 1 N) were used as transmitting- and receiving-transducers in the experiments. The longitudinal wave in air is generated by the transmittingtransducer and propagates through the Al plate with an incident angle. The longitudinal waves through the Al plates are detected by the receiving-transducer. As shown in Fig. 1, the receiving-sensor was translated parallel to the aperture-surface of the two sensors to obtain the maximum amplitude. This procedure is necessary to detect the Lamb Propagation time (ms).. Fig. 9 Received waveform through the 1-mm-thick aluminum plate immersed in air at incident angle and at frequency 7 khz. waves in the Al plates. Larger translation was needed for larger inclination of the Al plates. The transmission coefficients T exp were evaluated by measuring differences of gains between with and without the Al plate when the same amplitudes were obtained. T exp ¼ G plate ; ðþ G air where, G air and G plate are gains with and without the Al plate, respectively. Time domain signals of transmitted waves through the 1-mm-thick Al plate for incident angles (7 khz) are shown in Fig. 9. Clear and high S/N ( db) was obtained and confirmed. Values of both G air and G plate were 7 and 69.5 db for 33 khz, and were 7 and 73.5 db for 7 khz, respectively. The transmission coefficients for the 1-, 3- and 5-mm Al plates at 33 and 7 khz are shown in Figs. 1, 11 and 1. Lines and circles in Figs. 1, 11 and 1 indicate the theoretical and experimental results. transmission coefficients at the peak positions were extremely far from the theoretical estimated value of db in all the cases. The theoretical calculations were carried out under the conditions of continuous plane waves, thus the directivitydependency of the transmission coefficients took infinite resolution in principle. In contrast to this, the directivity pattern of the sensors having a finite aperture is extremely much broader than the peak distributions in all the cases of the theoretical transmission coefficients. This low-resolution directivity-dependency of the experimental system is one of the main reasons to be different from the theoretical estimates. On the other hand, the experimental results except around the peak positions agreed well with the theoretical estimates in all the cases because of the broader distributions of the transmission coefficients. Therefore, the obtained results indicate that the experimental results in the broader distributions were agreed well with the theory. The experimental transmission coefficients at the region around the

6 66 H. Nishino et al (a) Expeimental (b) 1 Fig. 1 Transmission coefficients of the 1-mm-thick aluminum plate immersed in air as a function of incident angle of longitudinal wave in air at (a) 33 khz and (b) 7 khz (a) (b) 9 1 Fig. 11 Transmission coefficients of the 3-mm-thick aluminum plate immersed in air as a function of incident angle of longitudinal wave in air at (a) 33 khz and (b) 7 khz (a) (b) 9 1 Fig. 1 Transmission coefficients of the 5-mm-thick aluminum plate immersed in air as a function of incident angle of longitudinal wave in air at (a) 33 khz and (b) 7 khz.

7 and Investigations of Transmission Coefficients of Longitudinal Waves through Metal Plates Immersed in Air 67 existence of the Lamb wave modes took 1 15 db higher than those in the other region. These outcomes indicate that the theoretical transmission coefficient is very useful information to determine the required sensitivity of the transducer system. For example, we need around 9 db gain for a metal plate immersed in air to obtain the signals, while we need at most db gain in water.. Conclusions Characteristics of the transmission coefficients through metal and polymer plates immersed in water and air were theoretically investigated. The theoretical predictions described are very useful guide to use the air-coupled ultrasounds for metal plates. The following theoretical outcomes were obtained. (1) The transmission coefficient takes high value, when the Lamb wave is generated due to the phase matching condition of the Snell s law. () In spite of the air-coupled ultrasound having an extremely high impedance gap, the total transmission occurs at the normal-incidence when the plate thickness equals to an integer multiple of the half wavelength of longitudinal wave of the plate material. (3) The transmission coefficients through plates in air are about 7 db smaller than those in water in almost all the incident angles to the plates. () Around 1 5 db differences between the steel-, aluminum- and polymer-plates were confirmed with respect to the transmission coefficients in air. (5) 6-dB-widths of the total transmissions in air are extremely narrow (about three or four digits smaller) to those in water in all the incident angles to the plates. At last of this paper, the experimental verifications were carried out using 1-, 3-, and 5-mm-thick aluminum plates. The obtained experimental results of the transmission coefficients almost agreed well with the theoretical predictions, however, some of the different results were confirmed based on the difference between the experimental and the calculation conditions. It is confirmed that the theoretical calculations are very useful to determine the required sensitivity of the air-coupled transducer for the NDT applications. REFERENCES 1) R. Farlow and G. Hayward: Insight 36 (199) 96. ) M. Castaings and P. Cawley: J. Acoust. Soc. Am. 1 (1996) 37. 3) M. Luukkala, P. Heikkila and J. Surakka: Ultrasonics (1971) 1. ) M. Luukkala and P. Merilainen: Ultrasonics (1973) 1. 5) D. W. Schindel, D. A. Hutchins, L. C. Zou and M. Sayer: IEEE Trans. UFFC (1995). 6) D. W. Schindel and D. A. Hutchins: IEEE Trans. UFFC (1995) 51. 7) W. M. D. Wright and D. A. Hutchins: Ultrasonics 37 (1999) 19. ) D. W. Schindel, D. A. Hutchins and W. A. Grandia: Ultrasonics 3 (1996) 61. 9) D. W. Schindel: Ultrasonics 35 (1997) ) D. W. Schindel: Ultrasonics 37 (1999) ) I. Yu. Solodov, R. Stossel and G. Busse: Res. Nondestr. Eval. 15 () 65. 1) D. W. Schindel, D. S. Forsyth, D. A. Hutchins and A. Fahr: Ultrasonics 35 (1997) 1. 13) D. Tuzzeo and F. Lanza di Scalea: Res. Nondestr. Eval. 13 (1) 61. 1) M. Cinquin, M. Cataings, B. Hosten, P. Brassierand and P. Peres: NDT and E 3 (5) ) M. Watanabe, M. Nishihira and K. Imano: JJAP 5 (6) 565. ) M. Castainings, P. Cawley, R. Farlow and G. Hayward: J. Nondestr. Eval. 17 (199) ) S. H. Holland and D. E. Chmenti: Appl. Phys. Lett. 3 (3) 7. 1) H. Reissner: Helv. Phys. Acta 11 (193) 1. 19) F. H. Sanders: Can. J. Res. 17 (1939). ) W. T. Thomson: J. Appl. Phys. 1 (195) ) L. M. Brekhovskikh: Waves in Layered media second edition, translated by R. T. Beyer, (Academic Press, 19) p. 7. ) W. T. Thomson: J. Appl. Phys. 1 (195) 9. 3) Y. Torikai: Nihon-onkyogakkai-shi (195) 1. (in Japanese) ) Y. Torikai and F. Fusao: Nihon-onkyogakkai-shi 1 (195) 9. (in Japanese) 5) A. Safaeinili, O. I. Lobkis and D. E. Chimenti: Mater. Eval. Oct. (1995) 1. 6) A. Safaeinili, O. I. Lobkis and D. E. Chimenti: Ultrasonics 3 (1996) ) D. E. Chimenti: Appl. Mech. Rev. 5 (1997) 7.