An analytical model for lithiation-induced concurrent plastic flow and phase transformation in a cylindrical silicon electrode

The plastic flow in a silicon electrode during lithiation can alter the stress state in the silicon electrode and retard the fracture of the silicon electrode. In this work, we develop a rate-dependent model to investigate the plastic flow and phase transformation, which concurrently occur during the lithiation of a cylindrical silicon electrode. Using a power law for the plastic-flow potential and neglecting elastic deformation, we obtain analytical solutions of the stresses in the silicon electrode, which are dependent on the temporal evolution of the interface between lithiated phase and un-lithiated phase. A simplified diffusion model, which captures the temporal evolution of the interface, is proposed in the framework of the Cahn-Hilliard phase-field theory. The numerical results are in good accord with the results from the phase-field model with finite deformation. Under galvanostatic operation, the stresses are dependent on the lithiation rate, and the stresses on the surface of the silicon electrode are independent of initial radius and lithiation time. Under potentiostatic operation, the stresses in a silicon electrode of a smaller radius is larger than that in a silicon electrode of a larger radius. The magnitudes of the stresses on the surface decrease with the increase of both initial radius and the lithiation time.