Crystal Plasticity Finite Element Analysis of Formability and Deformation Behavior in Ultra-thin Steel Sheet for Fuel Cell Bipolar Plate
- This dissertation is devoted to demonstrating the virtual material testing via microstructure-based simulation using crystal plasticity finite element method (CPFEM) as a robust and potential modelling tool and its application for the prediction of macroscopic mechanical behavior of automotive sheet metals. The focuses are on the investigations on the forming limit diagram (FLD), size effect on the formability and deformation behavior of the ultra-thin ferritic stainless steel (FSS) sheet, and then the process design of multi-stage forming for bipolar plate (BPP) in proton exchange membrane (PEM) fuel cell is proposed. These objectives are comprehensively addressed and summarized as follows.
Firstly, the CPFEM model was successfully developed by accurately reproducing mechanical behavior and yield loci of the material. Then, the CPFEM model was combined with Marciniak–Kuczynski approach in the analysis of forming limits. It revealed that the CPFEM–MK simulations using voxel-typed representative volume element (RVE) with the consideration of measured texture well matched with the experimental FLD.
Secondly, a hybrid cellular automata–Monte Carlo (CA–MC) model was developed to generate a ‘realistic’ RVE that accurately reconstructed the measured texture and grain boundary misorientation distribution (GBMD). The predicted FLD by the CPFEM–MK model with the realistic RVE shows a good agreement with the experimental results. In order to explore the size effect on the formability, the forming limit analyses were conducted using RVEs with various thickness-to-grain size ratios (t/d = 2~10). The results revealed a significant degradation of the formability of the ultra-thin FSS sheet as t/d decreased. With decreasing number of grains through the thickness, the stress and strain heterogeneities in the surface grains were noticeably increased due to the less constraint by the subsurface grains, which played an important role in the size effect. Furthermore, it was found that the surface strain hot spots in the material with low t/d could act as the geometrical imperfection to accelerate the failure, together with the increased stress triaxiality in the surface grains as the results of the localized strains and premature necking during the deformation. This attributed the decrease of forming limit strains to the early plastic flow instability in the ultra-thin sheet material with low thickness-to-grain size ratio.
Thirdly, the effect of free surface roughening on the formability of ultra-thin FSS sheet were addressed by in-situ electron backscatter diffraction (EBSD) and CPFEM simulation. The microstructural evolution during uniaxial tension was monitored by the in-situ EBSD technique. It revealed that as the strain increased, the microstructure of ultra-thin FSS sheet exhibited more significant heterogeneities in terms of surface morphology, kernel average misorientation (KAM) and geometrically necessary dislocation (GND) density distributions. The initial microstructure was then directly mapped onto the finite element mesh in the CPFEM simulation. The results showed that CPFEM predictions of stress and strain heterogeneities and the local hot spots of the ductile fracture initiation well matched with the experimental results. It was found that the localized deformation primarily distributed in the free surface grains which were less constrained and deformed easily, leading to the increased stress and strain heterogeneities. Furthermore, the free surface exhibited a considerable roughness due to the heterogeneous plastic deformation of grains under the applied strains, resulting in the increased thickness inhomogeneity which facilitated the strain localization, consequently the premature necking and fracture in the ultra-thin FSS sheet. This finding strongly supported to the previous elucidation that the early plastic flow instability induced from the localized deformation at subsurface grain was responsible for the decrease of forming limit strains.
Finally, based on these above findings, a special remedy of new muti-stage die design approach was proposed in order to prevent the local thinning and fracture in the ultra-thin FSS sheet for fuel cell BPP. The process design parameters of the proposed die shape were successfully optimized by the developed artificial neural network (ANN) model integrated with the genetic algorithm (GA). The micro-channel analysis by 2D finite element (FE) simulation of two-step forming process revealed a significantly decrease in the local thinning due to the decreased stress/strain heterogeneity. It also showed the more uniform distribution of thickness reduction in addition to the improved minimum thickness and thickness deviation in the micro-channel BPP. Furthermore, the 3D FE simulation of macro-scale BPP channel disclosed the noticeable reduction in the springback and distortions in terms of twist angle (~18%) and local curvature (~30%). This demonstrated the promising two-step multi-stage forming with a novel die design approach to significantly enhance the formability of ultra-thin metallic BPP by reducing the ruptures and shape error due to the excessively localized thinning and springback, respectively. In addition, this research suggested the beneficial method in the fabrication technologies of ultra-thin metallic BPP for PEM fuel cell.
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- Crystal plasticity finite element method; size effect; formability; deformation behavior; fuel cell bipolar plate
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