Finite element modelling of elastic wave scattering within a polycrystalline material in two and three dimensions

Finite element modelling is a promising tool for further progressing the development of ultrasonic non-destructive evaluation of polycrystalline materials. Yet its widespread adoption has been held back due to a high computational cost, which has restricted current works to relatively small models and to two dimensions. However, the emergence of sufficiently powerful computing, such as highly efficient solutions on graphics processors, is enabling a step improvement in possibilities. This article aims to realise those capabilities to simulate ultrasonic scattering of longitudinal waves in an equiaxed polycrystalline material in both two (2D) and three dimensions (3D). The modelling relies on an established Voronoi approach to randomly generate a representative grain morphology. It is shown that both 2D and 3D numerical data show good agreement across a range of scattering regimes in comparison to well-established theoretical predictions for attenuation and phase velocity. In addition, 2D parametric studies illustrate the mesh sampling requirements for two different types of mesh to ensure modelling accuracy and present useful guidelines for future works. Modelling limitations are also shown. It is found that 2D models reduce the scattering mechanism in the Rayleigh regime.