An investigation of the critical conditions leading to deintercalation induced fracture in two-phase elastic electrode particles using a moving interphase core-shell model

Abstract

Phase separation has been widely observed in various energy storage systems, and is known to severely impact mechanical integrity and electrochemical performance in lithium intercalation materials. Core-shell type models have been extensively used for modeling diffusion, phase transformation, deformation, and stress generation in phase changing energy storage materials. The purpose of this work is to present a systematic fracture mechanics analysis of two-phase electrode particles with core-shell structure subject to deintercalation using both numerical and analytical models. Mechanical behavior of the host solid is assumed to follow small deformation linear elasticity, and geometry of the particles is considered to be cylindrical/spherical. A moving interphase model accounting for the effect of solution non-ideality is utilized in combination with the weight function method of fracture mechanics to numerically calculate stress intensity factors (SIFs) for pre-existing cracks at the particle surface. Further, an analytical solution in the limit of small surface fluxes and a semi-analytical solution in the presence of large surface fluxes are also developed for the maximum SIF which could arise for a pre-existing surface crack during a complete deintercalation half-cycle. Implication of the results in terms of prediction of a critical particle size to avoid fracture in two-phase electrode particles is also presented. Numerical results along with their comparison with analytical predictions are presented in terms of the concentration and stress profiles, maximum tensile hoop stress, and maximum SIFs for a range of two-phase regular solid solutions and subject to a broad range of surface deintercalation fluxes. We further examine the results of this work by considering a lithium deintercalation system whose thermodynamic behavior is considerably different from that of a regular solution, and the results found using analytical and numerical models are compared.