Lithiation-induced buckling of wire-based electrodes in lithium-ion batteries: A phase-field model coupled with large deformation

Wire-based electrodes can experience buckling during lithiation, which can lead to the capacity fading of lithium-ion batteries. This work is focused on the buckling behavior of wire-based electrodes induced by a two-phase lithiation reaction process. A Cahn-Hilliard type phase-field model coupled with large deformation is proposed. A modified critical buckling load is proposed as a function of the state of charge, which can be used in the analysis of lithiation-induced instability of wire-based electrodes. The coupling equations are solved by the PDE (partial differential equation) module in the Multiphysics of COMSOL. The numerical results show that the critical buckling time for the onset of buckling decreases with the increase of the wire length and current density. The single-phase reaction case is also studied to compare with the two-phase reaction case. The numerical results reveal that the critical buckling time for a wire with the two-phase reaction is the same as that with the single-phase reaction for the same geometries and the same C-rate in accord with the analytical analysis. The constraints to the ends of a wire play an important role in determining the critical buckling time for both cases, and a “stronger” constraint will increase the critical buckling time. Numerical analysis is used to determine the critical length, above which the buckling occurs prior to the onset of phase separation, and reveal the dependence of the critical length on the C-rate and the constraint condition. The effect of the wire length on the critical buckling state of charge (SOC) is independent of the lithiation mechanism, which is consistent with the analytical solution from the theory of linear elasticity. The larger the aspect ratio, the closer is the interphase position at the onset of the buckling to the outer surface of the wire.