Capturing the stress evolution in electrode materials that undergo phase transformations during electrochemical cycling

The present work sheds light on the stresses generated in a spherical particle subjected to phase transformations during ion-insertion. In order to account for the physical process that occurs during electrochemical cycling, the models used are those of small deformation and account for the effects of phase transformation, chemo-mechanical coupling and concentration-dependent material properties. The two-phase lithiation is modeled by the Cahn–Hilliard equation. It is found that the DISs arise from the inhomogeneous volume expansions resulting from Li concentration gradients and the hydrostatic stress facilitates the diffusion of Li-ions under elastic deformation while it hinders diffusion in the plastic case. When the elastic modulus is reduced the magnitude of the diffusion-induced stress decreases but the strain increases under elastic deformation whereas the opposite occurs for the plastic case. Furthermore, if the electrode is assumed to undergo strain softening during plastic deformation, smaller stresses and higher plastic strains are predicted than when strain hardening is assumed. The novelty of this work is that the proposed models highlight the importance of chemo-mechanical coupling effects, concentration-dependent material properties and plastic deformation on diffusion-induced stresses. These findings render prospective insights for designing next-generation mechanically stable phase transforming electrode materials.