PSI - Issue 42

Vitor S. Barbosa et al. / Procedia Structural Integrity 42 (2022) 1177–1184 V. S. Barbosa and C. Ruggieri / Structural Integrity Procedia 00 (2019) 000–000

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on temperature for a wide range structural ferritic steels, including irradiated conditions, with a yield strength in the range of 275 MPa ∼ 825 MPa - see Joyce and Tregoning (2001); Wallin (2002); McCabe et al. (2005) for illustrative examples. In view of the technological importance of assessing the fracture integrity of containment vessels, engineering applications of the Master Curve procedure (American Society for Testing and Materials, 2019) have been primarily focused on describing the temperature dependence of fracture toughness for pressure vessel steels and low carbon structural steels. Moreover, the approach has also been shown to hold for tempered martensitic steels having very high strength, provided they can be considered as falling into the category of ferritic steels for which the Master Curve method is applicable. Indeed, recent works of Odette and co-workers (Odette et al., 2004; Yamamoto et al., 2007; Mueller et al., 2009), Neimitz et al. (2012, 2014) and Wallin et al. (2015) provide support to use the Master Curve approach in characterizing the fracture toughness transition behavior for this class of material. However, despite these advancements, more systematic studies to support the extension of the methodology to characterize the dependence of fracture toughness on temperature in ultra high strength steels (UHSS) with nominal strengths exceeding 1000 ∼ 1200 MPa remain limited. Consequently, further extensions and applications of the master curve methodology to describe the fracture toughness dependence of temperature for this class of material are largely justified as such studies can broaden the toughness-temperature relationship in the transition temperature for the existing toughness database of common structural steels to more advanced structural steels. As a step in this direction, this work addresses an experimental investigation of the brittle fracture behavior for an ultra high strength martensitic steel using fracture toughness data measured in the ductile-to-brittle transition region (DBT). While this class of ultra high strength steel having a martensitic microstructure is currently beyond the reach of ASTM E1921 (American Society for Testing and Materials, 2019), the analyses described here show that the predicted normalized curves of median fracture toughness vs. temperature are in good agreement with the experimental measurements.

2. Overview of the Master Curve Approach

This section describes essential characteristics and steps of the data analysis method to determine the reference temperature, T 0 , from experimentally measured fracture toughness values. Only salient features of the Master Curve (MC) methodology are described here. Readers are referred to the works of McCabe et al. (2005), IAEA TR429 (IAEA, 2005), ASTM E1921 (American Society for Testing and Materials, 2019) and references therein for details.

2.1. Single Temperature Method

Wallin (1991, 1993, 2002) advanced the concept of the ASME K Ic reference curve (American Society of Mechan ical Engineers, 2021) to develop a more accurate and more e ff ective procedure to characterize elastic-plastic fracture toughness data over the DBT region. The methodology led to the notion of a “master” fracture toughness transition curve and relies on the construction of a normalized curve of median fracture toughness values, defined in terms of the elastic-plastic stress intensity factor, K Jc , rather than J c , for high constraint fracture specimens having size of 1T ( B = 25 mm) geometries with temperature. The approach begins by considering a continuous probability function derived from weakest link statistics to characterize the distribution of K Jc -values in the form (Wallin, 1984) F ( K Jc ) = 1 − exp − K Jc − K min K 0 − K min α (1) which is a three-parameter Weibull distribution (Mann et al., 1974) defined by the Weibull modulus, α , the scale parameter or characteristic toughness, K 0 and the threshold fracture toughness, K min (observe that F ( K Jc ) = 0 for K Jc ≤ K min ). Following ASTM E1921 (American Society for Testing and Materials, 2019), parameter α takes the value of 4 under conditions pertaining to small scale yielding (SSY) near the crack tip and K min is conveniently assigned a value of 20 MPa √ m . Moreover, to insure small scale yielding (SSY) conditions at fracture, K Jc -values exceeding the measuring capacity of the specimen defined by K Jc − max = Eb 0 σ ys / M (1 − ν 2 ), where b 0 denotes the original crack ligament size and the deformation limit, M = b σ ys / J , is conservatively assigned a value of 30, are treated as censored data (Mann et al., 1974) - the above Eq. (1) thus becomes a right-censored Weibull distribution (Rinne, 2009).