Nonlinear mode III crack stress fields for materials obeying a modified Ramberg-Osgood law

In this paper, an analytical study is carried out on the work-hardening, elastic-plastic stress distributions in a cracked body under antiplane shear deformation. A modified Ramberg-Osgood law is introduced to describe the material behaviour, and stress and strain fields are derived in closed form. Compared with the conventional Ramberg-Osgood formulation, the new law includes the effect of a new parameter, κ, which allows the transition from the ideally elastic behaviour (low stress regime) to the power law behaviour (large stress regime) to be controlled, thus providing 1 more degree of freedom to better fit the actual behaviour of engineering materials. A discussion is carried out on the features of stresses and strains close to and far away from the crack tip.