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Torsional softening arising from the deformation-induced anisotropy of texture and dislocation substructure formation affects various regions of the forming limit diagram. The third invariant of overstress, is included in the kinematic and isotropic hardening equations to reflect the dislocation substructure and texture effect on the torsional softening for 304L stainless steel. Common J2 type theories that do not model the torsional softening exhibited in effective stress-strain curves of compression and torsion give rise to different responses at localization and failure and in the post-localization regime.