A Markov Chain Fracture Model for Intergranular Crack Propagation in Polycrystalline Materials

A model for intergranular damage propagation in polycrystalline materials is proposed, based on Markov Chain theory, Monte Carlo simulation and percolation concept. The model takes into account crack branching and coalescence, multiple crack nucleation sites, crack-turning etc., as well as the effect of grain boundary plane orientations with respect to the external stress direction. Both honeycomb and voronoi microstructures were utilized as the input microstructures. The effect of multiple crack nucleation sites has been found to have great influence on the crack propagation length. It has been observed that percolation threshold reported in the literature based on hexagonal microstructure is not applicable when the effect of external stress direction on the susceptibilities of grain boundaries is considered. The successful integration of voronoi algorithm with the Markov Chain and Monte Carlo simulations has opened up the possibilities of evaluating the intergranular crack propagation behaviour in a realistic manner.