Directional Dependence of Apparent Unloading Modulus in Steel Sheets and Its Effect on Predicted Springback Geometry in Roll Forming

The apparent unloading modulus of sheet metals decreases with plastic pre-strain, and its directional dependence may affect springback prediction. This study investigates its directional evolution in CN4301-4307+2B, DOCOL780DP+AM, and WBS235JR using cyclic loading–unloading–loading tensile tests at 0°, 45°, and 90° to the rolling direction. The chord modulus is used as the primary definition and described using Yoshida relations. Two alternative unloading modulus definitions are evaluated to assess the robustness of the directional comparison. At εp = 0.08, the directional spread of relative modulus reduction is 14.56 percentage points for CN4301-4307+2B, 7.95 percentage points for WBS235JR, and 3.03 percentage points for DOCOL780DP+AM. The directional ranking is retained for all investigated definitions, although the spread magnitude depends on the definition. A controlled numerical roll forming sensitivity analysis shows a maximum difference of 0.58° in the mean F1–F3 opening angle relative to the constant modulus reference. The results indicate that a direction-independent unloading modulus relation may neglect relevant directional effects and affect predicted springback geometry. When a single uniaxial relation is used in roll forming simulations, the 90° response may provide a physically motivated basis for the predominantly transverse cross-sectional bending.