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A mechanical model for simulating intergranular crack propagation ispresented. In order to understand fracture mechanics and processes that occur in apolycrystalline body it is necessary to accommodate a large number of parameters,including the macroscopic effects of load together with stress state and componentgeometry. A dislocation analysis based on the boundary element method is introducedto model crack growth through microstructures. Simulated microstructures aregenerated using the Voronoi algorithm. Each grain is assigned with a set of randomlyoriented slip directions in which plastic flow by shear is allowed. A uniform stress isapplied that drives the crack, emanating from a free surface, along the grainboundaries. The crack is advanced quasi-statically along a GB path, solving for thedistribution of dislocations within plastic zones emanating from the crack tip and thecrack opening. The stress intensity factor is calculated at each step. At each triplejunction the crack kinks towards the direction of the highest stress intensity. Asuperdipole (SD) algorithm is introduced to save simulation time without loosingimportant information and necessary geometric details. At the present time the factorscontrolling the path taken by a crack are not completely understood. By limiting thecrack advancement to grain boundaries and applying the introduced dislocation model,relations between crack advancement, CTOD and stress intensity factors (SIF) can bedetermined.