Weibull distribution of brittle failures in the transition region

摘要

The Weibull stress is a well-known means of predicting the likelihood of weakest link brittle fracture that has been shown to accurately model the behaviour of ferritic steels in the lower transition region. Weibull stress is based on its use of a two parameter Weibull distribution, a commonly used distribution in probabilistic engineering. The distribution is defined by a shape parameter, the Weibull modulus, and a scaling parameter. In the lower transition region, the Weibull modulus is relatively insensitive to temperature and the likelihood of failure can readily be defined by assuming it is constant and scaling the distribution with a 'measured' scaling parameter. This assumption, however, does not hold as the temperature increases into the upper transition zone and becomes less accurate as the upper shelf is approached. This manifests itself as a broadening of the failure distribution that can be attributed to the increased size of the plastic zone ahead of a defect, which in turn 'samples' more potential failure sites, while simultaneously increasing the likelihood of blunting these sites and initiating ductile tearing. Thus, while more potential cleavage initiation sites are sampled, the likelihood of an individual defect causing failure is reduced. This paper details the changes in the Weibull modulus and Weibull stress calculated from the 'Euro' fracture toughness data. The differences in the Weibull modulus and the mechanistic reason for these differences are explored to enable greater understanding of the factors that influence fracture toughness in the upper transition regime.