Modeling of transient ultrasonic wave propagation using the distributed point

Nonlinear scattering and mode conversion of Lamb waves at breathing cracks: An efficient numerical approach

This article presents an efficient numerical approach to the investigation of nonlinear scattering and mode conversion phenomena of Lamb waves as they interact with breathing cracks. A Local Interaction Simulation Approach (LISA) is adopted, which possesses the versatility to capture arbitrary damage profiles. The stick-slip contact dynamics is implemented in the LISA model via the penalty method, which captures the nonlinear interactions between Lamb waves and breathing cracks. The LISA framework achieves remarkable computational efficiency with its parallel implementation using Compute Unified Device Architecture (CUDA) executed on powerful GPUs. A small-size LISA model with absorbing boundaries is tailored for the purpose of extracting the Lamb wave scattering and mode conversion features. Due to the explicit parallel CUDA implementation and the small-size model setup, the computation is highly efficient. Numerical case studies on nonlinear scattering of Lamb waves from breathing cracks are given. Distinctive higher harmonic generation and selective mode conversion phenomena are presented using the complex-valued Wave Damage Interaction Coefficients (WDICs) containing both amplitude and phase information of the scattered wave field. The effect of oblique incident angle on nonlinear scattering phenomenon is investigated. The rough crack surface feature with initial openings and closures is also considered to better approximate fatigue cracks in practical engineering scenarios. In addition, the wave amplitude effect on the nonlinear scattering and mode conversion is studied. This research may provide guidelines for the effective design of sensor arrays utilizing nonlinear Lamb waves for fatigue crack detection.

Reflection at a liquid-solid interface of a transient ultrasonic field radiated by a linear phased array transducer

In order to put in evidence the specular reflection and the non-specular reflection in the transient case, we have used a model for the study of the transient ultrasonic waves radiated by a linear phased array transducer in a liquid and reflected by a solid plane interface. This method is an extension of the angular spectrum method to the transient case where the reflection at the plane interface is taken into account by using the reflection coefficient for harmonic plane waves. The results obtained highlighted the different components of the ultrasonic field: the direct and edge waves as well as the longitudinal head waves or leaky Rayleigh waves. The transient representation of these waves have been carefully analyzed and discussed by the rays model. Instantaneous cartographies allowed a clear description of all the waves which appear at the liquid-solid interface. The obtained results have been compared to those obtained with a finite element method package.

Combined analytical FEM approach for efficient simulation of Lamb wave damage detection

Lamb waves have been widely explored as a promising inspection tool for non-destructive evaluation (NDE) and structural health monitoring (SHM). This article presents a combined analytical finite element model (FEM) approach (CAFA) for the accurate, efficient, and versatile simulation of 2-D Lamb wave propagation and interaction with damage. CAFA used a global analytical solution to model wave generation, propagation, scattering, mode conversion, and detection, while the wave-damage interaction coefficients (WDICs) were extracted from harmonic analysis of local FEM with non-reflective boundaries (NRB). The analytical procedure was coded using MATLAB, and a predictive simulation tool called WaveFormRevealer 2-D was developed. The methodology of obtaining WDICs from local FEM was presented. Case studies were carried out for Lamb wave propagation in a pristine plate and a damaged plate. CAFA predictions compared well with full scale multi-physics FEM simulations and experiments with scanning laser Doppler vibrometry (SLDV), while achieving remarkable performance in computational efficiency and computer resource saving compared with conventional FEM.

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.

Application of the distributed point source method to rough surface scattering and ultrasonic wall thickness measurement

The distributed point source method is commonly used to predict the complex acoustic field emitted by ultrasonic transducers. In this paper, it is presented as an alternative to conventional approaches often used when solving rough surface scattering problems. Surface shadowing and multiple scattering effects are inherently included in the mesh-free semi-analytical simulation method through matrix manipulation making it very efficient and simple to implement. Results are presented which illustrate the improvement in accuracy gained over the Kirchhoff approximation and the decrease in computational load over the finite element method, culminating in greater than an order of magnitude decrease in required simulation time. The method is applied to the practical problem of online wall thickness monitoring within corrosive environments, illustrating the variability in reflected pulse shape that could be expected from rough surfaces with similar statistics. Three commonly implemented time-of-flight algorithms are used to analyze a large number of simulated signals from which it is concluded that those based on first arrival time are more stable under increasing roughness conditions than those which are based on reflected pulse shape.