Application of laser-based resonant ultrasound spectroscopy to study texture in copper

Abstract

Two copper specimens with distinct grain microstructures are investigated using laser resonant ultrasound spectroscopy (LRUS). One consists of randomly oriented crystallites and exhibits isotropic elastic behavior (two elastic constants), and the other has been highly textured by rolling and exhibits anisotropic elastic behavior (three elastic constants). The elastic constants are measured using electron backscatter diffraction, LRUS, and time domain laser ultrasound (LU). The elastic constants of the isotropic sample obtained via electron backscatter diffraction (EBSD), LU, and LRUS agree closely. However, for the anisotropic sample, there is considerable disagreement between results obtained using LRUS and results obtained using LU and EBSD. Analysis reveals that increasing the dimensionality of the modulus space leads to a questions of whether the LRUS results are unique to within experimental error. The consequence is that for anisotropic materials, small measurement uncertainties can lead to large uncertainties in the measured elastic constants. This observation has important implications for the use of LRUS to measure the elastic constants of thin texture samples.

Anisotropic elasticity of DyScO3substrates

“…the whole anisotropic tensor), especially if the RUS method is complemented by pulse-echo measurements of quasi-longitudinal wave velocity in directions perpendicular to the individual faces of the specimen [11,12]. On the other hand, if the RUS method is used in combination with the laser-Doppler interferometry [28][29][30] for the identification of the modal shapes as adopted also in this paper, it is more efficient to work with platelet-shaped specimens. The reason for this is that most of the lowest resonance modes of such specimens are bending (flexural) modes with the maximal displacements in the direction perpendicular to the surface of the platelet, i.e.…”

“…If, for example, all the frequencies depend sensitively on c A + c B , but are completely independent of c A − c B , the derivatives ∂f n /∂c A and ∂f n /∂c B are nonzero, but the coefficients c A and c B cannot be determined from the measurements. See [11] for more details and [30] for an illustrative example.…”

Resonant ultrasound spectroscopy: How much information lies in higher frequencies

“…However, to reduce the coupling between transducers and the sample, alternative non-contact transducer methods have been explored for RUS. These include the utilization of electromagnetic acoustic transducers [14] and lasers [15][16][17][18][19][20][21][22][23]. Such non-contact transducers have been employed to achieve effective RUS measurements while minimizing direct physical contact with the sample.…”

Resonant ultrasound spectroscopy: Sensitivity analysis for anisotropic materials with hexagonal symmetry

“…With these techniques, one desires that changes to a material property produce proportional effects on the computed spectrum. However this is not always the case, particularly for the elastic constants of anisotropic materials, where for certain crystallographic symmetries experimentalists have noted the weak effect of certain elastic constants on the resonant spectrum [15] and others have shown explicitly that the spectrum is insensitive to changes of elastic constants in certain linear combinations [16,17]. There has been various works studying sensitivity using partial derivatives.…”

“…Furthermore, if the number of independent elastic constants in an anisotropic material increases, say to 5 and more, then the number of possible combinations, increases drastically. In [16,17] for example, a material with cubic crystal symmetry is studied. To investigate the sensitivity, one elastic constant is assumed to be fixed, and the other two were varied.…”