Abstract
Diffusion-induced stress caused by the insertion and extraction of lithium ions can result in the swelling, fracture, and even pulverization of the battery electrodes. However, only a few previous studies consider the phenomenon of phase transformation in an electrode and rarely take the impacts of cylindrical shape with transversely isotropic properties into account. In this paper, by researching the electronic reaction and diffusion process, a new theoretical model is established to study the stress level and mechanical behavior in cylindrical electrodes with phase transformation under galvanostatic operation. From the model, the brittle center and edge cracks are analyzed to investigate the influence of the initiation position on crack propagation. The tangential stress plays an important role in cracking on the electrodes. Furthermore, it is found for the center crack that it tends to grow more easily in the first insertion when the crack locates at the phase interface position, while for the edge crack, it tends to grow more easily in the early stage of lithium ion extraction. Moreover, manufacturing the electrodes with the appropriate property ratios, the diffusion-induced stress level and brittle crack-induced stress intensity factor value may decrease, and the electrode fracture phenomenon could be alleviated to some degree. Overall, our work provides a theoretical basis for the electrode phase transformation and cracking when the battery is working, and it may help us understand more about the internal mechanical behavior of the battery electrodes.
Similar content being viewed by others
References
Lyu, D., Ren, B., Li, S.: Failure modes and mechanisms for rechargeable Lithium-based batteries: a state-of-the-art review. Acta. Mech. (2019). https://doi.org/10.1007/s00707-018-2327-8
Drozdov, A.D.: A model for the mechanical response of electrode particles induced by lithium diffusion in Li-ion batteries. Acta. Mech. (2014). https://doi.org/10.1007/s00707-014-1096-2
Chen, B., Zhou, J., Pang, X., Wei, P., Yunbo, W., Deng, K.: Fracture damage of nanowire lithium-ion battery electrode affected by diffusion-induced stress and bending during lithiation. RSC Adv. (2014). https://doi.org/10.1039/c4ra01724b
Zhang, Y.: Simulation of crack behavior of secondary particles in Li-ion battery electrodes during lithiation/de-lithiation cycles. Int. J. Mech. Sci. (2019). https://doi.org/10.1016/j.ijmecsci.2019.02.042
Chengjun, X., Weng, L., Ji, L., Zhou, J.: An analytical model for the fracture behavior of the flexible lithium-ion batteries under bending deformation. Eur. J. Mech. A-Solids (2019). https://doi.org/10.1016/j.euromechsol.2018.06.012
Hui, W., Xie, Z., Wang, Y., Chunsheng, L., Ma, Z.: Modeling diffusion-induced stress on two-phase lithiation in lithium-ion batteries. Eur. J. Mech. A-Solids (2018). https://doi.org/10.1016/j.euromechsol.2018.04.005
Hanzhong, X., Yulan, L., Wang, B.: Mechano-electrochemical and buckling analysis of composition-gradient nanowires electrodes in lithium-ion battery. Acta. Mech. (2019). https://doi.org/10.1007/s00707-019-02486-9
Weng, L., Zhou, J., Cai, R.: Analytical model of Li-ion diffusion-induced stress in nanowire and negative Poisson’s ratio electrode under different operations. Int. J. Mech. Sci. (2018). https://doi.org/10.1016/j.ijmecsci.2018.04.013
Chengjun, X., Weng, L., Chen, B., Zhou, J., Cai, R.: An analytical model for the fracture behavior in hollow cylindrical anodes. Int. J. Mech. Sci. (2019). https://doi.org/10.1016/j.ijmecsci.2019.04.035
Yuyang, L., Ai, K.S., Yong, N., Linghui, H.: Understanding size-dependent migration of a two-phase lithiation front coupled to stress. Acta. Mech. (2019). https://doi.org/10.1007/s00707-018-2303-3
Salvadori, A., Grazioli, D., Geers, M.G.D.: Governing equations for a two-scale analysis of Li-ion battery cells. Int. J. Solids Struct. (2015). https://doi.org/10.1016/j.ijsolstr.2015.01.014
Ovejas, V.J., Cuadras, A.: State of charge dependency of the overvoltage generated in commercial Liion cells. J. Power Sour. (2019). https://doi.org/10.1016/j.jpowsour.2019.02.046
Linda, Y., Lim, N., Liu, Y., Cui, M.F. Toney: understanding phase transformation in crystalline ge anodes for li-ion batteries. Chem. Mater. (2014). https://doi.org/10.1021/cm501233k
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. (2011). https://doi.org/10.1149/1.3565183
Chen, B., Zhou, J., Cai, R.: Analytical model for crack propagation in spherical nano electrodes of lithium-ion batteries. Electrochim. Acta (2016). https://doi.org/10.1016/j.electacta.2016.05.136
Esmizadeh, S., Haftbaradaran, H., Mossaiby, F.: An investigation of the critical conditions leading to deintercalation induced fracture in two-phase elastic electrode particles using a moving interphase core-shell model. Eur. J. Mech. A-Solids (2019). https://doi.org/10.1016/j.euromechsol.2018.10.019
Haftbaradaran, H., Maddahian, A., Mossaiby, F.: A fracture mechanics study of the phase separating planar electrodes: Phase field modeling and analytical results. J. Power Sour. (2017). https://doi.org/10.1016/j.jpowsour.2017.03.073
Woodford, W.H., Chiang, Y.-M., Carter, W.C.: “Electrochemical Shock” of intercalation electrodes: a fracture mechanics analysis. J. Electrochem. Soc. (2010). https://doi.org/10.1149/1.3464773
Cheng, G., Zhang, Y., Chang, T.-H., Liu, Q., Chen, L., Lu, W.D., Zhu, T., Zhu, Y.: In situ nano-thermomechanical experiment reveals brittle to ductile transition in silicon nanowires. Nano Lett. (2019). https://doi.org/10.1021/acs.nanolett.9b01789
Zhang, X.Y., Hao, F., Chen, H.-S., Fang, D.-N.: Diffusion-induced stresses in transversely isotropic cylindrical electrodes of lithium-ion batteries. J. Electrochem. Soc. (2014). https://doi.org/10.1149/2.0991414jes
Shen, L., Li, J.: Transversely isotropic elastic properties of single-walled carbon nanotubes. Phys. Rev. B (2004). https://doi.org/10.1103/PhysRevB.69.045414
Li, J., Fang, Q., Liu, F., Liu, Y.: Analytical modeling of dislocation effect on diffusion-induced stress in a cylindrical lithium ion battery electrode. J. Power Sour. (2014). https://doi.org/10.1016/j.jpowsour.2014.07.191
Cheng, Y.-T., Verbrugge, M.W. : Evolution of stress within a spherical insertion electrode particle under potentiostatic and galvanostatic operation. J. Power Sour. (2009). https://doi.org/10.1016/j.jpowsour.2009.01.021
Li, X., Fang, Q., Li, J., Hong, W., Liu, Y., Wen, P.: Diffusion-induced stress and strain energy affected by dislocation mechanisms in a cylindrical nanoanode. Solid State Ion. (2015). https://doi.org/10.1016/j.ssi.2015.08.016
Zhang, X., Shyy, W., Sastrya, A.M.: Numerical simulation of intercalation-induced stress in li-ion battery electrode particles. J. Electrochem. Soc. (2007). https://doi.org/10.1149/1.2759840
Song, Y., Shao, X., Guo, Z., Zhang, J.: Role of material properties and mechanical constraint on stress-assisted diffusion in plate electrodes of lithium ion batteries. J. Phys. D: Appl. Phys (2013). https://doi.org/10.1088/0022-3727/46/10/105307
Crank, J.: The Mathematics of Diffusion. Oxford University, Oxford (1975)
Tanmay, K., Bhandakkar, H.G.: Cohesive modeling of crack nucleation in a cylindrical electrode under axisymmetric diffusion-induced stresses. Int. J. Solids Struct. (2011). https://doi.org/10.1016/j.ijsolstr.2011.04.005
Li, Y., Zhang, K., Zheng, B., Yang, F.: Effect of local deformation on the coupling between diffusion and stress in lithium-ion battery. Int. J. Solids Struct. (2016). https://doi.org/10.1016/j.ijsolstr.2016.02.029
Guzmán, S., Gálvez, J.C., Sancho, J.M.: Modelling of chloride ingress into concrete through a single-ion approach. Application to an idealized surface crack pattern. Int. J. Numer. Anal. Meth. Geomech. (2014). https://doi.org/10.1002/nag.2273
Anderson, T.L.: Fracture Mechanics Fundamentals and Applications-Third Edition. CRC Press, Boca Raton (2005)
Tada, H., Paris, P.C., Irwin, G.R.: The Stress Analysis of Cracks Handbook. ASME Press, New York (2000)
Wang, X., Fan, F., Wang, J., Wang, H., Tao, S., Yang, A., Liu, A., Chew, H.B., Mao, S.X., Zhu, T., Xia, S.: High damage tolerance of electrochemically lithiated silicon. Nat. Commun. (2015). https://doi.org/10.1038/ncomms9417
Zhang, S., Zhao, K., Zhu, T., Ju, L.: Electrochemomechanical degradation of high-capacity battery electrode materials. Prog. Mater. Sci. (2017). https://doi.org/10.1016/j.pmatsci.2017.04.014
Zhang, L., Song, Y., He, L., Ni, Y.: Variations of boundary reaction rate and particle size on the diffusion-induced stress in a phase separating electrode. J. Appl. Phys. (2014). https://doi.org/10.1063/1.4897459
Huang, S., Fan, F., Li, J., Zhang, S., Zhu, T.: Stress generation during lithiation of high-capacity electrode particles in lithium ion batteries. Acta. Mater. (2013). https://doi.org/10.1016/j.actamat.2013.04.007
Xie, Z., Ma, Z., Wang, Y., Zhou, Y., Chunsheng, L.: A kinetic model for diffusion and chemical reaction of silicon anode lithiation in lithium ion batteries. RSC Adv. (2016). https://doi.org/10.1039/c5ra27817a
Acknowledgements
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 (KYCX19_0852), 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 well as the Ph.D. programs Foundation of Ministry of Education of China (20133221110008).
Author information
Authors and Affiliations
Corresponding authors
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Appendix
Appendix
See Table 1.
Rights and permissions
About this article
Cite this article
Weng, L., Xu, C., Chen, B. et al. Theoretical analysis of the mechanical behavior in Li–ion battery cylindrical electrodes with phase transformation. Acta Mech 231, 1045–1062 (2020). https://doi.org/10.1007/s00707-019-02589-3
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00707-019-02589-3