Analysis of a cylindrical silicon electrode with a pre-existing crack: Path-independent Ĵ-integral

Kai Zhang, Bailin Zheng, Fuqian Yang, Yong Li

Research output: Contribution to journalArticlepeer-review

6 Scopus citations


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.

Original languageEnglish
Article number105602
JournalInternational Journal of Mechanical Sciences
StatePublished - Jul 1 2020

Bibliographical note

Publisher Copyright:
© 2020 Elsevier Ltd


  • Crack
  • Fracture mechanics
  • Lithium-ion battery
  • Path-independent integral
  • Silicon electrode

ASJC Scopus subject areas

  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering
  • Aerospace Engineering
  • Ocean Engineering
  • Applied Mathematics
  • General Materials Science
  • Civil and Structural Engineering


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