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

Elastic Wave Scattering from Multiple and Odd Shaped Flaws

Using the T-Matrix or Null Field method elastic wave scattering from the following geometries have been studied (a) Rotationally symmetric configurations consisting of two spheroidal cavities separated by a finite distance and with different eccentricities. Exact calculations are compared with single scattering approximations. The frequency spectra are interpreted for various scattering geometries and compared with experiments. The effect of change in distance between the scatterers is also discussed. (b) Scattering from rotationally symmetric cavities with odd shapes like Pinnochio , Rockwell Science Center sample #73 and Micky Mouse , Rockwell Science Center sample #70 was also studied and compared with numerical results using other techniques as well as experiments. Several ways of studying such problems is also discussed. (c) A numerical technique is proposed to study dynamic stress concentrations

Spectral Analysis of Elastic Waves Scattered by Objects with Smooth Surfaces

This is a summary of the research on NDE performed during the last two years by the authors and Professor W. Sachse and Messrs . S. Sancar and G. C. C. Ku of the Department of Theoretical and Applied Mechanics at Cornell University. The report is divided into three parts: (1) Theoretical Spectra-Results based on the method of wave function expansion and the method of transition matrix (T-matrix) will be presented for the scattering by a circular cylindrical, elliptic cylindrical, spherical, and spheroidal (prolate or oblate) inclusions in solids. Additional results for the scattering by two circular cylindrical inclusions will also be shown. (2) Interpretation of Spectra - Spectra of a fluid inclusion may be interpreted on the basis of the theory of normal modes, and those of a cavity from the principle of interference. Spectra for two cylindrical cavities exhibit new features which are related to the interferences of waves diffracted by each cavity. (3) Comparison with Experiments - Some of the theoretical spectra are compared with experimental results obtained by Professor W. Sachse and his associates

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