PSI - Issue 52

Donato Perfetto et al. / Procedia Structural Integrity 52 (2024) 418–423 Donato Perfetto / Structural Integrity Procedia 00 (2019) 000–000

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situations carry more energy than higher-order modes. The sensitivity of these waves makes them an excellent tool for detecting damage in a structure. There are many techniques developed for damage detection that can be divided into two basic types: linear and non-linear. Linear damage detection techniques are based on linear guided wave phenomena, such as reflection, transmission, and mode conversion, considered to be at the same frequency as the excitation signal [2]. Damage detection using the linear technique involves comparing guided wave signals recorded in the damaged structure with signals gathered in a previous state of the structure (supposed to be damage free). However, the propagation of UGW within structures is a phenomenon whose analytical resolution is not easy [3]. This phenomenon is further complicated in the presence of operational loads [4,5] and complex geometries (curved/reinforced plates, presence of discontinuities [6–8]) that typically characterise real structures, i.e., the introduction of stiffeners to improve the structural response under critical loads [9,10]. Moreover, since it is well known that the thickness of a structure is a critical aspect for UGWs propagation, analysing their behaviour in plates with a non-constant cross-sectional area is an essential step. The authors Han et al. [11] analysed UGWs propagation on a quasi-isotropic composite plate with a step discontinuity due to thickness change. The experiment showed that the group velocity across the step discontinuity is close to that of thin region rather than that of thick region. The authors Zima and Moll performed several studies on structures with a variable cross section. It has been concluded that while the wave velocity does only depend by the thickness distribution, its amplitude strongly depends on the plate shape [12]. Moreover, after an experimental, numerical, and theoretical analysis of UGWs behaviour on metallic structures [13,14], it has been concluded that the irregular geometry leads to triggering more than one mode hindering the interpretation of the signals. Furthermore, non-isotropic materials, e.g., fibre-reinforced polymer (FRP) composites, cause wave modes to depend on the plate configuration, wave propagation direction, frequency, and boundary conditions. It is therefore necessary to use alternative methods to solve this problem. The most efficient way to study the phenomenon is to model it using numerical approaches to solve the characteristic equations [15]. In this work, numerical models based on the Finite Element (FE) method were developed to study the behaviour of UGWs in FRP composites plates with a variable thickness (i.e., variable cross-section). In particular, different modelling techniques were investigated: the 3D-Shell approach and the 2D-Shell one, the latter characterised by a different schematisation of the thickness for the shell elements. The results were thus compared considering the 3D-Shell approach as the reference, according to the literature [15], in order to determine the most efficient 2D-Shell scheme, in terms of both accuracy and computational costs, for the modelling of a variable thickness geometrical configuration, typical of real structures. 2. Methodology The purpose of this work is to carry out a preliminary study about the propagation of UGWs in a FRP composite panel using the FE approach. In particular, the panel is characterised by a geometrical discontinuity, represented by a variable thickness cross-section, while the FE method is used to determine the most efficient way to simulate the propagation mechanisms of UGWs in a such a complex geometrical scenario. The specimen examined in this study is a square-shaped carbon FRP (CFRP) composite panel with a side length of L=600mm. As shown in Figure 1, the geometric variation of the panel is identified by two end regions, a thinner one ( 2 = 1.8 mm) and a thicker one ( 1 = 3.6 mm), that are connected by a central region whose thickness varies linearly over a length of s = 5mm. The staking sequence of the two end regions ( 2 and 1 thickness) are [0 2 /±45 2 / 90 2 ] and [0 2 /±45 2 /90 2 ] 2 , respectively, where the 0-degree direction is defined as the one orthogonal to the geometric step. Mechanical properties of each lamina are listed in Table 1. Two lead zirconate titanate (PZT) transducers were modelled on the upper surface of the panel: the actuator (PZT 1) was surface mounted on the thin region, while the receiver (PZT 2) on the thick region. The thickness and diameter of the PZT disks are = 0.25mm and = 10mm, respectively, and the mechanical properties are listed in Table 1. Both sensors, whose position is shown in Figure 1a, are placed at W = 200 mm from the edges with homogeneous cross section and at H = 300 mm from the edges with variable cross section. This results in a mutual distance of d = 200 mm.