Model of wave propagation in anisotropic media of dissimilar and multi-layer welded joints

The purpose of this study is to verify the numerical simulation of the finite difference method of the time of flight diffraction (TOFD) in studies of welded joints and multi-layer models, for the case of multi-layer welded joints. In this way, the effects of a type of anisotropy, specifically transverse isotropy (system with elastic hexagonal or polar symmetry) can be evaluated in the propagation of waves in elastic media by ultrasonic inspection. The algorithm for the construction of the model applies the finite difference method and was created in FORTRAN language. The evaluated approach is in two-dimensional space. The evaluated case is composed of a cross-sectional model of a welded joint similar to the one shown in the Figure below, with the insertion of discontinuities to the material. This case aims mainly to evaluate the propagation behavior of the wave in relation to its interaction with discontinuities of different sizes and positions within the material. Thus, through the response of A-Scan signals (echogram), it was possible to evaluate the relevant parameters to obtain a satisfactory non-destructive inspection. The models of the welded joints are formed by a plane of depth xz with 5000 x 1500 points in the respective directions. For practical purposes, spatial sampling rules according to domain size were approximated in terms of the total number of arithmetic operations in finite difference schemes of higher order; for this, five points were used for the smallest wavelength defined by the minimum velocity in the model. In this way, all the simulated images (components of the displacement field and cross sections) are presented with a factor of five of mesh contraction, that is, the sample grid with 5000 x 1500 points becomes 1000 x 300 points (indicated in the figures). ). This transformation is important for the reduction of the arithmetic operations involved and in the computational time spent for the compilation of the elastic property files, but it does not present any visual alteration in the presentation of these images. The temporal sampling interval adopted for this case was 35.0s with temporal resolution of 4.7ns. In the simulations with the model (welded joints), A-Scan echograms were generated. The results are attached for wide dissemination