Plastic yielding from sharp notches

Abstract

In a previous paper a model of a relaxed crack has been treated in which the plastic relaxation round an isolated crack is represented by an array of dislocations collinear with the crack itself. A similar model is used here to consider the behaviour of an infinite row of relaxed cracks subject to a uniform stress at infinity. The model is used to represent a plastic notch in a plate of finite thickness and the results compared with numerical calculations for the same problem using the macroscopic theory of plasticity. Compared with the dislocation model of the isolated crack, the relaxation spreads further in the presence of other cracks and the length of the relaxed zone required to accommodate a given plastic displacement at a tip is increased by about 10%. Some applications of the results to the theory of notch brittleness and to high-strain fatigue are briefly discussed.