Rayleigh Wave Reflection Coefficients Research Articles

Characterization of Surface-Breaking Cracks on Tubular Structures Using Ultrasonic Phased Array with Rayleigh Waves

Surface-breaking cracks are typical defects in tubular structures. Compared with other types of defects such as internal voids, surface cracks often impose more serious threats to structural integrity. This study presents an approach to detect and characterize surface-breaking cracks on tubular samples through the use of ultrasonic phased array technology with surface acoustic waves (SAWs). A Rayleigh type surface wave is selected in our work as it is nondispersive and highly sensitive to surface and subsurface defects. Finite element (FE) analysis is used to simulate the interaction between Rayleigh waves and surface-breaking cracks with varying depths, inclined angles and profiles. The reflection coefficient of Rayleigh waves is calculated based on simulation results and fitted to a proper model. Crack depths and inclined angles can be evaluated from the fitted curves. Furthermore, a full matrix capture (FMC) data acquisition strategy is simulated in FE models with phased array to collect pulse-echo signals of Rayleigh waves. An array imaging algorithm is applied to FMC data and adapted to curved surface. The profile and location of surface cracks are reconstructed from imaging results. The configuration of phased array is optimized to increase the resolution of the method. The proposed approach is validated numerically and provides an efficient way to measure the length, depth and inclined angle of surface-breaking cracks on tubular component.

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.

Direct and continuous measurement of depth-dependent reflection coefficients of Rayleigh waves for surface discontinuity: Normal slot

A new method and principle were presented for the continuous measurement of the depth-dependent reflection coefficient of Rayleigh waves or their pulse interacting with various surface discontinuities. The method was to record the reflection echo amplitudes for varying depth during scanning the Rayleigh wave pulse with a small lateral beam width along a surface discontinuity with a small slope in depth. In the experiments using a declined slot and intensively focused Rayleigh waves, the coefficients were continuously measured with quite good reproducibility in the range of 0.05<d/λ (slot-depth/Rayleigh wave wavelength) <2.57. In 0.05<d/λ<1.4, the results showed good agreement with other experimental results that had been determined by conventional method [L. J. Bond, Ultrasonics 71, 71–77 (1979); M. Hirao et al., J. Acoust. Soc. Am. 72, 602–606 (1982); H. M. Frost et al., Proc. Ultrason. Symp. IEEE (1975), 604–607] as intermittent point-to-point data and several numerical results [L. J. Bond, Ultrasonics 71, 71–77 (1979); R. J. Blake and L. J. Bond, ibid. 28, 214–228 (1990); M. Munasinhe, Ph.D. thesis, McGill University, Canada 1973; A. K. Mal and L. Knopoff, Bull. Seismol. Soc. Am. 55, 319–334 (1965)]. Especially, in the extremely shallow range of 0.05<d/λ<0.3, the reflection coefficients, showing quite good agreement with the numerical estimation, were measured while any other experimental data for slots or down steps have not been reported in 0.05<d/λ<0.25. It was shown that the new method could be used to evaluate more conveniently and quantitatively the depth or depth profile of various surface features in the long-wavelength or shallow-depth region of about 0.05<d/λ<0.5.

Modeling and evaluating the scattering of Rayleigh waves by a linear distribution of surface cracks

A numerical evaluation model of the reflection coefficient of Rayleigh waves for a linear distribution of surface cracks is developed using the weight function estimation method. The numerical evaluation of the reflection coefficients varying with respect to the crack depth ratios, frequencies, and the number of the cracks for several commonly used engineering materials is performed. The results show that the model can effectively be used to evaluate the reflection coefficient for a linear distribution of the cracks. The crack depth which can be evaluated has been extended substantially and the evaluation results have been improved.

Ultrasonic scattering models for distribution of cracks

To evaluate the initiation and growth behaviour of a distribution of cracks, an acoustic scattering model for a planar distribution of cracks is developed based on generalized reciprocity theory and Kino's scattering formalism. Subsequently, an acoustic scattering model for a linear distribution of surface cracks in the form of the local stress intensity factors is derived by using the elastostatic energy balance of crack formation. The numerical evaluation of the reflection coefficient of Rayleigh waves for a linear distribution of semi-elliptic surface cracks is subsequently performed. The results show that the reflection coefficient, varying with respect to the crack depth ratio for a linear distribution of cracks, can effectively be evaluated by using the model.

Transmission and reflection of Rayleigh waves by a high impedance obstacle of finite length

A new method is presented for calculating the transmission and reflection coefficients of Rayleigh waves by a high impedance obstacle of finite length. The problem is formulated in terms of simultaneous integral equations which can be solved by a kind of iterative procedure. As a result, the transmission and reflection coefficients can be expressed by complex contour integrals along branch cuts associated with a function in the integrands. The transmission and reflection coefficients are computed numerically by assuming a fused‐silica substrate and are compared with those obtained by using Jones’s method of approximation. It is inferred that the present approach, though it takes more computing time when compared to Jones’s method, can predict the transmission and reflection coefficients with reasonable accuracy even if the obstacle is small.