Influence of Plate Wave Characteristics on the Angular Dependence of Ultrasonic Velocities

The angular dependence of the velocities of ultrasonic plane waves in a stressed, orthorhombic (orthotropic) continuum has recently been analyzed, and the results have been used to define scenarios for nondestructively measuring stress and preferred grain orientation [1,2]. These techniques make use of particular features which allow the two sources of anisotropy, stress and texture, to be separately determined. However, experimental realization of these ideas involves measurements at surfaces, and the influence of the surfaces on the plane wave solution must be considered. This paper treats the case of an orthorhombic plate, thin with respect to a wavelength. Discussions of the extensional and horizontal shear plate mode velocities appear in the mechanics literature, and their application to the characterization of the elastic constants of metal matrix composite plates has been investigated [3]. Here the theory is again briefly derived but in the previous notation [2] so as to allow the analytical expressions already obtained for the angular dependence of plane wave solutions to be directly compared to those for plate modes. Neglecting the effects of stress, the extent to which the So (extensional or fundamental symmetric) and SHo(fundamental horizontally polarized shear) plate solutions differ from their plane wave L (longitudinal) and SH (horizontally polarized shear) counterparts are discussed. Application of the results to weakly anisotropic metal polycrystals indicates a substantial difference in the anisotropics of the Soand L solutions. Implication of the results to the ultrasonic measurement of preferred grain orientation (texture) in metal polycrystals is discussed