# Phase Field Modeling of Chemomechanical Fracture of Intercalation Electrodes: Role of Charging Rate and Dimensionality

## TL;DR

This study uses phase-field modeling to analyze how charging rate and dimensionality influence crack formation in Li-ion battery cathodes, revealing different fracture behaviors in 2D and 3D geometries.

## Contribution

It introduces a thermodynamically consistent phase-field approach to quantify chemomechanical fracture in battery particles, including a derived power-law for critical flaw size dependence on charging rate.

## Key findings

- Critical flaw size depends on charging rate via a power-law.
- 2D and 3D crack propagation behaviors differ significantly.
- 3D cracks tend to bifurcate and limit inward penetration.

## Abstract

We investigate the fracture of Li-ion battery cathodic particles using a thermodynamically consistent phase-field approach that can describe arbitrarily complex crack paths and captures the full coupling between Li-ion diffusion, stress, and fracture. Building on earlier studies that introduced the concept of electrochemical shock, we use this approach to quantify the relationships between stable or unstable crack propagation, flaw size, and C-rate for 2D disks and 3D spherical particles. We find that over an intermediate range of flaw sizes, the critical flaw size for the onset of crack propagation depends on charging rate as an approximate power-law that we derive analytically. This scaling law is quantified in 2D by exhaustive simulations and is also supported by 3D simulations. In addition, our results reveal a significant difference between 2D and 3D geometries. In 2D, cracks propagate deep inside the particle in a rectilinear manner while in 3D they propagate peripherally on the surface and bifurcate into daughter cracks, thereby limiting inward penetration and giving rise to complex crack geometries.