Elsevier

Mechanics of Materials

Volume 161, October 2021, 104024
Mechanics of Materials

The effect of bending deformation on flexible electrodes during charging and discharging

https://doi.org/10.1016/j.mechmat.2021.104024Get rights and content

Highlights

  • A complete physical model of the flexible electrode is developed.

  • The charge/discharge-rate-dependent plastic deformation is discussed.

  • Evolutions of plastic stress and strain during charge/discharge are studied.

  • The viscoplastic finite element analysis confirms the theoretical results.

  • Two different physical origins of strain accumulations are studied.

Abstract

As the typical deformation mode, the bending deformation accompanies the entire useful life of flexible batteries. Due to the coupling of electrochemical processes, this bending behavior can severely damage flexible batteries. Herein, a complete physical model is developed to investigate the effect of bending deformation on flexible thin-film electrodes during the charge/discharge cycle. And the rate-dependent plastic flow in the electrode is modeled based on the evolution of the excess energy stored in the material. Two different bending forms of the flexible thin-film electrode are studied, and the stress and strain spectrums of the electrode during cyclic deformation are thoroughly discussed. The results show that the bending deformation has a significant effect on the evolution of the stress and strain of the electrode. Both constant bending deformation and cyclic bending deformation produce accumulated strain, but for entirely different reasons. The present work sheds light on the physical origin of strain accumulation for the flexible thin-film electrode and provides guidance for material design and the application of flexible batteries.

Introduction

Interest in flexible and wearable electronic devices has proliferated over the past few years. The flexible power supply devices that have high energy density and excellent flexibility are urgently required to accommodate rapidly evolving flexible electronic devices. Thus, a large number of researchers are working on the development of various types of flexible batteries (Qian et al., 2019; Lv et al., 2019), and many achievements have been made in material design and electrochemical performance (Sun et al., 2017; Cheng et al., 2015). With the development of new flexible structures and their application in flexible devices, the mechanical durability and reliability of the flexible batteries become an important issue. As the most common application requirement for flexible batteries, bending deformation tests are widely used to verify the mechanical reliability of flexible batteries (Zhou et al., 2014; Li et al., 2019). However, high-capacity electrode materials tend to plastically deform during electrochemical cycling, which will seriously affect the mechanical reliability of flexible batteries in bending deformation. Thus, how plastic deformation occurs in bending deformation and affects the mechanical reliability of the electrode material is a critical issue (Bagheri et al., 2021; Pouyanmehr et al., 2020).

As a typical electrode structure, considerable efforts have been made to study the diffusion-induced stress (DIS) of the thin-film electrode, including the experiments (Bower et al., 2011), theoretical analyses (Huang et al., 2013; Song et al. 2014, 2015) and finite element simulations (Guo et al., 2019; Haftbaradaran et al., 2017; Yang et al., 2012). The results show that in the absence of plastic flow, high stress levels are generated in the electrode materials (Xu et al., 2019a, Xu et al., 2019b; Xu et al., 2019a, Xu et al., 2019b). Li et al. (2015) studied the elastoplastic deformation of hollow spherical silicon electrodes, and they found that the radial and hoop stresses decrease sharply when plastic flow occurs. Ma et al. (2017) developed an electrochemical-irradiated plasticity model for a cylindrical electrode and found that active materials suffer from plastic softening during the charging process. Di Leo et al. (2015) developed a rate-dependent flow strength model to simulate the galvanostatic charging of silicon nanotubes, which found that plastic flow reduces the stress generated in the material. In addition to the effect on stress, such plastic deformation behavior could lead to the plastic strain accumulation during the charge/discharge cycle, which is known as the ratcheting effect (Huang et al., 2002; Yaguchi and Takahashi, 2005). Our recent work found that under the effect of bending stress, flexible electrodes continuously accumulate plastic strain during cycling (Xu et al., 2020). Recently, Song et al. (2018) conducted the fatigue test to the stretchable electrode, and found that after 1000 tensile cycles, the fatigue stress and tensile strength of the electrode were reduced by more than 30 %. To be concluded, the existing theoretical models well explain the stress-strain and deformation mechanisms of electrode structures such as thin films, spheres and cylinders. However, these models do not account for the coupling of bending to the electrochemical cycle and are not applicable to flexible thin-film electrodes. Moreover, to the best of our knowledge, theoretical models for plastic deformation of flexible thin-film electrodes during different bending forms are very rare. Thus, an accurate physical model is urgently needed to describe the evolution of plastic stress and strain of flexible electrodes during bending deformation.

In this work, a complete physical model is developed to investigate the stress and strain spectrums of the flexible thin-film electrode during cyclic deformation. First, the response of the plastic flow to the charge/discharge rate is studied, where the flow stress and excess energy of the electrode are discussed intensively. Then, the evolution of stress and strain on the electrode surface during charge/discharge are discussed and compared with the finite element method (FEM) results. Further, two different bending forms are studied, namely, constant bending and cyclic bending. And the stress and strain spectrums of the electrode during the charge/discharge and bending cycles are discussed. Finally, the present work is summarized with some concluding marks.

Section snippets

Methodology

As plotted in Fig. 1(a), the flexible battery based on multi-layered structure usually consists of electrodes, separators and current collectors. During usage, the flexible batteries are subject to bending deformation from time to time, and these complex mechanical behaviors can cause severe damage to flexible batteries. Therefore, to study the effect of bending deformation on flexible electrodes in detail, a bending thin-film electrode consisting of two active material plates bonded to a

Results and discussion

For illustration, the amorphous stannum (Sn) electrode is used in our model, and the specific parameter values are shown in Appendix A. Table 1. The temperature is set as 300 K, and the charge/discharge rates are expressed as the experimentally-relevant rates, i.e., C-rates. A charge rate of 1C means that under this current, the battery would deliver its nominal capacity in 1 h.

Conclusion

In this paper, a rate-dependent constitutive model is used to study the cyclic deformation of the flexible electrode, based on the evolution of excess energy stored in the electrode material. The present model can predict the flow stress and plastic strain as a function of the loading spectrum and charge/discharge rates.

First, the response of the thin-film electrode to the charge/discharge rate is studied, where the flow stress and excess energy are found to be positively correlated with the

Author Statement

Yutao Shi: Conceptualization, Data curation, Methodology, Writing – original draft, Writing – review & editing. Chengjun Xu: Conceptualization, Writing – original draft, Methodology, Data curation, Investigation. Li Weng: Conceptualization, Methodology. Yufeng Wei: Investigation, Visualization. Bingbing Chen: Methodology, Resources. Jianqiu Zhou: Conceptualization, Project administration, Writing – review & editing. Rui Cai: Conceptualization, Validation.

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.

Acknowledgments

This work was supported by the Guizhou Provincial General Undergraduate Higher Education Technology Supporting Talent Support Program (KY (2018)043), Postgraduate Research & Practice Innovation Program of Jiangsu Province (KYCX18_1117, KYCX20_1074), the National Natural Science Foundation of China (10502025, 10872087, 11272143), the Program for Chinese New Century Excellent Talents in university (NCET-12-0712), the Key University Science Research Project of Jiangsu Province (17KJA130002), as

References (29)

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