Pilarski and Pilarski and Rose used a critical angle technique to test samples with different strength [10-12]. Oblique incidence was also proposed by Pilarski and Rose to detect interfacial weakness between adhesive and adherent in adhesively bonded structures . More re- cently, Rose and co-workers suggested using guided waves for inspecting adhesive bonded joints to increase the inspection efficiency and sensitivity by exploiting their long-range/large- area characteristics as well as their variety of particle displacements and stresses distribu- tions through the entire bond structure . They sent a well-defined mode directly through the bond area and features of the reflected or transmitted wave mode were measured and correlated to bond quality. Among the features selected were their amplitude, frequency spectrum and propagation velocity. They suggested the use of multi-mode inspection of adhesively bonded structures, stressing the beneficial role of the mode field distributions, temporal mode pulse shape, the phase and group velocities, and the excitability and receptability of selected modes [15,16]. A number of techniques were proposed by Guyott, Cawley and Adams  including horizontally polarized (SH) waves to introduce shear traction at the bond line. However, these waves are difficult to excite with standard piezoelectric transducers and the same effect can be produced with guided waves which are easier to excite with standard equipment [18-21]. The most common transducers used are off-the-shelf, commercially available broadband ceramic or piezo-composite elements with variable or fixed angle beams. This paper outlines an approach to an effective and rapid inspection of layered joints using Lamb waves. Following an introduction to Lamb waves, it describes their generation, efficiency and sensitivity in a contact mode and how to design and select modes. Experimental results on tear straps and lap splice joints are presented, using variable angle transducers to excite Lamb waves.
Partial wave pattern of Lamb wave propagating in an isotropic plate
a) Phase velocity
b) Group Velocity Dispersion Curves
The phase velocities or wavenumbers of Lamb waves may be obtained by solving the following transcendental equation from [23,24]:
where d is the plate thickness, k = /Vph is the wave number, = 2 f is the circular frequency,
Vph is the Lamb wave phase velocity, and and are given by:
q = (k 2 - kl2)1/2 (2)
p = (k 2 - kt2)1/2 (3)
p = (k 2 - kt2)1/2 (3)
where kl = /Vl is the longitudinal wavenumber and kt = /Vt is the shear wave number, and the
velocities Vl and Vt are the longitudinal and shear waves velocities in bulk material. These velocities are given by:
where and µ are the Lame constants of the layer and its mass density. The exponent m in Equation (1) has the value +1 for symmetric modes and -1 for antisymmetric modes in the plate. The dispersion curves illustrated in Figure 2a are phase velocity dispersion curves for an aluminum plate whose material parameters were taken as Vl=6.37 Km/s, Vt=3.16 Km/s and =2,700 kg/m3 and are useful for experimental generation of Lamb wave modes and for r mode selection. The other dispersion curves illustrated in Figure 2b are group velocity dispersion curves for the same aluminum plate and are useful for mode identification and defect location. The group velocity dispersion curves can be calculated from the formula:
V g = d /dk (6)
In Figure 2a each continuous curve represents a guided wave mode which can be produced in the inspected specimen. Selecting modes for a certain application or defects type, require analysis of their wave structures (Figure 3). For example, it was noticed that the out-of-plane displacements are very sensitive for surface and interface defects where ultrasonic power is concentrated on the surface. Each mode from the dispersion curves has its own characteristic field distribution.
The wave structure diagrams are represented by the longitudinal Ux and normal Uz displacement components, stress components Szz , Sxx and Txz and time average longitudinal power P flux per unit width. These can be calculated for each point on the dispersion curve of each mode to determine which points on the dispersion curves are most sensitive to the defects of interest.
Lamb wave excitation:
There exist various methods and techniques for the excitation of ul- trasonic Lamb waves. It is convenient to recognize two general categories of excitation:
The first category is most widely employed for the excitation of ultrasonic Lamb waves in which we also can distinguish different excitation techniques as excitation by shearing perturbation created by a special Y-cut piezoelectric crystal, excitation by longitudinal normal perturbations created by usual X-cut piezoelectric element. These excitation techniques represent non-resonace methods, since they use broadband excitation and all possible modes for given frequency are excited at the same time. Lamb waves can also be generated in a given structure by resonance methods. One of the most well known is the coincidence technique of excitation. It is based on the conversion of longitudinal wave propagation in an angled wedge on the structure/plate in the contact mode or an ultrasonic beam at oblique incidence in the immersion mode into ultrasonic Lamb waves with sinusoidal distribution of perturbation in a plate (Figure 4b).
Figure 3: Wave Structure Diagrams
The coincidence principle requires an incidence angle (Figure 4a) for the excitation of a given phase velocity in the plate. This incidence angle is determined by using Snell's law and phase velocity from the dispersion diagrams (Figure 2a ).
where Vl is longitudinal wave speed in the wedge
This generation technique is controlled by the angle of incidence and the frequency of excitation; to excite different modes at a given point on the dispersion curves one needs to adjust the angle of incidence and the excitation frequency.
Figure 4: Schematic representation of angle wedge excitation
Experimental procedure: Experiments were made in a pitch-catch setup (Figure 6) using two variable angle broadband transducers, one as transmitter of the guided wave and the other as receiver. Thus, the inspected area with this setup is along a line between the two transducers. Good detection of disbonds was also achieved in pulse-echo with one transducer located on one side of the specimen, acting as both transmitter and receiver. Transducers were driven by a tone-burst pulser/receiver (Figure 6). This burst is initially formed of a continuous sine wave which is gated and subsequently amplified. The signal from the receiving transducer is transferred to the digital oscilloscope through the broadband receiver.
Figure 6: Schematic configuration of generalized tone-burst system
|Lap Splice joint inspection: Disbond assessments in a simulated lap splice joint structure was obtained using a pulse-echo setup with Lamb waves. The lap splice joint was simulated from two bonded 400x300x1.6 mm aluminum plates with disbonds introduced in the middle region of its overlapped part. The frequency used to generate the Lamb wave was optimized to maximize detectability and sensitivity of modes for disbonds-like defects. For this, out-of-plane particle displacements were maximized while in-plane displacements were minimized, and the ultrasonic power was concentrated in the middle of the inspected specimen.|| Figure 7: Results from Guided Lamb wave Scan with wedge excitation (42k)|
Lamb modes are dispersive waves and their velocities are function of the frequency-thickness product. Therefore, any thickness changes such as lack of adhesion between two layers will affect the propagating mode velocity, amplitude and its time-of-flight. An inspection test was performed in a pulse-echo setup with a 1 MHz broadband piezo-composite variable angled wedge transducer generating the So Lamb mode at 0.98 MHz with an incident angle of 30° . In Figure 7, Box 2 and Box 4 illustrate the waveform signals obtained from the results of Lamb wave scanning along the plate (Y-direction). The waveforms with high amplitude correspond to the reflection from the disbonded region where the transmitted energy does not leak into the other plate but hits the free edge of the plate and reflects back to the transducer in the receive mode. In the case of the second signal, the amplitude is lower because we have leakage of the transmitted energy into the bonded plate which is an indication of a good bond. Based on the principle of leaking or transfer of ultrasonic energy through bonded areas, a large reflected echo represents a disbonded region and a very small reflected echo repre- sents a good bond. Therefore, for an area where there are planted disbonds there would be less transfer of energy between the two plates and the transducer will receive signals of higher amplitudes reflected from the free edge. Figure 7 shows the ease of interpretation of the results using the imaging capability. Boxes 5 and 6 each represents a B-scan image which is function of transducer displacement (X- direction), in the B scan, time-of-flight (Y-direction in B scan) and signal amplitudes (Z- direction in the 3D projection in Box 6). They show signals acquired from Lamb wave scan along the plate in B-scan and 3-D images. In these pictures, signals with higher amplitudes easily identify the disbonded region and are represented by green and red color (or higher gray level). The sensitivity and efficiency of this inspection are demonstrated from the repeat- ability of Lamb wave C-scan in Box 1, where repeatedly three lines of scans were reproduced. Therefore, the scanning efficiency is high since a single pass is required and results can be presented in the form of an image to facilitate interpretation.
Tear strap inspection: In this experiment, we inspected a 285x255x1 mm aluminum plate on which a 200x50x1 mm aluminum strap was bonded with epoxy. The epoxy was uniformly spread between the first and second plate leaving 20x20 mm and 10x10 mm air gaps in two separate places between the plates to simulate disbonds. Measurements were first made in pitch-catch using two variable angle 1.5 MHz broadband transducers. The pitch-catch Lamb wave mode will travel from sender to receiver, producing relatively high amplitude RF signal when a disbond exists between the two bonded layers; otherwise the ultrasonic energy will leak into the tear strap if the bond is good, limiting the wave from being received by the re- ceiver. Relative amplitude changes which occur in the transmitted wave mode through bonded structures are an indication of the existence of disbond, corrosion or even a missing tear strap. Figure 8 shows the measured RF signals using a variable angle probe at 30° for the So mode at 1.48 MHz.
Figure 8 Transmission results with wedge excitation a) disbonded area b) bonded area
Results in Figure 8a were obtained with transducers positioned perpendicular to the defect area (area with bad bond). Results from Figure 8b are obtained with transducers perpendicu- lar to the area with good bond. A bad bond between the tear strap and the first layer which is the case in the first figure was identified, where good transmission of the generated mode from the sender to the receiver without any energy leakage in the tear strap was observed. On the other hand, results from Figure 8b demonstrate a good bond between the tear strap and the first layer since it is associated with a loss of the signal amplitude due to leakage of the transmitted ultrasonic energy into the tear strap.
|A second test was also performed on the tear strap specimen with the same setup. In this test, once again, a linear manual Lamb wave scan was performed by moving the transducer pair along the specimen in the Y-direction to compare signals obtained through the well bonded and disbonded areas. Experiments were carried out over the specimen (Figure 8) in a pitch-and-catch setup. Signals were acquired and stored for color imaging and analyses (Figure 9). In the second test, the ability of guided waves to detect and visualize disbonds lo- cated under the entire strap was investigated. Figure 9 (Box 6) clearly shows the disbonded regions where the amplitudes of the transmitted So mode are high. As mentioned, locating de- fects is accurate with conventional C-scan (bidirectional) technique but it requires covering the entire surface of the plate with the transducer, whereas the guided wave method can in- spect the entire plate with one unidirectional scan.|
Figure 9: Results from Guided Lamb wave Scan with wedge excitation (36k)
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