Home Search Collections Journals About Contact us My IOPscience Fatigue crack detection in metallic structures with Lamb waves and 3D laser vibrometry This article has been downloaded from IOPscience. Please scroll down to see the full text article. 2007 Meas. Sci. Technol. 18 727 (http://iopscience.iop.org/0957-0233/18/3/024) View the table of contents for this issue, or go to the journal homepage for more Download details: IP Address: 147.26.11.80 The article was downloaded on 12/05/2013 at 13:12 Please note that terms and conditions apply. INSTITUTE OF PHYSICS PUBLISHING MEASUREMENT SCIENCE AND TECHNOLOGY doi:10.1088/0957-0233/18/3/024 Meas. Sci. Technol. 18 (2007) 727–739 Fatigue crack detection in metallic structures with Lamb waves and 3D laser vibrometry W J Staszewski1, B C Lee1 and R Traynor2 1 Dynamics Research Group, Department of Mechanical Engineering, University of Sheffield, Mappin Street, Sheffield S1 3JD, UK 2 Lambda Photometrics Ltd, Lambda House, Batford Mill, Harpenden, Herts AL5 5BZ, UK E-mail: w.j.staszewski@sheffield.ac.uk Received 30 October 2006, in final form 13 December 2006 Published 24 January 2007 Online at stacks.iop.org/MST/18/727 Abstract The paper presents the application of ultrasonic guided waves for fatigue crack detection in metallic structures. The study involves a simple fatigue test performed to introduce a crack into an aluminium plate. Lamb waves generated by a low-profile, surface-bonded piezoceramic transducer are sensed using a tri-axis, multi-position scanning laser vibrometer. The results demonstrate the potential of laser vibrometry for simple, rapid and robust detection of fatigue cracks in metallic structures. The method could be used in quality inspection and in-service maintenance of metallic structures in aerospace, civil and mechanical engineering industries. Keywords: fatigue crack, crack detection, non-destructive testing, Lamb waves, 3D laser vibrometer (Some figures in this article are in colour only in the electronic version) 1. Introduction Structural health monitoring has become one of the major research activities in maintenance of aerospace, civil and mechanical infrastructure. Over recent years, a number of new technologies have evolved with the potential for automatic damage detection. Lamb wave inspection is the most widely used damage detection technique based on guided ultrasonic waves, i.e. ultrasonic wave packets propagating in bounded media. A number of different approaches have been developed over the last 20 years, as reported in the extensive literature; a summary of various aspects related to monitoring strategy, transducers used for damage detection, modelling, signal processing techniques and application examples is given in [1]. Although Lamb waves have demonstrated great potential for structural damage detection, to date, the practical commercial exploitation of ultrasonic guided waves has been very limited. This is related to three major drawbacks associated with current Lamb-wave-based damage detection techniques. Firstly, Lamb-wave-based monitoring strategies, often associated with complex data interpretation, are not 0957-0233/07/030727+13$30.00 © 2007 IOP Publishing Ltd appropriate for point-by-point field measurements taken by modestly qualified NDT technicians. Even a single Lamb wave mode used for monitoring may generate a variety of other modes due to interactions with structural boundaries such as stiffeners, joints or rivets, leading to complex response signals which are difficult to interpret. The subtleties of guided waves and the exceedingly complicated physics may be appreciated by experts in the field, but not necessarily by technical maintenance staff. Secondly, current signal processing and interpretation techniques used for damage detection utilize signal parameters requiring baseline measurements, i.e. data representing a ‘no damage’ condition. These parameters can change due to temperature or bad coupling between the transducer and the structure. Any developments that can avoid baseline measurements are thus very attractive for real engineering applications. Thirdly, a significant number of actuator/sensor transducers are required for monitoring of large structures. This is often not possible or acceptable, no matter how cheap the transducers are. From the logistic point of view, it is Printed in the UK 727 W J Staszewski et al not practical for a structure to have thousands of bonded or embedded transducers. A portable scanner (i.e. a pair of transducers) that can crawl on the surface of the monitored structure and conduct scanning is one possible solution. However, the difficulty is the need for liquid couplant. Dry coupling methods using non-contact electromagnetic acoustic transducers [2] and air-coupled transducers [3] can be used but these transducers have very low sensitivity due to large acoustic impedance mismatch between air and solid materials and the high attenuation of ultrasound in air at frequencies above 500 kHz. Non-contact approaches also include optical/laser techniques [4–8]. Laser-based techniques usually involve high-energy lasers which have safety and deployment implications. Applications of laser generation and sensing of Lamb waves for structural health monitoring are not new and include research work on damage detection in metallic [9, 10] and composite [11–13] structures. Laser-based Lamb wave sensing has found relatively less attention in practical applications than laser-induced Lamb wave generation due to perceptions of low sensitivity, high noise and high costs. Although area or multi-locational measurements are possible with electronic speckle interferometry, adaptive optical interferometry, shearography and laser vibrometers (e.g., [14–17]), the majority of recent applications involve single-point measurements. Scanning multi-point laser vibrometers are designed and widely used for vibration measurements, modal analysis and vibration-based damage detection in many areas of engineering applications, predominantly in the frequency domain. Examples in this area include [18–20]. Applications of Lamb wave sensing for structural health monitoring have been very limited and include damage detection in metallic [21–25] and composite [26] structures. These studies were based only on laser out-of-plane measurements of antisymmetric Lamb wave modes. Three-dimensional (3D) scanning laser vibrometers provide combined out-of-plane and in-plane measurements. A number of 3D configurations have been reported, implemented commercially and used for elastic wave propagation measurements (e.g., [27, 28]). However, 3D laser vibrometers have not been applied so far for Lamb wave sensing and Lamb-wave-based damage detection according to the best of the authors’ knowledge. The aim of the paper is to demonstrate the application of a 3D scanning laser vibrometer measuring Lamb waves for fatigue crack detection. The objective is to explore both the out-of-plane and in-plane scanning capability of 3D lasers for Lamb wave sensing and damage detection in metallic structures. The paper consists of four major parts. Section 2 describes the Lamb wave field used in the experimental work. For the sake of completeness, this includes a brief theoretical introduction to Lamb waves. The experimental work performed to introduce a fatigue crack into an aluminium plate is described in section 3. Section 4 gives details related to Lamb wave generation and sensing. Crack detection based on Lamb wave data is described in section 5. Finally, the paper is concluded in section 6. 728 Figure 1. Principles of various guided wave polarization and propagating directions. 2. Lamb wave propagation for damage detection Guided waves propagate as a result of interactions with boundaries. Lamb waves occur for traction-free forces on both surfaces of the plate. Lamb wave inspection has been proven to have great potential for damage detection in metallic structures. For the sake of completeness, this section briefly describes the theoretical background of Lamb waves. The focus is on theoretical definitions related to Lamb waves and practical aspects associated with damage detection. For more details, readers are referred to [29–32]. The short introduction to Lamb waves is followed by a simple experimental test leading to frequency selection of propagating waves used in the current work. 2.1. Background The unbounded medium supports longitudinal (P) and shear (S) waves, as illustrated in figure 1 where x and y directions indicate the in-plane vibration and z direction the out-of-plane vibration of the medium. Shear waves propagating in the plate can be polarized in a direction parallel to the plate surface leading to a series of SH modes. Perpendicular polarization to the plate surface results in a series of SV modes. These two series of wave modes exist in connection with the P wave. The combined P + SV waves are known as Lamb waves. Lamb waves are highly dispersive, i.e. their velocities of propagation depend on frequencies. A brief theoretical introduction to Lamb waves is given here following the developments from [31]. Lamb wave equations can be derived from the elastodynamic wave equation for the particle displacement given as ρ üi = (sij kl uk,l ),i (1) where ρ is the density, u is the displacement, s is the stiffness tensor and the standard tensor index convention is used. The method of potential transforms displacements in equation (1) into field variables φ and ψ using the Helmholtz decomposition. This results in uncoupled equations 1 ∂ 2ψ ∂ 2ψ ∂ 2ψ + = 2 2 2 ∂x1 ∂x3 cL ∂t 2 (2) ∂ 2ϕ ∂ 2ϕ 1 ∂ 2ϕ + 2 = 2 2 2 ∂x1 ∂x3 cT ∂t (3) describing propagation of longitudinal waves and shear waves, respectively. The constant CL indicates the velocity of longitudinal waves and CT is the velocity of shear waves in Fatigue crack detection in metallic structures with Lamb waves and 3D laser vibrometry equations (2) and (3). Physical displacements of the plate can be expressed in terms of the field variables used as ∂ϕ ∂ψ ∂ϕ ∂ψ + , u2 = 0, u3 = − . (4) u1 = ∂x1 ∂x3 ∂x3 ∂x1 Since the field variables involve sine and cosine functions which are odd and even functions, the above displacements are often split into symmetric and antisymmetric modes. The displacement for the symmetric modes can be given as u1 = ikC2 cos(px3 ) + qD1 cos(qx3 ) u3 = −pC2 sin(px3 ) − ikD1 sin(qx3 ) (5) (6) whereas the solution for the antisymmetric modes is u1 = ikC1 cos(px3 ) − qD2 sin(qx3 ) u3 = pC2 cos(px3 ) − ikD2 cos(qx3 ). (7) (8) The variables p and q in equations (5)–(8) are given as p 2 = (ω/CL )2 − k 2 , q 2 = (ω/CT )2 − k 2 (9) where k is the wave number and ω = 2πf is the circular frequency. The constants C1, C2, D1 and D2 in equations (5)– (8) can be obtained from the traction-free boundary conditions for the plane strain. Finally, the entire analysis leads to Rayleigh–Lamb wave frequency relations 4k 2 pq tan(qh) = 2 tan(ph) (q − k 2 )2 for symmetric modes and (10) (q 2 − k 2 )2 tan(qh) = (11) tan(ph) 4k 2 pq for antisymmetric modes, where h is the half of the plate thickness. The Rayleigh–Lamb equations can be solved numerically for a given material leading to the so-called dispersion characteristics, i.e. the phase velocity cp = ω/k or group velocity cg = dω/dk represented as functions of the f –d (frequency–thickness) product. In other words, for a given thickness of the plate these equations predict velocities of propagating Lamb wave modes. The dispersion characteristics result in a number of symmetric Si and antisymmetric Ai (i = 0, 1, 2, . . .) Lamb wave propagation modes. The fundamental S0 and A0 modes are the most widely used Lamb wave modes for damage detection. Lamb wave mode selection is important for damage detection. Both fundamental modes are very good in terms of the spatial resolution, i.e. they offer good compromise between the bandwidth of the excitation signal and its duration, as explained in [33]. The S0 mode is dominated by the longitudinal vibration component whereas the A0 mode is dominated by the shear component. The S0 mode is faster and has much lower attenuation than the A0 mode. It is also, less dispersive at lower frequencies if compared with the A0 mode. However, the A0 mode is considered to be more sensitive to damage. Nevertheless, a number of studies, summarized in [1], demonstrate that the S0 mode works better for damage detection than the A0 mode. It is important to mention that the wavelength, which is directly related to the excitation frequency, affects the sensitivity of damage detection; the shorter the wavelength, the larger the sensitivity to small Figure 2. Lamb wave dispersion characteristic for an aluminium plate. The curve is zoomed on the fundamental modes. damage severities. Also, the energy distribution for various Lamb wave modes is different through the thickness of the plate. This is due to the fact that in-plane and out-of-plane displacements vary across the thickness, as illustrated in [34]. Lower modes have more uniform energy distribution than higher modes and the S0 mode has a more uniform distribution than the A0 mode, which exhibits higher levels of energy at surfaces. 2.2. Wave propagation frequency—experimental analysis The complexity of Lamb wave propagation, briefly described in section 2.1, significantly affects damage detection procedures used in practice. The work presented in the paper involved the fundamental Lamb wave modes. In what follows, the mode selection procedure is briefly described. Firstly, the Rayleigh–Lamb dispersion characteristics were calculated numerically using equations (11) and (12) and material properties for the NS4 aluminium (Young’s modulus E = 71 GPa, density ρ = 2.711 g cm−3, Poisson’s ratio υ = 0.338, Lamé constants µ = 26.5 GPa and λ = 56.2 GPa). The dispersion characteristic for the 6 MHz mm range is given in figure 2. Then, a simple experiment involving a rectangular 400 × 150 mm2 aluminium plate of 2 mm thickness was performed. Two piezoceramic transducers were surface-bonded in the middle of the longer edges of the plate. One transducer was used as an actuator, whereas the second transducer acted as a sensor. A five-cycle sine tone burst was used as an excitation signal. This signal was modulated with a Hanning window. The peak-to-peak amplitude excitation signal was equal to 5 V. The excitation signal was generated using the TTi-TGA 1230 arbitrary waveform generator. The Lamb wave responses were R LT224 digital captured using the LeCroyTM WaveRunner
oscilloscope. In order to find the Lamb wave modes, the frequency range was altered from 30 to 500 kHz. This guaranteed that only fundamental Lamb wave modes would propagate in the plate used (see figure 2). When Lamb wave responses were gathered from the sensor, the group velocities were calculated and compared with the values in figure 2 in order to identify both fundamental modes. Maximum amplitudes were recorded for both modes over the frequency range mentioned before, resulting in the characteristics given in figure 3. This shows that the maximum amplitude was achieved at 115 kHz and 325 kHz for the A0 and S0 modes, respectively. The 325 kHz frequency was selected for the S0 729 W J Staszewski et al 4.1. Lamb wave generation Figure 3. Amplitude of the fundamental Lamb wave modes versus excitation frequency—experimental analysis. fundamental Lamb wave mode. The frequency for the A0 mode was selected as 75 kHz to keep approximately the same amplitude level for both fundamental modes (see figure 3). The 75 and 325 kHz frequencies led to single A0 and S0 wave mode propagation, respectively, i.e. only the A0 mode was present at 75 kHz whereas the amplitude of the S0 mode was negligible and only the S0 mode was present at 325 kHz whereas the amplitude of the A0 mode was negligible. Additionally, the 190 kHz frequency was selected since it led to two fundamental modes propagating together with approximately the same peak-to-peak amplitudes (see figure 3). In summary, the 75, 325 and 190 kHz frequencies were selected for Lamb wave generation in further experimental work. 3. Fatigue crack in metallic specimen—experimental work A simple fatigue test was performed to introduce a crack in an aluminium specimen identical to the plate used in the Lamb wave propagation experimental study in section 2.2. Eight holes of 15 mm diameter were drilled at the top and bottom of the plate to facilitate clamping in the fatigue machine. A hole of 0.5 mm diameter was drilled in the centre of the specimen and used to initiate a spark-eroded notch of 2 mm length. The plate was instrumented with five surface-bonded SMART R Layer
piezoceramic transducers of 5 mm diameter and 0.2 mm thickness, as shown in figures 4(a) and (b). The transducer A was used for Lamb wave generation in the current paper. The aluminium plate was clamped in a 240 kN Schenck fatigue-testing machine controlled via a Roell Amsler K7500 servo controller. The plate was fatigued up to 305 000 cycles using the tensile static loading of 20 kN and the dynamic cyclic loading of ±9 kN. This led to the 41.05 mm fatigue crack, illustrated in figure 4(c). The large severity of damage was selected intentionally for the explorative work with a 3D laser vibrometer. 4. Lamb waves sensing with 3D laser vibrometry This section describes Lamb wave generation and sensing procedures used for crack detection. The former was achieved using piezoceramic excitation whereas the latter was performed using a 3D scanning laser vibrometer. 730 The piezoceramic transducer A (see figures 4(a) and (b)) was used for Lamb wave generation. The actuator was excited by a series of burst signals comprising five cycles of sine wave with the Hanning window envelope. The peak-to-peak amplitude of excitation was equal to 20 V. The study involved three different frequencies of excitation, i.e. 75, 325 and 190 kHz, as selected experimentally and explained in section 2.2. The excitation signals were generated using the TTi-TGA-1230, arbitrary waveform generator. The excitation burst signals were triggered every 50 ms to minimize the overlapping of the oncoming and reflected waves. 4.2. Lamb wave sensing using 3D laser scanning mode Lamb wave responses were sensed using a 3D laser vibrometer. These vibrometers measure surface motion utilizing the Doppler shift phenomenon to obtain the velocity of the surface vibration. For a single measuring point, 3D components of out-of-plane and in-plane vibration can be obtained using three spatially independent laser heads focusing at this point. Sensor heads generate three laser beams which acquire the v1 , v2 and v3 velocity components along their lines of incidence (see figure 5). The measuring point is located in the intersection point of the laser beams which is the origin of the orthogonal coordinate system (X, Y, Z). All velocity amplitudes are measured with respect to this system. Alignment of the 3D scanning laser vibrometer comprised positioning the three sensor heads in a triangular configuration in front of the plate. Using a target volume encompassing the plate, with dimensions in both the X and Y axes, plus depth (Z axis), four to seven arbitrary positions within this volume were defined and measured for distance using the sensor head fitted with a rangefinding geometry scan unit. The other two heads were aligned to these points and angle and range data for the points and the positional relationship for all three sensor heads was calculated within the scanning vibrometer software. When completed, any locations visible to all three lasers within the volume could be accessed and measured for X, Y and Z motion. More details related to the alignment procedure can be found in [35]. A higher frequency variant of the standard 3D Polytec PSV-400-3D laser vibrometer was used in the current damage detection work for Lamb wave sensing. The experimental set-up used in this work is shown schematically in figure 5. The data were acquired using the near dc to 2 MHz frequency capability of the laser vibrometer. This vibrometer used consists of three independent PSV-I-400 LR (OFV-505) optical scanning heads (one fitted with a location/rangefinding Geometry Module), OFV-5000 controller, PSV-E-400-3D junction box and a data management computer system. The scanning heads were used simultaneously. The OFV-5000 provides power for the scanning heads, controls the rotation of the mirrors in the OFV-505 heads, scans the laser beams, and also processes the heterodyne interferometry signal from the OFV-505 sensors, outputting the signals as simple analogue time history voltage values. The PSV software in the data management computer system controls the measuring converters, laser focus/position, vibrometer electronics and the live video system. A velocity range of 10 mm (s V)−1 Fatigue crack detection in metallic structures with Lamb waves and 3D laser vibrometry (b) (a) (c) Figure 4. Aluminium specimen used in the experimental work: (a) schematic diagram, (b) photograph and (c) detailed view of the crack. was chosen to give adequate velocity (at an output voltage of approximately 5 V, equivalent to about 5 m s−1) with good resolution. The National Instruments PCI-6110E A/D card was used for data acquisition in the time domain. Signal lengths were equal to 2048 data samples. The maximum 2.56 MHz data acquisition frequency bandwidth of the laser system was used. The data were low-pass filtered to a frequency of 1.5 MHz. The data acquisition utilized 150 averages in order to improve the signal-to-noise ratio. The scanning laser vibrometer was aligned following the procedure described in section 4.2 and used to measure 3D vibration associated with Lamb waves propagating in the aluminium specimen. The calculations required to separate in-plane and out-of-plane vector components were performed automatically by the PSV system. Figure 6 gives examples of laser-sensed Lamb waves in X (horizontal in-plane), Y (vertical in-plane) and Z (out-of-plane) directions for the 75, 325 and 190 kHz. The 75 kHz excitation led to the A0 Lamb wave mode propagating in the plate. This mode is dominated by the out-of-plane component in figure 6(a) (right column). The first wave package in the response signal is the incident wave whereas the remaining wave packages are reflections from the plate boundaries and the crack. The amplitude of the in-plane components of the 75 kHz Lamb wave signal in figure 6(a) (left and middle columns) is relatively small when compared with the out-of-plane component, as expected. The 325 kHz excitation led to the S0 Lamb wave mode propagating in the plate. Again, as expected, this mode is dominated by the in-plane X-direction component in figure 6(b) (left column). Figure 6(c) shows the 190 kHz Lamb wave responses. Two dominant wave packages can be observed in the in-plane X-direction (left column) and the out-of-plane (right column) components. These two components are contributing to the S0 and A0 Lamb wave modes propagating in the plate. 5. Crack detection results The cracked aluminium plate was scanned using the 3D laser vibrometer. The scanned area was a 60 × 110 mm2 rectangle around the impact position, as indicated in figure 7. The grid of 420 points where measurements were taken is shown in figure 7; this is equivalent to 420 contact transducer measurements in classical Lamb wave inspection. This section describes the results obtained from the amplitude analysis. 731 W J Staszewski et al Arbitrary waveform generator Monitored specimen Data management system Piezoceramic actuator Fatigue crack Laser sensor heads Orthogonal coordinate system vx v1 v2 vY v3 vZ Figure 5. Experimental set-up for damage detection and measurement geometry of the 3D laser system. X direction −0.2 −0.6 0.3 0 −1 −2 0.15 0.2 −1 0.2 Time [ms] 0.3 0.4 0.2 Time [ms] 0.3 −0.2 −0.6 −1 0 0.4 Y direction 1 0 −1 −2 0.05 0.1 Time [ms] 0.15 0.2 0 −1 0.2 Time [ms] 0.3 0.4 0.3 0.4 Z direction 1 0 −1 −2 0 0.05 0.1 Time [ms] 0.15 0.2 0.3 0.4 Z direction 2 1 0.2 Time [ms] 2 −3 Y direction 0.1 0.1 3 2 −2 0 0.2 Amplitude [mm/s] 0 0.1 0.1 2 1 −2 0 −0.6 −3 0 X direction 2 −0.2 0.6 Amplitude [mm/s] 1 0.1 Time [ms] 0.2 3 2 0.05 0.6 −1 0 0.4 Amplitude [mm/s] Amplitude [mm/s] 0.2 Time [ms] X direction 3 −3 0 (c) 0.1 Z direction 1 Amplitude [mm/s] 0.2 (b) Amplitude [mm/s] Amplitude [mm/s] 0.6 −1 0 Y direction 1 Amplitude [mm/s] Amplitude [mm/s] (a) 1 1 0 −1 −2 0 0.1 0.2 Time [ms] Figure 6. Examples of Lamb wave responses acquired with the 3D laser vibrometer. Excitation frequency equal to: (a) 75 kHz, (b) 325 kHz and (c) 190 kHz. 5.1. Peak-to-peak amplitude analysis The first step involved the peak-to-peak amplitude analysis for all scanned grid points and different wave propagation 732 moments in time. This study allows for simultaneous wave propagation analysis in the spatial (for all scanned grid points) and time (for selected moments in time) domains. The results are presented in figures 8–12. Fatigue crack detection in metallic structures with Lamb waves and 3D laser vibrometry Piezoceramic actuator (a) 41.8 µs 48.8 µs 74.2 µs (b) 40.6 µs 46.5 µs 72.3 µs (c) 36.3 µs 55.1 µs 64.8 µs 110 mm Scanned area 60 mm Figure 7. Laser scanned area with indicated data grid points used for Lamb wave sensing. Figure 9. Lamb wave propagation contour plots in the time domain for 75 kHz excitation: (a) in-plane X direction, (b) in-plane Y direction and (c) out-of-plane Z direction. 55.5 µs 56.2 µs 58.2 µs 58.6 µs 60.5 µs 61.3 µs 62.5 µs 63.7 µs Figure 8. Example of 3D Lamb wave propagation. Figure 8 shows an example of the combined 75 kHz X–Y –Z 3D Lamb wave propagation plots for 35.5 and 50 µs. These (and figures 9–12) were taken from the animated sequential images obtained from the scanning vibrometer software, with all points phase-referenced to the triggered piezoceramic actuator burst excitation. Large peak-to-peak amplitude can be observed in the vicinity of the piezoceramic actuator in the 35.5 and 50 µs responses in figure 8. The wave energy is spread semicircularly in the plate. This pattern is disturbed (increased and decreased amplitude) in the 50 µs response in figure 8(b) when the wave hits the crack in the plate. The 3D wave propagation responses for the 75, 325 and 190 kHz were separated into in-plane and out-of-plane vibration components, as shown in figures 9–12. Figure 9 gives software animation snapshots showing the peak-to-peak time domain amplitude contour plots for the 75 kHz Lamb wave propagating in the plate at different times after plate excitation. These snapshots were selected to demonstrate features resulting from the wave interaction with the crack. The amplitude pattern, i.e. a semicircular geometric beam spreading profile of the actuator, can be seen in all vibration components. However, the strongest pattern can be observed in figure 9(c) where the out-of-plane Figure 10. Lamb wave interaction with the fatigue crack. The in-plane X direction contour maps in the time domain for 75 kHz excitation. component is presented. The in-plane X-direction component exhibits large amplitude in the vicinity of the actuator at 733 W J Staszewski et al (a) 12.5 µs 17.2 µs 19.1 µs (a) 22.3 µs 25.8 µs 33.6 µs (b) 12.5 µs 18.0 µs 19.5 µs (b) 20.3 µs 29.7 µs 39.1 µs (c) 12.5 µs 17.2 µs (c) 23.8 µs 28.1 µs 25.4 µs 39.5 µs Figure 11. Lamb wave propagation contour plots in the time domain for 325 kHz excitation: (a) in-plane X direction, (b) in-plane Y direction and (c) out-of-plane Z direction. Figure 12. Lamb wave propagation contour plots in the time domain for 190 kHz excitation: (a) in-plane X direction, (b) in-plane Y direction and (c) out-of-plane Z direction. 41.8 µs in figure 9(a) (left column). When the wave hits the crack (indicated schematically by two black lines in figure 9 and all subsequent figures in the paper) at 48.8 µs (middle column), two small areas of locally increased amplitude can be observed in front of the upper and lower parts of the crack. This is when the incoming incident wave constructively interferes with the outgoing wave reflected from the crack. This effect has previously been observed in experimental work with piezoceramic transducers and in numerical simulations [30]. The same feature is exhibited very strongly at 74.2 µs (right column). Here, the bottom part of the crack produces a larger amplitude increase than the upper part of the crack due to different orientation of the two sections of the crack; the upper part of the crack is not parallel to the plate edges. The in-plane Y-direction component, presented in figure 9(b) (middle and right columns), shows a similar crack feature. However, this feature is not exhibited by the upper part of the crack and the locally increased amplitude resulting from the wave interaction with the lower part of the crack is smaller than for the X-direction component. It is because at this point in the time snapshots, the wave does not have time to come back to interact with the crack. Also, the orientation of the widely dispersed, propogated and attenuated wave does not have the energy to show any meaningful interactions with the crack. The out-of-plane component in figure 9(c) shows that the semicircular wave propagation profile at 36.3 µs (left column) is broken by the crack at 55.1 (middle column) and 64.8 µs (right column); wave reflections from the crack and attenuation of the wave transmitted through the crack can be observed. Lamb wave interaction with the crack for the in-plane Xdirection component of the 75 kHz excitation can be observed in more details in figure 10, where eight different time-domain snapshots, gathered between 55.5 and 63.7 µs after plate excitation, are given. The study shows that the incident wave hits the bottom of the crack first. The interaction with the crack results in an area of locally increased amplitude, as explained above. The crack acts as a guide sweeping the area of large amplitude from the top to the bottom of the lower part of the crack between 55.5 and 62.5 µs. The intensity of this interaction is greatest at 60.5 µs. This is when the upper part of the crack is hit by the wave and the energy is guided to the lower part of the crack. The interaction with the upper part of the crack is intensified at 73.7 µs when the interaction with the bottom part of the crack is completed and the same effect is observed, but in the reverse direction. The peak-to-peak amplitude of Lamb wave responses has also been analysed for the 325 and 190 kHz responses. Figure 11 shows the results for the 325 kHz response dominated by the S0 Lamb wave mode. The results for the 190 kHz excitation are given in figure 12. The fundamental Lamb wave modes propagate with similar amplitudes for this 734 Fatigue crack detection in metallic structures with Lamb waves and 3D laser vibrometry C B C-D amplitude profile 0.25 0.2 0.15 0.1 0.05 0 A A-B amplitude profile Amplitude [mm/s] Amplitude [mm/s] 0.25 20 40 Distance [mm] 0.2 0.15 0.1 0.05 0 60 25 50 75 100 Distance [mm] 125 (a) D C B 0.15 0.1 20 40 Distance [mm] C-D amplitude profile 0.25 0.2 0.05 0 A A-B amplitude profile Amplitude [mm/s] Amplitude [mm/s] 0.25 0.2 0.15 0.1 0.05 0 60 25 50 75 100 Distance [mm] 125 (b) D C B A A-B amplitude profile 0.2 0.15 0.1 0.05 0 C-D amplitude profile 0.25 Amplitude [mm/s] Amplitude [mm/s] 0.25 20 40 Distance [mm] D 60 0.2 0.15 0.1 0.05 0 25 50 75 100 Distance [mm] 125 (c) Figure 13. RMS amplitude contour plots and amplitude profiles across the crack for 75 kHz Lamb wave propagation: (a) in-plane X direction, (b) in-plane Y direction and (c) out-of-plane Z direction. excitation. Similar features related to the fatigue crack, as described above for the 75 kHz component, can be observed in both analysed cases. The semicircular amplitude pattern of wave propagation, best seen in the in-plane components in figures 11(a) and (b) and figures 12(a) and (b), is broken when the wave hits the crack (middle and right columns). Also, the locally increased Lamb wave amplitude due to the positive interaction of the incoming incident wave and the outgoing wave reflected from the crack can be observed in the in-plane and out-of-plane components of the 325 and 190 kHz Lamb wave responses in figures 11 and 12 (right columns), respectively. 5.2. Root-mean-square amplitude analysis The root-mean-square (RMS) amplitude of Lamb wave inplane and out-of-plane components for all scanned grid points was analysed in the next step. In contrast to the peak-topeak amplitude analysis presented in section 5.1, the RMS amplitude was calculated for the entire length of the signal. The results, given in figures 13–15, reflect the energy spatial distribution of the propagating wave. Figure 13 gives the RMS amplitude contour plot and amplitude profiles for the in-plane and out-of-plane 75 kHz Lamb wave components. The contour plots for the in-plane 735 W J Staszewski et al C B 0.2 0.15 0.1 20 40 Distance [mm] C-D amplitude profile 0.3 0.25 0.05 0 A A-B amplitude profile Amplitude [mm/s] Amplitude [mm/s] 0.3 0.25 0.2 0.15 0.1 0.05 0 60 25 50 75 100 Distance [mm] 125 (a) D C B 0.2 0.15 0.1 20 40 Distance [mm] C-D amplitude profile 0.3 0.25 0.05 0 A A-B amplitude profile Amplitude [mm/s] Amplitude [mm] 0.3 0.25 0.2 0.15 0.1 0.05 0 60 25 50 75 100 Distance [mm] 125 (b) D C B A A-B amplitude profile 0.3 Amplitude [mm/s] Amplitude [mm/s] 0.3 0.25 0.2 0.15 0.1 0.05 0 20 40 Distance [mm] D 60 C-D amplitude profile 0.25 0.2 0.15 0.1 0.05 0 25 50 75 100 Distance [mm] 125 (c) Figure 14. RMS amplitude contour plots and amplitude profiles across the crack for 325 kHz Lamb wave propagation: (a) in-plane X direction, (b) in-plane Y direction and (c) out-of-plane Z direction. components in figures 13(a) and (b) exhibit locally increased amplitude in front of the centre of the crack. This effect can clearly be observed in the amplitude profiles in figures 13(a) and (b). Here, the RMS amplitude is increased sharply between 30 and 45 mm in the A–B profile along the wave propagation direction and in the C–D profile between 50 and 80 mm across the width of the plate. This increase is more pronounced for the X-direction than for the Y-direction component. When the out-of-plane Z-direction component is analysed in figure 13(c) the results are different. Firstly, the largest RMS amplitude, observed in the vicinity of the actuator, attenuates 736 exponentially, as illustrated in the amplitude contour plot in figure 13(c) and the amplitude A–B profile in figure 13(c). This effect is due to the actuator beam spreading profile when the wave propagates in the plate. Secondly, the amplitude is increased locally due to the crack in the plate. This can be observed in the amplitude contour plot in figure 13(c) near the centre of the crack. The damage can also be seen in amplitude profiles shown in figure 13(b), across the A–B and C–D paths indicated in figure 13(c). The RMS amplitude is increased locally between 30 mm and 45 mm in the A–B profile along the wave propagation direction and in the C–D profile between 25 and 75 mm across the width of the plate. The later Fatigue crack detection in metallic structures with Lamb waves and 3D laser vibrometry C B A-B amplitude profile 0.6 0.4 0.2 0 A 20 40 Distance [mm] C-D amplitude profile 0.8 Amplitude [mm/s] Amplitude [mm/s] 0.8 0.6 0.4 0.2 0 60 25 50 75 100 Distance [mm] 125 (a) D C B 0.4 0.2 20 40 Distance [mm] C-D amplitude profile 0.8 0.6 0 A A-B amplitude profile Amplitude [mm/s] Amplitude [mm/s] 0.8 60 0.6 0.4 0.2 0 25 50 75 100 Distance [mm] 125 (b) D C B A A-B amplitude profile 0.6 0.4 0.2 0 20 40 Distance [mm] D C-D amplitude profile 0.8 Amplitude [mm/s] Amplitude [mm/s] 0.8 60 0.6 0.4 0.2 0 25 50 75 100 Distance [mm] 125 (c) Figure 15. RMS amplitude contour plots and amplitude profiles across the crack for 190 kHz Lamb wave propagation: (a) in-plane X direction, (b) in-plane Y direction and (c) out-of-plane Z direction. profile is ‘broken’ around 35–40 mm due to the asymmetrical orientation of the crack. Thirdly, the amplitude sensed in the area behind the crack is attenuated. This time the attenuation is due to the crack. Both attenuation effects described in this section have previously been reported in experimental studies [23, 24, 36] and numerical simulations [36]. The RMS amplitude results for the 325 and 190 kHz Lamb wave responses in figures 14 and 15, respectively, are very similar to the 75 kHz results shown in figure 13. The crack presents similar in-plane and out-of-plane features. However, the background amplitude level in the in-plane vibration characteristics for the 190 kHz Lamb wave in figures 15(a) and (b) is much higher if compared with the relevant characteristics for the 75 and 325 kHz in figures 13(a), 15(a) and (b), respectively. 5.3. Discussion and summary A few interesting observations can be made regarding wave propagation and damage detection. Although the experimental work based on piezoceramic sensing was successful in selecting frequencies for which the amplitude of one of the fundamental modes was suppressed, the 3D laser vibrometer was sensitive enough to observe the existence of both modes in the Lamb wave responses investigated. 737 W J Staszewski et al The out-of-plane component attenuated significantly whereas the in-plane components did not show significant signs of attenuation in the Lamb wave responses investigated. This was revealed by the peak-to-peak amplitude contour plots and amplitude profiles along the direction of wave propagation. Since the A0 mode is dominated by the out-of-plane vibration and the S0 mode is dominated by the in-plane vibration, this confirms previous findings that symmetrical modes are less attenuated than antisymmetrical modes. The Lamb wave attenuation effect related to the actuator beam spreading profile was more significant that the attenuation due to the crack, as previously observed in [23, 24, 35]. The largest local increase of amplitude has been observed in the vicinity of the crack where the incoming incident wave interacts with the outgoing wave reflected from the crack. This not only confirms previously obtained numerical simulation [36] and experimental results [23, 24, 36] but also clearly demonstrates the first major advantage of the non-contact, laser-based scanning technique above any contact, sensorbased method. The best chance to detect damage is to position sensors in its proximity. However, this is not possible in practice when bonded, piezoceramic sensors are used since damage location is not known in advance. The quick and easy identification of the location of damage features is the second advantage of the laser-based technique. The locally increased amplitude of Lamb wave responses in the proximity of the crack, revealed when the specimen is scanned with a laser vibrometer, shows that baseline measurements can be avoided. This is the third major advantage of the method presented. In fact, the current study did not involve any laser scanning of the undamaged plate. The method not only allows for damage localization but also for the estimation of its severity. The C–D amplitude profiles are indicative of the length of the crack. Although, the increased amplitude across the width of the plate for the in-plane components (along 30 mm) underestimates and for the out-of-plane component (along 50 mm) overestimates the 41.05 mm crack, the averaged 40 mm value is very close to the actual crack length. The 3D laser-based method allows for easy separation of in-plane and out-of-plane Lamb wave components. The S0 Lamb wave mode is dominated by the in-plane vibration whereas the A0 mode is dominated by the out-of-plane component. The study shows that both in-plane and outof-plane Lamb wave vibrations can be used for impact damage detection in metallic plates. However, damage features observed and related to the in-plane and out-of-plane components were not the same. Also, very little difference was observed between the sensitivity of the in-plane and outof-plane vibration components. It is important to note the two crucial elements of the performed analysis: (a) Lamb wave dispersion characteristics are not needed for the crack detection work presented; (b) the study has not involved any complex signal processing and interpretation usually associated with Lamb waves. This is the fourth major advantage of the method presented. The RMS amplitude was easier to use than the peak-to-peak amplitude since it did not require any snapshot selection in the time domain to reveal the crack. Environmental aspects, such as temperature variation, are always a major issue in Lamb-wave-based damage 738 detection techniques which utilize piezoceramic transducers and baseline (i.e., undamaged condition) measurements. Since the method does not involve any piezoceramic sensors for sensing and baseline measurements for damage detection, temperature variations during the test are not an issue. This is the fifth advantage of the proposed technique. 6. Conclusions The application of Lamb waves and a 3D laser vibrometer for fatigue crack detection in metallic structures has been demonstrated. A full Lamb wave field has been obtained with a laser vibrometer working in a scanning mode. The 3D laser vibrometer has allowed for separation of in-plane and out-of-plane Lamb wave components. Simple laser scans of Lamb wave amplitude have been used to locate the crack and estimate its severity. The method allows for non-contact measurements at multiple locations that cannot be achieved with a small number of currently used contact transducers. No sensors needed to be fixed either permanently or temporarily to the structure, with associated risk of damage to that structure. Damage detection has not involved any studies of complex Lamb wave propagation in the monitored structures, neither any baseline measurements for undamaged structures, nor any signal post-processing performed to extract damage-related features. The analysis and interpretation of the results is very straightforward. The method is simple, fast and reliable and cannot be influenced by environmental effects. Although damage detection based on Lamb waves and utilizing a 3D scanning laser vibrometer has a great potential for impact damage detection in large metallic plate-like structures, further work is required regarding sensitivity to damage. 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