Elsevier

Ultrasonics

Volume 56, February 2015, Pages 409-416
Ultrasonics

Dispersion of Lamb waves in a honeycomb composite sandwich panel

https://doi.org/10.1016/j.ultras.2014.09.007Get rights and content

Highlights

  • Theoretical Lamb wave models for composites and honeycomb sandwich panels.

  • Waveguide FE method applied to an anisotropic composite laminate and a sandwich panel.

  • Real-world applicable laboratory experiments with surface-mounted pitch-catch setup.

  • Experimental verification of theoretical and numerical dispersion curves.

Abstract

Composite materials are increasingly being used in advanced aircraft and aerospace structures. Despite their many advantages, composites are often susceptible to hidden damages that may occur during manufacturing and/or service of the structure. Therefore, safe operation of composite structures requires careful monitoring of the initiation and growth of such defects. Ultrasonic methods using guided waves offer a reliable and cost effective method for defects monitoring in advanced structures due to their long propagation range and their sensitivity to defects in their propagation path. In this paper, some of the useful properties of guided Lamb type waves are investigated, using analytical, numerical and experimental methods, in an effort to provide the knowledge base required for the development of viable structural health monitoring systems for composite structures. The laboratory experiments involve a pitch-catch method in which a pair of movable transducers is placed on the outside surface of the structure for generating and recording the wave signals. The specific cases considered include an aluminum plate, a woven composite laminate and an aluminum honeycomb sandwich panel. The agreement between experimental, numerical and theoretical results are shown to be excellent in certain frequency ranges, providing a guidance for the design of effective inspection systems.

Introduction

Composite materials are highly susceptible to hidden flaws that may arise from manufacturing flaws and service related defects caused by mechanical or thermal fatigue, foreign object impact and other unexpected events. Hidden defects in composite structures can grow to reach a critical size, become unstable and cause catastrophic failure of the entire structure. An example of such a structural component is a honeycomb composite sandwich panel in which thin composite skins are bonded with adhesives to the two faces of an extremely lightweight and relatively thick metallic honeycomb core. Hidden defects in critical load bearing structural components require reliable and cost effective nondestructive inspection and maintenance strategy for their safe operation. Most of the current inspection techniques, e.g. visual, liquid penetrant, thermal, radiographic or electromagnetic, are time consuming and often require partial disassembly of the structure, resulting in significant expense and loss of service. In addition to acoustic emission monitoring, active ultrasonic nondestructive evaluation (NDE) is a relatively cost effective technique for defect detection in structural components. The most common ultrasonic method, using a single transducer in the pulse-echo mode, is highly effective in detecting defects that are located directly under the transducer. The method is, however, extremely time-consuming when inspecting large areas, and also insensitive to certain types of defects.

Guided waves offer a suitable complementary method for inspecting large plate-like structural components due to the fact that they can travel long distances. In addition, the propagation speed and amplitude of guided waves are strongly influenced by the presence of defects in their propagation path. A careful analysis of waves that are recorded by surface-mounted transducers can lead to significant improvement of the speed and reliability of damage detection and characterization in aircraft and aerospace structures. For successful application of these ultrasonic guided wave techniques to locate and estimate the severity of damages, it is extremely important to understand the propagation characteristics of ultrasonic waves in commonly used composite structural components. The characteristics of the waves are generally quite complex and depend on the laminate layup, direction of wave propagation, frequency, and interface conditions.

In one of his classic papers, Lamb [1] established the existence of guided elastic waves in a plate of finite thickness and infinite lateral dimensions, and determined the theoretical relationship between the phase velocity of the waves and frequency as well as the thickness and material properties of the plate. The propagation characteristics of guided waves in more complex media, e.g. isotropic multi-layered plates and half spaces, have since been studied by numerous authors [2], [3]. Approximate thin-plate theories, such as the classical plate theory under Kirchoff-Love kinematic assumption, and shear deformation plate theory or Mindlin theory, have been developed to obtain analytical solutions to a variety of problems involving the dynamic response of thin isotropic and anisotropic plates [4], [5]. Recently, theoretical studies in layered anisotropic media have been carried out, primarily because of the increasing use of composites in aircraft and aerospace structures. Most of these studies involve laminates consisting of a stack of unidirectional fiber-reinforced layers that are modeled as transversely isotropic solids with their symmetry axes on a plane parallel to the surface of the laminate. The velocity of guided waves in such laminates is very sensitive to the thickness, some of the stiffness constants and the condition of the interface between the layers of the laminate. Thus the degradation of these properties can in principle be monitored if the dispersion curves can be determined through nondestructive testing (NDT).

An experimental method based on the so called the Leaky Lamb Wave (LLW) phenomenon has been found to give highly accurate values of the phase velocity of guided waves in laboratory specimens. A nonlinear inversion algorithm has been used to estimate the material properties of the waveguide so that the theoretical dispersion function attains its minimum value in a multidimensional space [6], [7]. Although the method is successful in characterizing relatively small degradation in the material properties of both metallic and composite structural components in laboratory experiments, the requirement of water immersion makes the technique impractical for field applications. Other experimental methods to determine the dispersion curves require transducer placement on both faces [8] or on the edges of the plate, or variable angle wedge transducers [9], all of which suffer from various drawbacks for field application. A comprehensive review of recent research on guided waves in composite plates and their use in nondestructive material characterization is given by Banerjee et al. [10].

Almost all of the wave propagation studies mentioned above involve angle-ply laminates consisting of a stack of unidirectional fiber-reinforced materials with different orientations. In the theoretical models, each ply is assumed to be transversely isotropic with its symmetry axis on a plane parallel to the surface of the laminate. This homogenized model of the ply has been shown to be adequate when the wavelengths are large compared to the ply thickness. A reasonable homogenized model for the material of the whole woven composite plate is also transversely isotropic but with its symmetry axis normal to the plate surface. This is also true for the honeycomb material where the symmetry axis is parallel to the axis of the cells of the core [11].

In addition to theoretical and experimental studies, the finite element (FE) method is also a versatile tool to analyze this class of problems. For example, a dynamic finite element code has been developed for the calculation of acoustic emission (AE) waveforms in isotropic and anisotropic plates [12], [13]. This code has been validated with both experimental measurements and analytical predictions for a variety of source conditions and plate dimensions in isotropic materials. However, although the FE method can handle complex geometries and has the capability to handle reflections from lateral boundaries, it is computationally much more intensive than the analytical methods discussed above, and the numerical results are often difficult to interpret. Alternatively, different semi-analytical methods have been developed recently. The waveguide finite element (WFE) method [14] and the spectral finite element (SFE) method [15], [16], are two such modeling techniques. Due to their numerical efficiency, these methods have been successfully applied to various kinds of cylindrical structures [17], helical seven-wire cables [18], and even in the presence of parameter uncertainty [19]. However, the WFE method has not been applied to study wave propagation characteristics in complex anisotropic composites and sandwich structures.

This research focuses on a woven composite laminate and an aluminum honeycomb sandwich panel with composite face sheets. Due to aforementioned reasons, the theoretical problem for a woven composite plate is a homogeneous plate composed of a transversely isotropic material with symmetry axis normal to its surface. The model of the honeycomb sandwich panel is a three-layered transversely isotropic plate composed of the honeycomb core bonded to the composite skins. Theoretical solutions of the dispersion characteristics for these structures are not available in the literature, and are provided here. In addition to analytical solutions, also efficient numerical solutions are provided using the WFE method. The elastic constants of the two materials (woven composite and aluminum honeycomb) are determined from mixture type theories, and from destructive and ultrasonic nondestructive experiments. Furthermore, an experimental approach that is more amenable to practical implementation in which guided waves are generated and recorded by surface-mounted transducers is proposed and applied within this work. From the experiments, also the validity of the assumption of transverse isotropy in the considered frequency range is demonstrated. The experimentally determined dispersion curves are compared with those calculated from theoretical models and those from the WFE method. In addition to a woven composite laminate and a honeycomb composite sandwich structure, theory as well as numerical and experimental methods are also applied to an aluminum plate for validation purposes.

The theoretical models and the applied WFE method are described in Section 2. In Section 3, the general experimental setup is described. The results for the aluminum plate, the woven composite laminate and the honeycomb sandwich panel are presented in Section 4 and discussed in Section 5.

Section snippets

Theoretical models

In this section, theoretical models for the aluminum plate (Section 2.1.1), the woven composite laminate (Section 2.1.2) and the honeycomb sandwich panel (Section 2.1.3) are presented.

Experimental setup

The general experimental setup for ultrasonic testing is shown in Fig. 5. Broadband transducers (Digital Wave B225 and B1025) with a fairly flat response in the range of 50 kHz to 600 kHz are placed on the surface of the specimen with the aid of a Plexiglas face sheet, which incorporates an array of holes drilled with an accuracy of 0.1 mm and the diameter of the holes equal to that of the transducers. The Plexiglas sheet is placed on the surface of the specimen with masking tapes and guarantees

Results

In Section 2, both theoretical and numerical approaches are presented to determine the phase and group velocities for various kinds of plate structures. The results for an aluminum plate are shown in Section 4.1, for a composite laminate in Section 4.2 and for a honeycomb sandwich panel in Section 4.3. Moreover, in each case the measurements are conducted, as described in Section 3, and the results are compared with those from the theoretical and numerical models.

Conclusions

Propagation of Lamb waves in plate-like structures has been investigated theoretically, numerically and experimentally. It has been shown that results from the numerically efficient WFE method coincide with those from the theory.

For the experiments, a pitch-catch ultrasound setup has been used with an array of transducers placed on the same side of the specimens using a custom-made Plexiglas fixture. Experimentally determined group velocities for both an isotropic aluminum plate and a

Acknowledgement

This work was supported by a fellowship within the Postdoc-Program of the German Academic Exchange Service (DAAD).

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