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

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 orientations 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 material–both Class I–to highlight the influence of diagonal as well as off-diagonal 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.