Analytical model for crack propagation in spherical nano electrodes of lithium-ion batteries

To understand the mechanism of crack propagation in nano electrode materials due to lithium concentration variation during charging cycling, an analytical model is developed based on the diffusion induced stress evolution and crack propagation in a spherical particle electrode during phase transformation. In the model, the effect of the phase transformation on concentration variation, stress evolution and stress discontinuity is clarified. In addition, it has been found that concentration jumps result in hoop stress discontinuities, which can lead to crack at the interface. Then, the stress intensity factor is derived from the interface crack innano electrodes during galvanostatic charging. The stress intensity factors obtained indicate that interface crack will not propagate when stress intensity factor is less than the fracture toughness of electrode materials during lithiation. Significantly, failure mechanics criterion diagram with critical nanoparticle electrode size and current density is arrived. The present model maybe used to help the structural design for electrodes in lithium ion batteries.