Advertisement

Applied Mathematics and Mechanics

, Volume 39, Issue 11, pp 1567–1586 | Cite as

Two-way coupled analysis of lithium diffusion and diffusion induced finite elastoplastic bending of bilayer electrodes in lithium-ion batteries

  • Jun Yin
  • Xianjun Shao
  • Bo Lu
  • Yicheng Song
  • Junqian Zhang
Article
  • 35 Downloads

Abstract

A fully coupling model for the diffusion induced finite elastoplastic bending of bilayer electrodes in lithium-ion batteries is proposed. The effect of the mechanical stress on the lithium diffusion is accounted for by the mechanical part of the chemical potential derived from the Gibbs free energy along with the logarithmic stress and strain. Eight dimensionless parameters, governing the stress-assisted diffusion and the diffusion induced elastoplastic bending, are identified. It is found that the finite plasticity starting from the interface of the bilayer increases the chemical potential gradient and thereby facilitates the lithium diffusion. The full plastic flow makes the abnormal lithium concentration distribution possible, i.e., the concentration at the lithium inlet can be lower than the concentration at the interface (downstream). The increase in the thickness of the active layer during charging is much larger than the eigen-stretch due to lithiation, and this excess thickening is found to be caused by the lithiation induced plastic yield.

Key words

lithium ion battery bilayer electrode coupled diffusion finite elastoplastic bending 

Nomenclature

c

lithium molar concentration in the reference state

cmax

saturation concentration at the stoichiometric limit

Ω

partial molar volume

h1

initial thickness of the active layer

H1

thickness of the deformed active layer

hc

initial thickness of the current collector

Hc

thickness of the deformed current collector

λθ

in-plane stretch ratio

λr

transverse stretch ratio

εs

chemical volumetric eigen-strain

E

Young’s modulus

v

Poisson’s ratio

σθ

in-plane Cauchy stress

σr

transverse Cauchy stress

σeq

von Mises stress

σY

yield stress

F

Faraday’s constant

R

gas constant

T

temperature

in

electrical current density in the reference state

D

diffusion coefficient

Lθ

in-plane logarithmic stress

Lr

transverse logarithmic stresses

Q

state of charge (SOC)

Chinese Library Classification

O33 O29 

2010 Mathematics Subject Classification

65L12 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    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)CrossRefGoogle Scholar
  2. [2]
    MUKHOPADHYAY, A., TOKRANOV, A., SENA, K., XIAO, X., and SHELDON, B. W. Thin film graphite electrodes with low stress generation during Li-intercalation. Carbon, 49, 2742–2749 (2011)CrossRefGoogle Scholar
  3. [3]
    TAVASSOL, H., JONES, E. M., SOTTOS, N. R., and GEWIRTH, A. A. Electrochemical stiffness in lithium-ion batteries. Nature Materials, 15, 1182–1187 (2016)CrossRefGoogle Scholar
  4. [4]
    XIE, H., ZHANG, Q., SONG, H., SHI, B., and KANG, Y. Modeling and in situ characterization of lithiation-induced stress in electrodes during the coupled mechano-electro-chemical process. Journal of Power Sources, 342, 896–903 (2017)CrossRefGoogle Scholar
  5. [5]
    LI, D., WANG, Y., HU, J., LU, B., CHENG, Y. T., and ZHANG, J. In situ measurement of mechanical property and stress evolution in a composite silicon electrode. Journal of Power Sources, 366, 80–85 (2017)CrossRefGoogle Scholar
  6. [6]
    LANG, J., DING, B., ZHU, T., SU, H., LUO, H., QI, L., LIU, K., WANG, K., HUSSAIN, N., and ZHAO, C. Cycling of a lithium-ion battery with a silicon anode drives large mechanical actuation. Advanced Materials, 28, 10236–10243 (2016)CrossRefGoogle Scholar
  7. [7]
    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)CrossRefGoogle Scholar
  8. [8]
    YANG, B., HE, Y. P., IRSA, J., LUNDGREN, C., RATCHFORD, J., 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)CrossRefGoogle Scholar
  9. [9]
    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, 105307 (2013)CrossRefGoogle Scholar
  10. [10]
    HAFTBARADARAN, H., SONG, J., CURTIN, W., and GAO, H. Continuum and atomistic models of strongly coupled diffusion, stress, and solute concentration. Journal of Power Sources, 196, 361–370 (2011)CrossRefGoogle Scholar
  11. [11]
    SONI, S. K., SHELDON, B. W., XIAO, X., VERBRUGGE, M. W., DONGJOON, A., HAFT-BARADARAN, H., and GAO, H. Stress mitigation during the lithiation of patterned amorphous Si islands. Journal of the Electrochemical Society, 159, A38–A43 (2011)CrossRefGoogle Scholar
  12. [12]
    ZHAO, K., PHARR, M., CAI, S., VLASSAK, J. J., and SUO, Z. Large plastic deformation in high-capacity lithium-ion batteries caused by charge and discharge. Journal of the American Ceramic Society, 94, s226–s235 (2011)CrossRefGoogle Scholar
  13. [13]
    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, 804–828 (2011)MathSciNetCrossRefzbMATHGoogle Scholar
  14. [14]
    BOWER, A. and GUDURU, P. A simple finite element model of diffusion, finite deformation, plasticity and fracture in lithium ion insertion electrode materials. Modelling and Simulation in Materials Science and Engineering, 20, 045004 (2012)CrossRefGoogle Scholar
  15. [15]
    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, 293–310 (2013)MathSciNetCrossRefGoogle Scholar
  16. [16]
    CUI, Z., GAO, F., CUI, Z., and QU, J. A second nearest-neighbor embedded atom method interatomic potential for Li-Si alloys. Journal of Power Sources, 207, 150–159 (2012)CrossRefGoogle Scholar
  17. [17]
    JIA, Z. and LI, T. Intrinsic stress mitigation via elastic softening during two-step electrochemical lithiation of amorphous silicon. Journal of the Mechanics and Physics of Solids, 91, 278–290 (2016)CrossRefGoogle Scholar
  18. [18]
    ANAND, L. A Cahn-Hilliard-type theory for species diffusion coupled with large elastic-plastic deformations. Journal of the Mechanics and Physics of Solids, 60, 1983–2002 (2012)MathSciNetCrossRefzbMATHGoogle Scholar
  19. [19]
    DILEO, C. V., REJOVITZKY, E., and ANAND, L. Diffusion-deformation theory for amorphous silicon anodes: the role of plastic deformation on electrochemical performance. International Journal of Solids and Structures, 67, 283–296 (2015)CrossRefGoogle Scholar
  20. [20]
    PEIGNEY, M. Cyclic steady states in diffusion-induced plasticity with applications to lithium-ion batteries. Journal of the Mechanics and Physics of Solids, 111, 530–556 (2018)MathSciNetCrossRefGoogle Scholar
  21. [21]
    WU, C. H. The role of Eshelby stress in composition-generated and stress-assisted diffusion. Journal of the Mechanics and Physics of Solids, 49, 1771–1794 (2001)CrossRefzbMATHGoogle Scholar
  22. [22]
    GAO, Y. and ZHOU, M. Strong stress-enhanced diffusion in amorphous lithium alloy nanowire electrodes. Journal of Applied Physics, 109, 014310 (2011)CrossRefGoogle Scholar
  23. [23]
    LU, B., SONG, Y., and ZHANG, J. Time to delamination onset and critical size of patterned thin film electrodes of lithium ion batteries. Journal of Power Sources, 289, 168–183 (2015)CrossRefGoogle Scholar
  24. [24]
    LU, B., SONG, Y., ZHANG, Q., PAN, J., CHENG, Y. T., and ZHANG, J. Voltage hysteresis of lithium ion batteries caused by mechanical stress. Physical Chemistry Chemical Physics, 18, 4721–4727 (2016)CrossRefGoogle Scholar
  25. [25]
    SHENOY, V. B., JOHARI, P., and QI, Y. Elastic softening of amorphous and crystalline Li-Si phases with increasing Li concentration: a first-principles study. Journal of Power Sources, 195, 6825–6830 (2010)CrossRefGoogle Scholar
  26. [26]
    SETHURAMAN, V. A., SRINIVASAN, V., BOWER, A. F., and GUDURU, P. R. In situ measurements of stress-potential coupling in lithiated silicon. Journal of the Electrochemical Society, 157, A1253–A1261 (2010)CrossRefGoogle Scholar
  27. [27]
    HE, Y., YU, X., LI, G., WANG, R., LI, H., WANG, Y., GAO, H., and HUANG, X. Shape evolution of patterned amorphous and polycrystalline silicon microarray thin film electrodes caused by lithium insertion and extraction. Journal of Power Sources, 216, 131–138 (2012)CrossRefGoogle Scholar

Copyright information

© Shanghai University and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  • Jun Yin
    • 1
  • Xianjun Shao
    • 1
  • Bo Lu
    • 1
  • Yicheng Song
    • 2
    • 3
  • Junqian Zhang
    • 2
    • 3
    • 4
  1. 1.Shanghai Institute of Applied Mathematics and MechanicsShanghai UniversityShanghaiChina
  2. 2.Department of MechanicsShanghai UniversityShanghaiChina
  3. 3.Shanghai Key Laboratory of Mechanics in Energy EngineeringShanghai UniversityShanghaiChina
  4. 4.Materials Genome InstituteShanghai UniversityShanghaiChina

Personalised recommendations