Transmission Of Rayleigh Waves Research Articles

An ultrasonic approach for characterising subsurface fractures in concrete

ABSTRACT An ultrasonic Rayleigh wave detection method is proposed to determine the geometrical characteristics of subsurface small-scale fractures in concrete. A three-dimensional observation system, including an inclined wedge ultrasonic device, is used to obtain the Rayleigh wave wide-angle data to exhibit the azimuth-dependent scattered wave field. The anisotropic characteristics of Rayleigh wave transmission coefficient are used to determine the distribution range and dip angle of fractures. Fracture models in concrete with different dip angles are designed, and the dip angle is correlated with the degree of attenuation (transmission coefficient) anisotropy. The transmission coefficient characteristics are presented in a random observing system. A focusing approach can be adopted to distinguish the subsurface fracture and to verify the reliability and flexibility of the surface wave approach in practice. The tendencies of experimental results are consistent with patterns obtained from numerical simulation. The proposed method has important application prospects for the non-destructive testing of complex invisible fractures in concrete.

A Sensitive Frequency Range Method Based on Laser Ultrasounds for Micro-Crack Depth Determination.

The laser ultrasonic method using the characteristics of transmitted Rayleigh waves in the frequency domain to determine micro-crack depth is proposed. A low-pass filter model based on the interaction between Rayleigh waves and surface cracks is built and shows that the stop band, called the sensitive frequency range, is sensitive to the depth of surface cracks. The sum of transmission coefficients in the sensitive frequency range is defined as an evaluated parameter to determine crack depth. Moreover, the effects of the sensitive frequency range and measured distance on the evaluated results are analyzed by the finite-element method to validate the robustness of this depth-evaluating method. The estimated results of surface cracks with depths ranging from 0.08 mm to ~0.5 mm on the FEM models and aluminum-alloy samples demonstrate that the laser ultrasounds using the characteristics of Rayleigh waves in the frequency domain do work for quantitative crack depth.

Numerical simulation of angled surface crack detection based on laser ultrasound

As an important branch of non-destructive testing, laser ultrasonic testing has attracted increasing attention in the field of material testing because of its instantaneity, non-contact and wide adaptability. Based on the finite element method, the process of laser-excited ultrasonic signal is numerically simulated, and the influence of angled cracks on the ultrasonic signal is analyzed. In this paper, the effects of the time function, pulse width, and spot radius of a Gaussian light source are analyzed through the transient field. The different modes of the ultrasonic signal are used to fit the crack’s angle, depth, and width to complete the characteristic analysis of the surface angled crack. The results show that the displacement peak-valley difference of the direct Rayleigh wave is negatively correlated with the crack angle. The displacement extremes of the transmitted Rayleigh wave boundary are negatively correlated with crack depth and width, while the transmitted Rayleigh wave is positively correlated. This paper presents a method for the quantitative analysis of surface-angled cracks and provides a theoretical basis for further experimental verification.

NDE Characterization of Surface Defects on Piston Rods in Shock Absorbers Using Rayleigh Waves

In general, shock absorbers are components that can absorb shock and vibration energy caused by wheel behavior, and they provide handling stability. As a piston rod is an important component in shock absorbers, multiple processes are performed in order to guarantee its quality during manufacturing. Micro-defects can be generated on the surfaces of piston rods after processing. Because these defects can degrade the function of shock absorbers, proper non-destructive techniques are necessary to monitor the surfaces of piston rods. In this study, micro-defects were artificially machined on the surfaces of piston rods. In particular, a Rayleigh wave technique was adopted to detect defects on the surfaces of the piston rods, and Rayleigh wave behaviors were analyzed to establish beam profiles. In terms of the experimental method, defects were fabricated on the piston rods, and the optimal Rayleigh angle was determined using the pulse-echo method with ultrasonic transducers in a water tank. This was performed to evaluate the characteristics of the Rayleigh waves. In testing, regardless of the types of micro-defects on the surfaces of the pistons, it was found that the optimal inspection condition could be in the range of 5–10 mm, where ultrasonic signals were received with a high resolution. Moreover, the behaviors of the transmitted Rayleigh waves were simulated, and reflection, transmission, and scattering occurred due to defects at the interface between the water and steel. Thus, the propagation of Rayleigh waves and the optimal test conditions were implemented through FEM simulation to generate effective Rayleigh waves.

Finite element analysis of laser-generated Rayleigh wave for sizing subsurface crack in frequency domain

In order to realize the quantitative detection of subsurface cracks, finite element method (FEM) was used to study the interaction of laser-generated Rayleigh wave and subsurface crack with different buried depths and lengths in this paper. The transmitted and reflected Rayleigh waves of subsurface cracks were analyzed in frequency domain, it is found that the center frequency of transmission wave decreases with the increase of crack length when the buried depth of crack remains unchanged, and increases with the increase of crack depth when the crack length remains unchanged. The center frequency of reflected Rayleigh wave is independent of crack length, and has a quadratic function relation with the buried depth of subsurface crack. The relationships, between the ratio of buried depth to incident Rayleigh wavelength and the ratio of reflected Rayleigh wave frequency to incident Rayleigh wave frequency, and the ratio of crack length to incident Rayleigh wavelength and the ratio of transmitted Rayleigh wave frequency to incident Rayleigh wave frequency, were obtained respectively based on the frequency analysis. The relationships were verified by the simulation signals, it is found that the maximum relative error of the buried depth of the subsurface cracks determined by the proposed relationship is 5.939%, and the maximum relative error of the length of the subsurface cracks is 12.149%. The research results show that the proposed method is promising in quantitative characterization of the buried depth and length of subsurface cracks in metallic materials.

Control of Rayleigh wave propagation through imposing Mindlin boundary conditions on the surface

A resonant metasurface design based on boundary condition (BC) manipulation was recently established to control low-frequency Lamb waves in a plate. This study identifies the necessary BCs that forbid Rayleigh wave propagation in order to find a rational design methodology for an optimized BC-controlled meta-surface. An analytical study of Mindlin BCs, a type of Cauchy BCs, shows promise in surface wave control. The frequency-domain and time-domain finite element studies performed by imposing Mindlin BCs in the path of Rayleigh wave propagation are consistent with analytical predictions, exhibiting no Rayleigh wave transmission. The simulations reveal mode conversions from Rayleigh wave to bulk waves directed into the half-space and a low amplitude Rayleigh wave reflection. For a finite-sized BC patch, the radial beam spreading of the mode-converted bulk waves keeps some energy near the surface, which could convert back to Rayleigh waves at the end of the BC patch. Thus, the BC patch must be sufficiently long to effectively suppress surface waves. Finally, we show that the Mindlin BCs can be imposed by a rod-like prismatic resonator at the resonator’s longitudinal frequency. These findings provide new insights into the coupling that promotes surface wave control, potentially leading to novel metasurface designs.

Width and depth gauging of rectangular subsurface defects based on all-optical laser-ultrasonic technology

In this study, width and depth of rectangular subsurface defects have been successfully gauged based on all-optical laser-ultrasonic technology. A specific all-optical laser-ultrasonic system has been developed to obtain Rayleigh waves from subsurface defects. Time domain and frequency domain analysis of the obtained Rayleigh waves show that most of the high-frequency Rayleigh waves with small wavelengths transmit the subsurface defect. Only a small part of the low-frequency Rayleigh waves with large wavelengths are reflected by the subsurface defect. This phenomenon is completely different from that of surface defect, because surface defect reflects high-frequency Rayleigh waves and allows low-frequency Rayleigh waves to transmit. In addition, it is found that the transmitted mode-converted Rayleigh wave has the smallest amplitude but the highest center frequency compared with other obtained incident, reflected mode-converted and transmitted Rayleigh waves. Width and depth of subsurface defects are measured by the proposed three-step detection method, which is based on the arrival time of the incident, reflected mode-converted, transmitted and transmitted mode-converted Rayleigh waves, as well as the movement distance of samples. Agreement between experimental results and digital microscope measurement reference-results indicates applicability of the proposed three-step detection method in simultaneous measuring width and depth of rectangular subsurface defects.

Remote characterization of surface slots by enhanced laser-generated ultrasonic Rayleigh waves

Characterization of surface features is essential in many industrial applications, especially for features with large depths, high aspect ratios or under extreme conditions. This work presents a non-contact method to characterize surface slots with large lengths using ultrasonic Rayleigh waves generated by a pulsed laser. A delay-and-sum superposition technique is applied to enhance the signal to noise ratio of transmitted Rayleigh waves. The length of the slot can be calculated from the time-of-flight information of Rayleigh waves without any prior knowledge of its orientation, width or aspect ratio. Both numerical simulations and experiments are conducted to demonstrate the proposed method, showing excellent performance. Furthermore, mode conversion has been studied to understand its impact on the reconstruction accuracy. Given the non-contact feature of the laser ultrasonic technique, the proposed method provides a simple and feasible avenue for the rapid characterisation of normal and angled surface features with high aspect ratio in extreme environments.

All-optical laser-ultrasonic technology for width and depth gauging of rectangular surface-breaking defects.

In this paper, the width and depth of rectangular surface-breaking defects were successfully gauged using an all-optical laser-ultrasonic system. The finite element method was used to simulate propagating paths of defect-induced reflected and transmitted Rayleigh waves. It is observed that most Rayleigh waves with wavelengths less than the depth of the defect are reflected by the defect. A small part of the Rayleigh waves with wavelengths greater than the depth of the defect directly transmits through the bottom edge of the defect without acting on the left edge of the defect. Based on the simulation results, a three-step detection method of width and depth gauging of rectangular surface-breaking defects is proposed. In the first step, the pulsed laser and detection laser are irradiated on one side of the defect. In the second step, the sample is moved to a certain distance to ensure that both lasers reach the other side of the defect. In the third step, two lasers are irradiated on both sides of the defect. The width and depth of the defect are calculated according to the arrival time of the incident, reflected, and transmitted Rayleigh waves, as well as the movement distance of the sample. Experimental results are consistent with the reference-results measured by using a digital microscope. The proposed three-step detection method is proved to be feasible in simultaneous measurement of the width and depth of rectangular surface-breaking defects. Furthermore, it may be potentially useful for measuring other types of defect structures.

A Novel Method for Evaluation of Surface Breaking Crack Using Position-Time Graph

A large plate like structures can undergo some severe ruptures because of the stress created by the mass and shape. Ruptures are regularly started by surface cracks. For this aim, it is important to evaluate brutality of the noticeable cracks, by constant nondestructive assessments. In this work, a novel method for surface crack depth estimation based on Rayleigh waves by electromagnetic acoustic transducers (EMATs) is introduced. The method is based on a position-time (P-T) graph for direct transmitted Rayleigh waves between fixed transmitter and uniformly movable receiver on surface of the specimen. The process is repeated on different center frequencies both in the experiment as well as in two-dimensional finite element method simulation on steel plates. One of the specimens was without crack while the other one holds surface cracks with the depth ranging from 3–6 mm. Results obtained from simulation and experiment were significant to estimate crack depth with a maximum error of 7.5%.

Non-reciprocal Rayleigh wave propagation in space–time modulated surface

Research on non-reciprocal propagation of waves is of great significance in the field of photonic and phononic crystals for realizing flexible one-way propagation devices with potential engineering applications. Here, non-reciprocal Rayleigh waves are investigated in a continuous two-dimensional (2D) semi-infinite medium bound with an array of space–time modulated spring–mass oscillators. The involved modulation is a wave-like perturbation of the surface of the continuous medium that breaks time-reversal symmetry and reciprocity. To characterize the propagation of Rayleigh waves in such a complex 2D medium with continuous and discrete interface, an analytical study is performed to obtain dispersion-engineered bandgaps by adopting the asymptotic method and coupled mode theory, which is also validated by numerical simulation. Specifically, the non-reciprocal transmission of Rayleigh waves with one-way mode conversion is illustrated, and various relevant physical quantities, including conversion length and band gap size, are quantitatively estimated. This work sheds light on versatile control of Rayleigh wave propagation ranging from sensing and evaluation of engineering structures to guided wave-based damage detection techniques.

An underground barrier of locally resonant metamaterial to attenuate surface elastic waves in solids

The low frequency of seismic waves severely limits the regulation of wave propagation in earthquake protection engineering applications. In recent years, locally resonant metamaterials have been introduced for seismic wave attenuation. A barrier based on locally resonant metamaterials consisting of rows of wells is proposed to reduce the transmission of Rayleigh waves during propagation, achieving earthquake protection. First, comparisons are made between the wells of the metamaterial, empty wells, solid steel wells, and a continuous steel wall. It is evident that locally resonant metamaterials exhibit better performance than that of the other materials. Simulations of the relationships between the attenuation of Rayleigh waves and the depth, number of rows, and working frequency of the wells are presented. With a barrier of ten rows of wells, where the diameter of each well is less than one-twentieth of the wavelength of the Rayleigh wave and the depth of the wells is nearly four-fifths of the wavelength, the maximum attenuation reaches up to 16.2 dB when all the wells share the same working frequency, and the bandwidth is broader, but the maximum value is less when the rows have different working frequencies. Depending on the demand for a higher value or a broader bandwidth of the Rayleigh wave attenuation, this barrier promotes flexible and achievable improvements by adding rows or decentralizing the working frequencies of the wells. The vast potential of seismic wave attenuation from locally resonant metamaterials is anticipated in the future.

Surface circular-arc defects interacted by laser-generated Rayleigh wave

In this work, the finite element method (FEM) is used to investigate the propagation of laser-generated Rayleigh wave along the material surface at the quarter-arc transition surface under the thermoelastic regime, and to establish the relationship between the circular-arc radius and the time domain characteristics of reflected and transmitted Rayleigh waves. The simulation shows that the amplitude of the reflected Rayleigh wave decreases whereas the amplitude of the transmitted Rayleigh wave increases as the radius increases, which is significantly different from the well-studied interaction of Rayleigh waves with the perpendicular transition surface. By introducing the circular-arc defects which are easily formed in some engineering components during the material surface quenching, we find that the depth gauging of the surface circular-arc defects is more accurate in comparison to the surface rectangular defects based on the arrival time of the transmitted Rayleigh wave. This is further verified by the corresponding experimental results. These foundings are of practical values for detecting the depth of the arc defect quantitatively by the laser ultrasonic technique.

Multiple Wavemode Scanning for Near and Far-Side Defect Characterisation

The combination of ultrasonic inspections using different wavemodes can give more information than is available with single mode inspection. In this work, the response of shear and Rayleigh waves to surface-breaking defects propagating on the near-side and far-side of a sample is investigated. The directivity of shear waves generated by a racetrack coil electromagnetic acoustic transducer (EMAT) is identified and used to set an ideal separation for a pair of transmit-receive EMATs. Defects are indicated by a reduction in the transmitted Rayleigh wave amplitude, and by blocking of the shear wave. Used together, these can identify features in the bulk wave behaviour which are due to near-face surface-breaking defects, and give a full picture of both surfaces. By using a combination of the two wavemodes, the angle of propagation and length of any near-side defects can additionally be identified. A scanning method for samples is proposed.

Reduced-scale ultrasonic modelling of Rayleigh wave transmission over seismic barriers formed by periodic arrays of vertical holes

Seismic barriers are used widely to protect buildings from traffic-induced ground vibrations, mainly from propagating Rayleigh surface waves. Experimental investigations of real size seismic barriers at frequencies typical for traffic-induced ground vibrations, i.e. at 10-100 Hz, are costly and time consuming. In the present work, an alternative and much less expensive approach is proposed - a reduced-scale experimental modelling using ultrasonic Rayleigh wave propagation over very small-scale replicas of real seismic barriers. Experimental investigations of propagation of Rayleigh wave pulses with the central frequency of 1 MHz have been carried out for seismic barriers formed by periodic arrays of vertical holes in Aluminium samples. Measurements of transmission and reflection coefficients of Rayleigh waves for different types of arrays and for different incident angles have been carried out and compared with the earlier published results obtained for real seismic barriers.

Surface acoustic waves in acoustic superlattice lithium niobate coated with a waveguide layer

The effects of the waveguide layer on the band structure of Rayleigh waves are studied in this work based on a one-dimensional acoustic superlattice lithium niobate substrate coated with a waveguide layer. The present phononic structure is formed by the periodic domain-inverted single crystal that is the Z-cut lithium niobate substrate with a waveguide layer on the upper surface. The plane wave expansion method (PWE) is adopted to determine the band gap behavior of the phononic structure and validated by the finite element method (FEM). The FEM is also used to investigate the transmission of Rayleigh waves in the phononic structure with the interdigital transducers by means of the commercial package COMSOL. The results show that, although there is a homogeneous waveguide layer on the surface, the band gap of Rayleigh waves still exist. It is also found that increasing the thickness of the waveguide layer, the band width narrows and the band structure shifts to lower frequency. The present approach can be taken as an efficient tool in designing of phononic structures with waveguide layer.

Numerical study of Rayleigh wave propagation along a horizontal semi-infinite crack buried in half-space.

The present article investigates the propagation of Rayleigh waves along a horizontal semi-infinite crack, and its interaction with the crack tip. Finite element analysis was used to simulate wave propagation and study the interaction. An incident Rayleigh wave diffracts as bulk waves into the half-space upon interaction with the crack tip. It was observed that the diffracted bulk modes can interact with the half-space boundary, and mode converts into a Rayleigh wave traveling along the boundary. A qualitative analysis was performed to determine the effect of crack depth using transmission, reflection, and scattering coefficients. Moreover, the possibility of Lamb wave generation also arises since the crack face and boundary form a stress-free plate section. The source of the "turning" Lamb modes was also identified from the observations. The characteristics of the transmitted Rayleigh wave were also explored, and a certain degree of mode coupling between Rayleigh and shear waves was observed when the crack tip was farther away from the boundary.

Characterisation of aluminium nitride films and surface acoustic wave devices for microfluidic applications

Aluminium nitride (AlN) films with different thicknesses (from 2.3 to 4.7μm) were deposited onto high resistivity silicon substrates using magnetron sputtering. Crystalline and bonding structures of the deposited AlN films were characterised. The AlN films showed a highly c-axis texture. AlN film based surface acoustic wave (SAW) devices were fabricated and characterised. The SAW devices showed Rayleigh wave transmission band with a large side-lobe suppression of ∼15dB. With the increase in film thickness, both the central band frequency and electromechanical coupling coefficient were increased, and values of temperature coefficient of frequency was increased linearly from −21.3 to −27.4ppm/K. Microfluidic manipulations including streaming, pumping and jetting have been realised using AlN SAW devices. The applied RF power boundary between streaming and pumping and that between the pumping and jetting decreased with the increase of film thickness. The measured streaming and pumping velocities as well as device surface temperatures increased with the film thickness.

Probing of crack breathing by pulsed laser-generated acoustic waves

Experimental results on all-optical monitoring of the nonlinear motion of a surface-breaking crack are reported. Crack closing is induced by quasi-continuous laser heating, while Rayleigh surface acoustic pulses and bulk longitudinal surface skimming acoustic pulses are also generated and detected by lasers. By exploiting the strong dependence of the acoustic pulses reflection and transmission efficiency on the state—open or closed—of the contacts between the crack faces, the parametric modulation of ultrasonic pulses is achieved. It is observed that bulk acoustic waves, skimming along the surface can be more sensitive to crack motion than Rayleigh surface waves. It has been found that crack closure by thermo-elastic stresses modifies the propagation paths of the acoustic rays from the point source to the point receiver. Consequently, the arrival times of the acoustic waves contain information on the state of crack closure induced by a particular intensity of laser heating. An important dependence of the detected signals on the initial width/state of the crack and on the presence of necks in the crack opening profile is revealed. It is demonstrated that the mode conversion of the skimming longitudinal bulk waves incident on the crack into the transmitted Rayleigh waves is very sensitive to imperfectness of crack closure. The proposed interpretation of the experimental observations is supported by atomic force microscopy measurements.

Noncontact, Nondestructive Evaluation of Realistic Cracks with Surface Acoustic Waves by Scanning Excitation and Detection Lasers

Nondestructive evaluation of surface-breaking cracks with a scanning laser source, a scanning laser probe, or a scanning laser pump–probe setup is discussed. Multimode scattering of laser-excited surface acoustic wave pulses by artificial slots, realistic fatigue, or impulsive cracks is considered. This includes measuring the size of cracks in the micrometer-to-millimeter range by optical recording of the complete displacement or velocity field around the crack. Results obtained with a scanning pump–probe setup for a partially closed microcrack, generated by an elastic shock pulse in silica, are compared with those achieved with a scanning source or scanning probe for machined open notches. Crack size analysis based on the frequency spectrum of the reflected Rayleigh wave and the time lag of the transmitted Rayleigh wave is discussed. Signal enhancement effects observed in the displacement and velocity field near the crack are studied.