Michihiro Kitahara

Elastodynamic inversion for shape reconstruction and type classification of flaws

Two linearized inverse scattering methods are investigated to reconstruct the shape of flaws in the elastic solid. One is based on the Born approximation and the other is based on the Kirchhoff approximation. The Born inversion is sensitive to the volumetric flaw but not to a crack-like flaw. On the other hand, the Kirchhoff inversion reacts to both boundaries of volumetric and crack-like flaws. The combined use of Born and Kirchhoff inversions leads to the classification method of flaw type. The performance of the proposed classification procedure is demonstrated by the numerical simulations and then by the experimental measurements for the two-dimensional models of flaws. An example for the three-dimensional shape reconstruction is also shown by using the numerically calculated backscattering amplitudes.

Application of BEM for the Visualization of Scattered Wave Fields from Flaws

The elastodynamic boundary element method (BEM) is applied to the visualization of the scattered wave field through a fluid‐solid interface. In the formulation of BEM, the multigaussian beam model is introduced in order to express the incident wave field radiated from the immersion transducer. The unknown quantities on the crack boundary are determined by the BEM, then the wave field around the crack in solid is visualized with the integral representation of the scattered wave. To obtain the scattered waveforms in fluid, a far‐field expression of the Green’s function for a fluid‐solid coupling medium is adopted in this study.

Fast Imaging of 3‐D Flaw Using Linearized Inverse Scattering Methods

A high‐speed analysis of three‐dimensional linearized inverse scattering method is proposed for real time imaging of flaws. The principal operation of the linearized inverse method is the integration of the scattering amplitude in the K‐space. In this study, the three‐dimensional fast Fourier transform is introduced into the inversion algorithm to evaluate the integral in the K‐space. From the results of numerical investigations, it is shown that the computational time of the inversion is reduced without the loss of the image quality for the shape reconstruction.

A classification method of defect type by Born and Kirchhoff inversions

Two linearized inverse scattering methods are investigated to classify the defect type in an elastic body. The methods are based on the Born and Kirchhoff approximations for the unknown displacement in the integral representation of scattered field. From the result of experimental measurement, the Born inversion reconstructs the volume of defects and the Kirchhoff inversion reconstructs the surface of defects. The combination of two inversion methods leads to the classification between volumetric defect and crack.

Boundary Element Analysis of Multiple Scattering Waves in High Performance Concretes

Advances in computing have allowed for the development of high performance concretes mathematically. We develop a method which combines the generalized self consistent model together with the boundary element method and the statistical averaging procedure to study the multiple scattering of plane elastic waves in concrete containing randomly distributed parallel fibers. In analysis, the concrete matrix is modeled by dispersed aggregate structure. The physical properties for a fiber-reinforced concrete are obtained numerically and shown in graphs for various microstructures at designated frequencies.

Shape Reconstruction of Three‐Dimensional Flaw by the Measurement from the Side of Cylindrical Specimen

The three‐dimensional Born and Kirchhoff inversions are modified to the convenient form for cylindrical structures. Moving the measurement plane along the axis of the cylinder, cross‐sectional images are obtained by the modified method. The three‐dimensional flaw shape is reconstructed by piling up the cross‐sectional images. Cement paste and concrete cylinders with flaw models are prepared and ultrasonic measurements are carried out. The measured wave data are fed into the inversion method and the performance of the shape reconstruction is confirmed.

Shape reconstruction of defects in inhomogeneous material

A shape reconstruction method in an inhomogeneous material is investigated by using the ultrasonic waveforms in this study. The frequency characteristics of phase velocity due to inhomogeneity of the material are introduced to the Born and Kirchhoff inversion algorithms. Here, the mortar specimens containing volume fractions of 5% and 10% inclusions are prepared. The results show that the Born and Kirchhoff inversions reconstruct the shape and size of the artificial defect in mortar specimens.

Application of Linearized Inverse Scattering Methods to the Material with Flat Measurement Surface

The linearized inverse scattering methods based on Born and Kirchhoff approximations are utilized for the flaw reconstruction in an elastic material with flat surfaces. The flaw shape can be reconstructed through the 2‐D FFT of scattering amplitudes in the K‐space. The scattering amplitudes are extracted from the measured waveforms by data processing with the reference waveforms from a small circular hole.

Cross-Sectional Imaging of Three-Dimensional Flaw From Waveforms in a Restricted Measurement Surface

Three-dimensional Born and Kirchhoff inverse scattering methods are modified for a cylindrical specimen that includes three-dimensional flaws. The measurement area in the modified methods is restricted in the plane perpendicular to the axis of the cylindrical specimen. The incident wave with the Gaussian amplitude profile is introduced in the numerical analysis to examine the effect of the incident beam radius. The modified methods are applied to the aluminum specimen with a cylindrical flaw and the performance of the modified methods is confirmed by the experimental measurement.

A visualization technique for interaction of circumferential creeping waves with cracks

For the ultrasonic nondestructive evaluation, it is of primary importance to understand the wave propagation process from defects. In this study, the scattered waves from a cavity with a sub-surface inner crack are calculated by the boundary element method. The scattered wave motion in the vicinity of the cavity is visualized in order to interpret the interaction process of the circumferential creeping wave with the crack. The backscattered waveforms at the transducer position are then calculated by using the far field integral representation of the scattered wave. The effect of the sub-surface crack to the backscattered receiving signal is investigated from the results of near field visualizations and far field waveforms.