Fracture of Porous Ceramics: Application to the Mechanical Degradation of Solid Oxide Cell During Redox Cycling

Abstract

Solid Oxide Cell (SOC) is a high-temperature electrochemical device that can be operated in both fuel and electrolysis modes. It is constituted of a dense electrolyte in Yttria Stabilized Zirconia (YSZ) sandwiched between two porous electrodes. The hydrogen electrode is classically made of a cermet composed of Nickel and YSZ (Ni-YSZ). Because of system failures in operation (e.g. a fuel shortage or air re-introduction during the system shutdown), the Nickel is liable to be re-oxidized inducing its volume expansion. The Ni swelling within the cermet leads to a mechanical damage in the YSZ backbone [1] resulting in a degradation of the overall cell performances [2]. Therefore, it is still required to enhance the hydrogen electrode robustness for a higher redox tolerance. For this purpose, it is essential to predict accurately the formation and distribution of micro-cracks in the YSZ network during the re-oxidation. Nevertheless, the modeling of the initiation and propagation of cracks in complex microstructures of porous ceramics is still a subject of investigation. Moreover, there is also a lack of data on fracture properties for the porous YSZ material. In this frame, the present study was focused to propose a relevant model for the initiation and the growth of cracks in porous ceramics in order to simulate the fracture induced by Ni re-oxidation. For this purpose, a coupled experimental and modeling approach has been adopted (Fig.1). For the experimental part, the mechanical characterizations have been performed on thin YSZ membranes of different porosities representative of SOC microstructures. The compression test has been chosen as it generates a quasi-uniform stress field in the tested samples. To this end, micro-pillars of few tens of micro-meters in section have been milled in the YSZ membrane using a xenon plasma focused ion beam. For each investigated porosity, the compressive fracture strength has been measured on several pillars. The tested samples have been carefully characterized to assess the damage in the microstructure. As expected, the compressive strength was found to decrease with increasing the porosity. Moreover, a transition has been observed from a brittle behaviour at low porosity towards a local damage at high porosity [3]. All these experimental data have been used to validate a numerical tool to simulate the fracture in porous microstructure. In this study, a model based on the Phase Field Method (PFM) has been developed. In this approach, the crack is modeled implicitly through a smooth scalar damage variable and its width is controlled by a length scale parameter. Therefore, this method is well adapted to solve the fracture problem in complex and heterogeneous materials since it is mesh independent. The implemented model corresponds to the one proposed by C. Miehe et al. [4] who proposed a staggered scheme for the numerical resolution. A special attention has been paid in this work to evaluate the model capability to accurately predict the crack initiation for porous electrode material. For this purpose, the results of the PFM simulations have been compared to the mixed criterion proposed by D. Leguillon [5]. The study has been conducted on notched samples with different opening angles and for macro-cracks blunted by different cavity sizes. It has been highlighted that the two approaches provide consistent predictions for the crack initiation. Moreover, it has been checked that the PFM model is able to reproduce accurately the expected decrease of the fracture toughness when increasing the material porosity. Once these studies completed, the PFM model has been used to simulate the micro-compression test using a multiscale approach. It has been found that the model is able to reproduce correctly the decrease of the measured compressive fracture strength with the sample porosity. Moreover, the distribution of cracks in the simulations has enabled analysing the transition from a brittle to a local damage detected during the experiments. The validated model has been applied to simulate the fracture induced by the Ni re-oxidation. The repartition and density of micro-cracks in the YSZ backbone has been computed during the Ni reoxidation and the results have been confronted with an available tomographic data set. Finally, the impact on the cermet redox tolerance of the Yttrium content in YSZ has been discussed thanks to the modelling. [1] Faes, A. et al. J. Power Sources 193, 55–64. [2] Laurencin, J. et al. J. Power Sources 192, 344–352. [3] Meille, S. Et al . J. Eur. Ceram. Soc. 32, 3959–3967. [4] Miehe, C. et al. Comput. Methods Appl. Mech. Eng. 199, 2765–2778. [5] Leguillon, D. J. Mech. – A/Solids 21, 61–72. Figure 1