Brittle and ductile extension of a finite crack by a horizontally polarized shear wave

An integral representation of the displacement for problems of transient propagation of horizontally polarized shear waves is employed to investigate the diffraction of a plane wave by a crack of finite length. The stress intensity factors at small times are derived for an incident wave of arbitrary shape. For a step-stress wave the maximum stress intensity factors are shown to exceed the factors of the corresponding static problem by a factor 4 π. Brittle fracture is subsequently investigated by employing a balance of rate of energy. It is shown that for a step-stress wave the critical stress for brittle fracture is reduced by a factor π 4√2 as compared to the critical stress of the corresponding static problem. Ductile fracture is studied by assuming that yielding is restricted to a narrow band in the vicinity of the crack tips. The propagation velocity of the zone of yielding is computed and the location of the point of rupture is determined.