Cohesive zone model for crack propagation in crystalline silicon nanowires

A fracture of the active particle such as silicon anode results in a potential degradation in lithium-ion batteries with charge/discharge cycle. The massive volume expansion during the lithiation generates large stress which induces the cracking on its surface. We propose the finite element model to have a deep insight into the diffusion-induced stress with fracture process for crystalline silicon nanowires. This model is constructed based on the large deformation theory and cohesive zone model that can describe the failure of Si nanowires. At the beginning of lithiation, high compressive hoop stress is generated on its surface. However, further lithiation, the hoop stress near the surface become less compressive and tensile, which is associated with the “push out effect” as a result of the volume expansion of lithiated material near the phase boundary. When the diffusion induced tensile stress exceeds the fracture threshold, a crack is initiated on the surface and propagates continuously to the center of the silicon nanowire. This crack follows the phase boundary rapidly, but the crack growth speed decreases due to the neighboring compressive hoop stress generated near the phase boundary. From the observation of failure mechanism in Si, we characterize a critical size of Si nanowire, below which fracture can be averted, and we suggest a safe state of charge (safe SOC) depending on its radial size during lithiation.