PSI - Issue 45

Xianwen Hu et al. / Procedia Structural Integrity 45 (2023) 20–27 Hu, X., Liang, P., Ng, C.T., and Kotousov, A. / Structural Integrity Procedia 00 (2019) 000 – 000

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1. Introduction Nowadays, there is a growing concern about the safety issues of engineering assets (such as ship hulls, aircraft, storage tanks, vehicles, etc.). Structural health monitoring (SHM) techniques have been extensively studied to evaluate structural integrity. Earlier detection of damage improves safety because it allows more time to plan maintenance and replacement as required (Su & Ye, 2009). Guided wave testing is one of the most promising SHM techniques because guided waves have a series of advantages such as long propagation distance, fast wave speed, high sensitivity to various defects, and the ability to inspect inaccessible areas (Yang et al. 2018). Conventional linear guided wave damage identification techniques focus on the linear wave features in the time domain such as the change of time of flight (ToF) and the reflection level. Recently, nonlinear guided wave features have been reported to have a much higher sensitivity to small defects. The nonlinear guided wave features can be displayed in the frequency domain at a frequency different from the primary excitation frequency (Hu et al. 2022). Many studies have employed the nonlinear guided wave features to characterise different types of microscale defects, for example, material degradation caused by fatigue (Zhu, Ng & Kotousov, 2022; Sampath & Sohn, 2022; Hu, Ng & Kotousov 2022) and thermal (Li, Cho & Achenbach, 2012; Li & Cho, 2014; Li, Hu & Deng, 2018). Guided waves have multiple wave modes and can propagate along different structural wave-guide. The present research focuses on edge-guided waves, specifically the fundamental symmetric mode of edge wave (ES 0 ). To date, only a few studies were carried out to investigate the linear and nonlinear features of ES 0 . Wilde, Golub, and Eremin (2019) reported that the edge waves can be generated at the edge of an aluminum plate by using a bonded piezoelectric transducer (PZT). After that, the ES 0 was successfully utilised to detect corrosion defects and cracks in the flange of I-beams (Hughes et al. (2021a). Hughes, Kotousov, and Ng (2020) used ES 0 at a low frequency to generate second harmonics due to material nonlinearity in an aluminum plate edge. Hughes et al. (2021b) further investigated the behaviour of ES 0 with low and high frequency-thickness values (FTV). They concluded that there is no significant energy decay for ES 0 propagation at the low FTV (< 5) range, while the amplitude modulation phenomenon of ES 0 can be observed at the high FTV range, which can adversely affect signal processing. This paper presents numerical and experimental analyses of the nonlinear interaction between ES 0 and the microstructural features of the metallic plate. A three-dimensional (3D) finite element model (FEM) was developed and experimentally validated. Then, the experimentally validated FEM was employed to further investigate the effect of varying material nonlinearity on the nonlinear features of ES 0 . The following text is organised as follows. Section 2 describes the fundamental theory of edge waves. Section 3 describes the details of finite element (FE) simulations, which summarise the model geometry, material properties, and comparison between linear and nonlinear FEM. Section 4 describes the FEM validation, which presents the detailed set-up of the experiment and the comparison between numerical and experimental results. Section 5 presents the results of the parametric study. Eventually, the

conclusions and recommendations are drawn in Section 6. 2. Edge wave theory and dispersive characteristics

This section briefly describes the fundamental theory of linear edge waves. The material nonlinearity is not included in this part for simplicity but is considered in the numerical simulation (Section 3). Let us consider a linear elastic isotropic plate (thickness = H ) in the Cartesian coordinates x = ( x 1 , x 2 , x 3 ). As defined in Figure 1, the origin of the coordinate is defined as the center of the PZT bottom, h is the half-thickness of the plate, ha and la are the thickness and the radius of the PZT, respectively.