Acoustic emissions produced by elementary processes of deformation and fracture at a crack edge are investigated on the basis of elastodynamic ray theory. To obtain a two-dimensional canonical solution we analyze wavefront motions generated by an arbitrary distribution of climbing edge dislocations emanating from the tip of a semi-infinite crack in an unbounded linearly elastic solid. These wavefront results are expressed in terms of emission coefficients which govern the variation with angle, and phase functions which govern the intensity of the wavefront signals. Explicit expressions for the emission coefficients are presented. The coefficients have been plotted versus the angle of observation, for various values of the crack propagation speed. The phase functions are in the form of integrals over the emanating dislocation distributions. Specific dislocation distributions correspond to brittle fracture and plastic yielding at the crack tip, respectively. Acoustic emission is most intense for brittle fracture, when the particle velocities experience wavefront jumps which are proportional to the stress-intensity factors prior to fracture. An appropriate adjustment of the canonical solution accounts for curvature of a crack edge. Such effects as focussing, finite duration of the propagation event, and finite dimensions of the crack are briefly discussed. As a specific example, the first signals generated by brittle Mode I propagation of an elliptical crack are calculated.
A phase field modeling of dynamic brittle fracture at finite strains
