Absolute Nonlinear Parameter Estimation using Relative Nonlinear Parameter measured from Surface Acoustic Wave

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1 Absolute Nonlinear Parameter Estimation using Relative Nonlinear Parameter measured from Surface Acoustic Wave J. H. Jun 1, H. G. Seo 1, Y. D. Shim 1 and K. Y. Jhang 1, School of Mechanical Engineering, Hanyang University, 222 Wangsimni-ro, Seongdong-gu Seoul 04763, South Korea. kyjhang@hanyang.ac.kr 1 School of Mechanical Engineering, Hanyang University. Abstract The ratio of the relative acoustic nonlinear parameters measured from two different materials is same as the ratio of the absolute acoustic nonlinear parameter. This relationship means that the absolute nonlinear parameter of one of two materials can be estimated through the measurement of the ratio of two relative acoustic nonlinear parameters if we know the absolute nonlinear parameter of the other material. For the experimental verification of the relationship between absolute and relative acoustic nonlinear parameters, a surface acoustic wave is used. Four experimental setups which are the combinations of contact and non-contact ultrasound excitation and reception method are used. Also, the effect of both the propagation distance and the input power for ultrasound excitation are considered. Results showed the similar ratio values in all experimental setups, and the measured values were similar with the work of other researchers. Keywords: Nondestructive evaluation, Acoustic Nonlinear Parameter, Surface Acoustic Waves, Laser Ultrasound 1 Introduction The acoustic nonlinearity is a nondestructive evaluation (NDE) technique which can measure microstructural changes caused by fatigue or degradation that cannot be assessed by the linear ultrasonic techniques [1]. The acoustic nonlinear parameter is determined by the wave number of the fundamental frequency component, the propagation distance and the displacement of fundamental and second-order harmonic frequency components. However, it is hard to measure the displacement of the second-order harmonic frequency component because it is too small. Therefore, many researchers have measured the relative acoustic nonlinear parameter determined by the ratio of the received voltage. The relative acoustic nonlinear parameter is meaningful when monitoring structural integrity before and after damage. The ratio of the relative acoustic nonlinear parameter between two materials is equal to the ratio of the acoustic nonlinear parameter under the certain condition such that the propagation distance and measurement method are the same. It means that the change of the material before and after degradation can be determined by the ratio, even if the acoustic nonlinear parameter is not directly measured. [ID 249] 1

2 Surface acoustic waves have the advantages in the measurement of ultrasonic nonlinearity as well as field application. SAWs can be applied using only one side of the object, and diffraction and attenuation effects are small, so it can propagate a long distance without a significant energy loss. The best advantage of SAW in the measurement of acoustic nonlinearity is that it can control the propagation distance. In the case of longitudinal waves, the propagation distance is limited to the thickness of the specimen. However, since surface waves can set the propagation distance to the length desired by the experimenter, it is advantageous to grasp the influence of the nonlinearity on the propagation distance. In this study, SAWs are used to estimate the acoustic nonlinear parameter. Four experimental setups are used for verifying that measurement methods are irrelevant with the estimation. Additionally, if the propagation distance in each specimen is kept constant, the propagation distance is also independent of the acoustic nonlinearity parameter estimation. 2 Acoustic nonlinearity parameter of Surface acoustic waves Acoustic nonlinear parameter (β) in bulk acoustic waves is given as follow: ββ = 8 AA 2 kk 2 xx 2 AA (1) 1 where k is the wave number, x is the propagation distance, A 1 is the displacement amplitude of the fundamental frequency component and A 2 is the displacement amplitude of the second-order harmonic frequency component. Acoustic nonlinear parameter in surface acoustic waves (β saw) is derived as follow: ββ SSSSSS = 8 AA 2 kk 2 2 LL xx AA FF; 1 kk 2 TT kk 2 2 SS kk LL FF = kk ss (2kk 2 SS kk 2 TT ) (2) where k L, k T, and k S are the wave numbers for longitudinal waves, transverse waves, and SAWs, respectively [2]. F is the factor that consists of wave numbers. Under the condition that the propagation distance and wave number are constant, these constant parameters can be eliminated. Thus, the acoustic nonlinear parameter can be simplified as the relative acoustic nonlinear parameter (β ) [3]: ββ = AA 2 AA 1 2 (3) [ID 249] 2

3 To measure the relative acoustic nonlinear parameter (β ), the voltage amplitude is measured using an ultrasonic transducers instead of the displacement amplitudes, because the voltages are proportional to the displacement and are easy to measure. In this study also, the voltage amplitudes measured by PZT transducers were used. Through equation (2) and equation (3), under the condition that wave number and F factor of two materials are similar, the ratio of the relative acoustic nonlinear parameter is almost same with the ratio of the acoustic nonlinear parameter as follows: ββ AA ββ BB = FF AA ββ AA kk ll,aa xx FF BB ββ BB kk ll,bb xx ββ AA ββ BB (4) 3 Experiments 3.1 Specimens For the experiments, two kinds of aluminum alloys Al2024 and Al7075 blocks (1200 mm x 400 mm x 180 mm) are prepared. 3.2 Experimental setups In order to verify the influence of the experimental method, four experimental setups were used such that fully contact, two kinds of semi non-contact and fully non-contact. The experimental schemes for each setup are represented in Fig 2~5. For contact method, PZT transducer and wedge for SAWs were used. In excitation part, function generator, gated amplifier and 1.0 MHz PZT transducer were used to generate high power tone-burst signal. For contact reception, 2.25 MHz PZT transducer which has almost twice of resonance frequency than excitation frequency was used to receive second harmonic component more sensitively. For noncontact method, laser ultrasound was used. For non-contact excitation Nd:YAG pulsed laser and slit mask for 1.0 MHz burst signal were used. Laser interferometer was used for non-contact reception. In all experimental setups, the number of cycle in the tone-burst was six and the frequency was 1.0 MHz. In order to verify the influence of the propagation distance, three propagation distances were set and measured the relative acoustic nonlinear parameter with increasing energy at each propagation distance. [ID 249] 3

4 Figure 1: Experimental schematic of fully contact SAWs (PZT-PZT) Figure 2: Experimental schematic of semi-noncontact SAWs (PZT-LASER) Figure 3: Experimental schematic of semi-noncontact SAWs (LASER-PZT) Figure 4: Experimental schematic of fully-noncontact SAWs (LASER-LASER) [ID 249] 4

5 4 Results and Discussion The experimental results that the ratio of the relative acoustic nonlinear parameter between Al2024 and Al7075 are shown in Table 1. The results of the four experimental methods have similar values within a certain range. In addition, the ratio of nonlinear parameters at three propagation distances has similar values within the error range. Also, the results have similarity to the previously published literature data listed in Table 2. It means that the ratio of the relative nonlinear parameters is measurable regardless of the measurement method. Fully Contact (PZT-PZT) Semi Non-contact (PZT-LASER) Semi Non-contact (PZT-LASER) Fully Non-conatct (LASER-LASER) β' Al7025/β' Al ± ± ± ± 0.23 Table 1: Experimental results of four experiments, ratio β Al7025/β Al2024. Reference Material β β Al7025/β Al2024 (max-min) Yost et al. [4] Li et al. [5] Al ± 0.34 Al ± 0.18 Al7075-T ± 0.60 Al2024-T ± ( ) ( ) Reference Material β' Al7025/β' Al2024 (max-min) Thiele et al [6] Al7075-T651, Al2024-T ( ) Li et al [7] Al7075-T651, Al2024-T ( ) Table 2: Literature data of the acoustic nonlinearity parameters for Al2024 and Al7075 and the ratio β Al7025/β Al Conclusions In this study, the influences of the measurement method and propagation distance on the relative acoustic nonlinear parameter ratio between materials were verified experimentally using surface waves. Experimental results of each method and each distance had good agreement with the reference values. [ID 249] 5

6 From these results, it was verified that the propagation distance and measurement method are irrelevant in measuring the ratio of acoustic nonlinearity using surface waves. Acknowledgements This research was supported by the National Research Foundation of Korea (NRF) grant funded by the Korean government (NRF-2013M2A2A ). References [1] H, Seo et al. Assessment of Thermal Aging of Aluminum Alloy by Acoustic Nonlinearity Measurement of Surface Acoustic Waves, RNDE, vol 28, no 1, pp 3-17, January [2] G. Shu et al. A new technique for measuring the acoustic nonlinearity of materials using Rayleigh waves, Ndt & E International, vol. 41, no. 5, pp , July, [3] H, Jeong et al. A nondestructive method for estimation of the fracture toughness of CrMoV rotor steels based on ultrasonic nonlinearity, Ultrasonics, vol 41, no. 7 pp , September, [4] W. T. Yost and J. H. Cantrell, The effects of artificial aging of aluminum 2024 on its nonlinearity parameter, In Review of Progress in Quantitative Nondestructive Evaluation, 1993, pp [5] Peter. Li et al. Dependence of acoustic nonlinearity parameter on second phase precipitates of aluminum alloys, IEEE 1985 Ultrasonics Symposium. IEEE, 1985, pp [6] S. Thiele et al. Air-coupled detection of nonlinear Rayleigh surface waves to assess material nonlinearity, Ultrasonics, vol. 54, no. 6, pp , August, [7] D. Torello et al. Diffraction, attenuation, and source corrections for nonlinear Rayleigh wave ultrasonic measurements, Ultrasonics, vol 56, pp , Febuary, [ID 249] 6

Measurement of acousto-elastic effect by using surface acoustic wave

Measurement of acousto-elastic effect by using surface acoustic wave Y. D. Shim¹, J. H. Jun¹, S. M. Kim¹, J. You², C. H. Lim², H. C. Hyun² and K. -Y. Jhang¹ 1 School of Mechanical Engineering, Hanyang