Cohesive modeling of crack formation in two-phase planar electrodes subject to diffusion induced stresses using the distributed dislocation method

Abstract

Phase separation arises in many materials systems as a result of solute intercalation. It is in particular known that the mechanical stresses resulting from phase separation in lithium-ion batteries can be large enough to cause formation of a variety of defects and degradation of the host electrode upon cycling. Fracture mechanics models have been previously developed for identifying the critical conditions which lead to the growth of a pre-existing crack in two-phase electrode particles. Relying on a cohesive zone model in combination with the distributed dislocation technique, this work examines critical conditions corresponding to the onset of crack formation in an initially crack-free two-phase electrode. Considering a phase separating planar electrode, we utilize a Cahn-Hilliard type phase field model for capturing evolution of the concentration profiles during both intercalation and deintercalation half-cycles. Crack formation in the electrode subject to the diffusion-induced stresses is considered to result from strain localization at the place of pre-existing defects or weaknesses in the material whose behavior is modelled using a linearly softening traction-separation law. Numerical solution of the governing equations allows identification of a flaw-tolerant electrode thickness below which crack formation in the electrode becomes suppressed in the sense that the maximum opening along the cohesive zone cannot reach the critical separation required for crack formation, and hence, failure in the electrode is predicted to be dominated by the theoretical strength of the material rather than by crack formation. Since in the limit of small surface fluxes, uniform axial stresses develop in the individual phases, results of the analyses are also examined with reference to the results which follow from the analysis of the planar structure subject to uniform tension.