Abstract
Random percolation theory is a common basis for modelling intergranular -phenomena such as cracking, corrosion or diffusion. However, crystallographic constraints in real microstructures dictate that grain boundaries are not assembled at random. In this work a Monte Carlo method is used to construct physically realistic networks composed of high-angle grain boundaries that are susceptible to intergranular attack, as well as twin-variant boundaries that are damage resistant. When crystallographic constraints are enforced, the simulated networks exhibit triple-junction distributions that agree with experiment and reveal the non-random nature of grain-boundary connectivity. The percolation threshold has been determined for several constrained boundary networks and is substantially different from the classical result of percolation theory; compared with a randomly assembled network, about 50-75% more resistant boundaries are required to break up the network of susceptible boundaries. Triple-junction distributions are also shown to capture many details of the correlated percolation problem and to provide a simple means of ranking microstructures.
Original language | English (US) |
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Pages (from-to) | 711-726 |
Number of pages | 16 |
Journal | Philosophical Magazine |
Volume | 83 |
Issue number | 6 |
DOIs | |
State | Published - Feb 21 2003 |
Funding
ACKNOWLEDGEMENTS This work was performed under the auspices of the US Department of Energy at the University of California Lawrence Livermore National Laboratory under contract W-7405-Eng-48.
ASJC Scopus subject areas
- Condensed Matter Physics