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<p>Ultra-thin titanium bipolar plates are key components in proton exchange membrane fuel cells (PEMFCs), where high-aspect-ratio microchannels must be formed with tight dimensional tolerance. Two-step stamping is a widely adopted manufacturing process used to mitigate fracture and improve thickness uniformity. However, the accurate prediction of springback and channel geometry performance remains a significant challenge due to the material’s strong anisotropy, pronounced Bauschinger effect, and the degradation of its elastic modulus during deformation. In this study, the mechanical performance and deformation behavior of a 0.12-mm commercially pure titanium sheet were systematically characterized through uniaxial tension, tension-compression, and cyclic loading-unloading-reloading tests. To accurately capture these complex material behaviors, an anisotropic nonlinear kinematic hardening (NKH) constitutive model was developed, integrating the Hill48 yield criterion with a variable elastic modulus (VEM) formulation. To overcome the limitations of empirical parameter fitting from limited experimental data, a novel Gradient-Enhanced Physics-Informed Neural Network (GE-PINN) framework was utilized to robustly identify back stress and isotropic hardening parameters. The calibrated material model was implemented in Abaqus/Explicit to simulate the two-step stamping process. The Hill48 + VEM + NKH model yielded the smallest channel-depth prediction errors, 3.43&#xa0;μm for the first step and 5.73&#xa0;μm for the second step. Furthermore, comparative modeling revealed that accurately representing elastic modulus degradation is the most critical factor for predicting springback in ultra-thin titanium sheets, followed by the chosen hardening law. This combined experimental and data-driven modeling approach provides a robust framework for optimizing the design and forming performance of titanium PEMFC bipolar plates.</p>

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Experimental Characterization and GE-PINN Calibrated Constitutive Modeling for Two-Step Stamping of Ultra-Thin Titanium Bipolar Plates

  • 期刊论文

  • 发表日期：

    2026年6月23日

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  • Yao Xiao,
  • Zijie Ke,
  • Zeran Hou,
  • Junying Min

摘要

Ultra-thin titanium bipolar plates are key components in proton exchange membrane fuel cells (PEMFCs), where high-aspect-ratio microchannels must be formed with tight dimensional tolerance. Two-step stamping is a widely adopted manufacturing process used to mitigate fracture and improve thickness uniformity. However, the accurate prediction of springback and channel geometry performance remains a significant challenge due to the material’s strong anisotropy, pronounced Bauschinger effect, and the degradation of its elastic modulus during deformation. In this study, the mechanical performance and deformation behavior of a 0.12-mm commercially pure titanium sheet were systematically characterized through uniaxial tension, tension-compression, and cyclic loading-unloading-reloading tests. To accurately capture these complex material behaviors, an anisotropic nonlinear kinematic hardening (NKH) constitutive model was developed, integrating the Hill48 yield criterion with a variable elastic modulus (VEM) formulation. To overcome the limitations of empirical parameter fitting from limited experimental data, a novel Gradient-Enhanced Physics-Informed Neural Network (GE-PINN) framework was utilized to robustly identify back stress and isotropic hardening parameters. The calibrated material model was implemented in Abaqus/Explicit to simulate the two-step stamping process. The Hill48 + VEM + NKH model yielded the smallest channel-depth prediction errors, 3.43 μm for the first step and 5.73 μm for the second step. Furthermore, comparative modeling revealed that accurately representing elastic modulus degradation is the most critical factor for predicting springback in ultra-thin titanium sheets, followed by the chosen hardening law. This combined experimental and data-driven modeling approach provides a robust framework for optimizing the design and forming performance of titanium PEMFC bipolar plates.