An anisotropy index seeks to quantify how directionally dependent the properties of a system are. In this article, the focus is on quantifying the elastic anisotropy of crystalline materials. Previous elastic anisotropy indices are reviewed and their shortcomings discussed. A new scalar log-Euclidean anisotropy measure AL is proposed, which overcomes these deficiencies. It is based on a distance measure in a log-Euclidean space applied to fourth-rank elastic tensors. AL is an absolute measure of anisotropy where the limiting case of perfect isotropy yields zero. It is a universal measure of anisotropy applicable to all crystalline materials. Specific examples of strong anisotropy are highlighted. A supplementary material provides an anisotropy table giving the values of AL for 2,176 crystallite compounds.

A homogenization model is developed that describes the effective elastic constants of polycrystalline materials with constituent crystallites of general anisotropy (triclinic symmetry). The model is solved through an iterative technique where successive iterations improve the estimates of the polycrystal's elastic constants. Convergence of the solution provides the self-consistent elastic constants, which are the polycrystal's elastic constants resulting from continuity between local and far-field stress and strains. Iterative solutions prior to convergence are the bounds on the elastic constants including the Voigt-Reuss and Hashin-Shtrikman bounds. The second part of the article establishes a formal link between the present model and single-crystal elastic anisotropy. An analysis from a dataset containing 2176 inorganic crystalline compounds, spanning all crystallographic symmetries, is provided. The role of elastic anisotropy and related properties such as crystalline structure and elastic stability are discussed as it relates to the model.

This letter provides a theoretical extension to the elastic properties of polycrystals in order to describe elastic wave scattering from grain boundaries. The extension allows the longitudinal and shear attenuation coefficients for scattering to be derived and is valid for polycrystals containing crystallites of any symmetry class. Attenuation curves are given for polycrystalline SiO2, ZrO2, and SnF2, which contain monoclinic crystallites. This work will allow ultrasonic techniques to be applied to new classes of materials containing nontrivial microstructures.

Elastic wave scattering is used to study polycrystalline media for a wide range of applications. Received signals, which include scattering from the randomly oriented grains comprising the polycrystal, contain information from which useful microstructural parameters may often be inferred. Recently, a mode-converted diffuse ultrasonic scattering model was developed for evaluating the scattered response of a transverse wave from an incident longitudinal wave in a polycrystalline medium containing equiaxed single-phase grains with cubic elastic symmetry. In this article, that theoretical mode-converted scattering model is modified to account for grain elongation within the sample. The model shows the dependence on scattering angle relative to the grain axis orientation. Experimental measurements were performed on a sample of 7475-T7351 aluminum using a pitch-catch transducer configuration. The results show that the mode-converted scattering can be used to determine the dimensions of the elongated grains. The average grain shape determined from the experimental measurements is compared with dimensions extracted from electron backscatter diffraction, an electron imaging technique. The results suggest that mode-converted diffuse ultrasonic scattering has the potential to quantify detailed information about grain microstructure.

Diffuse ultrasonic backscatter describes the scattering of elastic waves from interfaces within heterogeneous materials. Previously, theoretical models have been developed for the diffuse backscatter of longitudinal-to-longitudinal (L-L) wave scattering within polycrystalline materials. Following a similar formalism, a mode-conversion scattering model is presented here to quantify the component of an incident longitudinal wave that scatters and is converted to a transverse (shear) wave within a polycrystalline sample. The model is then used to fit experimental measurements associated with a pitch-catch transducer configuration performed using a sample of 1040 steel. From these measurements, an average material correlation length is determined. This value is found to be in agreement with results from L-L scattering measurements and is on the order of the grain size as determined from optical micrographs. Mode-converted ultrasonic backscatter is influenced much less by the front-wall reflection than an L-L measurement and it provides additional microstructural information that is not accessible in any other manner.

Ultrasonic processing of solidifying metals in additive manufacturing can provide grain refinement and advantageous mechanical properties. However, the specific physical mechanisms of microstructural refinement relevant to laser-based additive manufacturing have not been directly observed because of sub-millimeter length scales and rapid solidification rates associated with melt pools. Here, high-speed synchrotron X-ray imaging is used to observe the effect of ultrasonic vibration directly on melt pool dynamics and solidification of Al6061 alloy. The high temporal and spatial resolution enabled direct observation of cavitation effects driven by a 20.2 kHz ultrasonic source. We utilized multiphysics simulations to validate the postulated connection between ultrasonic treatment and solidification. The X-ray results show a decrease in melt pool and keyhole depth fluctuations during melting and promotion of pore migration toward the melt pool surface with applied sonication. Additionally, the simulation results reveal increased localized melt pool flow velocity, cooling rates, and thermal gradients with applied sonication. This work shows how ultrasonic treatment can impact melt pools and its potential for improving part quality.