Numerical Optimization of Die Geometry to Minimize Forming Defects in a 1 GPa-Grade Ultra-High-Strength Steel Cross-Member

Ultra-high-strength steel (UHSS) cross-members with a high height-to-width ratio are prone to forming defects, such as splitting and wrinkling, due to localized stress concentration during the drawing process. In this study, the addendum geometry in first-stage of a two-stage drawing process was optimized to improve the formability of a cross-member made of 1 GPa-grade UHSS. The optimization was performed using the Sigma module of AutoForm, and Latin hypercube sampling was adopted for the design of experiments. The punch opening width, upper bar radius, wall angle, and lower die radius of the addendum were selected as design parameters, and multi-objective optimization was conducted to simultaneously minimize the maximum failure index and maximum wrinkle value, the two AutoForm forming-defect indicators used in this study. In the initial design, the maximum failure index was 1.044, exceeding the splitting criterion of 1.0; however, this value was reduced to 0.961 in the optimized design, thereby mitigating the risk of splitting. In addition, the maximum wrinkle value was reduced by 11.7% compared with that of the initial design. Pareto analysis was performed to quantitatively evaluate the effects of the design parameters on the forming defects, and the results confirmed that the punch opening width and lower die radius were the dominant parameters affecting both splitting and wrinkling. These results demonstrate that die addendum geometry optimization is effective for reducing splitting and wrinkling in 1 GPa-grade UHSS cross-members.