RECENT DEVELOPMENTS IN KIRCHHOFF CRACK TIP DIFFRACTION CORRECTION

摘要

This paper outlined an approach for computing crack tip diffraction corrections to supplement Kirchhoff scattering theory. The approach adapts of the principals the Geometrical Theory of Diffraction for robust application to arbitrarily shaped cracks. The nature of error encountered when Kirchhoff theory is applied to an unfavorably oriented crack was demonstrated. The formulation of the underlying asymptotic theory was outlined. Problems encountered when applying GTD theory to an arbitrarily shaped crack edge were noted. These problems arise from 1) inherent singularities in asymptotic saddle point analysis near phase inflection points, and 2) irrelevant phenomena in the GTD canonical problem associated with infinite crack/field dimensions. An algorithmic approach to robustly circumvent the first of these problems was demonstrated. Future work will target the second of these problems. Ongoing work is focusing on determining limits of validity of the diffraction corrected Kirchhoff results through comparison to boundary element computations for finite and semi-infinite cracks.