Stochastic modeling of the independent roles of particle size and grain size in transgranular cleavage fracture

The independent roles of grain size and particle size on sharp crack and rounded notch toughness are investigated over a range of temperatures from the lower shelf into the early ductile/brittle transition region. The results are interpreted in terms of a weakest link statistical model wherein the onset of failure coincides with the critical propagation of a particle microcrack into the matrix. It is shown that, for a fixed particle size distribution, both sharp-crack and rounded-notch toughness decrease with increasing grain size. However, at fixed grain size, the sharp-crack toughness increases, while the rounded-notch toughness decreases with increasing particle size. Such effects results primarily from the difference in the number of activated particles in the plastic zone.