Crack front waves

Abstract

We present simulations of 3 D dynamic fracture which suggest that a persistent elastic wave is generated in response to a localized perturbation of a propagating crack front, e.g., by a local heterogeneity of critical fracture energy. The wave propagates along the moving crack front and spreads, relative to its origin point on the fractured surface, at a speed slightly below the Rayleigh speed. The simulations were done using the spectral elastodynamic methodology of Geubelle and Rice (1995). They model failure by a displacement-weakening cohesive model, which corresponds in the singular crack limit to crack growth at a critical fracture energy. Confirmation that crack front waves with properties like in our simulation do exist has been provided by Ramanathan and Fisher (1997). Through a derivation based on the linearized perturbation analysis of dynamic singular tensile crack growth by Willis and Movchan (1995), those authors found by numerical evaluation that a transfer function thereby introduced has a simple pole at a certain ω κ ratio, corresponding to a non-dispersive wave. Further, we show that as a consequence of these persistent waves, when a crack grows through a region of small random fluctuations in fracture energy, the variances of both the local propagation velocity and the deformed slope of the crack front increase, according to linearized perturbation theory, in direct proportion to distance of growth into the randomly heterogeneous region. That rate of disordering is more rapid than the growth of the variances with the logarithm of distance established by Perrin and Rice (1994) for a model elastodynamic fracture theory based on a scalar wave equation. That scalar case, which shows slowly decaying (as t − 1 2 ) rather than persistent crack front waves, is analyzed here too.