Residual stresses in a co-sintered SOC half-cell during post-sintering cooling

Due to the thermal expansion mismatch between the layers of a Solid Oxide Cell, residual stresses (thermal stresses) develop during the cooling after sintering. Residual stresses can induce cell curvature for asymmetric cells but more importantly they also result in more fragile cells. Depending on the loading conditions, the additional stress needed to break the cells can indeed be smaller due to the initial thermo-mechanical stress state. The residual stresses can for a bilayer cell be approximated by estimating the temperature at which elastic stresses start to build up during the cooling, i.e. the reference temperature (Tref) or the strain difference based on the curvature. This approximation gives good results for bilayers with a defined cooling temperature profile, where the curvature of the bilayer defines a unique balance between the two unknown residual stress states in the two layers. This methodology is however not valid for more layers, as several configurations of residual stresses in the layers can result in the same curvature. Therefore the development of residual stresses of co-sintered multilayer cells during the cooling after sintering is here studied by a finite element model simulation taking into account the elastic response and creep of each layer. The model is validated by measuring the curvature and residual stresses of multi-layer cells.