Crack growth and fracture toughness of amorphous Li-Si anodes: Mechanisms and role of charging/discharging studied by atomistic simulations

摘要

Fracture is the main cause of degradation and capacity fading in lithiated silicon during cycling. Experiments on the fracture of lithiated silicon show conflicting results, and so mechanistic models can help interpret experiments and guide component design. Here, large-scale K-controlled atomistic simulations of crack propagation (R-curve K_I vs. Δa) are performed at Li_xSi compositions x=0.5,1.0,1.5 for as-quenched/relaxed samples and at x=0.5,1.0 for samples created by discharging from higher Li compositions. In all cases, the fracture mechanism is void nucleation, growth, and coalescence. In as-quenched materials, with increasing Li content the plastic flow stress and elastic moduli decrease but void nucleation and growth happen at smaller stress, so that the initial fracture toughness K_(Ic)≈1.0MPam decreases slightly but the initial fracture energy J_(Ic) ≈ 10.5J/m~2 is similar. After 10 nm of crack growth, the fracture toughnesses increase and become similar at K_(Ic)≈1.9MPam across all compositions. Plane-strain equi-biaxial expansion simulations of uncracked samples provide complementary information on void nucleation and growth. The simulations are interpreted within the framework of Gurson model for ductile fracture, which predicts J_(Ic)=ασ_yD where α ≃ 1 and D is the void spacing, and good agreement is found. In spite of flowing plastically, the fracture toughness of Li_xSi is low because voids nucleate within nano-sized distances ahead of the crack (D ≈ 1nm). Scaling simulation results to experimental conditions, reasonable agreement with experimentally-estimated fracture toughnesses is obtained. The discharging process facilitates void nucleation but decreases the flow stress (as shown previously), leading to enhanced fracture toughness at all levels of crack growth. Therefore, the fracture behavior of lithiated silicon at a given composition is not a material property but instead depends on the history of charging/discharging. These findings indicate that the mechanical behavior (flow and fracture) of lithiated Si must be interpreted within a fully rate- and history-dependent framework.