Models of crack propagation. II. Two-dimensional model with dissipation on the fracture surface

We discuss a model of steady-state crack propagation in a two-dimensional material whose displacements obey a massive scalar wave equation. The tractions on the fracture surface consist of a conventional cohesive stress plus a viscous dissipation. Much of the paper is devoted to the development of Wiener-Hopf methods for an analysis of this model. The most notable result is that, when the dissipation is sufficiently strong, the crack creeps very slowly at external stresses just above the Griffith threshold, and makes an abrupt transition to propagation at roughly the Rayleigh wave speed at higher stresses. Thus the model exhibits a dissipation-dependent effective threshold for fracture.