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Conventionally, the transition fracture toughness and upper-shelf fracture toughness of ferritic steels are viewed as separate properties: they are measured by tests conducted according to different standards, and neither toughness property can be estimated (except in very qualitative terms) based on knowledge of the other. Information presented in this paper demonstrates that quite the opposite is true: transition fracture toughness and upper-shelf fracture toughness are directly related because the microstructural features responsible for both the temperature dependence of fracture toughness and for the magnitude of fracture toughness at any given temperature are the same in both transition and on the upper shelf (the lattice structure controls the temperature dependence, while the size and distribution of second-phase particles control crack initiation and thus the magnitude of fracture toughness). These features bind the transition fracture tough. ness and upper-shelf fracture toughness together in a way that is extremely consistent for all ferritic steels. We present empirical evidence of this relationship based on fracture toughness data from a variety of ferritic steels: various heats of nuclear grade pressure vessel steels and welds (both before and after irradiation), copper precipitation hardened steels used in naval ship construction and mild steels used in ship construction. In total, these data span a broad range of To: from -180 °C to +140 °C. The combination of this theoretically motivated, empirically calibrated relationship between transition and upper-shelf toughness with Wallin's Master Curve (for toughness in fracture mode transition), and EricksonKirk's proposed Master Curve for toughness on the upper shelf, produces a model that predicts the temperature dependence of, and scatter in, fracture toughness of ferritic steels throughout the transition and upper-shelf temperature regimes. As input information, this model needs only the value of To, which can be estimated by performing fracture toughness tests according to the protocols of ASTM test standard E1921-05.

When assessing the resistance of a steel structure to failure under load, fracture toughness is a key input variable. Since it is usually not possible to establish a priori if the anticipated service temperature (or temperatures) is in the fracture mode transition or on the upper shelf, it is useful to know the temperature dependence of fracture toughness in both the transition and on the upper shelf. In the transition, the master curve proposed by Wallin defines both the variation of the median value of fracture toughness with temperature and the scatter of fracture toughness about this median value. However, Wallin's master curve does not quantify fracture toughness on the upper shelf. In this paper we assemble a database of upper shelf fracture toughness data ( J Ic ) for ferritic steels. These data demonstrate that the temperature dependence of upper J Ic is consistent for all ferritic steels contained in the database and has the same form as the temperature dependence of the flow strength anticipated from dislocation mechanics considerations. This similarity between the temperature dependence of flow strength and the temperature dependence of J Ic is physically expected because both directly depend upon the energy required for dislocation mobility in the ferrite matrix. Both the empirically derived model and the physical basis for the model are described.

In the 1960s and 1970s, when the surveillance programs for currently operating commercial nuclear reactors were established, state of knowledge limitations resulted in the use of Charpy-V notch (CVN) specimens rather than fracture toughness specimens. Reasonable success has since been achieved in correlating CVN and fracture toughness parameters. Such correlations provide an important part of the technical basis for both current regulations and ASME codes. These correlations imply that trends manifest in CVN data must also appear in fracture toughness data, even though empirical evidence demonstrate that this is not always true. For example, the temperature dependence of CVN energy (CVE) in transition is thought to be a unique feature of each specific sample of ferritic steel that is tested, a view in sharp contrast with the now widely accepted view of a “master curve” for transition fracture toughness (KJc). Also, effects of product form on CVE temperature dependence and property correlations are widely reported, despite the fact that product form effects are absent from KJc properties. These observations suggest that the mapping of CVE behavior onto fracture toughness implicit to correlation-based regulations and ASME codes may produce erroneous trends in estimated values of fracture toughness. In this paper we investigate the hypothesis that the apparent differences between CVE and fracture toughness arise due to differences in how the temperature dependence of CVE and KJc data have historically been modeled. Our analysis shows that when CVE data are analyzed in a manner consistent with KJc data (i.e., transition and upper shelf data are partitioned from each other and analyzed separately rather than being fit with a continuous tanh function), the apparent differences between CVE and toughness characterizations are minimized significantly, and may disappear entirely. These findings demonstrate the differences between CVE and fracture toughness data to be an artifact of the tanh analysis method rather than an intrinsic property of CVE.

Warm pre-stress, or WPS, is a phenomenon by which the apparent fracture toughness of ferritic steel can be elevated in the fracture mode transition if crack is first “pre-stressed” at an elevated temperature. Taking proper account of WPS is important to the accurate modeling of the postulated accident scenarios that, collectively, are referred to as pressurized thermal shock, and to the accurate modeling of routine cool-down transients. For both accident and routine cool-downs the transients begin at the reactor operating temperature (approximately 290°C for pressurized water reactors in the United States) and proceed to colder temperatures as time advances. The probabilistic fracture mechanics code FAVOR, which is being used by the NRC to provide the technical basis for risk-informed revisions of 10 CFR 50.61 and 10 CFR 50 Appendix G, adopts a model of WPS as part of its fracture driving force module. In this paper we assess the conservatism inherent to the FAVOR WPS model relative to a best-estimate WPS model constructed using data recently produced by the European Commission “SMILE” project and published by Moinereau and colleagues. Assessments of the conservatisms inherent to the so-called “conservative principle” WPS model, and also to a classic LEFM model that does not credit WPS are also made. The data presented herein demonstrate that, for an integrated analysis of PTS risk, the FAVOR and conservative principle WPS models both over-estimate the vessel failure risk by a factor of between 2 and 3× relative to the best estimate model. Our examination of the effect of WPS models on the predictions of individual transients reveals that for the severe transients that dominate risk there is little difference (usually less than 4×) between the conditional probabilities of crack initiation and of through wall cracking predicted by the different WPS models. There are considerable differences in the predictions of the various WPS and non-WPS models for low severity transients, however, the contribution of these transients to the total risk of vessel failure is small.Copyright © 2009 by ASME

In this paper we explore the crucial role played by the use of large databases in the identification, development, and refinement of models that describe the toughness behavior of ferritic steels. Specifically, we seek to emphasize and illustrate the point that when physical models are calibrated using large databases this process can reveal trends not previously seen, or foreseen. In support of this idea two examples are cited. First, the evidence for a CVE master curve in fracture mode transition is reviewed, as a counterpoint to the commonly held belief that each Charpy tanh transition curve is unique, with little commonality even within specific alloys, let alone across all ferritic steels. Second, new evidence is presented that the degree of prior hardening experienced by a ferritic steel has a systematic effect on the scatter exhibited by KJc data. This evidence suggests that the KJc Master Curve model, in which the scatter of KJc follows a Weibull distribution having a Kmin = 20 MPa√m and a slope (scatter magnitude) of 4, requires refinement, especially for the higher To values characteristic of steels that have been hardened by, for example, neutron irradiation damage.Copyright © 2009 by ASME

The effect of irradiation damage on the mechanical properties of reactor pressure vessel structures is monitored in operating nuclear reactors according to the provisions of 10 CFR Part 50 Appendix H. In these surveillance programs Charpy V-notch energy and tensile data are collected. Trends in these data have and continue to be used to identify and quantify embrittlement trends, which is a key aspect to maintaining the continued structural integrity of the operating reactor fleet. This paper presents the current results from an on-going investigation aimed at assessing the effect of different curve-fitting strategies on the insights that can be gained from these data trending activities.Copyright © 2008 by ASME and U.S. Government

The current regulations, as set forth by the United States Nuclear Regulatory Commission (NRC), to insure that light-water nuclear reactor pressure vessels (RPVs) maintain their structural integrity when subjected to planned reactor startup (heat-up) and shutdown (cool-down) transients are specified in Appendix G to 10 CFR Part 50, which incorporates by reference Appendix G to Section XI of the ASME Code. The technical basis for these regulations contains many aspects that are now broadly recognized by the technical community as being unnecessarily conservative and some plants are finding it increasingly difficult to comply with the current regulations. Consequently, a goal of current NRC research is to derive a technical basis for a risk-informed revision to the current requirements that reduces the conservatism and also is consistent with the methods previously used to develop a risk-informed revision to the regulations for accidental transients such as pressurized thermal shock (PTS). Previous publications have been successful in illustrating potential methods to provide a risk-informed relaxation to the current regulations for normal transients. Thus far, probabilistic fracture mechanics (PFM) analyses have been performed at 60 effective full power years (EFPY) for one of the reactors evaluated as part of the PTS re-evaluation project. In these previous analyses / publications, consistent with the assumptions utilized for this particular reactor in the PTS re-evaluation, all flaws for this reactor were postulated to be embedded. The objective of this paper is to review the analysis results and conclusions from previous publications on this subject and to attempt to modify / generalize these conclusions to include RPVs postulated to contain only inner-surface breaking flaws or a combination of embedded flaws and inner-surface breaking flaws.Copyright © 2008 by ASME and U.S. Government

Recently, the USNRC has proposed a voluntary alternative to the pressurized thermal shock (PTS) rule (10CFR50.61(a)) that may be used instead of the existing PTS rule (10CFR50.61) by power reactor licensees to demonstrate the safety of their RPVs. The reference temperature (RT) screening limits in 10CFR50.61(a) are less restrictive than those of 10CFR50.61; this relaxation being justified by the much more realistic models that underlie the technical basis of the revised rule. One of the many models that constitute this technical basis is used to estimate the effect of irradiation damage on the fracture toughness transition temperature. This relationship, which is called the embrittlement trend curve, or ETC, can change as time goes on due to the continued development of new knowledge (e.g., from on-going reactor vessel surveillance programs, from test reactor studies aimed at better understanding the physical mechanisms of irradiation damage, etc.). In this paper we present information that quantifies the effect of different ETCs on the through wall cracking frequencies that are calculated using the probabilistic fracture mechanics computer code that was used to establish the RT limits that have been proposed in 10CFR50.61(a).Copyright © 2008 by ASME and U.S. Government

In the 1960s and 1970s when the surveillance programs for currently operating commercial nuclear reactors were established state of knowledge limitations resulted in the use of Charpy-V notch (CVN) specimens rather than fracture toughness specimens. Reasonable success has since been achieved in correlating CVN and fracture toughness parameters. Such correlations provide an important part of the technical basis for both current regulations and ASME codes. These correlations imply that trends manifest in CVN data must also appear in fracture toughness data even though empirical evidence demonstrates that this is not always true. For example, the temperature dependence of CVN energy (CVE) in transition is thought to be a unique feature of each specific sample of ferritic steel that is tested, a view in sharp contrast with the now widely accepted view of a “Master Curve” for transition fracture toughness (KJc). Also, effects of product form on CVE temperature dependence and property correlations are widely reported despite the fact that product form effects are absent from KJc properties. These observations suggest that the mapping of CVE behavior onto fracture toughness implicit to correlation-based regulations and ASME codes may produce erroneous trends in estimated values of fracture toughness. In this paper we investigate the hypothesis that the apparent differences between CVE and fracture toughness arise due to differences in how the temperature dependence of CVE and KJc data have historically been modeled. Our analysis shows that when CVE data are analyzed in a manner consistent with KJc data (i.e., transition and upper shelf data are partitioned from each other and analyzed separately rather than being fit with a continuous tanh function) the apparent differences between CVE and toughness characterizations are minimized significantly, and may disappear entirely. These findings demonstrate the differences between CVE and fracture toughness data to be an artifact of the tanh analysis method rather than an intrinsic property of CVE.

Models to predict the fracture and arrest behavior of ferritic steels have long been under development. The current, most widely accepted model of fracture toughness behavior is the ASTM E1921-02 “Master Curve” that is used to predict the variation of the median cleavage fracture toughness (KJc) with temperature in the transition temperature region, as well as predicting the scatter of data about the median at any given temperature. Recently, models describing the variation of crack arrest fracture toughness (KIa) and of ductile initiation fracture toughness (JIc) with temperature have also been proposed. Moreover, models are also available that relate these various temperature dependencies to each other, and relate them all a common parameter, the cleavage crack initiation fracture toughness index temperature To. Research work continues to better quantify these relationships and to more firmly understand their physical bases. Nevertheless, the ample empirical evidence on which the models are based and the existing physical understanding underlying the models suggests that they can be used as a tool in both fitness-for-service assessment and in the design of experiments conducted to investigate the fracture toughness of ferritic materials. While still being developed, these toughness-based models offer clear advantages relative to alternative (correlative) approaches in terms of reduced prediction uncertainty. In this paper we amalgamate the results of previous publications to provide an algebraic expression for the variation of KJc, KIa, and JIc with temperature that includes explicit quantification of the uncertainty in each variable. We also discuss the implications and potential applications of this combined model.

Models to predict the fracture and arrest behavior of ferritic steels, particularly those in use in the nuclear industry, have long been under development. The current, most widely accepted model of fracture toughness behavior is the ASTM E1921-02 “Master Curve” that is used to predict the variation of the mean cleavage fracture toughness with temperature in the transition temperature region as well as predicting the scatter of data about the mean at any given temperature. Recently, models describing the variation of arrest fracture toughness and of ductile initiation toughness with temperature have also been proposed. A study has been conducted with the goal of assessing how the scatter in cleavage initiation toughness may vary with temperature and level of irradiation embrittlement, which utilizes the crack arrest and ductile crack initiation models to redefine limits of applicability of the Master Curve-assumed Weibull distribution by developing empirically-derived interrelationships between the three models. These relationships are expected as all three parameters, KIc, KIa, and JIc, are controlled by the flow behavior of the material. There is a physical basis for viewing the crack arrest toughness as an absolute lower bound to the distribution of crack initiation toughness values for a fixed material condition and temperature. This physically based relationship, borne of the fact that both cleavage crack initiation toughness and cleavage crack arrest toughness are controlled by dislocation mobility, has brought about the suggestion that crack arrest toughness could be used to modify the lower tails of the crack initiation fracture toughness distribution. Using both empirical evidence and a hardening model proposed by Natishan and Wagenhofer, we investigate the relationship between initiation and arrest toughness and the implications on use of toughness models.

In 1999, a study sponsored by the United States Nuclear Regulatory Commission (NRC) suggested that advances in the technologies associated with the physics of pressurized-thermal-shock (PTS) events developed since the derivation of the PTS regulations (established in the early-mid eighties) had the potential to establish a technical basis that could justify a relaxation in the current PTS-related regulations. A relaxation of these regulations could have profound implications for plant license extension considerations. Subsequently, the NRC initiated the interdisciplinary PTS Re-evaluation Project. During the five year project, an updated comprehensive computational methodology evolved, within the framework established by modern probabilistic risk assessment (PRA) techniques, through interactions among experts in relevant disciplines from the NRC staff, their contractors, and representatives from the nuclear industry. During 2004, the updated computational methodology was applied to three domestic commercial pressurized water reactors (PWRs). The most recent results of the PTS Re-evaluation Project provide a technical basis to support a relaxation of the current PTS regulations while continuing to provide reasonable assurance of adequate protection to public health and safety. The details of the updated computational methodology, the mathematical models, the analysis results, key findings, and supporting information have recently been drafted in several very detailed and lengthy formal reports. These reports are currently under review at the NRC. An objective of this paper is to provide a short overview of the improved computational methodology, analysis results, and key findings of the PTS re-evaluation project. To demonstrate that a technical basis has been established to support a relaxation of the current PTS regulations, it is helpful to understand the derivation of the current PTS regulations; therefore, another objective of this paper is to contrast the interpretation of the analysis results of the PTS re-evaluation to those performed in the eighties from which the current PTS regulations were derived.Copyright © 2005 by ASME