Elastic wave attenuation in polycrystalline materials.

Other conference contribution, 2025

An ultrasonic wave propagating through a polycrystalline material (typically a metal) undergoes grain scattering. The wave thus becomes dispersive and attenuated. As the grains are usually anisotropic with random orientation, the effective properties become isotropic. A classical approach to study such media is to replace the micro-inhomogeneous elastic material with a continuous random material characterized by a local elastic stiffness tensor with mean isotropic stiffness and random fluctuations. A volume integral approach may then be employed which is solved by a perturbative method assuming weak elastic fluctuations - this method is often called the second order approximation (SOA). There are several other approaches, including the finite element method (FEM). 

In the present work an analytical approach is adopted. First the scattering by a single anisotropic sphere in an infinite isotropic medium is solved. This leads to an explicit algebraic solution for low frequencies. To model a polycrystalline material, each grain is assumed to be a sphere and act as a scatterer in the average material of all the other grains. Multiple scattering is here disregarded, and the grains are assumed as completely filling the material in the sense that the total volume of all grains equals the volume of the material. The grains are also randomly located and oriented. Results for attenuation effects as a function of frequency are presented using the present approach, FEM, and the SOA method.