The Interrelationships of K_Ia, K_Ic, and J_Ic, and the Implications of These Relationships on Use of Fracture Models Over the Ranges of Hardening Observed in Ferritic Steels

Models to predict the fracture and arrest behavior of ferritic steels, particularly those in use in the nuclear industry, have long been under development. The current, most widely accepted model of fracture toughness behavior is the ASTM E1921-02 “Master Curve” that is used to predict the variation of the mean cleavage fracture toughness with temperature in the transition temperature region as well as predicting the scatter of data about the mean at any given temperature. Recently, models describing the variation of arrest fracture toughness and of ductile initiation toughness with temperature have also been proposed. A study has been conducted with the goal of assessing how the scatter in cleavage initiation toughness may vary with temperature and level of irradiation embrittlement, which utilizes the crack arrest and ductile crack initiation models to redefine limits of applicability of the Master Curve-assumed Weibull distribution by developing empirically-derived interrelationships between the three models. These relationships are expected as all three parameters, K_Ic, K_Ia, and J_Ic, are controlled by the flow behavior of the material. There is a physical basis for viewing the crack arrest toughness as an absolute lower bound to the distribution of crack initiation toughness values for a fixed material condition and temperature. This physically based relationship, borne of the fact that both cleavage crack initiation toughness and cleavage crack arrest toughness are controlled by dislocation mobility, has brought about the suggestion that crack arrest toughness could be used to modify the lower tails of the crack initiation fracture toughness distribution. Using both empirical evidence and a hardening model proposed by Natishan and Wagenhofer, we investigate the relationship between initiation and arrest toughness and the implications on use of toughness models.