Intrinsic Criterion of Plastic Instability.

Abstract

Necking phenomena, that is, diffuse necking and localized necking are associated with plastic instability. Diffuse necking was analyzed by Swift, who proposed the criterion that the loads in sheet plane become stationary simultaneously under plane stress. However, the loads obtained based on the criterion, in general, do not show the stationarity. In localized necking, the velocity gradient can become disontinuous on the necking plane. In the analyses by Hill and by Storen and Rice, the assumed mode of their necking plane does not satisfy normally the conformity for the discontinuous velocity gradient, and the volumetric strain is discontinuous across the necking plane. We proposed comprehensive criteria including modified diffuse and localized necking, deduced from the necessary condition for multiple solutions. However, it has not been examined whether or not the solution obtained is really multiple. The objective of this work is to perform this examination. Consequently, the sufficient condition for multiple solutions requires the nominal stress to be stationary, and the localized necking to have the defined two modes. They are satisfied in the intrinsic criterion of plastic instability.