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: γeff=(σmσ¯)f∫σZAdεp¯·D0 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, σf=[πEγeff2(1-ν2)r0]1/2 and thus the need for defining a characteristic distance.

In this paper we describe the details of this model used to predict fracture toughness behavior transition with temperature for ferritic steels. We then combine this model with a discussion of the uniformity of steel tensile properties to develop a method for predicting fracture toughness transition temperature shift due to irradiation from hardness tests.