Finite Element Simulation of Ultrasonic Scattering by Rough Flaws with Multi-Scale Distortions

The roughness of a flaw's surface significantly affects the scattering behavior of ultrasonic waves. It is vital to understand the impact of roughness on flaw echoes, especially when performing ultrasonic nondestructive inspection on safety-critical components. However, the current approach for creating rough flaw models fails to reconstruct complicated cracks with secondary cracks. Here, a multi-scale distortion method is developed to generate a rough flaw by using an optical microscope image of a real flaw. The finite element (FE) is then implemented to simulate the near-surface rough flaws in nickel-based bars, which are detected by an offsetting immersion transducer with mode-converted transverse waves. Numerical results show that the randomness and complexity of flaw echoes from rough flaws are exceptionally high. The gap between the maximum and minimum normalized amplitude values of flaw echoes from a rough crack with secondary cracks can reach 7.125 dB. Meanwhile, the maximum time of flight (TOF) is almost twice as large as the minimum TOF. Therefore, the present method can generate effective rough flaw models in terms of macroscopic rough geometry and microscopic rough surface. Moreover, the impact of the rough flaw surface on the flaw echoes goes beyond amplitude changes and may make flaw location challenging.

Numerical Study on Surface Roughness Measurement Based on Nonlinear Ultrasonics in Through-Transmission and Pulse-Echo Modes

Ultrasonic is one of the well-known methods for surface roughness measurement, but small roughness will only lead to a subtle variation of transmission or reflection. To explore sensitive techniques for surfaces with small roughness, nonlinear ultrasonic measurement in through-transmission and pulse-echo modes was proposed and studied based on an effective unit-cell finite element (FE) model. Higher harmonic generation in solids was realized by applying the Murnaghan hyperelastic material model. This FE model was verified by comparing the absolute value of the nonlinearity parameter with the analytical solution. Then, random surfaces with different roughness values ranging from 0 μm to 200 μm were repeatedly generated and studied in the two modes. The through-transmission mode is very suitable to measure the surfaces with roughness as small as 3% of the wavelength. The pulse-echo mode is sensitive and effective to measure the surface roughness ranging from 0.78% to 5.47% of the wavelength. This study offers a potential nondestructive testing and monitoring method for the interfaces or inner surfaces of the in-service structures.

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.

Acoustic Scattering Models from Rough Surfaces: A Brief Review and Recent Advances

This paper proposes a brief review of acoustic wave scattering models from rough surfaces. This review is intended to provide an up-to-date survey of the analytical approximate or semi-analytical methods that are encountered in acoustic scattering from random rough surfaces. Thus, this review focuses only on the scattering of acoustic waves and does not deal with the transmission through a rough interface of waves within a solid material. The main used approximations are classified here into two types: the two historical approximations (Kirchhoff approximation and the perturbation theory) and some sound propagation models more suitable for grazing observation angles on rough surfaces, such as the small slope approximation, the integral equation method and the parabolic equation. The use of the existing approximations in the scientific literature and their validity are highlighted. Rough surfaces with Gaussian height distribution are usually considered in the models hypotheses. Rather few comparisons between models and measurements have been found in the literature. Some new criteria have been recently determined for the validity of the Kirchhoff approximation, which is one of the most used models, owing to its implementation simplicity.

Grain Scattering Noise Modeling and Its Use in the Detection and Characterization of Defects Using Ultrasonic Arrays

In the field of ultrasonic array imaging for non-destructive testing (NDT), material structural noise caused by grain scattering is one of the main sources of error when characterizing defects that are found in the polycrystalline materials. The existence of grains can also severely affect the detection performance of ultrasonic testing, making small defects indistinguishable from the grain indications due to ultrasonic attenuation and backscatter. This paper proposes a model in which the statistical distribution of the defect data is obtained from different realizations of the grain structure. This statistical distribution, termed the defect+grains model in this paper, is shown to contain information that is needed for detection and characterization of defects. Hence, given a specific measurement configuration, the characterization result can be obtained by constructing a defect+grains model based on the multiple realizations of each possible defect and calculating their probability. The detection, classification, and sizing accuracy are shown to be predictable by quantifying the probabilities that an experimentally measured defect matches the different defect+grains models. This defect+grains modeling approach gives insight into the detection/characterization problem, leading to an evaluation of the fundamental limits of the achievable inspection performance.

Angular and frequency behaviour of elastodynamic scattering from embedded scatterers

The elastodynamic scattering behaviour of a finite-sized scatterer in a homogeneous isotropic medium can be encapsulated in a scattering matrix (S-matrix) for each wave mode combination. In a 2-dimension (2D) space, each S-matrix is a continuous complex-valued function of 3 variables: incident wave angle, scattered wave angle and frequency. In this paper, the S-matrices for various 2D scatterer shapes (circular voids, straight cracks, rough cracks and a cluster of circular voids) are investigated to find general properties of their angular and frequency behaviour. For all these shapes, it is shown that the continuous data in the angular dimensions of their S-matrices can be represented to a prescribed level of accuracy by a finite number of complex-valued Fourier coefficients that are physically related to the angular orders of the incident and scattered wavefields. It is shown mathematically that the number of angular orders required to represent the angular dimensions of an S-matrix at a given frequency is a function of overall scatterer size to wavelength ratio, regardless of its geometric complexity. This can be interpreted as a form of the Nyquist sampling theorem and indicates that there is an upper bound on the sampling interval required in the angular domain to completely define an S-matrix. The variation of scattering behaviour with frequency is then examined. The frequency dependence of the S-matrix can be interpreted as the Fourier transform of the time-domain impulse response of the scatterer for each incident and scattering angle combination. Depending on the nature of the scatterer, these are typically decaying reverberation trains with no definite upper bound on their durations. Therefore, in contrast to the angular domain, there is no lower bound on the sampling interval in the frequency domain needed to completely define an S-matrix, although some pragmatic solutions are suggested. These observations may help for the direct problem (computing ultrasonic signals from known scatterers efficiently) and the inverse problem (characterising scatterers from measured ultrasonic signals).

Ultrasonic defect characterization using parametric-manifold mapping

The aim of ultrasonic non-destructive evaluation includes the detection and characterization of defects, and an understanding of the nature of defects is essential for the assessment of structural integrity in safety critical systems. In general, the defect characterization challenge involves an estimation of defect parameters from measured data. In this paper, we explore the extent to which defects can be characterized by their ultrasonic scattering behaviour. Given a number of ultrasonic measurements, we show that characterization information can be extracted by projecting the measurement onto a parametric manifold in principal component space. We show that this manifold represents the entirety of the characterization information available from far-field harmonic ultrasound. We seek to understand the nature of this information and hence provide definitive statements on the defect characterization performance that is, in principle, extractable from typical measurement scenarios. In experiments, the characterization problem of surface-breaking cracks and the more general problem of elliptical voids are studied, and a good agreement is achieved between the actual parameter values and the characterization results. The nature of the parametric manifold enables us to explain and quantify why some defects are relatively easy to characterize, whereas others are inherently challenging.

Characterization of defects using ultrasonic arrays: a dynamic classifier approach

In the field of nondestructive evaluation, accurate characterization of defects is required for the assessment of defect severity. Defect characterization is studied in this paper through the use of the ultrasonic scattering matrix, which can be extracted from the array measurements. Defects that have different shapes are classified into different defect classes, and this essentially allows us to distinguish between crack-like defects and volumetric voids. Principal component analysis (PCA) is used for feature extraction, and several representational principal component subsets are found through exhaustive searching in which quadratic discriminant analysis (QDA) and support vector machine (SVM) are used as the pattern classifiers. Instead of choosing a single optimal classifier, the best classifier is dynamically selected for different measurements by estimating the local classifier accuracy. The proposed approach is validated in simulation and experiments. In simulation, the depths (lengths of the minor axes) of 4441 out of 4636 test samples are measured accurately, and the measurement errors (with respect to the defect size) are below 10%. Arbitrarily shaped rough volumetric defects are identified as ellipses, which are reasonably good matches in shape to the original defects. Experimentally, six subwavelength scatterers are characterized and sized to within 0.14λ.