Crack front perturbations revisited

The problem of the in-plane dynamic perturbation of a crack propagating with a front that is nominally straight is solved, to second order in the perturbation. The method of approach is a streamlined and generalized version of that previously applied to first order by the author and co-workers. It emerges, however, that the analysis at second order requires for its consistency the introduction of a new singular term, of a type not present at first order. The analysis is restricted to the case of Mode I loading, for clarity of exposition. It is carried out at a level of generality that incorporates viscoelastic response as well as propagation in a “vertically stratified” medium including, as a special case, propagation in a slab of finite thickness. For illustration, the general solution is specialized to the case of a stationary crack in an infinite elastic medium and agreement with a solution recently developed by methodology that is specific to the static case is confirmed.