Computing leaky Lamb waves for waveguides between elastic half-spaces using spectral collocation.

In non-destructive evaluation guided wave inspections, the elastic structure to be inspected is often embedded within other elastic media and the ensuing leaky waves are complex and non-trivial to compute; we consider the canonical example of an elastic waveguide surrounded by other elastic materials that demonstrates the fundamental issues with calculating the leaky waves in such systems. Due to the complex wavenumber solutions required to represent them, leaky waves pose significant challenges to existing numerical methods, with methods that spatially discretise the field to retrieve them suffering from the exponential growth of their amplitude far into the surrounding media. We present a spectral collocation method yielding an accurate and efficient identification of these modes, leaking into elastic half-spaces. We discretise the elastic domains and, depending on the exterior bulk wavespeeds, select appropriate mappings of the discretised domain to complex paths, in which the numerical solution decays and the physics of the problem are preserved. By iterating through all possible radiation cases, the full set of dispersion and attenuation curves are successfully retrieved and validated, where possible, against the commercially available software disperse. As an independent validation, dispersion curves are obtained from finite element simulations of time-dependent waves using Fourier analysis.

Attenuation of Rayleigh waves due to three-dimensional surface roughness: A comprehensive numerical evaluation.

The phenomenon of Rayleigh wave attenuation due to surface roughness has been well studied theoretically in the literature. Three scattering regimes describing it have been identified-the Rayleigh (long wavelength), stochastic (medium wavelength), and geometric (short wavelength)-with the attenuation coefficient exhibiting a different behavior in each. Here, in an extension to our previous work, we gain further insight with regard to the existing theory, in three dimensions, using finite element (FE) modeling, under a unified approach, where the same FE modeling techniques are used regardless of the scattering regime. We demonstrate good agreement between our FE results and the theory in all scattering regimes. Additionally, following this demonstration, we extend the results to cases that lie outside the limits of validity of the theory.

Appraising scattering theories for polycrystals of any symmetry using finite elements.

This paper uses three-dimensional grain-scale finite-element (FE) simulations to appraise the classical scattering theory of plane longitudinal wave propagation in untextured polycrystals with statistically equiaxed grains belonging to the seven crystal symmetries. As revealed from the results of 10 390 materials, the classical theory has a linear relationship with the elastic scattering factor at the quasi-static velocity limit, whereas the reference FE and self-consistent (SC) results generally exhibit a quadratic relationship. As supported by the results of 90 materials, such order difference also extends to the attenuation and phase velocity, leading to larger differences between the classical theory and the FE results for more strongly scattering materials. Alternatively, two approximate models are proposed to achieve more accurate calculations by including an additional quadratic term. One model uses quadratic coefficients from quasi-static SC velocity fits and is thus symmetry-specific, while the other uses theoretically determined coefficients and is valid for any individual material. These simple models generally deliver more accurate attenuation and phase velocity (particularly the second model) than the classical theory, especially for strongly scattering materials. However, the models are invalid for the attenuation of materials with negative quadratic coefficients. This article is part of the theme issue 'Wave generation and transmission in multi-scale complex media and structured metamaterials (part 1)'.

Leaky wave characterisation using spectral methods.

Leaky waves are an important class of waves, particularly for guiding waves along structures embedded within another medium; a mismatch in wavespeeds often leads to leakage of energy from the waveguide, or interface, into the medium, which consequently attenuates the guided wave. The accurate and efficient identification of theoretical solutions for leaky waves is a key requirement for the choices of modes and frequencies required for non-destructive evaluation inspection techniques. We choose a typical situation to study: an elastic waveguide with a fluid on either side. Historically, leaky waves are identified via root-finding methods that have issues with conditioning, or numerical methods that struggle with the exponential growth of solutions at infinity. By building upon a spectral collocation method, we show how it can be adjusted to find exponentially growing solutions, i.e., leaky waves, leading to an accurate, fast, and efficient identification of their dispersion properties. The key concept required is a mapping, in the fluid region, that allows for exponential growth of the physical solution at infinity, whilst the mapped numerical setting decays. We illustrate this by studying leaky Lamb waves in an elastic waveguide immersed between two different fluids and verify this using the commercially available software disperse.

Short Range Pipe Guided Wave Testing Using SH0 Plane Wave Imaging for Improved Quantification Accuracy.

Detection and criticality assessment of defects appearing in inaccessible locations in pipelines pose a great challenge for many industries. Inspection methods which allow for remote defect detection and accurate characterisation are needed. Guided wave testing (GWT) is capable of screening large lengths of pipes from a single device position, however it provides very limited individual feature characterisation. This paper adapts Plane Wave Imaging (PWI) to pipe GWT to improve defect characterization for inspection in nearby locations such as a few metres from the transducers. PWI performance is evaluated using finite element (FE) and experimental studies, and it is compared to other popular synthetic focusing imaging techniques. The study is concerned with part-circumferential part-depth planar cracks. It is shown that PWI achieves superior resolution compared to the common source method (CSM) and comparable resolution to the total focusing method (TFM). The techniques involving plane wave acquisition (PWI and CSM) are found to substantially outperform methods based on full matrix capture (FMC) in terms of signal-to-noise ratio (SNR). Therefore, it is concluded that PWI which achieves good resolution and high SNR is a more attractive choice for pipe GWT, compared to other considered techniques. Subsequently, a novel PWI transduction setup is proposed, and it is shown to suppresses the transmission of unwanted S0 mode, which further improves SNR of PWI.

Attenuation of Rayleigh waves due to surface roughness.

Rayleigh waves are well known to attenuate due to scattering when they propagate over a rough surface. Theoretical investigations have derived analytical expressions linking the attenuation coefficient to statistical surface roughness parameters, namely, the surface's root mean squared height and correlation length and the Rayleigh wave's wavenumber. In the literature, three scattering regimes have been identified-the geometric (short wavelength), stochastic (short to medium wavelength), and Rayleigh (long wavelength) regimes. This study uses a high-fidelity two-dimensional finite element (FE) modelling scheme to validate existing predictions and provide a unified approach to studying the problem of Rayleigh wave scattering from rough surfaces as the same model can be used to obtain attenuation values regardless of the scattering regime. In the Rayleigh and stochastic regimes, very good agreement is found between the theory and FE results both in terms of the absolute attenuation values and for asymptotic power relationships. In the geometric regime, power relationships are obtained through a combination of dimensional analysis and FE simulations. The results here also provide useful insight into verifying the three-dimensional theory because the method used for its derivation is analogous.

Investigation of guided wave propagation in pipes fully and partially embedded in concrete.

The application of long-range guided-wave testing to pipes embedded in concrete results in unpredictable test-ranges. The influence of the circumferential extent of the embedding-concrete around a steel pipe on the guided wave propagation is investigated. An analytical model is used to study the axisymmetric fully embedded pipe case, while explicit finite-element and semi-analytical finite-element simulations are utilised to investigate a partially embedded pipe. Model predictions and simulations are compared with full-scale guided-wave tests. The transmission-loss of the T(0,1)-mode in an 8 in. steel pipe fully embedded over an axial length of 0.4 m is found to be in the range of 32-36 dB while it reduces by a factor of 5 when only 50% of the circumference is embedded. The transmission-loss in a fully embedded pipe is mainly due to attenuation in the embedded section while in a partially embedded pipe it depend strongly on the extent of mode-conversion at entry to the embedded-section; low loss modes with energy concentrated in the region of the circumference not-covered with concrete have been identified. The results show that in a fully embedded pipe, inspection beyond a short distance will not be possible, whereas when the concrete is debonded over a fraction of the pipe circumference, inspection of substantially longer lengths may be possible.

On the dimensionality of elastic wave scattering within heterogeneous media.

Elastic waves scatter when the wavelength becomes comparable to random spatial fluctuations in the elastic properties of the propagation medium. It is postulated that within the long-wavelength Rayleigh regime, the scattering induced attenuation obeys a D = 1,2,3 dimensional dependence on wavenumber, kD+1, whilst within the shorter-wavelength stochastic regime, it becomes independent of the dimensions and thus varies as k2. These predictions are verified numerically with a recently developed finite element method in three dimensions (3D), two dimensions (2D), and one dimension (1D), for the example of ultrasonic waves propagating within polycrystalline materials. These findings are thought to be practically useful given the increasing uptake of numerical methods to study highly scattering environments which exhibit multiple scattering, but often remain limited to 2D given computational constraints. It is hoped that these results lay the groundwork for eventually producing computationally efficient 2D simulations that are representative of 3D.

Finite element modelling of elastic wave scattering within a polycrystalline material in two and three dimensions.

Finite element modelling is a promising tool for further progressing the development of ultrasonic non-destructive evaluation of polycrystalline materials. Yet its widespread adoption has been held back due to a high computational cost, which has restricted current works to relatively small models and to two dimensions. However, the emergence of sufficiently powerful computing, such as highly efficient solutions on graphics processors, is enabling a step improvement in possibilities. This article aims to realise those capabilities to simulate ultrasonic scattering of longitudinal waves in an equiaxed polycrystalline material in both two (2D) and three dimensions (3D). The modelling relies on an established Voronoi approach to randomly generate a representative grain morphology. It is shown that both 2D and 3D numerical data show good agreement across a range of scattering regimes in comparison to well-established theoretical predictions for attenuation and phase velocity. In addition, 2D parametric studies illustrate the mesh sampling requirements for two different types of mesh to ensure modelling accuracy and present useful guidelines for future works. Modelling limitations are also shown. It is found that 2D models reduce the scattering mechanism in the Rayleigh regime.

Fatigue state characterisation of steel pipes using ultrasonic shear waves.

The phenomenon of the reduction in the propagation speed of an ultrasonic wave when it travels through a fatigue zone has been well studied in the literature. Additionally, it has been established that shear waves are more severely affected by the presence of such a zone, compared with longitudinal waves. Our study utilises these phenomena to develop a method able to characterise the fatigue state of steel pipes. Initially, the existing theory regarding the increased sensitivity of shear waves to the presence of fatigue is validated through measuring and comparing the change in propagation speed of both longitudinal and bulk shear waves on flat geometries, at different fatigue states. The comparison is achieved with the aid of ultrasonic speed C-scans of both longitudinal and shear waves, with the latter now being obtainable through our implementation of advances in Electromagnetic Acoustic Transducers (EMAT) technology. EMATs have not been traditionally used for producing C-scans, and their ability do to so with adequate repeatability is demonstrated here; we show that shear wave scanning with EMATs now provides a possibility for inspection of fatigue damage on the inner surface of pressure-containing components in the nuclear power industry. We find that the change in ultrasonic wave speed is amplified when shear waves are used, with the magnitude of this amplification agreeing well with the theory. Following the verification of the theory, the use of EMATs allowed us to tailor the shear wave scanning method to pipe geometries, where C-scans with conventional piezoelectric transducers would not have been possible, with the results successfully revealing the presence of fatigue zones.

Finite-element and semi-analytical study of elastic wave propagation in strongly scattering polycrystals.

This work studies scattering-induced elastic wave attenuation and phase velocity variation in three-dimensional untextured cubic polycrystals with statistically equiaxed grains using the theoretical second-order approximation (SOA) and Born approximation models and the grain-scale finite-element (FE) model, pushing the boundary towards strongly scattering materials. The results for materials with Zener anisotropy indices A > 1 show a good agreement between the theoretical and FE models in the transition and stochastic regions. In the Rayleigh regime, the agreement is reasonable for common structural materials with 1 < A < 3.2 but it deteriorates as A increases. The wavefields and signals from FE modelling show the emergence of very strong scattering at low frequencies for strongly scattering materials that cannot be fully accounted for by the theoretical models. To account for such strong scattering at A > 1, a semi-analytical model is proposed by iterating the far-field Born approximation and optimizing the iterative coefficient. The proposed model agrees remarkably well with the FE model across all studied materials with greatly differing microstructures; the model validity also extends to the quasi-static velocity limit. For polycrystals with A < 1, it is found that the agreement between the SOA and FE results is excellent for all studied materials and the correction of the model is not needed.

How does grazing incidence ultrasonic microscopy work? A study based on grain-scale numerical simulations.

Grazing incidence ultrasonic microscopy (GIUM) is an experimental method for visualising the microstructures of polycrystals with local preferential orientations. It has previously been demonstrated on an austenitic stainless steel weld, exposing grains much smaller than the propagating wavelength, but the physical mechanism of the method has only been proposed as a hypothesis. In this paper, we use grain-scale finite element simulations based on the EBSD measurements to verify the principles behind GIUM images further and to assess how deep does the method penetrate the component under examination. The simulations indicate that while lateral contraction of grains contains microstructure signatures, the free surface effect is the crucial factor contributing to the generation of the images. Further, we show that only features up to the depth in the order of the average grain size in that direction can be visualised.

Can ultrasound attenuation measurement be used to characterise grain statistics in castings?

Industrial inspection protocols are qualified using mock-ups manufactured according to the same procedure as the plant part. For coarse-grained castings, known for their low inspectability, relying on mock-ups becomes particularly challenging owing to the variability of grain properties among components. Consequently, there is a keen interest in the capability to verify whether the grain size of the component under test matches the qualification specification in-situ. This paper investigates the potential of an attenuation measurement for assessing the ultrasonic inspectability of coarse-grained components using qualified procedures in a practical setting. The experimental part of the study focuses on an industrial Inconel 600 mock-up with spatially varying attenuation, measured across the entire sample in an immersion tank. Three zones with distinctly different attenuations were examined using metallography, which allowed for calculating classical grain size histograms and two-point correlation functions. For one of the zones, we synthesised the microstructure with the same statistical properties numerically and simulated the propagation of ultrasound using a grain-scale finite element model. The results showed good agreement with the experiment, and lead to several suggestions for the reasons for the discrepancy, the varying grain size statistics being the most likely. A parametric study, which followed, depicted the effect of the mean and standard deviation-to-mean ratio of the log-normal grain size distribution on the attenuation of ultrasound and its frequency dependence. Most notably, we demonstrated the known non-uniqueness of the relationship between the log-normal grain size distribution parameters and the attenuation. We suggested that the correlation length calculated from a single exponential fit to the two-point correlation function is a more robust metric describing grain statistics for this context, which can be obtained from attenuation. The correlation lengths estimated from measured attenuation using the second-order approximation model for the three zones of the studied mock-up yielded results of acceptable accuracy. We concluded that this metric could replace the average grain size in practical settings, as it retains more statistical information than the mean grain size and allows for linking measurements to the established theoretical attenuation models which this paper demonstrates.

A Guided Wave Inspection Technique for Wedge Features.

Numerous engineering components feature prismatic wedge-like structures that require nondestructive evaluation (NDE) in order to ensure functionality or safety. This article focuses on the inspection of the wedge-like seal fins of a jet engine drum, though the capabilities presented will be generic. It is proposed that antisymmetric flexural edge modes, feature-guided waves localized to the wedge tips, may be used for defect detection. Although analytical solutions exist that characterize the ultrasonic behavior of ideal wedges, in practice, real wedges will be irregular (containing, for example, truncated tips that are built onto an associated structure or have nonstraight edges), and therefore, generic methodologies are required to characterize wave behavior in nonideal wedges. This article uses a semianalytical finite-element (SAFE) methodology to characterize the guided waves in wedge-like features with irregular cross sections to assess their suitability for NDE inspection and compare them with edge modes in ideal wedges. The science and methodologies required in this article are necessary to select an appropriate operating frequency for the particular application at hand. In addition, this article addresses the practical challenge of excitation and detection of flexural edge modes by presenting a piezoelectric-based dry-coupled transducer system suitable for pulse-echo operation. This article, therefore, presents the scientific basis required for industrial exploitation, together with the practical tools that facilitate use. The study concludes with the experimental demonstration of the edge wave-based inspection of a seal fin, achieving a signal-to-noise ratio of 28 dB from a 0.75-mm radial tip defect.

Sizing Subwavelength Defects With Ultrasonic Imagery: An Assessment of Super-Resolution Imaging on Simulated Rough Defects.

There is a constant drive within the nuclear power industry to improve upon the characterization capabilities of current ultrasonic inspection techniques in order to improve safety and reduce costs. Particular emphasis has been placed on the ability to characterize very small defects which could result in extended component lifespan and help reduce the frequency of in-service inspections. Super-resolution (SR) algorithms, also known as sampling methods, have been shown to demonstrate the capability to resolve scatterers separated by less than the diffraction limit when deployed in representative inspections and therefore could be used to tackle this issue. In this paper, the factorization method (FM) and the Time Reversal Multiple-Signal-Classification (TR-MUSIC) algorithms are applied to the simulated ultrasonic array inspection of small rough embedded planar defects to establish their characterization capabilities. Their performance was compared to the conventional total focusing method (TFM). A full 2-D finite-element (FE) Monte Carlo modeling study was conducted for defects with a range of sizes, orientations, and magnitude of surface roughness. The results presented show that for subwavelength defects, both the FM and TR-MUSIC algorithms were able to size and estimate defect orientation accurately for smooth cases and, for rough defects, up to a roughness of 100 [Formula: see text]. This level of roughness is representative of the thermal fatigue defects encountered in the nuclear power sector. This contrasted with the relatively poor performance of TFM in these cases which consistently oversized these defects and could not be used to estimate the defect orientation, making through-wall sizing with this method impossible.

Measurement of the properties of fluids inside pipes using guided longitudinal waves.

A new technique for measuring the longitudinal bulk velocity and shear viscosity of a fluid contained inside a pipe without a need for extracting a sample from inside of the pipe is presented. It is based on the measurement of the change of the dispersion properties and attenuation of longitudinal guided modes propagating in the pipe due to the presence of the fluid. The technique to extract longitudinal bulk velocity and shear viscosity is discussed and experimentally demonstrated by measuring both low-viscosity (distilled water and glycerol) and highly viscous fluids. The measured properties of glycerol agreed well with conventional methods and literature data for both the longitudinal bulk velocity (within 0.8%) and the viscosity (within 4%). For highly viscous fluid, the accuracy of the velocity measurement was found to be reduced slightly (within 1%), and the viscosity measurement became more accurate (within 1%).

On the development and testing of a guided ultrasonic wave array for structural integrity monitoring.

The prototype of a guided ultrasonic wave array for the structural integrity monitoring of large, plate-like structures has been designed, built, and tested. The development of suitably small transducers for the excitation and measurement of the first antisymmetric Lamb wave mode Ao is described. The array design consists of a ring of 32 transducers, permanently bonded to the structure with a protective membrane, in a compact housing with the necessary multiplexing electronics. Using a phased addition algorithm with dispersion compensation and deconvolution in the wavenumber domain, a good dynamic range can be achieved with a limited number of transducers. Limitations in the transducer design and manufacture restricted the overall dynamic range achieved to 27 dB. Laboratory measurements for a steel plate containing various defects have been performed. The results for standard defects are compared to theoretical predictions and the sensitivity of the array device for defect detection has been established. Simulated corrosion pitting and a defect cut with an angle grinder simulating general corrosion were detected.

Experimental Studies of the Inspection of Areas With Restricted Access Using A0 Lamb Wave Tomography.

Corrosion damage in inaccessible regions presents a significant challenge to the petrochemical industry, and determining the remaining wall thickness is important to establish the remaining service life. Guided wave tomography is one solution to this and involves transmitting Lamb waves through the area of interest and, subsequently, using the received signals to reconstruct a thickness map of the remaining wall thickness. This avoids the need to access all points on the surface, making the technique well suited to inspection for areas with restricted access. The influence of these areas onto the ability to detect and size surface conditions, such as corrosion damage, using guided wave tomography is assessed. For that, a guided wave tomography system is employed, which is based on low-frequency A0 Lamb waves that are excited and detected with two arrays of electromagnetic acoustic transducers. Two different defect depths are considered with different contrasts relative to the nominal wall thickness, both of which are smoothly varying and well-defined. The influence of areas with restricted surface access, support locations, pipe clamps, and STOPAQ(R) coatings is experimentally tested, and their influence assessed through comparison to a baseline reconstruction without the respective restriction in place, demonstrating only a small influence on the detected value of the remaining wall thickness.

The excitation and detection of lamb waves with planar coil electromagnetic acoustic transducers.

Planar coil electromagnetic acoustic transducers (EMATs) are investigated for the excitation and detection of Lamb waves in nonferromagnetic metallic wave-guides. Such EMATs are attractive for certain applications due to their omni-directional sensitivity to wave modes with predominantly in-plane surface displacement, such as the So Lamb wave mode. A model is developed that enables the modal content of the radiated Lamb wave field from a transmitting EMAT to be calculated, and the output voltage from a receiving EMAT to be predicted when a Lamb wave mode is incident on it. The predictions from this model are compared with experimental data obtained from 12 different EMATs tested on a 5-mm thick aluminum plate, and good agreement is obtained. The model then is used to analyze the different effects that contribute to the overall Lamb wave modal sensitivity of an EMAT. The relationship between coil geometry and wavelength is examined.

Improved detection of rough defects for ultrasonic nondestructive evaluation inspections based on finite element modeling of elastic wave scattering.

Defects which possess rough surfaces greatly affect ultrasonic wave scattering behavior, usually reducing the magnitude of reflected signals. Understanding and accurately predicting the influence of roughness on signal amplitudes is crucial, especially in nondestructive evaluation (NDE) for the inspection of safety-critical components. An extension of Kirchhoff theory has formed the basis for many practical applications; however, it is widely recognized that these predictions are pessimistic because of analytical approximations. A numerical full-field modeling approach does not fall victim to such limitations. Here, a finite element (FE) modeling approach is used to develop a realistic methodology for the prediction of expected backscattering from rough defects. The ultrasonic backscatter from multiple rough surfaces defined by the same statistical class is calculated for normal and oblique incidence. Results from FE models are compared with Kirchhoff theory predictions and experimental measurements to establish confidence in the new approach. At lower levels of roughness, excellent agreement is observed between Kirchhoff theory, FE, and experimental data, whereas at higher values, the pessimism of Kirchhoff theory is confirmed. An important distinction is made between the total, coherent, and diffuse signals and it is observed, significantly, that the total signal amplitude is representative of the information obtained during an inspection. This analysis provides a robust basis for a less sensitive, yet safe, threshold for inspection of rough defects.