Oscillatory instability of crack propagations in quasi-static fracture

Crack propagations in quasi-static fracture are studied theoretically. The Griffith theory is applied to discuss a crack extension condition and motion of crack tips in straight propagations. Stability of the straight propagations is investigated based on the simple assumption that a curvature near the crack tip is determined by a singular shear stress. It is shown that straight propagations become unstable under ceatain conditions. Combined with boundary effects, this instability leads to an oscillatory propagation of cracks. The critical conditions are calculated quantitatively.