A statistical model of cleavage fracture

The aim of the paper is to provide a sound theoretical basis to the statistics of cleavage fracture in three-dimensional cracked structures. The probability of critically sized carbide being present in a Fracture Initiation Zone ahead of the crack tip has been derived, and shown to have a two-parameter Weibull distribution, with a shape parameter that is proportional to the strain-hardening exponent of the material. In a three-dimensional structure the cracking of such critically sized, intergranular carbide is necessary, but may not be sufficient to precipitate brittle fracture; this is because intergranular carbide is randomly orientated within the crack-opening stress field, so its orientation must also be unfavourable. It has been hypothesised that in three-dimensional structures the actual probability of fracture will be an extreme from the necessary distribution, in which case a sample of fracture toughness observations will be described by a Gumbel distribution, called here the LED model. After discussing the minimum number of fracture toughness observations needed to fit the model, its strength of evidence is compared with those of other candidate models, including the Master Curve model, and the LED model is shown to be the best.