A SINGLE TRANSDUCER BROADBAND TECHNIQUE FOR LEAKY LAMB WAVE DETECTION. P. B. Nagy*, W. R. Rose**, and L. Adler

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1 A SNGLE TRANSDUCER BROADBAND TECHNQUE FOR LEAKY LAMB WAVE DETECTON P. B. Nagy*, W. R. Rose**, and L. Adler Department of Welding Engineering The Ohio State University Columbus, Ohio NTRODUCTON The introduction of advanced composite materials into many of the new generat ion aircraft and spacecraft has given rise to a significant increase in al aspects of operational capability. These materials come in many forms; organic and non-organic, fibrous and particulate, and endlesscombinations of the above which not only give enhanced strength characteristics, but deliver them in very specific design directions. The more common uses are in both primary and secondary aircraft structures, however, considerable effort is also being put into designing composite materials for use in hostile environments such as those destined for use as jet engine turbine blades. The obvious advantage of these materials is in their high strength and stiffness to weight ratios. The anisotropy of the material allows strength to be utilized in a given design direction without the addition of extra weight resulting from strength in unnecessary directions, as is usually the case in isotropic materials. The use of these materials over their more conventional metallic counterparts can yield dramatic weight savings which can reduce fuel consumption and allow for carrying additional fuel or cargo. The present and future importance of these materials demands that unique methods be developed for their testing and evaluation. Their inherent anisotropy and non-homogeneity create problems for standard testing procedures, however, through the use of new techniques these can be overcome. The graphite/epoxy samples used in this work were manufactured from Hercules Corporation AS4/350l-6 Prepreg Tape. Each layer, or ply, in a given sample is made up of a thermo-set epoxy impregnated with unidirectional graphite fibers. The plies in a given laminate can al be in the same direction or the directions can be var ied as desired. Due to the two components present in each ply and because of the discrete directions of the fibers, these materials are non-homogeneous and anisotropic by nature. *Permanent Address: **Permanent Address: Applied Biophysics Laboratory, Technical University Budapest, Budapest, Hungary. Aerospace Maintenance Development Unit, Canadian Armed Forces, Trenton, Ontario, Canada. 483

2 LEAKY LAMB TECHNQUES Lamb waves are much better suited for interrogation of thin plates than the more conventional bulk wave techniques, because they propagate along the plates rather than through them. This study is limited to immersion techniques only, when the Lamb modes become "leaky" as they are highly attenuated by reradiating their energy into the liquid on both sides of the plate as they propagate. Fig. 1 shows the schematic diagram of leaky Lamb wave generat ion in a thin plate. When a narrow-band tone-burst signal is incident on the plate at an arbitrary angle of incidence, and there is no phase-matching between the compressional wave in the liquid and one of the Lamb modes in the plate, the incident wave is simply specularly reflected. The beam profile is undistorted in this case, as it is shown by digitalized schlieren photography in Fig. 2a. The Lamb modes are highly dispersive, therefore a small change in the carrier frequency can result in phase-matching at the same angle of incidence. Fig. 2b and c show the redistributed reflected and transmitted beam profiles in the case of phase-matching. The slowly decaying leaky fields are the same on both sides of the plate, but the presence of the somewhat reduced specular reflection results in a destructive interference on the front side. The most accurate technique to observe the Lamb resonances seems to be the detection of the beam split due to destructive interference between the specularly reflected component and the reradiated Lamb wave [1,2]. The main drawback of this method is its sensitivity to mechanical misalignments, especially in the case of highly anisotropic plates when the reradiated field of the leaky Lamb wave is shifted laterally not only in the plane of incidence, but out of it, also [3]. n spite of these difficulties, the outstanding accuracy and sensitivity of this technique ensureits important role as a basis for comparison for other methods. n the following, we shall discuss two broadband, single-transducer techniques of promising features for ultrasonic NDE of composite plates. NCDENT BUM AEFLECTED BEAM BACK SCATTEAEO BEAM TAANSMTTEO BEAM Fig. 1. Schematic diagram of leaky Lamb wave generation. 484

3 a, Specular reflection when there is no phase-matching. b, Redistributed reflection when there is phase-matching. c, Transmission when there is phase-matching. Fig. 2. Beam profiles by digitalized Schlieren photography. BACKSCATTERNG TECHNQUE Backscattering from fiber reinforced composite laminates was first studied by Bar-Cohen and Crane [4]. They found that in directions perpendicular to the fibers of one or more plies the backscattered signal was much higher than elsewhere, which suggests that the scattering inhomogeneity is mainly oriented parallel with the fibers. The obvious possibility that the strong scattering is directly due to the embedded fibers was discarded by Achenbach and Qu [5] on the basis that they are too small in diameter and too closely packed to give rise to strong backscattering in the applied 485

4 frequency range. The same authors explained the presence of strong backscattering even in seemingly porosity free, flawless plates by the irregularities of the fiber texture [6]. The physical nature of the scattered acoustic wave remained somewhat hidden in these studies, probably because many factors seem to contribute. Our experimental results show that the principal source of backscattering is the leaky Lamb wave generated in the plate. De Billy, Adler, and Quentin [7] found increased backscattering from macroscopically isotropic, but microscopically inevitably inhomogeneous plates at so-called Lamb angles using tone-burst technique. This phenomenon is analogous to the increased backscattering from liquid-solid interfaces at the Rayleigh angle, andcan be fully explained by the similarities of the Rayleigh and Lamb waves [8]. n our experiment, we used a broadband ultrasonic transducer in pulseecho mode. Fig. 3 shows the frequency spectrum of the backscattered signal at a particular fiber orientat ion and angle of incidence. The spectrum is modulated by random interference between uncorrelated inhomogeneities, therefore the Lamb resonances can not be recognized. Fig. 4 shows the same backscattered spectrum after spatial averaging and deconvolution by the transducer's frequency response. The arrows indicate the Lamb modes as measured by the well proven ac curate beam split reflection technique. The peaks of the average backscattered spectrum obviously correspond to these Lamb m~des, which indicates the important role of thes~ pl~te vibrations in the ~Acksr.attering gene,ation. E :: (J e a, e- C)~ ":>0 ;! -- ';25 (J... ':.5 (J o o 4 5 Frequency (MHz) Fig. 3. Frequency spectrum of the backscattered signal from a unidirectional plate (perpendicular to the fibers at 24 angle of incidence). Fig. 4. E :: (J e -- Ca, C) ~ 8.0 ":>0 C... :s ~ 4.0 -;:0 -- (J... C 2.0..l:- (J t t t t Lamb ca resonances ~~~.0~~0~~~~1~~~~t~5~~2~D~~2.~5~-3~.0~~3~. 5~-47.~0~4~.5~~~~O Frequency (MHz) Spatial averaged frequency spectrum of the backscattered signal (20 points, other parameters are the same as in Fig. 3). 486

5 TRANSMSSON TECHNQUE Due to the strong acoustic impedance mismatch between the composite plate and the surrounding liquid, the specular transmission through the sample is usually very weak. At the so-called Lamb resonances, the transmission is greatly enhanced by double mode conversion between the compressional wave in the liquid and the Lamb wave in the plate. Half of the Lamb wave energy leaks back into the liquid on the back side of the plate and propagates parallel with the incident beam. The schematic arrangement for detecting these transmission peaks is shown in Fig. 5. We use double transmission technique in order to simplify the mechanical alignment and enhance the contrast of the Lamb resonances. A broadband ultrasonic transducer is used to pick up the echo signal from a perpendicular plane reflector. The plate under study is placed somewhere between the transducer and the reflector, and the first double transmitted signal from the reflector is time-gated and frequency analyzed. There is no need for further alignment whatsoever. The lateral displacement of the throughtransmitted signal both in and out of the plane of incidence is fully compensated by this double way arrangement, as well as the sharpness of the resonance peaks is further enhanced. t is very easy to change the angle of incidence and plate orientat ion since the received signal is always well defined and sufficiently strong. Fig. 6 shows the frequency spectrum of the through-transmitted signal for a unidirectional plate at 30 angle of incidence. The arrows indicate the Lamb resonances as measured by the beam split reflection technique. Fig. 7 shows the dispersion curves for a unidirectional plate at normal fiber orientat ion. The phase velocity of the Lamb modes was control led by the angle of incidence. Owing to the outstanding stability of the suggested double transmission technique, the sample can be rotated around any axis normal to the transducer in order to get a similar dispersion curve. Reflector a Tronsducer..J lncldenl Beam Leoky Lamb b Transducer Composite Somple Reflector Reflected Beam SpeCular Fig. 5. Schematic diagram of the through-transmission method in (a) forward and (b) backward directions. 487

6 t Lamb resonanc t t o 'REQUEHCY(MHz) Fig. 6. Frequency spectrum of the through-transmitted signal (unidirectional plate at normal fiber orientation, 30 angle of incidence). 9 8 ';/ e 7.., o.z:.6?:5 u o 4i > 4 G.. r f r, ca -a3 f, t t f, "... f f ~ ' ~ f f f..,,,.' " "., "-, '"'...', ',,- '..: '.. 't.... l.." " "l.. 2 O frequency * thickness ~Hzmrri] 8 Fig. 7. Dispersion curves for a unidirectional plate at normal fiber orientation. Polar diagrams can be readily obtained by rotating the sample around any axis normal to the plate. Different modes have very different degrees of anisotropy, and, beside the phase and group velocities, the strength of the mode conversion changes as well as the fiber orientation. We found that the very modes showing the highest (phase velocity) anisotropy are bound to disappear at certain azimuthal angles. Therefore, we chose as an example in Fig. 8 one of the less anisotropic modes which can be followed easily through al azimuthal angles. 488

7 6~ ~ r--_ Fig fiber direction 5 6!MHzmm] Polar diagram for a unidirectional plane at 10 angle of incidence. CONCLUSONS We investigated two broadband, single-transducer techniques for Lamb wave interrogation on thin anisotropic plates. The backscattering technique was shown to yield the elastic properties of the plate after extensive spatial averaging, but its main field of application is probably the qualitative or even quantitative characterization of inhomogeneities inside the plate. A new double way through-transmission technique was introduced to determine the elastic properties of the plate as well. This simple, very stable arrangement yields superior signals with respect to other singletransducer techniques. Both (phase velocity) dispersion and anisotropy data are readily measured by this technique. The elastic properties of the plate can be mapped easily by scanning the sample at high speed. Furthermore, by measuring the amplitude of a certain Lamb resonance in the spectrum of the double through-transmitted signal, we can determine the attenuation coefficient of each mode at any point of the sample. ACKNOWLEDGEMENT This work was partially supported by the Canadian Armed Forces. REFERENCES 1. D. E. Chimenti and A. H. Nayfeh, "Leaky Lamb waves in fibrous composite laminates," J. App1. Phys. 58, 4531 (1985). 2. Y. Bar-Cohen and D. E. Chimenti: "Nondestructive evaluat ion of composite laminates," Review of Progress in Quantitative Nondestructive Evaluation Vo. 5B, D. O. Thompson and D. E. Chimenti, eds., (Plenum, New York, 1986) p W. R. Rose, S.. Rokhlin, and L.,Adler, "Evaluation of anisotropic properties of graphite/epoxy composite plates using Lamb waves," Review of Progress in Quantitative Nondestructive Evaluation Vo. 6, D. O. Thompson and D. E. Chimenti, eds., (Plenum, New York, in press). 489

8 4. Y. Bar-Cohen and R. L. Crane, "Acoustic backscattering imaging of subcritical flaws in composites," Mater. Eval. 40, 970 (1982). 5. J. D. Achenbach and J. Qu, "Backscattering from~law distributions in composite materials," Review of Progress in Quantitative Nondestructive Eva1uation Vo. 5B, D. o. Thompson and D. E. Chimenti, eds., (P1enum, New York, 1986) p J. Qu and J. D. Achenbach, "Ana1ytica1 treatment of polar backscattering from porous composites," Review of Progress in Quantitative Nondestructive Eva1uation Vo. 6., D. o. Thompson and D. E. Chimenti, eds., (P1enum, New York, in press). 7. M. de Bi11y, L. Ad1er, and G. Quentin, "Measurements of backscattered 1eaky Lamb waves in p1ates," J. Acoust. Soc. Am. 75, 998 (1984). 8. L. E. Pitts, T. J. P1ona, and W. G. Mayer, "Theoretical similarities of Ray1eigh and Lamb modes of vibration," J. Acoust. Soc. Am. 60, 374 (1976). 490