### ASA 126th Meeting Denver 1993 October 4-8

## 4aPA12. Waveform-based ultrasonics in anisotropic hemispheres.

**Eric S. Boltz
Vinod K. Tewary
Christopher M. Fortunko
**

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*Natl. Inst. of Standards and Technol., Mater. Reliability Div., Boulder,
CO 80303
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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.