Comparison of Residual Stress Measurement Methods in Solid Oxide Fuel Cell
Authors: Oshima Kento , Komaya Takumi , Yashiro Keiji , Iguchi Fumitada , Han Minfang , Wang Yige , Kawada Tatsuya 
Published: July 2021

SOFCs need to be able to operate for long periods of time without significant degradation in performance, and mechanical reliability and durability are problems that need to be addressed.
Since SOFC operate at high temperatures and in oxidizing and reducing atmospheres, it is difficult to measure residual stress in-situ under actual operating conditions. Therefore, evaluation methods during operation have not been fully developed.
Current methods for measuring residual stress in SOFC include curvature method, X-ray stress measurement method, and Raman scattering spectroscopy.
In the curvature method, the stress is obtained by combining curvature, anode substrate thickness, and elastic modulus. Therefore, it is not suitable for residual stress measurement during reduction and re-oxidation of anodes, where physical properties such as elastic modulus change with time.
In the X-ray stress measurement method, the change in lattice strain is measured, and the stress is obtained by multiplying the strain by an elastic constant. Typical methods of X-ray stress measurement are sin2ψ method and cosα method. The characteristics of the sin2ψ method are as follows;
(1)By using several measuring points to determine the stress value, the variation of the measured value can be suppressed, resulting in high measurement accuracy. Furthermore, the reliability limit of the measured value can be quickly evaluated from the linearity.
(2)A goniometer mechanism is used to measure the diffraction profile, which requires a large device.
(3)Measurement time is long because several points are measured by moving the angle of incidence.
Thus, although the sin2ψ method has high measurement accuracy, it is not very suitable for in-situ measurements.
The method devised to solve these problems is cosα method. The characteristics of the cosα method are as follows;
(1) Since it is single-incidence, the optical system is simple and does not require goniometric scanning, making it possible to reduce the size and weight of the measurement system. It is also possible to measure in a short time.
(2) From the slope of the cosα and sinα diagrams, vertical stress and shear stress can be measured simultaneously. In addition, the reliability of the stress values can be evaluated from the linearity of the diagram.
(3) In the case of coarse grains or strongly aggregated structure, only continuous rings can be obtained, or the strength may be significantly non-uniform, making stress measurement difficult.
It has been demonstrated that the measurement accuracy of the cosα method for vertical stress is comparable to that of the sin2ψ method, and moreover, it is suitable for in-situ residual stress measurement because of its rapidity and simplicity.
In Raman scattering spectroscopy, the change in lattice volume, i.e., the change in stress conditions, can be obtained by measuring the Raman shift. The characteristics of the Raman scattering spectroscopy are as follows;
(1) Since the measurement can be performed under atmospheric pressure and through glass, it is suitable for in-situ measurement in the SOFC operating environment where atmosphere control is usual.
(2)High spatial resolution (up to ~1µm resolution is possible with micro-Raman spectrometers) enables measurement of small areas.
(3) Since Raman peaks with sufficiently strong intensity need to appear in the Raman spectrum, there is a limit to the number of materials that can be measured. Among the SOFC constituent materials, ceria-based materials are the most suitable for observation.
As mentioned in (3), Raman scattering spectroscopy is used to calculate the stress value of the interlayer (ceria-based material). Therefore, the stress in the electrolyte is calculated by assuming that the electrolyte and the interlayer are rigid bodies under the operating conditions.
In this study, we performed in-situ measurement of residual stress in the anode-supported cell using sin2ψ method, cosα method and Raman scattering spectroscopy. And then we compared the results and summarized the advantages and disadvantages of each method. We used a commercially available general cell and a cell fabricated at Tsinghua University. In order to reproduce the actual operating conditions, the measurements were carried out under elevated temperature and under reduced temperature. Since the anode may be re-oxidized when the fuel runs out or during an emergency shutdown, the measurements were also conducted under re-oxidation. Furthermore, we proposed suitable conditions for each measurement method and conducted experiments under those conditions.