J. Cent. South Univ. (2019) 26: 623-631

DOI: https://doi.org/10.1007/s11771-019-4033-7

Stress relaxation behavior and life prediction of gasket materials used in proton exchange membrane fuel cells

LI Guo(李果)¹, GONG Jian-ming(巩建鸣)², TAN Jin-zhu(谈金祝)²,ZHU Da-sheng(朱大胜)¹, JIA Wen-hua(贾文华)¹

1. School of Mechanical Engineering, Nanjing Institute of Technology, Nanjing 211167, China;

2. School of Mechanical and Power Engineering, Nanjing Tech University, Nanjing 211816, China

Central South University Press and Springer-Verlag GmbH Germany, part of Springer Nature 2019

Abstract: Silicone rubber gaskets are employed to keep fuel gases and oxidation in their own zones. Due to the viscosity and elasticity, the assembly force could relax when the silicone rubber is compressed in a proton exchange membrane fuel cell. In this work, the stress relaxation behavior of silicone rubber samples is studied under different temperatures and simulated operating conditions. The results show that the stress relaxes exponentially with time at 25% strain level, especially at higher temperature or with higher acid concentration solution. The three-term Prony series can simulate the viscoelastic behavior well, and the Master curves are established by applying a time–temperature superposition method to estimate the life of the samples. It can save approximately 50% and 78% of the test time when an operating temperature and acid solution are chosen appropriately.

Key words: stress relaxation; gasket; silicone rubber; life prediction; fuel cell

Cite this article as: LI Guo, GONG Jian-ming, TAN Jin-zhu, ZHU Da-sheng, JIA Wen-hua. Stress relaxation behavior and life prediction of gasket materials used in PEM fuel cells [J]. Journal of Central South University, 2019, 26(3): 623–631. DOI: https://doi.org/10.1007/s11771-019-4033-7.

1 Introduction

Due to the energy crisis and pollution caused by fossil fuels, clean energy is becoming the focus [1, 2]. Proton exchange membrane (PEM) fuel cells are critically needed as a new power source due to their stability, durability, high current density and zero pollution. And the stability and durability are important to its electrochemical performance. According to Refs. [3, 4], PEM fuel cells applied to transportation have to operate stably for more than 5000 h at an extensive temperature range of 40–80 °C. Therefore, the durability of components at the normal operating conditions in PEM fuel cell environments plays a vital role in the performance of the fuel cell. WAN et al [5] illustrated the microplanning principle of micro-flow channel on bipolar plates and discussed the contact resistance in fuel cell. Another component, the elastic gasket, has been focused on by many researchers. Leaking of the gasket because of degradation can induce the mixing of gases and liquid. Therefore, the mechanical property is critical to the sealing of the gaskets and is a hot topic for researchers. Some researchers have studied the failure of the gasket sealing [6–8]. For instance, the failure mechanism of gaskets used in a fuel cell stack operated at different thermal cycling conditions was found [6]. The compartment leak between anode and cooling because of the failure of gaskets was discussed [7]. SCHULZE et al [8] revealed that the decomposed products coming from the chemical degradation of gasket seals could alter the feature of the electrodes and contaminate the catalyst. SRIDHAR et al [9] studied the mechanical behaviors of the membrane electrode assembly in a PEM fuel cell. Properties such as stress, strain and modulus were measured, and it was found that the study of these mechanical behaviors of the membrane electrode assembly compliments the other techniques and can be used in the post-mortem analysis of causes for degradation. The leaking of the seals is due to the loss of the functionality of silicone rubber gaskets. It could be owing to the chemical degradation, long-term mechanical aging, or both [4, 10–12]. Due to its viscoelastic property typically made of polymeric materials, the mechanical property–stress relaxation behavior of gaskets materials is being studied widely [13–16]. That means that the sealing force will gradually decrease at a constant strain or deformation until the gasket fails. For example, RAJAGOPAL [13] generalized the classical viscoelastic fluid model in describing the response of gaskets. The generalized Maxwell model including the springs and dashpots has been constructed to describe the response of complex viscoelastic fluids.

Some researchers employed the theory models, mostly the Maxwell model, to predict the service life of the polymeric materials [17–32]. MAZERAN et al [18] developed a mechanical model based on a generalized Kelvin-Voigt model to explain and fit the nanoindentation curves realized on three amorphous polymers (PC, PMMA and PS). CAI et al [19] made the first attempt to apply the fractal derivative to modeling viscoelastic behavior. The methodology of scaling transformation is utilized to obtain the creep modulus and relaxation compliance for the proposed fractal Maxwell and Kelvin models. Numerical results show that the proposed fractal models require fewer parameters, have simpler mathematical expressions and result in higher accuracy than the classical integer-order derivative models. The results further confirm that the proposed fractal models can characterize the creep behavior of viscoelastic materials. REY et al [21] studied the role of temperature on the stress relaxation of silicone rubbers with and without fillers and employed the neo-Hookean model to estimate the experimental data previously mentioned. YAMAGUCHI et al [22] studied the elastic recovery rate, creep and stress relaxation of a crosslinked natural rubber without fillers in tension. A method based on the Boltzmann superposition principle was applied to contrast the creep compliance to a test record of its recovery after relaxing from a series of constant loads at various times. SHI et al [23] studied the time- dependent property and constitutive model of EPDM, which is employed as sealing of the tunnel segment joints. The Arrhenius model is used by considering the degradation rate, and the constant is fitted by Matlab. KMMLING et al [24] determined that the heterogeneous aging led to decay of the whole performance, including compression set and stress relaxation in compressed HNBR and EPDM O-ring seals. It is suggested that the first material has better properties than the second material at 150 °C, which is not the case at 100 °C. By using the time-temperature superposition principle and the Arrhenius method, the exemplary CS values of 80% would be achieved after approximately 29 a for HNBR and after approximately 1100 years for EPDM. BRIODY et al [29, 30] modeled the normalized relaxation modulus data by a series of paralleled Maxwell elements including the spring and dashpot elements. The parameters of a 4th order and an 8th Prony series were fitted by using the least squares optimization method. An eight-term Prony series could fit the normalized stress relaxation test data more accurately.

The gaskets in a PEM fuel cell are not only under a humid, acidic environment but also under compression to keep the gases in their own regions. The sealing force decreases after assembly due to the stress relaxation of the polymeric gaskets. The gasket loses its sealing functionality when the stress of the gasket decreases below a certain value. This behavior of the gasket material can be affected by environmental parameters including temperature, acid, and others.

This work investigates the compression stress relaxation behaviors of silicone rubbers at 25% constant strain at different temperatures and in different environments. Compression stress relaxation tests of silicone rubbers are conducted in air and three different solutions at 25% strain level with different temperature conditions. The three-term Maxwell model is chosen to simulate the viscoelastic behavior of the gasket material. The time-temperature superposition (TTS) method is adopted to establish the master curves at a reference operating condition. The lifetime of the gaskets is estimated based on the master curve.

2 Experiments and theory

2.1 Material and preparation

Silicone rubber is a promising candidate material for gaskets in a PEM fuel cell because of its stable properties in a wide temperature range from –55 to 180 °C or even more. Generally, silicone is crosslinked by using peroxides. The fillers in rubber are usually calcium carbonate and carbon black. Silicone has a relatively low glass transition temperature of –123°C, so it can maintain its flexible and elastic properties in a wide temperature range. However, like most polymers, silicone rubber materials can display viscoelastic behavior, particularly at a higher temperature.

In the experiments, a commercial silicone rubber material was acquired in sheet form from a manufacturer in China. The silicone rubber is formulated by two parts. One part primarily composes of polydimethylsilicoxane with a vinyl side chain. The other part is polydimethylsilicoxane with hydrosilylation functionalities. These two parts are crosslinked by hydrosilylation. The fillers inside the rubber mainly comprise calcium carbonate, quartz and silica.

The materials are cut into cylindrical samples. The diameter and height of the samples are 13 and 6.3 mm, respectively. According to GB/T7759-1996 and GB/T1685-2008, for the compression stress relaxation test, it is convenient for the samples to be cut from the sheet by the tool rather than using the ring ones.

2.2 Instrument

The testing machine is manufactured by Mingzhu, China, and employed to perform the compression stress relaxation test. There are three independent testing rigs, which can test the samples at strain levels of 10%, 15% and 25%. The third level is chosen in this work. A furnace is used with the testing machine to control the test temperature during the compression process. The sealing force can be recorded continuously with time throughout the whole test period by a computer.

2.3 Experiments

The specimens shaped from silicone rubber materials were immersed in four different exposure environments—ambient air and three acidic environments. One acidic environment is called regular solution (marked RS) with 12×10^–6 H₂SO₄, 1.8×10^–6 HF and de-ionized water. This regular solution is close to the real fuel cell service condition, while the others are the accelerated durability test solutions (marked ADT1 and ADT2) compounded with 1 mol/L H₂SO₄, 12×10^–6 HF and 1 mol/L H₂SO₄, 30×10^–6 HF, respectively. The test temperatures are 30, 70 and 90 °C. The prepared samples were individually put into containers and kept warm at test temperatures in the furnace over time. Then, the exposed samples were detached and excess acid was removed by reagent grade water before they were used weekly for the compression stress relaxation test at room temperature. The test procedure follows the standard GB/T7759-1996 and GB/T1685-2008.

The experiments performed in this study are ex-situ. The experimental data are mainly used to analyze the influence of factors, such as temperature and acid on the mechanical behavior of the gasket seals. It is expected to find a suitable method for life prediction of gasket materials by the TTS principle, although the experimental results may not be applied directly for life prediction of seals in a real fuel cell assembly.

2.4 Viscoelastic theory and models

As mentioned above, silicone rubber is one kind of polymeric material with viscoelastic properties. Maxwell mode is chosen in this work, and it is usually used to represent the elasticity and viscosity of the polymers by connecting a spring and a dashpot in series, as shown in Figure 1. The dashpot represents the viscous fluids that have a movement rate in connection with stress. The spring represents elastic deformation which could respond simultaneously to each applied load.

Figure 1 Maxwell model

The mechanical properties of the spring are fitted to Hukoo’s law. The strain independence of time is linear to stress, as shown in Eq. (1). The stress–strain relation of the dashpot is shown in Eq. (2). The total stress of the Maxwell model is equal to that of each component. The total strain is the sum of each component. Therefore, we can obtain the rate of the total strain as Eq. (3).

                            (1)

where σ₁ is the stress of the spring; ε₁ is the strain of the spring; E is the elastic modulus; D is the creep compliance.

or                    (2)

where η is the viscosity of the dashpot; ε₂ is the strain of the dashpot; dε/dt is the rate of strain.

                          (3)

In the stress relaxation experiment, the strain level is fixed at 25%, that is dε/dt=0. Equation (3) is as follows:

or               (4)

When t=0, s=s₀. The integral of Eq. (4) is:

,                      (5)

If many Maxwell models are paralleled then a generalized Maxwell model is obtained, described by the following form:

                      (6)

where σ_∞ is the stress after a long time; σ_i is the stress relying on the strain level and the material properties; τ_i is a material constant.

Substitute Eq. (1) into Eq. (6) and obtain:

                      (7)

The normalized stress relaxation modulus is shown in Eq. (8). That is, the Prony series, a linear model for describing stress relaxation of viscoelastic material.

                    (8)

where and

For polymeric materials, the viscoelastic property is intensively dependent on the temperature due to the molecules moving faster at a higher temperature. Time–temperature superposition, which is a mathematical expression of Boltzmann’s superposition principle [4], is employed to describe the equivalence between the time (t) and the temperature (T), as shown in Eq. (9) and Figure 2.

                     (9)

where E(T₁, t₁) is the stress relaxation modulus at time t₁ and temperature T₁; T₀ and T₁ are two different temperatures; t is time; α_T is shift factor.

Figure 2 Schematic diagram of time–temperature superposition principle

The experimental data of stress relaxation is obtained and plotted in the figure at a certain temperature T₁. By using TTS, the curve in the figure can be shifted to a selected reference temperature T₀ horizontally by α_T as presented in logarithmic scale. The advantage of the TTS method is substituting long-term stress relaxation tests at a low temperature with a test at a high temperature but in a shorter test time for materials. The TTS method has been widely employed in studying viscoelastic behaviors of polymeric materials [24–30].

3 Results and discussion

The stress relaxation behavior of the silicone rubber material is obtained under 25% strain level at three temperatures 30, 70 and 90 °C for 1 week exposure in ambient air, as shown in Figure 3. The tendency of the three curves is similar to each other. In addition, there is another curve of unexposed samples for comparison. From this figure, it is obvious that the stress relaxation modulus E decreases dramatically at first. After approximately 10000 s, it decreases steadily with time. The stress relaxation modulus is the largest for samples exposed at 90 °C. Stress relaxation modulus increases with the increase of temperature, so the temperature has a strong influence on the stress relaxation behavior. The results indicate that the stress or the modulus E, which represents the elasticity property of the materials, exponentially decays with time. This shows that the stress of the samples decreases with time under constant strain, and the sealing property is deteriorating. The decrease of modulus E implies that the material is losing its elastic property.

Figure 3 Time-dependent compression stress relaxation modulus E of silicone rubber after 1 week exposure at different temperatures

Figure 4 shows the trend of normalized stress relaxation of samples compressed at 25% level strain and exposed to ambient air at three temperatures 30, 70 and 90 °C. Here, the test data is collected within 6 h because the long-term experiment is being conducted. Test data in Figure 4 indicates that the stress intrinsically decays exponentially with time. This is close to what is represented by the Maxwell model. From Figures 3 and 4, the results indicate that the stress relaxes very quickly at first and then reduces steadily with time until finally reaching a state of equilibrium. The stress relaxes most quickly for samples exposed at 90 °C. The results also indicate that the stress relaxes more quickly under a higher temperature condition.

Figure 4 Normalized stress relaxation data of silicone rubber aged for 1 week at different temperatures

The Prony series with three exponential terms, a mathematic expression of the Maxwell model, is chosen to describe the stress relaxation behavior as displayed in Figure 3. The parameters of the three-term Prony series based on the least squares method are listed in Table 1. The stress relaxation modulus in Figure 3 depends only on time despite the strain level. The Prony series could be calculated from test data at 25% strain level, and it could also be applied to simulate stress relations or elastic modulus curves at other strain levels.

Table 1 Fitted parameters of three-term Prony series at a reference temperature

By using time temperature superposition, three normalized stress relaxation modulus curves shown in Figure 4 are horizontally shifted by a certain amount listed in Table 2 to establish a master curve shown in Figure 5 at the reference temperature of 70 °C. The curve of experimental data at 30 °C should move horizontally to the left by 0.426 in logarithmic scale relative to the curve at 70 °C, and the curve of experimental data at 90 °C should move horizontally to the right by 0.398 in logarithmic scale relative to the curve at 70 °C. In Figure 5, all three curves are overlapped well. That is, the curve of time dependent modulus under the reference temperature has a similar tendency to the curve under any other temperature. From Figure 5, it can be predicted that the life of the gasket materials would be approximately 13 h at an operating temperature of 70 °C, while the experimental time is 6 h at an operating temperature of 90 °C. This result indicates that by applying the TTS principle, the life time can be extrapolated to be about twice the experiment time under an appropriate high temperature, which can save approximately 50% of the test time.

Table 2 Shift factors at a reference temperature of 70 °C

Figure 5 Master curve constructed for silicone rubber aged for 1 week at reference temperature of 70 °C

Figure 6 shows changes of the time dependent stress relaxation modulus at three exposure conditions, RS, ADT1 and ADT2, at a temperature of 70 °C for 2 weeks with 25% applied strain. It can be observed that the stress relaxation modulus E for the group of three experimental samples under different exposure environments decays exponentially with time. The trend of the three curves is the same. The stress relaxation modulus is the largest for samples immersed in ADT2 solution. Stress relaxation modulus increases with increasing acid concentration in the exposure environment. The acid can largely affect the elastic property of the silicone rubbers. The result implies that the elastic property becomes worse with time in highly acidic environments. The acid solution degrades the mechanical properties of materials due to the chemical structure changes caused by the acid.

Figure 6 Time dependent compression stress relaxation modulus E of samples exposed to three test environments for 2 weeks at 70 °C

Figure 7 displays the test curves of the normalized stress relaxation modulus at three exposure conditions, RS, ADT1 and ADT2, at a temperature of 70°C for two weeks with 25% applied strain. The tendency of the curves shown in Figure 7 is similar to that of curves obtained in air. It can be observed from the figures that the normalized stress relaxation modulus decreases sharply at first, indicating the stress relaxed fast and a higher acid concentration contributes to faster stress relaxation. This behavior can also be expressed by the Prony series. The parameters of the three-term Prony series are fitted based on the least squares method, listed in Table 3. The three-term Prony series can describe the viscoelasticity of silicone rubbers very well and could also be applied to estimate the tendency of stress relaxation elastic modulus under different strain levels.

According to TTS principle, the equivalence between t and the acid concentration was calculated. The master curve shown in Figure 8 for a reference solution of RS is built by shifting the curves horizontally by a certain amount, which is calculated and listed in Table 4. The curve of experimental data for the ADT1 operational condition should move horizontally to the right by 0.592 in logarithmic scale relative to the curve for the RS operational condition, and the curve of experimental data for the ADT2 operational condition should move horizontally to the right by 0.898 in logarithmic scale relative to the curve for the RS operational condition. In Figure 8, all three curves are overlapped well especially when the test time is more than 1000 s. Again, it can be seen that the predicted service life is longer than the experimental time. The life of the gasket materials is predicted to be approximately 27 h at RS conditions similar to a real PEM fuel cell while its experimental time is only 6 h at the ADT2 condition. This result indicates that by applying the TTS principle, the life time can be extrapolated to be approximately 4.5 times that of the experiment time under an appropriate high acid concentration solution, which can save approximately 78% of the test time. Although the three curves overlap relatively well, the equivalence between time and the acid concentration is also being investigated.

Figure 7 Normalized stress relaxation data of silicone rubber exposed to three test environments for 2 weeks at 70 °C

Table 3 Fitted parameters of three-term Prony series at a reference solution

Figure 8 Master curve constructed for silicone rubber aged for 2 weeks at a reference solution of RS at 70 °C

Table 4 Shift factors at a reference solution of RS

4 Conclusions

This work presents an experimental investigation of compressed stress relaxation of silicone rubbers in ambient air, RS and two ADT solutions at different temperatures. From the test results and analysis, it can be concluded that the three-term Maxwell model can describe the viscoelastic behavior of the silicone rubbers well. The master curves have been established to predict the long-term stress relaxation behaviors in a short experimental time by using the time–temperature superposition principle. This can save approximately 50% and 78% of test time, when an appropriate temperature and acid solution are respectively chosen. Further study is being performed, and the results will be written in the future.

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(Edited by FANG Jing-hua)

中文导读

质子交换膜燃料电池密封材料应力松弛行为研究及寿命预测

摘要：硅橡胶材料在燃料电池中主要用于保持燃料气体与氧化气体在各自区域不因泄露而混合。由于硅橡胶兼具黏性与弹性性质，在燃料电池中由于密封而处于压缩状态，所以预测力会随着时间的延长而产生松弛。本论文针对硅橡胶试样在不同温度及不同模拟操作工况下的压缩应力松弛行为进行了研究。结果表明，在25%应变状态下，材料的应力松弛行为随着时间的延长而呈指数下降趋势，特别是当试样在温度较高或酸度较高的试验环境下老化之后。文中采用三参数Prony 级数很好地模拟了硅橡胶材料的黏弹性行为，并且基于时温等效原理构建主曲线预测试样寿命。当加速试验时老化温度与酸浓度选择合适，相对于垫片材料在实际燃料电池环境中老化的力学损伤性能变化，可缩短50%甚至78%老化时间。

关键词：应力松弛；垫片；硅橡胶；寿命预测；燃料电池

Foundation item: Projects(51505212, 51505211, 11302097) supported by the National Natural Science Foundation of China; Project(XTCX201609) supported by the Open Research Fund of Jiangsu Collaborative Innovation Center for Smart Distribution Network, Nanjing Institute of Technology, China; Project(1301060B) supported by the Postdoctoral Science Foundation of Jiangsu Province, China; Project(11KJD130001) supported by the Natural Science Foundation of the Jiangsu Higher Education Institutions, China; Project(ZKJ201401) supported by the on-job Doctorate Foundation of Nanjing Institute of Technology, China; Project(JXKJ201511) supported by the Open Projects about Key Discipline in 2015, School of Mechanical Engineering, Nanjing Institute of Technology, China

Received date: 2017-11-20; Accepted date: 2018-05-24

Corresponding author: LI Guo, PhD, Assistant Professor; Tel: +86-18151007006; E-mail: liguoperfect@163.com; ORCID: 0000-0002- 4972-2405