4.14.1.3.1 History

Master Curve methodology is based on the observa­tion that the fracture toughness transition curve for any ferritic steel has the same shape, no matter the steel (see Figure 2). Thus, a single ‘Master Curve’ can be used for all ferritic steels; the curve is simply shifted along the temperature axis to match a mean fracture toughness value, which is established from measured fracture toughness data for the particular steel being evaluated. The primary material fracture

toughness parameter is the transition temperature, T0, which characterizes the Master Curve position, and is defined as the temperature where the median fracture toughness is 100 MPa Vm (Figure 2).

The advantages of Master Curve technology over past methods for estimating the fracture toughness of materials (particularly irradiated materials) are (1) it is based on direct measurements of the property of interest (e. g., fracture toughness); (2) it provides a direct method of establishing the transition curve for irradiated materials (instead of inferring a shift in an assumed baseline bounding curve using Charpy data); and (3) it can be used for materials even with a limited availability of archival materials.

The development of Master Curve methodology was started in the 1980s by Wallin and his coworkers by the introduction of a mathematical model to describe the probability of cleavage fracture initiation in a material containing a distribution of potential fracture initiators (flaws). The model was completed by including the temperature dependence of Kjc, which was estimated empirically from a dataset including various ferritic structural steels. The scat­ter definition, the size adjustment, and the definition of the temperature dependence are the basic ele­ments of the Master Curve methodology described in ASTM E 1921.6-8 The approach has been verified in several round-robin and research programs.9

The first version of the Master Curve standard comprised a procedure for analyzing only single­temperature test data; in later versions, the approach was extended to consider multitemperature test data. The multitemperature approach requires finding a maximum likelihood solution for the value of the transition temperature, T0, from data measured over a range of temperatures, rather than at a single tem­perature. The first version of ASTM E1921 was approved in 1997 and issued in 1998 (ASTM E 1921­97). The multitemperature approach was included in the second revision, after which several other revisions with some minor changes have been released. The present revision, ASTM E 1921-08, describes proce­dures for the experimental determination of the elas­tic-plastic fracture toughness, Kjc, estimation of the reference temperature, T0, and principles for the lower bound curve definition of fracture toughness (Figure 3). Further detailed descriptions on the meth­odology and applications are given in McCabe eta/.10 and Sattari-Far and Wallin11.

The model12 has also been validated numerically to more accurately describe the true fracture behavior and the stress-strain distribution of bcc steels on a

micromechanical scale.13 The advanced numerical assessment capabilities presently available for multi­scale modeling of materials have made it possible to validate the main elements of the model. Despite several further developments primarily related to material inhomogeneity (in the basic model material macroscopic homogeneity is assumed), the basic approach being applied today is essentially the same as that developed over 20 years ago. No other defi­ciencies or assumptions requiring readjustment have been identified. Further verification of the approach and the validity of the empirically determined tem­perature dependence have been conducted. Some aspects, such as the lower shelf definition (Kmin), are practically impossible to verify only using experimen­tal methods, so that numerical modeling studies have been very instructive.

The Master Curve methodology is currently being used in both structural integrity and lifetime assess­ments. Typical areas ofapplication are pressure vessels and piping, nuclear RPV surveillance programs, other energy production structures, off-shore structures, and various welded components and bimetallic joints.