A geometry and temperature dependent regression model for statistical analysis of fracture toughness in notched specimens

In this work, a novel methodology for fracture characterization of metallic notched components including the effect of notch root radius and temperature is proposed based on the brittle-to-ductile transition curve. To this aim, two different regression models are derived, either by considering temperature as an influencing variable or combined with the notch radius effect. In the former case, the compatibility condition between the statistical distributions of the fracture toughness for a given temperature and of the temperature for a given fracture toughness is applied. This allows the K-c-T field to be analytically defined proving that both distributions are interrelated and cannot be arbitrarily defined. The second regression model is based on the Theory of the critical distances by converting the experimental data at different notch radii to a reference value. In this way the so-called notch or apparent fracture toughness is calculated in a probabilistic manner for any combination of notch radii and temperature. The proposed methodology is applied to the results of a large experimental campaign on a S355J2 steel involving different temperatures and notch root radii conditions confirming its utility and suitability.