A phase field model for chemo mechanical induced fracture in lithium ion battery electrode particles
(c) 2016 John Wiley Sons, Ltd. Capacity fade in conventional Li ion battery systems due to chemo mechanical degradation during charge discharge cycles is the bottleneck in high performance battery design. Stresses generated by diffusion mechanical coupling in Li ion intercalation and deintercalation cycles, accompanied by swelling and shrinking at finite strains, cause micro cracks, which finally disturb the electrical conductivity and isolate the electrode particles. This leads to battery capacity fade. As a first attempt towards a reliable description of this complex phenomenon, we propose a novel finite strain theory for chemo elasticity coupled with phase field modeling of fracture, which regularizes a sharp crack topology. We apply a rigorous geometric approach to the diffusive crack modeling based on the introduction of a global evolution equation of regularized crack surface, governed by the crack phase field. The irreversible evolution of the crack phase field is modeled through a novel critical stress based growth function. A modular concept is outlined for linking of the diffusive crack modeling to the complex chemo elastic material response of the bulk material. Here, we incorporate standard as well as gradient extended Cahn Hilliard type diffusion for the Li ions, where the latter accounts for a possible phase segregation. From the viewpoint of the methodology, the separation of modules for the crack evolution and the bulk response provides a highly attractive and transparent structure of the multi physics problem. This structure is exploited on the numerical side by constructing a robust finite element method, based on an algorithmic decoupling of updates for the crack phase field and the state variables of the chemo mechanical bulk response. We demonstrate the performance of the proposed coupled multi field formulation by an analysis of representative boundary value problems.