Crack nucleation due to the piling-up of extrinsic grain-boundary dislocations around triple junctions was analyzed. The analysis was based upon a micro-mechanical model for interactions between pile-ups and a triple-junction crack, plus an approximate energy-based crack nucleation criterion. For a random microstructure in Al, the results showed that the crack orientation, the crack length and the energy decrease due to crack formation, had rectangular, skewed and normal probability density distributions, respectively. The effects of the remote loading state, of the magnitude of the load and of the mean grain size upon the means and standard deviations of the distributions were also quantified.

Prediction of Crack Statistics in a Random Polycrystal Damaged by the Pile-Up of Extrinsic Grain-Boundary Dislocations. M.S.Wu, M.D.He: Philosophical Magazine A, 1999, 79[2], 271-92