Perturbative simulations of crack front waves

Willis and Movchan [Willis, J.R., Movchan, A.B., 1995. Dynamic weight functions for a moving crack I. Mode I loading. J. Mech. Phys. Solids 43, 319.] devised weight functions for a dynamic mode I fracture, within the singular crack model, using a first order perturbation of in-plane crack motion from the 2D results. Ramanathan and Fisher [Ramanathan, S., Fisher, D.S., 1997. Dynamics and instabilities of planar tensile cracks in heterogeneous media. Phys. Rev. Lettr. 79, 877.] reformulated the Willis-Movchan’s result in terms of crack growth at constant fracture energy, thereby confirming the existence of a crack front wave. Such a wave, as a propagating mode local to the moving crack front, was seen in the non-perturbative numerical simulations based on a cohesive zone fracture model, equivalent to growth at constant fracture energy. In this paper, the result of Ramanathan and Fisher, given in the wavenumber–frequency domain, is recast in the wavenumber–time domain to analyze fracture propagation within first-order perturbations for the singular crack model. This allows application of a spectral numerical methodology and is shown to be consistent with the known 2D results. Through analysis of a single spatial mode of crack shape, the propagating crack front wave and its resonance are demonstrated. Crack propagation through a randomly heterogeneous zone, and growth of disorder with propagation distance, are also examined.