Capacity fade induced by chemo-mechanical degradation during charge-discharge cycles is the bottleneck in the design of high-performance batteries, especially high-capacity electrode materials. In this paper, a flexible sigmoid function is used to create the two-phase electrochemical lithiation profile, describing a sharp phase boundary that separates the pristine core from the lithiated shell of an electrode particle. According to such a phase transition, an analytical solution of the stress evolution is obtained by introducing an electrochemical reaction layer into the plastic model. Finally, based on the theory of diffusion-induced stress and the energy principle, we determine the critical thickness of radius of a lithiated layer, at which fracture occurs.