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.”

An upper-shelf fracture toughness master curve for ferritic steels

“…In this paper, we apply a methodology used previously to develop models of transition fracture toughness [3,4] to develop a model of upper shelf fracture toughness that, ultimately, will be a model that is physics-based, predictive, and quantitative. This method begins with the development of a qualitative physics-based description of the fracture process.…”

“…This value was established by an empirical analysis as best representing a large set of ferritic steel tensile data [8]. 3. As a starting value, a is set to 2.1 mm based on a preliminary analysis of a smaller set of J Ic values.…”

“…Particular emphasis is placed on determining if the upper shelf fracture toughness of different ferritic steels exhibits a common temperature dependence, as is found in the transition. Since the primary factor responsible for the temperature dependence of plastic flow, and thus toughness properties in BCC materials, is the atomic lattice structure [3,4], it is not unreasonable to examine J Ic data for the existence of a common temperature dependence, or ''master curve'' such as is observed for transition toughness.…”

“…A methodology for the development of physics-based toughness models, and a physical description of fracture toughness on the upper shelf of ferritic steels This section begins with a discussion of the methodology employed to develop physics-based models of fracture toughness behaviour, a methodology patterned after work performed previously on transition fracture toughness (K Jc ) data [3,4]. We then go on to provide a physical description, based on dislocation mechanics, of the factors that control both the temperature dependence and the magnitude of fracture toughness (J Ic ) on the upper shelf of ferritic steels.…”