The Plastic Yielding of Notched Bars Under Tension

The state of stress in the core of a notched bar is analysed at the moment when pronounced plastic yielding begins. The theory is two-dimensional and an ideal plastic-rigid material is assumed. Following a general analysis of the problem, the magnitude of the constraint factor is calculated for a deep notch with a semicircular root. The correct approach to problems of plane plastic strain is discussed, and is further illustrated by a re-examination of the classical work of Prandtl on indentation (which is closely related in principle with the notched bar problem).