Original Article
Thermo-mechanical analysis of 3D manufactured electrodes for solid oxide fuel cells

https://doi.org/10.1016/j.jeurceramsoc.2020.09.004Get rights and content

Highlights

  • Guidelines for the thermo-mechanical stability of ceramic pillars in SOFC electrodes.

  • Pillars increase the stress distribution by ca. 10 % compared to a flat electrode.

  • Thermal stress is dominant while applied external loads have a negligible effect.

  • Inaccuracies like rounded corners, roughness and misalignment can be tolerated.

Abstract

Additive manufacturing has widened the scope for designing more performing microstructures for solid oxide fuel cells (SOFCs). Structural modifications, such as the insertion of ceramic pillars within the electrode, facilitate ion transport and boost the electrochemical performance. However, questions still remain on the related mechanical requirements during operation. This study presents a comprehensive thermal-electrochemical-mechanical model targeted to assess the stress distribution in 3D manufactured electrodes. Simulations show that a dense pillar increases the stress distribution by ca. 10 % compared to a flat electrode benchmark. The stress is generated by the material thermal contraction and intensifies at the pillar-electrolyte junction while external loads have negligible effects. An analysis on manufacturing inaccuracies indicates that sharp edges, surface roughness and tilted pillars intensify the stress; nonetheless, the corresponding stress increase is narrow, suggesting that manufacturing inaccuracies can be easily tolerated. The model points towards robust design criteria for 3D manufactured electrodes.

Introduction

The emergence of solid oxide fuel cells (SOFCs) as an alternative electrochemical power generation system has brought in promising hopes to high‐efficiency energy production. SOFCs can use a variety of fuels and reach up to 60 % energy conversion without any combustion process, thus mitigating air pollution [1]. In addition, the prospect of providing cogenerative energy from the waste heat makes SOFCs an attractive green technology for stationary applications [2]. Conversely, their applicability for transportation and other portable devices remains limited due to both the brittleness of the ceramic materials and the relatively long start-up time [3,4], which can be effectively reduced in micro-SOFCs.

The SOFC operation relies on functional materials, among which a solid, ceramic electrolyte, such as yttria-stabilized zirconia (YSZ), and two porous electrodes, where Ni-YSZ represents the most popular anode [5,6]. These functional materials require proper mechanical strength at high temperatures against imposed stresses and these requirements are nowadays becoming a more and more important issue, especially for the mass production of large cells [7]. A number of previous publications have addressed some relevant experimental and computational issues associated with SOFC thermo-mechanical analysis [[8], [9], [10], [11]]. A comprehensive review is reported by Peksen [12], who summarised the status of numerical thermo-mechanical modelling of SOFCs and discussed issues such as geometrical idealisation, initial and boundary conditions as well as the strong coupling between fluid and solid mechanics. By coupling computational fluid dynamics and finite-element method (FEM) modelling, Peksen [13] analysed the long-term thermo-mechanical behaviour of a SOFC for operation with different fuels (namely, H2 and CH4 at different concentrations) in a furnace environment. In another study [14], the same author reported the optimisation of the heating-up strategies of a SOFC stack in order to limit temperature gradients which may result in differential thermal strain. In order to meet the reliability standards for market implementation, Greco et al. [15] developed a thermo-mechanical model of a SOFC stack aiming at capturing the stresses during the production and assembly of stack components. By investigating the effects of component tolerances on the thermo-mechanical reliability, Greco et al. [16] showed that the distribution of the simulated contact pressure on the active area is found to have different evolution during thermal cycling and operation.

All the previous works focused on the thermo-mechanical analysis of the SOFC stack components, production and assembly considering conventional geometries, that is, with homogeneous electrodes and electrolyte layers deposited one on the top of the others. Nevertheless, in the recent years advanced microstructures for SOFC electrodes have been proposed thanks to the advent of 3D printing and other novel manufacturing approaches [[17], [18], [19], [20], [21]]. 3D printing is an additive manufacturing technique best known for fabricating a wide range of structures and complex geometries by precisely locating and orienting them within the electrode volume [22]. The process is comprised of printing successive layers or, more generally, successive features of materials that are formed on top of each other [17]. This offers the opportunity to create geometric elements with different shapes or sizes embedded within the porous random electrode matrix, such as the insertion of conducting pillars [17,[23], [24], [25], [26]] to enhance gas and charge transport [27]. In addition, additive manufacturing and 3D printing may introduce microstructural reinforcements to the fragile areas with high mechanical stress caused by temperature gradients, ensuring microstructural stability and avoiding damages which might cause irreversible system failure [28].

A few papers have modelled the electrochemical performance of SOFC electrodes with embedded electrolyte pillars, showing that lower polarisation resistance and higher power densities can be attained [24,26,[29], [30], [31]]. However, questions still remain about whether the pillars can resist to the mechanical and thermal stress during operation. In fact, as the temperature gradients build up, the presence of dense pillars combined with the different thermal expansion coefficient of the materials can exacerbate the thermal stress and produce uneven stress distributions, which might produce cracks with related gas leakage that may inflict irreversible damage to the SOFC [1]. Moreover, while typically idealised pillar geometries are considered in electrochemical modelling [26,31], manufacturing tolerances and inaccuracies in pillar fabrication must be taken into account in order to predict where excessive stress might occur and so inform industrial manufacturers on the required accuracy and whether special treatments or structural reinforcements are necessary to avoid cracking and prolonging cell lifetime.

The aim of the current work is to propose a comprehensive thermo-electrochemical-mechanics modelling framework to provide design guidelines for an effective manufacturing of pillars in terms of thermal stress issues. Building upon our previous works on electrochemical modelling of 3D printed electrodes [27,32], which comprised isothermal ion, electron and gas transport, the current study extends the framework by including the energy balance and all the relevant thermo-mechanical phenomena. Such an extended model is used to predict the temperature distribution in an electrode with embedded YSZ pillars and subsequentially used to assess the stress distribution as a consequence of thermal gradients and applied loads. Special attention is paid on how manufacturing accuracy, such as surface roughness, the alignment of the pillar and the roundness of its corners, affect the stress distribution during high-temperature operation. From the systematic analysis of the thermal stress behaviour, specific considerations on the design and fabrication of electrodes with embedded pillars are discussed.

Section snippets

Modelling description

The thermo-electrochemical-mechanics modelling framework consists of the integration of two sub-models: a thermo-electrochemical model, which solves for charge and species conservation coupled to heat generation, and a thermo-mechanical model, which uses as an input the temperature distribution and the mechanical loads in order to solve for the resulting mechanical stress and deformation. Both models are implemented in Comsol Multiphysics v. 5.5 [33] and solved simultaneously. Since the primary

Flat electrode vs pillar

The first question to answer is how the insertion of a YSZ pillar into a porous electrode affects the mechanical behaviour compared to a conventional flat electrode. Fig. 2 compares the simulated distribution of von Mises stress σvM of a conventional flat electrode (on the left) with an electrode featuring an embedded YSZ pillar (on the right).

Simulations show that, in both cases, the electrodes experience a compressive stress as a consequence of the volumetric shrinking from the sintering

Conclusions

The study presented a numerical modelling tool allowing for thermo-electrochemical-mechanical simulations of 3D manufactured SOFC electrodes. This framework is an extension of the electrochemical models previously developed by the authors [27,32] by expanding the thermal and mechanical analysis with the effect of the thermal stress during fuel cell operation, with special focus on the mechanical requirements related to the insertion on a dense YSZ pillar in anode-supported SOFC anodes in order

CRediT authorship contribution statement

Chih-Che Chueh: Conceptualization, Funding acquisition, Investigation. Antonio Bertei: Conceptualization, Methodology, Investigation.

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgements

This study was partially supported by Ministry of Science and Technology (MOST), Taiwan, ROC, under grant no. MOST 108-2218-E-006-028-MY3. Any opinions, findings and conclusions for recommendations given in this article are those of the authors and don’t necessarily reflect the viewpoints of the MOST. Helpful discussions with Prof. Chyanbin Hwu (National Cheng Kung University) are gratefully acknowledged. The authors acknowledge the unknown reviewer whose insightful comments substantially

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