Plastic flow in a deeply notched bar with semi-circular root
The unsteady motion problem of a circular-notched bar pulled in tension in plane strain is considered. The theory of perfectly plastic solids is used. Large strains are analyzed so that the material can also be considered as plastic-rigid. The basic equations governing stress and velocity are integrated independently in the characteristic plane. The results are used to construct the boundary change in a step-bystep manner. The problem is greatly simplified because at each step the new free boundary of the plastic region can be approximated by a circle. The final shape of the boundary of an initially semi-circular notch is presented when plastic flow has reduced the initial connection at the root to a line contact between the shanks.