Gaussian-DPSM (G-DPSM) and Element Source Method (ESM) modifications to DPSM for ultrasonic field modeling

Ordinary state-based peri-ultrasound modeling to study the effects of multiple cracks on the nonlinear response of plate structures

Since it is almost impossible to carry out a comprehensive parametric investigation experimentally for internal cracks with different geometry and orientation, a good numerical modeling and simulation technique is necessary to have a clear understanding of the physics of wave propagation and its interaction with cracks. Such investigation is helpful for structural health monitoring (SHM) with ultrasonic techniques. This work presents a nonlocal peri-ultrasound theory based on ordinary state-based (OSB) peridynamics for modeling elastic wave propagation in three-dimensional (3-D) plate structures containing multiple cracks. A relatively new and promising nonlinear ultrasonic technique called Sideband Peak Count - Index (or SPC-I) is adopted to extract the nonlinearity generated from the interactions between elastic waves and multiple cracks. Effects of three main parameters - the distance between the acoustic source and the crack, the crack spacing and the number of cracks are investigated using the proposed OSB peri-ultrasound theory together with the SPC-I technique. For each of these three parameters investigation, different crack thicknesses were considered - 0 mm (crack-free), 1 mm (thin crack), 2 mm (intermediate thickness) and 4 mm (thick crack); thin and thick cracks are defined after comparing the crack thickness value with the horizon size mentioned in the peri-ultrasound theory. It is found that for obtaining consistent results the acoustic source should be placed at least one wavelength away from the crack and crack spacings also play an important role on the nonlinear response. It is concluded that the nonlinear response diminishes when the cracks become too thick, and thin cracks show higher nonlinearity than that of thick cracks and no cracks. Finally, the proposed method which is combining the peri-ultrasound theory and SPC-I technique is used for monitoring cracks' evolution process. The numerical modeling results are compared with the experimental findings reported in the literature. Consistent qualitative trends in SPC-I variations predicted numerically and obtained experimentally are observed, thus it gives confidence in the proposed method.

Compensation of a Second Harmonic Wave Included in an Incident Ultrasonic Wave for the Precise Measurement of the Acoustic Nonlinearity Parameter

The incident second harmonic wave is a problematic issue for the precise measurement of the acoustic nonlinearity parameter. This paper proposes a compensation method to remove the effect of the incident second harmonic component in the measurement of the absolute acoustic nonlinearity parameter using the calibration method. For this, the second harmonic component detected by the receiving transducer is considered as the sum of the component due to material nonlinearity and the component included in the incident signal and a numerical calculation model is developed as a function of the propagation distance. In the model, the factors related to the material nonlinear parameter and the magnitude of the incident second harmonic component are unknown and these are determined by finding a value that best matches the experimental data according to the change in the propagation distance; compensation for the incident second harmonic component is then achieved. The case where the phase of the second harmonic wave due to material nonlinearity is opposite to that of the fundamental wave is also considered. To verify the validity of the proposed method, fused silica and aluminum alloy Al6061-T6 specimens with different thicknesses corresponding to the propagation distance are tested. The experimental results show that the nonlinear parameters changed significantly according to the propagation distance before compensation but were very stable after compensation. Additionally, the average values of the nonlinear parameter are 11.04 in the fused silica, which is within the literature value range (10.1 to 12.4), and that for the Al6061-T6 is 6.59, which is close to the literature value range (4.5 to 6.12).

Virtual nondestructive evaluation for anisotropic plates using Symmetry Informed Sequential Mapping of Anisotropic Green's function (SISMAG)

In this article, a generalized computational method to simulate virtual nondestructive evaluation (NDE) of anisotropic composite plates is presented. The ultrasonic wave fields were computed using a modified and generalized version of Distributed Point Source Method (DPSM), a semi-analytical mesh-free technique. The anisotropic Green's functions required for DPSM implementation were calculated using Fourier transform method and Radon transform method and compared. It is established that the Green's functions obtained from two different methods are identical. Applying generalized mathematical formulations, NDE of different degrees of anisotropic: transversely isotropic, orthotropic and monoclinic material are simulated and reported in this article. To boost the computational efficiency, a Symmetry Informed Sequential Mapping of Anisotropic Green's function (SISMAG) is introduced with DPSM and discussed in detail. To prove the above claims, virtual NDE experiments of anisotropic plates with normal and angle incidence of the ultrasonic wave are simulated using a circular transducer of central frequency ∼1 MHz. Wave fields inside both the fluid and the solid media were calculated.

The influence of surface roughness on ultrasonic thickness measurements

In corrosion assessment, ultrasonic wall-thickness measurements are often presented in the form of a color map. However, this gives little quantitative information on the distribution of the thickness measurements. The collected data can be used to form an empirical cumulative distribution function (ECDF), which provides information on the fraction of the surface with less than a certain thickness. It has been speculated that the ECDF could be used to draw conclusions about larger areas, from inspection data of smaller sub-sections. A detailed understanding of the errors introduced by such an approach is required to be confident in its predictions. There are two major sources of error: the actual thickness variation due to the morphology of the surface and the interaction of the signal processing algorithm with the recorded ultrasonic signals. Parallel experimental and computational studies were performed using three surfaces, generated with Gaussian height distributions. The surfaces were machined onto mild steel plates and ultrasonic C-scans were performed, while the distributed point source method was used to perform equivalent simulations. ECDFs corresponding to each of these surfaces (for both the experimental and computational data) are presented and their variation with changing surface roughness and different timing algorithms is discussed.

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

The challenge of accurately simulating how incident scalar waves interact with rough boundaries has made it an important area of research within many scientific disciplines. Conventional methods, which in the majority of cases focus only on scattering in two dimensions, often suffer from long simulation times or reduced accuracy, neglecting phenomena such as multiple scattering and surface self-shadowing. A simulation based on the scalar wave distributed point source method (DPSM) is presented as an alternative which is computationally more efficient than fully meshed numerical methods while obtaining greater accuracy than approximate analytical techniques. Comparison is made to simulated results obtained using the finite element method for a sinusoidally periodic surface where scattering only occurs in two dimensions, showing very good agreement (<0.2 dB). In addition to two-dimensional scattering, comparison to experimental results is also carried out for scattering in three dimensions when the surface has a Gaussian roughness distribution. Results indicate that for two-dimensional scattering and for rough surfaces with a correlation length equal to the incident wavelength (λ) and a root mean square height less than 0.2λ, the scalar wave approximation predicts reflected pulse shape change and envelope amplitudes generally to within 1 dB. Comparison between transducers within a three-element array also illustrate the sensitivity pulse amplitude can have to sensor position above a rough surface, differing by as much as 17 dB with a positional change of just 1.25λ.