Analysis of a cylindrical silicon electrode with a pre-existing crack: Path-independent Ĵ-integral. (1st July 2020) - Zhang, Kai; Zheng, Bailin; Yang, Fuqian; Li, Yong
Highlights: We first demonstrate the path-independence of Ĵ -integral under chemomechanical loading. The path-independence of Ĵ -integral for active materials with concentration-dependent material properties is validated. We developed an incremental constitutive model accounting for the lithiation-induced plastic deformation. The effect of the crack size and the influx on the Ĵ-integral for a cylindrical Si-electrode with a central-slit crack is examined. Abstract: The cracking of the active materials in a lithium-ion battery as an adverse consequence of lithiation-induced deformation can significantly cause the capacity loss and likely result in catastrophic failure of the lithium-ion battery. Following the work by Kishimoto et al. [1], we introduce the Ĵ -integral for the elastoplastic deformation of an active material with a slit-type crack under chemomechanical loading in this work and prove that the Ĵ -integral is path-independent. We also demonstrate that the classical J -integral is path-dependent and is not appropriate for the fracture analysis of the lithiation-induced cracking of the active materials in lithium-ion batteries. Using the incremental constitutive model developed in this work, we numerically analyze the size dependence of the Ĵ -integral under a constant influx for a cylindrical Si-electrode with a central-slit crack. The numerical results reveal that the value of the Ĵ -integral increases with the increase of the crack size and the influx at the same lithiation time, and there exists a maximum value of the Ĵ -integral for a given physical-geometrical configuration. The lithiation-induced softening has a limited effect on the value of the Ĵ -integral. All of these results suggest that the Ĵ -integral can be used to analyze the lithiation-induced propagation of cracks in active materials.