On size effect and scaling behavior of ferritic steels in and near the ductile-brittle transition region

The stochasticity of fracture toughness of ferritic steels in the ductile-brittle transition (DBT) region arises primarily from aleatory uncertainty. Key micromechanical aspects include a Griffith microcrack nucleation by a breakage of the critical second-phase particle, randomly located ahead of the crack front, triggering an unstable propagation leading to a catastrophic failure. The scaling-based, weakest-link approach, proposed recently for the size effect modeling across the DBT region, was founded on the two-parameter Weibull distribution. This approach is further developed in this article to improve the physical robustness and flexibility of the two-step-scaling (2SS) procedure and to render the comparison with the standard Master Curve (MC) method more transparent. Specifically, the original 2SS method is enhanced by adding a lower limit on fracture toughness, resulting in a three-parameter Weibull (3P-W) distribution. Well-known datasets, corresponding to specimens of various sizes taken from a single segment of a reactor-pressure-vessel forging 22NiMoCr37, are analyzed to explore the reliability of the 2SS predictions. The empirical 2SS method is compared with the standard MC method, demonstrating its application flexibility and clarifying their relationship. Additionally, the proposed 3P-W 2SS variant incorporates a predetermined safety factor to enable a conservative assessment of fracture toughness.