Abstract
This study extends the second-order attenuation (SOA) model for elastic waves in texture-free inhomogeneous cubic polycrystalline materials with equiaxed grains to textured polycrystals with ellipsoidal grains of arbitrary crystal symmetry. In term of this work, one can predict both the scattering-induced attenuation and phase velocity from Rayleigh region (wavelength >> scatter size) to geometric region (wavelength << scatter size) for an arbitrary incident wave mode (quasi-longitudinal, quasi-transverse fast or quasi-transverse slow mode) in a textured polycrystal and examine the impact of crystallographic texture on attenuation and phase velocity dispersion in the whole frequency range. The predicted attenuation results of this work also agree well with the literature on a textured stainless steel polycrystal. Furthermore, an analytical expression for quasi-static phase velocity at an arbitrary wave propagation direction in a textured polycrystal is derived from the SOA model, which can provide an alternative homogenization method for textured polycrystals based on scattering theory. Computational results using triclinic titanium polycrystals with Gaussian orientation distribution function (ODF) are also presented to demonstrate the texture effect on attenuation and phase velocity behaviors and evaluate the applicability and limitation of an existing analytical model based on the Born approximation for textured polycrystals. Finally, quasi-static phase velocities predicted by this work for a textured polycrystalline copper with generalized spherical harmonics form ODF are compared to available velocity bounds in the literature including Hashin–Shtrikman bounds, and a reasonable agreement is found between this work and the literature.
Highlights
Polycrystals or polycrystalline materials are solid aggregates of numerous individual crystallites of varying morphology, size and crystallographic orientation, where the grains are bonded together by grain boundaries
We examine the real part of the perturbed wavenumber that governs the phase velocity in textured polycrystalline materials, and it has never been studied in previous studies [6,39,40,59]
The second-order attenuation (SOA) model is validated by comparison to reported experimental attenuation data and finite element modeling results for a
Summary
Polycrystals or polycrystalline materials are solid aggregates of numerous individual crystallites (or grains) of varying morphology, size and crystallographic orientation, where the grains are bonded together by grain boundaries. Polycrystals are heterogeneous materials in grain scale. The majority of inorganic solids such as common metals, ceramics and rocks are polycrystals Due to their significance in various industries, polycrystals are one of the major objects of study in non-destructive evaluation (NDE) and seismology. One significant but challenging topic related to polycrystals in NDE and seismology is the elastic wave scattering and the resulting attenuation in polycrystals. It has been studied for decades [1,2,3,4,5,6,7,8] but elastic wave scattering in complex polycrystals is still not well understood
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