No abstract

This work is motivated by the need for realistic ultrasonic probability of detection (POD) models in nondestructive evaluation (NDE). Past POD models have utilized flaw farfield scattering amplitudes along with other system parameters to predict the expected signal in postulated measurement geometries [1}. However, numerical evaluations of scattering amplitudes have generally been restricted to idealized fl aw shapes and , t o our knowledge , no scheme to calculate scattering amplitude s of arbitrary shape has ever been implemented in 3D. Volumetric shapes with an axis of symmetry have been examined with T-matrix and MOOT [2,3] but the axisymmetric limitation precludes a large portion of all expected flaw shapes. Furthermore, a quasi-plane wave assumption is often made. This assumption can become inappropriate for critical flaw sizes on the order of the beam size . A truly general POD model needs to have these assumptions removed.

Background on Elastic Wave Scattering 6 Background of the Boundary Element Method 9 A Note about the Dissertation Organization 12 PART I.

Time-harmonic elastic wave scattering problems such as those encountered in ultrasonic non destructive evaluation are solved by the boundary element method (BEM). Selected results for spherical and spheroidal shaped voids and inclusions are compared with analytical and other numerical solutions. Results for ellipsoids, which require a full three-dimensional formulation, are provided as a benchmark for comparison when other numerical methods would be developed for this problem class in the future. The modelling of cracklike defects with this formulation is discussed. Recent theoretical findings regarding the fictitious eigenfrequency difficulty (FED) are confirmed by a numerical study.

Methods for solving elastic wave scattering problems in three dimensions (3D) with multiple inhomogeneities are discussed. A problem of homogeneous, isotropic elastic defects in an otherwise homogeneous, isotropic elastic full-space is formulated as a boundary integral equation. This equation is solved by discretizing the surface of each scatterer in a fashion known as the boundary element method. The resulting matrix equation may be solved in a fully implicit manner, but an implicit-iterative method is more efficient. With this hybrid method, a portion of the nonsingular integral operator is expanded in a Neumann series. Terms in this series correspond physically to N th-order Born approximations of the scatterers' interaction. The relative advantage of this hybrid scheme depends on the number of iterations required. Except for closely situated strong scatterers, terms beyond the first few orders are not significant and thus the method can be quite advantageous. When the separation is large, another approximate method which ignores the evanescent portion of the near scattered field and further neglects the curvature of scattered waves is appropriate. Results from the converged, implicit-iterative approach are compared with this far-field approximation for many situations involving spheroidal voids. The validity of this approximation is explored in the near field.