Path and dynamics of a crack propagating in a disordered material under mode i loading

ABSTRACT: The propagation of a single crack in a disordered material is theoretically investigated. Restricting first our analysis to perfectly brittle materials, we show within the framework of the linear elastic fracture mechanics that a crack is described by two independent equations: A path equation, that gives the trajectory followed by the crack within the disordered material, and a motion equation providing the local velocities along the crack front during its propagation. Theoretical predictions resulting from the path equation are found in good agreement with the statistical properties of experimental rough fracture surfaces resulting from perfectly brittle fracture. The motion equation is then studied and predictions for the crack growth velocity dependence with the applied stress intensity factor are given. The path and the dynamics of a crack propagating in a quasi-brittle material is also discussed using a natural extension of the previous description that takes into account the effects of damage and microcracks.