International Journal of Mechanical Sciences (00207403)290
Solid-state batteries are promising candidates for the next-generation energy storage technology, as they circumvent the cyclic stability and safety issues of the traditional liquid-electrolyte Li-ion technology. Solid electrolytes are less reactive and enable using Li-metal anodes, increasing the energy density of battery cells. However, Li dendrites nucleating at pores, grain boundaries, and cracks, particularly when the current density exceeds a critical level, have been found to penetrate the solid electrolyte, resulting in short circuit and battery failure. While existing fracture mechanics-based models of dendrite usually examine Li-filled cracks, recent experiments have shown that a Li dendrite formed inside a crack can induce fracture growth well before filling it. This work aims to develop a model for this largely unexplained behaviour by considering a Li dendrite as it grows inside a crack from an initially small nucleus. The model couples solid electrolyte deformation, stress-driven Li diffusion along the dendrite-electrolyte interface, and stress-dependent Butler-Volmer kinetics of Li deposition into the crack. A finite element formulation developed for solving the governing equations is applied to two types of solid electrolytes to examine simultaneous evolution of the stress profile, dendrite thickness profile, dendrite length, and the stress intensity factor. By considering a realistic range of model parameters, it is shown that dendrite thickening, as compared to lengthening, promoted by a lower interfacial diffusivity, a higher interfacial resistance, and a higher applied current density, can mediate crack growth before dendrite fills the crack. Both assumptions and predictions of the model are discussed with reference to the existing literature, and model predictions are compared to the experiments. © 2025
