A Micromechanical Evaluation of the Master Curve

Abstract

The cleavage fracture model of Wallin et al. [1] suggests that the variation of median and bounding values of fracture toughness with temperature is predictable on a micro-mechanical basis. ASTM has recently adopted a standard [ASTM Standard Test Method for the Determination of Reference Temperature, To, for Ferritic Steels in the Transition Range (E 1921–98)] for characterizing the variation of the fracture toughness of ferritic steels in the transition temperature range that draws heavily on the work of Wallin et al. and on subsequent developments [1–5]. The new standard expresses the median toughness transition for a 1T specimen as: KJc|median=30+70⋅exp⁡[0.019(T−To)] where temperature is measured in degrees Celsius and KJc is measured in MPa√m. Similar equations express the variation of bounding toughness values (e.g., 95% lower bound) with temperature. The numeric coefficients in all of these equations do not depend on the type of steel tested. This invariance suggests that chemistry, heat treatment, and other metallurgical variables are not thought to influence the exponential increase with temperature of the plastic work necessary for crack propagation, the dominance of carbides as the particles that initiate cleavage fracture, or the distribution of carbide particles. The ASTM E 1921 Master Curve represents existing fracture toughness data well for nuclear pressure vessel steels and their weldments [6]. This empirical evidence suggests that the material invariance attributed to the Master Curve coefficients in ASTM E 1921 is at least approximately correct for this class of steel. But the microstructural bounds of applicability for the Master Curve are not clear. In this paper we examine the physical basis for the Wallin et al. Master Curve with the aim of distinguishing the classes of steels to which the methodology applies from those to which it does not. We use this physical understanding to calculate the temperature dependence of the plastic work for ferritic steels to demonstrate theoretical validity of a single “master curve.”