T-Matrix Calculations for Spheroidal and Crack Like Flaws

Numerical calculations are presented for the scattering of elastic (P- and S-) waves from prolate and oblate spheroids and two-dimensional, rough, crack-like flaws for various angles of incidence, observation and frequencies using the T-matrix approach

Elastic Wave Scattering by Rough Flaws and Cracks

The scattering of elastic waves by three dimensional rough flaws and cracks is analyzed using the T-matrix approach. The scattering cross section is obtained for spheroidal cavities with a periodically corrugated surface which may be used as a model for flaws with a rough surface. The dependence of the scattering cross section on the wavelength of the corrugations is studied as a function of the incident wavelength. Cracks are modelled as degenerate oblate spheroids and the scattering cross section is obtained for incident P-waves, Multiple scattering analysis of two cavities is also discussed with some numerical results

Testing the Inverse Born Procedure for Spheroidal Voids

Previously we have shown that the inverse Born approximation allows an accurate determination of the radius of spherical flaws in Ti. Here we report the results of extending that analysis to spheroidal voids. Both oblate and prolate spheroids are considered. Using scattering amplitude generated by the T-matrix method, we find that both the major and minor axes of 2-1 spheroids are accurately determined. Inversion results using experimental data will be presented for the 2-1 oblate spheroid: a comparison of the experimental and theoretical results will be given

Sensitivity of Failure Prediction to Flaw Geometry

The assumption of ellipsoidal flaw geometry has been widely used in calculations of the probability of structural failure conditioned on nondestructive (ND) measurements. Clearly, in most cases the flaw geometry is not ellipsoidal and in the particular case of cracks the actual geometry may deviate significantly from a degenerate ellipsoid (i.e., a planar crack with an elliptical plan-view shape). We have investigated the sensitivity of a late stage of the evolution of fatigue failure to model errors of the latter type (i.e., deviations from elliptical shape for planar cracks) by considering two different overall theoretical processes. In the first, we start with a non-elliptical crack and calculate its geometry after a given large number of cycles of uniaxial stress applied perpendicular to the crack plane. In the second process, we start with the same crack but perform a simulated set of ND measurements coupled with an inversion procedure based on the assumption of elliptical geometry and then calculate the geometry of this initially elliptical crack after subjection to the above stress history. A measure of sensitivity to model error is then provided by a comparison of the two terminal geometries. Results for several choices of non-elliptical crack shapes and sets of ND measurements will be discussed