Perturbation of a dynamic planar crack moving in a model viscoelastic solid

Weight functions, which give stress intensity factors in terms of applied loading, are constructed, for three-dimensional time-dependent loading of a semi-infinite crack, propagating at uniform speed. Both a model problem, governed by a scalar wave equation, and the full vectorial problem for Mode I loading, are considered. The medium through which the crack propagates is viscoelastic; the approach is general but explicit formulae are given when the medium is a Maxwell fluid. The weight functions are exploited to develop formulae for the first-order perturbations of stress intensity factors when the crack edge is no longer straight but becomes slightly wavy. Implications for stability, and for ‘‘crack front waves’’ in the case of the Mode I problem, are discussed