Fractal properties of dynamic recrysatallized grain boundaries

Miki Takahashi, Hiroyuki Nagahama

Research output: Contribution to journalConference articlepeer-review

3 Citations (Scopus)


Microstructures (e.g., grain boundary structure) as manifestations of the mechanical behavior of deformed materials have several fractal properties. Here taking an example of grain boundary of recrystallized quartz shape produced under various deformation conditions (high temperature and strain rate), fractal properties of the boundary profiles are shown. Fractal analysis by using box-counting method for each grain gives an individual fractal dimension DI of each profile, that by using area-perimeter method for various sizes of grains gives a collective fractal dimension DC representing structural property. DI shows larger variation as grain size decreased, and DI converges to Dc as the grain size increases. Since the boundary serration during dynamic recrystallization should be determined by relative movement of its surrounded gains, DI becomes to vary from grain to grain. On the collective fractal dimension Dc, Dc correlates positively, linearly to logarithmic of Zener-Hollomon parameter combining the strain rate and the temperature. Based on the fractal concepts, the relationship can be explained theoretically by a modified grain boundary migration model, and the number of cross points on the grain boundary sectioned by an Euclidian curve can be interpreted as the structural parameter related to the Zener-Hollomon parameter.

Original languageEnglish
Pages (from-to)3563-3568
Number of pages6
JournalMaterials Science Forum
Issue number4
Publication statusPublished - 2003
EventThermec 2003 Processing and Manufacturing of Advanced Materials - Madrid, Spain
Duration: 2003 Jul 72003 Jul 11


  • Collective fractal dimension
  • Dynamic recrystallization
  • Fractal dimensional increment
  • GBM model
  • Grain boundary
  • Individual fractal dimension


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