The mode III full-field solution in elastic materials with strain gradient effects

L. Zhang, Y. Huang*, J. Y. Chen, K. C. Hwang

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

70 Scopus citations


The near-tip asymptotic field and full-field solution are obtained for a mode III crack in an elastic material with strain gradient effects. The asymptotic analysis shows that, even though the near-tip field is governed by a single parameter B (similar to the mode III stress intensity factor), the near-tip field is very different from the classical KIII field; stresses have r-3/2 singularity near the crack tip, and are significantly larger than the classical KIII field within a zone of size l to the crack tip, where l is an intrinsic material length, depending on microstructures in the material. This high-order stress singularity, however, does not violate the boundness of strain energy around a crack tip. The parameter B of the near-tip asymptotic field has been determined for two anti-plane shear loadings: the remotely imposed classical KIII field, and the arbitrary shear stress tractions on crack faces. The mode III full-field solution is obtained analytically for an elastic material with strain gradient effects subjected to remotely imposed classical KIII field. It shows that the near-tip asymptotic field dominates within a zone of size 0.5l to the crack tip, while strain gradient effects are clearly observed within 5l. It is also shown that the conventional way to evaluate the crack tip energy release rate would lead to an incorrect, infinite value. A new evaluation gives a finite crack tip energy release rate, and is identical to the J-integral.

Original languageEnglish (US)
Pages (from-to)325-348
Number of pages24
JournalInternational Journal of Fracture
Issue number4
StatePublished - 1998


  • Full-field solution
  • Strain gradient effects

ASJC Scopus subject areas

  • Computational Mechanics
  • Modeling and Simulation
  • Mechanics of Materials


Dive into the research topics of 'The mode III full-field solution in elastic materials with strain gradient effects'. Together they form a unique fingerprint.

Cite this