On the statistical modeling of cleavage fracture toughness of structural steels

•Three major statistical models of cleavage fracture toughness are scrutinized.•They are not normative by defying the precedence of plastic yielding over cleavage.•The Master Curve approach is an empirical model with a weak theoretical foundation.•A recent non-Weibull statistical model of cleavage fracture toughness is extended.•The Euro fracture toughness dataset is employed to assess these four models. The prevailing statistical models of cleavage fracture of structural steels for probabilistic risk assessment all infer a two- or three- parameter Weibull distribution of fracture toughness with a modulus of 4 and a fixed-value threshold independent of temperature and plastic constraint. This work starts with a critical review of three major statistical models of cleavage fracture toughness, namely the Beremin model, the Master Curve approach and the Prometey Unified Curve model, with a focus on their theoretical foundations, followed by a brief introduction and further extension of a newly developed statistical cleavage fracture toughness model. Then the Euro fracture toughness dataset is employed to assess these four models. The basic formulations of all the three existing models are not normative and defy the assumption of plastic yielding as a prerequisite to cleavage fracture. The key points of the new model are validated by the Euro dataset that cleavage fracture toughness does not necessarily obey the Weibull statistics while the threshold fracture toughness varies with temperature and plastic constraint.