Application of Geometrical Diffraction Theory to QNDE Analysis

The direct problem of the diffraction of time-harmonic·waves by cracks in elastic solids is analyzed for high-frequencies, when the wavelengths are of the same order of magnitude as a characteristic length dimension, a, of the crack. It is shown that good approximations at high frequencies can be obtained on the basis of elastodynamic ray theory. An elastodynamic version of geometrical diffraction theory is briefly reviewed. We also present a hybrid theory, wherein the crack opening displacement is computed on the basis of geometrical diffraction theory, and the scattered field is subsequently obtained by the use of a representation theorem. This hybrid approach avoids the difficulties at shadow boundaries and caustic surfaces that plague a direct application of geometrical diffraction theory. Explicit results are computed for slits and penny-shaped cracks, and these results are compared with numerical results obtained on the basis of exact integral equation formulations. The relatively simply structure of the expressions for the scattered fields displays some characteristic features, whose possible role in the inverse problem is discussed