Stress and strain distributions in plastically deformed notched bars

Abstract

A numerical method is proposed to obtain the strain distribution from hardness test results at the net section of plastically deformed notched bars. The effect of notch radius and deformation on the strain and stress distributions has been determined. The equivalent stress and strain distributions become mildly concave with deformation and notch radius, while the strain at the centre of the net section increases rapidly beyond 95 per cent of the maximum load, Pmax. The equivalent strain distribution on the central axis near the net section is convex. This convex distribution is transformed into a decreasing one for a mild notch owing to the rapid deformation around the centre of the net section. The stress triaxiality at the centre of the net section decreases rapidly with deformation, being less than the value determined by finite element analysis beyond Pmax, which is nearly independent of deformation. At the notch root the stress triaxiality decreases slightly with deformation and is accurately predicted by finite element analysis prior to Pmax.