Investigation of ultrasonic backscatter using three-dimensional finite element simulations

Theoretical models are commonly used to describe ultrasonic backscattering in polycrystalline materials. However, although a full multiple scattering formalism has been derived, due to the difficulty in evaluation, currently only the single and double scattering effects have been evaluated. Three-dimensional finite element (3D FE) models have recently been demonstrated to be capable of predicting ultrasonic attenuation in polycrystalline materials and thereby show great potential in overcoming this limitation. In this paper, the application of 3D FE models is extended to the backscatter problem. First, longitudinal-to-longitudinal backscattering amplitudes from single grains are predicted, where the setup and configuration of the finite element (FE) model are verified with an isotropic spherical inclusion for which an exact solution is available. Subsequently, backscatter in terms of the root-mean-square noise levels in two different pulse-echo scenarios is investigated; the first is an idealised configuration with plane wave transmission and point reception; the second represents a more realistic finite-size transducer acting with the same apodization in both transmission and reception. Comparisons of FE predictions and approximate theoretical solutions within a range of validity show good agreement; however, the results demonstrate that 3D FE is useful where the simple Independent Scatterer models break down. As computing power increases, 3D FE is an increasingly viable tool to further the understanding of wave propagation in polycrystalline materials.