Damage Modeling of Solid Oxide Fuel Cells Accounting for Redox Effects

Abstract

This paper applies a multiscale mechanistic damage model developed for porous brittle ceramics and implemented in finite element analysis (FEA) packages [1] to study progressive damage in solid oxide fuel cells (SOFC) subjected to thermomechanical loading under operating and shutdown states. The damage model captures the micromechanics of stiffness reduction due to material porosity change and microcracking and integrates the as-obtained stiffness reduction law into a continuum damage mechanics (CDM) formulation for the evolution of microcracks up to fracture. An Eshelby-Mori-Tanaka approach (EMTA) [2-3] is first used to model the ceramic containing pores and aligned microcracks regarded as inclusions with negligible stiffness. The stiffness of the actual porous ceramic is obtained from the EMTA solution averaged over all possible microcrack orientations using an orientation averaging method. The evolution of microcracking damage is described by a CDM formulation derived from our previous model [4]. Apart from the operating and shutdown states, additional damage that may occur due to reduction and re-oxidation (redox cycling) of Ni/YSZ anodes is also studied. The reduction of NiO into Ni leads to changes in volume and porosity of the anode layer that consequently change its physical and thermomechanical properties. The volume change or volumetric “swelling” during redox cycling may affect the structural integrity of the anode and may cause fracture of the electrolyte under high tensile stresses leading to operational failure for SOFCs. In the constitutive relations, volumetric swelling is treated in a similar way to thermal expansion using the models developed in Refs [5-6] for fusion energy ceramic materials. However, while thermal expansion vanishes if temperature change tends to zero, swelling is irreversible and significantly contributes to degrade SOFC stacks during redox cycling.This damage model was implemented in the commercial FEA software ABAQUS© and ANSYS© via user subroutines. First, it has been validated through predictions of strength and stress-strain response for the typical SOFC ceramic materials. Figs 1(a) and 1(b) show the predicted stress-strain responses as a function of temperature for dense NiO/YSZ and Ni/YSZ, respectively. These figures also illustrate the predicted responses at 750°C with prescribed initial values of porosity. The damage model predicts significant reductions in strength and elastic modulus with higher initial porosity and higher temperatures, and the predicted trends are in good agreement with the experimental findings [7-8].Next, the damage model was applied to predict the potential for degradation in a generic planar SOFC stack with large active area cells modeled in ANSYS. Stack models with single and multi-cells were simulated in both co-flow and counter-flow configurations. The thermomechanical loads representing the operating and shutdown conditions were simulated. The realistic thermal gradients that occur in an operating stack were imposed in the models by solving the electrochemistry under various operating conditions using the in-house SOFC multiphysics code (SOFC MP-3D) [9-10]. In addition to the operating and shutdown conditions, a constant temperature redox cycle was also simulated to capture overall cell electrode damage due to volumetric swelling of the Ni/YSZ anode in the anode supported cells. The results from single cell stack models showed little damage at operating and shutdown conditions which could be attributed to enough out-of-plane support for the PEN assembly. The results from the multicell stacks (Fig. 2) showed higher damage in counter-flow configuration. Within the stack, the top cells experienced the highest damage and the middle cells experienced the lowest. Overall, no significant damage that may lead to total failure of the cells was observed in the multicell stack models with the operating conditions considered in this study.