Prediction of the Shape of the K_J Ductile-to-Brittle Transition Temperature Curve for Ferritic Pressure Vessel Steels Using the Material's Resistance to Crack Extension K_J versus Δa Curve

Fracture toughness (K_{J (cleavage)}) measurements made within the ductile-to-brittle transition region for ferritic pressure vessel steels are not always described by the shape of the Master Curve currently given in ASTM Standard E 1921. The objective of this paper is to show how the shape of the transition toughness curve may be related to the shape of the material's resistance to crack extension curve (K_JR) once the crack tip starts to blunt and ductile crack extension precedes cleavage failure. Using an empirical relationship between the mean ductile crack extension (Δa) prior to the onset of cleavage failure and temperature (Δa=λ exp(ϕT)), then the relationship between K_J and T may simply be given by K_J=K_A+α[λ exp(ϕT)]^β, where K_A, α, and β are simply the coefficients to an offset power law to K_J versus Δa data given by K_JR=K_A+α(Δa)^β. For specimens of different sizes, a reference temperature T_K may be defined for a given reference level of Δa or equivalent K_J. Unique curves may be defined for materials with differing crack extension resistance curves through plots of K_J versus (T−T_Δa(ref)) or (T−T_K(ref)). The generalized form of the transition curve may be given by K_J=K_A+α{Δa_(ref) exp[ϕ(T−T_Δa(ref) >^β or K_J=K_A+(K_(ref)−K_A){exp[ϕ(T−T_K(ref) >^β. Experimentally, ϕ has been estimated as approximately 0.08 for nuclear pressure vessel materials such as A533B/A508. Using a specific situation wherein the value of $KA=30MPa√m,K(ref)=100MPa√m$⁠, and β=0.25 then, for a B=25-mm specimen, within experimental scatter this provides an almost exact match to the Master Curve given by K_J=30+70 exp[0.019(T−T_K100)]. The predictions of transition curve shape using the material's resistance to crack extension curve are believed to be complementary to the Master Curve method, and may describe the shape of the transition curve when there is ductile crack extension prior to cleavage failure. Further work is recommended to investigate the relationship between the predicted ductile-to-brittle transition curve and the Master Curve for probabilities of cleavage failure post-initiation.