Numerical solutions of hypersingular integral equations for interface circular crack under axisymmetric loadings

Abstract

Based on the coupled oscillatory characteristic of mode-1 and mode-2 near the interface crack tip, one kind of element for the relative displacements of the upper and lower surfaces of the axisymmetric interface crack is constructed. A universal numerical method for solving hypersingular integral equations of axisymmetric interface circular crack is established. For arbitrary normal and shear axisymmetric loadings, they are expanded into Taylor series, and the first five loadings are numerically calculated in a wide range of bimaterial constant ε=0-0.15. The detailed numerical results of the stress intensity factors K1 and K2 are given in tabular form. Comparisons with the existing exact solutions show that the numerical results in this paper have high accuracy. For arbitrary axisymmetric loadings, the stress intensity factors can be determined from the tabular numerical results by using the superposition principle.