Modelling of Lamb Waves Propagation in Orthotropic Plate

Modelling of Lamb Waves Propagation in Orthotropic Plate

Salah Nissabouri (FST Settat, Morocco), Mhammed El Allami (CRMEF Settat, Morocco & FST Settat, Morocco) and El Hassan Boutyour (FST Settat, Morocco)
DOI: 10.4018/978-1-7998-0117-7.ch012


In this chapter, we model by Finite Element Method (FEM) the Lamb waves' propagation and their interactions with symmetric and asymmetric delamination in sandwich skin. Firstly, a theoretical model is established to obtain the equation of lamb modes propagation. Secondly, dispersion curves are plotted using Matlab program for the laminate [0]4. The simulations were then carried out using ABAQUS CAE by exciting the fundamental A0 Lamb mode in the frequency 300 kHz. The delamination was then estimated by analyzing the signal picked up at two sensors using two techniques: Two Dimensional Fast Fourier Transform (2D-FFT) to identify the propagating and converted modes, and Wavelet Transform (WT) to measure the arrival times. The results showed that the mode A0 is sensible to symmetric and asymmetric delamination. Besides, based on signal changes with the delamination edges, a localization method is proposed to estimate the position and the length of the delamination. In the last section, an experimental FEM verification is provided to validate the proposed method.
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The detection of defects in isotropic and composite structures is becoming a priority, particularly in the aeronautical industries. Indeed, most parts are subjected to different constraints during their manufacturing process and life cycle. These mechanical or thermal constraints cause internal or surface defects. So, reliable methods must then be found to diagnose the state of pieces health. NDT (Non Destructive Testing) techniques are used to assess the health of the part without destruction. Some NDT methods use: x-rays, laser holography, or microscopy to locate defects. These methods are expensive and require specific conditions of use. For that reason, Lamb waves are an attractive tool used to control long distances such as pipes. However, they are dispersive, which means that they change frequency by propagating through the structure. So, before performing the control, the authors have to choose an adequate frequency based on dispersion curves. Moreover, Multilayer structures, or multilayer composites, may contain critical internal defects such as: delamination facilitating rapid alteration and leading to further problems.

Nondestructive Testing of Composite Material

A composite material is an assembly of at least two materials that has different properties. The first which is called fiber that ensures the mechanical strength. The second named matrix consisting of plastic, metal or ceramic material. The figure 1 shows the component of unidirectional composite.

Figure 1.

Unidirectional composite


Composites are designed to improve mechanical proprieties of structures. They are widely used in different fields especially in aeronautic industry. Their characteristics are influenced by the proportions of the matrix and the reinforcements. There are other parameters that also affect the properties of a composite like: size, orientation and distribution of the fiber. The heterogeneity of composites structures lead to their weakness and facilitates the appearance of internal and external damages such as: fiber breakage, matrix cracking, through-thickness hole, local delamination.

Composite structures require careful monitoring and inspection to identify damage and take corrective action to ensure safe and continuous operation. In metal structures, the control mainly concerns corrosion, tensile stress cracking, and stress corrosion. In composite structures, control is also concerned with delamination growth, compression fatigue, manufacturing defects, fiber degradation and failure. These types of damage usually occur below the surface and cannot be easily detected.

One of composite structures is Sandwich materiel made from two thin skins bonded to a thick core (see figure 2). The skin studied in this paper is an orthotropic plate [0]4 with three mutually perpendicular planes of symmetry.

Figure 2.

Sandwich structure


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