Table of Contents ECNDT '98
Session: Steel Industry
Defect Detection with Rayleigh and Lamb Waves Generated by a Self-Focusing Phased ArrayW.A.K. Deutsch, Karl Deutsch, Prüf- und Meßgerätebau, Wuppertal, Germany
A. Cheng, J.D. Achenbach
Center for Quality Engineering and Failure Prevention
Northwestern University, Evanston, IL 60208-3020, USA
Corresponding Author Contact:
Email: firstname.lastname@example.org, URL: http://www.karldeutsch.de
|TABLE OF CONTENTS|
The self-focusing of Rayleigh waves was also investigated theoretically [4,5]. Starting from the general expressions of surface wave motion  in a linearly-elastic half space, a simple expression for the sound field generated by a single element of the array is developed. It has been shown by the authors [4,5] that this expression satisfies the equations of motion in an approximate sense in the far field of the array element. The sound field of the entire array is obtained by superposition. The model for both a single element and the simulated displacement of the entire array was compared to experimental results obtained with a laser interferometer . Good agreement of model and experiment was observed.
Fig. 1. Steps of the self-focusing procedure, a) firing center element, b) receiving with all elements, c) determination of time-of-flight differences, d) transmission focusing, e) reception focusing, and f) superposition gives focused signal.
The time shifts determined by the cross-correlation are the time delays for reception. The element which received the signal last (i.e. has the longest path) has the biggest time delay. In transmission focusing, the waves sent out by all elements arrive at the defect at the same time (Fig. 1d). The excitation times for transmission focusing are obtained by reversing the receiving time delays. The element with the longest path is fired first. Transmission focusing ensures that the sound energy at the defect location is much larger compared to a conventional transducer with the same aperture. After scattering of the focused wave by the defect (Fig. 1e), reception focusing uses the previously determined receiving time delays to align the signals received by all elements. After the alignment, the positive and negative half-waves of the ultrasonic signals match (Fig. 1f). A superposition of all shifted signals then leads to constructive interference and produces the focused signal.
Fig. 2. Self-Focusing System.
The linear transducer array consists of a single slice of piezoelectric material which was cut into elements after being glued to the backing material. This ensures perfect alignment of the individual elements. The thickness of the slice determines the center frequency which is 5 MHz. The size of each element is 3.5 by 8.3 mm.
The transducer array is coupled to the specimen through an acrylic wedge. Custom-made wedges are used for the excitation of Rayleigh and Lamb waves. The wedge angle has to be chosen so that the refraction angle of the desired wave type is 90°.
The position of the transducer has to be maintained during an experiment. Also, bending of the thin sheets in the case of Lamb wave testing has to be avoided. A wooden base supports the specimen and does not affect the propagation of the waves in the specimen. A fixture is used to mount the array in the desired position on top of the specimen.
The measurements are performed in the pulse-echo mode, and the ultrasonic reflections are collected with the transducer array. The receiver units (Panametrics 5055PR) amplify the signals by 40 dB. The data acquisition is done with a digital oscilloscope (Tektronix TLS216) than can acquire the signals of all eight channels at a time. The data is transferred via a GPIB interface to the PC.
Fig. 3 shows the obtained signals for the smaller hole which was located 12.5 cm away from the array with a steering angle of 5°. Initially, all elements which were fired at the same time, i.e. unfocused transmission (Fig. 3a). No receiving time delays were specified to shift the signals (Fig. 3b), i.e. unfocused reception. The superposition of the signals (Fig. 3c) shows no clear defect reflection. After applying the self-focusing procedure, the array automatically focuses on the defect (Fig. 3d-f). If the elements are fired with the appropriate transmitting time delays, all eight generated waves arrive at the defect at the same time. Note that the peak-to-peak amplitude for each channel increases significantly and that the shape of the waveform improves. This focused wave is scattered by the defect, and the signals are collected by all elements (Fig. 3d). The receiving time delays are determined with the cross-correlation and are used to shift the signals in time (Fig. 3e). The superposition of the signals in Fig. 3e is the focused signal (Fig. 3f). More experiments on self-focusing for Rayleigh waves in the case of multiple reflectors in the steering range and self-focusing of Lamb waves are discussed in .
Fig. 3. Self-focusing of Rayleigh surface waves for off-axis defect, a) unfocused transmission, b) unfocused reception, c) superposition of unfocused signals, d) transmission focusing, e) reception focusing, and f) focused signal.
Equation 1 satisfies the equations of motion in an approximate sense for the far field of a single element [4,5]. The polar coordinates r and ? represent the location on the surface of the half-space, and C is a constant which is determined by an experimental calibration. This surface wave (Eq. 1) travels with the same wave speed cR as a plane surface wave . The function f represents the shape of the propagating wave pulse. Eq. 1 implies that the amplitude decays with distance from the source as r -1/2, and that the angular dependence is of Gaussian shape where in Eq. 1 is the width of the Gaussian.
Equation 1 has been experimentally verified by interferometric measurements  of the normal surface displacement (Fig. 4a). The measurement locations (Fig. 4b) were chosen in order to prove that the surface motion follows Eq. 1. Model and experiment show good agreement for the radial dependence (Fig. 4c) and for the angular dependence (Fig. 4d).
|Fig. 4. Experimental verification of the model for a single transducer element, a) setup, b) measurement locations, c) result along the center axis, and d) result for varied angle.|
where n represents the element number. Each element is located at a different position Pos(n), and is fired at a different time Tn. The time delays are the delays for transmission focusing and ensure that the maximum amplitude of each element arrives at the focal point at the same time. The self-focusing procedure is based on ultrasonic reflections from a defect. For the simulation an arbitrary focal point has to be chosen.
Snapshot of the simulated surface displacement for on-axis focusing around the focal point.
An algorithm to represent the surface wave motion produced by the array has been implemented. A measured surface wave pulse f(t-r/cR) has been used for the simulation. The spacing of the array elements in the simulation matches the experimental setup. Fig. 5 shows a snapshot of the surface displacement around the focal point (x1 = 20 mm, x2 = 0 mm). If the observation time is larger than the largest transmitting time delay, each element contributes to the overall field. The observation time in Fig. 5 coincides with the time where the maximum amplitudes of all elements arrive at the focal spot. Large amplitudes at the focal point are observed.
Fig. 6. Simulated surface displacement, a) [zoom] sound field of array exhibits a main lobe and side lobes, b) cut across the center axis, c) cut across the focal point (simulation vs. experiment).
An efficient model for the representation of the surface wave motion generated by a linear array of surface wave transducers has been developed. The model describes the surface motion caused by a single element of the array where the radial decay follows r -1/2, and the behavior across the beam is approximated by a Gaussian distribution. It is shown that the model is in accordance with the equations of motion in an asymptotic sense [4,5]. Then, the motion of the entire array is computed by means of superposition. The model was experimentally verified by measuring the normal surface displacement for both the displacement produced by a single array element and by the focused array. For this purpose a heterodyne laser interferometer was used. Good agreement of model and experimental results has been obtained.
This work was carried out on projects funded by the Air Force Office of Scientific Research (Contract F 49620-93-1-0257) and the Federal Aviation Administration (95G32).