Three-dimensional crack-face weight functions for the semi-infinite interface crack - II: Integrodifferential equations on the weight functions and resolution

In Part I, we considered a small coplanar perturbation of the front of a semi-infinite interface crack and derived the expression of the resulting variation of the stress intensity factors along that front. In the present Part II, we apply this result to some special loadings, namely those which define the crack-face weight functions, and to some special perturbation, namely a rotation of the crack front about the direction normal to the crack plane; the interest of such a perturbation is that it preserves the shape of the crack so that the perturbed stress intensity factors are still expressible in terms of crack-face weight functions. The result consists in some integrodifferential equations for these functions. These equations are transformed into ordinary differential equations through Fourier transformation in the direction of the crack front. The solution is obtained in closed form to first order in the "bimaterial constant" ε. Its sole non-elementary feature is the appearance of indefinite integrals of the form ∫ [In x/(x + a)] dx.