# Vulnerable Window of Yield Strength for Swelling-Driven Fracture of Phase-Transforming Battery Materials

## TL;DR

This paper uses a phase-field model to identify a critical yield strength window where swelling-driven fractures occur in phase-transforming battery materials, revealing different fracture modes and the impact of geometry on stability.

## Contribution

It introduces a multi-physics phase-field approach to explicitly model fracture in phase-transforming battery materials, advancing understanding of fracture mechanisms beyond Griffith's criterion.

## Key findings

- Identification of a vulnerable yield strength window for fracture
- Different fracture modes depending on yield strength
- Hollow nanopillar geometry enhances fracture resistance

## Abstract

Despite numerous experimental and theoretical investigations of the mechanical behavior of high-capacity Si and Ge Li-ion battery anodes, our basic understanding of swelling-driven fracture in these materials remains limited. Existing theoretical studies have provided insights into elasto-plastic deformations caused by large volume change phase transformations, but have not modeled fracture explicitly beyond Griffith's criterion. Here we use a multi-physics phase-field approach to model self-consistently anisotropic phase transformation, elasto-plastic deformation, and crack initiation and propagation during lithiation of Si nanopillars. Our results reveal the existence of a vulnerable window of yield strength inside which pillars fracture during lithiation. They identify two different modes of fracture inside that window with and without surface localization of plastic deformation prior to fracture for lower and higher yield strength, respectively, and highlight the importance of taking into account this localization to accurately predict the onset of fracture within Griffith theory. The results further demonstrate how the increased robustness of hollow nanopillars can be understood as a direct effect of anode geometry on the size of this vulnerable window. Those insights provide an improved theoretical basis for designing mechanically stable phase-transforming battery materials undergoing large volume changes.