Second-order coplanar perturbation of a semi-infinite crack in an infinite body

There has been considerable interest in recent years in theoretical formulae providing, for various crack configurations, the local variation of the stress intensity factors resulting from some small but otherwise arbitrary coplanar perturbation of the crack front. In this work, we establish the expression of the variation of the mode I stress intensity factor up to second order in the perturbation, in the specific case of a semi-infinite tensile crack embedded in some infinite body. The treatment is basically simple and uses earlier results of Rice [34]. Formulae are given in both the physical space and Fourier’s space. They differ from earlier ones established by Adda-Bedia et al. [1] for the same problem, using a more complex method of solution. Finite element computations performed for sinusoidal perturbations support the new formulae, rather than the older ones. As an application, it is finally shown that the mean value of the energy-release-rate along the front of a perturbed semi-infinite tensile crack is exactly the same, up to second order in the perturbation, as if the front were straight.

► We consider a small coplanar perturbation of the front of a semi-infinite tensile crack.
► We derive a new formula for the second-order variation of the stress intensity factor.
► This formula differs from earlier ones of Adda-Bedia et al. and Katzav et al.
► Two independent verifications of the new formula proposed are provided.