The long-term operating strategy of nuclear plants must ensure the integrity of the vessel, which is subjected to neutron irradiation, causing its embrittlement over time. Embrittlement trend curves used to predict the dependence of the Charpy transition-temperature shift, ΔT_41J, with neutron fluence, such as the one adopted in ASTM E900-15, are empirical or semi-empirical formulas based on parameters that characterize irradiation conditions (neutron fluence, flux and temperature), the chemical composition of the steel (copper, nickel, phosphorus and manganese), and the product type (plates, forgings, welds, or so-called standard reference materials (SRMs)). The ASTM (American Society for Testing and Materials) E900-15 trend curve was obtained as a combination of physical and phenomenological models with free parameters fitted using the available surveillance data from nuclear power plants. These data, collected to support ASTM’s E900 effort, open the way to an alternative, purely data-driven approach using machine learning algorithms. In this study, the ASTM PLOTTER database that was used to inform the ASTM E900-15 fit has been employed to train and validate a number of machine learning regression models (multilinear, k-nearest neighbors, decision trees, support vector machines, random forest, AdaBoost, gradient boosting, XGB, and multi-layer perceptron). Optimal results were obtained with gradient boosting, which provided a value of R² = 0.91 and a root mean squared error ≈10.5 °C for the test dataset. These results outperform the prediction ability of existing trend curves, including ASTM E900-15, reducing the prediction uncertainty by ≈20%. In addition, impurity-based and permutation-based feature importance algorithms were used to identify the variables that most influence ΔT_41J (copper, fluence, nickel and temperature, in this order), and individual conditional expectation and interaction plots were used to estimate the specific influence of each of the features.

The use of mini-CT specimens for the fracture characterization of structural steels is currently a topic of great interest from both scientific and technical points of view, mainly driven by the needs and requirements of the nuclear industry. In fact, the long-term operation of nuclear plants requires accurate characterization of the reactor pressure vessel materials and evaluation of the embrittlement caused by neutron irradiation without applying excessive conservatism. However, the amount of material placed inside the surveillance capsules used to characterize the resulting degradation is generally small. Consequently, in order to increase the reliability of fracture toughness measurements and reduce the volume of material needed for the tests, it is necessary to develop innovative characterization techniques, among which the use of mini-CT specimens stands out. In this context, this paper provides a review of the use of mini-CT specimens for the fracture characterization of ferritic steels, with particular emphasis on those used by the nuclear industry. The main results obtained so far, revealing the potential of this technique, together with the main scientific and technical issues will be thoroughly discussed. Recommendations for several key topics for future research are also provided.

The standard ASTM E900-15 provides an analytical expression to determine the transition temperature shift exhibited by Charpy V-notch data at 41-J for irradiated pressure vessel materials as a function of the variables copper, nickel, phosphorus, manganese, irradiation temperature, neutron fluence, and product form. The 26 free parameters included in this embrittlement correlation were fitted through maximum likelihood estimation using the PLOTTER—BASELINE database, which contains 1878 observations from commercial power reactors. The complexity of this model, derived from its high number of free parameters, invites a consideration of the possible existence of overfitting. The undeniable goal of a good predictive model is to generalize well from the training data that was used to fit its free parameters to new data from the problem domain. Overfitting takes place when a model, due to its high complexity, is able to learn not only the signal but also the noise in the training data to the extent that it negatively impacts the performance of the model on new data. This paper proposes the resampling method of Monte Carlo cross-validation to estimate the putative overfitting level of the ASTM E900-15 predictive model. This methodology is general and can be employed with any predictive model. After 5000 iterations of Monte Carlo cross-validation, large training and test datasets (7,035,000 and 2,355,000 instances, respectively) were obtained and compared to measure the amount of overfitting. A slightly lower prediction capacity was observed in the test set, both in terms of R² (0.871 vs. 0.877 in the train set) and the RMSE (13.53 °C vs. 13.22 °C in the train set). Besides, strong statistically significant differences, which contrast with the subtle differences observed in R² and RMSE, were obtained both between the means and the variances of the training and test sets. This result, which may seem paradoxical, can be properly interpreted from a correct understanding of the meaning of the p-value in practical terms. In conclusion, the ASTM E900-15 embrittlement trend curve possess good generalization ability and experiences a limited amount of overfitting.