Physical Decomposition of the Critical Fracture Load P c in Ductile‐To‐Brittle Transition Toughness Testing: Toward Integrated Statistical‐Deterministic Characterization

The integrated statistical‐deterministic characterization of cleavage fracture toughness in the ductile‐to‐brittle transition (DBT) regime of ferritic steels remains an open challenge. Focusing on the raw fracture load P c rather than the derived fracture toughness K J c , this study examines whether P c admits a multiplicative decomposition P c = P c,central · Θ—separating a deterministic component P c,central governed by tensile properties and specimen geometry from a statistical residual Θ—and demonstrates that this decomposition is physically consistent. To establish physical grounding, the Buckingham π theorem is applied to derive a dimensionally consistent scaling law for P c,central from a 306‐specimen ferritic steel database; validity is assessed a posteriori as consistent with the Weibull‐type distribution of Θ (shape parameter ~3.59), in line with weakest‐link statistics. This decomposition provides a first‐order foundation for a physically grounded, integrated statistical‐deterministic framework for characterizing DBT fracture toughness from tensile properties and specimen geometry.