A cumulative failure probability model for cleavage fracture in ferritic steels

•A self-consistent statistical model of cleavage fracture is developed.•A statistical model of cleavage fracture toughness is also presented.•The threshold stress for cleavage fracture varies with yield stress and constraint.•The Beremin model defies the premise of plastic yielding before cleavage fracture.•The Beremin model violates the normality axiom of probability. The fundamental physical assumption of plastic deformation as a prerequisite to the cleavage fracture event demands to rule out the contribution of elastic stress components to the occurrence of fracture from both the pure elastic zone and the elastoplastic zone. It also commands the threshold stress for cleavage fracture to be no less than the yielding stress. Based on this understanding, a model of the cumulative failure probability for cleavage fracture in ferritic steels is developed. Further, a self-consistent statistical model of cleavage fracture toughness is also derived. The Beremin model does not conform to the normality axiom of probability, as it defies the premise of plastic yielding before cleavage fracture by counting in the elastic stress components inside the plastic zone to calculate the cumulative probability. Examples are given in several homogeneous uniaxial and multiaxial loading conditions to highlight the differences between the Beremin model and the presented model in probability calculation, model calibration, and interpretation of the temperature and constraint dependence of microscopic cleavage fracture stress. [Display omitted]