Attenuation of Rayleigh waves due to surface roughness

Rayleigh waves are well known to attenuate due to scattering when they propagate over a rough surface. Theoretical investigations have derived analytical expressions linking the attenuation coefficient to statistical surface roughness parameters, namely, the surface's root mean squared height and correlation length and the Rayleigh wave's wavenumber. In the literature, three scattering regimes have been identified—the geometric (short wavelength), stochastic (short to medium wavelength), and Rayleigh (long wavelength) regimes. This study uses a high-fidelity two-dimensional finite element (FE) modelling scheme to validate existing predictions and provide a unified approach to studying the problem of Rayleigh wave scattering from rough surfaces as the same model can be used to obtain attenuation values regardless of the scattering regime. In the Rayleigh and stochastic regimes, very good agreement is found between the theory and FE results both in terms of the absolute attenuation values and for asymptotic power relationships. In the geometric regime, power relationships are obtained through a combination of dimensional analysis and FE simulations. The results here also provide useful insight into verifying the three-dimensional theory because the method used for its derivation is analogous

Elastic shear wave scattering by randomly rough surfaces

Characterizing cracks within elastic media forms an important aspect of ultrasonic non-destructive evaluation (NDE) where techniques such as time-of-flight diffraction and pulse-echo are often used with the presumption of scattering from smooth, straight cracks. However, cracks are rarely straight, or smooth, and recent attention has focussed upon rough surface scattering primarily by longitudinal wave excitations. We provide a comprehensive study of scattering by incident shear waves, thus far neglected in models of rough surface scattering despite their practical importance in the detection of surface-breaking defects, using modelling, simulation and supporting experiments. The scattering of incident shear waves introduces challenges, largely absent in the longitudinal case, related to surface wave mode-conversion, the reduced range of validity of the Kirchhoff approximation (KA) as compared with longitudinal incidence, and an increased importance of correlation length. The expected reflection from a rough defect is predicted using a statistical model from which, given the angle of incidence and two statistical parameters, the expected reflection amplitude is obtained instantaneously for any scattering angle and length of defect. If the ratio of correlation length to defect length exceeds a critical value, which we determine, there is an explicit dependence of the scattering results on correlation length, and we modify the modelling to find this dependence. The modelling is cross-correlated against Monte Carlo simulations of many different surface profiles, sharing the same statistical parameter values, using numerical simulation via ray models (KA) and finite element (FE) methods accelerated with a GPU implementation. Additionally we provide experimental validations that demonstrate the accuracy of our predictions

Attenuation of Rayleigh waves due to three-dimensional surface roughness: A comprehensive numerical evaluation

The phenomenon of Rayleigh wave attenuation due to surface roughness has been well studied theoretically in the literature. Three scattering regimes describing it have been identified-the Rayleigh (long wavelength), stochastic (medium wavelength), and geometric (short wavelength)-with the attenuation coefficient exhibiting a different behavior in each. Here, in an extension to our previous work, we gain further insight with regard to the existing theory, in three dimensions, using finite element (FE) modeling, under a unified approach, where the same FE modeling techniques are used regardless of the scattering regime. We demonstrate good agreement between our FE results and the theory in all scattering regimes. Additionally, following this demonstration, we extend the results to cases that lie outside the limits of validity of the theory

Ultrasonic attenuation and phase velocity of high-density polyethylene pipe material

Knowledge of acoustic properties is crucial for ultrasonic or sonic imaging and signal detection in nondestructive evaluation (NDE), medical imaging, and seismology. Accurately and reliably obtaining these is particularly challenging for the NDE of high-density polyethylene (HDPE), such as is used in many water or gas pipes, because the properties vary greatly with frequency, temperature, direction and spatial location. Therefore the work reported here was undertaken in order to establish a basis for such a multiparameter description. The approach is general but the study specifically addresses HDPE and includes measured data values. Applicable to any such multiparameter acoustic properties dataset is a devised regression method that uses a neural network algorithm. This algorithm includes constraints to respect the Kramers-Kronig causality relationship between speed and attenuation of waves in a viscoelastic medium. These constrained acoustic properties are fully described in a multidimensional parameter space to vary with frequency, depth, temperature, and direction. The resulting uncertainties in acoustic properties dependence on the above variables are better than 4% and 2%, respectively, for attenuation and phase velocity and therefore can prevent major defect imaging errors

A displacement-based finite element formulation for solving elastic wave problems in coupled fluid-solid media on a GPU

Ultrasonic wave propagation and scattering involving both solids and fluids underpins many key configurations in non-destructive testing and underwater acoustics. The resulting interactions are highly dependent on both material parameters and geometries and are difficult and expensive to investigate experimentally. Modelling capabilities are often used to overcome this, but these are also complex and computationally expensive due to the complexity of the fluid-solid interactions. We introduce a novel explicit time-domain finite element method for simulating ultrasonic waves interacting with fluid-solid interfaces. The method is displacement-based, and relies on classical hourglassing control, in addition to a modified time-stepping scheme to damping out shear motion in an inviscid fluid. One of the key benefits of the displacement-based approach is that nodes in the fluid have the same number of degrees of freedom as those in the solid. Therefore defining a fluid-solid model is as easy as defining an all-fluid or all-solid model, avoiding the need for any special treatments at the interfaces. It is thus compatible with typical elastodynamic finite element formulations and ready for implementation on a graphical processing unit. We verified the method across a range of problems involving millions of degrees of freedom in fields such as non-destructive testing and underwater acoustics

Fatigue State Characterization of Steel Pipes Using Ultrasonic Shear Waves

The phenomenon of the reduction in the propagation speed of an ultrasonic wave when it travels through a fatigue zone has been well-studied in the literature. In addition, it has been established that shear waves are more severely affected by the presence of such a zone, compared with longitudinal waves. Our study uses these phenomena to develop a method able to characterize the fatigue state of steel pipes. Initially, the existing theory regarding the increased sensitivity of shear waves to the presence of fatigue is validated through measuring and comparing the change in propagation speed of both longitudinal and bulk shear waves on flat geometries, at different fatigue states. The comparison is achieved with the aid of ultrasonic speed C-scans of both longitudinal and shear waves, with the latter now being obtainable through our implementation of advances in electromagnetic acoustic transducers (EMATs) technology. EMATs have not been traditionally used for producing C-scans, and their ability do to so with adequate repeatability is demonstrated here; we show that shear wave scanning with EMATs now provides a possibility for inspection of fatigue damage on the inner surface of pressure-containing components in the nuclear power industry. We find that the change in ultrasonic wave speed is amplified when shear waves are used, with the magnitude of this amplification agreeing well with the theory. Following the verification of the theory, the use of EMATs allowed us to tailor the shear wave scanning method to pipe geometries, where C-scans with conventional piezoelectric transducers would not have been possible, with the results successfully revealing the presence of fatigue zones

Ultrasonic methods for the detection of near surface fatigue damage

Fatigue zones in a material can be identified using ultrasonic waves, as it has been shown that their propagation speed will reduce when travelling through such a zone. However, as fatigue damage is usually concentrated in a thin near-surface layer, through-thickness measurements result in very small changes of the average propagation speed across the full thickness, which are potentially difficult to reliably correlate to specific fatigue states. In this study, we have completed fatigue state assessments using Rayleigh waves, which travel on the surface of a material, to maximise those changes. We found that the use of Rayleigh waves amplifies the changes in speed, after propagation in the damaged region, by a factor of up to ten. The monotonic nature of the reduction in wave speed was verified against the theory using dislocation density measurements. Finally, a stiffness-reducing finite-element modelling technique, able to capture the effects of fatigue on the time of flight of longitudinal bulk and Rayleigh waves, was also derived and verified against the experimental measurements