- Email: [email protected]
Nonlinear modulation technique for NDE with air-coupled ultrasound
Ultrasonics 42 (2004) 1031–1036 www.elsevier.com/locate/ultras
Nonlinear modulation technique for NDE with air-coupled ultrasound E.M. Ballad a, S.Yu. Vezirov a, K. Pfleiderer b, I.Yu. Solodov b
b,*
, G. Busse
b
a Department of Physics, Moscow State University, Moscow 119899, Russia Institute for Polymer Testing and Polymer Science (IKP)––Nondestructive Testing, Stuttgart University, Pfaffenwaldring 32, D-70569 Stuttgart, Germany
Abstract The present study is aimed at expanding flexibility and application area of nonlinear acoustic modulation (NAM-) technique by combining the benefits of noncontact ultrasound excitation (remote locating and imaging of defects) with sensitivity of nonlinear methods in a new air-coupled NAM-version. A pair of focused air-coupled transducers was used to generate and receive (highfrequency) longitudinal or flexural waves in plate-like samples. Low-frequency (LF-) vibrations were excited with a shaker or a loudspeaker. Temporal and spectral analysis of the output signal revealed an extremely efficient nonlinear amplitude modulation and multiple frequency side-bands for sound transmission and flexural wave propagation through cracked defects. On the contrary, a negligible modulation was observed for large and medium scale inclusions and material inhomogeneities (linear defects). A new subharmonic mode of the NAM was observed at high excitation levels. It was also shown for the first time that nonlinear vibrations of cracks resulted in radiation of a very high-order harmonics (well above 100) of the driving excitation in air that enabled imaging of cracks remotely by registration their highly nonlinear ‘‘acoustic emission’’ with air-coupled transducers. 2003 Elsevier B.V. All rights reserved. Keywords: Air-coupled ultrasound; Nonlinearity; Modulation; Acoustic imaging
1. Introduction Nonlinear acoustic modulation (NAM) is a developing NDE technique for damage diagnostics in materials and products. It is usually based on nonlinear interaction of a low- (X) and high- (x) frequency acoustic waves that yields the combination frequency (x X) output. The experimental observation of the effect goes back to 1966 when Zarembo and co-workers [1] revealed an efficient frequency mixing of acoustic waves in an Al-rod resonator. Since that time, the idea of acoustic wave resonance frequency mixing has been developed in a number of studies aimed at NDE-applications. The NAM was successfully used for monitoring defect accumulation in steel resonators subjected to tensile stress [2]. In a practically-oriented NAM-version applied to crack detection [3], the low-frequency excitation was implemented by tapping a sample with a hammer. Applications of both versions for damage *
Corresponding author. Fax: +49-0711-685-2066. E-mail address: [email protected] (I.Y. Solodov).
0041-624X/$ - see front matter 2003 Elsevier B.V. All rights reserved. doi:10.1016/j.ultras.2003.12.022
detection in materials and automobile components were also shown [4]. A new NAM-mode [5] is based on a transfer of modulation to a weak acoustic wave due to additional dissipation induced by an intense counterpart. To move from detection to location of defects, the efforts have been made recently in developing pulsemodulation NAM-options [6]. A flexible operation in any of nonlinear NDE-modes can be provided by using noncontact acoustic wave excitation. A decent spatial resolution for locating and imaging of defects is obtained in scanning modes which use focused beams. In this paper, we demonstrate for the first time that these merits can be combined in the scanning version of the NAM air-coupled NDE-methodology.
2. Phenomenology of air-coupled NAM Consider transmission of a small amplitude air coupled ultrasound (frequency x) through a cracked defect area in a plate-like sample subjected to a LF-vibrations
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Fig. 1. Experimental configuration of air-coupled NAM.
(X) (Fig. 1). The transmission coefficient T depends on the gap between the crack edges and can assumed to be constant only for infinitesimally small amplitude of LFvibrations (linear transmission mode): Vout ðtÞ ¼ T Vin ðxtÞ. Otherwise, the open crack gap changes harmonically, first, and T ðtÞ ! ðT0 þ T ðXtÞÞ causing linear modulation of the output signal: Vout ðtÞ ¼ ðT0 þ T ðXtÞÞ Vin ðxtÞ. In addition to the probing wave of frequency x, its spectrum acquires combination frequency components (x X) whose relative amplitudes are proportional to (T =T0 ). Further increase in the pump amplitude causes ‘‘clapping’’ of the crack edges and eventually results in a pulse-type modulation of the crack gap and stiffness (contact acoustic nonlinearity [7]). The open crack works like a modulator with nonlinear transmission coefficient T ðtÞ ! ðT0 þ P T ðnXtÞÞ and provides multiple side-band specn¼1 n tral components around the fundamental frequency (nonlinear modulation). For a closed crack, one may assume T0 to be much smaller than that for the open crack and the relative side-band amplitudes (T =T0 ) increase dramatically. In the P extreme case T0 ! 0, the output signal is: Vout ðtÞ ¼ n¼1 Tn ðnXtÞ Vin ðxtÞ and the spectrum contains only side-band components.
3. Experimental methodology In our experiment (Fig. 1), commercially available piezoelectric composite material transducers were used to radiate and receive a focused ultrasound beam (fundamental frequency 450 kHz, diameter of the transducers 18 mm, full angular transducer aperture ffi20, focus distance ffi40 mm, and focus neck 2 mm). CW voltage (10 Vpp/50 X) was applied to the transducer to generate the acoustic wave; two-step amplification of the receiver and narrow-band ( 12 kHz/3 dB) filter provided ffi40 dB signal-to-noise ratio of the output of the PC-operated system. 2D-scanning of the co-axial
transducers over plate-like samples was implemented by a stepping motor controlled scanning assembly (ISEL). LF-vibrations (frequency range 1–20 kHz; maximum acceleration 740 m/s2 ; displacement up to 20 lm at 1 kHz) were excited in a specimen by using a shaker (Br€ uel & Kjaer, type 4809) or even with a loudspeaker. After a 12-bit A/D converter, the output of the air-coupled transducer can be displayed in time or at any FFT– spectral line within the transducer bandwidth. Two acoustic modes of operation have been used in experiments. In the normal transmission (detection) mode (NTM), the transducers were aligned normally to the sample surface (h0 ¼ 0 in Fig. 1) and thus only a narrow beam of longitudinal waves was transmitted through the sample. In the slanted transmission mode (STM) [8], the angle of incidence was adjusted to satisfy the phase matching conditions h0 ¼ arcsinðvair =va0 Þ (v is the wave velocity) and provide the generation of the a0 mode of Lamb waves along the sample. The a0 -mode reradiates energy from the rear side of the sample and is detected by the second co-axial air-coupled transducer (Fig. 1). The STM normally also results in ‘‘resonance’’ increase in the transmitted signal by 15–20 dB.
4. Experimental results 4.1. Air-coupled NAM To initiate the air-coupled NAM we studied ultrasound normal transmission mode (NTM) through a thin plate (d ffi 1:15 mm) of polystyrene with some simulation defects in the presence of LF-vibrations. Fig. 2 shows a B-scan for a pair of holes (diameters 1 and 2 mm) (a) and the distribution of a difference frequency side-lobes (X=2p ¼ 20 kHz; x=2p ¼ 462 kHz) along the sample length (b) obtained after the FFT of a series of A-scans in Fig. 2(a). The peaks in Fig. 2(b) show the modulation effect which must, evidently, be stronger when the defect size is about the diameter of the focused beam ( 2 mm). In this case, a displacement of the hole ‘‘shades’’ a part of the incident beam and modulates the transmission coefficient most efficiently. Such a simple ‘‘shutter’’ model (assumed in Section 2) is supported by a sub-linear dependence of the side-band output on the low-frequency amplitude (Fig. 3). A linear behaviour of Vout ðx XÞ with high-frequency input Vin ðxÞ (Fig. 4) indicates that their ratio is independent of the input which also substantiates the above modulation mechanism based on a ‘‘passive’’ transmission of the probing wave. The latter assumption seems to be reasonable because the Mach number of the air-coupled ultrasound in the focus spot was estimated as 4 · 10 4 thus producing displacement of 50 nm-amplitude. The efficiency of the NAM is introduced as the ratio Vout ðx XÞ=Vout ðxÞ (modulation strength) and even for
E.M. Ballad et al. / Ultrasonics 42 (2004) 1031–1036
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Fig. 5. Amplitudes of fundamental (right) and difference frequency (left) signals for a linear defect.
Fig. 2. NAM-B-scan of 1 mm- (left) and 2 mm- (right) holes (a); spatial distribution of a difference frequency component.
sideband amplitude (rel. units)
Fig. 6. Air-coupled NAM by a vibrating crack: harmonic (a) and ‘‘clapping’’ (b) modes. 7 6 5 4 3 2 1 0
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 -6
low-frequency amplitude (10 m)
sideband amplitude (rel. units)
Fig. 3. First side-band amplitude as a function of low-frequency excitation.
0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0
0
5 10 15 20 25 30 35 fundamental amplitude (rel. units)
Fig. 4. First side-band as a function of amplitude of high-frequency wave.
the ‘‘optimal’’ size defect is found as low as 2.5% (Fig. 5) (linear defect). The NAM development for NTM through a realistic cutting crack made by an impact hammering in the same specimen is shown in Figs. 6 and 7. A striking modu-
Fig. 7. Nonlinear modulation spectrum for NTM-mode (fundamental frequency 452 kHz).
lation efficiency is clearly seen in the temporal presentations: as the low-frequency amplitude increases, the sinusoidal modulation of the output grows up to 100% (Fig. 6(a)); further increase of the input brings about the pulse-type modulation (‘‘clapping’’ mode’’) (Fig. 6(b)). Instructively, that the shape of the pulse-modulation in Fig. 6(b) remains unchanged when the probing wave amplitude varies. This is another evidence for the dominant role of the low-frequency vibrations in the aircoupled NAM-mechanism. Spectra of the transmitted sound also reveal a dramatic rise in the modulation strength and essentially nonlinear modulation (multiple side-lobes) at higher LF-amplitudes (Fig. 7). In the slanted transmission mode, the NAM is concerned with the flexural wave propagation through a crack. Due to a strong scattering, the transmission coefficient through the crack for these waves (without LF-excitation) is normally lower than that for the NTM [8]. We may, therefore, assume that the STM of aircoupled NAM develops on the closed crack scenario
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Fig. 8. Fundamental frequency (a) and suppression in NAM-spectrum (b) for STM-mode.
(Section 2) with an extremely efficient side-lobe generation. The spectra shown in Fig. 8(a) and (b) support this assumption. A single carrier-frequency spectral line in the absence of the LF-vibrations (Fig. 8(a)) changes for a group of side-lobes, virtually, with no fundamental frequency component observed (Fig. 8(b)). The vertical scales are identical in the above spectra, so that they reveal the fundamental frequency suppression by the onset of LF-vibrations. In terms of Section 2, this shows that reduction in the time-average transmission (from a certain level T0 corresponding to Fig. 8(a)) up to an extreme case T0 ! 0 is induced by the LF-variations of the crack gap. The latter is a direct consequence of the ‘‘clapping’’ NAM-mechanism: modulation of the crack gap is asymmetrical with an evident predominance of extension so that the time-average gap increases (contact ‘‘rectification’’ effect [7]). Thus, a total transmission coefficient takes the form: T ðtÞ ¼ T0 þ Tdc þ P n¼1 Tn ðnXtÞ, where Tdc is the ‘‘dc’’ term due to the ‘‘rectification’’. Since the gap extension reduces the flexural wave transmission through the crack, Tdc must of negative sign and as the LF-amplitude grows it nullifies the time-average in the above expression and turns P the NAM-spectrum into: Vout ðxÞ ¼ n¼1 Vn ½ðx nXÞt , which is in a full compliance with the experimental data in Fig. 8(a) and (b). It is known that at high vibration amplitudes of a nonlinear oscillator (a crack itself or a sample with a crack), the contact acoustic nonlinearity gives rise to a threshold subharmonic generation [9]. This change in a crack gap dynamics would modify the transmission P coefficient into: T ðtÞ ¼ T0 þ n¼1 Tn ½nðX=2Þt and cause the subharmonic components (x nðX=2Þ) in the air-coupled NAM-spectrum. Such a subharmonic NAM-mode is demonstrated for the STM in Fig. 9. It develops in an avalanche-like manner as soon as the LFinput exceeds a certain threshold value. 4.2. Defect-selective imaging in air-coupled NAM-mode The air-coupled NAM-effects described above develop locally within the cracked area only and therefore can be used for locating and imaging of defects. Scan-
Fig. 9. Subharmonic NAM- for STM-mode on a crack (fundamental frequency 452.2 kHz).
Fig. 10. Crack imaging in a linear (451.4 kHz) NTM (a) first side-lobe NAM: difference frequency 449.7 kHz and (b); sum frequency 453.1 kHz (c). (Scanning distance in Figs. 10–12 and 14 is 10 cm.)
Fig. 11. NAM-crack imaging in STM: fundamental frequency 452.7 kHz; first side-lobe 454.4 kHz (b) and second side-lobe 456.1 kHz (c) images.
Fig. 12. Linear (a) and first side-lobe (b and c) NAM-imaging of a drop of water (left in (a)) and a crack (right) on a surface of a polystyrene sample.
ning a sample area in both the NTM- and STM-NAM modes combined with an output tuned to a side-lobe frequency delivers information solely on the nonlinear cracked defects. The results confirming an opportunity for such a defect-selective NAM-imaging are shown in Figs. 10–12. Fig. 10(a–c) demonstrate the NTM-linear and side-lobe B-scans of an impact crack in 1.15 mmthick polystyrene plate (a CD-case). Both linear and NAM-images clearly discern the crack by a local increase in a linear transmission (a), and side-lobe generation (b) and (c). However, the contrast of the images was measured to be very different: DV =V 5 for the linear image (at fundamental frequency 451.4 kHz) which is much lower than DV =V 80 at the first lower side-band component (449.7 kHz).
E.M. Ballad et al. / Ultrasonics 42 (2004) 1031–1036
The NAM-results for a single crack in the STM-mode (Fig. 11(a–c)), firstly, show an inverse contrast of the image: the fundamental frequency output drops down due to flexural wave scattering while the side-band signals rise sharply because of the local nonlinear generation. Secondly, the measurements of the image contrast reveal an evident priority of the NAM-imaging: DV =V 0:5 for the linear image (452.7 kHz) and DV =V 10 at the higher side-band line of 454.4 kHz. A defect-selective NAM-capability is demonstrated in Fig. 12(a–c) for the STM of a linear (a drop of water) and nonlinear (a crack) defects. The linear transmission image clearly reproduces both defects with a comparable contrast (DV =V 0:6) as one would expect due to flexural wave scattering and damping. On the contrary, the side-band images exhibit a selective rise in the nonlinear output (DV =V 20) in the crack area only.
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Fig. 13. Linear (a) and second harmonic (b) air-coupled images of impacts in CFRP.
4.3. Nonlinear air-coupled ‘‘acoustic emission’’ It is known, that a high efficiency of the contact acoustic nonlinearity of the cracks provides not only frequency mixing but also a strong higher harmonic (HH-) generation inside a solid sample [7]. For surface or cutting cracks, this, presumably, must be accompanied by the HH-radiation in surrounding air. In this case, the air-coupled equipment can be used for remote detection of such a nonlinear ‘‘cry’’ of a defect (‘‘acoustic emission’’) and applied to nonlinear imaging of cracks similar to the NAM-case considered above. To study a feasibility of the HH-air-coupled mode with a pair of 450 kHz-transducers, acoustic waves at subharmonic frequencies (450 kHz/n) are generated in a specimen with a contact piezo-electric transducer. One of the focused air-coupled transducers is used for detection and scanning the distribution of the HHexcitations over the surface of a specimen. Fig. 13(a) and (b) show a linear NTM (a), and the second harmonic (n ¼ 2) (b) image of a group of impacts in CFR–plastic. The nonlinear image reproduces a core part of the impact where the fractured damage mainly occurs which supports the above mechanism of air-coupled HH-generation by ‘‘clapping’’ cracks. Another clear evidence for that is given in Fig. 14(a) and (b). Low-frequency (19 kHz) vibrations were excited in the cracked polystyrene plate while 450 kHz-aircoupled focused transducer was probing the HH-field over the cracked area. Its output spectrum (Fig. 14(a)) is a clear cut indication of the presence of 23rd (437 kHz) and 24th (456 kHz) harmonics above the sample surface. B-scans in Fig. 14(b) show that the source of the emitted nonlinear field can be localised and imaged neatly with a focused air-coupled transducer tuned to a particular HHfrequency line. Instructively to note, that the air-coupled HHs were observed in the bandwidth of the high-frequency transducer (440–460 kHz) when the cracked
Fig. 14. 23rd and 24th air-coupled higher harmonics of crack vibrations (a); crack imaging at 24th harmonic (b).
sample was excited at a resonant frequency of 1.73 kHz (order of the HHs is above 250). Nonlinear radiation of such a high-frequency ultrasound in response to a lowfrequency impact on a crack emphasises similarity between this effect and a regular acoustic emission.
5. Summary Nonlinear vibrations of a cracked defect cause an efficient amplitude modulation of air-coupled ultrasound transmitted through the defect area. A simple ‘‘shutter’’ model which accounts for nonlinear variation of a gap between edges of a crack reasonably describes basic experimental manifestations of the air-coupled NAM including linear, nonlinear and subharmonic modulation. Both normal and slanted transmission NAM-modes demonstrate flexible capabilities of remote scanning and high contrast nonlinear defect-selective imaging with air-coupled ultrasound. Nonlinear vibrations of a crack are accompanied by the high-order harmonic radiation in surrounding air (nonlinear ‘‘acoustic emission’’) that also enables to locate and image cracked defects remotely. A striking efficiency, compatibility with linear scanning acoustic instruments
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along with unique capabilities of noncontact nonlinear imaging of cracks advance the developed nonlinear aircoupled techniques as a potent tool for acoustic NDE and material characterisation. References [1] L.K. Zarembo, V.A. Krasilnikov, V.N. Sluch, O.Yu. Serdobolskaya, Akust. Zh. 12 (1966) 486. [2] A.S. Korotkov, M.M. Slavinskii, A.M. Sutin, Akust. Zh. 40 (1994) 80.
[3] A.S. Korotkov, A.M. Sutin, Acoust. Lett. 18 (1994) 59. [4] K.E.-A. Van Den Abele, P.A. Johnson, A. Sutin, Res. Nondestr. Eval. 12 (2000) 17. [5] V.Yu. Zaitsev, V. Gusev, B. Castagnede, Ultrasonics 40 (2002) 627. [6] V.V. Kazakov, A. Sutin, P. Johnson, Appl. Phys. Lett. 81 (2002) 646. [7] I.Yu. Solodov, Ultrasonics 36 (1998) 383. [8] R. Stoessel, S. Predak, I. Solodov, G. Busse, Nondestr. Mat. Characterisation XI, in: R.E. Green Jr., B.B. Djordjevic, M.P. Hentschel, Springer Verlag, Berlin, 2003, p. 117. [9] I.Yu. Solodov, N. Krohn, G. Busse, Ultrasonics 1 (2002) 621.
Nonlinear modulation technique for NDE with air-coupled ultrasound E.M. Ballad a, S.Yu. Vezirov a, K. Pfleiderer b, I.Yu. Solodov b
b,*
, G. Busse
b
a Department of Physics, Moscow State University, Moscow 119899, Russia Institute for Polymer Testing and Polymer Science (IKP)––Nondestructive Testing, Stuttgart University, Pfaffenwaldring 32, D-70569 Stuttgart, Germany
Abstract The present study is aimed at expanding flexibility and application area of nonlinear acoustic modulation (NAM-) technique by combining the benefits of noncontact ultrasound excitation (remote locating and imaging of defects) with sensitivity of nonlinear methods in a new air-coupled NAM-version. A pair of focused air-coupled transducers was used to generate and receive (highfrequency) longitudinal or flexural waves in plate-like samples. Low-frequency (LF-) vibrations were excited with a shaker or a loudspeaker. Temporal and spectral analysis of the output signal revealed an extremely efficient nonlinear amplitude modulation and multiple frequency side-bands for sound transmission and flexural wave propagation through cracked defects. On the contrary, a negligible modulation was observed for large and medium scale inclusions and material inhomogeneities (linear defects). A new subharmonic mode of the NAM was observed at high excitation levels. It was also shown for the first time that nonlinear vibrations of cracks resulted in radiation of a very high-order harmonics (well above 100) of the driving excitation in air that enabled imaging of cracks remotely by registration their highly nonlinear ‘‘acoustic emission’’ with air-coupled transducers. 2003 Elsevier B.V. All rights reserved. Keywords: Air-coupled ultrasound; Nonlinearity; Modulation; Acoustic imaging
1. Introduction Nonlinear acoustic modulation (NAM) is a developing NDE technique for damage diagnostics in materials and products. It is usually based on nonlinear interaction of a low- (X) and high- (x) frequency acoustic waves that yields the combination frequency (x X) output. The experimental observation of the effect goes back to 1966 when Zarembo and co-workers [1] revealed an efficient frequency mixing of acoustic waves in an Al-rod resonator. Since that time, the idea of acoustic wave resonance frequency mixing has been developed in a number of studies aimed at NDE-applications. The NAM was successfully used for monitoring defect accumulation in steel resonators subjected to tensile stress [2]. In a practically-oriented NAM-version applied to crack detection [3], the low-frequency excitation was implemented by tapping a sample with a hammer. Applications of both versions for damage *
Corresponding author. Fax: +49-0711-685-2066. E-mail address: [email protected] (I.Y. Solodov).
0041-624X/$ - see front matter 2003 Elsevier B.V. All rights reserved. doi:10.1016/j.ultras.2003.12.022
detection in materials and automobile components were also shown [4]. A new NAM-mode [5] is based on a transfer of modulation to a weak acoustic wave due to additional dissipation induced by an intense counterpart. To move from detection to location of defects, the efforts have been made recently in developing pulsemodulation NAM-options [6]. A flexible operation in any of nonlinear NDE-modes can be provided by using noncontact acoustic wave excitation. A decent spatial resolution for locating and imaging of defects is obtained in scanning modes which use focused beams. In this paper, we demonstrate for the first time that these merits can be combined in the scanning version of the NAM air-coupled NDE-methodology.
2. Phenomenology of air-coupled NAM Consider transmission of a small amplitude air coupled ultrasound (frequency x) through a cracked defect area in a plate-like sample subjected to a LF-vibrations
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E.M. Ballad et al. / Ultrasonics 42 (2004) 1031–1036
Fig. 1. Experimental configuration of air-coupled NAM.
(X) (Fig. 1). The transmission coefficient T depends on the gap between the crack edges and can assumed to be constant only for infinitesimally small amplitude of LFvibrations (linear transmission mode): Vout ðtÞ ¼ T Vin ðxtÞ. Otherwise, the open crack gap changes harmonically, first, and T ðtÞ ! ðT0 þ T ðXtÞÞ causing linear modulation of the output signal: Vout ðtÞ ¼ ðT0 þ T ðXtÞÞ Vin ðxtÞ. In addition to the probing wave of frequency x, its spectrum acquires combination frequency components (x X) whose relative amplitudes are proportional to (T =T0 ). Further increase in the pump amplitude causes ‘‘clapping’’ of the crack edges and eventually results in a pulse-type modulation of the crack gap and stiffness (contact acoustic nonlinearity [7]). The open crack works like a modulator with nonlinear transmission coefficient T ðtÞ ! ðT0 þ P T ðnXtÞÞ and provides multiple side-band specn¼1 n tral components around the fundamental frequency (nonlinear modulation). For a closed crack, one may assume T0 to be much smaller than that for the open crack and the relative side-band amplitudes (T =T0 ) increase dramatically. In the P extreme case T0 ! 0, the output signal is: Vout ðtÞ ¼ n¼1 Tn ðnXtÞ Vin ðxtÞ and the spectrum contains only side-band components.
3. Experimental methodology In our experiment (Fig. 1), commercially available piezoelectric composite material transducers were used to radiate and receive a focused ultrasound beam (fundamental frequency 450 kHz, diameter of the transducers 18 mm, full angular transducer aperture ffi20, focus distance ffi40 mm, and focus neck 2 mm). CW voltage (10 Vpp/50 X) was applied to the transducer to generate the acoustic wave; two-step amplification of the receiver and narrow-band ( 12 kHz/3 dB) filter provided ffi40 dB signal-to-noise ratio of the output of the PC-operated system. 2D-scanning of the co-axial
transducers over plate-like samples was implemented by a stepping motor controlled scanning assembly (ISEL). LF-vibrations (frequency range 1–20 kHz; maximum acceleration 740 m/s2 ; displacement up to 20 lm at 1 kHz) were excited in a specimen by using a shaker (Br€ uel & Kjaer, type 4809) or even with a loudspeaker. After a 12-bit A/D converter, the output of the air-coupled transducer can be displayed in time or at any FFT– spectral line within the transducer bandwidth. Two acoustic modes of operation have been used in experiments. In the normal transmission (detection) mode (NTM), the transducers were aligned normally to the sample surface (h0 ¼ 0 in Fig. 1) and thus only a narrow beam of longitudinal waves was transmitted through the sample. In the slanted transmission mode (STM) [8], the angle of incidence was adjusted to satisfy the phase matching conditions h0 ¼ arcsinðvair =va0 Þ (v is the wave velocity) and provide the generation of the a0 mode of Lamb waves along the sample. The a0 -mode reradiates energy from the rear side of the sample and is detected by the second co-axial air-coupled transducer (Fig. 1). The STM normally also results in ‘‘resonance’’ increase in the transmitted signal by 15–20 dB.
4. Experimental results 4.1. Air-coupled NAM To initiate the air-coupled NAM we studied ultrasound normal transmission mode (NTM) through a thin plate (d ffi 1:15 mm) of polystyrene with some simulation defects in the presence of LF-vibrations. Fig. 2 shows a B-scan for a pair of holes (diameters 1 and 2 mm) (a) and the distribution of a difference frequency side-lobes (X=2p ¼ 20 kHz; x=2p ¼ 462 kHz) along the sample length (b) obtained after the FFT of a series of A-scans in Fig. 2(a). The peaks in Fig. 2(b) show the modulation effect which must, evidently, be stronger when the defect size is about the diameter of the focused beam ( 2 mm). In this case, a displacement of the hole ‘‘shades’’ a part of the incident beam and modulates the transmission coefficient most efficiently. Such a simple ‘‘shutter’’ model (assumed in Section 2) is supported by a sub-linear dependence of the side-band output on the low-frequency amplitude (Fig. 3). A linear behaviour of Vout ðx XÞ with high-frequency input Vin ðxÞ (Fig. 4) indicates that their ratio is independent of the input which also substantiates the above modulation mechanism based on a ‘‘passive’’ transmission of the probing wave. The latter assumption seems to be reasonable because the Mach number of the air-coupled ultrasound in the focus spot was estimated as 4 · 10 4 thus producing displacement of 50 nm-amplitude. The efficiency of the NAM is introduced as the ratio Vout ðx XÞ=Vout ðxÞ (modulation strength) and even for
E.M. Ballad et al. / Ultrasonics 42 (2004) 1031–1036
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Fig. 5. Amplitudes of fundamental (right) and difference frequency (left) signals for a linear defect.
Fig. 2. NAM-B-scan of 1 mm- (left) and 2 mm- (right) holes (a); spatial distribution of a difference frequency component.
sideband amplitude (rel. units)
Fig. 6. Air-coupled NAM by a vibrating crack: harmonic (a) and ‘‘clapping’’ (b) modes. 7 6 5 4 3 2 1 0
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 -6
low-frequency amplitude (10 m)
sideband amplitude (rel. units)
Fig. 3. First side-band amplitude as a function of low-frequency excitation.
0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0
0
5 10 15 20 25 30 35 fundamental amplitude (rel. units)
Fig. 4. First side-band as a function of amplitude of high-frequency wave.
the ‘‘optimal’’ size defect is found as low as 2.5% (Fig. 5) (linear defect). The NAM development for NTM through a realistic cutting crack made by an impact hammering in the same specimen is shown in Figs. 6 and 7. A striking modu-
Fig. 7. Nonlinear modulation spectrum for NTM-mode (fundamental frequency 452 kHz).
lation efficiency is clearly seen in the temporal presentations: as the low-frequency amplitude increases, the sinusoidal modulation of the output grows up to 100% (Fig. 6(a)); further increase of the input brings about the pulse-type modulation (‘‘clapping’’ mode’’) (Fig. 6(b)). Instructively, that the shape of the pulse-modulation in Fig. 6(b) remains unchanged when the probing wave amplitude varies. This is another evidence for the dominant role of the low-frequency vibrations in the aircoupled NAM-mechanism. Spectra of the transmitted sound also reveal a dramatic rise in the modulation strength and essentially nonlinear modulation (multiple side-lobes) at higher LF-amplitudes (Fig. 7). In the slanted transmission mode, the NAM is concerned with the flexural wave propagation through a crack. Due to a strong scattering, the transmission coefficient through the crack for these waves (without LF-excitation) is normally lower than that for the NTM [8]. We may, therefore, assume that the STM of aircoupled NAM develops on the closed crack scenario
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Fig. 8. Fundamental frequency (a) and suppression in NAM-spectrum (b) for STM-mode.
(Section 2) with an extremely efficient side-lobe generation. The spectra shown in Fig. 8(a) and (b) support this assumption. A single carrier-frequency spectral line in the absence of the LF-vibrations (Fig. 8(a)) changes for a group of side-lobes, virtually, with no fundamental frequency component observed (Fig. 8(b)). The vertical scales are identical in the above spectra, so that they reveal the fundamental frequency suppression by the onset of LF-vibrations. In terms of Section 2, this shows that reduction in the time-average transmission (from a certain level T0 corresponding to Fig. 8(a)) up to an extreme case T0 ! 0 is induced by the LF-variations of the crack gap. The latter is a direct consequence of the ‘‘clapping’’ NAM-mechanism: modulation of the crack gap is asymmetrical with an evident predominance of extension so that the time-average gap increases (contact ‘‘rectification’’ effect [7]). Thus, a total transmission coefficient takes the form: T ðtÞ ¼ T0 þ Tdc þ P n¼1 Tn ðnXtÞ, where Tdc is the ‘‘dc’’ term due to the ‘‘rectification’’. Since the gap extension reduces the flexural wave transmission through the crack, Tdc must of negative sign and as the LF-amplitude grows it nullifies the time-average in the above expression and turns P the NAM-spectrum into: Vout ðxÞ ¼ n¼1 Vn ½ðx nXÞt , which is in a full compliance with the experimental data in Fig. 8(a) and (b). It is known that at high vibration amplitudes of a nonlinear oscillator (a crack itself or a sample with a crack), the contact acoustic nonlinearity gives rise to a threshold subharmonic generation [9]. This change in a crack gap dynamics would modify the transmission P coefficient into: T ðtÞ ¼ T0 þ n¼1 Tn ½nðX=2Þt and cause the subharmonic components (x nðX=2Þ) in the air-coupled NAM-spectrum. Such a subharmonic NAM-mode is demonstrated for the STM in Fig. 9. It develops in an avalanche-like manner as soon as the LFinput exceeds a certain threshold value. 4.2. Defect-selective imaging in air-coupled NAM-mode The air-coupled NAM-effects described above develop locally within the cracked area only and therefore can be used for locating and imaging of defects. Scan-
Fig. 9. Subharmonic NAM- for STM-mode on a crack (fundamental frequency 452.2 kHz).
Fig. 10. Crack imaging in a linear (451.4 kHz) NTM (a) first side-lobe NAM: difference frequency 449.7 kHz and (b); sum frequency 453.1 kHz (c). (Scanning distance in Figs. 10–12 and 14 is 10 cm.)
Fig. 11. NAM-crack imaging in STM: fundamental frequency 452.7 kHz; first side-lobe 454.4 kHz (b) and second side-lobe 456.1 kHz (c) images.
Fig. 12. Linear (a) and first side-lobe (b and c) NAM-imaging of a drop of water (left in (a)) and a crack (right) on a surface of a polystyrene sample.
ning a sample area in both the NTM- and STM-NAM modes combined with an output tuned to a side-lobe frequency delivers information solely on the nonlinear cracked defects. The results confirming an opportunity for such a defect-selective NAM-imaging are shown in Figs. 10–12. Fig. 10(a–c) demonstrate the NTM-linear and side-lobe B-scans of an impact crack in 1.15 mmthick polystyrene plate (a CD-case). Both linear and NAM-images clearly discern the crack by a local increase in a linear transmission (a), and side-lobe generation (b) and (c). However, the contrast of the images was measured to be very different: DV =V 5 for the linear image (at fundamental frequency 451.4 kHz) which is much lower than DV =V 80 at the first lower side-band component (449.7 kHz).
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The NAM-results for a single crack in the STM-mode (Fig. 11(a–c)), firstly, show an inverse contrast of the image: the fundamental frequency output drops down due to flexural wave scattering while the side-band signals rise sharply because of the local nonlinear generation. Secondly, the measurements of the image contrast reveal an evident priority of the NAM-imaging: DV =V 0:5 for the linear image (452.7 kHz) and DV =V 10 at the higher side-band line of 454.4 kHz. A defect-selective NAM-capability is demonstrated in Fig. 12(a–c) for the STM of a linear (a drop of water) and nonlinear (a crack) defects. The linear transmission image clearly reproduces both defects with a comparable contrast (DV =V 0:6) as one would expect due to flexural wave scattering and damping. On the contrary, the side-band images exhibit a selective rise in the nonlinear output (DV =V 20) in the crack area only.
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Fig. 13. Linear (a) and second harmonic (b) air-coupled images of impacts in CFRP.
4.3. Nonlinear air-coupled ‘‘acoustic emission’’ It is known, that a high efficiency of the contact acoustic nonlinearity of the cracks provides not only frequency mixing but also a strong higher harmonic (HH-) generation inside a solid sample [7]. For surface or cutting cracks, this, presumably, must be accompanied by the HH-radiation in surrounding air. In this case, the air-coupled equipment can be used for remote detection of such a nonlinear ‘‘cry’’ of a defect (‘‘acoustic emission’’) and applied to nonlinear imaging of cracks similar to the NAM-case considered above. To study a feasibility of the HH-air-coupled mode with a pair of 450 kHz-transducers, acoustic waves at subharmonic frequencies (450 kHz/n) are generated in a specimen with a contact piezo-electric transducer. One of the focused air-coupled transducers is used for detection and scanning the distribution of the HHexcitations over the surface of a specimen. Fig. 13(a) and (b) show a linear NTM (a), and the second harmonic (n ¼ 2) (b) image of a group of impacts in CFR–plastic. The nonlinear image reproduces a core part of the impact where the fractured damage mainly occurs which supports the above mechanism of air-coupled HH-generation by ‘‘clapping’’ cracks. Another clear evidence for that is given in Fig. 14(a) and (b). Low-frequency (19 kHz) vibrations were excited in the cracked polystyrene plate while 450 kHz-aircoupled focused transducer was probing the HH-field over the cracked area. Its output spectrum (Fig. 14(a)) is a clear cut indication of the presence of 23rd (437 kHz) and 24th (456 kHz) harmonics above the sample surface. B-scans in Fig. 14(b) show that the source of the emitted nonlinear field can be localised and imaged neatly with a focused air-coupled transducer tuned to a particular HHfrequency line. Instructively to note, that the air-coupled HHs were observed in the bandwidth of the high-frequency transducer (440–460 kHz) when the cracked
Fig. 14. 23rd and 24th air-coupled higher harmonics of crack vibrations (a); crack imaging at 24th harmonic (b).
sample was excited at a resonant frequency of 1.73 kHz (order of the HHs is above 250). Nonlinear radiation of such a high-frequency ultrasound in response to a lowfrequency impact on a crack emphasises similarity between this effect and a regular acoustic emission.
5. Summary Nonlinear vibrations of a cracked defect cause an efficient amplitude modulation of air-coupled ultrasound transmitted through the defect area. A simple ‘‘shutter’’ model which accounts for nonlinear variation of a gap between edges of a crack reasonably describes basic experimental manifestations of the air-coupled NAM including linear, nonlinear and subharmonic modulation. Both normal and slanted transmission NAM-modes demonstrate flexible capabilities of remote scanning and high contrast nonlinear defect-selective imaging with air-coupled ultrasound. Nonlinear vibrations of a crack are accompanied by the high-order harmonic radiation in surrounding air (nonlinear ‘‘acoustic emission’’) that also enables to locate and image cracked defects remotely. A striking efficiency, compatibility with linear scanning acoustic instruments
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along with unique capabilities of noncontact nonlinear imaging of cracks advance the developed nonlinear aircoupled techniques as a potent tool for acoustic NDE and material characterisation. References [1] L.K. Zarembo, V.A. Krasilnikov, V.N. Sluch, O.Yu. Serdobolskaya, Akust. Zh. 12 (1966) 486. [2] A.S. Korotkov, M.M. Slavinskii, A.M. Sutin, Akust. Zh. 40 (1994) 80.
[3] A.S. Korotkov, A.M. Sutin, Acoust. Lett. 18 (1994) 59. [4] K.E.-A. Van Den Abele, P.A. Johnson, A. Sutin, Res. Nondestr. Eval. 12 (2000) 17. [5] V.Yu. Zaitsev, V. Gusev, B. Castagnede, Ultrasonics 40 (2002) 627. [6] V.V. Kazakov, A. Sutin, P. Johnson, Appl. Phys. Lett. 81 (2002) 646. [7] I.Yu. Solodov, Ultrasonics 36 (1998) 383. [8] R. Stoessel, S. Predak, I. Solodov, G. Busse, Nondestr. Mat. Characterisation XI, in: R.E. Green Jr., B.B. Djordjevic, M.P. Hentschel, Springer Verlag, Berlin, 2003, p. 117. [9] I.Yu. Solodov, N. Krohn, G. Busse, Ultrasonics 1 (2002) 621.