Post-critical deformation pattern in plane strain plastic flow with yield-surface vertex effect

This work is concerned with the formation of multiple macroscopic shear bands viewed as a mechanism of large plastic deformation of polycrystalline metals. The plastic deformation pattern in a time-independent material with a yield-surface vertex effect is investigated numerically in plane strain beyond the critical instant of ellipticity loss under quasi-static loading. The energy criterion of path instability applied to a family of post-critical solutions eliminates unstable paths and enables the overall deformation pattern to be determined, although the solutions remain locally indeterminate due to the absence of an internal length scale. In particular, the volume fraction of incipient shear bands is found to have a well-defined value irrespective of the mesh size in finite element calculations. As an apparently novel qualitative result, the formation of coarse, differently aligned secondary bands is observed at later stages of simulation.