A phase-field model for chemo-mechanical induced fracture in lithium-ion battery electrode particles


MIEHE C., DAL H. , SCHAENZEL L. -. , RAINA A.

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, vol.106, no.9, pp.683-711, 2016 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 106 Issue: 9
  • Publication Date: 2016
  • Doi Number: 10.1002/nme.5133
  • Title of Journal : INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING
  • Page Numbers: pp.683-711
  • Keywords: fracture, phase-field modeling, chemo-mechanics, swelling, finite strains, Li-ion batteries, DIFFUSION-INDUCED STRESS, SOFTENING CONSTITUTIVE-EQUATIONS, INTERCALATION-INDUCED STRESS, BRITTLE CRACK-PROPAGATION, CAHN-HILLIARD-TYPE, VARIATIONAL-PRINCIPLES, STRONG DISCONTINUITIES, STORAGE PARTICLE, SOLID MECHANICS, GENERATION

Abstract

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. Copyright (c) 2015 John Wiley & Sons, Ltd.