Scattering of near normal incidence SH waves by sinusoidal and rough surfaces in 3-D: comparison to the scalar wave approximation

Deep learning based ultrasonic reconstruction of rough surface morphology

This paper introduces a methodology to recover the morphology of a complex rough surface from ultrasonic pulse echo measurements with an array of equidistant sensors using the one dimensional convolution neural network (1DCNN). The neural network is trained by the datasets simulated from high-fidelity finite element simulations for surfaces with a range of roughness parameters and is tested on both numerical and real experimental data. To assess the performance of our proposed method, the rough surface reconstruction results from the deep learning approach are compared with those obtained from conventional ultrasonic array imaging methods. Unlike array imaging-based methods that require a large number of sensors (e.g., 128, 64 or 32), the deep learning-based method uses pulse echo signals and can achieve accurate results with much fewer sensors. The developed deep learning approach has the potential to enable low-cost, accurate, and real-time reconstruction of complex surface profiles.

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 and analytical study for ultrasonic testing of internal delamination defects considering surface roughness

The improvement of detection accuracy and reliability of micro delamination defect is restricted by the rough surface. The flat bottom holes (FBHs) are frequently employed as reference targets to evaluate the sensitivity of ultrasonic testing for internal defects. A roughness-modified analytical model for ultrasonic testing of FBHs is established based on the principle of multi-Gaussian beam and phase-screen approximation. The signal of reference reflector is obtained from two-dimensional ultrasonic simulation model. The amplitude changes of echo signals and noises of FBHs with different diameters and depths under rough surfaces are presented. The analyses results indicate that the root-mean-square (rms) height plays a dominant role in the amplitude change of signals compared with the correlation length. The reflected wave amplitude of FBHs decreases nonlinearly with an increase of roughness whereas the amplitude of noise increases slightly. Subsequently, a method is proposed further combining the noise amplitude acquired from numerical simulation and the echo signal amplitude obtained by the analytical model, which is to predict and estimate the detection accuracy of internal defects under different surface roughness. The parallel experiments are performed on several samples with different roughness to validate the evaluation method.

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).

Distributed point source modeling of the scattering of elastic waves by a circular cavity in an anisotropic half-space

The Distributed Point Source Method (DPSM) is a modeling technique based on superposition of fundamental solutions corresponding to individual pair of source and target points. A collection of source points distributed over the boundaries and interfaces are responsible for transmission, reflection, and refraction of acoustic waves in the solution domain. The strength of the source points may not be known a priory. By imposing the prescribed conditions on the boundaries and interfaces, a system of equations with the source strengths as the unknowns is obtained. After finding the source strengths as the solution to this system of equation, the amount of the solution at any target point in the domain is obtained by superimposing the effect of all source points on that target point. DPSM is an efficient modeling technique for ultrasonic problems since it does not require discretization of the whole solution domain but only the boundaries and interfaces. The fundamental solution, or the Green's function, between a pair of source and target points serves as the building block for DPSM. For an ideal fluid or a homogeneous isotropic solid the elastodynamic Green's function is available as closed form algebraic expressions. But for an anisotropic solids, the set of governing equations are considerably more complex and the elastodynamic Green's function needs to be evaluated numerically. In this study, an anisotropic half-space containing a flaw in the form of a circular hole is considered. The solid half-space is in contact with fluid and a transducer is located in fluid facing the solid half-space. Some efforts have been made to alleviate the computational intensity of the numerical evaluation of anisotropic Green's function for this problem. Firstly, a technique called "windowing" is used to exploit the repetitive pattern of relative positions of the source and target points in order to considerably reduce the number of Green's function evaluations. Secondly, the resolution of the integration for evaluation of the anisotropic Green's function is changed based on the distance between the source and target points, and a calibration technique based on an equivalent isotropic stiffness tensor is suggested. This calibrated multi-resolution integration technique is combined with the windowing technique, and the developed DPSM model is applied to a numerical example containing a transversely isotropic half-space, to show the applicability and effectiveness of DPSM modeling for this class of problems. Important applications like non-destructive evaluation of composite materials may benefit from such modeling capability.

Effect of Surface Roughness on Ultrasonic Testing of Back-Surface Micro-Cracks

Surface roughness is one of the main factors that affect the ultrasonic testing of micro-cracks. This article theoretically analyzes the relationship between the changes in the energy intensity of crack echo waves and roughness-modified transmission coefficients. A series of simulations are carried out using two-dimensional sinusoidal curves as rough surface. Then, parallel experiments are performed on sample surfaces with different arithmetic average heights (Ra). The signal amplitude ratio factor (SARF) is defined to assess the ultrasonic detection capacity for micro-cracks. Both finite element analysis and experimental results show that signal amplitude decreases with an increase in Ra, resulting in signal-to-noise ratio loss. Amplitude attenuation caused by the rough back surface is less than that caused by the rough front surface. It is difficult to identify the signal of micro-cracks with a depth less than 400 μm when the Ra of the front surface is larger than 15 μm. Cracks with depths of more than 200 μm can be distinguished when the back-surface roughness is less than 24 μm. Furthermore, the amplitude of the micro-crack signal increases slightly with variation in the horizontal parameter (Rsm). This study provides a valuable reference for the precision evaluation of micro-cracks using ultrasonic inspection.