Anisotropic effects on ultrasonic guided waves propagation in composite bends
Introduction
Fiber reinforced composites are increasingly utilized in high-performance structural applications in aerospace, naval, and automotive industries, because of their high specific strength and stiffness, lightweight, and inherent corrosion resistance. This brings new challenges in the manufacturing of components as well as in the non-destructive testing (NDT) of the structure throughout its service life. Composite laminated structures are sensitive to impacts and thus prone to damages, such as matrix cracking, delamination, and fiber failure, which can severely degrade their mechanical properties and compromise the structural integrity [1], [2], [3]. Moreover, such damages may be barely visible from the surface of the structure, but can propagate deep underneath, therefore making them difficult to detect.
Among available NDT techniques to inspect composites, ultrasonic testing methods have been the most widely applied, because they are easy to implement, and have high penetration depth and good sensitivity to small defects [4], [5], [6], [7], [8]. The conventional bulk wave testing may be carried out either with a single transducer in pulse-echo mode or with two transducers in through-transmission mode. Both cases however, involve point-by-point local inspection, which require scanning with the transducer over the whole region of interest, and are thus time consuming and tedious. Ultrasonic guided wave testing can be an attractive alternative [9], [10], [11], [12], [13], [14] as it potentially allows for rapid screening of large areas with a fixed transducer position and remote inspection of structures with difficult access, such as composite fuselages on airplanes and the inner surface of laminated pressure vessels. Guided waves are capable of interrogating the entire cross sectional area of the inspected structure and have high sensitivity to various defects [15], [16]. However, guided wave based inspection of composites is challenging due to the complicated wave propagation in anisotropic viscoelastic media [17], [18], [19]. Multiple modes usually exist, and their dispersive behavior is critically influenced by anisotropic properties of each lamina and also by the stacking sequence of the laminate [20], [21], [22]. Moreover, guided waves in composites yield unique effects such as steering effect, mode coupling, and multiple energy velocities [23], [24]. In addition, attenuation of guided waves is much higher than that in most metallic materials, mainly resulting from viscoelastic properties of matrix phases and often influenced by the operational frequency, which significantly limits their use at higher frequencies [25], [26]. In recent aerospace structural applications, fiber reinforced composites have been molded into complex shapes, such as bends, spars, stiffeners, and ribs. Apart from the influence of anisotropy, wave propagation in such structures is also affected by the geometric variation, which adds complexity to the guided wave based NDT.
The aim of this paper is to investigate both anisotropic and geometric effects on guided waves propagation in complex-shaped composite structures, which is intended to lay a foundation for identifying proper guided wave modes and choosing operational frequency for the inspection of such structures. In this connection, there is much interest in a class of guided wave modes confined in plate bends, similar to feature guided wave (FGW) phenomena in isotropic structures, discussed in the literature extensively in recent years [27], [28], [29], [30], [31]. Guided wave propagation characteristics in composites can be predicted by using the matrix techniques such as the Transfer Matrix method and the Global Matrix method [32], or by exploiting the Semi-Analytical Finite Element (SAFE) method [33], [34], [35], which allows for solving problems for waveguides with arbitrary cross section. In this study, to understand the anisotropic effects in regular structures, fundamental guided modes at low frequencies are investigated in highly anisotropic, unidirectional carbon fiber/epoxy (CF/EP) laminates. Then the laminates are formed into 90° transverse bends being typical elements to compose the wing spars and stiffeners in the aerospace industry, as shown in Fig. 1. Due to stress concentration the bends are prone to failure during the in-service use, hence critical regions to be inspected, in which the characteristics of guided waves are essential to be understood. The SAFE method is adopted for modal studies, evaluating the performance of different guided wave modes in the anisotropic bends.
Two special types of modes have been identified as their propagation energy strongly confined to the bend region, indicating that the topographical feature created by geometric variation can be a special, ‘local’ waveguide for the transport of guided wave energy. This property can be very promising to the long-range testing of composite bends since it offers the possibility of using guided waves to particularly interrogate such structural features. As noted above, this is related to FGW phenomena discussed in the literature [27], [36], [28], [29], [31]. The existence of the energy concentration phenomena in bent composite plates, is supported by the three-dimensional (3D) Finite Element (FE) simulations and validated by experiments. Finally, the influences of the fiber orientation and the frequency on such energy trapping effect are discussed, after which the paper concludes with directions for future work.
Section snippets
Guided waves in flat laminates
The composite material used in the present study is T700/340 CF/EP lamina. A 14-ply unidirectional laminate was manufactured with stacking thickness of 2.28 mm, and its mass density is 1480 kg/m3. The laminated plate is considered to be elastic (undamped) and in transversely isotropic symmetry. As in much of the literature the reference coordinate system used to defined fibrous materials is set such that the fibers are aligned in the direction, as shown in Fig. 2(a). The elastic properties
Semi-Analytical Finite Element (SAFE) modeling
Modal studies of representative composite structural bends were carried out by applying the well-known SAFE method. This method solves an eigenvalue problem of the solid with constant cross section to find all possible guided modes along the wave propagation direction (i.e. axis in Fig. 5) at a chosen frequency. In the SAFE modeling approach, only the finite element discretization of the cross section is needed, and the harmonic motion is assumed along the waveguide.
The schematic of the SAFE
Experimental setup and procedures
The experimental setup for ultrasonic measurements is shown in Fig. 9. The experiments were performed on a CF/EP bent plate with same elastic properties and critical geometry as those used for modeling. The composite bend was manufactured by laminating and molding 14 plies SE84LV prepregs (Gurit Inc., USA) containing the T700 carbon fibers embedded in 340 epoxy resin, with the fibers orientated along the bend direction. The ultrasonic excitation was launched by coupling a commercially
Influence of fiber direction on energy trapping effect
The guided wave energy trapping effect in the composite bend has been predicted by the SAFE method, supported by 3D FE simulations and validated by experiments. To further understand its physics, factors affecting such effect were investigated. Varied fiber angles (0–5°) were assigned to the SAFE model of the bend (detailed in Section 3.1) at 300 kHz to study the influence of fiber direction on the energy concentration capability of the bend-guided modes. Fig. 12 shows the variation of axial
Conclusions
In this paper, anisotropic and geometric effects on ultrasonic guided waves propagation have been studied in unidirectional CF/EP laminates and typical structural bends. The energy trapping effect carried by two types of bend-guided modes has been found in such anisotropic bends by applying the SAFE method, which is supported by the 3D FE simulations and validated by the experiments.
The discovered energy focusing capability is attractive for long-range rapid inspection of composite bends, in
Acknowledgment
This work was supported by the Start Up Grant (SUG) from the Nanyang Technological University.
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