Localization in a plastically anisotropic void-sheet

Pre-existing voids distributed as a single, but inclined layer are used to represent material defects leading to void growth and strain localization in a sheet. Small elastic but finite plastic strain deformations are accounted for in an elastic-plastically anisotropic material hardening three-dimensional finite element framework. Localization is here defined as the stage of deformation, where the straining in the layer relative to the overall prescribed straining grows to infinity, i.e 104 or higher. Three different materials are consider using the classical Hill-48 anisotropic yield surface (Hill, 1948). As a reference case, one of them is the isotropic Mises case, whereas the other two are anisotropic cases. Yield surfaces and Lankfords coefficients are provided for all three materials. For each material two different void volume fractions and several different loading triaxialities as well as void band inclinations are presented and compared. The strain for localization is given and corresponding deformed void band orientations are discussed. Qualitatively, the responses of the two anisotropic sheets are similar to that of the isotropic Mises case: A minimum in strain at a distinct initial void-band orientation can be identified. Except for one case, all cases studied here result in a simple shift of the critical strain level at localization. However, under uniaxial plane strain tension the isotropic and anisotropic sheet localizes at almost the same value of straining.