Interpreting the softening of nanomaterials through gradient plasticity

Xu Zhang, Katerina E. Aifantis

Research output: Contribution to journalArticlepeer-review

21 Scopus citations


Experimental and simulation studies have shown that decreasing the grain size below a critical value results in softening rather than hardening in both the yield stress and flow stress of nanomaterials. In this work, a gradient plasticity framework is presented that can capture this softening behavior by treating grain boundaries as a separate phase with a finite thickness. The theoretical expression obtained for the yield stress as a function of the grain size can capture numerous experimental data that exhibit this "normal" to "abnormal" Hall-Petch transition, and an analytical equation is obtained that can predict the grain size at which this transition occurs. Furthermore, analytical expressions are obtained for the flow stress in nanomaterials, and they are in precise agreement with atomistic simulations on nanocrystalline Cu, which predict that below a critical grain size the flow stress decreases proportional to it.

Original languageEnglish (US)
Pages (from-to)1399-1405
Number of pages7
JournalJournal of Materials Research
Issue number11
StatePublished - Jun 14 2011
Externally publishedYes

ASJC Scopus subject areas

  • Materials Science(all)
  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering


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