An Analytical Model for Investigations on the Stress Distribution in Planar Solid Oxide Fuel Cells
Authors: Guski Vinzenz , Iritsuki Keita , Kamijo Motohisa , Schmauder Siegfried 
Published: February 2020

Solid oxide fuel cells (SOFC) have evolved to successful energy conversion devices for many applications, e.g. auxiliary power units (APU) or combined heat power generation systems (CHP). However, operation conditions under elevated temperatures as well as repeated temperature changes imply extreme demands for the materials involved, questioning durability and reliability of these fuel cells. These properties are important criteria which are not yet resolved satisfyingly. Especially, the effect of internal stresses in cell components arising from thermal shocks or heat cycles on the lifetime of a SOFC still remains unsolved. The residual stress induced by the production process influence the strength of the cell, either. A determination of the stress state is essential to improve the strength of the fuel cells.
An analytical model is presented to determine the residual stress distribution in planar SOFCs during the whole production process. The residual stress is generated due to deposition process (e.g. quenching in thermal spraying or sputtering) and the CTE mismatch due to cooling from deposition temperature to ambient temperature. This model is based on the analytical model proposed by Y.C. Tsui and T.W. Clyne, which was adapted to the production process of SOFCs [1]. The model formulations relate to planar geometries. As boundary conditions, the substrate is clamped at one end and is free to bend during the whole process. Linear elastic material behavior without temperature dependency was assumed for all materials. The intrinsic stress and the thermal stress are introduced layer-by-layer in progressively deposited coating systems. By adding one layer for each deposition step, the residual stress distribution in the specimen can be predicted. A schematic representation of the stress generation coming from both contributions is shown in figure 1. The intrinsic stress is considered in the anode layer and in the electrolyte layer, respectively. In the anode layer the intrinsic stress, which is in the tensile range, is caused by shrinkage due to sintering. However the intrinsic stress in the electrolyte layer is compressive. This is mainly due to ion bombardment on the surface during sputtering. Thermal stress due to CTE mismatch is calculated for the different production steps, which require different temperatures. The final total residual stress is obtained by adding the contributions of deposition and thermal stress.
The investigated SOFC is a MSC type with a porous ferritic Cr-steel substrate, a Ni/YSZ anode layer and an 8YSZ electrolyte layer on top [2, 3]. A polished cross section is shown in figure 2. In this study, the influence of the cathode layer on the stress distribution is neglected due to the low mechanical stability of this layer. For validation purposes a numerical model was built by means of Finite Element Methods (FEM) and compared with the analytical results. In the framework of this study a sensitivity analysis was conducted with respect to the geometric parameters as well as the intrinsic stress.
The calculated stress distribution is comparable to the numerical results. However, differences in terms of magnitude between the two models can be observed. After anode deposition, the total stress level is in the tensile range. This observation can be explained by the large tensile intrinsic stress, which dominates the compressive thermal stress. The electrolyte deposition results in large compressive stress in the electrolyte layer, which is a consequence of the compressive intrinsic stress, but still tensile stress remains in the anode layer. These insights lead to the conclusion that thermal stress due to CTE mismatch has minor influence on the residual stress in contrast to the intrinsic stress, which are determined by the production process. These observations hold for several parameter sets. A validation of the models with experimental results is planned in the future.

Figure 1