In-plane perturbation of the tunnel-crack under shear loading II: Determination of the fundamental kernel

For any plane crack in an infinite isotropic elastic body subjected to some constant loading, Bueckner–Rice's weight function theory gives the variation of the stress intensity factors due to a small coplanar perturbation of the crack front. This variation involves the initial SIF, some geometry independent quantities and an integral extended over the front, the “fundamental kernel” of which is linked to the weight functions and thus depends on the geometry considered. The aim of this paper is to determine this fundamental kernel for the tunnel-crack. The component of this kernel linked to purely tensile loadings has been obtained by Leblond et al. Int. J. Solids Struct. 33 (1996) 1995]; hence only shear loadings are considered here. The method consists in applying Bueckner–Rice's formula to some point-force loadings and special perturbations of the crack front which preserve the crack shape while modifying its size and orientation. This procedure yields integrodifferential equations on the components of the fundamental kernel. A Fourier transform in the direction of the crack front then yields ordinary differential equations, that are solved numerically prior to final Fourier inversion.