Elastic wave velocity dispersion in polycrystals with elongated grains: Theoretical and numerical analysis

Spatial and directional characterization of wire and arc additive manufactured aluminum alloy using phased array ultrasonic backscattering method

Pores, grains, or textures can collectively cause microstructural inhomogeneity and anisotropy in metallic materials fabricated by additive manufacturing. In this study, a phased array ultrasonic method is developed to characterize the inhomogeneity and anisotropy of wire and arc additively manufactured components by performing both beams focusing and steering. Two backscattering features, i.e., the integrated backscattering intensity and the root mean square of the backscattering signals, are employed to quantify the microstructural inhomogeneity and anisotropy, respectively. An experimental investigation is performed using an aluminum sample fabricated by wire and arc additive manufacturing. The ultrasonic measurements, performed on wire and arc additive manufactured 2319 aluminum alloy, show that the sample is inhomogeneous and weakly anisotropic. Metallography, electron backscatter diffraction, and X-ray computed tomography are used to verify the ultrasonic results. An ultrasonic scattering model is used to identify the influence of grains on the backscattering coefficient. Compared with a wrought aluminum alloy, the complex microstructure in additively manufactured material significantly influence the backscattering coefficient, and the presence of pores cannot be neglected in ultrasonic-based nondestructive evaluation for wire and arc additive manufactured metals.

Appraising scattering theories for polycrystals of any symmetry using finite elements

This paper uses three-dimensional grain-scale finite-element (FE) simulations to appraise the classical scattering theory of plane longitudinal wave propagation in untextured polycrystals with statistically equiaxed grains belonging to the seven crystal symmetries. As revealed from the results of 10 390 materials, the classical theory has a linear relationship with the elastic scattering factor at the quasi-static velocity limit, whereas the reference FE and self-consistent (SC) results generally exhibit a quadratic relationship. As supported by the results of 90 materials, such order difference also extends to the attenuation and phase velocity, leading to larger differences between the classical theory and the FE results for more strongly scattering materials. Alternatively, two approximate models are proposed to achieve more accurate calculations by including an additional quadratic term. One model uses quadratic coefficients from quasi-static SC velocity fits and is thus symmetry-specific, while the other uses theoretically determined coefficients and is valid for any individual material. These simple models generally deliver more accurate attenuation and phase velocity (particularly the second model) than the classical theory, especially for strongly scattering materials. However, the models are invalid for the attenuation of materials with negative quadratic coefficients. This article is part of the theme issue 'Wave generation and transmission in multi-scale complex media and structured metamaterials (part 1)'.

Influence of tessellation morphology on ultrasonic scattering

Material properties, such as hardness, yield strength, and ductility, depend on the microstructure of the material. If the microstructural organization can be quantified nondestructively, for example, with ultrasonic scattering techniques, then it may be possible to predict the mechanical performance of a component. Three-dimensional digital microstructures have been increasingly used to investigate the scattering of mechanical waves within a numerical framework. These synthetic microstructures can be generated using different tessellation algorithms that result in different grain shapes. In this study, the variation of ultrasonic scattering is calculated for microstructures of different morphologies for a nickel polycrystal. The ultrasonic properties are calculated for the Voronoi, Laguerre tessellations, and voxel-based synthetic microstructures created by DREAM.3D. The results show that the differences in the two-point statistics and ultrasonic attenuation for different morphologies become more significant at wider size distributions and higher frequencies.

Surface acoustic wave attenuation in polycrystals: Numerical modeling using a statistical digital twin of an actual sample

Grain boundary scattering-induced attenuation and phase-velocity dispersion of Rayleigh-type surface acoustic waves are studied with a time-domain finite-element method (FEM). The FEM simulation incorporates a realistic material model based on matching the spatial two-point correlation function of a Laguerre tessellation with that obtained from optical micrographs of a previously studied aluminum sample. Plane surface acoustic waves are excited in a multitude of statistically equivalent virtual polycrystals, and their surface displacement fields are averaged for subsequent extraction of the coherent-wave attenuation coefficient and phase velocity. Comparisons to previous laser-ultrasonic experiments, an analytical mean-field model, and the FEM results show good agreement in a broad frequency range from about 10 to 130MHz. Observed discrepancies between models and measurement reveal the importance of spatial averaging in the context of mean-field approaches and suggest improvement strategies for future experimental studies and advanced analytical models. A different attenuation power law for Rayleigh waves is found in the stochastic scattering regime compared to bulk acoustic waves.

Finite-element and semi-analytical study of elastic wave propagation in strongly scattering polycrystals

This work studies scattering-induced elastic wave attenuation and phase velocity variation in three-dimensional untextured cubic polycrystals with statistically equiaxed grains using the theoretical second-order approximation (SOA) and Born approximation models and the grain-scale finite-element (FE) model, pushing the boundary towards strongly scattering materials. The results for materials with Zener anisotropy indices A > 1 show a good agreement between the theoretical and FE models in the transition and stochastic regions. In the Rayleigh regime, the agreement is reasonable for common structural materials with 1 < A <  3.2 but it deteriorates as A increases. The wavefields and signals from FE modelling show the emergence of very strong scattering at low frequencies for strongly scattering materials that cannot be fully accounted for by the theoretical models. To account for such strong scattering at A > 1, a semi-analytical model is proposed by iterating the far-field Born approximation and optimizing the iterative coefficient. The proposed model agrees remarkably well with the FE model across all studied materials with greatly differing microstructures; the model validity also extends to the quasi-static velocity limit. For polycrystals with A < 1, it is found that the agreement between the SOA and FE results is excellent for all studied materials and the correction of the model is not needed.

Some Theoretical and Experimental Extensions Based on the Properties of the Intrinsic Transfer Matrix

The work approaches new theoretical and experimental studies in the elastic characterization of materials, based on the properties of the intrinsic transfer matrix. The term 'intrinsic transfer matrix' was firstly introduced by us in order to characterize the system in standing wave case, when the stationary wave is confined inside the sample. An important property of the intrinsic transfer matrix is that at resonance, and in absence of attenuation, the eigenvalues are real. This property underlies a numerical method which permits to find the phase velocity for the longitudinal wave in a sample. This modal approach is a numerical method which takes into account the eigenvalues, which are analytically estimated for simple elastic systems. Such elastic systems are characterized by a simple distribution of eigenmodes, which may be easily highlighted by experiment. The paper generalizes the intrinsic transfer matrix method by including the attenuation and a study of the influence of inhomogeneity. The condition for real eigenvalues in that case shows that the frequencies of eigenmodes are not affected by attenuation. For the influence of inhomogeneity, we consider a case when the sound speed is varying along the layer's length in the medium of interest, with an accompanying dispersion. The paper also studies the accuracy of the method in estimating the wave velocity and determines an optimal experimental setup in order to reduce the influence of frequency errors.

Inversion methodology for ultrasonic characterization of polycrystals with clusters of preferentially oriented grains

Titanium alloys are widely used in the aerospace industry. However, due to presence of microtexture, which is characterized by preferred crystallographic orientation clustering of thousands of alpha crystallites, cold dwell fatigue may significantly reduce the part life. To satisfy the practical need for nondestructive microtexture characterization, an inverse ultrasonic methodology is proposed to quantify mean parameters of microtexture regions (MTRs) having ellipsoidal shapes. One limitation of previous model-based ultrasonic inversion methods is required knowledge of elastic constants of the crystallites, which are rarely available for engineering alloys. This study overcomes this constraint by adopting the far field attenuation model, JASA, 137 (5), 2655-2669 (2015), and the backscattering model for ultrasonic wave interaction with microtexture. In the methodology developed, all necessary averaged MTR characteristics are obtained solely from directional ultrasonic measurements (backscattering, attenuation, and velocity) without a prior knowledge of material microstructures or elastic properties of different material phases. The inversion method is illustrated by simulations. To support the inversion methodology, the mean MTR sizes, morphology, and elastic scattering factors are determined from the ultrasonic experiment on a Ti-6242 alloy sample. The inversion results are compared with destructive electron backscatter diffraction (EBSD) analysis from which the MTRs are segmented using a non-contiguous grouping criteria. Good agreement is found.

Finite element evaluation of a simple model for elastic waves in strongly scattering elongated polycrystals

A simple semi-analytical model for longitudinal scattering-induced attenuation and phase velocity is proposed for strongly scattering cubic polycrystals with statistically elongated grains. It is formulated by iterating the Born approximation of the far-field approximation model and by empirically increasing the coefficient in the quadratic term for the elastic scattering factor. The comparison with the three-dimensional grain-scale finite element calculations shows excellent performance of the semi-analytical model for both attenuation and phase velocity in all studied frequency ranges and especially in the Rayleigh regime in which, for strongly scattering materials, the existing analytical models significantly disagree with the numerical results.

Longitudinal wave attenuation in polycrystals with elongated grains: 3D numerical and analytical modeling

This work develops a second-order approximation (SOA) model and a three-dimensional (3D) finite element (FE) model to calculate scattering-induced attenuation for elastic wave propagation in polycrystals with elongated grains of arbitrary crystal symmetry. The SOA model accounts for some degree of multiple scattering, whereas the 3D FE model includes all scattering possibilities. The SOA model incorporates the accurate geometric two-point correlation function obtained from the FE material systems to enable comparative studies between the two models. Also, the analytical Rayleigh and stochastic asymptotes are presented to provide explicit insights into propagation behaviors. Quantitative agreement is found between the FE and analytical models for all evaluated cases. In particular, the FE simulations support the SOA model prediction that grain shape does not exert influence on attenuation in the Rayleigh regime and its effect emerges as frequency increases to the stochastic regime showing anisotropy in attenuation. This attenuation anisotropy intensifies with the increase in frequency, but it exhibits a complicated behavior as frequency transits into the geometric regime. Wavefield fluctuations captured from the FE simulations are provided to help observe these complex scattering behaviors. The proportionality of attenuation to elastic scattering factors is also quantitatively evaluated.