Lamb Wave Behavior in Bridge Girder Geometries

Transcription

1 Lamb Wave Behavior in Bridge Girder Geometries I. J. Oppenheim a*, D. W. Greve b, N. L. Tyson a a Dept. of Civil and Environmental Engineering, Carnegie Mellon University, Pittsburgh, PA b Dept. of Electrical and Computer Engineering, Carnegie Mellon University, Pittsburgh, PA ABSTRACT Lamb waves in plates and in cylindrical pipes have been the subject of extensive study, largely because they propagate great distances with little attenuation, and can therefore be used to detect flaws. In this paper we report finite element simulations and experimental studies of Lamb waves in steel bridge girder geometries. In our studies the Lamb waves are generated by PZT wafer-type transducers mounted on the girder web, driven by a windowed sinusoidal pulse; the pulse center frequency is chosen to yield a frequency-thickness product of roughly 1 MHz-mm, at which the group velocities of the S0 and A0 waves are well separated, and at which waves in higher modes are theoretically absent. Transient dynamic finite element simulations, both in 2D and in 3D, were performed using FEMLAB and ABAQUS. The simulations show that transmission at the web-flange joint creates guided waves in the flanges that travel at different velocities from the Lamb waves in the web, and that reflection at the web-flange joint creates a largely straight-crested wavefront for the Lamb waves in the web remote from the source. Simulation studies also illustrate the acoustic influence of plate girder transverse stiffeners, which is observed to be relatively small. A welded steel plate girder laboratory specimen was fabricated with proportions typical of highway bridge members, at approximately half-scale. The web height is 920 mm and thickness is 3.2 mm, for a representative height-thickness ratio of 288; the flange width is 100 mm and thickness is 6.4 mm, for a representative width-thickness ratio of 16. Small PZT transducers, roughly 6.4 x 6.4 x 0.6 mm, excited at less than 10 V, produce ample signals. We compare simulation results and experimental measurements for Lamb wave illumination of the plate girder segment. We also discuss the detection of cracks, simulated experimentally by saw cuts of varying dimensions in the laboratory girder specimen. Keywords: Finite element simulation, Lamb waves, plate girders, ultrasonics, wafer-type transducer. 1. INTRODUCTION In earlier work we conducted experimental and simulation studies of Lamb waves generated in thin elastic plates by piezoceramic wafer-type transducers [1, 2], expanding results reported by Giurgiutiu [3]. The experiments confirmed our expectations that Lamb waves can return reflections from cracks or other discontinuities, and we obtained simple guidelines for choosing the transducer dimensions and the forcing function for selective mode generation. Because plate girders are fabricated from thin plates, we expect Lamb waves to be useful for monitoring their structural condition. However, the joints and geometric complexity may make it difficult to interpret reflected waveforms. In this paper we combine finite element simulations with selected experiments to study aspects of wave propagation in these structures. Our simulations are performed with FEMLAB 2.3, FEMLAB 3.0, and ABAQUS-EXPLICIT in the time-stepping mode. The excitation is a 5-cycle pulse, a shaped sinusoid with center frequency f, of the form sin(2πft) sin( F t) = 0 2 π 10 ( ft) t < 5 / t 5 / f f. * Contact author: ijo@cmu.edu; ; Carnegie Mellon University, Department of Civil and Environmental Engineering, Pittsburgh, PA,

2 2. SIMULATION OF LAMB WAVE TRANSMISSION/REFLECTION AT A CRACK Reflections from flaws in a plate have been simulated by Rose et al. 4, by Lowe and Diligent 5, and others. We describe our plane strain simulation of Lamb waves, generated by a wafer-type transducer, interacting with a part-thickness slot to simulate a crack-like defect. The model was an aluminum plate with a thickness of 1.59 mm containing a rectangular slot 0.1 mm wide penetrating halfway through the thickness, and a wafer-type PZT transducer 6.4 mm long and 0.64 mm thick. Simulations were performed for a plate with a length of 0.6 m, symmetric about x = 0, excited by a pulsed voltage waveform with center frequency f = 400 khz. Figure 1. Particle velocity (y-direction) at bottom surface Figure 1 is a time-history plot of bottom surface particle velocity, in the y direction. In this analysis we choose to plot the y velocity because A0 and S0 modes both have significant displacement normal to the surface, and therefore both modes can be observed in one plot. At t = 25 μs we see both A0 and S0 modes to have been generated by the transducer. The f-d product for the center frequency of 400 khz is MHz-mm, at which the A0 mode is slower, has a shorter wavelength, and exhibits more dispersion than the S0 mode. The S0 mode begins to interact with the slot at t = 35 μs and the A0 mode begins to interact with the slot at t = 55 μs. Interaction of the S0 mode with the slot results in four distinct pulses: transmitted and reflected S0 modes, and transmitted and reflected A0 modes produced by mode conversion. The A0 mode also results in transmitted and reflected pulses, although mode conversion to S0 is not discernible in these simulation results. It is interesting to observe the mode conversion, reflection, and transmission behavior at the new boundary represented by the simulated flaw, all of which can be traced with clarity in Figure 1. However, our main motivation in structural

3 health monitoring is more typically the inverse problem, to deduce the presence of a flaw from a signal. The number of pulses resulting from interaction with simple defects represents a challenge for the practical application of Lamb waves for flaw detection, in that it would be impractical simply to look for a defect-related echo as done in traditional ultrasonic inspection. At this time, we envision the most practical approach to be a referenced method, comparing a signal to some base case or signature. In such cases it will also be useful to understand the interaction of Lamb waves with typical beam geometries, as introduced in the remainder of this paper. 3. SIMULATION OF LAMB WAVE TRANSMISSION/REFLECTION AT A T GEOMETRY We suggest that the girder web is a preferred location for an emitter, because our motivating concern is typically fatigue crack development within the web. We also suggest that emission of an S0 wave in the web is preferred, because waves in that mode are most easily interpreted and will be strongly indicative of a discontinuity at a crack. We conducted 2-D simulation studies of Lamb wave transmission/reflection at a T joint, revealing an interesting effect; in close examination of animation results, we often saw an incident S0 wave in the web transmit an A0 wave into the flange. Figure 2. S0 wave in web, approaching web-flange joint Figure 3. Reflected S0 wave in web, transmitted A0 wave in flange Simulations were performed for a flange-web thickness ratio between 1.0 and 3.0, and Figures 2 and 3 illustrate the results most clearly. They display contours of particle displacement (in the y-direction as oriented on the page) in a simulation study of Lamb wave transmission and reflection at a T-joint between a 12-mm web and a 15-mm flange, under excitation at a center frequency of 150 khz. Figure 2 shows the contours when the wave (in the web) approaches

4 the joint, and they are plainly characteristic of an S0 wave. Figure 3 shows the contours when that wave has just reflected from the joint. The reflected wave in the web remains in the S0 mode, and the intensity is slightly diminished as compared to Figure 2. The transmitted wave in the flange propagates transversely, and is plainly characteristic of an A0 (flexural) wave. In retrospect, this behavior is largely predictable. Particle displacements in the S0 web wave are largely in the y-direction, or vertical in Figures 2 and 3. Applying a time-varying displacement in that geometry as an excitation to the flange, it is readily apparent that the predominant response of the flange will be flexural. This effect typically holds, but is most clear at certain combinations of center frequency, web thickness, and flange thickness. In related simulation studies [6], for the same 2-D case of plane strain, we observed that relatively little energy (less than 10%) is reflected back into the web from an intact web flange-joint, especially for practical ratios of flange thickness to web thickness. 4. SIMULATION OF LAMB WAVE PROPAGATION IN A PLATE GIRDER Three-dimensional simulations for a rolled beam were conducted in FEMLAB [6], and here we describe simulations performed in ABAQUS-EXPLICIT for a model with the dimensions of a plate girder located on a major bridge in the Pittsburgh area, which is being instrumented for active Lamb wave sensing in a research project conducted by coworkers. The design dimensions, as originally expressed in inches, are a 72x7/16 web, 22x1 flanges, and 6x3/8 intermediate stiffeners (one side) spaced at 64 in; larger stiffeners, both sides, are employed at bracing and bearing locations. Figure 4 depicts the model used for the finite element analysis, with a wafer type transducer located on the web at a position 0.5 m below the flange. The transducer is at the origin, and the bottommost and leftmost boundaries are modeled with mechanical symmetry. (We note that the transducer is not at the mid-height of the web, so symmetry about the bottommost boundary is not perfect. However, in the analysis interval no reflections are returned from the bottom flange, and only negligible error is introduced by this modeling assumption.) Figure 4 also shows highlighted nodes where displacement time histories are obtained. Excitation at a center frequency of 100 khz was applied. Figure 4. Plate girder model showing web, flange, and intermediate stiffener; time histories of x-direction (surface) particle displacements obtained at highlighted nodes Figures 5 and 6 show the simulated particle displacements at nodes A and B, on the bottom boundary 0.35 and 0.65 m from the origin, bisected by the intermediate stiffener located 0.5 m from the origin. Noting that the center of the excitation waveform occurs at t = 25 μsec, the first and second arrivals in Figure 5 are reasonably attributed to the S0 and A0 waves after a travel distance of 0.35 m. Figure 5 shows three subsequent arrivals that correspond to reflections (in some instances with mode conversion) at the stiffener. Figure 6 then shows the arrival of S0 and A0 waves after a travel distance of 0.65 m, along with other arrivals attributed to a wave converted from S0 to A0 during transmission past the stiffener, and to waves reflected back into the web from the free edge of the stiffener.

5 Figures 7 and 8 depict wave formation in the plate girder geometry. Figure 7, showing stress contours, freezes the frame when the first major crest reaches the end of the web, 1.5 m longitudinally from the origin. The wave in the web is approaching a straight-crested geometry, but a longitudinal Lamb wave in the flange is much slower to develop. The corresponding animation shows the most intense activity in the flange to occur closest to the origin, and Figure 8 further illustrates the behavior. The plot shows the particle displacement at node C, a point on the flange surface 0.05 m from the centerline and 0.35 m longitudinally from the origin; it shows that the wave behavior first induced in the flange is a wave traveling away from the web, reflecting from the free edges, and then reflecting multiple times in the transverse direction. Geometric spreading occurs along every segment of wave travel; with a sufficient number of reflections, over a longer time than shown in Figures 7 and 8, the flange will act as a waveguide and a Lamb wave traveling longitudinally will become apparent. In other simulations [6] of a rolled beam, more compact as a cross-section than the plate girder, the development of the straight-crested Lamb wave in the web is strongly displayed, as is the development of the Lamb wave traveling longitudinally in the flange; in those simulations, owing to the difference in thickness between web and flange, the two Lamb wave speeds differ from one another. Figure 5. Particle displacement in web at node A Figure 6. Particle displacement in web at node B

6 Figure 7. Stresses in plate girder model, showing development of straight-crested wave moving longitudinally in web Figure 8. Particle displacement in flange at node C, showing reflections of wave moving transversely 5. EXPERIMENTAL STUDY OF WAVE PROPAGATION We conducted a preliminary experimental study using a laboratory specimen of a steel plate girder, scaled to realistic cross-sectional proportions. The web is 91 cm deep and 3.2 mm thick, for a height-thickness ratio of 284, and the flange is 10 cm wide and 6.4 mm thick, for a width-thickness ratio of 16; the specimen is 61 cm long, with no transverse stiffeners. A PZT transducer (6 mm diameter) is located on the web 15 cm from a free edge and 30 cm from the upper flange, with a transmit/receive switch for operation in pulse-echo mode. Figure 9 shows the reflected signals at three different center frequencies, corresponding to f-d products between 0.88 and 1.08 MHz-mm. The first reflection (after the input circuit recovers from the exciting signal) is a strong reflection of the S0 mode from the nearest free surface.

7 This is followed by the A0 mode reflection from that surface, and then a weak reflection from the S0 mode reflected from the flange; a weak reflection from the flange is consistent with the simulations presented above. The remaining reflections that have significant amplitude can be assigned to reflections from the more distant free edge and flange. 61 cm 30 cm 91 cm 15 cm Figure 9. Measured reflections, at three center frequencies, for model plate girder 61 cm 91 cm 30 cm 15 cm Figure 10. Measured reflections, comparing absence and presence of weld discontinuity Figure 10 shows results from a second series of experiments, conducted at a center frequency of 379 khz, in which the PZT wafer-type transducer was located on the web 15 cm from the web-flange joint and 30 cm from the nearest free edge, permitting a relatively clear interpretation of reflections from that joint. A flaw was introduced by a sawcut, 3 cm in length, located in the web along the web-flange joint. Figure 10 shows the measured reflections in the unflawed and flawed cases. The first arrival, at approximately 65 μsec, corresponds to the S0 wave reflecting from the web-flange joint; as expected, in the flawed state the reflection is several times greater in amplitude than observed in the unflawed state. 6. CONCLUSIONS Simulation studies in 2D and in 3D show reflection and transmission of Lamb waves between web, flange, and stiffeners in a typical steel plate girder geometry. With Lamb waves generated by a wafer-type transducer mounted on the web,

8 detectable reflections are observed at intact joints, but the majority of the energy is transmitted, especially at the webflange joint where the flange is invariably thicker than the web. These results demonstrate that Lamb waves can illuminate a relatively large girder segment. However, the many detectable reflections, particularly in complex geometries, motivate the development of improved techniques to distinguish flaw reflections in the damaged state from baseline reflections in the undamaged state. Pulse-echo experiments have been performed, using wafer-type transducers mounted on the web, that extend Lamb wave studies from the two-dimensional geometry of flat plates to the three-dimensional geometry of plate girders. The experiments indicate that reflections from the web-flange joints are relatively weak, corroborating the observations made in the simulation studies. The experiments also show that a discontinuity in a web-flange weld, oriented normal to the direction of the Lamb waves, produces strong reflections. ACKNOWLEDGEMENTS The authors wish to acknowledge support from the National Science Foundation under grant CMS Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation. REFERENCES 1. Nieuwenhuis, J. H., Neumann, J., Greve, D. W., and Oppenheim, I. J., Generation and detection of guided waves using PZT wafer transducers, IEEE Trans. Ultrasonics, Ferroelec. and Freq. Ctl., Vol. 52(11), , Greve, D., Neumann, J., Nieuwenhuis, J., Oppenheim, I., and Tyson, N., Use of Lamb Waves to Monitor Plates: Experiments and Simulations, SPIE Smart Structures/NDE Joint Conference, Paper , San Diego, Giurgiutiu, V., Lamb Wave Generation with Piezoelectric Wafer Active Sensors for Structural Health Monitoring, SPIE Smart Structures Conference, San Diego, Cho, Y., Hongerholt, D.D., and Rose, J.L., Lamb wave scattering analysis for reflector characterization, IEEE Trans. Ultrasonics, Ferroelectrics, and Frequency Control 44, 46 (1997). 5. Lowe, M. J. S., and Diligent, O., Low-frequency reflection characteristics of the S0 Lamb wave from a rectangular notch in a plate, J. Acoust. Soc. Am. 111 (1), Pt. 1, Jan Greve, D., Oppenheim, I., and Tyson, N., Interaction of defects with Lamb waves in complex geometries, IEEE Ultrasonics Conference. Rotterdam, October, 2005.