Dugdale model for an expanding crack under shear stress

Relaxation of an expanding crack by plastic flow under a uniform in-plane or anti-plane shear stress is studied using Dugdale model. Explicit relations among the applied stress, yield stress, plastic zone size, and crack speed are established. Expressions for the relative crack face displacements and the rates of plastic work are also obtained. It is shown that at a fixed applied stress the relative plastic zone size, the normalized relative crack tip displacement, and the normalized energy release rate decrease with increasing crack speed. Furthermore, the inertial effect is the most significant for mode I, followed by modes III and II.