Attenuation and Phase Velocity of Elastic Wave in Textured Polycrystals with Ellipsoidal Grains of Arbitrary Crystal Symmetry

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.

Elastic wave propagation in anisotropic polycrystals: inferring physical properties of glacier ice

“…Our method is inspired by, and builds on, the methodology of Gusmeroli et al [21] and Lutz et al [37], but is free of constraints that the ODF must be of a predetermined type, made possible by expanding the c-axis distribution function in terms of a spherical harmonic series (non-parametric approach) similar to developments made in the broader material sciences community (e.g. [44,50,53–55]). Using the same ice-core data as Lutz et al [37] from the shear margin of Priestley glacier, Antarctica, we demonstrated that our method is a feasible approach for inferring both the ODF of ice-core samples and the effective grain elastic parameters of the homogenization scheme.…”

“…Here, we extend the methodology of Gusmeroli et al [21] and Lutz et al [37] by reformulating the optimization (inverse) problem such that no particular fabric anisotropy is presupposed, made possible by expanding the c-axis ODF in terms of a spherical harmonic series, inspired by the broader material sciences community (e.g. [44,50,53–55]). Using this representation, we demonstrate how either the ODF can be inferred if the effective elastic parameters of grains are known or vice-versa, followed by discussing the well-posedness of the inverse problem, relevant for future applications in glaciology, geology and elsewhere.…”

“…Following previous work (e.g. [44,50,53–55,62,63]), we expand ψ in terms of a spherical harmonic series ψfalse(θ,ϕfalse)=∑l=0L∑m=−llψlmYlmfalse(θ,ϕfalse),where ψlm are the complex expansion coefficients, and L is the wave-mode truncation above which finer-scale structure in ψ is unresolved. In this case, the total number of grains is simply N=4πψ00, and ψ being real implies that ψl−m=false(−1false)mfalse(ψlmfalse)∗.…”

Detection and Function of Elastic Wave Tomography of Foundation Piles of High-Rise Buildings under the Background of Internet of Things

“…The most commonly used waveforms for ultrasonic nondestructive testing are shear wave and longitudinal wave [19]. The propagation speed of transverse waves Wireless Communications and Mobile Computing and longitudinal waves are different, and the particle will cause the superposition of the two vibrations, and then, the conversion of vibration modes will occur.…”

Ultrasonic Scattering Attenuation in Nodular Cast Iron: Experimental and Simulation Studies

“…Rokhlin et al [37] presented a model that includes second-order multiple scattering, applicable to all frequency ranges, providing small relative errors on both longitudinal and transverse attenuations for low anisotropy. Sha [38] extended the second-order attenuation (SOA) model for elastic waves in texture-free materials to textured polycrystals with ellipsoidal grains of arbitrary crystal symmetry. The predicted attenuation results of this work agree well with the literature on a textured stainless steel polycrystal.…”