Comparison between experimental and 2-D numerical studies of multiple scattering in Inconel600® by means of array probes

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

“…19 More recently, researchers [16][17][18][19][20] have considered Finite Element (FE) modelling to overcome this 20 limitation and confront more challenging scattering scenarios. In contrast to existing theoretical 21 approaches, its ability to simulate time-domain signals, incorporating both attenuation and noise, whilst 22 also including complex physics such as multiple scattering 17 , makes FE a promising candidate. Its 23 flexibility and high fidelity will probably be instrumental to further progressing the development of 24 ultrasonic NDE of polycrystalline materials.…”

“…Finite Element modelling of polycrystalline materials has been successfully undertaken in various fields 11 of research [25][26][27] including NDE [16][17][18][19][20] where it has been limited to 2D. Although several approaches have 12 been adopted, all of those mentioned here that consider geometrically varying grains, rely on Voronoi 13 tessellations 28 to numerically generate a morphology which is geometrically similar to a naturally 14 occurring polycrystalline microstructure.…”

“…Generating a random polycrystalline microstructure, as achieved in [16][17][18][19][20] , starts by randomly distributing 19 points, or seeds, in a 2D Euclidian space. An example of this is shown in Figure 1a where the seed 20 density will determine the resulting average grain size.…”

“…For a single phase material, each crystallite should be assigned the 18 same anisotropic stiffness properties but with a random crystallographic orientation to define a 19 macroscopically isotropic material (see Figure 1d). To achieve this, the three reference Euler angles, 20 which define orientation, may be randomly distributed such that their orientations lie equally spaced on 21 the surface of a sphere, as explained by Shahjahan 17 for example. Figure 3 shows the result of rotating 22 orientation angles in 3D for 2000 grains, illustrated by polar plots.…”

“…In this case however, whether using a structured or unstructured mesh, the objects 5 to model, the crystallites, are often an order of magnitude smaller than the wavelength, which demands 6 denser meshes which far exceed the said wavelength criteria. Two possibilities exist, which have 7 previously each been adopted, either an unstructured mesh utilizing triangular FE elements (see Figure 8 4a) to conform to the complex boundaries of the Voronoi tessellation, or an approximation of the grains 9 with a structured mesh 17 (see Figure 4b). The hazard with a structured mesh is that it leads to 10 "staircasing" effects 31 which become a poor approximation at coarse mesh densities and can lead to tip 11 diffraction from edges, and also to disproportionately strong reflections from waves that are normally 12 incident to the plane of the flats.…”