Line source representations for shear wave birefringence measurements in transversely isotropic materials using laser ultrasonics

Abstract

Line source representations for thermoelastic, laser excitation of transversely isotropic materials are developed to model shear wave birefringence effects that can occur in these materials. Continuum descriptions for elastic wave propagation are used to generate equations of motion that are solved using transform methods. Analytical solutions are presented for epicentral waveforms for propagation parallel and perpendicular to the axis of symmetry. These solutions are particularly simple and allow for rapid examination of the influence of various components of the stiffness tensor on wave propagation. In particular, for propagation perpendicular to the axis of symmetry, line source orientation parallel and perpendicular to this axis yield two cases that demonstrate shear wave birefringence. This effect is computed for titanium as well as for a nearly isotropic materialboth Class Ito highlight the influence of diagonal as well as offdiagonal components of the stiffness tensor on the character of laser ultrasonic waveforms when the tensor is referenced to the principal coordinate system. The results presented in this work should be used to guide the interpretation of laser ultrasonic, line source measurements in transversely isotropic materials when birefringence effects are present.

Theory and application of laser ultrasonic shear wave birefringence measurements to the determination of microstructure orientation in transversely isotropic, polycrystalline graphite materials

“…For a transversely isotropic material, the elastic moduli that can be extracted from the laser ultrasonic measurements indicated for Cases III and IV correspond to c 11 , c 44 and c 66 [52] which were 12.5, 4.84 and 5.13 GPa respectively for the NBG-25 used in this work. Interpreting these results within the framework of a textured, polycrystalline material using microcrackmodified values for the components of the single crystal stiffness tensor along with a modified Hill averaging approach yields values of W 200  0.00196 and W 400  0.000757 for the orientation distribution coefficients.…”

“…Results obtained in sample NBG-25-1 appear to approximate this condition. In contrast, if Cases III and IV correspond to propagation perpendicular to the axis of symmetry then the line source orientation will affect the shear wavespeeds leading to shear wave birefringence [52]. This condition appears to be true for the sample NBG-25-2 since the times-of-flight for the shear wave arrivals in this sample differ (indicated by t Shear in Fig.…”