Abstract
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.
Highlights
London, Exhibition Road, London, SW7 2AZ, United Kingdom.of attenuation (Chassignole et al, 2009; Feuilly et al, 2009)
The capability of 3D finite element (FE) to model the physics of wave scattering in polycrystals has been proved in recent FE modelling papers (Van Pamel et al, 2015; Van Pamel et al, 2016; Van Pamel et al, 2018; Van Pamel et al, 2017) and this paper introduces a new application of it to the backscatter problem
By comparing the FE predictions with those given by the existing theoretical models, the main conclusions are: (1) The 3D FE results of the rms of L-L backscattering amplitudes from single grains agree well with the theoretical predictions
Summary
Exhibition Road, London, SW7 2AZ, United Kingdom. of attenuation (Chassignole et al, 2009; Feuilly et al, 2009). The theoretical models to describe the L-L scattering of a plane wave by an inclusion in an isotropic host material have been well established; for example, the exact solution for an isotropic spherical inclusion has been given in Ying and Truell (1956), and a more general solution applicable to a small weakly-scattering inclusion, shown in Gubernatis et al (1977) and Schmerr and Song (2007) has been developed based on the Born approximation. Where DC3333, which will be written as DC33 in the following text, denotes the difference between the 3333 elastic constant of the inclusion and the medium
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