A method for the probabilistic method assessment of structures containing defects
This thesis begins by noting that the current safety justification of pressurised water reactor pressure vessels is deterministic. To enable probabilistic structural integrity safety cases of reactor pressure vessels to be carried out, a need for a new analysis of the statistical properties of fracture toughness is identified. Fracture is linked to the cracking of critically sized carbide, and a preliminary analysis showed that the distribution of carbide in steel could be described by an exponential distribution. Initially the failure of an individual fracture toughness test specimen is considered. The volume of material at the tip of a flaw, within which fracture initiation can take place, is then shown to be dependent on the stress intensity factor and material properties of the steel. Using these results, the underlying probability for the presence of critical carbide is derived, and shown to have a Weibull distribution. Fracture toughness is then hypothesised to be an extreme of this distribution, so the probability of a sample of fracture toughness observations would have a Gumbel distribution. The model so obtained has a physical basis, only needs two parameters, and is dependent on the number of data available. The model is validated, along with other models, against a large data set, and shown to be the best candidate model. An analytic expression, based on material properties and the underlying distribution, is derived for the temperature dependence of fracture toughness, and exhibits lower and upper shelf properties, linked by a transition region. A further expression is derived that relates the minimum probability with which fracture toughness can be predicted to the number of data that the prediction is based on. These findings are used to produce probability contours of fracture toughness. Then, using Bayesian statistics, these contours are made unconditional on the assumed probability distribution, and only dependent on the data. These unconditional predictions do not differ significantly from those produced using the Gumbel distribution. However, it is this unconditional quality that would allow a statistical approach in structural integrity to be robust. Finally, for irradiated steel, the model is shown to predict the reduction in fracture toughness, and the decrease in its rate of increase, with temperature, that is observed experimentally.