Effect of Lode parameter on plastic flow localization after proportional loading at low stress triaxialities

The effect of the stress state on the localization of plastic flow in a Levy–von Mises material is investigated numerically. A unit cell model is built with a spherical central void that acts as a defect triggering the onset of flow localization along a narrow band. Periodic boundary conditions are defined along all boundaries of the unit cell. Shear and normal loading is applied such that the macroscopic stress triaxiality and Lode parameter remain constant throughout the entire loading history. Due to the initially orthogonal symmetry of the unit cell model the deformation-induced anisotropy associated with void shape changes, both co-rotational and radial loading paths are considered. The simulation results demonstrate that the macroscopic equivalent plastic strain at the onset of localization after monotonic proportional loading decreases in stress triaxiality and is a convex, non-symmetric function of the Lode parameter. In addition to predicting the onset of localization through unit cell analysis, an analytical criterion is proposed for monotonic proportional loading which defines an open convex envelope in terms of the shear and normal stresses acting on the plane of localization.