Shear Vertical Wave Research Articles

Detection and Characterization of Hidden Crack Inside a Stainless Steel Material Using Shear Vertical Waves and PLSR Technique

Industrial equipment can be exposed to various types of damage during their long exploitation in harsh environments which might lead to corrosion cracking. Typically, a hidden crack is very dangerous since it is difficult to be detected by Non-Destructive Testing (NDT) techniques. Moreover, the integrity requirements of metallic structures cannot be satisfied by simply detecting the existence of cracks. However, the quantitative description of the cracks is still an issue that should be solved. This paper introduces a new approach to estimate the dimensions of hidden cracks inside a stainless steel plate based on Shear Vertical (SV) waves generated by an Electromagnetic Acoustic Transducer (EMAT). The Finite Elements Method (FEM) has been used to model the acquired signal by EMAT. Then, the characterization of hidden cracks is carried out by combining two methods; Time-of-Flight (ToF) technique that has been used to evaluate the crack height, and the Partial Least Square Regression (PLSR) method that has been used to estimate the crack width. The obtained results demonstrate the efficiency and the reliability of the adopted approach concerning the quantitative evaluation of the crack dimensions.

Modeling of physical processes during the propagation of ultrasonic waves in metallic media

The paper deals with the features of modeling physical processes during the propagation of ultrasonic waves in metallic media. A mathematical model for the propagation of shear vertical (SV) ultrasonic waves generated by a single element of a 32-element electromagnetic acoustic phased array has been developed. The calculation of the acoustic field of the 32-element SV electromagnetic acoustic transducer (EMAT) phased array was made. The total displacements for models with defects and without them were calculated. A computer simulation of the process of reflection of the ultrasonic beam from a defect was made. The developed model allows one to study the influence of shape, size, location of defects in the plate as well as the plate geometric parameters on the formation of the reflected signal.

Multi-parameters optimization for electromagnetic acoustic transducers using surrogate-assisted particle swarm optimizer

In ultrasonic testing field, the design and optimization of point-focusing shear vertical waves electromagnetic acoustic transducer (PFSV-EMAT) with high energy conversion efficiency have been a challenging task. In this work, a novel multi-parameter optimization method is described to improve PFSV-EMATs’ conversion performance, which integrates the newly proposed hybrid surrogate modeling (HSM) approach and particle swarm optimization (PSO) algorithm for efficient optimization. Based on the established finite element model of EMATs, the amplitudes of the displacement components at the observation point of a plate is the objective function to be maximized with five parameters pertaining to the cylindrical magnets, coaxial meander-line coils, and excitation signal, as design variables. Then, a brand-new HSM-assisted PSO algorithm is proposed and the superiority and rationality of the HSM strategy are proven. In addition, the multi-parameter optimization of PFSV-EMATs is conducted with the proposed HSM-PSO algorithm. Finally, experiments are carried out to verify the validation of optimization results, indicating that the increased signal amplitude of 12 times can be achieved by the optimized PFSV-EMAT, which has the improved signal amplitude and consistent point-focusing behavior, compared with the non-optimized one.

Reflection of thermo-elastic wave in semiconductor nanostructures nonlocal porous medium

The current work is an extension of the nonlocal elasticity theory to fractional order thermo-elasticity in semiconducting nanostructure medium with voids. The analysis is made on the reflection phenomena in context of three-phase-lag thermo-elastic model. It is observed that, four-coupled longitudinal waves and an independent shear vertical wave exist in the medium which is dispersive in nature. It is seen that longitudinal waves are damped, and shear wave is un-damped when angular frequency is less than the cut-off frequency. The voids, thermal and non-local parameter affect the dilatational waves whereas shear wave is only depending upon non-local parameter. It is found that reflection coefficients are affected by nonlocal and fractional order parameters. Reflection coefficients are calculated analytically and computed numerically for a material, silicon and discussed graphically in details. The results for local (classical) theory are obtained as a special case. The study may be useful in semiconductor nanostructure, geology and seismology in addition to semiconductor nanostructure devices.

Ultrasonic beam focusing characteristics of shear-vertical waves for contact-type linear phased array in solid**Project supported by the National Natural Science Foundation of China (Grant Nos. 11774377 and 11574343).

We investigate the beam focusing technology of shear-vertical (SV) waves for a contact-type linear phased array to overcome the shortcomings of conventional wedge transducer arrays. The numerical simulation reveals the transient excitation and propagation characteristics of SV waves. It is found that the element size plays an important role in determining the transient radiation directivity of SV waves. The transient beam focusing characteristics of SV waves for various array parameters are deeply studied. It is particularly interesting to see that smaller element width will provide the focused beam of SV waves with higher quality, while larger element width may result in erratic fluctuation of focusing energy around the focal point. There exists a specific range of inter-element spacing for optimum focusing performance. Moreover, good beam focusing performance of SV waves can be achieved only at high steering angles.

Optimal design of shear vertical wave electromagnetic acoustic transducers in resonant mode

In this paper, a new electromagnetic acoustic resonance (EMAR) transducer is proposed for precise thickness measurement in specimen. The new EMAR is composed of a mirror symmetric coil (MSC) and a pair of Nd-Fe-B permanent magnets with the different polarity for enhancing the generation and detection of resonant signals. Firstly, a finite element model was established to simulate the distributions of Lorentz force produced by new EMAR and the resonant process of shear waves. Furthermore, the relationship between the frequency response characteristic of the new EMAR and the common EMAR were explored. Finally, to verify the performance of the EMAR, several experiments were performed. Compared with the common EMAR transducer, the resonant amplitude of the new EMAR transducer was increased by 121.74% and the signal-to-noise ratio was increased by 28.35%, and the resonance frequency interval of the new EMAR was twice that of the common mode in the frequency domain simulation experiment, this advantage effectively reduced the error rate of measurement. The results show that the new EMAR transducer with mirror coil structure has higher accuracy in thickness detection of specimens.

Design of elastic metasurfaces for controlling shear vertical waves using uniaxial scaling transformation method

Controlling wave propagation is a popular research field; however, progress with regard to the study of elastic waves is slow because of the coupling of different types of waves. In this paper, we report a novel approach to design elastic metasurfaces for controlling elastic shear vertical (SV) waves in solids. The metasurface is composed of separate parallel thin plates connected at both ends to half-space solids. The elastic SV-waves in solids were controlled by manipulating the induced flexural waves in the thin plates of the metasurface. Based on the form invariance of the governing equation for flexural waves in a thin plate under linear coordinate transformations, the uniaxial scaling transformation method (USTM) has been put forward to alter the material to constitute the thin plates of the metasurface. The transformed material is transversely isotropic, which greatly reduces implementation difficulties. To tune the traveling times of the flexural waves in the thin plates, different values of the scaling parameter α and plate thickness h were assigned for different thin plates based on the Kirchhoff plate theory. By combining the plate thickness variation approach with the USTM, the plate length of the metasurface could be effectively controlled to be smaller than the wavelength at the working frequency. To demonstrate the performance of the proposed approach, two designs of elastic metasurfaces for wave focusing and abnormal refraction were described in detail, and full numerical simulations were conducted. The present approach opens a promising avenue toward the realization of metasurfaces for controlling elastic waves.

Numerical evaluation of focal position selection by line-focusing electromagnetic acoustic transducer with experimental validation

As the focal position of a line-focusing electromagnetic acoustic transducer (LF-EMAT) affects the intensity of the focal signal, we measure the displacement signal and the selection method of the focal line position is then studied in this work to improve the signal intensity and detection precision for a shear-vertical (SV) wave LF-EMAT. We calculate the magnetostatics field and bulk wave propagation utilizing the finite element method (FEM). We simulate the characteristics of the SV wave, and we find that the radiant distance and propagation direction has a great influence on the amplitude of the displacement of the specimen. The superposition area of SV waves from different sources possesses better focusing ability, and the triangular area (normalized amplitude of the SV waves lower than 10%) near the surface of a specimen should be avoided to be chosen when designing the meander line coils. As for the line-focusing EMAT described in this manuscript, the selection of focal positions for different thickness specimens or detection depth is completely different. Moreover, we perform an experiment to validate the simulation results and lead to a conclusion that the position of the focal point is required to be appropriately close to the excitation coils to enhance the intensity of the signal, while the best focal position should be calculated.

Asymmetric transmission of elastic shear vertical waves in solids

In this work, we propose an asymmetric transmission structure (ATS) for elastic shear vertical (SV) waves in solids, which has been relatively unexplored. The ATS is constituted by a metasurface and a phononic crystal (PC) possessing a directional band gap. While the metasurface aims to redirect the incident wave, the PC acts as a directional filter. The metasurface is composed of a stacked array of composite plates with two connecting parts made of different materials. To examine the performance of the designed ATS, full numerical simulations have been conducted. The numerical results indicate that the proposed ATS offered a relatively broad working frequency band and had a one order of magnitude difference in terms of transmission between the positive and negative incidences. Our study provides an alternative method to control elastic SV waves and could benefit applications in various fields, such as Micro-Electro-Mechanical System (MEMS), in which thin plates are frequently used components.

REFLECTION OF PLANE WAVES FROM SURFACE OF A THERMOELASTIC SATURATED POROUS SOLID HALF-SPACE WITH IMPEDANCE BOUNDARY CONDITIONS

In the present paper, a problem on reflection of plane waves from a plane thermally insulated as well as isothermal surfaces of a half-space is studied in the context of Lord-Shulman (LS) and Green-Naghdi (GN) theories of generalized thermoelasticity of a saturated porous medium. The mechanical boundary conditions at the surface of the half-space are considered as impedance boundary conditions, where the normal and shear force tractions are assumed to vary linearly with the normal and tangential displacement components multiplied by the frequency, respectively. The impedance corresponds to the constants of proportionality. The governing equations are specialized in the x-z plane. The plane wave solution of these equations shows the existence of three coupled longitudinal waves and a shear vertical wave in a generalized thermoelastic saturated porous medium. For an incident plane wave (longitudinal or shear), four reflected waves will propagate in the medium. The appropriate potentials for incident and reflected waves in a half-space are formulated, which satisfy the required boundary conditions with the help of Snell's law. Finally, a nonhomogeneous system of four equations is obtained in the amplitude ratios, where the ratios depend on the material parameters, impedance parameter, angle of incidence, thermal relaxation, and speeds of plane waves. For relevant material parameters, the amplitude ratios are computed numerically for certain ranges of impedance parameters and the angle of incidence. For the purpose of validation, the numerical results are compared with those without thermal and porous parameters.

Reflection of Plane Waves from Surface of a Generalized Thermo-Viscoelastic Porous Solid Half-Space with Impedance Boundary Conditions

Abstract A phenomenon of reflection of plane waves from a thermally insulated surface of a solid half-space is studied in context of Lord-Shulman theory of generalized thermo-viscoelasticity with voids. The governing equations of generalized thermo-viscoelastic medium with voids are specialized in x–z plane. The plane wave solution of these equations shows the existence of three coupled longitudinal waves and a shear vertical wave in a generalized thermo-viscoelastic medium with voids. For incident plane wave (longitudinal or shear), three coupled longitudinal waves and a shear vertical wave reflect back in the medium. The mechanical boundary conditions at free surface of solid half-space are considered as impedance boundary conditions, in which the shear force tractions are assumed to vary linearly with the tangential displacement components multiplied by the frequency. The impedance corresponds to the constant of proportionality. The appropriate potentials of incident and reflected waves in the half-space will satisfy the required impedance boundary conditions. A non-homogeneous system of four equations in the amplitude ratios of reflected waves is obtained. These amplitude ratios are functions of material parameters, impedance parameter, angle of incidence, thermal relaxation and speeds of plane waves. Using relevant material parameters for medium, the amplitude ratios are computed numerically and plotted against certain ranges of impedance parameter and the angle of incidence.

Wavefront steering of elastic shear vertical waves in solids via a composite-plate-based metasurface

We report a novel approach to control the wavefronts of shear vertical (SV) waves in solids using metasurfaces constituted by a stacked array of composite plates, which are composed of two connecting parts made of different materials. The metasurfaces are connected at two ends to the half-space solids where the elastic SV waves propagate. The incident SV waves in the left half-space solid induce flexural waves in the composite plates and subsequently are converted back to SV waves in the right half-space solid. The time delay of flexural waves in each composite plate of the metasurfaces is tuned through the varying length of the two connecting components. To quantitatively evaluate the time delay in each composite plate, a theoretical model for analyzing the phase of the transmitted SV waves is developed based on the Mindlin plate theory. To control the SV waves at will, each composite plate in the metasurface is delicately designed according to the proposed theoretical model. For illustrative purposes, two metasurfaces are designed and numerically validated.

Optimal Design of Point-Focusing Shear Vertical Wave Electromagnetic Ultrasonic Transducers Based on Orthogonal Test Method

The lower conversion efficiency is the main drawback of electromagnetic acoustic transducers (EMATs) compared with other transducers, which limits their use in many industrial applications. In this paper, for enhancing the performance of point-focusing shear vertical wave EMATs (PFSV-EMATs), 18 orthogonal tests with seven factors and three levels are conducted through finite-element simulations. First, the degree of seven factors on the signal amplitude, axial focus offset, and radial focus offset is obtained by range analysis and compared. It indicates that the effect of the liftoff distance and the exciting current on signal amplitude is the largest, while the effect of the inner radius of concentric meander-line coils on the axial and radial focal offset is the largest. Then, the influence degree of various factors on test results is analyzed at frequencies of 1.5, 2, and 2.5 MHz, showing that the relatively low frequency, i.e., the sparser coil spacing, is favorable for signal amplitude and detrimental for point-focusing ability. Finally, experiments are carried out to verify the validation of optimization results, which indicates that the increased signal amplitude of 88.78%, smaller axial focus offset, and zero radial focus offset can be achieved by the optimized PFSV-EMAT, which has the improved signal amplitude and point-focusing behavior, compared with the non-optimized one.

Influence of aperture angles and design focal depths on the performance of point-focusing shear vertical wave electromagnetic acoustic transducers.

Electromagnetic acoustic transducers (EMATs) with concentric meander-line (CML) coils possess the capability of producing point-focusing shear vertical (PFSV) waves. For the CML coil, an intercepted circular arc of the concentric circle with a continuously changing spacing, the aperture angle is a key factor effecting the point-focusing performance. Thus, the influence of aperture angles of CML coils on the point-focusing behavior of PFSV-EMATs is analyzed using the established finite element modeling in detail, which also considers the effect of lift-off distance on the signal amplitude. The beam directional pattern is characterized quantitatively by the half-power beam width, indicating the relationship between the aperture angle and beam width. In addition, since the focus offset is sensitive in depth direction, the effect of design focal depths on focal offset is also carefully studied. Three CML coils with an aperture angle of 30°, 90°, and 150° are fabricated by printed circuit board technique and experimentally analyzed; the experimental results are well consistent with the simulation results. These findings can be used to design optimized PFSV-EMATs with good point-focusing performance.

Dynamic Response to Seismic Waves at the Shallow Slope Supported by Bolts

In the soil slope supported by bolts, longitude waves instead of transverse waves, generated by earthquakes, first reach the slope surface. With the dynamic response of the P (pressure) wave along the anchorage structure, first, a theoretical study was conducted to investigate the propagation characteristics of the interference superposition, generated by the SV (shear-vertical) and the P waves. The SV wave was formed by the wave, originating from the bottom and reflected from the free surface of the slope, whereas the latter was the incident P wave, propagating in the slope. In addition, the structural measures, restraining the seismic wave, and the characteristics of the restraint effect at the free segment of the bolt were investigated. According to the wave-way difference between the incident P wave and the reflected SV wave, the minimum critical slope angle, influenced by the interference at the shallow slope, and the maximum influencing depth of the dynamic response, acting vertically to the slope surface, were obtained. The results indicate that the maximum influencing depth linearly correlated with the slope angle. Furthermore, based on the propagation characteristics of the P wave along the bolt, and the coupled relation between the wave length and the anchorage design parameters, the axial acceleration of the wave propagating along the bolt axis was obtained. Then, the theoretical length of the anti-seismic bolt, subjected to seismic waves, and the compensation force of the anchorage structure were obtained. Finally, a numerical study, based on FlAC3D, properly verified the theoretical conclusions.

Simultaneous multi-band valley-protected topological edge states of shear vertical wave in two-dimensional phononic crystals with veins

The introduction of the concept of valley pseudospin to phononic crystals has made a remarkable topologically protected interface transport of sound, which opens a novel research area referred to as valley Hall topological insulators. Here, we demonstrate the simultaneous multi-band edge states of shear vertical waves in two-dimensional phononic crystals with veins. The multi-band edge states are topologically valley-protected and are obtained by simultaneously gapping multiple Dirac points at K (or K′) under the inversion symmetry breaking. As the relative radius of the two adjacent steel columns varies, the band diagram undergoes a topological transition which can be characterized by topological charge distributions and opposite valley Chern numbers. Subsequently, the vortex chirality of the bulk valley modes is unveiled. With numerical simulations, simultaneous multi-band valley dependent edge states and the associated valley-protected backscattering suppression around the curved waveguide are further demonstrated. Our work could become a promising platform for applications of multi-functional topological acoustic devices.

Inspection of stress corrosion cracking in welded stainless steel pipe using point-focusing electromagnetic-acoustic transducer

Point-focusing electromagnetic-acoustic transducers (PF-EMATs) for shear-vertical (SV) waves were developed for crack inspection of stainless-steel pipes. The transducer has improved defect detectability by accumulating SV waves generated by concentric line sources at a focal point in phase. An optimum frequency for defect detection was found to be 2MHz, with which a crack of 0.5mm depth near a weld was clearly detected. The EMAT exhibited defect detectability comparable to that of a conventional phased-array piezoelectric transducer, indicating that this new EMAT is highly practical for the non-contacting evaluation of stress-corrosion cracking in stainless steels.

Development of shear-vertical-wave point-focusing electromagnetic acoustic transducer

A shear-vertical-wave point-focusing electromagnetic acoustic transducer is developed for the purpose of detecting stress corrosion cracking in stainless steel. The transducer is composed of a permanent magnet and two identical concentric meander-line coils, one for the transmitter and the other for the receiver, and the shear-vertical waves are excited and detected by the Lorentz force mechanism. The meander-line coils are designed so that the phases of all the excited shear-vertical waves are focused in phase at a focal point. The focal area is evaluated experimentally, and it is confirmed that the developed transducer is capable of detecting slit defects deeper than 0.05 mm at the bottom surface of a stainless-steel plate 20 mm thick.

On Reflection and Transmission of p- and Sv-Waves Phenomena at the Interface Between Solid-Liquid Media with Magnetic Field and Two Thermal Relaxation Times

In this research, we studied the reflection and transmission of thermoelastic wave at a solid-liquid interface under influence of two thermal relaxation times and magnetic field. The governing equations are introduced taking into consideration Green-Lindsay theory and Maxwell's stresses. After solving the governing equations, we found the two reflections and transmission coefficients of incident p-(primary) and SV- (Shear Vertical) waves in the presence of thermal relaxation times and a magnetic field. The boundary conditions at the interface have been applied. The appropriate expressions to find the amplitude ratios for the two incidence waves (p- and SV-waves) have been obtained. A numerical calculation is made for the reflection and transmitted coefficients of the incident waves, in which we study the effect of thermal relaxation times and magnetic field. The results obtained are presented graphically for the effect of magnetic field and relaxation times to display the phenomena physical meaning.

Converging ultrasonic shear-vertical waves generated by a double-line laser and its application for surface defect detection

A double-line laser source as an irradiation pattern for the generation of ultrasonic waves is proposed. Simulated results show that the shear-vertical (SV) waves generated by the double-line laser source superimpose and produce a convergence effect at the center axis with a fixed angle. The amplitude of the converging SV wave is significantly improved compared to the ultrasonic field generated by a single-line source under the same condition of the thermoelastic regime. Simulations show good agreement with experimental results, which demonstrate that the SV waves in a steel plate subjected to the double-line laser source converge efficiently at the center axis. Then, a method using the converging SV to detect surface defect on a steel plate is proposed. The characterization of the surface defect has been quantitatively measured with high accuracy by the well-designed double-line source.