Characterization and Application of the Uncertainties in Fracture Toughness Kic Based on the Weibull Statistical Distribution and Master Curve Method

Abstract

Fracture toughness at different temperature is important in the field of engineering for the probabilistic fracture mechanics (PFM) assessment of reactor pressure vessels. However, the large dependence on temperature and scatter in the ductile-to-brittle transition temperature (DBTT) region, along with the application of different indexing parameters, results in mass uncertainties in fracture toughness. We quantified and characterized these uncertainties in this study to describe the fracture toughness in the DBTT region. Based on the Oak Ridge National Laboratory (ORNL) KIc database, we proposed an uncertainty analysis that distinguishes between epistemic and aleatory uncertainties. The reference nil-ductility transition temperature (RTNDT) and Master Curve reference temperature (T0) were used as indices for the epistemic uncertainties. The quantity RTNDT – T0 was characterized by a three-parameter Weibull distribution using the commonly used parameter estimation methods of the moment method (MM), maximum likelihood estimation (MLE), and probability weight moment method (PWMM). The results of different goodness-of-fit criteria indicated that the low-order PWMM provided the most accurate estimation. Moreover, combining the weakest link theory, a Weibull statistical model of KIc vs. (T – T0) was established to account for the aleatory uncertainties, which showed good agreement with the KIc data. Finally, a procedure involving the treatment of epistemic and aleatory uncertainties for PFM analysis was proposed and applied to a case study. The results showed that considering both epistemic and aleatory uncertainties in fracture toughness significantly contributed to the removal of over-conservatism for the probability of crack initiation.

Keywords: Fracture toughness, Uncertainty, Weibull distribution, Master curve, Parameter estimation, Probabilistic fracture mechanics