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

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.