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Acta Mechanica

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29-06-2021 | Original Paper

Transient analysis of diffusion-induced stress for hollow cylindrical electrode considering the end bending effect

Authors: Xingquan Wang, Xia Liu, Qingsheng Yang

Published in: Acta Mechanica | Issue 9/2021

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Abstract

Lithiation and delithiation in electrodes lead to the evolution of internal stresses which may cause the mechanical degradation of batteries. In this work, the diffusion-induced stress of a hollow cylindrical electrode under either galvanostatic or potentiostatic charging is analytically solved based on a diffusion and mechanical coupled continuum model. The stress distributions at the end faces of the electrode with both ends traction free or fixed are also analyzed, the end effect of diffusion-induced bending is taken into account, and the resulting bending stresses are of practical importance for the stress distribution at the end faces. Using the obtained analytical expressions, a numerical example is given, and the results show that the stress distributions at the end faces change dramatically compared to the stresses remote from ends, both the charging mode and end constraints have significant effects on the distribution of stresses at the end faces of the electrodes, and the most dangerous location during the charging process is affected by the end’s constraint conditions.

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Yan, P., Zheng, J., Gu, M., Xiao, J., Zhang, J.G., Wang, C.M.: Intragranular cracking as a critical barrier for high-voltage usage of layer-structured cathode for lithium-ion batteries. Nat. Commun. 8, 14101 (2017). https://doi.org/10.1038/ncomms14101CrossRef

Palacin, M.R., de Guibert, A.: Why do batteries fail? Science 351(6273), 1253292 (2016). https://doi.org/10.1126/science.1253292CrossRef

Zhang, S., Zhao, K., Zhu, T., Li, J.: Electrochemomechanical degradation of high-capacity battery electrode materials. Prog. Mater .Sci. 89, 479–521 (2017). https://doi.org/10.1016/j.pmatsci.2017.04.014CrossRef

Shi, F., Song, Z., Ross, P.N., Somorjai, G.A., Ritchie, R.O., Komvopoulos, K.: Failure mechanisms of single-crystal silicon electrodes in lithium-ion batteries. Nat. Commun. (2016). https://doi.org/10.1038/ncomms11886CrossRef

Zhang, S.: Chemomechanical modeling of lithiation-induced failure in high-volume-change electrode materials for lithium ion batteries. NPJ Comput. Mater. (2017). https://doi.org/10.1038/s41524-017-0009-zCrossRef

Mendez, J.P., Ponga, M., Ortiz, M.: Diffusive molecular dynamics simulations of lithiation of silicon nanopillars. J. Mech. Phys. Solids 115, 123–141 (2018). https://doi.org/10.1016/j.jmps.2018.03.008MathSciNetCrossRef

Koohbor, B., Sang, L., Çapraz, Ö.Ö., Gewirth, A.A.: In situ strain measurement in solid-state Li-ion battery electrodes. J. Electrochem. Soc. 168(1), 010516 (2021). https://doi.org/10.1149/1945-7111/abd60bCrossRef

Prussin, S.: Generation and Distribution of dislocations by solute diffusion. J. Appl. Phys. 32(10), 1876–1881 (1961). https://doi.org/10.1063/1.1728256CrossRef

Lee, S., Wang, W.L., Chen, J.R.: Diffusion-induced stresses in a hollow cylinder. Mater. Sci. Eng. 285(1–2), 186–194 (2000)CrossRef

10.

Cheng, Y.-T., Verbrugge, M.W.: The influence of surface mechanics on diffusion induced stresses within spherical nanoparticles. J. Appl. Phys. (2008). https://doi.org/10.1063/1.3000442CrossRef

11.

Deshpande, R., Cheng, Y.-T., Verbrugge, M.W.: Modeling diffusion-induced stress in nanowire electrode structures. J. Power Sour. 195(15), 5081–5088 (2010). https://doi.org/10.1016/j.jpowsour.2010.02.021CrossRef

12.

Zhang, X.-Y., Chen, H.-S., Fang, D.: Effects of surface stress on lithium-ion diffusion kinetics in nanosphere electrodes of lithium-ion batteries. Int. J. Mech. Sci. (2020). https://doi.org/10.1016/j.ijmecsci.2019.105323CrossRef

13.

Cheng, Y.-T., Verbrugge, M.W.: Evolution of stress within a spherical insertion electrode particle under potentiostatic and galvanostatic operation. J. Power Sour. 190(2), 453–460 (2009). https://doi.org/10.1016/j.jpowsour.2009.01.021CrossRef

14.

Yang, X.-G., Bauer, C., Wang, C.-Y.: Sinusoidal current and stress evolutions in lithium-ion batteries. J. Power Sour. 327, 414–422 (2016). https://doi.org/10.1016/j.jpowsour.2016.07.070CrossRef

15.

Deshpande, R., Qi, Y., Cheng, Y.-T.: Effects of concentration-dependent elastic modulus on diffusion-induced stresses for battery applications. J. Electrochem. Soc. 157(8), A967–A971 (2010). https://doi.org/10.1149/1.3454762CrossRef

16.

Cai, X., Guo, Z.: Influence of Li concentration-dependent diffusion coefficient and modulus hardening on diffusion-induced stresses in anisotropic anode particles. J. Electrochem. Soc. 168(1), 010517 (2021). https://doi.org/10.1149/1945-7111/abd82eCrossRef

17.

Deshpande, R., Cheng, Y.-T., Verbrugge, M.W., Timmons, A.: Diffusion induced stresses and strain energy in a phase-transforming spherical electrode particle. J. Electrochem. Soc. 158(6), A718–A724 (2011). https://doi.org/10.1149/1.3565183CrossRef

18.

Zhang, X., Hao, F., Chen, H., Fang, D.: Diffusion-induced stress and delamination of layered electrode plates with composition-gradient. Mech. Mater. 91, 351–362 (2015)CrossRef

19.

Hu, H., Yu, P., Suo, Y.: Stress induced by diffusion and local chemical reaction in spherical composition-gradient electrodes. Acta Mech. 231(7), 2669–2678 (2020). https://doi.org/10.1007/s00707-020-02652-4CrossRefMATH

20.

Christensen, J., Newman, J.: Stress generation and fracture in lithium insertion materials. J. Solid State Electrochem. 10(5), 293–319 (2006). https://doi.org/10.1007/s10008-006-0095-1CrossRef

21.

Bower, A.F., Guduru, P.R., Sethuraman, V.A.: A finite strain model of stress, diffusion, plastic flow, and electrochemical reactions in a lithium-ion half-cell. J. Mech. Phys. Solids 59(4), 804–828 (2011). https://doi.org/10.1016/j.jmps.2011.01.003MathSciNetCrossRefMATH

22.

Zhang, X., Shyy, W., Sastry, A.M.: Numerical simulation of intercalation-induced stress in Li-ion battery electrode particles. J. Electrochem. Soc. 154(10), A910–A916 (2007). https://doi.org/10.1149/1.2759840CrossRef

23.

Bower, A.F., Guduru, P.R., Chason, E.: Analytical solutions for composition and stress in spherical elastic-plastic lithium-ion electrode particles containing a propagating phase boundary. Int. J. Solids Struct. 69–70, 328–342 (2015). https://doi.org/10.1016/j.ijsolstr.2015.05.018CrossRef

24.

Christensen, J., Newman, J.: A mathematical model of stress generation and fracture in lithium manganese oxide. J. Electrochem. Soc. 153(6), A1019–A1030 (2006). https://doi.org/10.1149/1.2185287CrossRef

25.

Cui, Z., Gao, F., Qu, J.: A finite deformation stress-dependent chemical potential and its applications to lithium ion batteries. J. Mech. Phys. Solids 60(7), 1280–1295 (2012). https://doi.org/10.1016/j.jmps.2012.03.008MathSciNetCrossRef

26.

Anand, L.: A Cahn-Hilliard-type theory for species diffusion coupled with large elastic-plastic deformations. J. Mech. Phys. Solids 60(12), 1983–2002 (2012). https://doi.org/10.1016/j.jmps.2012.08.001MathSciNetCrossRefMATH

27.

Zhang, K., Li, Y., Wang, F., Zheng, B., Yang, F., Lu, D.: An analytical model for lithiation-induced concurrent plastic flow and phase transformation in a cylindrical silicon electrode. Int. J. Solids Struct. 202, 87–98 (2020). https://doi.org/10.1016/j.ijsolstr.2020.06.008CrossRef

28.

Chen, Y., Chen, H., Luan, W.: Shakedown, ratcheting and fatigue analysis of cathode coating in lithium-ion battery under steady charging-discharging process. J. Mech. Phys. Solids 150, 104366 (2021). https://doi.org/10.1016/j.jmps.2021.104366MathSciNetCrossRef

29.

Drozdov, A.D.: A model for the mechanical response of electrode particles induced by lithium diffusion in Li-ion batteries. Acta Mech. 225(11), 2987–3005 (2014). https://doi.org/10.1007/s00707-014-1096-2MathSciNetCrossRefMATH

30.

Bagheri, A., Arghavani, J., Naghdabadi, R., Brassart, L.: A theory for coupled lithium insertion and viscoplastic flow in amorphous anode materials for Li-ion batteries. Mech. Mater. (2021). https://doi.org/10.1016/j.mechmat.2020.103663CrossRef

31.

Larché, F., Cahn, J.W.: A linear theory of thermochemical equilibrium of solids under stress. Acta Metall. 21(8), 1051–1063 (1973). https://doi.org/10.1016/0001-6160(73)90021-7CrossRef

32.

Liu, Y., Lv, P., Ma, J., Bai, R., Duan, H.L.: Stress fields in hollow core-shell spherical electrodes of lithium ion batteries. Proc. R. Soc. A Math. Phys. Eng. Sci. (2014). https://doi.org/10.1098/rspa.2014.0299

33.

Haftbaradaran, H., Qu, J.: Two-dimensional chemo-elasticity under chemical equilibrium. Int. J. Solids Struct. 56–57, 126–135 (2015). https://doi.org/10.1016/j.ijsolstr.2014.11.025CrossRef

34.

Gao, X., Fang, D., Qu, J.: A chemo-mechanics framework for elastic solids with surface stress. Proc. R. Soc. A Math. Phys. Eng. Sci. (2015). https://doi.org/10.1098/rspa.2015.0366

35.

Ryu, I., Choi, J.W., Cui, Y., Nix, W.D.: Size-dependent fracture of Si nanowire battery anodes. J. Mech. Phys. Solids 59(9), 1717–1730 (2011). https://doi.org/10.1016/j.jmps.2011.06.003CrossRef

36.

Eshghinejad, A., Li, J.: The coupled lithium ion diffusion and stress in battery electrodes. Mech. Mater. 91, 343–350 (2015). https://doi.org/10.1016/j.mechmat.2015.09.015CrossRef

37.

Bagheri, A., Arghavani, J., Naghdabadi, R.: On the effects of hydrostatic stress on Li diffusion kinetics and stresses in spherical active particles of Li-ion battery electrodes. Mech. Mater. (2019). https://doi.org/10.1016/j.mechmat.2019.103134CrossRef

38.

Chen, H., Huang, H.-Y.S.: Modeling and simulation of the non-equilibrium process for a continuous solid solution system in lithium-ion batteries. Int. J. Solids Struct. 212, 124–142 (2021). https://doi.org/10.1016/j.ijsolstr.2020.11.014CrossRef

39.

Holzapfel, M., Buqa, H., Scheifele, W., Novak, P., Petrat, F.M.: A new type of nano-sized silicon/carbon composite electrode for reversible lithium insertion. Chem. Commun. 12, 1566–1568 (2005). https://doi.org/10.1039/b417492eCrossRef

40.

Patel, P., Kim, I.S., Kumta, P.N.: Nanocomposites of silicon/titanium carbide synthesized using high-energy mechanical milling for use as anodes in lithium-ion batteries. Mater. Sci. Eng. B Solid State Mater. Adv. Technol. 116(3), 347–352 (2005). https://doi.org/10.1016/j.mseb.2004.05.046CrossRef

41.

Zhu, X., Xie, Y., Chen, H., Luan, W.: Numerical analysis of the cyclic mechanical damage of Li-ion battery electrode and experimental validation. Int. J. Fatigue 142, 105915 (2021). https://doi.org/10.1016/j.ijfatigue.2020.105915CrossRef

42.

Chan, C.K., Peng, H., Liu, G., McIlwrath, K., Zhang, X.F., Huggins, R.A., Cui, Y.: High-performance lithium battery anodes using silicon nanowires. Nat. Nanotechnol. 3(1), 31–35 (2008). https://doi.org/10.1038/nnano.2007.411CrossRef

43.

Xiao, X., Liu, P., Verbrugge, M.W., Haftbaradaran, H., Gao, H.: Improved cycling stability of silicon thin film electrodes through patterning for high energy density lithium batteries. J. Power Sour. 196(3), 1409–1416 (2011). https://doi.org/10.1016/j.jpowsour.2010.08.058CrossRef

44.

Bhandakkar, T.K., Gao, H.: Cohesive modeling of crack nucleation in a cylindrical electrode under axisymmetric diffusion induced stresses. Int. J. Solids Struct. 48(16–17), 2304–2309 (2011). https://doi.org/10.1016/j.ijsolstr.2011.04.005CrossRef

45.

Yao, Y., McDowell, M.T., Ryu, I., Wu, H., Liu, N., Hu, L., Nix, W.D., Cui, Y.: Interconnected silicon hollow nanospheres for lithium-ion battery anodes with long cycle life. Nano Lett. 11(7), 2949–2954 (2011). https://doi.org/10.1021/nl201470jCrossRef

46.

Zhang, K., Li, Y., Zheng, B., Wu, G., Wu, J., Yang, F.: Large deformation analysis of diffusion-induced buckling of nanowires in lithium-ion batteries. Int. J. Solids Struct. 108, 230–243 (2017). https://doi.org/10.1016/j.ijsolstr.2016.12.020CrossRef

47.

Zhang, K., Li, Y., Wu, J., Zheng, B., Yang, F.: Lithiation-induced buckling of wire-based electrodes in lithium-ion batteries: a phase-field model coupled with large deformation. Int. J. Solids Struct. 144–145, 289–300 (2018). https://doi.org/10.1016/j.ijsolstr.2018.05.014CrossRef

48.

Zhang, K., Li, Y., Wang, F., Zheng, B., Yang, F.: Stress effect on self-limiting lithiation in silicon-nanowire electrode. Appl. Phys. Express (2019). https://doi.org/10.7567/1882-0786/ab0ce8CrossRef

49.

Xing, H., Liu, Y., Wang, B.: Mechano-electrochemical and buckling analysis of composition-gradient nanowires electrodes in lithium-ion battery. Acta Mech. 230(12), 4145–4156 (2019). https://doi.org/10.1007/s00707-019-02486-9MathSciNetCrossRef

50.

Zhang, Y., Zhan, S., Zhang, K., Zheng, B., Lyu, L.: Buckling behavior of a wire-like electrode with a concentration-dependent elastic modulus based on a deformed configuration. Eur. J. Mech. A. Solids 85, 104111 (2021). https://doi.org/10.1016/j.euromechsol.2020.104111MathSciNetCrossRefMATH

51.

Chakraborty, J., Please, C.P., Goriely, A., Chapman, S.J.: Combining mechanical and chemical effects in the deformation and failure of a cylindrical electrode particle in a Li-ion battery. Int. J. Solids Struct. 54, 66–81 (2015). https://doi.org/10.1016/j.ijsolstr.2014.11.006CrossRef

52.

Guo, Z., Zhang, T., Hu, H., Song, Y., Zhang, J.: Effects of hydrostatic stress and concentration-dependent elastic modulus on diffusion-induced stresses in cylindrical li-ion batteries. J. Appl. Mech. (2013). https://doi.org/10.1115/1.4025271CrossRef

53.

Yang, F.: Effect of diffusion-induced bending on diffusion-induced stress near the end faces of an elastic hollow cylinder. Mech. Res. Commun. 51, 72–77 (2013). https://doi.org/10.1016/j.mechrescom.2013.05.006CrossRef

54.

Zhang, X.L., Zhong, Z.: A coupled theory for chemically active and deformable solids with mass diffusion and heat conduction. J. Mech. Phys. Solids 107, 49–75 (2017). https://doi.org/10.1016/j.jmps.2017.06.013MathSciNetCrossRef

55.

Wang, X.-Q., Yang, Q.-S.: An analytical solution for chemo-mechanical coupled problem in deformable sphere with mass diffusion. Int. J. Appl. Mech. (2020). https://doi.org/10.1142/s1758825120500763CrossRef

56.

Haftbaradaran, H., Song, J., Curtin, W.A., Gao, H.: Continuum and atomistic models of strongly coupled diffusion, stress, and solute concentration. J. Power Sour. 196(1), 361–370 (2011). https://doi.org/10.1016/j.jpowsour.2010.06.080CrossRef

57.

Timoshenko, S.: Strength of Materials, Part 2: Advanced Theory and Problems, 3rd edn. Van Nostrand Reinhold Company, New York (1958)MATH

58.

Crank, J.: The Mathematics of Diffusion, 2nd edn. Oxford University Press, Oxford (1975)MATH

59.

Song, Y., Lu, B., Ji, X., Zhang, J.: Diffusion induced stresses in cylindrical lithium-ion batteries: analytical solutions and design insights. J. Electrochem. Soc. 159(12), A2060–A2068 (2012). https://doi.org/10.1149/2.079212jesCrossRef

60.

Song, X., Lu, Y., Wang, F., Zhao, X., Chen, H.: A coupled electro-chemo-mechanical model for all-solid-state thin film Li-ion batteries: The effects of bending on battery performances. J. Power Sour. (2020). https://doi.org/10.1016/j.jpowsour.2020.227803CrossRef

Title: Transient analysis of diffusion-induced stress for hollow cylindrical electrode considering the end bending effect
Authors: Xingquan Wang
Xia Liu
Qingsheng Yang
Publication date: 29-06-2021
Publisher: Springer Vienna
Published in: Acta Mechanica / Issue 9/2021
Print ISSN: 0001-5970
Electronic ISSN: 1619-6937
DOI: https://doi.org/10.1007/s00707-021-03014-4

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Transient analysis of diffusion-induced stress for hollow cylindrical electrode considering the end bending effect

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