PHILOSOPHICAL MAGAZINE, 2003, VOL. 83, NO. 6, 711–726 Connectivity and percolation in simulated grain-boundary networks Christopher A. Schuh, Roger W. Minich and Mukul Kumary University of California, Lawrence Livermore National Laboratory, Livermore, California 94550, USA [Received 21 June 2002 and accepted in revised form 2 October 2002] 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. } 1. Introduction Intergranular phenomena, including corrosion, cracking and diffusion, have fre- quently been regarded as percolative phenomena (Wells et al. 1989, Lim and Watanabe 1990, Palumbo et al. 1991, Aust et al. 1994, Watanabe 1994, Pan et al. 1995, Gertsman and Tangri 1997, Lehockey et al. 1998, Kononenko etal. 2001). In this framework, grain boundaries are classified as being either ‘susceptible’ or ‘resis- tant’ to intergranular attack, and random bond percolation theory (for example Stauffer and Aharony (1992)) has commonly been used to predict, firstly, the size scale of susceptible boundary paths or, secondly, the threshold fraction of resistant boundaries required to disrupt the percolating network of susceptible boundaries. For example, Wells et al. (1989) have calculated the percolation threshold for ran- domly assembled two-dimensional (2D) and three-dimensional (3D) grain-boundary networks and applied the results to intergranular stress corrosion cracking data for austenitic stainless steel. Palumbo and co-workers have also predicted the scale of the susceptible grain-boundary network on the basis of random probabilistic analy- sis and thereby estimated the resistance of microstructures to intergranular attack (Palumbo et al. 1991, Aust et al. 1994, Lehockey et al. 1998). Philosophical Magazine ISSN 01478–6435 print/ISSN 1478–6443 online # 2003 US Government http://www.tandf.co.uk/journals DOI: 10.1080/0141861021000056681 { Email: mukul@llnl.gov.