Elsevier

Journal of Power Sources

Volume 351, 31 May 2017, Pages 8-16
Journal of Power Sources

Transient deformational properties of high temperature alloys used in solid oxide fuel cell stacks

https://doi.org/10.1016/j.jpowsour.2017.03.059Get rights and content

Highlights

  • The use of unified viscoplastic theory with an isotropic hardening parameter.

  • A creep model for the transient behavior of alloys in SOFC stack.

  • Experimental procedures to determine the necessary parameters for the model.

  • Validation of the model results against experimental measurements.

Abstract

Stresses and probability of failure during operation of solid oxide fuel cells (SOFCs) is affected by the deformational properties of the different components of the SOFC stack. Though the overall stress relaxes with time during steady state operation, large stresses would normally appear through transients in operation including temporary shut downs. These stresses are highly affected by the transient creep behavior of metallic components in the SOFC stack. This study investigates whether a variation of the so-called Chaboche's unified power law together with isotropic hardening can represent the transient behavior of Crofer 22 APU, a typical iron-chromium alloy used in SOFC stacks. The material parameters for the model are determined by measurements involving relaxation and constant strain rate experiments. The constitutive law is implemented into commercial finite element software using a user-defined material model. This is used to validate the developed constitutive law to experiments with constant strain rate, cyclic and creep experiments. The predictions from the developed model are found to agree well with experimental data. It is therefore concluded that Chaboche's unified power law can be applied to describe the high temperature inelastic deformational behaviors of Crofer 22 APU used for metallic interconnects in SOFC stacks.

Introduction

During construction of planar solid oxide fuel cell (SOFC) stack, metallic alloys are commonly used as an interconnector between the cells. This is particularly the case in SOFCs operating at intermediate temperatures, i.e. between 600 and 800 °C [1], [2]. At these temperatures, metallic alloys can also potentially be used as supports [3], [4]. Metallic alloys are often preferred owing to their low cost and workability compared to the more expensive, poorer conducting and less workable ceramic counterparts [5]. In order to achieve better mechanical stability of the entire SOFC stack, metallic alloys should have suitable creep resistance or compliance (depending on its design) on top of other requirements with regards to corrosion resistance, chemical stability, thermal and electrical conductivity, etc.

High-Cr ferritic stainless steels are often used in the assembly of planar SOFCs due to their good electrical conductivity, corrosion resistance and coefficient of thermal expansion (CTE) matching with those of the electro-chemically active ceramic components [1], [2]. The matching of the CTE of metallic alloy is very important to minimize stresses within the planar stack [1], [6]. Metallic alloys used in the SOFC stacks are also preferred to have good workable property (ductility) so they can be manufactured or shaped easily to a geometry that can allow easy flow of fuel and gasses in the SOFC stack [7].

Currently, it can be anticipated that a SOFC stack should sustain a number thermal cycles from startup, variations of operational load and shut down phases. The thermal differences are however not only in time but also spatially, e.g. across the stack when heat is generated by the internal electrochemical reactions. The stresses from differences in thermal expansion either due to variations in CTEs or temperature can cause plastic deformations and progressive damage, for instance in the brittle interface between metallic interconnects and cells, which eventually can lead to contact loss in the stack [8], [9], [10].

To avoid such failures, investigation of the mechanical reliability of the SOFC stack at operational conditions is necessary. One of the major goals of thermo-mechanical analysis of the SOFC stack is to be able to simulate the stress-strain responses and predict its reliability during operation. In order to achieve accurate simulations, material models for all SOFC stack components and initial stress fields must be known. This work focuses on the deformational behavior of metallic alloys because of their importance in affecting the distribution of stresses in SOFC stack. Due to lack of detailed constitutive relations, previous works often rely on engineering data on the properties of alloys used in the SOFC stacks [8], [9], [10]. Engineering data of alloys at high temperatures are often subject to specific test conditions (e.g. strain rate), which reduces their use under varying conditions (e.g. different sets of strain rates or environment).

The high temperature deformational properties of ferritic alloys often require detailed models. For instance, at operational temperatures of SOFC, the thermally activated strain in the metallic interconnect (MIC) gives rise to a complex deformational behavior involving elastic as well as inelastic deformations. The inelastic deformations in the MIC are associated with temperature and rate dependent characteristics producing strain hardening and dynamic recovery. Such kind of deformational behaviors can be explained using viscoplastic theories describing creep, stress relaxation and strain hardening/softening phenomena of material at high temperature [11].

Previous works on metallic alloys used in SOFC stacks mainly focus on characterization of secondary creep [1], [2], [3]. For instance, Chiu et al. [2] and Boccacini et al. [3] showed that the minimum creep rate is related to the applied stress using power law creep model, in which a linear variation of strain rate as a function of stress is presented. Chiu et al. also discussed the variation of stress exponent in the power law model with the magnitude of the steady state temperature. However, modeling the creep behavior of metallic alloys using power law model has sometimes limitations due to variations of the stress exponent with a range of loadings as shown by Kuhn et al. [1].

The use of simplified power law model to describe the inelastic deformations in metallic alloys might also be insufficient to capture the complex nature of inelastic deformations caused by cyclic loadings involving not only creep (time dependent plasticity) but also time independent plasticity. The possible occurrence of time independent plasticity in metallic alloys at operational temperature of SOFCs is discussed by Nakajo et al. and Lin et al. [9], [10]. Material hardenings at high temperature should also be considered while developing a constitutive model for particle strengthened alloys like Crofer 22 H, as it has an effect on primary creep during constant load deformational properties [12], [13], [14].

Therefore, it is necessary to have a model incorporating time dependent (creep) as well as time independent plasticity together with strain hardening effects. From the point of view of continuum mechanics, time dependent plasticity as well as time independent plasticity are assumed to arise from similar mechanisms involving dislocation motions [11]. Hence, a unified viscoplastic framework for the deformational behavior of metallic alloys at high temperature is suitable. Furthermore, unlike power law creep models, viscoplastic models based on sine hyperbolic relationships are capable of describing the creep behavior of metals in a wider range of stresses [15], [16]. The effect of strain hardening can also be incorporated using a single-scalar internal variable to represent the average isotropic deformational resistance due to microstructural changes at high temperature [17].

In this work, it is investigated whether a material model based on a unified viscoplastic theory, a variation of the so-called Chaboche's unified power law, including the effect of material hardening can be utilized for Crofer 22 APU, a widely used steel for interconnect in SOFC stacks. Calibration of viscoplastic and hardening parameters are made using constant strain rate and relaxation experiments at different stresses and operational temperatures of SOFC. In addition, validation of the model with the help of cyclic loading and creep experiments on Crofer 22 APU is also presented. The model is developed based on sine hyperbolic law for the inelastic deformations incorporating a non-linear strain hardening internal variable. The implementation of the model is achieved through a user-defined material (UMAT) model in commercial finite element (FE) software ABAQUS™ and use of Matlab.

Section snippets

Material model

It is assumed that the metal undergoes deformations with a total strain, ε, at high temperature that can be additively decomposed to elastic, εel, thermal, εth, and viscoplastic, εvp, strain tensors as:ε=εel+εth+εvp

The elastic contribution of the deformation can be modeled by the Hooke's law considering the Young's modulus, E, and Poisson's ratio, v, for an applied stress, σ, as shown in Eq (2).εel=1+vEσvEtr(σ)IHere, tr(σ), is the trace of stress tensors given by the sum of principal stresses

Finite element model implementation

The model discussed in Section 2 is implemented into commercial finite element software ABAQUS™ using an external user defined material subroutine or so-called UMAT. The UMAT requires defining the stress increment at the end of each time step. Hence, the increment in stress, Δσ, is defined using the multi-axial form of the Hooke's law using a stiffness matrix, C, together with Eq (1) as:Δσ=C:ΔεelΔσ=C:(ΔεΔεthΔεvp)

During simulation, if viscoplasticity is present, i.e. f>0, an implicit

Experimental setup and conditions

Stress relaxation as well as constant strain rate properties of specimens were conducted using uniaxial tensile loading of samples on an in-house built displacement controlled tensile testing set up equipped with a heating furnace. A unique setup involving remotely installed laser micrometer was used to achieve precise and in-situ strain measures of the samples at high temperature. Details of the experimental setup built to characterize the high temperature time dependent mechanical behaviors

Calibration of material parameters

In this section, the elastic, viscoplastic and hardening material parameters of the material model presented in Section 2 are determined from the relaxation and constant strain rate experiments at isothermal conditions involving 600, 700 and 800 °C. The methodologies used in this work to determine all the necessary parameters of the model are discussed.

Validation of material model

The material model with the material parameters determined by the above procedure using relaxation experiments and constant strain rate experiments was validated by comparison with results from additional experiments with constant strain rate, cyclic loading and creep experiments conducted at isothermal conditions.

For comparison, a finite element (FE) model is developed to reproduce the test results with the help of a user-defined material (UMAT) implemented in ABAQUS™. The UMAT is programed

Discussion

The stress relaxation of Crofer 22 APU shown in Fig. 2 indicates that almost 90% of the stress developed in Crofer 22 APU at 800 °C disappears within half an hour. This is beneficial to alleviate stresses generated due to changes in points of operation in SOFC stacks. Also this is useful as it also indicates that gentle shift between points of operation can counteract previous plastic deformations, which will inevitably accumulate over time with a moderate stress level and hereby avoiding

Conclusions

Stresses during operation of solid oxide fuel cell (SOFC) stacks can generate a time dependent plastic deformations (creep) in the metallic interconnects, which can cause mechanical failures within the stack. This is particularly the case during changes in points of operation of the SOFC, where transient creep should be considered while analyzing the behavior of metallic interconnects.

It is therefore investigated whether a constitutive law based on unified viscoplastic theories can describe the

Acknowledgements

The research leading to these results has received funding from the European Union's Seventh Framework Programme (FP7/2007- 2013) for the Fuel Cells and Hydrogen Joint Technology Initiative under grant agreement no 325278 and from Energinet.dk under the Public Service Obligation, ForskEL contract 2014-1-12236.

References (23)

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