Hypersingular integral equation method for a circular crack in a bimaterial plane with a circular interface

According to the study for the fundamental solution of elasticity on a bi-material plane with the circular interface subjected to the radial and circular unit concentrated forces, the stresses and displacements of the problem about the circular crack are derived by use of Betti's reciprocal theorem, geometric relationship and Hooker's law. Considering the stress boundary conditions of the problem, the equations to describe this crack problem are derived, in which the unknown functions are the displacement discontinuities on the crack surface. Cauchy singular integral and hypersingular integrals contained in the equations are calculated by the finite-part integral principles, then a numerical method is first established to solve the problem of a circular crack contained in the bi-material plane with circular interface in the polar coordinate. Finally, the non-dimensional stress intensity factors of the crack under the uniform pressure are calculated for various parameters, such as the crack position c, the radius r0 of interface, and so on. When r0 is sufficiently large, the calculated results by the present method are consistent with those published in literature for the line crack parallel to the interface.