A Model for Predicting Fracture Toughness of Steels in the Transition Region from Hardness

Given the nature of fracture in the lower transition region where final fracture by cleavage is preceded by some amount of plastic deformation, it is appropriate to use a combined strength-strain criterion to describe the conditions at fracture. A dislocation- based model for predicting fracture toughness of steels in the transition region has been developed where the primary feature describing the temperature dependence of fracture toughness is a plastic work term of the following form: where γeff is the effective plastic work to fracture, dε^p is the effective plastic strain increment, σ_m/¯σ is the triaxiality ratio and r₀ is the length scale of the critical fracture event typically taken as carbide cracking*(and thus D₀ = r₀ is the critical carbide radius). The σ_ZA term represents the flow stress from the Zerilli-Armstrong constitutive equation for bcc metals. This term introduces a temperature dependency based on dislocation mechanics considerations. Inserting the first equation into the Griffith-Orowan equation for fracture stress leads to the elimination of the carbide radius from the equation, and thus the need for defining a characteristic distance.