Plastic Flow in a V-Notched Bar Pulled in Tension

Abstract

Abstract A V-notched bar pulled in tension in plane strain as shown in Fig. 1 is considered. The distribution of stress and deformation are determined from the analysis of the motion with large strains as the initial notch width pulls down toward line contact as the test proceeds. The analysis is based upon the theory of flow of a so-called Saint Venant-Mises material, which flows at a constant yield limit given by the Mises criterion, and obeys the Mises flow-type relationship between stress and strain increments. The successive configurations of an initially square grid on the cross section of the notch are obtained to illustrate the strain distribution. This solution is of interest in investigating the initiation of fracture in a notch-bar tension test. In such a test the foregoing type of solution applies until plastic flow is arrested by the appearance of a fracture crack. The variation of the solution with notch angle is of interest in connection with the determination of the technical cohesive strength of a metal using Kuntze’s technique. The present solution indicates a contrast with Kuntze’s hypothesis, in that it predicts the possibility of a plastic-flow type of rupture at a stress depending only upon the yield stress of the metal.