Quantitative Crack Depth Study in Homogeneous Plates Using Simulated Lamb Waves.
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1 More Info at Open Access Database Quantitative Crack Depth Study in Homogeneous Plates Using Simulated Lamb Waves. Mohammad. (. SOORGEE, Aghil. YOUSEF)-KOMA Nondestructive Testing Lab. Faculty of Mechanical and Energy Engineering, Shahid Beheshti University, Tehran, )ran. Phone: +, Fax: +, Faculty of Mechanical Engineering, University of Tehran, Tehran, )ran, Abstract: Ultrasonic guided waves are widely used for damage monitoring in shell like structures. The depth of any crack in the structure is one of the most important features of the damage witch is crucial for remaining life prediction and repair strategy selection. )n this paper, a D numerical model created by ABAQUS FEM package is considered for crack depth study, using fundamental A and S Lamb modes. Pure mode excitation is possible in FEM simulations and has been used here to study A and S modes sensitivity to the crack depth, independently. Mode conversion occurs while the Lamb mode interact the crack, and both A and S modes are generated at the damage location, moving forward transmitted waves and backward reflected waves. )t is seen that increasing the depth of the crack from % to % of the plate thickness leads to the following results. The reflected amplitude of the mode which is the same as the exited mode is monotonically increased. The reflected amplitude of the opposite mode with the excited mode in first increased and then decreased. The transmitted amplitude of the mode which is the same as the excited mode is monotonically decreased. The transmitted amplitude of the opposite mode with the excited mode in first increased and then decreased. Keywords: ultrasonic testing UT, Lamb waves, crack depth, transmission, reflection 1 Introduction Ultrasonic guided waves are widely used for damage detection purposes in several types of structures mainly made of shell features. Their unique characteristics including large area inspection capability, high sensitivity to damage and possibility of online monitoring of the structure, made them a good candidate for Structural (ealth Monitoring S(M applications as well as Noe-Destructive Testing NDT. The theoretical and fundamental aspects of guided waves are discussed in [, ]. New opportunities and challenges of guided waves are discussed in [ ]. A proper guided wave damage detection scenario consists of multiple steps including dispersion curve and wave structure analysis for mode and frequency selection, sensor and actuator selection and placement, firing the actuator s and obtaining sensor s signal s, signal processing, feature extraction and finally damage characterization. A comprehensive literature review of these steps is presented in [ ]. Among several damages which can be detected by guided waves, surface opened cracks are of interest. One of the main features of any crack in a plate structure is its depth, as the remaining life of the structure highly depends on the depth of the crack, which is one of the factors that defines the severity of the damage. Ultrasonic waves has been employed for detection the depth of cracks in [, ], Using Rayleigh wave and optimization techniques based on extracted features from elastic wave signals. Although several works has been done on crack depth detection, the problem of crack depth detection by Lamb waves is still a challenging topic to be investigated.
2 )n order to define the depth of a crack, it is necessary to study the behavior of transmitted and reflected waves, quantitatively, which is the subject if this paper. A simple D plain strain model of a plate with a surface opened crack has been employed. Fundamental A and S Lamb modes has been excited while the depth of the crack has been increased gradually. As any Lamb mode interacts the defect, mode conversion occurred and both A and S modes transmitted as well as reflected. The amplitude ratio of the transmitted and reflected modes has been consideredd as sensitive feature to depth of the crack. 2 Problem definition The goal of the present work is to study the effect of the depth of crack variation to the amplitude ratio of the transmitted and reflected Lamb modes. The geometry of the model is shown in Figure. A mm thickness aluminum plate with a pair of actuator and sensor at the distance of mm has been modeled. A cycle, K(z, tone-burst signal has been used for actuation. Figure. Geometry of the simulated model; Ds=Da= mm The depth of the crack has been changed from % to % of the thickness while at any crack depth, two independent simulations for A and S mode excitation has been performed. Pure mode excitation has been achieved by applying symmetric for S mode and anti-symmetric for A mode out of plane displacements at the actuator location. The modules of elasticity and Poisson ratio for aluminum have been considered as GPa and., respectively. 3 Dispersion curves and wave structures As stated before, a -cycle tone burst actuation signal has been employed for excitation. Figure. Phase and group velocity dispersion curves Phase and group velocity dispersion curves for aluminum plate with mentioned elastic properties are shown in Figure. Also wave structures for both fundamental modes are shown in Figure. As it is seen, the in plane displacement of S mode has the maximum
3 normalized value between displacement components. A mode is less dispersive at selected frequency comparing to S mode, obtained from group velocity dispersion curve. Also the in-planon the surface, and thus expected to be more sensitive to the vertical crack. displacement component of S mode is the largest displacement vector Figure. Wave structures of A and S modes for a mm thickness AL plate at F= K(z 4 Finite element simulation A two dimensional plain strain model has been developed in ABAQUS for simulation of the problem shown in Figure. There are two numerical procedures for transient dynamic simulations: explicit and implicit. While both procedures has been used for wave propagation simulation applications in literature, explicit dynamic method has shown better results, thus it is employed in this work. A four-node bilinear plane strain quadrilateral, reduced integration element CPE R has been selected for meshing the plate. Six elements have been used in the thickness of the plate. Figure showss scaled snapshots from A mode wave propagation in plate before and after interaction with the % depth crack. Figure. Scaled snapshots from interactionn of A Lamb mode with the % depth crack. a Before interaction with the crack, b After interaction with the crack As it is seen, before arriving at the crack, there is only A mode, propagating from left to right, in the plate, while there are both A and S modes reflected from and transmitted throughh the crack. The S mode has generated here due to mode conversion phenomena. The same phenomenon has happened for interaction of pure S mode with the crack, as shown in Figure 5. As it is seen, both A and S modes are scattered from the crack, travelling to the right transmitted and left reflected.
4 Figure 5. Scaled snapshots from interactionn of S Lamb mode with the % depth crack. a Before interaction with the crack, b After interaction with the crack Both transmitted and reflected waves contain both A and S modes. The interesting fact here is the amplitude of reflected and transmitted A and S modes varies with the crack depth, and these amplitudes will be key features for quantitative study. 5 Results and discussion (aving done ABAQUS FE simulationss for various crack depths with both A and S modes individual excitations, the in-plane and out of plane displacements of sensor and actuator have been captured. As explicit dynamic procedure has been utilized, piezoelectric elements have not been available to be used as transducer model, thus an equivalent variable has been defined, based on captured displacements. Soorgee et al [ ], has introduced an equivalent variable based on measured strains multiplied by piezoelectric material strains coefficients and verified it both numerically and experimentally. The same formula has been used here, but displacement components of sensor and actuator related nodes have been applied, instead of strains. The equivalent variable is thus as below: Based on the variable in equation, the normalized peak to peak amplitude of transmitted and reflected signals has been extracted. The signals are normalized by dividing by the magnitude of the excitation signal. 5.1 Pure A 0 mode excitation As stated before, both A and S modes have been individually investigated. )n order to excite pure A mode, the same sign out of plane displacements have been applied to the top and bottom of the actuator region on the plate. This has led to pure A mode generation in the plate, as shown in Figure -a. The normalized amplitude of reflected and transmitted wave's signalss is shown in Figure -a and -b, respectively. Two peaks can be seen in both plots, whichh are reflected and transmitted S and A modes, as marked in the plot. As the group velocity of S mode is larger than A, shown in Figure, the arrival time of both transmitted and reflected S
5 modes are smaller than the A mode. The S mode related peaks in Figure, in both reflected -a and transmitted -b signals are the results of mode conversion occurred at the crack. Figure. Amplitude of normalized reflected and transmitted signals for various depths of crack at pure A mode excitation As the crack depth increases, the converted S mode amplitude increases in both transmitted and reflected waves, and then decreases. This can also be seen in Figure, where the normalized peak to peak amplitudes are plotted vs crack depth. Based on theoretical aspects of Lamb waves, and as shown in Figure -a, the out of plane component t, which the in-plane displacement component of S mode is considerably larger than with a vertical crack, whichh is perpendicular to the in plane displacement direction, makes the S mode to be more generated and consequently transmitted and reflected from the crack. Figure. Normalized peak to peak amplitude of reflected and transmitted A and S modes for various depths of cracks at pure A mode excitation There is also the original excited A mode reflected and transmitted from the crack, as shown in Figure - a and - b. The second peak in each plot, as marked, is related to the A mode. As the crack depth increases, the amplitude of the reflected A mode increases monotonically, while the transmitted A mode amplitude decreases, as it is seen in Figure. The normalized amplitude of the reflected A mode is smaller than the reflected S,
6 even the excitation is pure A mode. )t is the same for the transmitted waves, except for the crack depth equal to % of plate thickness. 5.2 Pure S 0 mode excitation The same procedure has been repeated for pure S mode excitation. Opposite sign displacements vectors have been applied to the top and bottom of the actuator region in order to produce S mode excitation, as shown in Figure -a. As the S mode interacts with the crack, it is partially transmitted as well as reflected. As mode conversion n occurs, both A and S modes exist in reflected and transmitted waves. The normalized peak to peak amplitude of reflected and transmitted signals are shown in Figure -a and -b respectively. Also the amplitude of reflected and transmitted A and S related peaks, are shown in Figure -a and -b. Figure. Amplitude of normalized reflected and transmitted signals for various depths of crack at pure S mode excitation Figure 9. Normalized peak to peak amplitude of reflected and transmitted A and S modes for various depths of cracks at pure S mode excitation The reflected S mode amplitude increases considerably as the crack depth increases, while the reflected A increases and then decreases. For the transmitted wave, the amplitude of S peak decreases monotonically as the crack depth increases, while the transmitted A mode related peak behaves like the reflected A.
7 For quantitative comparison, the ratio of A related peak to the S, in both transmitted and reflected waves, for the both pure A and S modes excitation, is extracted and plotted in Figure. The Amplitude ratio is defined as below, for both excitation cases:, The term stands for the reflected A mode peak to peak stands for the transmitted A mode peak to peak amplitude. amplitude, while Figure. The amplitude ratio of the A mode related peak to the S mode in reflected and transmitted waves. a A mode excitation. b. S mode excitation S mode excitation has led to monotonic changes in AR R and AR T comparing to A mode, as shown in Figure -a and b. The S mode excitation is thus more convenient for quantitative crack depth study, based in Figure -b. For small crack depths, the reflected wave amplitude ratio is considerably larger than the transmitted times larger, while as the crack depth increases, AR R and AR T tends to each other, at the crack depth equal to % of the thickness, and for deep cracks, most of the wave energy is reflected in the form of S mode, causes AR R decreases and AR T increases, as shown in Figure -b. 6 Conclusions The interaction of both fundamental Lamb modes, A and S with variable depth crack, is studied via simulation. )t is seen that increasing the depth of the crack from % to % of the plate thickness leads to the following results. The reflected amplitude of the mode which is the same as the exited mode is monotonically increased. The reflected amplitude of the opposite mode with the excited mode in first increased and then decreased. The transmitted amplitude of the mode which is the same as the excited mode is monotonically decreased. The transmitted amplitude of the opposite mode with the excited mode in first increased and then decreased. An amplitude ratio is definedd for reflected and transmitted waves, as the ratio of reflected/transmitted A mode to S, and it is shown that S mode is more suitable for quantitative crack depth investigation based on AR feature.
8 7 References [ ] J. L. Rose, Ultrasonic Waves in Solid Media Cambridge, UK: Cambridge University Press, [ ] V. Giurgiutiu, Structural health monitoring: with piezoelectric wafer active sensors: Academic Press, [ ] J. L. Rose, "A baseline and vision of ultrasonic guided wave inspection potential," Journal of Pressure Vessel Technology, vol., pp. -,. [ ] Z. Su and L. Ye, )dentification of damage using Lamb waves- from fundamentals to applications vol., Berlin, Germany: Springer,. [ ] T. -T. Wu, J. -S. Fang and P. -L. Liu; "Detection of the depth of a surface-breaking crack using transient elastic waves", Journal of Acoustical Society of America., [ ] R.S. Edwards, S. Dixon, X. Jian; "Depth gauging of defects using low frequency wideband Rayleigh waves"; Ultrasonics; Volume, )ssue, January, Pages [ ] M. (. Soorgee, C. J. Lissenden, J. L. Rose, A. Yousefi-Koma, "Defect sensitivity of peizoelectric fiber composite strip transducers based on planar Lamb waves.", Journal of )ntelligent Material Systems and Structures,, Vol.
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