Ultrasonic damping in polycrystalline materials

The grains in a polycrystalline material, typically metals, act as scatterers of ultrasonic waves and thus give rise to attenuation of the waves. The grains have anisotropic stiffness properties, typically orthotropic or cubic. A new approach is proposed to calculate damping in a 2D setting starting from the scattering by an anisotropic circle in an isotropic surrounding. This problem has recently been solved, giving explicit, simple expressions for the elements of the transition (T) matrix (which gives the relation between the the incoming and scattered fields) when the circle is small compared to the ultrasonic wavelengths. The T matrix can be used to calculate the total scattering cross section, which in turn can be used to estimate the damping in the material. Explicit expressions for the damping coefficient for longitudinal and transverse waves are obtained in this way.