RESUMEN
An analytical approach to develop explicit formulas of attenuation coefficient in both 2D and 3D cases is proposed. It results in a better understanding of the grain scattering mechanisms within a polycrystalline material and the grain size effects on the attenuation of an ultrasonic wave. It is based on the Stanke and Kino's model and uses the Born approximation. An explicit formula is deduced for untextured polycrystals with equiaxed grains of cubic symmetry and allows a rigorous comparison of the attenuation coefficient between both 2D and 3D cases. It confirms that the attenuation in the Rayleigh region is higher in 2D simulation than in 3D one, while very similar coefficients are obtained in the stochastic region for both cases. The study of the explicit formula allows the decomposition of the attenuation coefficient into various scattering-induced components, which leads to a better understanding of different grain scattering mechanisms. The reflection/transmission at grain boundaries between wave modes of a same type mainly explains a same attenuation coefficient in the stochastic region for both 2D and 3D modelings. The conversion at grain boundaries between different types of wave modes provides some explanations for a higher attenuation value given by the 2D modeling in the Rayleigh region. The effect of the grain size on the attenuation coefficient is then predicted by the 2D analytical calculation and by the FE simulation. The analytical-numerical comparison validates the numerical calculations and the approach suggests a way of using the 2D FE calculations to predict the evolution of the attenuation coefficient with the wave frequency in 3D.
RESUMEN
The correlation between ultrasonic wave propagation and polycrystalline microstructures has significant implications in nondestructive evaluation. An original numerical approach using the finite element method to quantify in both time and frequency domains the ultrasonic noise scattering due to the elastic heterogeneity of polycrystalline microstructures is presented. Based on the reciprocity theorem, it allows the scattering evaluation using mechanical data recorded only on the boundary of polycrystal instead of within its volume and is applicable to any polycrystalline aggregate regardless of its crystallographic or morphological characteristics. Consequently it gives a more realistic and accurate access of polycrystalline microstructures than the classical analytical models developed under the assumption of single scattering and the Born approximation. The numerical approach is proposed within the same unified theoretical framework as the classical analytical models, so it is possible to validate it in the cases of idealized microstructures for which the considered analytical models remain relevant. As an original result, assuming single phase, untextured and equiaxed microstructures, two-dimensional (2D) theoretical formulas are developed and a frequency-dependent coefficient is found compared to the classical three-dimensional (3D) formulas. 2D numerical simulations are then performed for idealized microstructures composed of hexagonal grains with a uniform grain-size. Three grain sizes are considered herein and involve different scattering regions. Good comparisons are obtained between theoretical and numerical estimates of the backscattering coefficient, which validate the numerical approach. Effects of the grain boundary orientations are analyzed by modeling an irregular hexagonal grain morphology and a random grain morphology generated by an established Voronoi approach. The origin of the significant oscillation level of backscattering is then investigated and discussed.
RESUMEN
We present the first X-ray spectrum obtained by the Low-Energy Transmission Grating Spectrometer (LETGS) aboard the Chandra X-Ray Observatory. The spectrum is of Capella and covers a wavelength range of 5-175 Å (2.5-0.07 keV). The measured wavelength resolution, which is in good agreement with ground calibration, is Deltalambda approximately 0.06 Å (FWHM). Although in-flight calibration of the LETGS is in progress, the high spectral resolution and unique wavelength coverage of the LETGS are well demonstrated by the results from Capella, a coronal source rich in spectral emission lines. While the primary purpose of this Letter is to demonstrate the spectroscopic potential of the LETGS, we also briefly present some preliminary astrophysical results. We discuss plasma parameters derived from line ratios in narrow spectral bands, such as the electron density diagnostics of the He-like triplets of carbon, nitrogen, and oxygen, as well as resonance scattering of the strong Fe xvii line at 15.014 Å.