Scale effects induced by strain-gradient plasticity and interfacial resistance in periodic and randomly heterogeneous media

K. E. Aifantis, J. R. Willis

Research output: Contribution to journalArticlepeer-review

40 Scopus citations

Abstract

A recently introduced variational formulation for strain-gradient plasticity with an additional potential that penalises the build-up of plastic strain at interfaces is summarised and applied to some one-dimensional examples. Novel features include a new strict upper bound for the effective potential of a single nonlinear medium containing interfaces distributed according to a Poisson process and approximate mean stress versus mean plastic strain curves for media with two power-law nonlinear phases separated by interfaces with their own nonlinear potential. Two-phase media with periodic and random microstructure are considered. In the case of random media, the results depend on the statistics of points, taken two at a time, in the combinations medium-medium, medium-interface, and interface-interface. In every case, the effective relation displays a Hall-Petch type of effect, the effective response becoming stiffer as the scale of the microstructure is refined. The admission of the interfacial potential removes a limitation of earlier work, that the response could not exceed the "Voigt" or "Taylor" bound of the corresponding classical material.

Original languageEnglish (US)
Pages (from-to)702-716
Number of pages15
JournalMechanics of Materials
Volume38
Issue number8-10
DOIs
StatePublished - Aug 1 2006

Keywords

  • Hall-Petch effect
  • Random medium
  • Strain-gradient plasticity
  • Three-point bound
  • Two-point bound
  • Variational principle

ASJC Scopus subject areas

  • Instrumentation
  • Materials Science(all)
  • Mechanics of Materials

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