# Observation and modeling of thermal stresses in cells and cell stacks.pdf

Observation and modeling of thermal stresses in cells and cell stacks H. Yakabe Tokyo Gas Co., Ltd., Tokyo, Japan 1 INTRODUCTION There are mainly four types of stresses in cells (see also Mechanical stability, Volume 5). The first one is the resid- ual stress in the cell induced by a mismatch of thermal expansion behaviors among the cell components. A rigid connection of each cell component with different ther- mal expansion coefficients (TECs) causes residual stresses. The electrolyte and electrodes are fabricated and connected at a high temperature (see MEA/cell preparation meth- ods: Europe/USA, Volume 4). If the thermal expansion behaviors are not identical among the components, residual stresses occur in the cell at room temperature. For stacks, similar residual stresses occur by a mismatch of thermal expansion behaviors among cells and other stack compo- nents. The second one is the thermally induced stress. In start-up or shutdown procedures of solid oxide fuel cells (SOFCs), a temperature distribution is developed inside cells or stacks. Under a power generation, a temperature distribution also occurs in the cells or cell stacks (see Internal reforming, Volume 4). This temperature distribution causes thermal stresses inside the cells or cell stacks. The third one is a physically or chemically induced stress. Occasionally, physical properties, in particular, the molar volume of the cell components, may change, causing stresses in the cell components. For example, it is known that the structure of yttria stabilized zirconia (3YSZ), which is used as the electrolyte, undergoes transformations between the monoclinic and the orthorhombic one at several hundreds of degrees Celsius. [1] Although Ni in the anode is in a metallic state under a reducing fuel gas, it is oxidized by the air that leaks to the fuel side (see Methane reforming kinetics, carbon deposition, and redox durability of Ni/8 yttria-stabilized zirconia (YSZ) anodes, Volume 6). It is known that the structure of doped-LaCrO 3 , which is used as an interconnect, changes between the orthorhombic and the rhombohedral one at a certain temperature. [2] In addition, its lattice constant changes with regard to the ambient partial pressure of oxygen. [3] These changes in the physical state due to the ambient conditions induce stresses inside the cell components. The fourth one is the stress from mechanical loads on cell components (see System design, Volume 4). In the case of cell stacks of planar cells, in particular, many cells are piled vertically to obtain a high voltage and a load is sometimes placed on top of the stack. This load induces a stress inside the cell stacks. These four stresses affect the mechanical reliability of SOFCs that sometimes results in the destruction of cells or stacks. Therefore, these stresses must be reduced as much as possible (see Mechanical stability, Volume 5). 2 NUMERICAL CALCULATIONS FOR THE STRESSES IN CELLS AND CELL STACKS Stress calculations are carried out by the finite ele- ment method. Here, the commercial finite method code “ABAQUS” (Hibbit, Karlsson, and Sorensen, Inc.) is used. Handbook of Fuel Cells – Fundamentals, Technology and Applications. Edited by Wolf Vielstich, Hubert A. Gasteiger, Arnold Lamm and Harumi Yokokawa. ? 2010 John Wiley thus, three-dimensional meshes are used for the stress calculation. Since the division of a model space into individual tetrahedrons sometimes faces difficulties of visu- alization and could easily lead to errors in numbering, eight-cornered brick elements are convenient to use. The element types used for the stress simulation here are three- dimensional solid elements of an eight-node linear brick. In the coupled calculation between the thermofluid calculation and the stress calculation, the same mesh model is used. To calculate the thermal expansion behavior of the model, the TEC is necessary as the calculating parameter. If the TEC is temperature dependent, the temperature dependence must be considered in the calculation. Here, the temperature data at the nodes is transferred from the STAR-CD to the ABAQUS. 3 MEASURING THE STRESS IN THE CELL AND CELL STACK 3.1 Principle of the stress measurements To evaluate the reliability of cells, it is necessary to measure the practical stresses in the cells. Here, the measurements of the stresses in cells are presented. The X-ray diffraction method is used to measure the residual stresses in the cells or cell stacks and a synchrotron radiation is used as an excellent X-ray source; this enables to evaluate stresses in cells with high accuracy. The principle of the X-ray stress measurement is as follows. When a sample is sustaining stresses, the interplanar spacing d between the specified diffracting planes of a crystallite in a microscopic grain can be expressed as d = 1 + ν E d 0 σsin 2 ψ + braceleftBig 1 ? ν E (σ 1 + σ 2 ) bracerightBig d 0 (1) where d 0 is the interplanar spacing under a stress-free con- dition, ψ is the tilting angle of the specified diffracting plane in the crystallite from the normal to the sample surface, E is the Young’s modulus, ν is the Poisson’s ratio, σ is the stress in the grain, and σ 1 and σ 2 are the principal stresses in direc- tions 1 and 2. Modifying equation (1), σ is expressed by σ = E 1 + ν × 1 d 0 × ?d ? sin 2 ψ (2) This equation indicates that the stress σ is proportional to the slope of the d–sin 2 ψ diagram. Thus, by measur- ing the interplanar spacing d by tilting the incident beam angle and making the d–sin 2 ψ diagram, the residual stress can be estimated. To derive equation (2), it is assumed that the sample is isotropic and elastic. In addition, there is no stress perpendicular to the sample surface because only the stresses near the sample surface are measured using the X-ray diffraction method. 3.2 Method for the stress measurements In the stress measurement, the isoinclination method and the fixed ψ 0 method are employed. The configurations for the diffraction measurements and stress analyses is indicated in Figure 1. In Figure 1, ψ 0 is the angle between the nor- mal to the sample surface and the incident beam and 2ψ is the scattering angle of the specified diffracting plane in the crystallite. In the fixed ψ 0 method, 2θ scan is carried out at afixedψ 0 and +ψ and ?ψ are determined as follows (for +ψ, the sample normal tilts to the diffraction beam and, for ?ψ, the sample normal tilts to the incident beam). To elimi- nate the effect of an orientation of the crystalline or an irreg- ularity of the grain on the stress measurements, the sample is oscillated by ±1 ? around the fixed ψ 0 with a sufficiently high speed as compared with the scanning speed of 2θ. A synchrotron radiation is used as an X-ray source. The synchrotron radiation is an ultrabright, highly directional, and collimated light. In addition, a wide spectrum of wave- lengths ranging from infrared to X rays can be used. There Incident beam Diffracted beam Plane normal Surface normal 2θ ψ 0 ?ψ hkl plane +ψ (a) (b) Figure 1. Schematic diagram of the X-ray stress measurement, isoinclination method, and fixed ψ 0 method. The tilt of the sample is (a) +ψ and (b) ?ψ. [Reprinted from H. Yakabe, Y. Baba, T. Sakurai and Y. Yoshitaka, Journal of Power Sources, 135, (2004), with permission from Elsevier.] Observation and modeling of thermal stresses in cells and cell stacks 3 are many advantages of using the synchrotron radiation as the beam source in the residual stress measurements. [4] The stress measurements presented in this section are performed at the BL09XU or BL19B2 lines at SPring8. For the stress measurements, an X-ray energy of 8.05keV (λ = 0.1541nm), which corresponds to the Cu K α line, is selected to compare the measured results with those measured using a commercial X-ray diffraction apparatus. The attenuation length of the X ray of λ = 0.1541nm in ZrO 2 at a fixed angle of 90 ? is calculated to be around 10μm. The typical thickness of the electrolyte is around 30μm, which is almost triple that of the attenuation length of the X ray in ZrO 2 , and thus the contribution of the anode part to the diffraction beam is negligible. The beam size at the sample point is adjusted to 1mm (H) × 1mm (V) using W slits. The diffraction of the (531) plane of 8YSZ is selected for the stress measurements. 3.3 Specimens for the stress measurements As an example of residual stresses in cells, stresses in an anode-supported cell are presented here. Anode- supported cells are suitable for operations at lower temper- atures because of the substantially lower ohmic resistance of the electrolyte (see MEA/cell preparation methods: Japan/Asia, Volume 4). By lowering the operating temper- ature of SOFCs below 800 ? C, conventional metal alloys can be used in interconnectors or other components; this can result in high mechanical reliability of a cell stack and lower manufacturing costs. Thus, anode-supported SOFCs have been receiving considerable interest. [5–9] The anode- supported cells fabricated by cofiring both the electrolyte and anode at 1500 ? C [10] are used for the stress mea- surements. The 8YSZ electrolyte is first screen printed or dip coated on the green NiO/YSZ substrate. To avoid generations of cracks and micropores in the electrolyte, the particle sizes of the raw powders for the NiO/YSZ substrate and YSZ electrolyte are selected carefully. After cofiring, the anode-supported cell is cooled down to room tempera- ture. A typical cell size is 50mm × 50mm × 2mm, and the thickness of the electrolyte is about 20–40μm(thecell image is shown in Figure 2). As compared to the anode sub- strate, the electrolyte is sufficiently thin for the assumption that the direction of the main stress in the electrolyte is par- allel to the film surface and thus equation (2) is applicable. To investigate the stress distribution in the anode-supported cell, two 10mm × 10mm pieces are cut from the center and corner of the sample. This is because of the restriction on the size of the sample stage. In this measurement, the resid- ual stresses for seven different samples are measured. The characteristics of the samples are listed in Table 1. Sam- ples 1 and 2 are cut from an as-grown cell. Usually, the as-grown cell warps toward the electrolyte side. If the cells warp, it is difficult to contact each cell properly, and the electric connection between the cells becomes poor. Hence, the warp is reformed and the cell is flattened using a dis- tributed load on the electrolyte at 1400 ? C. Samples 3 and 4 are cut from the flattened cell. Before a cell operation, the anode of the cell has to be exposed to a reducing atmo- sphere to reduce NiO to Ni in the anode. Samples 5 and 6 are the reduced samples. The lattice constant of Ni is smaller than that of NiO by 20%. As a result, the reduction of the anode causes shrinkage of the anode and may change the residual stress in the electrolyte. For samples 1–6, the electrolyte is screen printed on the surface of the anode sub- strate first and cofired. Only for sample 7, the electrolyte is dip coated on the surface of the anode substrate. 4 RESULTS FOR THE NUMERICAL CALCULATIONS ON THE STRESSES 4.1 Simulated residual stresses in the single cell After modeling the geometry of the cell of the elec- trolyte/anode bilayer, the residual thermal stresses were calculated at room temperature. The cell model was divided into 10 by 10 meshes in the in-plane direction and into 20 Cathode (LaSrCoFeO 3 ) Electrolyte Anode (a) (b) Figure 2. Photograph of the anode-supported cell (a) and its structure (b). [Reprinted from H. Yakabe, Y. Baba, T. Sakurai and Y. Yoshitaka, Journal of Power Sources, 135, (2004), with permission from Elsevier.] 4 Advanced diagnostics, models, and design Table 1. Properties of samples used for stress measurement. a ID Electrolyte material Manufacturing process Post treatment Anode state Position 1 8YSZ Screen print As-sintered Oxidized Center 2 8YSZ Screen print As-sintered Oxidized Corner 3 8YSZ Screen print Flattened Oxidized Center 4 8YSZ Screen print Flattened Oxidized Corner 5 8YSZ Screen print Flattened Reduced Center 6 8YSZ Screen print Flattened Reduced Corner 7 8YSZ Dip coat Flattened Oxidized Corner a Reprinted from H. Yakabe, Y. Baba, T. Sakurai and Y. Yoshitaka, Jour- nal of Power Sources, 135, (2004), with permission from Elsevier. Table 2. Mechanical properties and cell sizes used for the stress simulation. Young’s modulus (GPa) Poisson’s ratio TEC (K ?1 ) Thickness (mm) Electrolyte 206 a 0.33 a 10.56 × 10 ?6b 40 × 40 × 0.03 Anode 96 c 0.3 d 12.22 × 10 ?6b 40 × 40 × 2 a Reprinted from H. Yakabe, Y. Baba, T. Sakurai and Y. Yoshitaka, Jour- nal of Power Sources, 135, (2004), with permission from Elsevier. b Assumed from the temperature dependence of TEC below 1000 ? C. c From four-point bending tests at room temperature. d Assumed value. [12] submeshes in the out-plane direction. In the calculation, it was assumed that both the electrolyte and the anode con- strain each other below 1400 ? C and the origin of residual stresses in the cell is only a mismatch of TEC between the electrolyte and the anode. The model geometry was 50mm × 50mm × 2mm. The mechanical properties and cell sizes used for the stress calculation are listed in Table 2. Figure 3 shows the simulated stress distribution in the electrolyte for the anode-supported cell at room tempera- ture. Except at the edge, stresses have almost homogeneous values of 640–700MPa over the whole electrolyte plane. This is not clear in the figure; however, it is found that the ?6.60e+02 ?6.60e+02 ?6.60e+02 ?6.63e+02 ?6.67e+02 ?6.70e+02 ?6.73e+02 ?6.77e+02 ?6.80e+02 Maximum =?6.32e+02 Minimum =?7.06e+02 Principal stress (MPa) Figure 5. Simulated residual stress at the electrolyte of the anode-supported cell stack at room temperature. Negative stress means that the stress is compressive. [Reprinted from H. Yakabe, Y. Baba, T. Sakurai, I. Hirosawa and Y. Yoda, Journal of Power Sources, 131, (2004), with permission from Elsevier.] 160 140 120 100 80 60 40 20 160140120100806040 (531) (620) (311) (222) (400) (331) (420) (500) (333) (440) (600) (533) (220) Intensity (arb unit) 2θ (°) Figure 6. X-ray diffraction pattern for the electrolyte of the anode-supported cell. The diffraction peaks indicated by arrows are used for stress measurements. [Reprinted from H. Yakabe, Y. Baba, T. Sakurai and Y. Yoshitaka, Journal of Power Sources, 135, (2004), with permission from Elsevier.] 400 × 10 3 300 200 100 Intensity (arb unit) 125.4125.2125.0124.8124.6124.4124.2124.0 2θ (°) sin 2 ψ = 0.6 sin 2 ψ = 0.5 sin 2 ψ = 0.4 sin 2 ψ = 0.3 sin 2 ψ = 0.2 sin 2 ψ = 0.1 sin 2 ψ = 0 Figure 7. Shift of the diffraction peak of YSZ (531) plane with ψ. [Reprinted from H. Yakabe, Y. Baba, T. Sakurai and Y. Yoshitaka, Journal of Power Sources, 135, (2004), with per- mission from Elsevier.] Figure 7 shows the change in the diffraction peak of YSZ (531) plane with a change in ψ measure