A Note on the Effect of Statistical Sample Size on Fracture Toughness Characterization in the DTB Transition Region

Abstract

The ferritic steels, widely used as pressure-vessel materials in nuclear industry, are prone to embrittlement when exposed to neutron irradiation or temperature reduction within the DTB (ductile-to-brittle) transition region. This embrittlement may be accompanied by the increased size effect, which is a pronounced consequence of fracture mechanics not exhibited in the traditional plasticity theory. Therefore, the fracture toughness in the DTB transition temperature region is a stochastic extrinsic property well known for its aleatory variability. Consequently, the extremely-pronounced experimental data scatter necessitates the use of the statistical approach to material characterization. The recently proposed two-step-scaling approach to estimate the size effect of fracture toughness CDF (cumulative density function) in the DTB transition region relies heavily on regularity of arrangement of experimental data points for the two input sample sizes. This regularity of measurement values becomes an inherently iffy proposition in the case of statistically small data sets. Therefore, the ability of our novel approach to predict objectively the fracture toughness probability outside the experimental domain may be impaired in absence of the sufficient statistical size of the input data sets. Since the large-scale fracture toughness tests for nuclear pressure-vessel steels at low temperatures are very expensive, the present study is concerned with this issue of the statistically sufficient sample size. There are various statistical techniques to determine the sample size needed for a study, including power analysis and sample size calculation formulas. The appropriate method depends on the type of study, the research question, and the statistical analysis planned. These issues are addressed in this article.