Guided Wave Testing of Water Loaded Structures
by Joseph
L. Rose*
This month's "NDT Solution" presents the solution for guided wave testing of water loaded structures. This is another example of taking the technology from the laboratory into industrial applications. The author also presents how this solution enabled the development of a wing ice detection system for aircraft.
G.P Singh
Associate Technical Editor
Introduction
How is guided wave testing conducted on a structure that is water loaded? One can guess that attenuation will occur in a plate or in a pipe that is water loaded. In general, there is leakage of energy into the fluid. If we consider how leakage might occur, we can imagine two kinds of displacement on the surface of a plate or pipe that contains water. In plane displacement on the surface of a plate or pipe will not leak into the water, since water cannot support shear wave propagation. There is no shear modulus. On the other hand, the out of plane displacement component applies a pressure component to the fluid that can easily propagate into the fluid as a compressional wave. As the wave propagates in the solid structure, we can easily imagine series of disturbances that propagate into the fluid, hence the term "leaky wave."
Wave Propagation
In Figure 1, note the series of spherical waves that propagate into the fluid. As the point source moves along the interface, consider Huygen's principle of spherical wave propagation from the point source for homogeneous isotropic media. As a result, spherical waves also propagate into the fluid. The tangent to the spherical waves is the leaky wave wavefront. This cannot happen for a shear loading of the fluid or the in plane displacement load. Now that we know what happens, the solution for guided wave testing of water loaded structures is simply to find a wave that has no out of plane component (or, hence, only an in plane component).
Pipes or tubes, therefore, can be tested even if external or internal water loading is present.
This can be accomplished by using a horizontal shear wave in a plate, which is basically equivalent to a torsional wave in a tubular structure. A lamb wave could also be used if we could find a point on the dispersion curve with a dominant in plane displacement component that has very little out of plane displacement. If we can find any of these two situations from an experimental testing point of view, we will indeed be able to propagate guided waves in a structure over a very long distance, with very little energy loss due to a leaky wave.
Figure 1 - Leaky wave propagation principle.
Lamb and Shear Horizontal Waves
Figure 2 shows the particle displacement vector for lamb and shear horizontal waves. Note that propagation characteristics of a shear horizontal wave in a plate are the same as torsional waves in a pipe.Figure 2 - Lamb versus shear horizontal wave displacement components in a plate. Wave vector k is in the direction of wave propagation with u and w displacement for the lamb wave case and only v for the shear horizontal case.
For a lamb wave, if we were to consider along the vertical axis of a phase velocity dispersion curve the actual dilatational wave velocity value (the fastest bulk wave velocity that could occur in a material) and sketch a horizontal line across the dispersion curve, the intersection of this horizontal line with all of the symmetric modes is at a point that has a totally in plane longitudinal displacement component (Pilarski et al., 1993). All other points on the curves have some out of plane component. As a result of using lamb waves in a structure that is water loaded, any one of these points on the dispersion curve could be selected to conduct the test. On the other hand, if we were to use horizontal shear or torsional modes the problem's solution is more straightforward, since only in plane displacement components exist at all points on the dispersion curve and all points would therefore work quite effectively. No energy leakage will take place into the fluid. Keep in mind, however, that a reflected wave from a three dimensional discontinuity could have associated with it a leaky wave because of the complex mode conversion with u, v, and w displacement components.
Water Loaded Structures
Pipes or tubes, therefore, can be tested even if external or internal water loading is present. Either lamb or torsional modes could be used. Consider two simple experiments on a 76 mm (3 in.) diameter schedule 40 steel pipe, with a small 30% deep saw cut notch. Nonaxisymmetric waves via partial loading (not encircling) were considered, but tests were conducted where a maximum value occurs at the discontinuity with respect to the circumferential profile around the pipe. Whether axisymmetric loading or nonaxisymmetric loading were used, the basic principle is the same. For these tests, however, nonaxisymmetric modes were used. To know more about nonaxisymmetric waves in pipe, see Li and Rose (2001) for details. For the 310 kHz lamb wave probe selected, see Figure 3. A 6 dB drop in amplitude occurs as a result of water loading. Figures are on a same scale basis. Frequency tuning could improve the result. Amplitude will in general, however, be a little smaller because of the source influence of the finite sized transducer used in the experiment. This leads to a phase velocity spectrum which excites more points on the phase velocity dispersion curve than just the intersection point of the dilatational wave velocity and the symmetric modes. See Rose (1999) for more details.Figure 3 - Lamb waves in a dry and water loaded pipe (a variable angle beam transducer was used for the test): (a) schematic; (b) dry pipe; (c) water loaded pipe.
On the other hand, for a torsional mode, virtually identical results are obtained for a dry and a water loaded pipe (Figure 4). By choosing parameters of the exciting source such as frequency, incident angle or circumferential angle, it is possible to detect discontinuities with limited access to the structural surface and cross sectional area even in a water loaded pipe.
Figure 4 - Torsional waves in a dry and water loaded pipe (a shear horizontal electromagnetic acoustic transducer was used for the test): (a) schematic; (b) dry pipe; (c) water loaded pipe.
Future Work
The idea presented here on water loading was also the basis of the development of a wing ice detection system for aircraft (Hongerholt et al., 2002). By controlling the mode and frequency of the guided waves in a structure via in plane or out of plane displacement, it becomes possible to determine water, glycol or ice presence on the wing of an aircraft. For example, guided waves with a dominant in plane displacement on the surface will leak into ice but not into water.
References
Hongerholt, D.D., G. Willms and J.L. Rose, "Summary of Results from an Ultrasonic In-Flight Wing Ice Detection System," Review of Progress in Quantitative Nondestructive Evaluation, Vol. 21A, D.O. Thompson and D.E. Chimenti, eds., Melville, New York, AIP, 2002, pp. 1023-1028.Li, J. and J.L. Rose, "Excitation and Propagation of Non-axisymmetric Guided Waves in a Hollow Cylinder," Journal of the Acoustical Society of America, Vol. 109, 2001, pp. 457-464.
Pilarski, A., J.J. Ditri and J.L. Rose, "Remarks on Symmetric Lamb Waves with Dominant Longitudinal Displacements," Journal of the Acoustical Society of America, Vol. 93, 1993, pp. 2228-2230.
Rose, J.L., Ultrasonic Waves in Solid Media, Cambridge, Cambridge University Press, 1999.
* Department of Engineering Science and Mechanics, Pennsylvania State University, 212 Earth and Engineering Science Building, University Park, PA 16802; (814) 863-8026; fax (814) 863-8164; e-mail <jlresm@engr.psu.edu>.
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