On the elastic-plastic deformation of a sheet containing an edge crack

The solution of the planar tension and bending of an edge-cracked sheet of elastic-plastic material is given when the plastic deformation is represented by a Dugdale model. The analysis assumes conditions of generalized plane stress (for which the model of plastic relaxation is often a suitable one), but the usual transformation of elastic constants may be used to obtain the results also for plane-strain conditions. The method of solution involves the use of a Mellin transform and a Weiner-Hopf technique. Computed results for the size of the plastic zone and the opening at the crack tip are presented, and asymptotic results are obtained for small-scale and large-scale yielding. The results suggest that, when the material is constrained to fracture close to its ultimate tensile stress, the extra severity of a surface flaw compared with a corresponding internal crack is significantly greater than that predicted by linear elastic fracture mechanics.