Acoustic nonlinearity parameters for transversely isotropic polycrystalline materials

This article considers polycrystalline materials with macroscopic elastic anisotropy and the effect of the anisotropy on the quadratic nonlinearity parameter used to describe second harmonic generation in solids. The polycrystal is assumed to have transversely isotropic elastic symmetry, which leads to a directional dependence of the nonlinearity parameters. Additionally, the anisotropy leads to second harmonic generation from an input shear wave. Estimates of the longitudinal and shear wave nonlinearity parameters are given as a function of single-crystal elastic constants, macroscopic anisotropy constants, and propagation direction. An inverse model is presented that relates measured nonlinearity parameters to the macroscopic anisotropy constants. The estimates of the nonlinearity parameters can be used to approximate the damage-free or baseline nonlinearity parameter of structural components, which helps the effort toward absolute measures of material damage.