A 3-dimensional dislocation cellular automaton model was developed to study the evolution of dislocation configurations in face-centered cubic single crystals. Crystallographic {111} slip planes with 3-fold symmetry were discretized into equilateral triangular patches with sides along <110> directions. These patches slip provided there was a sufficient driving force associated with reduction in system energy. Perfect <110>/{111} dislocations were considered. The resulting variables were the triangular patch size and dislocation core cut-off, measured relative to Burgers vector magnitude b. Three examples involving operation of a Frank–Read source were chosen to highlight the benefits and drawbacks of the method. A benefit to discretization was that dislocation evolution may be analyzed via spatial averaging over collections of patches, so that the discrete versus continuum nature of the results may be studied. Further, dislocation reactions and cross slip were accommodated easily and, in principle, Monte Carlo schemes could be integrated into the evolution formalism. A drawback was that collections of patches did not reflect a smooth variation in configuration so that artificial fluctuations in dislocation line length and direction could result. Overall the discrete nature of the method was attractive for incorporating the kinetics of thermally activated states and for simplifying the range of geometries and threshold criteria associated with dislocation reactions.

A Three-Dimensional Cellular Automaton Model of Dislocation Motion in FCC Crystals. Q.Li, P.M.Anderson: Modelling and Simulation in Materials Science and Technology, 2004 12[5], 929-43