Guided wave based material characterisation of thin plates using a very high frequency focused PVDF transducer
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1 Guided wave based material characterisation of thin plates using a very high frequency focused PVDF transducer Anoop U and Krishnan Balasubramanian More info about this article: Centre for non destructive evaluation, Department of Mechanical Engineering, Indian Institute of Technology Madras, Chennai , Tamil Nadu India. anoop.u58@gmail.com Abstract There exists a strong relation between the elastic properties and acoustic characteristics of a particular material. A non-dispersive determination of elastic properties is possible by measuring the dispersion curves. This paper discusses about an experimental approach for the generation and determination of lamb wave modes in thin plates immersed in water. The defocusing measurement system employs a 50MHz lens-less point focused transducer which uses a Polyvinylidene fluoride (PVDF) film as its active element. Experiments are conducted on Copper, Brass and Aluminum plates with 54µm, 53µm and 45µm thickness respectively. Wave formation in the materials are studied and compared. A time frequency analysis using STFT spectrogram is performed to identify the wave modes generated in the material. The experimental results are verified by comparing with theoretically obtained dispersion curves. Keywords: Leaky lamb waves, Thin plates,pvdf Transducer,Time frequency analysis 1 Introduction When the plate is immersed in a coupling medium, a part of energy of the Lamb-type guided ultrasonic waves that are propagating within the plate will also leak into the surrounding coupling medium.in such a situation the wave is called Leaky lamb wave. One of the key features of guided waves is that multiple modes of guided waves can simultaneously propagate as based on the nature of excitation, the material properties, the frequency and the geometry of the plate. Predominancy of a particular mode in a material depends on the frequency-thickness product and the angle of incidence of the wave on material surface. Quantitative ultrasonic evaluation using dispersion charachteristics of Lamb wave propagation is extensively used in many applications like defect detection and material characterisation. Some of the excisting methods for lamb wave measurements are using air-coupled transducers [1],laser ultrasonics [2],EMAT transducers [3] etc. [ID215] 1
2 Most commom method used for Lamb wave measurements is the angular arrangement of two transducers in a pitch catch mode with one as transmitter and the second one as receiver. However alingnment and simultaneous maneuverability of the two transducers are quiet inconvenient and time consuming. This paper discuss about the generation and identification of high frequency Lamb wave modes in immersed (very) thin plates using Acoustic Microscopy type of approach. A single PVDF transducer and a defocusing measurement method is used for the generation of different wave modes. Lamb wave generation in thin plates using a single PVDF transducer is introduced by Lee et al [4]. We conducted experiments on Copper, Brass and Aluminum plates with 54µm, 53µm and 45µm thickness respectively. A time frequency analysis using Short Time Fourier Transform (STFT) is used for the identification of wave modes generated in plates. Experimentally obtained results are compared with theoretical dispersion curves for the identification of guided wave modes. Since the experimental set up involves only one transducer, these measurments can be performed in a relatively convenient and more reliable manner. 2 Experimental Setup and Wave formation Coommercially obtained PVDF transducer was constructed using a spherically concave polyvinylidene fluoride (PVDF) film which is piezoelectric in nature. Since the PVDF film itsef is the active element radius of curvature and focal length are same for a focused PVDF transducer.the experimental setup includes a 50 MHz point focused PVDF(PI50-2:Panametrics) transducer with an element diameter of 0.25 inches and a radius of curvature of 0.5 inches. Figure 1: Experimental Setup [ID215] 2
3 Figure 1 shows the experimental setup which is used for generation of lamb wave modes in this work. The transducer is attached to a holder which can be adjusted manually for coarse and fine movement in all the three directions. The sample is immersed in a water tank which is mounted on a motorized linear positioning stage. Deionised water is used as the coupling medium for the experiments. PI M-5x1linear positioning stages with a minmum step size of 0.1µm are used for automated movement in x,y and z directions. For electrical excitation of the transducer and amplification of the received signal a dual pulser/receiver (DPR-500, JSR Ultrasonics) with a remote pulser (RP-L2, JSR Ultrasonics) is used. For digitizing the received signal a data acquisition card (NI PXI-5153) with a maximum sampling rate of 1GHz is used. To automate the waveform measurement and data acquisition a suitable computer program is developed using LabVIEW. Figure 2: Schematic showing the guided wave formation inside the plate using a single transducer defocus measurment Pulser receiver excites the point focused transducer to generate an ultrasonic wave which travels through the coupling fluid and encounters the sample surface. Here we use the ray theory approach to describe wave formation inside the plate[5]. There are two rays which are of interest, specular reflected ray and guided wave ray. Specular reflected ray has a normal incidence with the plate surface and guided wave ray has an angular incidence. The maximum angle of incidence depends on the half aperture angle of the PVDF transducer. When the guided way ray encounters the plate surface at an angle, depending on the thickness of plate lamb wave modes are generated. If the angle of incidence is more than first critical angle, then a lateral surface wave is also generated. The lamb waves travel along the plate and will leaks into the coupling fluid at an angle same as the incident angle. Leaky lamb waves travels back to the transducer surface as bulk longitudinal wave. The distance travelled by lamb waves in water is termed as water path and the same along the plate sample is termed as sample path. [ID215] 3
4 Figure 3: Defocus measurement on a 45µm aluminium plate When transducer is focused on the plate surface, water path of specular reflected ray is equal to that of guided wave ray. Since the time taken for both rays to reach back the transducer surface are same, there will be a single signal in the time domain representation. As we move the transducer close to plate surface (defocusing) there is a difference between water path of the rays. From fig(2) we can see that as defocusing increases the sample path for lamb waves increases and the water path decreases. As a result time of flight of the lamb wave will be more when compared to the specular reflected wave. Initially the transducer is focused on surface of the plate. Experiment is done by doing a line scan from 2mm defocus to 7mm defocus with an increment of 5µm for each measurement. Thus a toal of 1000 waveforms are obtained in one scan. A goup of typical waveforms obtained after a defocusing measurement on a 45 µm Aluminium plate are shown in fig(3). The waveforms are shifted in time so that the arrival time of specular reflection is coincided with a reference position in the time axis. From the fig(3) we can see that as the defocus distance increases, sample path of the lamb wave increases and as a result the separation between specular reflection and lamb wave increases. [ID215] 4
5 3 Time frequency analysis using Short time fourier transform. Typically STFT spectrogram analysis for the identification of Lamb wave modes are applied when the wave propagation is only through a single medium. However, in this case the lamb wave propagates through two mediums, coupling fluid and plate. Hence a time of flight compensated STFT spectrogram analysis is used [6]. A time domain signal corresponding to a particular defocus position is selected and the short time Fourier transform is obtained using a standard algorithm. STFT spectrogram represents the energy distribution of a time domain signal on a time-frequency plane. Theoretical dispersion curves for the plate is derived using disperse software [7]. The velocity coordinates of group velocity dispersion curve can be transformed to time by using the following equation. = + + (1) Where t is the total time of flight of lamb wave mode, d s and d w are the sample and water paths respectively. Cg and Cw are the velocities of the wave in plate and coupling fluid respectively. Td is the trigger delay used as experimental parameter. By using transducer dimensions like element size and focal length, water and sample path of the lamb wave is calculated for all the defocus positions. The velocity of coupling fluid is calculated as 1485m/sec. 4 Results and discussion Figure 4: STFT spectrogram of a 45µm aluminium plate at different defocus positions [ID215] 5
6 From the STFT spectrogram we can clearly visualize the separation of Lamb wave from the specular reflection as we increase the defocus distance. Figure 5: Dispersion curves overlayed on STFT spectrogram From the comparison of experimentally and theoretically obtained results, we can see that dispersion curves for S0 and A1 coincides with the energy distribution corresponding to guided lamb wave in the spectrogram. Half aperture angle of the PVDF transducer is smaller than the incident angle required for generation of S0 mode in all the cases studied in this work. Hence the lamb wave mode generated in all the plates studied in this work is identified as A1. Central frequency and bandwidth of the lamb wave mode depends on material and thickness of the plate. 5 Conclusions Lamb wave modes can be generated in thin plates using a single PVDF point focused transducer and a defocusing measurement method. The STFT spectrogram based time frequency anlaysis can be used as an efficient tool for the identification of the wave modes. [ID215] 6
7 References [1] M. Castaings and P. Cawley, The generation, propagation, and detection of Lamb waves in plates using air coupled ultrasonic transducers, J. Acoust. Soc. Am., vol. 100, no. 5, pp , [2] W. Gao, C. Glorieux, and J. Thoen, Laser ultrasonic study of Lamb waves: determination of the thickness and velocities of a thin plate, Int. J. Eng. Sci., vol. 41, no. 2, pp , [3] Z. Guo, J. D. Achenbach, and S. Krishnaswamy, EMAT generation and laser detection of single lamb wave modes, Ultrasonics, vol. 35, no. 6, pp , [4] Y.-C. Lee, Y. F. Tein, and Y. Y. Chao, A Point-Focus PVDF Transducer for Lamb Wave Measurements, J. Mech., vol. 18, no. 1, pp , [5] W. Parmon and H. L. Bertoni, Ray interpretation of the material signature in the acoustic microscope, Electron. Lett., vol. 15, no. 21, p. 684, [6] J. Li and S. Liu, The application of time-frequency transform in mode identification of Lamb waves, in 17th World Conference on Nondestructive Testing, 2008, pp [7] B. Pavlakovic, M. Lowe, D. Alleyne, and P. Cawley, Disperse: a general purpose program for creating dispersion curves, in Review of progress in quantitative nondestructive evaluation, Springer, 1997, pp [ID215] 7
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