The spread of plastic yield from a notch

Abstract

A calculation is made of the length of plastic zone needed to accommodate a given plastic displacement at the root of a notch in a uniformly stressed solid. In an optimum range of stress this zone is about 1000 times larger than the plastic displacement and about five times longer than the notch. The distribution of plastic-elastic strain in the yielded region can be represented by an inverted pile-up of dislocations. The results are related to the problem of notch-brittleness in steel and it is concluded that a condition of `far-reaching' yield should replace the condition of general yield for starting a fracture. Various factors important to notch-brittleness are briefly discussed.