SYMPOSIA PAPER Published: 01 January 2003

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: γeff=(σmσ¯)fσZAdεp¯·D0 where γeff is the effective plastic work to fracture, p is the effective plastic strain increment, σm/¯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 σZA 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.

Author Information

Wagenhofer, M
University of Maryland, College Park, MD
Natishan, ME
Phoenix Engineering Associates, Inc., Davidsonville, MD
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Developed by Committee: E08
Pages: 672–688
DOI: 10.1520/STP11100S
ISBN-EB: 978-0-8031-5472-8
ISBN-13: 978-0-8031-2899-6