Three-dimensional cellular automata modelling of cleavage propagation across crystal boundaries in polycrystalline microstructures

Anton Shterenlikht, Lee Margetts

Research output: Contribution to journalArticle (Academic Journal)peer-review

19 Citations (Scopus)
247 Downloads (Pure)

Abstract

A three-dimensional cellular automata (CA) with rectilinear layout is used in this work to create and cleave polycrystalline microstructures. Each crystal is defined by a unique randomly generated orientation tensor. Separate states for grains, grain boundaries, crack flanks and crack fronts are created. Algorithms for progressive cleavage propagation through crystals and across grain boundaries are detailed. The mesh independent cleavage criterion includes the critical cleavage stress and the length scale. Resolution of an arbitrary crystallographic plane within a 26-cell Moore neighbourhood is considered. The model is implemented in Fortran 2008 coarrays. The model gives realistic predictions of grain size and mis-orientation distributions, grain boundary topology and crack geometry. Finally, we show how the proposed CA model can be linked to a finite-element model to produce a multi-scale fracture framework.
Original languageEnglish
Article number20150039
Number of pages19
JournalProceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Volume471
Issue number2177
Early online date8 May 2015
DOIs
Publication statusPublished - 8 May 2015

Keywords

  • cellular automata
  • finite-elements
  • cleavage
  • polycrystals
  • grain boundary
  • three-dimensional

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