Effect of the cube orientation on formability for FCC materials: a detailed comparison between full-constraint and self-consistent predictions

Abstract

A rate-dependent self-consistent (VPSC) polycrystal-plasticity model, in conjunction with the MK approach, has been used successfully to address and explain plastic deformation features and localization conditions that cannot be treated with the full-constraint (FC) Taylor scheme. Signorelli and Bertinetti [On the role of constitutive model in the forming limit of FCC sheet metal with cube orientations, International Journal of Mechanical Sciences, 51: 473–480, 2009] investigated FCC sheet-metal formability, focusing on how the cube texture affects localized necking. In the present work, we extent this research to include two types of textures experimentally observed in aluminum alloys: the {100} 〈001〉 Cube orientation rotated 45° with respect to the sheet normal direction; and the {100} 〈uvw〉 orientations. The effect of these orientations on the FLD is studied numerically, and a detailed comparison between MK-FC and MK-VPSC, derived from orientation stability and geometrical hardening, is made. The classical MK model, based on strain-rate imposed boundary conditions, was generalized in order to explicitly and correctly includes stress boundary conditions for materials with changes in anisotropy during deformation. In plane-strain stretching, the enhanced formability of the rotated 45° {100} 〈001〉 orientations has been correlated with texture evolution. In equi-biaxial stretching, the MK-FC approach predicted greater limit-strain values than did the MK-VPSC model. Qualitative differences in geometrical hardening/softening were also found.