Shear Vertical Wave Research Articles

Evaluation of fatigue cracks by an angle beam EMAT–ET dual probe

In this study, the authors propose an EMAT–ET dual probe for evaluation of fatigue cracks. The probe consists of a permanent magnet, a meander-line coil to emit and receive shear-vertical waves propagating obliquely in the material to be inspected, and a racetrack-shaped coil to pick up the ET signals. The experimental results show that the EMAT and ET modes of the proposed probe can detect and size both, shallow and deep cracks on the back side of specimens, respectively, which indicates that the proposed probe provides reliable evaluation of fatigue cracks within a wide range of depth values.

A study of the noncollinear ultrasonic-wave-mixing technique under imperfect resonance conditions

Geometrical and material property changes cause deviations in the resonant conditions used for noncollinear wave mixing. These deviations are predicted and observed using the SV(ω1)+L(ω2)→L(ω1+ω2) interaction, where SV and L are the shear vertical and longitudinal waves, respectively, and ω1, ω2 are their frequencies. Numerical predictions, performed for the scattered secondary field in the far field zone, show three field features of imperfect resonance conditions: (1) rotation of a scattered beam, (2) decrease in the beam amplitude, and (3) beam splitting.The response of the nonlinear ultrasonic wave mixing technique is verified experimentally in two ways: (1) detection of a kissing bond between two polyvinyl chloride (PVC) plates, and (2) detection of subsurface micro-cracks in polymethyl methacrylate (PMMA). A predominant decrease in nonlinear wave energy is observed in both experiments. Beam rotation and splitting is observed in the kissing-bond experiment, while a minor increase in the nonlinear wave energy up to 100% is observed in the micro-cracked PMMA specimen.

Green Lindsay model on reflection and refraction of p- and SV-waves at interface between solid-liquid media presence in magnetic field and initial stress

In this paper, the reflection and transmission of thermoelastic wave at a solid-liquid interface in presence of initial stress and magnetic field is investigated in context of GL model. After solving the governing equations, we can find the two reflection and refraction coefficients of incident p-(pressure) and SV- (shear vertical) waves in presence of initial stress and magnetic field. The boundary conditions at the interface that: (i) displacement continuity, (ii) vanishing the tangential displacement, (iii) continuity of normal force per unit initial area, (iv) tangential force per unit initial area must vanish, and (v) continuity of temperature is applied. The appropriate expressions to find the amplitude ratios for the two incidence waves (p- and SV-waves) have been obtained. A numerical example is considered for the reflection and transmitted coefficients of the incident waves, in which we study the effect of initial stresses and magnetic field. The results obtained are presented graphically for the effect of magnetic field and initial stress to display the phenomena physical meaning.

GL Model on Reflection of P and SV Waves from the Free Surface of Thermoelastic Diffusion Solid Under Influence of the Electromagnetic Field and Initial Stress

This article is devoted to estimating the influence of magnetic field, electric field and initial stress in an elastic solid half-space under thermoelastic diffusion. The governing equations in the xz-plane are solved taking into consideration the Green–Lindsay (GL) model. The Reflection of dilatational (P) wave and Shear Vertical (SV) wave split into four waves: namely, P wave, thermal wave, mass diffusion wave and SV wave. The reflection phenomena of P and SV waves from the free surface of an elastic solid with thermoelastic diffusion under influence of magnetic field, electric field and initial stress is considered. The expressions for the reflection coefficients for the four reflected waves are obtained. These reflection coefficients are found to depend upon the angle of incidence θ of P and SV waves, thermoelastic diffusion, magnetic field, electric field and initial stress and other material parameters. The numerical values for the reflection coefficients are calculated analytically and presented graphically for varying values of these parameters.

Numerical and experimental analysis of unidirectional meander-line coil electromagnetic acoustic transducers

The elastic waves generated by traditional meander-line coil electromagnetic acoustic transducers (EMATs) propagate in two directions, overlapping the echo signals from defects with the same distances, and the defect echo signal is hard to distinguish from the edge-reflected signal when the EMATs are near the edge of a specimen. In this paper, a unidirectional EMAT with two meander-line coils is proposed. A finite element model is used to simulate the directivity of the Rayleigh and shear vertical waves generated by these EMATs. Six transducers are fabricated using the printed circuit technique. The unidirectional Rayleigh wave and shear vertical wave are tested, and the results agree well with the simulation.

Wave Propagation in a Green–Naghdi Thermoelastic Solid with Diffusion

The Green and Naghdi theory of thermoelasticity is applied to study plane-wave propagation in an elastic solid with thermo-diffusion. The governing equations of an elastic solid with generalized thermo-diffusion are solved to show the existence of three coupled longitudinal waves and a shear vertical (SV) wave in a two-dimensional model of the solid with thermo-diffusion. The reflection of plane waves from a thermally insulated stress-free surface of an elastic solid with thermo-diffusion is also studied. A non-homogeneous system of four equations in reflection coefficients is obtained. The speeds of the plane waves are computed numerically and plotted against frequency for a particular range. The complex absolute values of the reflection coefficients of all reflected waves are computed numerically and plotted against the angle of incidence of the striking wave at the free surface. The effects of diffusion parameters are shown graphically for speeds and reflection coefficients of plane waves.

A study of pressure-shear vertical wave propagation in periodically layered fluid and piezoelectric structure

In this paper, the pressure (P) and shear vertical (SV) wave propagation in the periodically layered fluid and piezoelectric structure are theoretically studied. A single piezoelectric layer is first analyzed for three scenarios: piezoelectricity-ignored, electrically open, or electrically closed. It is observed that both the Lamb wave dispersion curves and the transmission coefficients are affected by piezoelectricity and electrical boundary conditions under any incident angle. From the analyses of the periodically layered structure, it is further found that the piezoelectricity and the electrical boundary conditions have influence on band gaps for a given incident angle.

Synthesis of spatially correlated ground motions at varying sites based on Vector-valued Seismic Hazard Deaggregation

This paper presents a comprehensive and rational approach of synthesizing spatially correlated earthquake ground motions. The physically compliant seismological spectra, which have been used in simulating ground motion at a single location, is extended to synthesize spatially varying ground motion (SVGM). The seismological spectra are then related to Vector-valued Seismic Hazard Deaggregation, based on which a simulation framework is proposed to resolve the problem that a number of simulations need to be carried out for ground motion generation based on uniform hazard spectra. The proposed approach of synthesizing SVGMs accounts for local site effect, including consideration of random and spatially variable soil profiles, combined P-wave, shear horizontal (SH) wave and shear vertical (SV) wave motions for simulating tri-directional SVGMs, and the effect of degree of water saturation.

Effect of Columnar Grain Orientation on Ultrasonic Plane Wave Energy Reflection and Transmission Behaviour in Anisotropic Austenitic Weld Materials

This article describes a comprehensive quantitative analysis on effect of columnar grain orientation on ultrasonic plane wave energy reflection and transmission behaviour in acoustically anisotropic austenitic weld materials. The quantitative results are presented for following general interfaces (a) Isotropic-Anisotropic, (b) Anisotropic-Isotropic, (c) Fluid-Anisotropic, (d) Anisotropic-Fluid, (e) Anisotropic-Anisotropic, (f) Anisotropic-Free surface occur during the ultrasonic non destructive evaluation of austenitic weld materials. Explicit analytical expressions are presented for energy reflection and transmission coefficients at an interface between two arbitrarily oriented transversely isotropic materials. By applying explicit analytical expressions for energy reflection and transmission coefficients, numerical results are presented for several columnar grain orientations of the transverse isotropic austenitic weld material including both real and complex domain of the reflected and transmitted normal component of slowness vectors. Valid domains of incident wave vector angles, angular dependency of energy reflection and transmission coefficients and critical angles for reflected and transmitted waves are discussed. The existence of a reflected (or) transmitted second branch of quasi shear vertical waves and its consequence to the ultrasonic non destructive testing of austenitic weld materials are investigated. The presented comprehensive quantitative evaluation provides an overview on the effect of anisotropic properties on energy reflection and transmission coefficients in columnar grained austenitic weld materials.

Influences of magnetic field on wave propagation in generalized thermoelastic solid with diffusion

This paper is devoted to estimation of the influence of magnetic field in an elastic solid half-space under thermoelastic diffusion. The governing equations in xz -plane are solved taking into consideration the GL model. The reflection of dilatational (P) wave and shear vertical (SV) wave splits into four waves, namely: P wave, thermal wave, mass diffusion wave and SV wave. The reflection phenomena of P and SV waves from the free surface of an elastic solid with thermoelastic diffusion, under the influence of magnetic field is considered. The expressions for the reflection coefficients for the four reflected waves are obtained. These reflection coefficients are found to depend upon the angle of incidence θ of P and SV waves, thermoelastic diffusion, magnetic field and other material parameters. The numerical values for the reflection coefficients are calculated analytically and presented graphically for various values of these parameters. Relevant results of previous investigations are deduced as special cases from this study.

Refracting characteristics of backward propagating Lamb modes

Lamb waves are acoustic modes propagating along thin plates or shells and result from the coupling of longitudinal waves and shear vertical waves (polarized along the thickness direction), taking place at the surface boundaries for satisfying the boundary conditions of the waveguide. Their nature being a composition of two differently polarized components, it permits that, for some combination of frequency and wavenumber, a Lamb mode is propagating which has its group velocity contradirected with respect to the phase velocity. These are the so-called “backward” Lamb modes, and one of them takes place at the starting region (low wave number) of the S1 mode dispersion curve in aluminum. Peculiar features of a wave packet of a symmetric Lamb mode S1, backward propagating in an aluminum waveguide, are observed and anomalous behavior in refraction, diffraction and interference of this peculiar mode is experimentally put in evidence. Particularly, contradirected refraction is put in evidence, as it takes place at the boundary where a forward propagating mode is coupled to a backward propagating one, and change from forward to backward mode is obtained in case of a wedge shaped laminar plate, which goes through a zero point of the group velocity.

Discussion on Transmission and Reception of Shear Vertical Wave Propagating along Surface of Test Object

It is shown that a shear vertical (SV) wave propagating along a surface of a test object can be transmitted and received by angle probes whose angle of refraction is close to a critical angle. In order to investigate this phenomenon, simulation is carried out using the finite difference time domain method. According to the acoustic fields obtained by the simulation, the beam width of a SV wave increases with propagation, and energy associated with the SV wave exists at the surface. Therefore, the transmitted pulse can be received. The phenomenon of SV wave propagation is referred to as SVC (SV wave for a critical angle). This simulation result is verified by an experiment, which showed that the transmitted pulse is applicable to the measurement of SV wave velocity.

Wave propagation in a generalized thermoelastic material with voids

The governing equations for two-dimensional homogeneous, isotropic generalized thermoelastic half-space with voids are solved in context of Lord–Shulman theory. Three compressional waves and a shear vertical (SV) wave are shown to exist. The reflection phenomena of compressional or shear wave from the free surface of a thermoelastic solid with voids is considered. The boundary conditions at stress-free thermally insulated surface are satisfied to obtain a system of four equations in the reflection coefficients of various reflected waves. These reflection coefficients depend on the angle of incidence of striking wave, void, thermo-void and other elastic parameters. Numerical values of the complex modulus of the reflection coefficients are also visualized graphically to observe the effects of void parameters.

2차원 경계요소법에 의한 초음파 산란음장의 해석과 응용

A two-dimensional boundary element method was used for the scattering analysis of side-drilled hole(SDH). The far-field scattering amplitude was calculated for shear vertical(SV) wave, and their frequency and time-domain results were presented. The time-domain scattering amplitude showed the directly reflected wave from the SDH leading edge as well as the creeping wave. In an immersion, pulse-echo testing, two measurement models were introduced to predict the response from SDHs. The 2-D boundary element scattering amplitude was converted to the 3-D amplitude to be used in the measurement model. The receiver voltage was calculated for SV wave incidence at 45° on the 1 ㎜ diameter SDH, and the result was compared with experiment.

Reflection of SV waves from the free surface of an elastic solid in generalized thermoelastic diffusion

The governing equations for two-dimensional generalized thermoelastic diffusion in an elastic solid are solved. There exist three compressional waves and a shear vertical (SV) wave. The reflection phenomena of SV wave from the free surface of an elastic solid with generalized thermoelastic diffusion is considered. The closed-form expressions for the reflection coefficients for various reflected waves are obtained. These reflection coefficients are found to depend upon the angle of incidence of SV wave, thermoelastic diffusion parameter and other material constants. The numerical values of modulus of the reflection coefficients are presented graphically for different thermal and diffusion parameters.

Reflection of P and SV waves from free surface of an elastic solid with generalized thermodiffusion

The governing equations for generalized thermodiffusion in an elastic solid are solved. There exists three kinds of dilatational waves and a Shear Vertical (SV) wave in a two-dimensional model of the solid. The reflection phenomena of P and SV waves from free surface of an elastic solid with thermodiffusion is considered. The boundary conditions are solved to obtain a system of four non-homogeneous equations for reflection coefficients. These reflection coefficients are found to depend upon the angle of incidence of P and SV waves, thermodiffusion parameters and other material constants. The numerical values of modulus of the reflection coefficients are presented graphically for different values of thermodiffusion parameters. The dimensional velocities of various plane waves are also computed for different material constants.

Nonlinear acoustic scattering by a partially closed surface-breaking crack

A theoretical model describing the nonlinear scattering of acoustic waves by surface-breaking cracks with faces in partial contact is presented. The nonlinear properties of the crack are accounted for by suitable boundary conditions that are derived from micromechanical models of the dynamics of elastic rough surfaces in contact. Both linear and nonlinear responses of the crack are shown to be largest for a shear vertical wave incident on the surface containing the crack at an angle just above the critical angle for longitudinal waves. These findings question the fitness for the purpose of a conventional inspection method, which utilizes shear vertical waves at 45 degrees of incidence to search for surface-breaking cracks in many engineering components. For angles of incidence proximal to the critical angle of longitudinal waves, the efficiency of the second harmonic's generation appears to be the highest. Thanks to the increased sensitivity to surface-breaking cracks, this configuration seems to offer a solution to the localization problem, a task that has eluded nonlinear techniques operating under other circumstances. Finally, this model suggests a simple interpretation of the highly localized nonlinear response of delaminations in composite materials.

A note on the sensitivity of SV wave scattering to surface-breaking cracks

The results presented in this communication show that the conventional configuration adopting a shear vertical wave at 45° of incidence to detect cracks breaking the surface opposite the one on which the inspecting transducer is placed is not optimal when the crack depth is of the order of one wavelength of the inspecting wave or smaller. Angles of incidence proximal to the critical angle of longitudinal wave should be used instead.

Nonlinear interaction of plane ultrasonic waves with an interface between rough surfaces in contact.

A theoretical investigation of the nonlinear interaction between an acoustic plane wave and an interface formed by two rough, nonconforming surfaces in partial contact is presented. The macroscopic elastic properties of such a nonlinear interface are derived from micromechanical models accounting for the elastic interaction that is characteristic of spherical bodies in contact. These results are used to formulate set of boundary conditions for the acoustic field, which are to be enforced at the imperfect interface. The scattering problem is solved for plane wave incidence by using a simple perturbation approach and the harmonic balance method. Sample results are presented for arbitrary wave polarization and angle of incidence. The relative magnitude of the nonlinear signals and their potential use toward the nondestructive evaluation of imperfect interfaces are assessed. In particular, attention is drawn to the enhanced nonlinear response of an interface insonified by a shear vertical wave in the neighborhood of the longitudinal critical angle. The motivation for this investigation is provided by the need to develop nondestructive methods to detect and localize small, partially closed cracks in metals with coarse microstructures.

Line-focusing electromagnetic acoustic transducers for the detection of slit defects

This paper describes the design principles of a line-focusing electromagnetic acoustic transducer (LF-EMAT) and the results of a feasibility test for detecting slit-type defects in metals. The LF-EMAT excites shear vertical (SV) elastic waves and focuses them to a line in a metal body. It consists of a permanent magnet block and a meanderline coil, whose spacing is continuously varied so that the excited SV waves become coherent on a focal line after traveling oblique paths. The measured directivity of generation and reception show a sharp peak at the designed focal line. The LF-EMATs are then applied to detecting slit defects in the bottom surface of steel blocks, on which the focal lines are located. Portions of the scattered defect signals are received by the same EMAT. When operated at 4 MHz, the LF-EMATs are capable of detecting slits deeper than 0.05 mm. The sensitivity decreases with liftoff and the LF-EMATs are usable with liftoff up to 0.6 mm.