Shape effect of elongated grains on ultrasonic attenuation in polycrystalline materials

Longitudinal and transverse wave attenuation coefficients are obtained in a simple integral form for ultrasonic waves in cubic polycrystalline materials with elongated grains. Dependences of attenuation on frequency and grain shape are described in detail. The explicit analytical solutions for ellipsoidal grains in the Rayleigh and stochastic frequency limits are given for a wave propagating in an arbitrary direction relative to ellipsoid axes. The attenuation exhibits classic frequency dependence in those frequency limits. However, the dependence on the grain shape in the stochastic limits is unexpected: it is independent of the cross-section of the ellipsoidal grains and depends only on the grain dimension in the propagation direction. In the Rayleigh region attenuation is proportional to effective volume of the ellipsoidal grain and is independent of its shape. A complex behavior of attenuation on the grain shape/size and frequency is exhibited in the transition region. The results obtained reduce to the classic dependences of attenuation on parameters for polycrystals with equiaxed grains.