The statistical modelling of brittle fracture in homogeneous and heterogeneous steel microstructures

Analyses of the distributions of fracture toughness, K1c, values are described for single bainite, single auto-tempered martensite and mixed bainite/martensite microstructures in the pressure-vessel steel A533B. Single phase microstructures and a fine-grained mixed microstructure are shown to behave in a “quasi-homogeneous” manner, i.e. the cumulative distribution functions (CDFs) of K1c plot as straight lines on normal probability paper, the standard deviations are little greater than experimental measurement errors, and the values can be extrapolated to low probabilities with a degree of confidence. The coarse-grained mixed microstructure is classified as “heterogeneous” and unreasonably ultra-pessimistic conclusions may be obtained if the CDF distribution is extrapolated in the same way. The reasons for this behaviour are related to the local micro-mechanisms of fracture. The value of the conventional fitting of data to Weibull distributions in this context is questioned.