Grain boundary toughness effects on crack propagation in brittle polycrystals

Quasi-static crack advance has been statistically analysed as a function of interfacial toughness using a randomized two-dimensional, polycrystalline model. The average macroscopically observable toughness is calculated to be a strong function of interfacial toughness if the interfaces, grain boundaries in this case, have a fracture resistance less than approximately 12 that of the grains. Alternatively, the relative amount of crack deflection, as indicated by the percentage of interfacial failure, is a relatively homogeneous function of the interfacial toughness if interfacial fracture resistance is higher than about 0.3Γint. Combining these predictions gives a quantitative measure of both the expected material strength and resulting fracture surface roughness. Results exhibit good agreement with a similar analytical model which considers a deterministic approach for a similar geometry. Finally, the method employed here is general enough to be used for any polycrystalline ceramic.