Oscillatory instability of crack propagations in quasistatic fracture

Quasistatic crack propagations in a thin plate are studied theoretically. The Griffith theory is applied to determine a crack extension condition and the motion of crack tips in straight propagation. A linear stability problem for the straight propagation is formulated, based on the assumption that the crack tip moves in such a way that a singular shear stress is made to vanish. It is shown that straight propagations become unstable under certain conditions and that an oscillatory propagation appears. The critical conditions are calculated quantitatively, and the results are compared with the corresponding experiments.