Lamb Wave Velocity Research Articles

Efficient zigzag theory-based spectral element model for guided waves in composite structures containing delaminations

Lamb wave-based structural health monitoring offers excellent potential for real-time delamination detection in laminated structures. It necessitates fast and accurate numerical simulation of guided wave interaction with delaminations. Towards this objective, we present an efficient layerwise zigzag theory (ZIGT) based time-domain spectral element for wave propagation analysis of composite beam- and panel-type structures (strips) containing delamination at arbitrary locations. The ZIGT delivers accuracy like layerwise theories by allowing slope discontinuities in the in-plane displacement field at layer interfaces while maintaining computational efficiency like equivalent single-layer (ESL) theories, making it ideal for such analyses. The high-order elemental nodes at Lobatto points have only four displacement variables, irrespective of the number of layers in the laminate. Delamination is modelled using the region approach, adapting the recently proposed hybrid point-least squares continuity method to satisfy the nonlinear displacement field continuity at the delamination fronts. The model’s efficacy is examined vis-à-vis elasticity-based elements, ESL theory-based elements, and the ZIGT-based standard finite element for free vibration and guided wave propagation responses of composite strips featuring multiple delaminations. The present model shows superior overall efficiency, accuracy, and convergence. An application of the model is also explored for identifying delamination locations from Lamb wave velocity fields.

Estimation of the stiffness tensor from Lamb wave velocity profiles measured on steel with different texture

It is important that steel meets the designated material parameters after production. Ideally, relevant parameters should be measured inline to have the ability to control the process during production. This requires a method that determines material parameters, such as the texture and various stiffness matrix components. These material properties can be derived from ultrasonic Lamb wave velocity measurements for different angles relative to the rolling direction. Objectives A method for estimating relevant stiffness matrix components needs to be developed, tested on simulation results and applied on measurements. Work performed A set of 10 cold-rolled Interstitial Free (IF) steel samples is provided by Tata Steel. These samples have different microstructures and thus different elastic properties. The ultrasonic Lamb wave velocity is measured for each of those samples over 360°. For each sample, a digital representative volume element (RVE) is generated using periodic Voronoi diagrams with a very large number of grains (10,000 – 100,000), based on through-thickness microstructural characterization by Electron Backscatter Diffraction (EBSD). The set of 10 RVEs is used in 3D Finite Difference simulations where grains are included individually and modelled as single crystals with specific orientations. The wave propagation of the S0 and SH0 modes is simulated. An inversion scheme has been developed to estimate a large number of components of the stiffness matrix from a velocity profile. Results Velocity profiles obtained from simulations are compared with those from measurements. For each sample, the results are very similar. The inversion scheme has been tested on simulations and applied to measurements from the IF samples. Results indicate that an acceptable accuracy can be achieved, although not all components are resolved equally well in the measurements. Conclusions The proposed inversion scheme enables the estimation of all relevant stiffness tensor components from a Lamb wave velocity profile with sufficient accuracy.

Novel acoustic radiation force optical coherence elastography based on ultrasmall ultrasound transducer for biomechanics evaluation of in vivo cornea.

We developed a novel acoustic radiation force optical coherence elastography (ARF-OCE) based on an ultrasmall ultrasound transducer for quantitative biomechanics evaluations of in vivo cornea. A custom single-sided meta-ultrasonic transducer with an outer diameter of 1.8 mm, focal spot diameter of 1.6 mm, central frequency of 930 kHz, and focal length of 0.8 mm was applied to excite the sample. The sample arm of the ARF-OCE system employed a three-dimensional printed holder that allowed for ultrasound excitation and ARF-OCE detection. The phase-resolved algorithm was combined with a Lamb wave model to depth-resolved evaluate corneal biomechanics after keratoconus and cross-linking treatments (CXL). The results showed that, compare to the healthy cornea, the Lamb wave velocity was significantly reduced in the keratoconus, increased in the cornea after CXL, and increased with cross-linked irradiation energy in the cornea. These results indicated the good clinical translation potential of the proposed novel ARF-OCE.

Air-Coupled Ultrasound Sealing Integrity Inspection Using Leaky Lamb Waves in a Simplified Model of a Lithium-Ion Pouch Battery: Feasibility Study.

Inspecting the sealing integrity of lead tabs is an important means of ensuring the reliability and safety of pouch-type lithium-ion (Li-ion) batteries with a thin multi-layered aluminum (Al) laminated film. This paper presents a new air-coupled ultrasonic non-destructive testing (NDT) inspection method based on leaky Lamb wave transmission; and reception for evaluating the sealing integrity between the lead tab and the Al pouch film. The proposed method uses the critical incidence angle between the air and the layer with the fastest Lamb wave velocity to maximize the signal-to-noise ratio in the through-transmission mode. To determine the critical incidence angle, phantom experiments with two test pieces (i.e., an Al tab and an Al tab sealed with an Al pouch film) are conducted. In addition, 2D scans are performed at various incidence angles for an inhouse pouch-type Li-ion battery with a 1-mm-wide foreign material inserted as a defect. At the critical incidence angle (i.e., 22°), the proposed air-coupled ultrasonic NDT method in through-transmission mode successfully identifies the shape and location of the defect through c-scan image reconstruction. These preliminary results indicate that the proposed air-coupled ultrasonic NDT method with leaky Lamb waves can be used to inspect the sealing integrity of Li-ion pouch batteries in dry test conditions.

A dynamic criterion for failure probability prediction of GFRP laminates using Lamb wave velocity with improved accuracy and consistency

This paper presents a dynamic criterion for improving the performance on fatigue life and failure probability prediction of GFRP laminates using Lamb wave velocity. A statistic damage model is built upon a Lamb wave velocity degradation model by introducing a normal distributed random variable to represent the uncertainties. The posterior distributions of the model parameters are obtained by Bayesian inference and Metropolis-Hastings algorithm with noninformative and informative prior distributions. Most importantly, a dynamic criterion is proposed to obtain a specimen-specific failure threshold value based on an assumption that the critical damage stage (CDS) of each specimen differs due to the randomicity of initial flaws. Experimental validation is conducted to compare the predicted fatigue life with both the dynamic criterion and traditional static criterion. The results show that applications of the dynamic criterion can improve the predicting accuracy and consistency, especially during early stages when available data is limited.

Corneal Lamb wave imaging for quantitative assessment of collagen cross-linking treatment based on comb-push ultrasound shear elastography

Keratoconus, a serious corneal disorder, often causes highly irregular astigmatism and different degrees of visual impairment. Riboflavin/UVA corneal collagen cross-linking(CXL) is currently approved for effective treatment of keratoconus by enhancing the mechanical strength of collagen fibers in the cornea. However, few methods are capable of quantitatively and non-destructively assessing the mechanical properties of the cornea before and after CXL treatments. This study developed a corneal viscoelasticity imaging method based on comb-push ultrasound shear elastography (CUSE) and implemented this method on a Verasonics™ Vantage 256 ultrasound open system with a high-frequency linear array ultrasound transducer. Push beams were generated by three teeth each consisting of 10 elements (working frequency = 10.41 MHz) for inducing Lamb wave propagation in the cornea, and then the system immediately switched to the plane wave imaging mode using 60 elements in the middle (working frequency = 18 MHz). This method can provide a high-resolution 2D Lamb wave velocity image overlapping with a B-mode image as well as quantitative viscoelasticity estimation according to experimentally obtained phase velocity dispersion of Lamb waves. The validation experiments were performed on ex vivo porcine corneas, and the accuracy of elasticity estimation was verified by a tensile test. The results showed that the shear elasticity increased and the viscosity decreased after CXL treatment. The shear elasticity results (reported as mean ± standard deviation) of one control group with no CXL treatment and three CXL-treated groups named as 10 min, 30 min, and 60 min groups according to UV irradiation time were 14.62 ± 3.38 kPa, 49.47 ± 3.63 kPa, 116.54 ± 23.99 kPa, and 197.89 ± 39.64 kPa, respectively, which was in agreement with the results of tensile tests. The ultrasound safety measurement indicated that this method could have acceptable safety, but further to ocular tissue and vision function. The study demonstrated the possibility of using a commercial ultrasound system to obtain high-resolution images of corneal mechanical properties as well as the ability to quantify changes induced by CXL treatment. Therefore, the proposed method could serve as a helpful tool in the studies related in corneal biomechanics.

A nondestructive guided wave propagation method for the characterization of moisture-dependent viscoelastic properties of wood materials

The in-situ monitoring and characterization of the mechanical properties of wood and timber materials is of great importance due to their broad structural applications. The purpose of this study was to propose a nondestructive method to assess the moisture-dependent viscoelastic behavior of structural wood using the guided Lamb wave propagation. Twelve green poplar wood specimens with different moisture content (MC) underwent the Lamb wave propagation tests and the wave characteristics were acquired. The viscoelastic properties of the wood specimens, including the shear storage and shear loss moduli and the loss factor, were then estimated through the solution of the corresponding inverse Lamb wave propagation problem using the experimentally measured Lamb wave characteristics. The structural stiffness and damping of wood specimens were affected by their MC, as the Lamb wave amplitude and velocity significantly decreased with MC. While the shear storage modulus decreased with MC, the shear loss modulus and loss factor increased with MC, resulting in a higher viscoelastic behavior. The loss factor of the wood specimens was estimated to be between 5.88% and 8.49% for different classes of MC, showing an increase of 44% with MC. The Lamb wave propagation method offers a strong tool for nondestructive characterization of the viscoelastic properties of wood materials and structures over a broad MC range. Wood materials show a significant viscoelastic behavior which is highly impacted by their MC. The loss factor can play an important role in the characterization and classification of structural wood and timber with different MC.

Prediction of the mechanical properties of wood using guided wave propagation and machine learning

Accurate nondestructive prediction of the mechanical properties of wood is a critical quality control task for timber grading. Currently, the ultrasonic wave method is widely used for this purpose, which overestimates the static mechanical properties of wood. To resolve this challenge, this paper proposes a robust machine learning-based model for predicting the modulus of elasticity (MOE) and modulus of rupture (MOR) of wood with varying moisture content (MC) using the guided Lamb wave propagation method. It combines the Lamb wave velocity with the “group method of data handling” to predict the mechanical properties of wood. The effect of MC and density on the Lamb wave velocity and the mechanical properties of seventy green poplar wood specimens were analyzed and discussed. It was shown that the Lamb wave velocity is highly sensitive to the MC, density, and mechanical properties of wood. It enables the guided Lamb wave propagation to be used as a reliable method for nondestructive timber characterization. The MOE and MOR of wood specimens predicted by the developed machine learning model were compared with those from the three-point bending tests, and the obtained accuracy was revealed to be higher than that obtained in the literature using the conventional ultrasonic method. It was concluded that the proposed combined Lamb wave propagation and machine learning method offers a strong tool for nondestructive prediction of the mechanical properties of wood.

Lamb wave propagation method for nondestructive characterization of the elastic properties of wood

Nondestructive evaluation (NDE) of the mechanical properties of structural wood is of great importance for quality control purposes in wood industries and construction applications. The currently used ultrasonic and stress wave methods fail to accurately estimate the elastic properties of wood. The present study aimed to propose an NDE method for accurate characterization of the elastic properties of wood using the Lamb wave propagation method. Lamb wave propagation and mechanical three-point-bending tests were performed on the green poplar wood specimens with different moisture content (MC) levels. The fundamental antisymmetric Lamb wave mode was propagated in specimens using an ultrasonic actuator, and an ultrasonic sensor was used to acquire the wave signal at different locations of the specimens along the propagation direction. The Lamb wave velocity was measured for the wood specimens with different MC and found to be in very good agreement with those from semi-analytically obtained dispersion curves. Afterwards, the corresponding inverse Lamb wave propagation problem was solved and the modulus of elasticity (MOE) of the specimens was estimated. The maximum difference between the MOE calculated by the proposed Lamb wave propagation method and that measured from the three-point bending test was less than 2%, proving the validity of the proposed method for nondestructive characterization of wood.

Fatigue life prediction of GFRP laminates using averaged Bayesian predictive distribution and Lamb wave velocity

This paper presents a fatigue life prediction approach for GFRP laminates using laser ultrasonic technique for data acquisition and a hierarchical Bayesian model for damage characterization as well as life prediction. Fatigue damage is measured as the degradation of the Lamb wave velocity and described using a scalar damage variable. Due to the complexity of the damage mechanisms involved in the fatigue process and the difficulties in distinguishing different damage modes, i.e. fiber breakage, matrix cracks and delamination, from a single damage variable, multiple degradation models of various levels of complexity are proposed to form a meta-model. Bayesian inference is applied to obtain the distributions of model parameters to include uncertainty information. Then a stacking approach is applied to average the predictive distributions to obtain the optimal combination of each sub-model to generate a meta-prediction with the least diverge from the experimental observation. Experimental results of both traditional stiffness data and Lamb wave velocity data are used for validation. A credible interval (CI) based criterion is also proposed for fatigue life prediction, where consistent results are achieved with reasonable use of informative priors.

Surface effects on frequency dispersion characteristics of Lamb waves in a nanoplate

Dispersion of Lamb waves in a nanoplate where surface effects exist is investigated in this work by combining the wave theory with the surface elasticity theory. The frequency dispersion equations of the symmetric and the anti-symmetric modes are derived and numerically solved. It is found that surface effects give rise to the thickness-dependent frequency dispersion, and that the phase velocity of Lamb waves increases with the decrease of the plate thickness. Two surface elastic constants featuring surface effects in terms of the surface elasticity theory exhibit significant influence on the wave frequency dispersion in the nanoplate. The larger the surface elastic constants, the higher the wave phase velocity. Moreover, the impact of surface effects is more prominent for the symmetric Lamb waves within the low frequency range. In particular, the symmetric Lamb wave velocity of the fundamental mode can be correlated to the surface elastic constants and the plate thickness when the wave frequency tends to zero. Finally, based on the frequency dispersion characteristics of the symmetric Lamb waves, an analytical expression is given to determine the surface elastic constants according to the wave phase velocity.

Peridynamic modeling of Lamb wave propagation in bimaterial plates

In this study the nonlocal bond-based peridynamic (PD) theory was applied to simulate Lamb wave transmission in 2D bimaterial plates. Plates of unlike materials were jointed end-to-end to make a bimaterial plate. The surface of the plate was then excited tangentially by single-frequency and multi-frequency force signals. The influence of changing material properties on travelling of the symmetric and antisymmetric Lamb waves were studied in detail. The phase and group velocities of travelling wave in bimaterial plates were calculated and it was found that dissimilar material properties of two joint plates can significantly alter the amplitude and arrival time of the wave. Moreover, Fast Fourier Transform (FFT) of the time history of symmetric Lamb wave velocity was calculated and verified. Accuracy and consistency of PD wave model was confirmed entirely using Spectral Finite Element Method (SFEM). The comparison between the results of two applied methods shows a good agreement.

Effects of debonding on Lamb wave propagation in a bonded composite structure under variable temperature conditions

Bonded composite structures are a special type of sandwich-like structures in which multiple carbon-fibre laminates are bonded with adhesives, and debonding can appear at the bond layer due to variable loading and uncertain operating conditions. This study aims to investigate the debonding effects on Lamb wave propagation in a bonded composite structure under variable ambient temperature conditions. In the process, a combined theoretical analysis, time-domain spectral element simulation and experimental analysis of elastic wave propagation in a carbon-fibre reinforced adhesively-bonded composite structure have been carried out. It is shown that theoretical analysis and spectral formulation are effectively able to capture the behaviour of Lamb modes in the healthy structure due to variations in ambient temperature. It is found that the primary anti-symmetric Lamb wave mode amplitude and velocity decrease with an increase in ambient temperature. Furthermore, the spectral formulation accurately captures the effects of debonding on the Lamb wave signals under variable temperature conditions that are consistent with the experimental results. Finally, temperature correction factors are proposed for the primary anti-symmetric mode velocity and amplitude difference calculations and the effectiveness of the factors is successfully verified for selected study cases.

Characterization of fatigue damages in composite laminates using Lamb wave velocity and prediction of residual life

In this paper, the S0-mode Lamb wave phase velocity at low frequency range is chosen to characterize fatigue damages accumulated in composite laminates under cyclic loadings. A stiffness/velocity degradation model is proposed based on three distinctive damage mechanisms: fiber breaks, matrix cracks and delamination, all of which are always involved in fatigue damage process. In order to reduce the complexity of the damage model, fiber damage is treated as an independent damage and delamination is coupled with matrix cracks. An approximation of shear-lag model is then proposed to avoid any direct measurements of crack density for it is highly impractical in real applications. Following this, energy release rate for formation of matrix cracks is extracted based on measured phase velocity and damage evolution is realized by incorporating a modified Paris law. Controlled fatigue experiments were conducted where in-situ phase velocity was measured by a laser ultrasonic system. The fatigue damages were then characterized using the proposed damage model with the measured velocity. Finally, the ability of proposed model to predict residual lives was also validated and good accuracy has been obtained.

Higher order acoustoelastic Lamb wave propagation in stressed plates.

Modeling and experiments are used to investigate Lamb wave propagation in the direction perpendicular to an applied stress. Sensitivity, in terms of changes in velocity, for both symmetrical and anti-symmetrical modes was determined. Codes were developed based on analytical expressions for waves in loaded plates and they were used to give wave dispersion curves. The experimental system used a pair of compression wave transducers on variable angle wedges, with set separation, and variable frequency tone burst excitation, on an aluminum plate 0.16 cm thick with uniaxial applied loads. The loads, which were up to 600 με, were measured using strain gages. Model results and experimental data are in good agreement. It was found that the change in Lamb wave velocity, due to the acoustoelastic effect, for the S1 mode exhibits about ten times more sensitive, in terms of velocity change, than the traditional bulk wave measurements, and those performed using the fundamental Lamb modes. The data presented demonstrate the potential for the use of higher order Lamb modes for online industrial stress measurement in plate, and that the higher sensitivity seen offers potential for improved measurement systems.

A facility for measuring the thickness of thin metal films

A facility is described for measuring the thickness of a thin metal film. A measurement method is proposed that is based on the dependence of the phase velocity of harmonic antisymmetric Lamb waves that propagate along the film on the film thickness. A continuous method for excitation of acoustic waves has been applied to velocity measurements. It makes it possible to eliminate the effect of dispersion of the Lamb-wave velocity on the measurement accuracy.

Using Lamb Waves to Monitor Moisture Absorption in Thermally Fatigued Composite Laminates

Nondestructive evaluation for material health monitoring is important in aerospace industries. Composite laminates are exposed to heat cyclic loading and humid environment depending on flight conditions. Cyclic heat loading and moisture absorption may lead to material degradation such as matrix breaking, debonding, and delamination. In this paper, the moisture absorption ratio was investigated by measuring the Lamb wave velocity. The composite laminates were manufactured and subjected to different thermal aging cycles and moisture absorption. For various conditions of these cycles, not only changes in weight and also ultrasonic wave velocity were measured, and the Lamb wave velocity at various levels of moisture on a carbon-epoxy plate was investigated. Results from the experiment show a linear correlation between moisture absorption ratio and Lamb wave velocity at different thermal fatigue stages. The presented method can be applied as an alternative solution in the online monitoring of composite laminate moisture levels in commercial flights.

Characterization of Degradation Progressive in Composite Laminates Subjected to Thermal Fatigue and Moisture Diffusion by Lamb Waves.

Laminate composites which are widely used in the aeronautical industry, are usually subjected to frequency variation of environmental temperature and excessive humidity in the in-service environment. The thermal fatigue and moisture absorption in composites may induce material degradation. There is a demand to investigate the coupling damages mechanism and characterize the degradation evolution of composite laminates for the particular application. In this paper, the degradation evolution in unidirectional carbon/epoxy composite laminates subjected to thermal fatigue and moisture absorption is characterized by Lamb waves. The decrease rate of Lamb wave velocity is used to track the degradation evolution in the specimens. The results show that there are two stages for the progressive degradation of composites under the coupling effect of thermal cyclic loading and moisture diffusion. The present work provides an alternative to monitoring the degradation evolution of in-service aircraft composite Laminates.

Novel Dispersion Curves Extraction Method for Waveguides Affected by Nonuniform Transient Temperature Field

Guided waves sensitivity to environmental and operational conditions, especially temperature fluctuations, is one of the major problems when the method is considered for real engineering applications. The aim of this paper is to propose a novel dispersion curves extraction method for waveguides affected by nonuniform transient temperature field. Essentially, the method is based on a simple and robust approach, consisting in a few series of modal analyses for a representative part of the inspected structure. To consider the effect of temperature, a thermal stress calculation based on finite element method is presented. In this way, for different wave lengths, the mode shapes and corresponding natural frequencies can be obtained by solving some thermal-eigenvalue problems. To test the theoretical thermal effect of the dispersion curves a experiment on an isotropic plate is conducted. Those theoretical dispersion curves, consisting of only dominant modes, are compared with dispersion curves obtained from experiment. Finally, this method is used to extract the dispersion curves of the aero-engine casing considering the nonuniform temperature field. The results not only give us insight to how temperature affects Lamb wave velocities in different frequency ranges but also will help those extracting dispersion curves for waveguides affected by nonuniform transient temperature field.

Theoretical and Experimental Estimation of Lamb Wave Velocity in Plates Using Distributed Lead Zirconate Titanate Sensors

Theoretical and Experimental Estimation of Lamb Wave Velocity in Plates Using Distributed Lead Zirconate Titanate Sensors