Studies of residual stresses in planar solid oxide fuel cells

Planar solid oxide fuel cells (SOFCs) are composites consisting of porous and dense functional layers as electrodes and electrolyte, respectively. Due to the thermo-elastic mismatch between the individual layers residual stresses develop during manufacturing that result in warping for unconstrained cells. The residual stress of half-cells specimens with oxidized anode has been determined as a function of temperature. Two complementary techniques, X-ray diffraction analyses and measurements of cell curvature were applied. Moreover, changes in electrolyte residual stress associated with cell brazing to a steel interconnect were measured. The joining was carried out with symmetric cell composites having an anode layer sandwiched between two electrolyte layers. In addition to this test the effect of brazing and welding on the stress situation in the electrolyte of a real cell was tested.     

Residual stress and redox cycling of segmented-in-series solid oxide fuel cells

Residual stresses in the electrolytes of segmented-in-series solid oxide fuel cells (SIS-SOFCs) and anode-supported cells (ASCs) were estimated at room temperature by X-ray diffraction. In the SIS-SOFCs, the residual stresses in the electrolyte were smaller than in the ASCs and did not change significantly after redox cycling. For both designs, numerically calculated values of the residual stresses in the electrolyte were found to be comparable to the experimental results. Next, in order to simulate the reoxidation reaction, the anode was subjected to forced expansion, and the residual stresses were estimated at high temperatures. It was found that in the SIS-SOFC, the dimensional changes and residual stresses were smaller than those in the ASC. The high redox tolerance of the SIS-SOFC is considered to stem from the fact that the electrically insulated substrate prevents the expansion and deformation of the positive electrode-electrolyte-negative electrode structure.     

Simulation and analysis of sintering stress and warpage displacement in anode supported planar solid oxide fuel cells

During the sintering process of solid oxide fuel cells (SOFCs), the mismatch in the thermophysical properties of materials can lead to excessive local thermal stress and warpage. By establishing a 3D multiphysics model, the stress distribution and displacement during sintering are studied. The results show that when the anode and electrolyte thicknesses are 0.2 mm and 0.02 mm, respectively, the maximum sintering stress is 38.8 MPa, which is 48% lower than the maximum value of all simulation results. In this study, when the anode thickness is 0.7 mm and the electrolyte thickness is 0.008 mm, the maximum warpage displacement is the smallest at 0.14 mm. A sintering preparation method for partially coated cells is proposed. These results can be used to optimize the sintering process of SOFCs and greatly reduce the sintering stress and warpage of SOFCs.     

Effect of Al2O3 film on thermal stress in the bonded compliant seal design of planar solid oxide fuel cell

This paper uses finite element method to study the effect of Al₂O₃ film on thermal stresses in the bonded compliant seal (BCS) design of a planar solid oxide fuel cell. The effects of Al₂O₃ thickness, operating temperature, window frame thickness, foil thickness and cell length on thermal stresses have been discussed. The results show that compressive stresses are generated in Al₂O₃ film. A bowing deformation is generated due to the BCS design, which can trap and relax some thermal stresses. With Al₂O₃ thickness increase, compressive stresses in Al₂O₃ film and foil are decreased slightly, while tensile stresses in BNi₂ and frame are increased. With operating temperature increase, compressive stress in Al₂O₃ is increased greatly, while the stresses in foil, BNi2 and frame are increased slightly. The bowing deformation is increased with operating temperature increase. The window frame thickness has little effect on thermal stresses and bowing deformation. With sealing foil thickness increase, thermal stresses and bowing deformation are increased. The cell length has little effect on thermal stresses, but reducing the cell length can decrease the bowing deformation.     

Thermal stress and thermo-electrochemical analysis of a planar anode-supported solid oxide fuel cell: Effects of anode porosity

A 3D integrated numerical model is constructed to evaluate the thermal-fluid behavior and thermal stress characteristics of a planar anode-supported solid oxide fuel cell (SOFC). Effects of anode porosity on performance, temperature gradient and thermal stress are investigated. Using commercial Star-CD software with the es-sofc module, simulations are performed to obtain the current-voltage (I-V) characteristics of a fuel cell as a function of the anode porosity and the temperature distribution within the fuel cell under various operating conditions. The temperature field is then imported into the MARC finite element analysis (FEA) program to analyze thermal stresses induced within the cell. The numerical results are found to be in good agreement with the experimental data. It is shown that the maximum principal stress within the positive electrode-electrolyte-negative electrode (PEN) increases at a higher current and a higher temperature gradient. It is recommended that the temperature gradient should be limited to less than 10.6 °C mm⁻¹ to maintain the structural integrity of the PEN.     

Thermal stress modeling of anode supported micro-tubular solid oxide fuel cell

An anode-supported micro-tubular solid oxide fuel cell (SOFC) is analyzed by a two-dimensional axisymmetric numerical model, which is validated with the experimental I-V data. The temperature distribution generated by the thermo-electrochemical model is used to calculate the thermal stress field in the tubular SOFC. The results indicate that the current transport in the anode is the same at every investigated position. The stress of the micro-tubular cell occurs mainly because of the residual stress due to the mismatch between the coefficients of thermal expansion of the materials of the membrane electrode assembly. The micro-tubular cell can operate safely, but if there is an interfacial defect or a high enough tensile stress applied at the electrolyte, a failure can arise.     

Application of infrared thermal imaging to the study of pellet solid oxide fuel cells

The application of infrared thermal imaging to the study of solid oxide fuel cells is demonstrated. The temperature increase accompanying polarisation of gadolinium doped ceria pellet cells is measured and the effect of temperature increase on polarisation characteristics is modelled. Temperature increases of the order of 2.5 °C were measured for heavily loaded pellet cells. Measurement accuracy of 0.1 °C and spatial resolution of 0.5 mm allow temperature distribution heterogeneity to be clearly discerned. A total heat transfer coefficient is derived from experimental results that allow the development of a model that predicts the extent of self-heating. For pellet fuel cells, self-heating is not expected to have a large effect on the polarisation characteristics; however, for thin electrolytes and high current density the effect becomes appreciable.     

Numerical simulation and analysis of thermal stress distributions for a planar solid oxide fuel cell stack with external manifold structure

A three-dimensional numerical model based on the finite element method (FEM) is constructed to calculate the thermal stress distribution in a planar solid oxide fuel cell (SOFC) stack with external manifold structure. The stack is composed of 5 units which include cell, metallic interconnect, seal and anode/cathode current collectors. The temperature profile is described according to measured temperature points in the stack. It can be clearly seen that the maximum stress concentration area appears at the corner of the components when the stack is heated from room temperature (RT) to 780 °C. The effects of stack components on maximum stress concentration have been investigated under the operation temperature, as well as the thermal stress simulation results. It is obvious that the coefficient of thermal expansion (CTE) mismatch between the interconnect and the seal plays an important role in determining the thermal stress distribution in the stack. However, different compressive loads have almost no effect on stress distribution, and the influence of glass-based seal depends on the elastic modulus. The simulation results can be applied for optimizing the structural design of the stack and minimizing the high stress concentration in components.     

Effect of phase transformation of zirconia on the fracture behavior of electrolyte-supported solid oxide fuel cells

Zirconia solid electrolyte provides the functions of mechanical support, electronic insulation and oxygen ions conductivity for electrolyte-supported solid oxide fuel cell. Ferritic stainless steel is used as current collector to study the structural stability of the two cells during the cooling process. The sample using fully-stabilized zirconia is cracked after the cooling process, while the partially-stabilized zirconia sample has no obvious changes. Thermal expansion coefficient of the two samples is similar, which exhibits that TEC is not the main factor to result in the fracture. In-situ X-ray diffraction results indicated that the conflict between the compression state in cell due to TEC and the volume expansion of the fully-stabilized zirconia sample due to phase transformation can cause cracking. Partially-stabilized zirconia sample can be transformed from tetragonal to cubic phase during the temperature rising, while can be recovered to its initial state during cooling. Even much more cubic phase can be transformed to the tetragonal phase induced by pressure stress during cooling, which plays an important role on the anti-cracking performance.     

Numerical investigation of flow/heat transfer and structural stress in a planar solid oxide fuel cell

The present work investigates the effects of the temperature and thermal stress distributions in a planar solid oxide fuel cell (SOFC) unit cell. A computational fluid dynamic (CFD) analysis of a planar anode-supported SOFC that considers electrochemical reactions is performed, and the thermal stresses are calculated. The static friction coefficients are assumed to range from 0.05 to 0.3, and conservatively, a perfectly bonded condition is assumed. The results show that the electrolyte is the weakest component and has the maximum stress because the electrolyte is the thinnest and the Young modulus is the highest. Thus, the contact between the anode electrode and the electrolyte, and between the cathode electrode and the electrolyte, would be the perfectly bonded condition. As a result, this research showed that the stresses induced by constraint forces with various contact conditions were dominant for the structural stability in a SOFC. Therefore, static friction coefficients on operative high temperature conditions are important to predict the structural integrity in a SOFC, and they will be investigated in future works in order to improve the structural stability in a stack design as well as in a SOFC.     

Effect of air flow rate distribution and flowing direction on the thermal stress of a solid oxide fuel cell stack with cross-flow configuration

This study investigates the effect of non-uniform distribution of the air inlet flow rate and change of air flowing direction on the thermal stress of a solid oxide fuel cell stack with cross-flow configuration. This study considers three patterns of air inlet flow rate in the transverse direction of each stack, and five patterns of air inlet flow rate in the stacking direction. The software package for simulation is reliable through an accuracy comparison, and it analyzes the current density, temperature, and thermal stress distribution of a SOFC stack with 20 layers. The results show that the progressively increasing profile of the air inlet flow rate along the x direction drops the cell thermal stress of a SOFC unit. Moreover, the non-uniform profile of air inlet flow rate in the stacking direction affects the position of the region with high thermal stress of the SOFC stack, and changing flow direction of the air obviously drops down the thermal stress without affecting the power generation of the SOFC stack.     

Understanding thermal and redox cycling behaviors of flat-tube solid oxide fuel cells

The performance stability of solid oxide fuel cells (SOFCs) under thermal and redox cycles is vital for large-scale applications. In this work, we investigated the effects of thermal and redox cycles on cell performances of flat-tube Ni/yttria-stabilized zirconia (Ni/YSZ) anode-supported SOFCs. Cell performance was considerably affected by the duration of oxidation during redox cycles and the heating rate during the thermal cycles. The cell tolerated 20 short-term redox cycles (5 min oxidation) without significant performance degradation. Besides, the cell exhibited superior stability during 8 thermal cycles with a slow heating rate (4 °C min⁻¹) to that with a fast heating rate (8 °C min⁻¹). These results reflected that the thick anode support (2.7 mm) offered strong resistance to the shocks caused by redox and thermal cycling. Moreover, the morphological changes of the Ni phase during the redox and thermal cycling were investigated using Ni-film anode cells. Agglomeration of Ni particles and dissociation between the Ni film and the YSZ substrate were confirmed after 5 redox cycles, whereas no significant changes in Ni film emerged after 8 thermal cycles.     

A model for oxidation-induced stress analysis of Ni-based anode-supported planar solid oxide fuel cell

A critical hurdle in realizing commercially viable anode-supported solid oxide fuel cell (SOFC) is the re-oxidation of cermet anode during the cell abnormal operation. In this paper, the analysis of energy dispersive X-ray spectroscopy on a partially oxidized half-cell demonstrates a particular inhomogeneous oxidation mechanism that a portion of anode near the air/anode interface is oxidized with a graded NiO content, while the remaining region hold a reduced status. Based on this observation, an analytical oxidation-induced stress model is developed to provide in-depth information about the mechanical behavior of the half-cell suffered from various oxidation. The dependences of the mechanical performance of half-cell on the NiO distribution and thickness of oxidation-graded zone are revealed. The results show that an increase in oxidation-graded zone elevates the stress level of electrolyte, but decreases the curvature under the same global degree of oxidation (DoO). In addition, the influence of thickness of oxidation-graded zone on the electrolyte failure probability is also investigated. According to these results, we conclude that the thickness of oxidation-graded zone should be as thin as possible in order to delay the electrolyte cracking.     

Residual stress and plastic strain analysis in the brazed joint of bonded compliant seal design in planar solid oxide fuel cell

This paper uses finite element method (FEM) to predict the residual stress and plastic strain in the brazed joint of sealing foil-to-window frame in bonded compliant seal (BCS) design in a planar solid oxide fuel cell (PSOFC). The effects of window frame material type, sealing foil thickness, filler metal thickness and window frame thickness on residual stress and plastic strain are discussed. Large residual stress is generated in the joint, and the stress and strain are concentrated around the fillet. It is proved that the BCS design can mitigate and trap some residual stress by plastic deformation within the sealing foil. The residual stress and the ability of trapping stress of sealing foil are affected by window frame material and structure thickness. Based on the comprehensive considerations of the impact of residual stress and plastic strain, Alloy 625 as a window frame material is found to be better than Haynes 214, Hastelloy X and SUS 316L. The optimum thickness of sealing foil and filler metal BNi2 are found to be 150 μm and 75 μm, respectively. The residual stress and plastic strain are increased with the increase of window frame thickness.     

Effect of BaO addition on magnesium lanthanum alumino borosilicate-based glass-ceramic sealant for anode-supported solid oxide fuel cell

We report the effect of BaO addition on thermal, crystallization, electrical and mechanical behavior of the magnesium lanthanum alumino borosilicate glass-ceramics. The glass forming region has been found to be quite narrow with respect to BaO content. Casting and annealing of completely transparent and amorphous glasses within this system has been possible only at an optimum BaO content of 25 mol% without any La₂O₃ and Al₂O₃. On further optimization of the developed glasses in terms of different borosilicate ratios, one of the developed compositions having MgO and BaO content of 22 and 25 mol% respectively, with a glass former ratio of 3 (SiO₂:B₂O₃) has been found to be quite promising in terms of its mechanical property, excellent joining, minimum chemical interaction and lowest leak-rate with the metallic interconnect such as Crofer22APU, and thus fulfills the major requirements for SOFC sealing application.     

A braze system for sealing metal-supported solid oxide fuel cells

A composite braze, consisting of Ag–Cu–Ti braze alloy and particulate Al₂TiO₅ filler, was used to produce metal/braze/metal and metal/braze/YSZ joints to seal and interconnect metal-supported SOFC membranes. The addition of Al₂TiO₅ to the braze alloy lowers the coefficient of thermal expansion (CTE) of the resulting composite sufficiently so as to produce joints in which the YSZ does not crack due to CTE mismatch. Optimization of the reactive element (Ti) loading is discussed with regard to its effect on electrolyte conductivity. Electronic conductivity, sealing ability, and strength of the braze alloy remain acceptable after complete oxidation at 700 °C in air. Joints were also tested in air/fuel dual atmosphere environment at 700 °C. After this exposure, the joint remains hermetically sealed, and no significant degradation of the joint was observed. This is in contrast to a free-standing foil of the braze alloy, which failed upon dual atmosphere exposure. The composite braze material was used to seal a metal-supported thin-film YSZ cell. The sealed cell was thermally cycled 30 times very rapidly without any deterioration of the open circuit voltage.     

Effect of interface morphology on the residual stress distribution in solid oxide fuel cell

Solid oxide fuel cell directly and efficiently converts chemical energy to electrical energy. However, the necessity for high operating temperatures can result in mechanical failure. Fuel cell is a multilayer system and its stress distribution is greatly affected by the interface morphology. In this work, cosine interfaces with different amplitudes are used to approximate the fluctuation of actual interface. The effects of interface morphology on stress state, energy release rate of crack and creep behavior have been investigated. The results show that if the interface is planar, the residual normal stress component is zero on the interface, while the nonplanarity of interface can cause the normal stress S_n and shear stress S_t on the interface. When the amplitude is relatively small, the max values of S_n and S_t on the interfaces vary linearly with increasing amplitudes in both anode and cathode. Above a certain value, nonlinearity of the interface becomes important. Max tensile S_n always occurs at the peak of convex interface, but the position of max compressive S_n varies. Max shear stress is prone to occur at 1/4 of the wavelength at small amplitude and moves towards 1/2 of the wavelength when the amplitude increases. Fracture mechanics analysis shows that the surface crack possibly penetrates into the anode function layer and then is constrained by the stiff electrolyte. On the other hand, the horizontal crack likely penetrates into the electrolyte layer when the interface is not planar. Creep analysis shows that 11 800 hours of continuous operation at high temperature cannot remove stress undulation introduced by nor-planar interface but can make max value of Sn and St decrease around 30%.     

Long-term thermal cycling of Phlogopite mica-based compressive seals for solid oxide fuel cells

Planar solid oxide fuel cells (SOFCs) require sealants to function properly in harsh environments at elevated temperatures. The SOFC stacks are expected to experience multiple thermal cycles (perhaps thousands of cycles for some applications) during their lifetime service in stationary or transportation applications. As a result, thermal cycle stability is considered a top priority for SOFC sealant development. In previous work, we have developed a hybrid mica-based compressive seal with very low leak rates of 2–4 × 10⁻² to 10⁻³ sccm cm⁻¹ at 800 °C, and showed stable leak rates over limited thermal cycles. In this paper we present results of long-term thermal cycle testing (>1000 thermal cycles) of Phlogopite mica-based compressive seals. Open-circuit voltage (OCV) was measured on a 2 in. × 2 in. 8-YSZ plate with the hybrid Phlogopite mica seals during thermal cycling in a dual environment (2.75% H₂/Ar versus air). During two long-term cycling tests, the measured OCVs were found to be consistent with the calculated Nernst voltages. The hybrid mica seal showed excellent thermal cycle stability over 1000 thermal cycles and can be considered a strong candidate for SOFC applications.