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Analysis of diffusion induced elastoplastic bending of bilayer lithium-ion battery electrodes

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Abstract

Bilayer electrode, composed of a current collector layer and an active material layer, has great potential in applications of in-situ electrochemical experiments due to the bending upon lithiation. This paper establishes an elastoplastic theory for the lithiation induced deformation of bilayer electrode with consideration of the plastic yield of current collector. It is found that the plastic yield of current collector reduces the restriction of current collector to an active layer, and therefore, enhances in-plane stretching while lowers down the rate of electrode bending. Key parameters that influence the elastoplastic deformation are identified. It is found that the smaller thickness ratio and lower elastic modulus ratio of current collector to an active layer would lead to an earlier plastic yield of the current collector, the larger in-plane strain, and the smaller bending curvature, due to balance between the current collector and the active layer. The smaller yield stress and plastic modulus of current collector have similar impacts on the electrode deformation.

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References

  1. Tarascon, J. M. and Armand, M. Issues and challenges facing rechargeable lithium batteries. nature, 414(6861), 359–367 (2001)

    Article  Google Scholar 

  2. Bourlot, S., Blanchard, P., and Robert, S. Investigation of aging mechanisms of high power Li-ion cells used for hybrid electric vehicles. Journal of Power Sources, 196, 6841–6846 (2011)

    Article  Google Scholar 

  3. Zhang, J., Lu, B., Song, Y., and Ji, X. Diffusion induced stress in layered Li-ion battery electrode plates. Journal of Power Sources, 209, 220–227 (2012)

    Article  Google Scholar 

  4. Song, Y., Shao, X., Guo, Z., and Zhang, J. Role of material properties and mechanical constraint on stress-assisted diffusion in plate electrodes of lithium ion batteries. Journal of Physics D: Applied Physics, 46(10), 105307 (2013)

    Article  Google Scholar 

  5. Yang, B., He, Y. P., Irsa, J., Lundgren, C. A., Ratchford, J. B., and Zhao, Y. P. Effects of composition-dependent modulus, finite concentration and boundary constraint on Li-ion diffusion and stresses in a bilayer Cu-coated Si nano-anode. Journal of Power Sources, 204, 168–176 (2012)

    Article  Google Scholar 

  6. Song, Y., Lu, B., Ji, X., and Zhang, J. Diffusion induced stresses in cylindrical lithium-ion batteries: analytical solutions and design insights. Journal of the Electrochemical Society, 159(12), A2060–A2068 (2012)

    Article  Google Scholar 

  7. Sethuraman, V. A., Chon, M. J., Shimshak, M., Srinivasan, V., and Guduru, P. R. In situ measurements of stress evolution in silicon thin films during electrochemical lithiation and delithiation. Journal of Power Sources, 195, 5062–5066 (2010)

    Article  Google Scholar 

  8. Bower, A. F., Guduru, P. R., and Sethuraman, V. A. A finite strain model of stress, diffusion, plastic flow, and electrochemical reactions in a lithium-ion half-cell. Journal of the Mechanics and Physics of Solids, 59(4), 804–828 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  9. Cui, Z., Gao, F., and Qu, J. Interface-reaction controlled diffusion in binary solids with applications to lithiation of silicon in lithium-ion batteries. Journal of the Mechanics and Physics of Solids, 61(2), 293–310 (2013)

    Article  MathSciNet  Google Scholar 

  10. Liu, P., Sridhar, N., and Zhang, Y. W. Lithiation-induced tensile stress and surface cracking in silicon thin film anode for rechargeable lithium battery. Journal of Applied Physics, 112(9), 093507 (2012)

    Article  Google Scholar 

  11. Liu, X. H., Zheng, H., Zhong, L., Huang, S., Karki, K., Zhang, L. Q., and Huang, J. Y. Anisotropic swelling and fracture of silicon nanowires during lithiation. Nano Letters, 11(8), 3312–3318 (2011)

    Article  Google Scholar 

  12. Zhao, K., Wang, W. L., Gregoire, J., Pharr, M., Suo, Z., Vlassak, J. J., and Kaxiras, E. Lithiumassisted plastic deformation of silicon electrodes in lithium-ion batteries: a first-principles theoretical study. Nano Letters, 11(7), 2962–2967 (2011)

    Article  Google Scholar 

  13. Zhao, K., Pharr, M., Vlassak, J. J., and Suo, Z. Inelastic hosts as electrodes for high-capacity lithium-ion batteries. Journal of Applied Physics, 109(1), 016110 (2011)

    Article  Google Scholar 

  14. Brassart, L., Zhao, K., and Suo, Z. Cyclic plasticity and shakedown in high-capacity electrodes of lithium-ion batteries. International Journal of Solids and Structures, 50(7), 1120–1129 (2013)

    Article  Google Scholar 

  15. Gao, Y. F., and Zhou, M. Coupled mechano-diffusional driving forces for fracture in electrode materials. Journal of Power Sources, 230, 176–193 (2013)

    Article  Google Scholar 

  16. Song, Y., Li, Z., and Zhang, J. Reducing diffusion induced stress in planar electrodes by plastic shakedown and cyclic plasticity of current collector. Journal of Power Sources, 263, 22–28 (2014)

    Article  Google Scholar 

  17. Qi, Y., Guo, H., Hector, L. G., and Timmons, A. Threefold increase in the Young’s modulus of graphite negative electrode during lithium intercalation. Journal of the Electrochemical Society, 157(5), A558–A566 (2010)

    Article  Google Scholar 

  18. Zhang, X., Shyy, W., and Sastry, A. M. Numerical simulation of intercalation-induced stress in Li-ion battery electrode particles. Journal of the Electrochemical Society, 154(10), A910–A916 (2007)

    Article  Google Scholar 

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Correspondence to Yicheng Song.

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Project supported by the National Natural Science Foundation of China (Nos. 11332005 and 11172159) and the Innovation Program of Shanghai Municipal Education Commission (No. 13ZZ070)

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Li, D., Li, Z., Song, Y. et al. Analysis of diffusion induced elastoplastic bending of bilayer lithium-ion battery electrodes. Appl. Math. Mech.-Engl. Ed. 37, 659–670 (2016). https://doi.org/10.1007/s10483-016-2079-8

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  • DOI: https://doi.org/10.1007/s10483-016-2079-8

Key words

Chinese Library Classification

2010 Mathematics Subject Classification

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