FACTORISATION OF A CERTAIN WIENER-HOPF MATRIX ARISING IN DIFFRACTION THEORY

摘要

Ultrasonic inspection is a widely used method for determining the existence of defects in components. It relies on specular reflection and diffraction of elastic waves at crack faces and edges to locate and size possible defects. The redistribution of energy into a range of diffracted angles is a purely local phenomenon and is determined by the properties of the material at the crack tip and its shape. As all materials are naturally anisotropic, it is clearly necessary to understand how diffraction is modified by anisotropy. An understanding of the effects of anisotropy could therefore help to optimise inspection techniques and justify procedures for detecting and sizing crack-like defects. The quantity of interest is the diffraction coefficient, which relates the vector amplitude of a ray incident on a crack edge to the amplitudes of the diffracted rays. The geometrical theory of diffraction (GTD) is the most useful approach for determining diffraction coefficients. However using GTD it is not possible to consider arbitrary angles of incidence, on arbitrarily oriented defects in materials with low degrees of symmetry. The only previously known results for diffraction coefficients are where there is a high degree of symmetry in the material. These include the three dimensional isotropic case and the two dimensional transversely isotropic problem, considered in [3]. Temple and White attempted to determine diffraction coefficients in more general materials numerically using time dependent finite difference simulations, with limited success.