ABSTRACTAngle beam immersion and contact techniques are commonly used ul-

trasonic nondestructive testing (NDT) techniques. Since the incidentangle of the longitudinal wave is not normal, the mode conversion of thewaves will occur at the interface. Due to diffraction, wave interference andthe complexity of mode conversions, the accuracy of transmitted shearwave NDT is not always better than transmitted longitudinal wave NDT.In this study, we try to determine the optimum wave type of the transmit-ted wave and optimum incident angle of the longitudinal wave, so that wecan use appropriate transducers and wedges, whose characteristics can beobtained from the manufacturer to perform the angle beam ultrasonicNDT efficiently and effectively.

The cumulative transmission energies of longitudinal and shear waveswere calculated and some angle beam ultrasonic NDT experiments wereperformed. Our results indicate that the transmitted longitudinal wave isrecommended for scanning cracks in a lightweight alloy of aluminum (over90%), copper, magnesium and manganese, whose oblique angles are lessthan 34 degrees for the angle beam immersion test. The transmitted shearwave should be used to scan oblique cracks greater than 34 degrees. More-over, for angle beam contact testing, the transmitted longitudinal wave canbe used to scan the oblique cracks in the aluminum alloy whose oblique an-gles are less than 61 degrees and the transmitted shear wave can be used toscan the oblique cracks greater than 61 degrees. The wavelength of trans-mitted shear waves is shorter than that of longitudinal waves at the samefrequency; hence the transmitted shear wave has better resolution thantransmitted longitudinal waves. However, for the same frequency andpropagation distance, the transmitted shear wave will be attenuated fasterthan transmitted longitudinal waves. Hence, it is not suitable to use trans-mitted shear waves to detect deep discontinuities and to test strongly at-tenuated material.Keywords: converted wave, shear wave, nondestructive testing.

INTRODUCTIONIn ultrasonic nondestructive testing (NDT), ultrasound is used

to nondestructively detect discontinuities or estimate the physicalcharacteristics of a material. The most frequently used ultrasonicwave is the longitudinal wave, due to the simplicity of generationand the ability to acoustically couple the transducer to the test spec-imen. However, the other wave types (shear and surface waves)have their merits. For instance, shear waves have a better resolutionfor detecting small discontinuities than do longitudinal waves atthe same frequency. Some kinds of discontinuities reflect shearwaves much better than longitudinal waves and shear waves canalso be used to test near vertical cracks (Kuttruff, 1991).

Shear waves are usually produced by mode conversion for lon-gitudinal waves impinging on an interface at an incident angleother than normal in ultrasonic NDT. Therefore, the pulse/echoangle beam and immersion techniques are the common forms ofshear wave NDT (Bar-Cohen, 1991; Chang, 1991). An example ofshear waves used in ultrasonic NDT is the time of flight of a longi-tudinal wave and refracted shear wave used to calculate the veloci-ty C-scans for estimating the elastic modulus variation in ceramicsand composites (Gruber et al., 1988). In addition, shear waves areproduced by mode conversion from a focused acoustic beam beingincident from water to a solid material and a high resolution of theimage of deep subsurface can be obtained using the shear waveacoustic microscope method (Zhang and Crean, 1991). Further-more, shear waves can be generated, focused and steered usingpulsed laser arrays for ultrasonic NDT (Noroy et al., 1995). More-over, a converted shear wave at the water/solid interface is used forscanning tomographic acoustic microscopy; the resolution of ashear wave scanning tomographic acoustic microscope is betterthan a longitudinal wave scanning tomographic acoustic micro-scope (Ko and Meyyappan, 1997). The diffraction and interferenceproblems in angle beam shear wave NDT may, however, degradethe technique’s accuracy. Fortunately, these problems can be sup-pressed and the accuracy can be improved using digital imagingtechniques (Chang and Hsieh, 2002; Steinberg, 1992; Ylitalo and Er-mert, 1994).

The characteristics of mode conversion for a longitudinal waveimpinging an interface depend on the media’s acoustic imped-ances, the longitudinal wave’s incident angle and the beam angle,beam diameter, probe index and near field of transducer. The nearfield effect of a transducer has been discussed by Zemanek (1971).The beam angle and probe index of an ultrasonic angle probe canbe obtained using a numerical calculation (Fukuhara et al., 1985).The beam angle and beam diameter can be measured using the in-ternational standard reference blocks (International Organizationfor Standardization, 1999). After recognizing what material and forwhat kind of discontinuity one will be testing, the optimum wavetype and optimum incident angle must be determined before per-forming ultrasonic angle beam NDT.

In this study, the cumulative transmission energies of the trans-mitted longitudinal and shear waves specularly reflected from adiscontinuity using angle beam techniques are theoretically calcu-lated. Some experiments are implemented for verifying the theoret-ical calculation and to show the capability and applicability of anglebeam shear wave NDT.

REFLECTION AND TRANSMISSION AT AN INTERFACEWhen a plane elastic wave impinges on a plane interface, the

waves will be reflected and transmitted at the interface. If the inci-dent angle of the wave is not normal, the converted waves wouldbe produced at the interface and then reflect and transmit from the

Materials Evaluation/August 2005 827

Angle Beam Shear Wave Nondestructive Testing

by Young-Fo Chang* and Tzong-Ying Wu†

Submitted September 2004

* Institute of Applied Geophysics, National Chung Cheng University,Min-hsiung, Chia-yi 621, Taiwan; 886 5 272 0411 X66208; fax 886 5 2720807; e-mail <seichyo@eq.ccu.edu.tw>.

† Institute of Applied Geophysics, National Chung Cheng University,Min-hsiung, Chia-yi 621, Taiwan.

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interface. For example, if a plane longitudinal wave is incident on asolid/solid interface at an abnormal incident angle, some of the en-ergy of the incident longitudinal wave can be reflected and trans-mitted at the interface. The other energy would be converted toshear waves and the converted shear waves would reflect andtransmit at the interface. The propagation directions of the wavesare assumed to obey Snell’s law. For similar effects of a plane shearwave impinging on a solid/solid interface at an abnormal incidentangle, some of the energy of the incident shear wave would be con-verted to longitudinal waves and the converted longitudinal waveswould then reflect and transmit at the interface. The angle and en-ergy of the reflected and transmitted waves can be found in Ewinget al. (1957).

Angle beam immersion testing provides the versatility of choos-ing any desired incident angle. In addition, ultrasonic discontinuitydetection is usually used to test metals and water is the commonfluid used as the couplant in ultrasonic immersion testing. There-fore, the reflection and transmission of ultrasound on a water/alu-minum alloy interface is considered first (alloy over 90% alu-minum, with copper, magnesium and manganese).

In water, ■ longitudinal wave velocity = 1500 m/s (4920 ft/s)■ shear wave velocity = 0 m/s (0 ft/s)■ density = 1 g/cm3 (0.06 lb/ft3).

In the aluminum alloy,■ longitudinal wave velocity = 6400 m/s (21 000 ft/s)■ shear wave velocity = 3200 m/s (10 500 ft/s)■ density = 2.7 g/cm3 (0.2 lb/ft3).

Figure 1a shows the geometric relationship between the incidentlongitudinal wave (P), reflected longitudinal wave (Rp), transmittedlongitudinal wave (Tp) and converted transmitted shear wave (Tsv)for an ultrasonic beam impinging on the water/alloy interface.Since the liquid cannot support the shear force, only the longitudi-nal wave can exist in the liquid. Figure 1b shows the calculated en-ergy ratio of the waves for different incident angles θ. The first andsecond critical angles of the wave are about 14 and 28 degrees, re-spectively. The energy of the transmitted longitudinal wave isgreater than the transmitted shear wave for 0 to 14 degree incidentangles. However, the energy of the transmitted shear wave for 15 to28 degree incident angles is greater than that for all transmitted lon-gitudinal waves.

If the transmitted longitudinal wave is specularly reflected fromthe discontinuity surface and transmits into the water, then the cu-mulative transmission energy of longitudinal waves coming intoand out of the water/alloy interface can be calculated. It is the samefor the transmitted shear wave. The configuration of the ray pathsof the transmitted longitudinal and transmitted shear waves isshown in Figure 2a and their cumulative transmission energies areshown in Figure 2b. The figures exhibit that the energy of the trans-mitted shear wave used in angle beam immersion testing with anincident angle between the first and second critical angles is greaterthan that for the transmitted longitudinal wave.

For angle beam contact testing, the wedge is used between thetransducer and test specimen for driving a particular incident angleof the longitudinal wave. In this study, the acrylic/aluminum alloyinterface is considered as the wedge/specimen interface. The veloc-ities of longitudinal and shear waves are 2730 and 1430 m/s (8960and 4690 ft/s) and the density of the acrylic is 1.2 g/cm3

(0.07 lb/ft3). The configuration of the ray paths of the transmitted lon-gitudinal and transmitted shear waves for the acrylic/alloy interfaceis shown in Figure 3a and the cumulative transmission energy is

828 Materials Evaluation/August 2005

Figure 1 — A plane longitudinal wave impinges the water/alloyinterface with an incident angle θ: (a) the geometric relationshipbetween the incident longitudinal wave (P), reflected longitudinal wave(Rp), transmitted longitudinal wave (Tp) and converted transmittedshear wave (Tsv); (b) the energy ratio of reflected and transmittedwaves.

(a)

(b)

Figure 2 — Longitudinal wave impinges a water/alloy interface and thetransmitted longitudinal and transmitted shear waves are specularlyreflected from the discontinuity surface: (a) the configuration of the raypaths of transmitted longitudinal and transmitted shear waves; (b) thecumulative transmission energy of transmitted longitudinal andtransmitted shear waves.

(a)

(b)

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shown in Figure 3b. The first and second critical angles of the waveare 26 and 58 degrees, respectively. Except that the incident angle ofthe wave is close to the first critical angle, the energy of the trans-mitted longitudinal wave reflected from the crack is greater thanthat of the transmitted shear wave.

EXPERIMENTS AND RESULTSAn angle beam immersion testing system is designed for per-

forming shear wave NDT (Figure 4). A pulser/receiver inpulse/echo mode (transmitting/receiving) is used to excite thetransducer, receive the signal and synchronize the digital oscillo-scope. The received signal is displayed on the digital oscilloscope. Apersonal computer retrieves the digitized radio frequency signalfrom the oscilloscope via a IEEE-488 general purpose interface busand processes them. A step motor controlled by the personal com-puter is used to automatically move the probe. A 20 MHz and3 mm (0.1 in.) diameter immersion transducer is used to transmitand receive the ultrasound. Three specimens were fabricated andscanned. Water was used as the couplant. In this study, the distancebetween the probe and specimen in the water was 10 mm (0.4 in.)and the scanning interval in space was 1 mm (0.04 in.).

15 Degree Oblique CrackAn aluminum alloy block 30 mm (1.2 in.) in height, 30 mm

(1.2 in.) wide and 100 mm (3.9 in.) in length with a 15 degreeoblique planar crack through the specimen (Figure 5a) is scanned.The pulse/echo angle beam immersion B-scan image is shown inFigure 5b with a 4 degree incident angle of the transmitted longitudi-nal wave, which can impinge the planar crack perpendicularly. Theordinate is the travel time of the waves and the abscissa is the posi-tion along the scanning line on the top surface of the specimen. Theimage of the 15 degree oblique planar crack, marked as Tp in thefigure, can be clearly seen in the B-scan image. The B-scan image

with an 8 degree incident angle for the transmitted shear wave im-pinging the planar crack perpendicularly is shown in Figure 5c.Since the velocity of the shear wave is half that of the longitudinalwave, the travel time is shown from 19 to 26 µs for clearly dis-playing the transmitted shear wave. The amplitudes in Figures 5band 5c are displayed in the same grayscale, the black and white

Materials Evaluation/August 2005 829

Figure 3 — Longitudinal wave impinges an acrylic/alloy interface andthe transmitted longitudinal and transmitted shear waves arespecularly reflected from the discontinuity surface: (a) the configurationof the ray paths of transmitted longitudinal and transmitted shearwaves; (b) the cumulative transmission energy of transmittedlongitudinal and transmitted shear waves.

(a)

(b)

Figure 4 — Block diagram of the automatic angle beam immersionscanning system.

Figure 5 — A 15 degree oblique planar crack specimen was scanned bythe angle beam transmitted longitudinal and transmitted shear waves:(a) the configuration of the 15 degree oblique planar crack specimen;(b) the transmitted longitudinal wave B-scan image with a 4 degreeincident angle; (c) the transmitted shear wave B-scan image with an8 degree incident angle.

(a)

(b)

(c)

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expressing the maximum and zero amplitudes of the waves andthe change from black to white being linear. The transmitted shearwave reflected from the crack can be seen in Figure 5c. The multipletransmitted longitudinal waves, which are the multireflection oftransmitted longitudinal waves between the top surface of thespecimen and the crack, are in front of the transmitted shear wavesand their amplitudes are the same as the transmitted shear waves.

75 Degree Oblique CrackAn aluminum alloy block with a 75 degree oblique planar crack

cut at the center of the specimen is shown in Figure 6a. Thepulse/echo angle beam immersion B-scan image is shown in Fig-ure 6b with a 13 degree incident angle for the transmitted longitu-dinal wave impinging the crack perpendicularly. The image of a75 degree oblique planar crack can be clearly seen in the B-scanimage. The B-scan image with a 28 degree incident angle for thetransmitted shear wave impinging the crack perpendicularly isshown in Figure 6c. The amplitudes of transmitted shear waves re-flected from the crack are greater than those of the transmitted lon-gitudinal waves. However, the decay rate of the transmitted shearwaves along the depth is greater than that of the transmitted longi-tudinal waves.

A Thin Layer in the Rear of the 75 Degree Oblique CrackA 1.5 mm (0.06 in.) thick piece of the aluminum alloy is glued to

the left part of the 75 degree oblique crack specimen for testing theresolution of the transmitted longitudinal and transmitted shearwaves (Figure 7a). The arrangement of scanning is the same as thatused in Figure 6. The reflections from the bottom of the thin alloysheet cannot be resolved in the transmitted longitudinal B-scanimage (Figure 7b). However, they can be seen in the transmittedshear wave image (Figure 7c); even the multireflection of the trans-mitted shear wave in the thin piece of the alloy can be observed. InFigure 7c, it can be easily seen from the top right direction (shownby an arrow).

DISCUSSIONS AND CONCLUSIONSIn reality, the sound beam of the transducer is not a thin line and

the beam diverges in the far field (Zemanek, 1971). The half angle,which is the beam angle spread between –6 dB points, of the trans-ducer used in this study in water and the aluminum alloy is 0.7 and3.2 degrees, respectively. The near field distances of the sound beamin water and the alloy are 30 and 7 mm (1.2 and 0.3 in.), respective-ly. The longitudinal wave excited by the transducer is not monofre-quency. Therefore, the energy of the transmitted longitudinal ortransmitted shear waves reflected from the crack is an averaged ef-fect within the sound beam contributed by all frequencies of thewave. It is difficult to quantitatively estimate the energy ratio be-tween transmitted longitudinal and transmitted shear waves re-flected from the crack. However, the quality of the energy ratio oftransmitted longitudinal to transmitted shear waves can still bemade.

Based on Snell’s law, with the calculation of the cumulativetransmission energy of the waves at the water/alloy interface (Fig-ure 2) for the angle beam immersion testing, the energy of the trans-mitted longitudinal wave is found to be greater than that of thetransmitted shear wave reflected from the crack when the incidentangles are from 0 degrees to the first critical angle (14 degrees).However, if the incident angle is greater than 15 degrees, the energyof the transmitted shear wave reflected from the crack is greaterthan that of the transmitted longitudinal wave. The transmittedshear wave will deviate 34 degrees from normal if the longitudinalwave impinges the interface with a 15 degree incident angle. There-fore, when the oblique angle of cracks is less than 34 degrees, itseems that the transmitted longitudinal wave is better than thetransmitted shear wave in detecting these cracks. For obliquecracks greater than 34 degrees, the transmitted shear wave is betterthan the transmitted longitudinal wave. Hence, in Figure 5, for the15 degree oblique crack, the energy of the transmitted longitudinalwave reflected from the crack is greater than that of the transmittedshear wave and, as shown in Figures 6 and 7, the energy of the

830 Materials Evaluation/August 2005

Figure 6 — A 75 degree oblique planar crack specimen was scanned bythe angle beam transmitted longitudinal and transmitted shear waves:(a) the configuration of the 75 degree oblique planar crack specimen;(b) the transmitted longitudinal wave B-scan image with a 13 degreeincident angle; (c) the transmitted shear wave B-scan image with a28 degree incident angle.

(a)

(b)

(c)

Figure 7 — A thin layer in the rear of a 75 degree oblique crackspecimen was scanned by the angle beam transmitted longitudinal andtransmitted shear waves: (a) the configuration of the thin layer glued toa 75 degree oblique planar crack specimen; (b) the transmittedlongitudinal wave B-scan image with a 13 degree incident angle;(c) the transmitted shear wave B-scan image with a 28 degree incidentangle.

(a)

(b)

(c)

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transmitted shear wave reflected from the 75 degree oblique crackis greater than that of the transmitted longitudinal wave.

The cumulative transmission energy of the waves at theacrylic/alloy interface (Figure 3), which is used to simulate theangle beam contact testing for metal, the energy of transmitted lon-gitudinal waves is greater than that of the transmitted shear wavesexcept that the incident angle (22 degrees) is close to the criticalangle (26 degrees). The transmitted longitudinal wave will deviate61 degrees from normal if the longitudinal wave impinges the in-terface with a 22 degree incident angle. Therefore, except for thevery high oblique angle crack (61 degrees), the transmitted longitu-dinal wave will be better than the transmitted shear wave for con-tact testing.

For the same frequency, the wavelength of the shear wave isshorter than that of the longitudinal wave that yields a better reso-lution of small discontinuities. Therefore, the transmitted shearwave can resolve the thin piece of the aluminum alloy and thetransmitted longitudinal wave cannot (Figure 7). The attenuation ofthe wave’s amplitude in material can be expressed as

(1)

whereQ = the quality factord = travel distanceλ = wavelength.

In common material, the difference of Q values between longitudi-nal and shear waves is not large. For the same propagation dis-tance, the transmitted shear wave will be attenuated faster than thetransmitted longitudinal wave since its wavelength is shorterthan that of the transmitted longitudinal wave. Therefore, thedecay of the amplitude of the transmitted shear wave along thedepth is faster than that of the transmitted longitudinal wave(Figures 6c and 7c). Hence, the transmitted shear wave is notsuitable for detecting deep discontinuities and testing stronglyattenuated materials.

The real challenges surrounding B-scan images of angle beamimmersion or contact testing may be more complex than those de-scribed in this study. The other mode conversion wave types mayoccur at any interface if the wave is not of normal incidence to theinterface — for example, if the transmitted waves convert at thecrack surface (transmitted longitudinal or transmitted shear

waves). Also, multiple longitudinal or shear waves could exist be-tween any two interfaces. All of them add to the complexity of theimage. However, these complex events can be reduced if the correctwave type and incident angle is used in the scanning. Therefore, theimportance of using the optimum wave type and incident angle inangle beam ultrasonic NDT is emphasized.

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Chang, F., “Ultrasonic Pulse Echo Contact Techniques,” Nondestructive Test-ing Handbook, second edition: Volume 7, Ultrasonic Testing, Columbus,Ohio, American Society for Nondestructive Testing, 1991, pp. 187-217.

Chang, Y.F. and C.I. Hsieh, “Time of Flight Diffraction Imaging for Double-probe Technique,” IEEE Transactions on Ultrasonics, Ferroelectrics and Fre-quency Control, Vol. 49, 2002, pp. 776-783.

Ewing, W.M., W.S. Jardetzky and F. Press, Elastic Waves in Layered Media,New York, McGraw-Hill, 1957.

Fukuhara, H., T. Saito and K. Kimura, “Numerical Calculation of ProbeIndex and Beaming Angle of Ultrasonic Angle Probe,” Proceedings of the11th World Conference on NDT, Vol. 2, Las Vegas, Nevada, 1985, pp. 1032-1039.

Gruber, J.J., J.M. Smith and R.H. Brockelman, “Ultrasonic Velocity C-scansfor Ceramic and Composite Material Characterization,” Materials Evalua-tion, Vol. 46, 1988, pp. 90-96.

International Organization for Standardization, ISO 12715, Ultrasonic Nonde-structive Testing: Reference Block and Test Procedures for the Characterizationfor Contact Search Unit Beam Profiles, Geneva, Switzerland, InternationalOrganization for Standardization, 1999.

Ko, D. and A. Meyyappan, “Scanning Tomographic Acoustic MicroscopyUsing S-waves,” IEEE Transactions on Ultrasonics, Ferroelectrics and Fre-quency Control, Vol. 44, 1997, pp. 425-430.

Kuttruff, H., Ultrasonics Fundamentals and Applications, London, Elsevier Ap-plied Science, 1991.

Noroy, M.H., D. Royer and M.A. Fink, “Shear-wave Focusing with a Laser-ultrasound Phased-array,” IEEE Transactions on Ultrasonics, Ferroelectricsand Frequency Control, Vol. 42, 1995, pp. 981-988.

Steinberg, B.D., “Digital Beamforming in Ultrasound,” IEEE Transactions onUltrasonics, Ferroelectrics and Frequency Control, Vol. 39, 1992, pp. 716-721.

Ylitalo, J.T. and H. Ermert, “Ultrasound Synthetic Aperture Imaging: Mono-static Approach,” IEEE Transactions on Ultrasonics, Ferroelectrics and Fre-quency Control, Vol. 41, 1994, pp. 333-339.

Zemanek, J., “Beam Behavior within the Near Field of a Vibrating Piston,”Journal of the Acoustical Society of America, Vol. 49, 1971, pp. 181-191.

Zhang, D. and G.M. Crean, “S-wave Imaging for Deep NondestructiveEvaluation,” Electronics Letters, Vol. 27, 1991, pp. 2248-2250.

ed

Q−

λ

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