A validated model of membrane mechanics for micro SOFC

The design of a single Micro Solid Oxide Fuel Cell is built upon multi-layered ceramic membranes. Although advantageous properties related to this design, like a favourable strength-to-weight ratio, high fatigue endurance, and, strong corrosion resistance, the laminated thin membrane structure may exhibit some functional problems. Actually, it has a low resistance against peeling stress at the interface between different layers where cracks (delamination) may appear. In addition, the thin ceramic film is subjected to in-plane compressive stresses associated to a mismatch thermal expansion and to fabrication process, and then, it may exhibit an instability transition by buckling. Both buckling and cracks reduce the load carrying capacity of the structure, and further, crack propagation can lead to a failure mode limiting the service life of the fuel cell. In the framework of OneBat Project three institutes SAMLAB-EPFL, NIM-ETHZ and ICP-ZHAW are participating to this study which aims to analyse the different thermo-mechanical failure modes during the manufacturing stages of micro-SOFC and to develop a strategy to avoid them. Our main effort at ICP-ZHAW is focused on the numerical analysis and physical modelling of the buckling and the delamination phenomena when the experimental tests are contributed by the partner institutes. Buckling of an elastic thin film is modelled in the light of the principle of minimum potential energy and by applying the Rayleigh-Ritz method. An energy minimization procedure is applied to calculate the unknown coefficients to describe the buckling shape and amplitude. A comprehensive treatment of the Rayleigh Ritz Method on the light of eigen modes superposition is introduced, including derivation of the stability criteria, physical interpretation of the buckling shape, numerical code implementation in Mathematica 8.0, and, some selected simulations. Comparison between simulation and experimental results show the efficiency of this method to provide a realistic modelling of the buckling phenomena at micro scale level. In addition, due to imperfections in a ceramic material, crack can be initiated in the middle of membrane surface. To control the fracture toughness of the laminated thin films a model based on Griffith criterion for crack growth is applied. Therefore, we perform numerical simulation using the eXtended (or enriched) Finite Element Method (XFEM). This approach allows one to represent accurately the stress singularity at the crack tip and the discontinuity on crack faces and avoid the remeshing along the internal boundary of the crack. Within the framework of XFEM which is already implemented in the open source GETFEM package, the concept of the partition of unity is employed to incorporate special local enrichment functions into the basis of the standard FEM to take into account the presence of the aforementioned singularity and discontinuity