Estimation of the Stress Intensity Factors for Surface Cracks in Spherical Electrode Particles Subject to Phase Separation

Experiments have frequently shown that phase separation in lithium-ion battery electrodes could lead to the formation of mechanical defects, hence causing capacity fading. The purpose of the present work has been to examine stress intensity factors for pre-existing surface cracks in spherical electrode particles during electrochemical deintercalation cycling using both analytical and numerical methods. To this end, we make use of a phase field model to examine the time-dependent evolution of the concentration and stress profiles in a phase separating spherical electrode particles. By using a geometrical approximation scheme proposed in the literature, stress intensity factors at the deepest point of the pre-existing surface cracks of semi-elliptical geometry are calculated with the aid of the well-established weight function method of fracture mechanics. By taking advantage of a sharp-interphase core-shell model, an analytical solution for the maximum stress intensity factors arising at the deepest point of the surface cracks during a complete deintercalation half-cycle is also developed. Numerical results for evolution of the concentration profile and the distribution of the hoop stresses in the particle are presented; further, the stress intensity factors found numerically based on the phase field model are compared with those predicted by the analytical core-shell model. The results of the numerical model suggest that the maximum stress intensity factor could significantly vary with changes in the surface flux, increasing potentially by a factor of two within the range of parameters considered here, when the concentration difference between the two phases is decreased.