9. Ultrasonics, Bulk Waves
Further results are presented for the direct problem of scattering of high-frequency waves by cracks in elastic solids. Results for a penny-shaped crack, obtained on the basis of geometrical diffraction theory, are compared with experimental data. For simple crack geometries a hybrid method, whereby the crack-opening displacement is computed by ray theory, and the scattered field is subsequently obtained by the use of a representation theorem, is tested by comparison with exact results. The simple form of the far-field high-frequency solutions to the direct scattering problem suggests the application of Fourier-type integrals to solve the inverse problem. Two different inversion integrals are discussed. The inversion method is checked by applying it to the scattered field of a flat elliptical crack, for which an analytical expression is derived. Some computational technicalities are discussed, and numerical results are presented.
Achenbach, J. D., "Direct and Inverse Methods for Scattering by Cracks at High Frequencies" (1980). Proceedings of the DARPA/AFML Review of Progress in Quantitative NDE, July 1978–September 1979. 57.