Eric S. Boltz Vinod K. Tewary Christopher M. Fortunko
Natl. Inst. of Standards and Technol., Mater. Reliability Div., Boulder, CO 80303
Conventional ultrasonic materials characterization methods rely heavily upon measurements of acoustic wave velocities and amplitudes which are often ambiguous. Waveform-based ultrasonics, however, seeks to extract valuable information from the actual ultrasonic waveforms. This computational portion of the work seeks to mathematically represent ultrasonic waves propagating in a bounded, three-dimensional, anisotropic hemisphere. An integral representation for the exact solution of the Christoffel equation for wave propagation in anisotropic hemispheres is developed using a wavelet transform developed at NIST. This representation allows the computation of material displacements as a function of both position and time for a given source. This wavelet is a function of the slowness vector, rather than the wave vector, and is better suited to anisotropic solids where the direction of energy flow is parallel to the slowness vector. The source case considered is pencil lead break in the center of the flat side of an anisotropic hemisphere. Surface displacements are computed for various materials. Where possible, comparison with previous work and with experimental data are presented.