Analyzing batch-to-batch and part-to-part springback variation of DP600 steels using a double-loop Monte Carlo simulation

Many automobile companies are actively exploring the use of high-strength dual-phase steels as an alternative to aluminum and magnesium alloys owing to their light weight, low cost and durability. However, dual-phase steels have a tendency to springback more than other structural steels in a forming operation owing to their high tensile strength. In addition, variations in manufacturing process parameters and material properties cause springback variation over different manufactured parts. Therefore, it is an important task to reduce the magnitude of springback, as well as its variation within, to produce robust and cost-effective parts. This article investigates minimization of the magnitude and variation of springback of DP600 steels in U-channel forming within a robust optimization framework. The computational cost was reduced by utilizing metamodels for prediction of the springback and its variation during optimization. Three different allowable sheet thinning levels were considered in solving the robust optimization problem, and it was found that, as the allowable thinning increased, the die radius decreased, thereby the magnitude and variation of springback reduced. A simple sensitivity analysis was performed and the yield stress was found to be the most important random variable. Finally, a double-loop Monte Carlo simulation method was proposed to calculate part-to-part and batch-to-batch springback variations. It was found that, as the batch-to-batch variation of yield stress increased, the batch-to-batch springback variation increased, while the part-to-part springback variation remained unchanged.