Wave localized finite-difference-time-domain modelling of scattering of elastic waves within a polycrystalline material

Abstract

Ultrasonic studies based on the first arrived signals are of utmost importance when dealing with heterogeneous material especially to seismology, biomedical imaging, as well as for nondestructive evaluation and structural health monitoring applications. Numerical modelling of elastic waves through polycrystalline features has been primarily held back by huge computational requirements. This article discusses the development of a robust and efficient numerical scheme based on finite-difference-time-domain (FDTD) by introducing wave-localized approach to simulate elastic waves in polycrystalline media. The numerical scheme adopts a rotated staggered grid in velocity-stress configuration. The numerical efficiency is improved by adopting parallel computing using efficient graphical processors and by introducing wave-localized computations. It is demonstrated that the proposed tool, especially with the introduction of wave-localized approach, is computationally faster and can handle large-scale grains in comparison with the commercial finite element software, especially when dealing with first arrived signals. This article reports an optimal ratio of FDTD grids per grain to minimize the staircasing effects at the polycrystalline boundaries and was found to be valid over a range of grain sizes. The article also addresses the orientation averaging requirements achieving statistically significant first arrived signal and suggests optimal averaging trials for various grain size models. The developed two-dimensional model shows good agreement with the prediction across the Rayleigh and Stochastic scattering regimes for the chosen model material (Inconel 600) having a cubic symmetry.

Estimation of Grain Size and Composition in Steel Using Laser UltraSonics Simulations at Different Temperatures

“…Efforts to model the ultrasonic wave propagation in materials with a microstructure have mainly focused on calculating attenuation and wave velocities in 3D, but backscattering has also been considered. Increasing computational power and the development of sophisticated computational methods such as finite difference (FD) or finite-difference time-domain (FDTD) methods [33,34] and finite element methods (FEM) [24,[35][36][37], have enabled the modelling and computation of large three-dimensional samples. In these studies, materials with (poly)crystalline structures, consisting of different phases, or with inclusions, voids or cracks have been modelled.…”

Laplace Domain Boundary Element Method for Structural Health Monitoring of Poly-Crystalline Materials at Micro-Scale

“…Poly-crystalline materials [1] are commonly used in many engineering structures as they are able to resist severe environmental conditions thanks to their high mechanical and thermal properties. The poly-crystalline structure at the micro-scale is characterized by the random spatial distribution of crystals, also known as grains.…”

“…Therefore, utilizing wave-material interactions is possible to characterize material properties, as well as to detect and localize defects in poly-crystals in the NDT-SHM framework [10][11][12]. However, because of the experimental challenges in acquiring detailed information about micro-structure architecture and defect characterization, different numerical and computational methods have been proposed to represent the randomness of the micro-structure and the presence of defects in poly-crystalline materials [1,2,[13][14][15]. In recent years, various numerical methods based on elastodynamics theory have been used to study wave propagation and scattering.…”