Non-existence of separable crack tip field in mechanism-based strain gradient plasticity

M. X. Shi, Y. Huang*, H. Gao, K. C. Hwang

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

35 Scopus citations


We investigate the structure of asymptotic crack tip fields associated with the recently developed theory of mechanism-based strain gradient (MSG) plasticity. The MSG plasticity theory directly connects micron scale plasticity to dislocation theories via a multiscale, hierarchical framework linking Taylor's dislocation hardening model to strain gradient plasticity. We show that the crack tip field in MSG plasticity does not have a separable form of solution. In contrast, all previously known asymptotic fields around stationary crack tips have separable form of solutions such as the classical K field, HRR field, crack tip field in the couple stress theory of strain gradient plasticity, and the crack tip field in the Fleck-Hutchinson phenomenological theory of strain gradient plasticity. The physical significance of this lack of separable solution of the crack tip field in MSG plasticity is that stresses at a distance on the order of dislocation spacing from a crack tip can no longer be characterized by a single parameter as in classical J-controlled crack tip fields. This difficulty can be overcome by combining MSG plasticity theory with a cohesive model of fracture.

Original languageEnglish (US)
Pages (from-to)5995-6010
Number of pages16
JournalInternational Journal of Solids and Structures
Issue number41
StatePublished - Oct 11 2000


  • Crack tip field
  • Mechanism-based strain gradient plasticity

ASJC Scopus subject areas

  • Modeling and Simulation
  • Materials Science(all)
  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering
  • Applied Mathematics


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