Transducer-modeling in general transversely isotropic media via point-source-synthesis: Theory

Based on a theory of elastic wave propagation in arbitrarily oriented transversely isotropic media, which has been presented recently, the radiation characteristics of ultrasonic transducers in these media are determined. Using the directivity patterns for normal and transverse point sources on the free surface of such (semi-infinite) materials—the derivation is based on the reciprocity theorem—the radiated wave fields are obtained by the method of point-source-synthesis, i.e., by superposing the wave fields of numerous point sources located within the transducer aperture. Since ultrasonic inspection of anisotropic materials, especially weld material in nuclear power plants, suffers from the well-known effects of beam splitting, beam distortion, and beam skewing, valuable information in view of an optimized inspection is provided. Focusing on transversely isotropic weld material specimens, numerical evaluation is performed for several grain orientations with respect to the transducer-normal. The approach presented is particularly useful in view of an appropriate extension to inhomogeneous welds and the consideration of time-dependent RF-impulse functions.