Andrea P. Arguelles

Bounds and self-consistent estimates of the elastic constants of polycrystals

The Hashin-Shtrikman bounds on the elastic constants have been previously calculated for polycrystalline materials with crystallites having general elastic symmetry (triclinic crystallite symmetry). However, the calculation of tighter bounds and the self-consistent estimates of these elastic constants has remained unsolved. In this paper, a general theoretical expression for the self-consistent elastic constants is formulated. An iterative method is used to solve the expression for the self-consistent estimates. Each iteration of the solution gives the next tighter set of bounds including the well-known Voigt-Reuss and Hashin-Shtrikman bounds. Thus, all of the bounds on the elastic constants and the self-consistent estimates for any crystallite symmetry are obtained in a single, computationally efficient procedure. The bounds and self-consistent elastic constants are reported for several geophysical materials having crystallites of monoclinic and triclinic symmetries. HighlightsA homogenization model for the elastic constants of polycrystals is given.An iterative solution produces the effective bulk and shear modulus.Voigt-Reuss and Hashin-Shtrikman bounds are obtained within the iterative solution.Self-consistent elastic constants are obtained when the iterative solution converges.The model applies to isotropic polycrystals containing crystallites of any symmetry.

Ultrasonic attenuation of polycrystalline materials with a distribution of grain sizes

Elastic wave scattering at grain boundaries in polycrystalline media can be quantified to determine microstructural properties. The amplitude drop observed for coherent wave propagation (attenuation) as well as diffuse-field scattering events have been extensively studied. In all cases, the scattering shows a clear dependence on grain size, grain shape, and microstructural texture. Models used to quantify scattering experiments are often developed assuming dependence on a single spatial length scale, usually, mean grain diameter. However, several microscopy studies suggest that most metals have a log normal distribution of grain sizes. In this study, grain size distribution is discussed within the context of previous attenuation models valid for arbitrary crystallite symmetries. Results are presented for titanium using a range of distribution means and widths assuming equiaxed grains and no preferred crystallographic orientation. The longitudinal and shear attenuations are shown to vary with respect to the frequency dependence for varying distribution widths even when the volumetric mean grain size is held constant. Furthermore, the results suggest that grain size estimates based on attenuation can have large errors if the distribution is neglected. This work is anticipated to play an important role in microstructural characterization research associated with ultrasonic scattering.

Mode-converted ultrasonic scattering in polycrystals with elongated grains

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.

Ultrasonic backscatter from elongated grains using line focused ultrasound

HIGHLIGHTSUltrasonic grain scattering is measured from elongated grains.Measurements use a single normally incident line‐focus transducer.A ray‐based model is provided.Shear wave scattering from an incident longitudinal field is observed and is sensitive to grain elongation.Application for nondestructively monitoring grain elongation. ABSTRACT Ultrasonic backscattering from polycrystalline materials with elongated grains is investigated. A normal incident line‐focus transducer is employed such that refracted longitudinal and transverse waves are focused within the polycrystal and scatter at grain boundaries back to the transducer. A ray‐based scattering model is developed to explain the dependence of the statistics of scattering measurements on grain elongation. The spatial variance of measured scattered signals from Al alloy (7475‐T7) is compared to the model. This work promotes the ultrasonic backscatter technique for monitoring grain elongation of metals using one transducer with access to a single sample face.

Evaluating grain size in polycrystals with rough surfaces by corrected ultrasonic attenuation

HIGHLIGHTSWe study the effects of diffraction and surface roughness on ultrasonic attenuation.The MGB model is used to formulate the diffraction correction coefficient.We develop an approximate inverse function of Weavers model.Grain size evaluation results reveal the better accuracy of the presented method. ABSTRACT Surface roughness of a sample has a great effect on the calculated grain size when measurements are based on ultrasonic attenuation. Combining modified transmission and reflection coefficients at the rough interface with a Multi‐Gaussian beam model of the transducer, a comprehensive correction scheme for the attenuation coefficient is developed. An approximate inverse model of the calculated attenuation, based on Weavers diffuse scattering theory, is established to evaluate grain size in polycrystals. The experimental results showed that for samples with varying surface roughness and matching microstructures, the fluctuation of evaluated average grain size was ±1.17 &mgr;m. For polished samples with different microstructures, the relative errors to optical microscopy were no more than ±3.61%. The presented method provides an effective nondestructive tool for evaluating the grain size in metals with rough surfaces.

Ultrasonic harmonic generation from materials with up to cubic nonlinearity

This letter considers the combined effects of quadratic and cubic nonlinearity on plane wave propagation in generally anisotropic elastic solids. Displacement solutions are derived that represent the fundamental, second-, and third-harmonic waves. In arriving at the solutions, the quadratic and cubic nonlinearity parameters for generally anisotropic materials are defined. The effects of quadratic and cubic nonlinearity are shown to influence the amplitude and phase of the fundamental wave. In addition, the phase of the third-harmonic depends on a simple combination of the quadratic and cubic nonlinearity parameters. Nonlinearity parameters are given explicitly for materials having isotropic and cubic symmetry. Lastly, acoustic nonlinearity surfaces are introduced, which illustrate the nonlinearity parameters as a function of various propagation directions in anisotropic materials.

Diffuse ultrasonic backscatter using a multi-Gaussian beam model

Diffuse ultrasonic backscatter is widely used to evaluate microstructural parameters of heterogeneous materials. Recent singly scattered response (SSR) models utilize a single-Gaussian beam (SGB) assumption which is expected to have limitations. Following a similar formalism, a model is presented using a multi-Gaussian beam (MGB) assumption to characterize the transducer beam for longitudinal-to-longitudinal scattering at normal incidence through an interface with arbitrary curvature. First, the Wigner transform of the transducer field is defined using conjugate double-layer MGB expressions. The theoretical analysis shows that ten groups of Gaussian beams are sufficient for convergence. Compared with the SGB-SSR curve, the shape of MGB-SSR curve is positive skewed. Differences between the MGB-SSR model and the SGB-SSR model are quantified and shown to be complex functions of frequency, sample curvature, transducer parameters, and focal depth in the material. Finally, both models are used to fit experimental spatial variance data from a 304 stainless steel pipe with planar, convex, and concave surfaces. The results show that the MGB-SSR has some characteristics suggesting a better fit to the experiments. However, both models result in grain size estimates within the uncertainty of the optical microscopy suggesting that the SGB is sufficient for normal incidence pulse-echo measurements.

On the acoustoelasticity of polycrystalline materials

A linear relation between the strains and stresses of a crystallite within a polycrystal is used to homogenize the polycrystals elastic properties. The homogenization parallels the self-consistent method that is used for estimating the polycrystals linear elastic properties. Acoustoelasticity for a macroscopically isotropic polycrystal is then formulated using a homogenized constitutive equation with initial stress. Simple expressions are given for the phase velocities and polarization directions for a uniaxially stressed polycrystal. The present model is compared with the model of Man and Paroni [J. Elast. 45, 91-116 (1996)]. Strong anisotropy of the crystallite elastic constants causes the present model to differ noticeably from the model of Man and Paroni.

On the harmonic scattering amplitudes from a nonlinear elastic spherical inclusion

In this paper, the interaction of an incident finite amplitude longitudinal wave with a localized region of nonlinearity is considered. This interaction produces a secondary field represented by a superposition of first-, second-, and third-harmonic components. The secondary field is solely a result of the quadratic and cubic elastic nonlinearity present within the region of the inclusion. The second-harmonic scattering amplitude depends on the quadratic nonlinearity parameter

Influence of material heterogeneity on the distortion of a focused ultrasonic beam

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