Low frequency wave propagation in multiphase polycrystalline materials

Wave propagation in a multiphase polycrystalline material is investigated by evaluating the effective wavenumbers for low frequencies. The grains in the polycrystal are assumed to be orthotropic and can be of more than one type, for example a duplex material, and may have a distribution in size. The orientation of the grains are random so that the effective properties are isotropic. A generalized Foldy approach is used with an independent scattering approximation, and for low frequencies, it is possible to obtain explicit expressions for the wavenumbers, and hence, for the attenuation and phase speeds. For a distribution in size, it is shown that it is the third moment of the distribution in radius that determines the attenuation. Numerical examples for duplex materials are given as a function of volume concentration of each phase.