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This study introduces a simple analytical model for fracture toughness to bridge the length scales from grain size to bulk thickness by assembling a virtual crack path from the angles recorded on an unfractured microstructure, which is a great challenge in fracture mechanics due to the high geometrical complexity. Good agreement is found between a crack deflection angle distribution measured from 5764 crack segments and the prediction by the model and the possible influence of residual stress is quasi quantitatively discussed. A total of 7.4% of the crack segments observed acted as crack bridges, while 7.3% was predicted by the model. A quantification of how high an angle needs to be to turn crack deflection into crack bridging is given. The ratio of fracture toughness from grain boundary to grain, G 1c(gb) /G 1c(g) , was measured indirectly from all samples to be between 0.3 and 0.35.

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The crack bridging behaviors of silicon nitride (Si 3 N 4 ) ceramics based on the advancing cracks have been evaluated at cryogenic temperatures in contrast with those happened at ambient temperatures. R-Curve behavior of Si 3 N 4 ceramics was determined to compare the cumulative effect of bridging at 77 and 293 K. The detailed changes in crack morphologies and crack opening displacement profiles at different temperatures were investigated. The bridging stress maps around a bridging ligament were recorded by in situ Raman spectroscopy. It was found that the highest tensile stress measured at 77 K (~1.0 GPa) is much higher than that at 293 K (~0.7 GPa). The experimental results suggested that Si 3 N 4 ceramics at cryogenic temperatures possessed a higher probability of crack bridging with a higher closing force, which could make them a promising candidate for cryogenic applications.