Size-Effect-Based Forming Behavior and Multi-Objective Die Optimization of Metallic Fuel Cell Bipolar Plates

Ultra-thin metal bipolar plates are critical components of proton exchange membrane fuel cells (PEMFCs), and their forming characteristics decisively influence service performance. This study proposes a constitutive model incorporating size effects to elucidate how sheet thickness and grain size govern stress-strain responses and formability of ultra-thin plates. The verified model is employed in finite element analysis for formability of ultra-thin plates. Based on the results of simulation, key stamping die parameters were optimized using Random Forest and XGBoost surrogate models. Results indicate that increasing grain sizes reduces grain boundary density, leading to stress localization within coarse grains and promoting local thinning. This effect increases stored elastic energy and simultaneously raises the maximum stress, thinning rate, and springback angle. Conversely, the increasing sheet thickness strengthens triaxial constraint and raises forming stress, while suppressing thinning and springback through enhanced strain redistribution and plastic dissipation. Thus, grain coarsening degrades formability overall, whereas increasing thickness introduces a trade-off between higher forming stress and improved dimensional stability. Both surrogate models demonstrated high predictive accuracy on unseen data (maximum error is 2.01%), identifying a non-standard parameter combination (α = 16.0°, R = 0.30 mm, h = 0.48 mm, W = 1.46 mm, S = 0.73 mm) that yields a thinning rate of 4.43% and a springback angle of 0.151°, a level of precision that is difficult to achieve using conventional orthogonal experimental design. This result was verified by additional finite element simulations. The proposed constitutive model and optimization approach provide a theoretical framework and practical guideline for micro-scale bipolar plate die design.