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

Abstract

Analyses of the distributions of fracture toughness, K 1c, 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 K 1c 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.