Elastic Wave Scattering by Cracks - Interfacial Forces and High Frequency Diffraction

Abstract: This thesis treats elastic wave scattering by cracks with interfacial forces. The results are of practical interest in ultrasonic testing and includes development of numerical methods used to predict such testing.

First the canonical problem of two-dimensional (2-D) diffraction from a semi-infinite crack is solved. The boundary conditions on the crack are the distributed spring boundary conditions. The solution includes integral transform techniques and scalar Wiener-Hopf calculations. Both the geometrical elastodynamic and the edge diffracted body waves are computed, the latter as high frequency approximations expressed in terms of diffraction coefficients. Similarly the diffraction coefficients for body-to-surface and surface-to-body waves are computed. Some of the quantities entering the solution are calculated numerically.

The 2-D diffraction coefficients for the distributed spring boundary conditions are implemented in the program PEDGE, which is a part of a program package from Nuclear Electric (Manchester, UK), formerly Central Electricity Generating Board. Several numerical calculations are performed for different realistic testing situations of finite, smooth and planar cracks. The boundary conditions allow a wide range of crack types and in particular a crack partially closed by a static background pressure is studied.

A numerical comparison for the 2-D horizontally polarized transverse scattering is made for a planar and a nonplanar crack. Here a numerical exact solution for the 2-D scattering problem is obtained by use of the null field approach. The development of the null field solution also shows the importance of using the correct edge conditions. The Geometrical Theory of Diffraction (GTD) solution includes a multiply diffracted field, due to the interaction between the two cracktips, and this multiply diffracted field is shown to be of great importance. Generally the GTD solution yields accurate results even for quite low frequencies.

In the last part of the thesis the full three-dimensional (3-D) scattering problem of a plane wave from a semi-infinite crack with spring boundary conditions is solved. As in the corresponding 2-D calculation the solution is expressed as a high frequency approximation in terms of diffraction coefficients. The calculations involve matrix Wiener-Hopf techniques. Numerical examples are given.