Scattering of the fundamental anti-symmetric Lamb wave at delaminations in composite laminates

An analysis of the scattering characteristics of the fundamental anti-symmetric (A(0)) Lamb wave at a delamination in a quasi-isotropic composite laminate is presented. Analytical solutions for this problem do not exist due to the anisotropic nature and multilayer characteristics of composite laminates. This study uses a three-dimensional finite element (FE) method and experimental measurements to provide physical insight into the scattering phenomena. Good agreement is found between simulations and experimental measurements. The results show that the A(0) Lamb wave scattering at a delamination in composite laminates is much more complicated than the scattering at a defect in isotropic plates. Scatter amplitudes and scatter directivity distributions depend on the delamination size to wavelength ratio and the through-thickness location of the delamination damage. The study also investigates the feasibility of the common experimental practice of simulating delamination damage by bonding masses to the surface of composite laminates for guided wave damage detection and characterization methodologies verifications. The results suggest that care is required to use bonded masses to simulate delamination damage for verifying and optimizing damage characterization techniques. In summary, the results of the investigation help to further advance the use of the A(0) Lamb wave for damage detection and characterization.     

Analytical and finite element prediction of Lamb wave scattering at delaminations in quasi-isotropic composite laminates

This paper presents a theoretical and finite element (FE) investigation of the scattering characteristics of the fundamental anti-symmetric (A₀) Lamb wave at delaminations in a quasi-isotropic (QI) composite laminate. Analytical models based on the Mindlin plate theory and Born approximation are presented to predict the A₀ Lamb wave scattering at a delamination, which is modelled as an inhomogeneity, in an equivalent isotropic model of the QI composite laminate. The results are compared with FE predictions, in which the delamination is modelled as a volume split. The equivalent isotropic model and QI composite laminate are used to investigate the feasibility of the common theoretical approach of modelling the delamination as the inhomogeneity. A good correlation is observed between the theoretical solutions and FE results in the forward scattering amplitudes, but there exists a larger discrepancy in the backward scattering amplitudes. The FE results also show that the fibre direction of the outer laminae has a pronounced influence on the forward and backward scattering amplitudes, which is not predicted by the analytical models.     

Scattering characteristics of Lamb waves from debondings at structural features in composite laminates

This article investigates the scattering characteristics of Lamb waves from a debonding at a structural feature in a composite laminate. This study specifically focuses on the use of the low frequency fundamental antisymmetric (A(0)) Lamb wave as the incident wave for debonding detection. Three-dimensional finite element (FE) simulations and experimental measurements are used to investigate the scattering phenomena. Good agreement is obtained between the FE simulations and experimental results. Detailed parameter studies are carried out to further investigate the relationship between the scattering amplitudes and debonding sizes. The results show that the amplitude of the scattered A(0) Lamb wave is sensitive to the debonding size, which indicates the potential of using the low frequency A(0) Lamb wave as the interrogating wave for debonding detection and monitoring. The findings of the study provide improved physical insights into the scattering phenomena, which are important to further advance damage detection techniques and optimize transducer networks.     

Acousto-ultrasonic sensing for delaminated GFRP composites using an embedded FBG sensor

In this paper, an active damage detection system for composite laminates is introduced. A fiber Bragg grating (FBG) was employed as an embedded sensor for detecting ultrasonic Lamb wave generated by a piezoelectric (PZT) actuator, inside the laminates. There were two different configurations for the system, making use of a broadband light source and a laser source, respectively. It was found that the use of a laser source could provide a higher sensitivity, so it was preferred in an ultrasonic signal acquisition unit for damage detection. When a delamination is developed in composite structures, the propagation characteristics of Lamb wave is then changed. According to altered signals, the types and natures of delamination inside the structures can be evaluated. In this experiment, glass fiber-reinforced epoxy (GFRP) composite beams were used to study the feasibility of our proposed detection technique. FBG sensors were embedded in different layers of the composite beams. The responses of FBG sensors from both intact and delaminated composite beams were then compared. Finally, the acquired Lamb wave signals corresponding to different delamination sizes and locations were examined.     

The propagation of coupled Lamb waves in multilayered arbitrary anisotropic composite laminates

Based on linear three-dimensional elasticity theory, the wave equations of coupled Lamb waves in multilayered arbitrary anisotropic composite laminates are derived using a Legendre orthogonal polynomial approach. The elastodynamic solution for the propagation of coupled Lamb waves in composite plates is also presented to determine the characteristics of coupled Lamb waves. To verify the applicability and validity of the method, two cases of bi-layered plates formed with isotropic components and anisotropic components, respectively, are primarily manipulated for comparison with earlier known results. Next, the dispersion curves, displacements and stress distributions of Lamb waves in multilayered anisotropic laminates are calculated. The effects of coupling and fiber orientation on the characteristics of the Lamb waves are illustrated. The potential usefulness of the fundamental modes of the coupled Lamb waves is discussed in detail.     

The group velocity variation of Lamb wave in fiber reinforced composite plate

Experimentally measured Lamb wave group velocities in composite materials with anisotropic characteristics are not the same as the theoretical group velocities which is calculated with the Lamb wave dispersion equation. This discrepancy arises from the fact that the angle between the group velocity direction and the phase velocity direction in anisotropic materials exists. Wave propagation in a composite material with anisotropic characteristics should be considered with respect to magnitude correction in addition to direction correction. In this study, S0 mode phase velocity dispersion curves are depicted with the variation of degree with respect to the fiber direction using a Lamb wave dispersion relation in the unidirectional, bidirectional, and quasi-isotropic composite plates. Slowness surface is sketched by the reciprocal value of the phase velocity curves. The magnitude and direction of the group velocity could be calculated from the slowness surface. The recalculated group velocities with consideration of the magnitude and direction from the slowness surface are compared with experimentally measured group velocities. The proposed method shows good agreements with theoretical and experimental results.     

Micro-crack detection of nonlinear Lamb wave propagation in three-dimensional plates with mixed-frequency excitation

We propose a nonlinear ultrasonic technique by using the mixed-frequency signals excited Lamb waves to conduct micro-crack detection in thin plate structures. Simulation models of three-dimensional(3D) aluminum plates and composite laminates are established by ABAQUS software, where the aluminum plate contains buried crack and composite laminates comprises cohesive element whose thickness is zero to simulate delamination damage. The interactions between the S_0 mode Lamb wave and the buried micro-cracks of various dimensions are simulated by using the finite element method.Fourier frequency spectrum analysis is applied to the received time domain signal and fundamental frequency amplitudes,and sum and difference frequencies are extracted and simulated. Simulation results indicate that nonlinear Lamb waves have different sensitivities to various crack sizes. There is a positive correlation among crack length, height, and sum and difference frequency amplitudes for an aluminum plate, with both amplitudes decreasing as crack thickness increased, i.e.,nonlinear effect weakens as the micro-crack becomes thicker. The amplitudes of sum and difference frequency are positively correlated with the length and width of the zero-thickness cohesive element in the composite laminates. Furthermore,amplitude ratio change is investigated and it can be used as an effective tool to detect inner defects in thin 3D plates.     

Three-Dimensional Scattering of an Incident Plane Shear Horizontal Guided Wave by a Partly through-Thickness Hole in a Plate

We investigate the three-dimensional(3D) scattering problem of an incident plane shear horizontal wave by a partly through-thickness hole in an isotropic plate,in which the Lamb wave modes are also included due to the mode conversions by the scattering obstacle in the 3D problem.An analytical model is presented such that the wave fields are expanded in all of propagating and evanescent SH modes and Lamb modes,and the scattered far-fields of three fundamental guided wave modes are analyzed numerically for different sizes of the holes and frequencies.The numerical results are verified by comparing with those obtained by using the approximate Poisson/Mindlin plate model for small hole radius and low frequency.It is also found that the scattering patterns are different from those of the SO wave incidence.Our work is useful for quantitative evaluation of the plate-like structure by ultrasonic guided waves.     

Ultrasonic Lamb wave diffraction tomography.

Ultrasonic guided waves, Lamb waves, allow large sections of aircraft structures to be rapidly inspected. Unlike conventional ultrasonic C-scan imaging that requires access to the whole inspected area, tomographic algorithms work with data collected over the perimeter. Because the velocity of Lamb waves depends on thickness the travel times of the fundamental modes can be converted into a thickness map of inspected region. Lamb waves cannot penetrate through holes and other strongly scattering defects and the assumption of straight wave paths, essential for many tomographic algorithms, fails. Diffraction tomography is a way to incorporate scattering effects into tomographic algorithms in order to improve image quality and resolution. This work describes the iterative reconstruction procedure developed for Lamb wave tomography and allowing for ray bending correction for imaging of moderately scattering objects.     

Quantitative damage imaging using Lamb wave diffraction tomography

In this paper, we investigate the diffraction tomography for quantitative imaging damages of partly through-thickness holes with various shapes in isotropic plates by using converted and non-converted scattered Lamb waves generated numerically. Finite element simulations are carried out to provide the scattered wave data. The validity of the finite element model is confirmed by the comparison of scattering directivity pattern(SDP) of circle blind hole damage between the finite element simulations and the analytical results. The imaging method is based on a theoretical relation between the one-dimensional(1D) Fourier transform of the scattered projection and two-dimensional(2D) spatial Fourier transform of the scattering object. A quantitative image of the damage is obtained by carrying out the 2D inverse Fourier transform of the scattering object. The proposed approach employs a circle transducer network containing forward and backward projections, which lead to so-called transmission mode(TMDT) and reflection mode diffraction tomography(RMDT),respectively. The reconstructed results of the two projections for a non-converted S0 scattered mode are investigated to illuminate the influence of the scattering field data. The results show that Lamb wave diffraction tomography using the combination of TMDT and RMDT improves the imaging effect compared with by using only the TMDT or RMDT. The scattered data of the converted A0 mode are also used to assess the performance of the diffraction tomography method. It is found that the circle and elliptical shaped damages can still be reasonably identified from the reconstructed images while the reconstructed results of other complex shaped damages like crisscross rectangles and racecourse are relatively poor.     

A computational analysis of the ballistic performance of light-weight hybrid composite armors

The ability of hybrid light-weight fiber-reinforced polymer-matrix composite laminate armor to withstand the impact of a fragment simulating projectile (FSP) is investigated using a non-linear dynamics transient computational analysis. The hybrid armor is constructed using various combinations and stacking sequences of a high-strength/high-stiffness carbon fiber-reinforced epoxy (CFRE) and a high-ductility/high-toughness Kevlar fiber-reinforced epoxy (KFRE) composite laminates of different thicknesses. The results obtained indicate that at a fixed thickness of the armor both the stacking sequence and the number of CFRE/KFRE laminates substantially affect the ballistic performance of the armor. Specifically, it is found that the armor consisting of one layer of KFRE and one layer of CFRE, with KFRE laminate constituting the outer surface of the armor, possesses the maximum resistance towards the projectile-induced damage and failure. The results obtained are rationalized using an analysis of the elastic wave reflection and transmission behavior at the inter-laminate and laminate/air interfaces.     

基于模式分离的兰姆波逆时偏移成像

应用频率域逆时偏移方法实现各向同性和各向异性板中缺陷的兰姆波成像.由于缺陷引起的多模态散射信号会在重建图像中形成伪像,根据基本导波模式振动对称性的差别进行了模式分离预处理.基于多元阵列超声技术,开展了铝板和复合板内缺陷频率域逆时偏移超声成像方法的数值仿真研究.首先,建立有限元模型,采用环形传感器数值采集由缺陷引起的兰姆波散射信号,然后,将采集到的多模式散射信号进行模式分离处理,再将模式分离后的兰姆波散射信号经时间反转后并在相应的接收器处重新激励,在频域中运用格林函数反向传播兰姆波散射信号,获取监测区域的声场信息,与正向传播声场进行互相关,重建缺陷图像.首先对铝板中单缺陷以及复合材料板中相邻的两个相同缺陷进行数值仿真,对比有无模式分离处理的缺陷逆时偏移成像效果,体现出模式分离的重要性.在此基础上,采用逆时偏移方法对复合板材内位置邻近、深度不同的双缺陷进行识别.数值结果表明,模式分离预处理后的缺陷重建图像能够有效去除多模式干扰产生的伪像.文中提出的成像方法对各向同性板和各向异性板内缺陷的检测和成像具有很好的发展潜力,可以准确地探测多个缺陷的形状、尺寸和深度.     

Frequency dependent directivity of guided waves excited by circular transducers in anisotropic composite plates

Lamb wave propagation in fiber-reinforced composite plates is featured by a pronounced directivity of wave energy transfer along the fibers from a point surface source. In the case of non-point (sized) source, the main lobe of radiation diagram may turn with frequency up to the orthogonal to the fibers direction. This effect has been theoretically studied and physically explained in the context of semi-analytical integral-equation based mathematical model. The present paper gives its experimental verification.     

Scattering of plane acoustic waves by a transversely isotropic cylindrical shell—application to material characterization

Scattering of obliquely incident plane acoustic wave by an air-filled, transversely isotropic cylindrical shell immersed in water is investigated theoretically and experimentally. The normal mode expansion technique is employed for analyzing the scattering field, and then resonance modes of the shell appearing in modal scattering form functions are identified performing the resonance scattering analysis. Dispersion curves for Sholte-Stoneley, SH and Lamb waves are obtained and their characteristics are interpreted. Calculated backscattering and resonance spectra as well as dispersion curves are compared with those from ultrasonic experiments for two composite samples having the same nominal composition but fabricated under different conditions. Sensitive change of the dispersion curves is observed for both normal and oblique incidences, which demonstrates the feasibility of systematic inverse evaluation of damage or elastic constants of the composite shell using data from the acoustic scattering measurements.     

An experimental study on the behavior of Ao mode transduced using misaligned air-coupled transducers in composite laminates

Air-coupled transducers can be employed for generation and reception of Lamb waves in composite laminates. To generate and receive a particular Lamb mode, the transducers are oriented in a particular angle. The orientations of transducers also determine amplitude of a particular Lamb mode of interest. Any deviation (misalignment) from the right orientation results in a reduction in the amplitude. Therefore, an attempt has been made to establish variation in amplitude of the fundamental anti-symmetric Lamb mode (A_o) when misalignments were purposefully introduced in the air-coupled probes. In the present work, three different misalignments – linear, orientation and synchronized orientation were envisaged. Experiments were performed on two laminates – unidirectional ([0₃]_s) and cross-ply ([0/90₂/0]_s) of GFRP (Glass Fiber Reinforced Plastic) material. Curves were fitted on experimental data to characterize variation in amplitude of A_o mode in each misalignment. Moreover, wave splitting and merging was observed when the probe(s) was (were) rotated in a particular direction in orientation and synchronized orientation misalignments.     

The band gaps of Lamb waves in a ribbed plate: A semi-analytical calculation approach

In this paper a semi-analytical method is proposed to investigate the transmission band gaps of Lamb waves through repetitive structures in a waveguide. For a unit cell the scattering matrix is obtained by the Lamb mode matching technique at each artificially sliced interface and then substituted into the Bloch theorem to solve the eigenproblem incurred by cell repetition. The method is implemented on a ribbed plate. The band gaps in the dispersion curves are confirmed by the dips of Lamb wave transmission coefficients, and attributed to the coupled vibrations of Lamb modes in different sliced sections of the unit cell.     

A model and experimental study of fiber orientation effects on shear wave propagation through composite laminates

The strong elastic anisotropy of the discrete unidirectional plies in a composite laminate interacts sensitively with the polarization direction of a shear ultrasonic wave propagating in the thickness direction. The transmitted shear wave can therefore be used to detect errors in the ply orientation and stacking sequence of a laminate. The sensitivity is particularly high when the polarization directions of the shear wave transmitter and receiver are orthogonal to each other. To understand the interaction between normal-incident shear waves and ply orientations in a laminate, a complete analytical model was developed using local and global transfer matrices. The model predicted the transmitted signal amplitude as a function of polarization angle of the transmitter and time (or frequency) for a given laminate and input signal. To alleviate the experimental problems associated with shear wave coupling, electromagnetic acoustic transducers (EMATs) and metal delay lines were used in the angular scan of the transmitted signal. The EMAT system had the added advantage of being applicable to uncured composite laminates. Experiments were performed on both cured and uncured laminates with common layups for model verification. The sensitivity of the measured shear wave signals to fiber misorientation and stacking sequence errors was also demonstrated.     

Classification of flaw severity using pattern recognition for guided wave-based structural health monitoring

In this paper, the authors present a formal classification routine to characterize flaw severity in an aircraft-grade aluminum plate using Lamb waves. A rounded rectangle flat-bottom hole is incrementally introduced into the plate, and at each depth multi-mode Lamb wave signals are collected to study the changes in received signal due to mode conversion and scattering from the flaw. Lamb wave tomography reconstructions are used to locate and size the flaw at each depth, however information about the severity of the flaw is obscured when the flaw becomes severe enough that scattering effects dominate. The dynamic wavelet fingerprint is then used to extract features from the raw Lamb wave signals, and supervised pattern classification techniques are used to identify flaw severity with up to 80.7% accuracy for a training set and up to 51.7% accuracy on a series of validation data sets extracted from independent plate samples.     

Lamb wave topological imaging for blind hole defects in isotropic plates

The research aims at validating the ability of topological imaging to blind holes in isotropic plates using Lamb waves. Due to the defect is not symmetric around the midplane of the plate, the effect of Lamb mode conversion will have to be taken into account.The imaging method is based on two computations of ultrasonic fields, one forward and one adjoint, performed for the defect-free reference medium. The excited signal and scattered Lamb waves caused by the blind hole, are used as emitting sources to compute the forward problem and the adjoint problem, respectively. With the help of the finite element simulations,the natural refocusing process of the multimode Lamb waves at the defect location is visually demonstrated by the transient acoustic field snapshots at the different moments to strengthen the physical mechanism of the topological imaging method. The numerical results demonstrate that topological imaging has relatively stronger applicability to the blind hole in contrast to classical Delay And Sum(DAS) method and Time Reversal(TR) method. The topological imaging could handle complex Lamb wave signals containing mode conversions without the imaging quality being affected. The proposed imaging method presents a certain developing potential for detecting and imaging asymmetric defects in plate-like configurations using Lamb waves.     

各向同性板中盲孔缺陷的兰姆波拓扑成像

将拓扑成像用于各向同性板中盲孔缺陷的兰姆波检测。由于缺陷关于板中面是非对称的,兰姆波模式转换的影响不能忽略。成像方法是基于无缺陷参考媒质中两个超声场(直接声场和伴随声场)的计算。以传感器激励信号为声源,计算直接声场;以盲孔引起的兰姆波散射信号为声源,计算伴随声场。拓扑成像通过直接声场与伴随声场的相乘,可消除无缺陷处多模式混叠的干扰,提高成像分辨率。建立有限元模型,通过不同时刻的瞬态声场图可视化地显示多模式兰姆波在缺陷处的聚焦过程,揭示拓扑成像方法的物理机理。数值结果表明,相对于经典的延迟求和以及时间反转方法,拓扑成像对盲孔缺陷有更强的适应能力。即使对于复杂的包含模式转换的兰姆波信号,拓扑图像的质量依然没有受到影响。文中提出的成像方法对板类结构中非对称缺陷的兰姆波检测具有一定的应用潜力。