Elastic wave propagation in polycrystals

Ming Huang, Peter Cawley, Michael Lowe
2021
Scattering occurs as elastic waves propagate through a random polycrystalline medium, exhibiting scattering-induced attenuation and velocity dispersion. These behaviours carry bulk information about microstructure and can therefore be used for microstructure characterisation. The purpose of this thesis is to gain knowledge about the behaviour of elastic waves in polycrystals in order to facilitate the characterisation of microstructure. This thesis contributes mainly in six aspects. First, a
more » ... spects. First, a theoretical second-order approximation (SOA) model is developed to calculate the scattering-induced attenuation and velocity dispersion of plane elastic waves in random polycrystals. This model provides solutions of second-order accuracy in material inhomogeneity that are valid across all scattering regimes and partially account for multiple scattering. It applies to statistically equiaxed and elongated grains of arbitrary crystal symmetries, with decoupled geometric and elastic statistics represented respectively by the two-point correlation (TPC) function and the elastic covariance. A simple Born approximation, with a reduced accuracy considering only single scattering, is formulated based on the SOA model, and analytical asymptotes are derived for the low-frequency Rayleigh and high-frequency stochastic regimes. Second, a three-dimensional (3D) finite element (FE) method is advanced to solve the wave propagation problem in the time domain. This method uses grain-scale spatial representation, in significant sample volumes of large numbers of grains, to describe polycrystalline materials. It captures the exact interactions of waves with grains without low-order scattering approximations. The numerical errors and statistical uncertainties of the FE method are minimized to deliver very accurate calculations of attenuation and phase velocity. The TPC function of the FE model is accurately determined and incorporated into the SOA model to enable a direct comparison of both models. Then, the SOA and FE models are used to study th [...]
doi:10.25560/87502 fatcat:444lplalrnazxn4bno2b47r63u