Fatigue failure theory for lithium diffusion induced fracture in lithium-ion battery electrode particles

To gain better insights into the structural reliability of lithium-ion battery electrodes and the nucleation as well as propagation of cracks during the charge and discharge cycles, it is crucial to enhance our understanding of the degradation mechanisms of electrode particles. This work presents a rigorous mathematical formulation for a fatigue failure theory for lithium-ion battery electrode particles for lithium diffusion induced fracture. The prediction of fatigue cracking for lithium-ion battery during the charge and discharge steps is an particularly challenging task and plays an crucial role in various electronic-based applications. Here, to simulate fatigue cracking, we rely on the phase-field approach for fracture which is a widely adopted framework for modeling and computing fracture failure phenomena in solids. The primary goal here is to describe a variationally consistent energetic formulation for gradient-extended dissipative solids, which is rooted in incremental energy minimization. The formulation has been derived as a coupled system of partial differential equations (PDEs) that governs the gradient-extended elastic-chemo damage response. Additionally, since the damage mechanisms of the lithium-ion battery electrode particles result from swelling and shrinkage, an additive decomposition of the strain tensor is performed. Several numerical simulations with different case studies are performed to demonstrate the correctness of our algorithmic developments. Furthermore, we investigate the effect of randomly distributed micro cavities (voids) and micro notches on fracture resistance.