Variation in the dispersion of axisymmetric waves in infinite circular rods with crystallographic wire texture

Abstract

This paper presents the solution to the frequency equation for a number of polycrystalline, textured circular rods having transverse isotropy. The effective, second-order elastic stiffness tensors were estimated using the recursive general Hill arithmetic mean (GHAM). The velocity dispersion curves for a number of combinations of materials and crystallographic fiber or wire textures were calculated and the variation due to texture displayed. At large wavelengths, the velocity dispersion of fiber textured materials exhibits a lowest-order axisymmetric mode which varies only with the directional Poisson’s ratios in a manner similar to that of isotropic aggregates. In this wavelength regime, the waves propagate nondispersively at the wave speed, C0, as dictated by the directional Young’s modulus. At wavelengths smaller than the rod radius, the dispersion curves were more influenced by the full anisotropy of the wire textures. At these wavelengths, the dispersion curves for the anisotropic materials deviated significantly from those of the isotropic materials and one another with the higher axisymmetric vibration modes exhibiting extreme differences. This deviation is a function of the single crystal anisotropy and nature of the wire textures.