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. (C) 2000 Elsevier Science Ltd. All rights reserved.