The purpose. Determination of radii ranges for cylindrical and convex (semi-spheroidal) parts of the solid oxide fuel cell (SOFC) semi-spheroidal shape anode based on stress and strain parameters calculated; comparison of 3D graphs of stress/strain distribution in anodes of proposed and spheroidal shapes; substantiation of the semi-spheroidal anode potential to withstand deformation and stress gradient under operational conditions.
The research method. The object of research is a solid oxide fuel cell anode of a semi-spheroidal shape loaded with a fixing pressure along the closed-loop fixing and with an external gas pressure applied to the anode working surface. Stress and strain distributions in the anode were calculated by finite element analysis using software for calculating three-dimensional tasks Mechanical Desktop 6 Power Pack. Three-dimensional (3D) dependences of stress/strain distribution in anodes of proposed and spheroidal shapes at a variety of R / Rc ratios were plotted. Based on these curves, 3D surfaces of stress distribution along the axis and closed-loop fixing of semi-spheroidal shape anodes were constructed.
Results. Three-dimensional curves of the graphic intersections of the surfaces of stress distribution along the axis and closed-loop fixing of semi-spheroidal shape anodes, with their projections on three coordinate planes, were plotted. The curves display the values of balanced stresses depending on geometric parameters. Domains of these curves were also defined.
The scientific novelty. The proposed method of building 3D surfaces of stress/strain distribution in anodes depending on their geometric parameters shows for the first time that there exists an area of geometric parameters that allows the appropriate stress level to be reached ensuing safe long-term operation of the semi-spheroidal shape anode. The domain of this area was graphically defined. Based on the plotted isolines showing levels of strain in anodes with the 0.5 mm, 1 mm, and 1.5 mm thick cylindrical parts and a variety of spheroid to cylinder radii ratios, an advantage of a semi-spheroidal shape anode over spheroidal one was substantiated.
The practical value. The obtained calculation results and their 3D graphical interpretation can be used in the study of the stress state and, respectively, to evaluate the strength and stiffness of the anode supported SOFCs of various shapes.
 R. Knibbe, et al., “Durability of solid oxide cells”, Green, vol. 52, issue 2, pp. 5747–5756, Jan. 2011. https://doi.org/10.1515/green.2011.015
 A. Faes, et al., “A review of RedOx cycling of solid oxide fuel cells anode”, Membranes, vol. 2, issue 3, pp. 585–664, Aug. 2012. https://doi.org/10.3390/membranes2030585
 Ye. Brodnikovskyi, et al., “Influence of reduction conditions of NiO on its mechanical and electrical properties”, Journal of Electrochemical Science and Engineering, vol. 6, issue 1, pp. 113–121, Jan. 2016. https://doi.org/10.5599/jese.220
 Y. Wang, et al., “Effects of powder sizes and reduction parameters on the strength of Ni–YSZ anodes”, Solid State Ionics, vol. 177, issues 17–18, pp. 1517–1527, Oct. 2006. https://doi.org/10.1016/j.ssi.2006.07.010
 M. Ettler, et al., “Durability of Ni anodes during reoxidation cycles”, Journal of Power Sources, vol. 195, issue 17, pp. 5452–5467, Sept. 2010. https://doi.org/10.1016/j.jpowsour.2010.03.049
 A. Atkinson, et al., “Advanced anodes for high-temperature fuel cells”, Nature Materials, vol. 3, issue 1, pp. 17–27, Jun. 2004.
 B. D. Vasyliv, “Improvement of the electrical conductivity of the material of anode in a fuel cell by the cyclic redox thermal treatment”, Mater. Sci., vol. 46, issue 2, pp. 260–264, Nov. 2010. https://doi.org/10.1007/s11003-010-9282-4
 V. Ya. Podhurs’ka, et al., “Structural transformations in the NiO-containing anode of ceramic fuel cells in the course of its reduction and oxidation”, Mater. Sci., vol. 49, issue 6, pp. 805–811, May 2014. https://doi.org/10.1007/s11003-014-9677-8
 V. Podhurska, B. Vasyliv, “Influence of NiO reduction on microstructure and properties of porous Ni–ZrO2 substrate”, in Proc. Int. Conf. Oxide Materials for Electronic Engineering (ОМЕE-2012), Lviv, Ukraine, September 3–7, 2012, pp. 293–294. https://doi.org/10.1109/OMEE.2012.6464761
 B. Vasyliv, et al., “Preconditioning of the YSZ–NiO fuel cell anode in hydrogenous atmospheres containing water vapor”, Nanoscale Research Letters, vol. 12, issue 1, article number 265, Apr. 2017. https://doi.org/10.1186/s11671-017-2038-4
 A. Wood, D. Waldbillig, “Preconditioning treatment to enhance redox tolerance of solid oxide fuel cells”, U.S. Patent 8 029 946 B2, October 04, 2011.
 B. D. Vasyliv, et al., “Sposib obrobky NiO-vmisnykh anodiv tverdooksydnoi palyvnoi komirky” [“A method of treatment of NiO-containing anodes for a solid oxide fuel cell”], UA Patent 78992, April 10, 2013. [in Ukrainian].
 J. Huiming, S. Maosong, “Study of integrity of NiO oxide film by acoustic emission method”, in Proc. 5th Int. Conf. Natural Computation (ICNC-2009), Tianjin, China, August 14–16, 2009, vol. 6, pp. 252–256. https://doi.org/10.1109/ICNC.2009.133
 V. Lawlor, et al., “Review of the micro-tubular solid oxide fuel cell: Part I. Stack design issues and research activities”, Journal of Power Sources, vol. 193, issue 2, pp. 387–399, March 2009.
 R.-H. Song, D.-R. Shin, J.-H. Kim, “Anode-supported flat-tubular solid oxide fuel cell stack and fabrication method of the same”, U.S. Patent 7285347 B2, October 23, 2007.
 Y. Bai, et al., “Dip coating technique in fabrication of cone-shaped anode-supported solid oxide fuel cells”, Journal of Alloys and Compounds, vol. 480, issue 2, pp. 554–557, Sept. 2009. https://doi.org/10.1016/j.jallcom.2009.01.089
 Y. Zhang, et al., “Redox cycling of Ni‑YSZ anode investigated by TRP technique”, Solid State Ionics, vol. 176, issues 29–30, pp. 2193–2199, Nov. 2005. https://doi.org/10.1016/j.ssi.2005.06.016
 M. Radovic, E. Lara-Curzio, “Mechanical properties of tape cast nickel-based anode materials for solid oxide fuel cells before and after reduction in hydrogen”, Acta Materialia, vol. 52, issue 20, pp. 5747-5756, Jul. 2004. https://doi.org/10.1016/j.actamat.2004.08.023
 T. Miyazawa, “Flat-plate solid oxide fuel cell”, U.S. Patent 20 110 091 785 A1, April 21, 2011.
 B. D. Vasyliv, “A procedure for the investigation of mechanical and physical properties of ceramics under the conditions of biaxial bending of a disk specimen according to the ring–ring scheme”, Mater. Sci., vol. 45, issue 4, pp. 571–575, Jul. 2009. https://doi.org/10.1007/s11003-010-9215-2
 B. Sun, et al., “Effect of thermal cycling on residual stress and curvature of anode-supported SOFCs”, Fuel Cells, vol. 6, pp. 805–813, Jul. 2009. https://doi.org/10.1002/fuce.200800133
 O. P. Ostash, B. D. Vasyliv, V. Ya. Podhurska, “Sposib vyhotovlennia anoda-pidkladky dlia palyvnoi komirky” [“A method of fabrication of an anode substrate for a fuel cell”], UA Patent 109256, August 25, 2016. [in Ukrainian].
 I. Kuzio, et al., “Substantiation of the shape of a solid oxide fuel cell anode using the stress-strain and shape-dependent crack deceleration approaches”, Ukrainian Journal of Mechanical Engineering and Materials Science, vol. 5, no. 1, pp. 29–38, 2019. https://doi.org/10.23939/ujmems2019.01.029
 B. Vasyliv, Crack initiation and retardation in ceramics. Techniques and applications. Riga, Latvia: LAMBERT Academic Publishing, 2019.