Uncertainties in Probabilistic Fracture Mechanics Calculations

This paper addresses uncertainties in probabilistic fracture mechanics (PFM) calculations for pressure boundary components at commercial nuclear power plants. Such calculations can predict the probability that a component will have failed after a specified period of operation, but with large uncertainties that are difficult to quantify. PFM models only approximate details of as-built components as well as actual operating conditions over the lifetime of the component. Statistical distributions used as inputs to the calculations are subject to uncertainties, which also results in large uncertainties in calculated failure probabilities. This paper describes from the author’s perspective various uncertainties that are associated with PFM calculations. Efforts to quantify PFM uncertainties are described along with their impacts on calculated failure probabilities. Many uncertainties are explicitly addressed by statistical distributions for input parameters to the PFM models (e.g. crack growth rates, material strengths, probabilities of flaw detection, etc.). Other calculations have gone further by estimating uncertainties in the parameters of these statistical distributions along with uncertainties in parameters treated as deterministic inputs to the PFM models. Examples from the author’s experience with uncertainty analyses for pressure vessels and piping components are described.