The scattering of the fundamental torsional mode from axi-symmetric defects with varying depth profile in pipes

Application of the reciprocity principle to evaluation of mode-converted scattered shear horizontal (SH) wavefields in tapered thinning plates

The interaction of guided waves with wall thinning can be complex, depending on the thinning geometry and the frequency. At a high frequency-thickness, when a shear-horizontal (SH) guided wave mode impinges upon a tapered wall thinning region, there is mode conversion to other propagating SH modes, either in reflection or transmission, which heavily depends on the shape of the taper. In this paper, we have combined the reciprocity theorem of elastodynamics and the theory of multiple reflections, in order to analytically calculate the scattered SH wavefield in plates, due to the interaction with an arbitrary tapered thinning. The taper is discretized into several sections and the formulation is addressed in matrix notation, in order to tackle several modes which arise due to mode interconversion distributed within the taper. The method was validated with experimental and numerical data at linear tapered thinning, in the high-frequency-thickness regime. It was also applied to provide understanding of the reflection behaviour within smoother taper profiles, namely, raised-cosine and Blackman window tapers, and to visualize the propagating field of each mode. It is shown that for a linear taper profile, the reflection within the taper is virtually constant, which produces an interference pattern in the overall reflection from the whole taper. Such a mechanism is broken with smoother tapers, since they impose lower reflection close to the taper ends. The method proves itself useful for analytically investigating the scattering from arbitrary wall thinning when mode-conversion arises.

Excitation of Single-Mode Shear-Horizontal Guided Waves and Evaluation of Their Sensitivity to Very Shallow Crack-Like Defects

Inspection is a key part of the asset management process of industrial plants and there are numerous plate-like structures that require inspection. Ultrasonic guided waves have been extensively used to detect various types of defect by monitoring reflected and transmitted signals because they enable faster screening of large areas. However, ultrasonic guided wave testing becomes difficult for very shallow, sharp defects as current inspection techniques suffer from a lack of sensitivity to such features. Previous studies, obtained by comparing various inspection techniques, suggest that the SH1 mode in particular, at around 3 MHz · mm, would be suitable when testing for shallow defects; however, it is clear that both the SH0 and SH1 modes can exist at this frequency-thickness product. This can complicate the inspection process and, therefore, limit defect detectability. This article investigates the possibility of a single-mode excitation of the SH1 mode at around 3 MHz · mm. The ability of this method toward detecting very shallow defects (<10% cross-sectional thickness loss) has also been studied. By means of analytical predictions and finite element, it is shown that a signal dominated by the SH1 mode can be generated using a single permanent periodic magnet (PPM) electromagnetic acoustic transducer (EMAT) (PPM EMAT). All predictions are then backed up by experimental measurements. It is also shown that, by studying the reflection coefficient of the SH1 mode, the pure SH1 mode can be used to detect defects as shallow as 5% thickness loss from a 500-mm stand-off. These defects would otherwise be missed by standard, lower frequency guided wave testing.

Mode matching in axisymmetric fluid-filled pipes: Scattering by a flange

Long range ultrasonic testing of pipelines sends an ultrasonic wave along a pipe wall and then detects scattering from defects present. It is well known that scattering by pipe fixtures and fittings, such as a flange, can cause distortion and interfere with the ability to identify defects. This article develops a theoretical model to investigate scattering from a flange in a fluid-filled pipe with elastic walls. Mode matching is used as this is a computationally efficient way to examine long lengths of pipe and for enforcing the appropriate axial continuity conditions over area discontinuities. A recent article presented a mode matching approach for a similar problem, and it is demonstrated here that a re-casting of the equations is necessary to ensure all of the appropriate matching conditions are enforced. Mode matching predictions are also compared with an alternative point collocation approach in order to provide an independent benchmark. Excellent agreement between mode matching and point collocation is demonstrated, and reflection and transmission coefficients are generated in order to show the resonant behaviour of a flange and illustrate that its influence is significant and strongly frequency dependent.

Scattering of the Fundamental Shear Guided Wave From a Surface-Breaking Crack in Plate-Like Structures

Cracks in critical sections of steel structures pose a major safety concern in many industries. Existing high-frequency ultrasonic techniques offer high detection sensitivity to cracks but have poor inspection volume coverage, limiting their practical use for monitoring large areas of structures. Low-frequency guided waves have relatively high inspection area coverage and are currently used in pipeline monitoring for corrosion defects but face challenges in detecting critical cracks that often cause over an order of magnitude lower cross-sectional area loss. A study of scattering from small cracks in a thin-walled (<12 mm) section with an incident plane SH0 guided wave at higher frequencies but remaining below the SH1 cutoff is presented here using quasi-static approximations, the aim being to explore the possibility of using this regime for crack growth monitoring applications. A 3-D solution was developed using dimensional analysis, which showed that the SH0 reflection ratio is proportional to frequency to the power 1.5, to the effective crack size cubed, and is inversely proportional to the plate thickness and to the square root of the distance from the crack to the receiving sensor. Finite element analysis was used to validate these power coefficients and to calculate the proportionality constant. The results show that a higher inspection frequency offers improved sensitivity, but the validity of the results here is limited to the SH1 cutoff frequency. The predicted 3-D solution was validated by measurements on a pipe with a progressively grown notch.

Pure SH1 Guided-Wave Generation Method with Dual Periodic-Permanent-Magnet Electromagnetic Acoustic Transducers for Plates Inspection

High frequency guided-waves offer a trade-off between the high sensitivity of local bulk ultrasonic thickness measurements and the large area scanning of lower frequency guided-waves, so it has been a growing interest for corrosion inspection with the dispersive SH1 mode. However, according to the dispersive curve, it is hard to generate the pure SH1 mode since the non-dispersive SH0 mode will be excited simultaneously. Thus, this paper investigates a transducer design method to generate a pure SH1 guided-wave, where the dual periodic-permanent-magnet electromagnetic acoustic transducers (PPM EMATs) are placed on exactly opposite positions either side of the plate symmetrically. The suppression effect for SH0 and the enhancement effect for SH1 of the dual PPM EMATs are mainly discussed by theoretical analysis and simulation analysis, and the influence of positioning errors of PPM EMATs placed on opposite sides of the plate on its performances are analyzed. Employing the proposed dual PPM EMATs, some experiments are performed to verify the reliability of finite element simulation. The results indicate that the dual PPM EMATs can suppress the SH0 mode and generate the pure SH1 mode effectively. Moreover, the longitudinal and lateral positioning errors can affect the dual PPM EMATs performances significantly.

Development of ultrasonic guided wave inspection methodology for steam generator tubes of prototype fast breeder reactor

An ultrasonic guided wave based methodology is developed for inspection of steam generator tubes of the prototype fast breeder reactor. To this aim, axisymmetric longitudinal mode (L(0,2)) at the frequency of 250 kHz is optimized using 3D-finite element simulation and experiments. The group velocity of mode L(0,2) at 250 kHz is found to be 5387 m/s. First, the long range propagation of the L(0,2) mode at 250 kHz is examined and the mode is found to propagate over a distance of 45.6 m with a sufficiently good SNR. Secondly, the detection of multiple defects such as circumferential, axial, partial-pinholes and tapered defects lying in the same line of sight is investigated using 3D-finite element simulation and the results obtained are validated experimentally for the first three cases. The sensitivities achieved are 0.23 mm depth (10%WT) for circumferential, axial and tapered defects and for partial-pinholes: 1 mm diameter and 1.38 mm depth (60%WT). Thirdly, 3D-FE simulations with ID and OD pinhole defects are performed which show that the ID and OD defects are detected by L(0,2) with a fairly similar sensitivity. Finally, study on the thermal expansion bend (with three successive bends) shows that the bend does not have much influence on the mode and the multiple circumferential defects considered in the bend are detected with good sensitivity.

Interaction Between SH0 Guided Waves and Tilted Surface-Breaking Cracks in Plates

The interaction between SH₀ guided waves and simple defects is well understood and documented, and the SH₀ and related torsional guided waves are commonly used in inspection. However, tilted and branching cracks, for which vertical notches are a poor approximation, are found in some environments, particularly when pipes are buried in alkaline soils. This paper studies the interaction between SH₀ guided waves and tilted, surface-breaking cracks, investigating the effect of the tilt and depth of the defect. The incident wave interacts with the tilted crack to generate a transmitted wave, a reflected wave, and a wave trapped below the crack. It is shown that the direction of the tilt of the crack relative to the incident wave direction does not affect the scattering behavior. In addition, the axial extent of the crack plays a major role in the reflectivity of the crack, leading to transmission nulls in some configurations. These transmission nulls appear for all crack depths, the frequency range over which the transmission is significantly reduced increasing with crack depth. This behavior is shown to be analogous to the acoustic energy flow in a duct when a Helmholtz resonator is introduced. The null is not seen above the SH₁ cutoff as the propagating signals are no longer monomodal. The existence of a transmission null and corresponding reflection maximum is promising for the detection of small defects and measurement of the frequency at which the null occurs will assist with defect characterization. Experimental validations of the key results are presented.

Detection, Localisation and Assessment of Defects in Pipes Using Guided Wave Techniques: A Review

This paper aims to provide an overview of the experimental and simulation works focused on the detection, localisation and assessment of various defects in pipes by applying fast-screening guided ultrasonic wave techniques that have been used in the oil and gas industries over the past 20 years. Major emphasis is placed on limitations, capabilities, defect detection in coated buried pipes under pressure and corrosion monitoring using different commercial guided wave (GW) systems, approaches to simulation techniques such as the finite element method (FEM), wave mode selection, excitation and collection, GW attenuation, signal processing and different types of GW transducers. The effects of defect parameters on reflection coefficients are also discussed in terms of different simulation studies and experimental verifications.

Relative Ability of Wedge-Coupled Piezoelectric and Meander Coil EMAT Probes to Generate Single-Mode Lamb Waves

Ultrasonic guided waves are used extensively when checking for defects in petrochemical and other industries and are mostly generated using piezoelectric transducers on an angled wedge or electromagnetic acoustic transducers (EMATs) in different configurations. Low-frequency inspection allows for long-distance propagation, but it is best suited for detecting relatively large defects, while at higher frequencies, the presence of multiple wave modes limit defect detectability, so achieving practical single Lamb mode excitation via careful transduction is very beneficial. This paper investigates the relative ability of angled piezoelectric and meander coil EMAT probes to produce single-mode transduction in the medium (~1-5 MHz-mm) and high (>5 MHz-mm) frequency-thickness regions of the dispersion curves. The nature of each transducer is studied analytically by simulating the corresponding surface forces, followed by the use of a Fourier transform in time and space (2-D fast Fourier transform) to highlight the excitation region in the wavenumber-frequency space. With angled wedge excitation there is a linear relationship between the excitation frequency and the wavenumber which means that the excitation tends to track typical dispersion curves, allowing for easier pure mode generation. In contrast, the EMAT controls frequency and wavenumber separately which makes it more difficult to generate a pure mode when dispersion curves are close together; however, by narrowing the frequency bandwidth via a large number of cycles in the excitation signal, pure mode generation via an EMAT was shown to be possible even in areas of closely spaced modes. As example cases, analytical results, backed up by experiments, showed that signals dominated by the A0 mode at 1.5 MHz-mm and also the A1 mode at 18 MHz-mm can be generated with both angled piezoelectric and EMAT probes.

Use of the reciprocity theorem for a closed form solution of scattering of the lowest axially symmetric torsional wave mode by a defect in a pipe

Guided waves can effectively be used for inspection of large scale structures. Surface corrosion is often found as major defect type in large scale structures such as pipelines. Guided wave interaction with surface corrosion can provide useful information for sizing and classification. In this paper, the elastodynamic reciprocity theorem is used to formulate and solve complicated scattering problems in a simple manner. The approach has already been applied to scattering of Rayleigh and Lamb waves by defects to produce closed form solutions of amplitude of scattered waves. In this paper, the scattering of the lowest axially symmetric torsional mode, which is widely used in commercial applications, is analyzed by the reciprocity theorem. In the present paper, the theorem is used to determine the scattering of the lowest torsional mode by a tapered defect that was earlier considered experimentally and numerically by the finite element method. It is shown that by the presented method it is simple to obtain the ratio of amplitudes of scattered torsional modes for a tapered notch. The results show a good agreement with earlier numerical results. The wave field superposition technique in conjunction with the reciprocity theorem simplifies the solution of the scattering problem to yield a closed form solution which can play a significant role in quantitative signal interpretation.

Efficient generation of receiver operating characteristics for the evaluation of damage detection in practical structural health monitoring applications

Permanently installed guided wave monitoring systems are attractive for monitoring large structures. By frequently interrogating the test structure over a long period of time, such systems have the potential to detect defects much earlier than with conventional one-off inspection, and reduce the time and labour cost involved. However, for the systems to be accepted under real operational conditions, their damage detection performance needs to be evaluated in these practical settings. The receiver operating characteristic (ROC) is an established performance metric for one-off inspections, but the generation of the ROC requires many test structures with realistic damage growth at different locations and different environmental conditions, and this is often impractical. In this paper, we propose an evaluation framework using experimental data collected over multiple environmental cycles on an undamaged structure with synthetic damage signatures added by superposition. Recent advances in computation power enable examples covering a wide range of practical scenarios to be generated, and for multiple cases of each scenario to be tested so that the statistics of the performance can be evaluated. The proposed methodology has been demonstrated using data collected from a laboratory pipe specimen over many temperature cycles, superposed with damage signatures predicted for a flat-bottom hole growing at different rates at various locations. Three damage detection schemes, conventional baseline subtraction, singular value decomposition (SVD) and independent component analysis (ICA), have been evaluated. It has been shown that in all cases, the component methods perform significantly better than the residual method, with ICA generally the better of the two. The results have been validated using experimental data monitoring a pipe in which a flat-bottom hole was drilled and enlarged over successive temperature cycles. The methodology can be used to evaluate the performance of an installed monitoring system and to show whether it is capable of detecting particular damage growth at any given location. It will enable monitoring results to be evaluated rigorously and will be valuable in the development of safety cases.

Efficient generation of receiver operating characteristics for the evaluation of damage detection in practical structural health monitoring applications

Permanently installed guided wave monitoring systems are attractive for monitoring large structures. By frequently interrogating the test structure over a long period of time, such systems have the potential to detect defects much earlier than with conventional one-off inspection, and reduce the time and labour cost involved. However, for the systems to be accepted under real operational conditions, their damage detection performance needs to be evaluated in these practical settings. The receiver operating characteristic (ROC) is an established performance metric for one-off inspections, but the generation of the ROC requires many test structures with realistic damage growth at different locations and different environmental conditions, and this is often impractical. In this paper, we propose an evaluation framework using experimental data collected over multiple environmental cycles on an undamaged structure with synthetic damage signatures added by superposition. Recent advances in computation power enable examples covering a wide range of practical scenarios to be generated, and for multiple cases of each scenario to be tested so that the statistics of the performance can be evaluated. The proposed methodology has been demonstrated using data collected from a laboratory pipe specimen over many temperature cycles, superposed with damage signatures predicted for a flat-bottom hole growing at different rates at various locations. Three damage detection schemes, conventional baseline subtraction, singular value decomposition (SVD) and independent component analysis (ICA), have been evaluated. It has been shown that in all cases, the component methods perform significantly better than the residual method, with ICA generally the better of the two. The results have been validated using experimental data monitoring a pipe in which a flat-bottom hole was drilled and enlarged over successive temperature cycles. The methodology can be used to evaluate the performance of an installed monitoring system and to show whether it is capable of detecting particular damage growth at any given location. It will enable monitoring results to be evaluated rigorously and will be valuable in the development of safety cases.

The scattering of torsional guided waves from Gaussian rough surfaces in pipework

In older sections of industrial pipework there are often regions of general corrosion that typically have a Gaussian thickness distribution. During guided wave inspection this corrosion causes an increase in the background noise and a significant attenuation of the inspection wave. These effects are investigated in this paper through finite element modelling of the interaction of torsional guided waves with rough surfaces in pipes. Pipes of different diameter and rough surface profile are modelled and it is found that the attenuation of waves is explained by significant mode conversion and scattering within the rough surface. This mode conversion is greatest when the non-axisymmetric modes to which energy is scattered are close to the cutoff frequency or when the ratio of surface correlation length to wavelength is around 0.2-0.25. Mode conversion increases with increasing surface roughness and is a strong function of frequency-diameter product, with larger pipes causing more mode conversion. When this mode conversion occurs the energy is lost mostly to those waves with a displacement profile closest to the original torsional inspection wave. Resulting attenuation of the inspection signal can be severe; for example a mean wall thickness loss of 28% can cause 2.7 dB/m attenuation in a pulse-echo configuration.

Pipe Attrition Acoustic Locater (PAAL) from multi-mode dispersion analysis

Multi-mode dispersion imaging shows that pure dispersion-free torsional waves are reflected at a pipe end and flexural wave modes are suppressed. This effect can be used to locate and assess internal damage. The end reflection coefficient of this single propagating mode decreases with increasing wear. The pipe damage is located from the travel time of the torsional wave component reflected from the damage point.

Excitation of Single-Mode Lamb Waves at High-Frequency-Thickness Products

Guided wave inspection is used extensively in petrochemical plants to check for defects such as corrosion. Long-range low-frequency inspection can be used to detect relatively large defects, while higher frequency inspection provides improved sensitivity to small defects, but the presence of multiple dispersive modes makes it difficult to implement. This paper investigates the possibility of exciting a single-mode Lamb wave with low dispersion at a frequency thickness of around 20 MHz-mm. It is shown by finite element (FE) analysis backed up by experiments that a signal dominated by the A1 mode can be generated, even in a region where many modes have similar phase velocities. The A1 mode has relatively little motion at the plate surface which means that only a small reflection is generated at features such as T-joints; this is verified numerically. It is also expected that it will be relatively unaffected by surface roughness or attenuative coatings. These features are very similar to those of the higher order mode cluster (HOMC) reported by other authors, and it is shown that the A1 mode shape is very similar to the deflected shape reported in HOMC.

High-frequency lowest torsional wave mode ultrasonic inspection using a necked pipe waveguide unit

We propose an effective method to transmit only the non-dispersive lowest torsional wave mode at a high frequency range even above the cutoff frequency of the third torsional mode. Unlike existing methods that tune the wavelength or phase of the target wave mode, the proposed method is based on the thickness change and the cutoff phenomenon. A specially configured necked waveguide, consisting of three regions of which the middle region is thinner than the so-called cutoff thickness, is put in end-to-end contact with a test pipe to transmit only the first torsional wave mode to a test pipe. After explaining the underlying role of the proposed necked waveguide, we propose a technique to mainly transmit the lowest torsional wave mode at a frequency where higher modes can also propagate. Numerical simulations and damage detection experiments were carried out to show the effectiveness of the proposed method.

Enhancement of the excitation efficiency of a torsional wave PPM EMAT array for pipe inspection by optimizing the element number of the array based on 3-D FEM

Electromagnetic acoustic transducers (EMATs) can generate non-dispersive T(0,1) mode guided waves in a metallic pipe for nondestructive testing (NDT) by using a periodic permanent magnet (PPM) EMAT circular array. In order to enhance the excitation efficiency of the sensor, the effects of varying the number of elements of the array on the excitation efficiency is studied in this paper. The transduction process of the PPM EMAT array is studied based on 3-D finite element method (FEM). The passing signal amplitude of the torsional wave is obtained to represent the excitation efficiency of the sensor. Models with different numbers of elements are established and the results are compared to obtain an optimal element number. The simulation result is verified by experiments. It is shown that after optimization, the amplitudes of both the passing signal and defect signal with the optimal element number are increased by 29%, which verifies the feasibility of this optimal method. The essence of the optimization is to find the best match between the static magnetic field and the eddy current field in a limited circumferential space to obtain the maximum circumferential Lorentz force.

Measuring the wavenumber of guided modes in waveguides with linearly varying thickness

Measuring guided waves in cortical bone arouses a growing interest to assess skeletal status. In most studies, a model of waveguide is proposed to assist in the interpretation of the dispersion curves. In all the reported investigations, the bone is mimicked as a waveguide with a constant thickness, which only approximates the irregular geometry of cortical bone. In this study, guided mode propagation in cortical bone-mimicking wedged plates is investigated with the aim to document the influence on measured dispersion curves of a waveguide of varying thickness and to propose a method to overcome the measurement limitations induced by such thickness variations. The singular value decomposition-based signal processing method, previously introduced for the detection of guided modes in plates of constant thickness, is adapted to the case of waveguides of slowly linearly variable thickness. The modification consists in the compensation at each frequency of the wavenumber variations induced by the local variation in thickness. The modified method, tested on bone-mimicking wedged plates, allows an enhanced and more accurate detection of the wavenumbers. Moreover, the propagation in the directions of increasing and decreasing thickness along the waveguide is investigated.