An analytical model for the fracture behavior in hollow cylindrical anodes

Silicon cylindrical anodes suffer from chemo-mechanical degradation and unpredictable fracture problems in high performance lithium-ion batteries, which resulting in capacity fade. A new fracture model based on core-shell structure is derived in this work, which combines diffusion-induced stress and surface stress, to demonstrate the mechanical behavior including the evolution of diffusion-induced stress and stress intensity factor in the hollow cylindrical anode during lithiation and delithiation. By evaluating the evolution of the radial and circumferential cracks, we find that maximum stress intensity factor for the radial crack is larger than the circumferential crack, both for internal and external cracks, which indicates that the radial crack is more dangerous than the circumferential crack for a cylindrical anode. Furthermore, the critical sizes of the hollow cylindrical anode among various crack configurations are obtained. The radial cracks caused by the hoop stress are found to be more essential in determining critical size of the electrode. The present work provides the fracture behavior in Si cylindrical anode during lithiation, which is helpful to the understanding the chemo-mechanical degradation.