On the history and status of reactor pressure vessel steel ductile to brittle transition temperature shift prediction models

Journal of Nuclear Materials 526 (2019) 151863

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Journal of Nuclear Materials journal homepage: www.elsevier.com/locate/jnucmat

On the history and status of reactor pressure vessel steel ductile to brittle transition temperature shift prediction models G.R. Odette a, *, T. Yamamoto a, T.J. Williams b, R.K. Nanstad c, C.A. English d a

UC Santa Barbara, Santa Barbara, CA, 93106, USA Rolls-Royce, Derby, UK c Oak Ridge National Laboratory, Oak Ridge, TN, 37830, USA d National Nuclear Laboratory, Culham, Abingdon, OX14 3EB, UK b

a r t i c l e i n f o

a b s t r a c t

Article history: Received 13 September 2019 Received in revised form 22 October 2019 Accepted 22 October 2019 Available online 13 November 2019

This paper melds an overview of the history of Reactor Pressure Vessel (RPV) embrittlement research, focusing on predicting ductile-to-brittle transition temperature shifts (DT), along with an assessment of the current status of these efforts, especially for extended life operation. The 60-year history of RPV research reveals remarkable progress on a very complex and challenging problem that has, for several decades, been a paradigm for a ‘science in service of engineering’ approach to a critical technological challenge. This research has laid the foundation for properly analyzing modestly accelerated materials test reactor (MTR) data to make robust DT predictions beyond the current low flux (4) power reactor surveillance database. We show that most current models, that are accurate at lower fluence (4t), systematically and significantly underpredict DT at high 4t, largely owing to the currently unaccounted for contribution of late blooming MnNiSi precipitates (MNSPs). We propose a simple empirical approach to predicting DT between 4t z 4
1023 n/m2 (the currently reliable DT model limit) and 14
1023 n/m2 (for extended life). The method is shown to be empirically robust, and is supported by a microstructurally informed physical model. In addition to quantifying the role of MNSPs, important observations include approximately linear DT dependence at high 4t (versus the previous z √4t trend at lower 4t), and a diminution of the effect of 4. The decreased 4 effect at high 4t has very important implications for the use of accelerated MTR data to predict service relevant DT. © 2019 Elsevier B.V. All rights reserved.

Keywords: RPV embrittlement Charpy shifts Copper rich precipitates Manganese-nickel-silicon precipitates Radiation-enhanced diffusion Avrami models Irradiation hardening

Contents 1.

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4.

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.1. Objective of the paper . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.2. Stages of DT model development . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.3. Framework for predictive model development . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.4. Organization of the paper . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 DT and the structural integrity assessments of RPVs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.1. RPVs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.2. RPV integrity assessments and DT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 DTc predictions and KIR indexing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.3. A brief history of embrittlement research . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 3.1. RPV surveillance and early embrittlement research . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 3.2. Towards MBC DTc models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 3.3. Multitechnique characterization studies, irradiation experiments, MBC and MSM z2000 to 2019 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 The EONY DT MBC model and the IVAR database . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

* Corresponding author. E-mail address: [email protected] (G.R. Odette). https://doi.org/10.1016/j.jnucmat.2019.151863 0022-3115/© 2019 Elsevier B.V. All rights reserved.

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4.1. EONY model development and calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 4.2. Comparison of EONY model predictions with IVAR data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 4.3. Flux effects revealed in IVAR data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 Summary of major microstructural observations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 5.1. CRPs and MNSPs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 5.2. Phosphides . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 5.3. Dislocation loops and network dislocations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 Embrittlement mechanisms and models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 6.1. Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 6.2. Cascade defect-solute cluster complexes and mobile defect production in aged cascades . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 6.3. Excess defect fluxes, RED and RIS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 6.4. Flux effects on RED . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 6.5. Precipitation mechanisms and models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 6.6. Advanced precipitation thermo-kinetics models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 6.7. Avrami based models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 6.8. Irradiation hardening and DTc . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 The UCSB ATR-2 experiment and the Odette, Wells, Almirall, Yamamoto (OWAY) DT model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 7.1. Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 7.2. An ATR-2 CF . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 7.3. Intermediate to high 4t dependence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 7.4. The ATR-2 4te and a diminished 4 dependence at high 4t . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 7.5. Low 4 high 4t DT model predictions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 Concluding remarks and outstanding issues . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 Appendix A. The EONY model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 Appendix B. The solute trap recombination model gs (4) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

1. Introduction 1.1. Objective of the paper The objective of this paper is to provide a historical overview and status summary on predicting neutron irradiation embrittlement of light water reactor (LWR) pressure vessel (RPV) steels. Here we define embrittlement as the degradation of fracture resistance of RPV steels in specimens, or vessels, with sharp cracks. More than 2400 papers are listed in an All Categories search of Web of Science papers on the topic of “RPV embrittlement or reactor pressure vessel embrittlement”; and a review of the titles of papers published in 2019 suggests that about 80e90% of the papers are actually pertinent to the topic. And far more papers have been published in proceedings that are not listed on the Web of Science. Thus, we have chosen to narrow the focus of this paper to research to predict increases (shifts) in the temperature, DT, marking the transition from unstable brittle cleavage, to stable ductile microvoid coalescence, crack propagation modes. This means that many other topics related to embrittlement, including fundamental modeling, dosimetry, damage production, fracture mechanics, and so on, could not be covered. The objective of this introduction is to summarize what is discussed in more detail in the sections that follow. It is useful to define three approaches to predicting DT. The earliest method was the use of what we call engineering trend curves (ETC). ETCs are based on mathematical relations between DT and the set of identified independent embrittlement variables, which provide the best statistical representation of a fitted database. The second method is mechanistically based correlations (MBC), which are also based on statistical fits to DT databases; but rather than using simple algebraic equations, MBC fitting forms are physically (and microstructurally) motivated. The third approach is multiscale models (MSM), which involve minimal fitting and maximum physics. We

hasten to add that different terminologies are used in practice, and the lines between the three approaches are often blurred. However, we will refer to ETC, MBC and MSM (DΤ) models in what follows. Our emphasis is on the MBC models, and the micromechanical and microstructural foundation needed to quantitatively predict DT, especially beyond the current database. Specifically, we seek quantitative, predictive relations between DT and the combination of metallurgical and irradiation variables as: DT ¼ f[Cu, Ni, Mn, Si, P, …product form/processing history (initial microstructure), flux (4), fluence (4t), irradiation temperature (Ti)]. 1.2. Stages of DT model development The development of increasingly robust DT models occurred in several distinct stages.1 In late 1960s the effects of trace Cu (
1

Except in one case, we defer long lists of references to the following sections.

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characterization tools, as well as the development of advanced fracture mechanics methods. Many MTR irradiations were carried out around the world from the early 1970s to the 2000s; for example, some explored the effects of Ni, 4 and other newly recognized embrittlement variables. These studies included two large controlled, variable-combination MTR irradiations in the US, the first beginning in the early 1980s and the second beginning in the mid 1990s. Both of these experiments involved more than 1500 alloy-irradiation condition variable combinations; and the alloy matrices included specially prepared compositionally tailored steels. Small specimen and semi-automated test methods enabled large-scale post irradiation examination (PIE) campaigns. Mechanical property measurements were complemented by extensive microstructural characterization studies, and the results were used to further develop MBC models. The synergistic thermokinetics effects of Cu, Ni, Mn and Si were first modeled in the early to mid1990s, leading to predictions of large contributions to DT from MnNi-Si precipitates (MNSPs) at high 4t, that were then dubbed late blooming phases (LBP). In the first decade of this century, large-scale MTR PIE studies of both mechanical property and microstructural evolutions provided a clear understanding (and an empirical map) of the combined composition and irradiation variable effects on DT. These experimental insights led to refined МВC models that were used to fit much larger surveillance databases. MTR PIE revealed strong and systematic 4 effects at low 4t, quantified Cu-Mn-Ni synergistic interactions and provided the first experimental hints of MNSPs. However, the resulting MBC DT models, still in use to this day, are reliable only up to z 4
1023 n/m2 (>1 MeV), and do not include the effects of MNSPs that are important at higher 4t. During this period large-scale MSM embrittlement research began in Europe, first as the REVE project, followed by the EU PERFECT (PERFORM 60) and LONGLIFE programs. The EU research included development of a wide range of advanced modeling tools (e.g., density functional theory based defect and solute energies, molecular dynamics, dislocation dynamics and various Monte Carlo methods) and sub-models of various embrittlement mechanisms (defect obstacle interactions, solute transport, defect solute complex formation, etc.).2 However, this MSM effort did not get as far as directly predicting DT for operating vessels suitable for engineering application. Multiscale modeling was more recently reinitiated in the US, by D. Morgan’s group at the University of Wisconsin, in collaboration with UCSB (see Section 6). While the UW-UCSB MSM are not yet as quantitatively precise as DT database fitted MBC models, they predict all of the major embrittlement variable trends based on clearly defined physics. Over the last decade, the implications of MNSPs, and other high 4t hardening features, like dislocation loops, have been an increasing focus of embrittlement research. The major current challenge is the development of low 4 high 4t MBC models for extended plant life operation.

2 The reader is directed to major EU modeling contributions from: D. Bacon at Liverpool University in the UK; S. Jumel, C. Domain and G. Monnet at EDF, C. Becquart at the University of Lille and A. Barbu and F. Soisson at CEA in France; G. Bonny, D. Terentyev and L. Malerba at SCK in Belgium; P. Olsson at KTH in Sweden, K. Nordland at the Helsinki Institute of Physics in Finland. Notably, the PERFECT and LONGLIFE projects also involved highly coordinated and well-designed experimental research programs, including microstructural studies by F. Bergner at the Dresden Helmholtz Research Center and fracture studies by H. Hein at Areva in Germany, both involving a network of EU researchers. US modeling contributions included work by Y. Osetsky and R. Stoller at ORNL in and, more recently, MSM developed by D. Morgan at the University of Wisconsin in collaboration with UCSB (see Section 7). However, further historical discussion of this large body of outstanding modeling research is beyond the scope of this paper, which mainly emphasizes integrated MBC predictive modeling of DTc.

3

1.3. Framework for predictive model development The basic elements of embrittlement are: a) production of primary and defect-solute complex in cascades generated by high energy neutron-nuclear interactions; b) accelerated solute precipitation due to radiation enhanced diffusion and segregation; c) precipitate and defect solute cluster hardening; and, d) hardening induced ductile to brittle transition temperature increases. Each of these sub-processes can be integrated into a hierarchical multiscale embrittlement model as described in an MSM paper published in 2000 [1]. The hierarchical MSM concept is illustrated in Fig. 1 that was prepared at that time. It illustrates parallel tracks of experiment and modeling. The first two rows are related to near atomic scale processes of defect production and solute (and defect) clustering (precipitation). The next two rows illustrate micromesoscale to continuum processes of hardening and embrittlement, respectively. The last row compares DT predictions of a MBC model (Eason, Wright and Odette) to both: a) the surveillance data available at the time; and, b) a comparison of corresponding predictions of the effects of Cu and Ni to early independent results from the UCSB Irradiation Variables (IVAR) program. An updated MBC model (Eason, Odette, Nanstad and Yamamoto) and IVAR data comparisons are discussed in Section 4. Embrittlement microstructures and mechanisms are reviewed in Sections 5 and 6. ETC models are typically structured as DT ¼ CFxFF, where CF is a chemistry factor and FF is a 4t function. Most MBC models are currently founded on a two-feature concept, including hardening from: a) defect clusteresolute complexes, that are now often called stable matrix features (SMF as indicated by the subscript m), which are found in both Cu bearing (z 0.07 wt%) and low Cu ( MNSPs in low Cu steels; and, CRPs e> CRPs þ MNSP appendages (plus some SMFs - > MNSPs) in Cu bearing steels. The hardening due to the continuum evolution of these multiple embrittlement features is illustrated in Fig. 2. MBC models must be mechanistically informed by MTR data, and ideally calibrated to surveillance databases. Surveillance and MTR databases are complementary in dealing with limitations of either one alone. Advantages of MTR data include the possibility of more precisely controlled and specified combinations of 4, 4t and Ti, for irradiations of large, well-controlled, combinatorial matrices of diverse alloys and alloy compositions. These alloy matrices have included both surveillance and special heats of tailored steels, with controlled variations in their compositions (e.g., Cu, Mn, Ni, Si, P,....) and starting microstructures. Other key elements needed to develop predictive MBC DT models, include: a) small specimen test procedures, to enable the combinatorial irradiation PIE studies of large embrittlement variable matrices; b) development and application of state-of-the-art microstructural characterization tools, such as atom probe tomography (APT), small angle neutron scattering (SANS) and transmission electron microscopy (TEM); c) mechanism models and experiments relating irradiation variables to microstructural evolutions (DMS), microstructure evolutions to dislocation-mediated constitutive properties (DMS -> Dsy), and constitutive to mesoscopic continuum scale properties (Dsy -> DT). The advantages of MBC over ETC models are worth emphasizing. While ETC models may be capable of interpolating within a wellstructured DT surveillance database, they are not reliable for

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Fig. 1. Illustration of how MSM link atomic to continuum scale processes to ultimately predict DTc: top - defect production and precipitation; middle top - precipitation hardening; middle bottom - hardening induced DT. The bottom three figures show how predictions a MBC model fit to the US surveillance database compares to measured DTc (left) as well as to an independent MTR database on Ni and Cu effects (middle and right).

extrapolation; and they generally lack the advantage of guidance from independent well-established physics and microstructural insight. This is shown by the significant diversity of ETC models. A notable example of the issue of extrapolation is the 4t dependence of DT. Essentially, all previous ETC and MBC models included a DT contribution that varied with 4tm, where m ranged from z0.3 to 0.6 at low to intermediate 4t. However, as discussed in Section 7, it has been recently observed that between intermediate and high 4t,

m z 1. This can be understood and modeled by including the effects of MNSP. A physical basis now exists for predicting DT at high 4t based on thermokinetic models and a better understanding of 4 effects, again as discussed in Section 7. This more focused (on DT predictions) paper is intended to complement broader RPV and RPV embrittlement reviews including: an excellent recent book edited by N. Soneda [2]; book chapters by C. English [3], T.J. Williams [4] and M. Brumovsky [5];

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range of cutting edge experimental and modeling research on microstructural characterization and mechanical property measurements that have impacted a wide range of materials science and technology. These contributions include the Local Electrode Atom Probe (LEAP), the master curve method for measuring fracture toughness, and advanced electronic and atomic scale modeling methods. 2. DT and the structural integrity assessments of RPVs 2.1. RPVs

Fig. 2. An example of a multi-feature RPV irradiation hardening model with transient SMF hardening and two Avrami precipitation hardening contributions for CRPs and MNSPs fitted to z0.41Cu, 0.86Ni, 1.35Mn, 0.005P wt.% (LC) steel (data not shown).

and review papers by G.E. Lucas [6] and J.C. van Duysen [7].3 We also note a very recent review of international embrittlement surveillance programs edited by W.L. Server and M. Brumovsky [8].

1.4. Organization of the paper This paper is organized as follows. Section 2 briefly describes how DT predictions are used in vessel integrity assessments. Section 3 provides a historical overview, summarizing progress on developing improved DT predictions over the last six decades (undoubtedly incompletely). This progress includes growing DT and Dsy databases, which along with multiscale-multimechanism experiments and models, are the basis for developing robust MBC DT predictions that reflect the underlying physics of embrittlement. The unique role of the International Group on Radiation Damage Mechanisms (IGRDM) in facilitating research on embrittlement is noted. Section 4 notes various historical international ETC and MBC approaches to predicting DT; but, as a specific example, focuses on the Eason, Odette, Nanstad, Yamamoto (EONY) MBC model, including comparing EONY predictions to an independent database from the UC Santa Barbara (UCSB) Irradiation Variables (IVAR) experiment. Section 5 summarizes key observations of embrittled microstructures as the critical foundation for MBC and MSM. Section 6 describes the authors’ current understanding of embrittlement mechanisms and lays out in some detail the quantitative basis for constructing both complex and reduced order rigorous, physically based, hierarchical DT models. Section 7 outlines the status of ongoing efforts to develop a new low 4, high 4t MBC DT model for extended RPV life. Section 8 briefly summarizes some outstanding issues. Obviously, it is not possible to cite the many hundreds of researchers worldwide, or to discuss their various contributions to the topic of RPV steel embrittlement that they made over the past six decades. We apologize to the many institutions and contributors and contributions that we have missed. In closing this section, it is important to note that RPV embrittlement studies reviewed here have played a leading role in a broad

3

Many papers on RPV embrittlement can be found in this journal, ASTM STP Proceeding on Irradiation Effects on Materials, ASME Pressure Vessel and Piping Conference Proceedings, IAEA meeting proceedings and coordinated research program reports on embrittlement, and MRS Symposium Proceedings on Microstructure Evolution During Irradiation.

Excellent reviews of RPV technology and vessel structural integrity analysis can be found in [4,5,7,8]. Briefly, the primary function of a RPV in light water reactors (LWRs) is to increase the coolant-moderator pressure in order to elevate its boiling point and the reactor’s energy conversion efficiency. Water temperatures range from z270 to 330  C, at pressures of z16 and 7 MPa in PWRs and BWRs, respectively. Thus, thick-walled (heavy section) pressure vessels are required. Although they vary considerably, PWR RPVs have a prototypic diameter of z5 m, a height of z12 m and a wall thickness of z0.25 m nominally weighing z400 metric tons. Here we will focus on PWRs, since they experience a peak 4t that is much higher than in BWRs. RPVs are manufactured from quenched and tempered low alloy Mn-Mo-Ni-Si-C steels, in the form of rolled plate and ring forging base metals, that are joined by heavy section welds [4,5,7,8]. Ring forgings only require circumferential welds, while plate sections also require axial welds. Vessel specifications evolved over the years, both due to technological improvements and observations of embrittlement sensitivity to steel impurity and alloying elements. Some early US vessels used Mn-Mo steels with relatively low z0.2 wt% Ni, like A302B, with mixed ferrite-bainite microstructures. Later US and Japanese vessels typically used medium z0.6e0.8 wt% Ni bainitic steels, like A533 grade B, with greater strength and toughness. European vessels also typically used medium Ni alloys with specifications similar to A508 grades II and III, often in the form of ring forgings. However, some European RPV steels have higher Ni, of up to z1.6 wt%. RPVs are factory manufactured, primarily using stress-relieved submerged arc welding (SAW) methods, and transported to the nuclear plant site. The base and weld metals chemistry and weld fluxes vary between vessel fabricators, different vessels from the same fabricator, and even within a vessel, especially in the case of welds, with compositions that can even differ at various locations. The key embrittling elements are Cu, Ni and P while Mn and Si play a smaller role. Notably, impurity Cu is found in recycled steels; and some early US vessels were fabricated using Cu coated weld wire. Since the topic is beyond the scope of this paper, we note only in passing that former Soviet Union RPVs typically contain 1 wt% Cr, higher P, lower Cu (in most cases), and generally lower (VVER 440) or higher (VVER 1000) Ni contents compared to western vessels [5,8]. The Cu contents of some RPV base metals, and particularly welds, were higher in some of the first US vessels, compared to later vessels used in most other countries. As noted above, the elements mediating DT generally include Cu (0.02e0.4), Ni (0.2e1.7), Mn (0.6e2.0), Si (0.2e0.6) and P (0.003e0.04), in units of wt.%. 2.2. RPV integrity assessments and DT A second function of the RPV is to act as a barrier to the release of radioactivity under all conceivable circumstances, requiring very large structural integrity margins to prevent rapid brittle vessel fracture. As well as DT predictions, vessel integrity assessments involve a wide range of engineering disciplines, databases and

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computational tools, including: neutron dosimetry, thermal hydraulics, solid mechanics, fracture mechanics, non-destructive flaw detection, fatigue analysis, probabilistic risk assessment and so on. Considerable progress has been made on all of these topics over the past 50 years. In the US, vessel integrity assessment procedures are dictated by the U.S. Nuclear Regulatory Commission (NRC), in the form of regulations published in Title 10 Part 50 of the U.S. Code of Federal Regulations (10CFR50). The NRC regulations rely on American Society of Mechanical Engineers (ASME) Codes and the ASTM International Standard Practices [see overviews in 4,5,7,8]. RPV integrity assessment requirements are complex and have evolved over the years. Thus a detailed discussion of this topic is beyond the scope of this paper. Here we focus on using DT to establish an irradiated lower bound fracture toughness-temperature curve. This has been generally based on the ASME reference KIR(T) curve developed in 1971 by a Pressure Vessel Research Committee (PVRC) Task Group. The ASME KIR(T) curve is a lower bound of the then available KIc quasi-static elastic fracture toughness, KId dynamic fracture toughness, and KIa crack-arrest toughness data, plotted on a reference temperature (RTNDT) indexed temperature scale (T - RTNDT). The indexing RTNDT is determined by a combination of drop-weight nil-ductility transition temperature tests and Charpy V-notch (CVN) impact tests [8]. The KIR curve was incorporated in the ASME Boiler and Pressure Vessel Code in 1972 [9,10], using ASTM testing standards [11,12]. Within severe constraints fracture toughness, KIc(T), can be considered to be a property of a particular steel condition [13]. Unstable elastic (brittle) crack propagation initiates when a computable applied stress intensity factor (KI) is equal to the steel elastic fracture toughness, KIc [13]. This is analogous to the condition that the start of plastic deformation in a tensile test, or structure, occurs when the applied stress, sa, equals the yield stress, sy. KI is related to stresses in the vessel and the crack dimensions and geometry [13,14]. Regulations require that MKI  KIR, where M is a safety factor. Fig. 3a illustrates how the KIR(T) reference curve is indexed on an absolute temperature scale by the RTNDT for a particular steel condition, as KIR(T- RTNDT) [15]. The KIR curve is

currently incorporated in Section XI of the ASME Code, where KIR is represented by the crack-arrest KIa, but the curves are identical. At the start of life, brittle fracture of a vessel is not an issue since the unirradiated KIR values fall well above any applied KI value. However, fast neutrons emitted from the reactor core increase the RTNDT (DRTNDT), which is the main focus of this paper. The irradiated (i) reference temperature, RTNDTi, is RTNDTu þ DT þ margin, where u denotes the unirradiated condition. Charpy V-notch impact (CVN), and drop weight tests are used to determine RTNDTu. In the US, absent of complications arising from low CVN upper shelf energy, DT is determined by the shift (DTc) in the CVN energytemperature curve at 41J, and RTNDTi ¼ RTNDTu þ DTc þ margin. More recently, the fracture toughness based Master Curve (MC) method [16], KJm(T e To), was approved by the NRC for use as an alternative to KIR(T- RTNDT). The KJm(T e To) invariant MC shape is indexed by a fracture toughness reference temperature (To), where To is the temperature at a median KJc ¼ 100 MPa√m, adjusted to a 25.4 mm thick, deeply fatigue precracked specimen, again for a particular steel condition. The J in KJc denotes the J-integral based elastic-plastic toughness, which permits the use of much smaller specimens than are needed to measure KIc. The MC method was first proposed by Wallin [17e19] and has been the subject of a large body of international research [20] leading to widespread use of the ASTM E1921-19 Standard Test Method [16] for measuring To. The universal median MC is given by KJm(T) ¼ 30 þ 70exp[0.019(T e To)]

(1)

Fig. 3b shows the mean MC KJm(T e To) for a large body of quasi static fracture toughness data, along with the corresponding master curves at the 1, 3, 5, 95, 97 and 99% tolerance bounds [21]. This means, for example, that 99% of the measured KIc toughness data should fall above the 1% tolerance bound curve. Notably, To can be measured using a relatively small number of relatively small specimens, based on a combination of elastic-plastic fracture mechanics and statistical methods, as described in ASTM E1921-19 [16]. Unfortunately, further discussion of major progress in fracture mechanics is beyond the scope of this paper.

Fig. 3. (a) The ASME KIR ¼ KIa curve in Section XI of the ASME Code on a (T- RTNDT) indexed temperature scale [15]; (b) the median Master Curve KJm(T e To) for a large body of quasi static fracture toughness data, along with the corresponding curves at the 1, 5, 95 and 99% confidence intervals [21].

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2.3. DTc predictions and KIR indexing The key point is that the DT (almost exclusively currently DTc, but DTo is now permitted) must be predicted as a function of vessel 4t. As a result, there are very large DTc and, to a lesser extent DTo, databases, both from vessel specific surveillance programs and MTR irradiations. There are also a large number of ETC and MBC. As an example, the MBC EONY model is discussed further in Section 4 [22e24]. While details differ, international regulators generally use procedures that are broadly similar to US NRC practices, which are summarized in what follows. NRC Regulatory Guide 1.99, Revision 2 [25], specifies the DTc for normal plant operation; this RG was also used in Part 50.61 of Title 10 CFR for Pressurized Thermal Shock (PTS) evaluations. An alternative PTS rule, in 10 CFR 50.61a, uses the more recent EONY DTc model [22e24]. Both correlations are based on analyses of the DTc surveillance database that were available at the time. Note that actual regulatory practices are more complex than described here; however, further discussion of this topic is beyond the scope of this paper. Finally, since in most cases embrittlement is the result of, and can be related to, irradiation hardening characterized as the change in the yield stress, Dsy is often used as an experimental surrogate for DT [26]. Thus Dsy and DT will be used interchangeably in this paper. 3. A brief history of embrittlement research 3.1. RPV surveillance and early embrittlement research Fig. 4 illustrates the history of RPV embrittlement research. The inner blue boxes, read in the clockwise direction, represent stages in the development of DT prediction methods, indicating examples

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of ETC, MBC and MSM. The outer green boxes show the main drivers and enablers associated with the evolution. The unboxed text provides some examples associated with the box to which they are connected. In most cases the enablers and drivers have affected more than one type of model. The dashed arrows indicate where they have been most influential in the evolution of predictive DTc models. The need to deal with RPV embrittlement was recognized in the 1950s. The first classified DTc measurements were surveillance programs to monitor the toughness of PWR vessels used in nuclear submarines, including the Nautilus, which was commissioned in 1954. The Shippingport nuclear power plant, which was the first US commercial PWR to generate electricity for the grid beginning in 1958, also included surveillance capsules. Surveillance capsules contain Charpy specimens of (nominally) the most sensitive vessel steels. They are attached to the inner vessel wall, thus reach a higher neutron 4t than the RPV itself. Measured surveillance DTc have been used to give early indications of vessel embrittlement ever since, and to populate what, in the US, is now the Power Reactor Engineering Database [27]. Notably, M. T. Kirk, at the US Nuclear Regulatory Commission (NRC), recently led a task group for the American Society of Testing and Materials (ASTM) E10.02 committee that compiled the most current and comprehensive international DTc database, including both surveillance and test reactor results [28]. Perhaps the first results of unclassified test reactor irradiation experiments to measure DTc, were on an A212B steel, published in the 1950s by R. Berggren and co-workers at Oak Ridge National Laboratory (ORNL) [29]. In the late 1960s and early 1970s irradiation experiments on a limited number of RPV steels, carried out by J.R. Hawthorne and coworkers at Naval Research Laboratory (NRL), found that DTc is primarily controlled by the steel trace Cu and P

Fig. 4. The historical stages in the evolution of irradiation DT prediction methods.

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contents [30,31]. Notably, P and Cu are common impurities in steels; and many early US RPV submerged arc welds contained high Cu levels introduced by the use of Cu coated welding wires. While this paper focuses on low alloy LWR RPV steels, we note that Cu and P were also associated with the embrittlement of the mild C-steels used in the United Kingdom (UK) Magnox gas cooled reactors (see below). A recent publication describes extensive surveillance programs, to monitor embrittlement in Magnox steels [32]. The crosscutting overlap of embrittlement mechanisms between Magnox and LWR steels was important in promoting international research, with extensive early scientific exchanges between members of the International Group on Radiation Damage Mechanisms (IGRDM) in RPV steels (see below). However, the nanoscale defects involved in irradiation hardening and embrittlement were not resolvable in early TEM studies. Hence, they were widely known as “no see ums”, in (black) humor reference to the viciously biting, but nearly invisible, flies populating US northeastern forests. Surveillance data began to accrue during this period and formed the basis for the first NRC embrittlement (DTc) regulatory guide, RG 1.99, issued in 1975; RG 1.99 was soon superseded by 1.99 Rev 1 in 1977 [33]. Embrittlement research continued in the late 1970s through the 1980s, with perhaps the most notable result being the first ETC and MBC models, which included a large Ni contribution to DTc [34e36]. Indeed, the role of Ni emerged as a topic of worldwide research interest during this period. While the identity of the hardening features largely remained a mystery, in the early 1970s TEM observations at NRL by F. A. Smidt and co-workers, suggested that vacancy loop solute cluster complexes were the culprit [37]. An early Atom Probe Field Ion Microscopy (APFIM) study, by S. S. Brenner at the University of Pittsburgh and collaborators, found Cu-vacancy cluster type nanoscale features [38e40]; and SANS measurements by F. Frisius and co-workers at GKSS Research Center in Germany, indicated the presence of Cu clusters in a paper published in 1983 [41]. Surveillance data continued to accumulate around the world during this period. The Electric Power Research Institute (EPRI) sponsored research on embrittlement beginning in the 1970s, including extensive fracture mechanics studies by R. Wullaert and W. Server at Fracture Control Corporation (FCC) in Goleta, CA. The EPRI sponsored FCC research first focused on fracture toughness data collection, baseline testing and an unexpectedly large DTc found for the high Cu Maine Yankee surveillance weld. As part of this effort, EPRI also funded work on embrittlement modeling by G. R. Odette and G. E. Lucas at UC Santa Barbara (UCSB). This soon led to a large, controlled multivariable irradiation experiment at the University of Virginia (UVA) Reactor (see below) carried out by UCSB in the 1980s. 3.2. Towards MBC DTc models In 1980 Odette proposed a model for embrittlement by Cucoated nanovoids formed in displacement cascades [42], which was consistent with the early APFIM observations by Brenner. In 1983 Odette published a follow-up paper on the dominant mechanism of embrittlement, proposing that radiation enhanced diffusion (RED) accelerated the precipitation hardening by highly supersaturated Cu [43]. The model treated diffusion controlled growth of a specified number density (N) of pre-existing precipitate nuclei to effective matrix Cu depletion. The Cu-precipitate volume fractions (f) and diameters (d) were related to Dsy using the Russell-Brown hardening model [44]. The Dsy was then converted to a shift as DTc ¼ CcDsy, where Cc was a micromechanically justified, empirical estimate of z0.5  C/MPa, pertinent to lower Dsy and DT experienced up to that time [26]. This first simple, but mechanistically linked, multiphysics model was shown to agree well with

the observed Cu and 4t dependence of DTc, as well as APFIM observations of Miller [45]. As discussed below, and in Section 5, it was soon found that the Cu rich precipitates (CRPs) are alloyed with Ni and Mn (and, it was soon found, Si as well). Again, CRPs form in steels with > z 0.07 wt% Cu [22e24]. J. Varsik and S. Byrne, at Combustion Engineering, published an ETC model in 1978 that included a strong effect of Ni [34]. In the early 1980s, based on insight from his RED accelerated Cu precipitation model, Odette fitted a single feature MBC DTc ¼ f(Cu,Ni, 4t) form to the then US surveillance database, composed of 151 plate and 65 weld data points [35]. This MBC model had a Cu and Ni dependent CF, and a power law FF, 4tm, with m z 0.18 for welds above z 1023 n/m2, and m ¼ 0.28 for plates. G. Guthrie, at the Hanford Engineering Development Laboratory in the US, also fitted a single feature ETC model to a similar surveillance database [36]. N. Randall, at the US NRC, used a blend of the Odette and Guthrie models to revise DTc predictions in Regulatory Guide (RG) 1.99 Rev. 2, issued in 1988 [25,46]. RG 1.99 Rev 2 also included guidance on extrapolating DTc through the vessel wall. As noted previously, RG 1.99 Rev 2 still represents the formal US NRC regulatory position on embrittlement for normal RPV operation. Independent research at the UK CEGB Berkeley Laboratory by S. A. Fisher, J. T. Buswell, and R. B. Jones, also beginning in the early 1980s, focused on Cu precipitation hardening in mild carbon steels used in Magnox gas cooled reactor vessels. This work led to a MBC model by Fisher and coworkers, based on estimates of the ratio of the RED to thermal diffusion coefficients, that were used to index an empirical thermal Cu precipitation-hardening curve on a 4t scale [47]. Most notably, Fisher’s model also included a separate term to account for a DTc contribution that is independent of Cu, now usually called a stable matrix feature (SMF). Fisher’s model introduced the two-feature (CRP þ SMF) concept, commonly used in MBC used for fitting surveillance data to this day, like in the EONY model [22e24]. In 1987 Fisher published a similar DTc model for low alloy steels [48]. In the late 1980s to early 2000s there was also significant research on non-hardening radiation enhanced temper embrittlement in C-Mn steels, due to accelerated P segregation induced weakening of grain boundaries, led by workers in the U.K. at Harwell and Berkeley Laboratories [49e54]. However, this mechanism is not significant in most western low alloy RPV steels. Note, non-hardening embrittlement is a central theme of a very large Soviet RPV embrittlement literature [55]; however, again, this topic is beyond the scope of this paper, which focuses on western low alloy RPV steels. Test reactor irradiation programs expanded in the 1980se2000s. In the US, they included research by R. Nanstad, M. Sokolov, W. Corwin and coworkers, as part of the NRC sponsored ORNL Heavy Section Steel Technology (HSST) and Irradiation (HSSI) Programs [56e61]. The EPRI and the NRC sponsored irradiation experiments conducted by UCSB (see below) and Materials Engineering Associates (MEA). For example, Hawthorne at MEA used compositionally tailored alloys to explore Cu, P, Ni and 4 effects [62,63]. There was also considerable activity in the UK on embrittlement research, focused on mechanistic understanding, the development of MBC models and advanced microstructural techniques. Most notably, a vigorous embrittlement research program aimed at developing MBC models was led by T. J. Williams (and more recently by K. Wilford and N. Riddle) at Rolls-Royce (RR), beginning in the late 1970’s, in collaboration with C.A. English, W.J. Phythian, J. M. Hyde and others at Harwell and the University of Oxford [64e76]. The RR program involved irradiations, in four MTRs, of nine low (<0.5%) and three high (z1.6%) Ni welds, including some with deliberate copper additions, and four A533B plates. The irradiation variables studied included 4, 4t, neutron spectrum and Ti

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(225  Ce315  C). Mechanical property measurements (Charpy and microhardness) were complemented by extensive TEM, SANS and APT microstructural characterization studies. The RR-Harwell research led to the development of MBC for low alloy steels [64e70] based on modified versions of Odette and Fisher models fitted to the RR database. Further, workers in the UK were among the leaders of the application of field emission scanning TEM (FEGSTEM) [72,73], APT [3], and SANS [71] to the study of RPV steels, leading to notable advances in understanding of the effect of irradiation and material variables on the structure, composition and volume fraction of the precipitates, and the mechanisms of solute cluster formation [73,76]. Auger and FEGSTEM were also used to characterize sub monolayer P coverage on grain boundaries [74]. Above all the UK research confirmed the importance of microstructural observations and mechanistic understanding to correctly interpret and underpin the empirical data and models. With the support of EPRI, Odette and Lucas at UCSB, carried out what can be described as the first large-scale combinatorial irradiation experiment in UVA Reactor from 1982 to 1985 [77]. The objective of this experiment was to characterize the relationship between embrittlement (measured in terms of Dsy or equivalent) and the combined set of key irradiation and metallurgical variables. The irradiation covered a wide range of 4, 4t and Ti conditions. The UVA alloy matrix consisted of z100 model ferritic binaries and ternaries alloys and complex steels, with a wide range of compositions and starting microstructures, that were irradiated in a variety of small specimen geometries. Notably, for the first time, the steel matrix included a large matrix of a compositionally tailored series of small split melt plates, with controlled combinations of Cu, Ni, P and heat treatment, While the final report on the UVA irradiation was published 1989 [77], this was preceded by a number of key papers [78e83]. Perhaps most notably, in 1986 Odette and Lucas that proposed a two-feature MBC model for predicting DTc as a function of Cu, Ni, P, 4, 4t and Ti, including a strong effect of Ni in both the SMF and CRP terms [78]. This MBC model self-consistently rationalized a very wide range of microstructural and embrittlement observations. The Odette and Lucas paper also analyzed data reported by Pachur [84], showing that, beyond a threshold 4t, the DTc in low Cu steels is greatly enhanced by high Ni, foreshadowing the effect of what was later to be called LBP MNSPs (see Sections 5 to 7). The UVA irradiations also showed that the volume fraction (f) of CRPs increases with higher Ni, and found that CRPs contain both Ni and Mn [80]. Around the same time, an APFIM study published by S. P. Grant at Baltimore Gas and Electric and M. G. Burke at the University of Pittsburgh in the US, also found early stages of Cu, Mn and Ni clustering, that was remarkably prescient of later CRP observations [85]. The previous discussion dealt mostly with US and UK research leading to, or directly supporting, MBC models. Several other countries also carried out MTR irradiation experiments prior to about 2000, that were mainly published as reports or proceedings, including for International Atomic Energy Agency (IAEA) Coordinated Research Programs [86,87], and proceedings of IAEA expert meetings, as a four ASTM book series, Radiation Embrittlement of RPV Steels: An International Review, edited by L. Steele [88e91]. Many RPV embrittlement papers were also published in the ASTM STP Irradiation Effects on Materials Proceedings series. Note, in many countries, surveillance data were considered to be commercially proprietary, hence were not openly published. Thus, a very important milestone in RPV research in the late

4 The IGRDM chairs, who all have been major contributors to embrittlement research are in sequence: Colin English, G. Robert Odette, Jean-Claude van Duysen, Tim Williams, Gene Lucas, Naoki Soneda, Philippe Pareige and Eric van Walle.

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1980’s, was the founding of the International Group on Radiation Damage Mechanisms (IGRDM) in RPV steels.4 While the first formal meeting of IGRDM was at the Harwell Laboratory in the UK in 1987, Odette and Hawthorne organized a by-invitation precursor workshop following the Second International Symposium on Environmental Degradation of Materials in Nuclear Power Systems e Water Reactors meeting held in Monterey, CA in 1985. The objective of IGRDM, initially sponsored by the NRC and EPRI, was “to provide a forum for technical interaction in research on radiation damage mechanisms in RPV steels and the transfer of the results to engineering models of property changes.” In the 20 meetings that followed, IGRDM has emerged as the major forum for technical exchanges on RPV embrittlement. Again IGRDM’s broad objective was to encourage fundamental research with high practical technical impact. IGRDM members are elected based on their capability and willingness to present important information, often far in advance, or even in the absence of publication. The extensive meeting record of presentations is restricted to members and their organizations, and cannot be further disseminated without written author permission. Invited guests, often students and post docs, also make presentations at IGRDM. Beyond these formalities, IGRDM has been free of organizational limitations and complexities, and has been hugely successful, not only in encouraging more fundamental research and facilitating information exchange on embrittlement, but also in promoting international collaborations. The 22nd meeting of IGRDM is planned for the fall of 2020 in Monterey, California. The other important venue for information exchanges on embrittlement during this period, was the ASTM symposium series on Radiation Effects in Materials, again published as ASTM STP Proceedings. IGRDM promoted a much more fundamental approach to embrittlement research, with considerable emphasis on microstructural characterization, and studies to establish the separate and combined effects of the irradiation and metallurgical variables. This research included: a) extensive application of SANS to characterize CRPs [92e98], that continues to this day [99e102]; b) to a more limited extent, use of transmission electron microscopy (TEM) [98,103] and scanning TEM (STEM) [104]; and, c) the beginning of widespread APT studies of CRPs [105e111]. In the US, PhD research by E. Mader [94] and B. Wirth [95], used extensive SANS measurements to characterize microstructural evolutions and tensile and microhardness tests to measure irradiation hardening. Mader carried out extensive post irradiation annealing (PIA) experiments over a wide range of temperatures, times and steel conditions to characterize the CRP and SMF hardening contributions as a function of combinations of all the significant metallurgical and irradiation variables [94,112,113]. Mader’s low temperature short time PIA was especially helpful in characterizing 4 effects [113]. Wirth took a deep dive into the detailed character of CRPs, again as a function of the combination of key metallurgical and irradiation variables [95,114], mobile cascade interstitial cluster (prismatic loop) defect dynamics [115], and kinetic lattice Monte Carlo (KLMC) studies of long time cascade aging [116]. The understanding of mechanisms that accumulated in the 1980s and 1990s led to the Eason, Wright and Odette (EWO) MBC model, that was fit to the then PREDB, published in 1998 [117]. The EWO model is broadly similar to the EONY model that is discussed in Section 4. The microstructural studies were closely linked to cluster dynamics (CD) thermokinetic models of CRP and MNSP evolutions [118e122]. For example, based on the SANS, STEM and APT insight, Calphad based modeling studies by Odette and co-workers in the early 1990s, rationalized the CRP compositions, and predicted the formation of Mn-Ni precipitates (MNPs), and subsequently Mn-Ni-

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Si MNSPs, even in low-Cu steels. Odette’s model predicted that MNSPs would nucleate and grow slowly compared to rapidly formed and quickly saturating CRPs, hence, he described them as late blooming phases. The typical Mn þ Ni þ Si content in RPV steels is  2 wt%, which is much larger than impurity Cu content (<0.3 wt% in solution). Thus, the corresponding MNSP f, Dsy and DTc is potentially much larger at high 4t, compared to that due to saturating CRPs and a smaller contribution from SMF, where the latter first increases with the √4t. MNSP formation is primarily driven by the steel Ni content, and is promoted by lower 4 and Ti, and even trace amounts of Cu [120,121]. Early Lattice Monte Carlo simulations showed CRPs to have Cu-rich core Mn-Ni-Si rich shellappendage like structures [122]. These early thermodynamic models led to an experimental search for MNSPs that were first found in low Cu steels as reported in 2004 [123]. 3.3. Multitechnique characterization studies, irradiation experiments, MBC and MSM z2000 to 2019 The period from about 2000 to the present saw continued progress in fundamental understanding of embrittlement. APT emerged as the most powerful tool to characterize precipitates (or solute clusters). Some examples include papers published by: M. Miller and coworkers at ORNL in the US [124e130]; P. Pareige, B. Radiguet and coworkers at the University of Rouen in France [106,109,131e133]; J. M. Hyde and coworkers at the National Nuclear Laboratory in the UK [134e138]; N. Soneda, K. Dohi and coworkers at the Central Research Institute of Electric Power Industry (CRIEPI) in Japan [139, 140]; and many others [141e151]. A major advance in APT was the development of the Local Electrode Atom Probe (LEAP) by T. Kelly at then the Imago Corporation in Madison, WI [152]; other APT innovations include the reflectron, developed by A. Cerezo and G. Smith at Oxford University [153]. While APT has become the most common method to characterize irradiated RPV precipitate microstructures, SANS studies have continued [99e102]. APT measurements are broadly consistent with SANS results for N and d, but not with the nominal reconstructed APT precipitate Fe contents, that are typically reported to be 50e70%. The presence of a large amount of Fe in CRPs and MNSPs is now believed by most to be an APT artifact due to trajectory aberrations as shown in [73,154e156], including complementary APT, SANS and TEM EDS measurements [155,156]. TEM is playing an increasingly important role, especially for observing dislocations and loops, which has been enhanced by the development of weak beam scanning TEM (STEM) techniques [157,158] and STEM EDS methods [73,155]. It is impossible to overemphasize the importance of using multiple complementary techniques to characterize embrittlement microstructures. Perhaps the most notable result of APT and other microstructural studies, is confirmation that precipitates contain large quantities of Mn, Ni and Si, first formed as shells around and later as MNSP appendages to the Cu rich region in Cu bearing steels; or simply MNSPs in low Cu-steels [124,125,127,130,135,136,141]. Again, these observations are highly consistent with the much earlier predictions by Odette [118e122]. The APT data demonstrate the very strong effect of Ni on MNSPs at high 4t. High 4t MNSP evolution is discussed further in Sections 5 to 7. Beginning around 1990, positron annihilation spectroscopy (PAS) techniques were used to study both open volume defects (like vacancies, vacancy clusters and dislocation loops) and precipitates [142,159e170]. Notable PAS contributions were made by the M. Hasegawa, Y. Nagai and T. Toyama group, at the Tohoku University Oarai Research Center [142,159e166]; and B. Wirth and the positron group at Lawrence Livermore National Laboratory [167e169]. PAS studies led to a number of conclusions about precipitates and SMFs in complex steels, including: a) positron lifetime

measurements of around 170ps are most consistent with annihilation at dislocations (network and loops), or single vacancies, but not larger vacancy clusters; b) in Cu bearing steels Orbital Electron Momentum-Coincidence Doppler Broadening (OEMS-CBD) data are consistent with positron annihilation at precipitates composed of various amounts of Cu, Ni and Mn; c) the low momentum and open volume longer lifetime component increases with 4, 4t and Ni; d) short time PIA recovers the open volume component at temperatures from z375 to 425  C; e) hardness recovery tracks the low momentum positron component of OEMS; f) the PIA recovery temperature increases with decreasing 4 and increasing 4t, presumably due to a corresponding increase in the thermal stability of the open volume features, which are generally associated with SMF; g) spin reversal OEMS-CBD measurements showed that the precipitates are not, or only weakly, magnetic. In the mid 1990’s UCSB conceptually designed, and ORNL built and operated, what is arguably the largest and most comprehensive, combinatorial Irradiation Variables (IVAR) irradiation experiment ever carried out, in the University of Michigan Ford Research Reactor. The experimental procedures used in the IVAR irradiation and the PIE are described in [22,171,172]; and [22,28,172] contain comprehensive tabulations of the tensile data for the IVAR steels. Additional results of the effect of heat treatment on both the unirradiated sy and Dsy, as well as on the initial Cu in solution, were reported in [171]. IVAR PIE was primarily carried out from 1998 to 2005. A comprehensive series of experiments in the BR2 Research Reactor was carried out over the last 20 years by R. Chaouadi at SCK in Belgium, as part of the RADAMO (and several other) irradiation series [173,174]. The BR2 studies focused on high 4t hardening and embrittlement, to support developing engineering MBC models. K. Fukuya at the Institute of Nuclear Safety Systems (INSS) in Japan reported a series of fundamental ion and neutron irradiation studies that have contributed to a general understanding of embrittlement mechanisms [175]. Other irradiation studies have been led by M. Brumovsky at the Nuclear research Institute Rez in the Czech Republic [8]; it should be noted that Professor Brumovsky has made a large number of seminal contributions to RPV embrittlement, and other nuclear materials research, over a period of more than 50 years. In the US, Odette and T. Yamamoto carried out the large scale UCSB ATR-1 and UCSB ATR-2 MTR irradiation experiments in the Idaho National Laboratory (INL) Advanced Test Reactor (ATR), at high [176] and ultra high 4 and 4t [177], to explore hardening pertinent to extended vessel life. Many other irradiations around the world were conducted over the last two decades, but a discussion of them is beyond the scope of this paper. Development of improved ETC and MBC models for application to national RPV fleets continued in the last decade, for example, in work by M.T. Kirk in the US [28,178], P. Todeschini at EDF in France [179] with update of the ETC FIS and FIM formulas and N. Soneda in Japan [180] with a revised (JEAC) 4201. As a result, there has been a growing awareness of, but little understanding of, the differences between the DTc prediction curves for different RPV fleets. Kirk at the NRC [28], and S. Ortner at the UK National Nuclear Laboratory [181], carried out extensive statistical assessments of various ETC and MBC, based on analysis of Kirk’s very large ASTM E10 database [28]. Section 4 focuses on the MBC EONY model [22e24]. The period from the late 1990’s to present also saw major new efforts to model various sub mechanisms of embrittlement at the atomic and electronic structure scales. The first MSM research REVE program in Europe, was led by Van Duysen at EDF [182e184]. The objective of REVE was to develop an integrated multiscale RPV embrittlement simulation code, hierarchically linking electronic to macroscopic continuum physics over huge ranges of time and length scales. The EU MSM work continued as part of the EU PERFORM60 [185] and LONGLIFE [186] programs. While, further

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general discussion of this large body of outstanding modeling research is beyond the scope of this paper, which emphasizes integrated MBC predictive DTc modeling, some specific examples of the EU work are cited in Section 6. 4. The EONY DT MBC model and the IVAR database 4.1. EONY model development and calibration A comprehensive review chapter by N. Soneda on the history of ETC and MBC models, including a useful timeline, can be found in [187], so they will not be repeated in detail here. Briefly, a number of ETC models adopt DTc ¼ CFxFF type forms, that include US NRC Reg. Guide 1.99 Rev.2 [25], the French FIS and FIM [188], and the more recently updated FIS equations [179]. Current two feature MBC models in the form of DTc ¼ CFmFFm þ CFpFFp, include EONY [22], ASTM E900 [28] and the Japan Electric Association Code [189e191]. While the RG 1.99 Rev.2 ETC remains the official US NRC Regulatory Guide on embrittlement for normal vessel operation, in practice it has been supplanted by the newer MBC that are fitted to much larger databases, like EONY [22e24] and E900 [28,187]. Note Soneda’s timeline also shows the dates for Russian WWER-440 and 1000 ETC and MBC models [192e194] as well as MBC models proposed by Williams [68,70,195] and Debarbaris [196,197], which are mainly based on MTR data. Here we focus on the EONY model, which was published as an ORNL report in 2007 [22], with two follow up papers [23,24], and the independent supporting IVAR database. The EONY model was calibrated by nonlinear least squares fits to the US surveillance database at that time, which was composed of 855 DTc data points. After testing a huge number of trial forms, the final EONY model provided good statistical predictions, with no significant residual error trends and with all fit parameters established at a high confidence level [22e24]. Some features of the EONY model are purely empirical, like variations in product form coefficients, the absence of a Ni effect on DTm and an athermal DTp (see below), while others are physically based, or are consistent with independent test reactor results from the IVAR program (see below). However, a key ground rule was that the EONY model was calibrated using only the US surveillance data (as verified and corrected by ASTM Committee E10.02), and the final model selection was based on a statistically justified minimum predicted minus measured DTc least square fit standard deviation (SD) criterion. As a consequence some variable effects that are not large relative to the scatter in the PREDB are

11

absent in EONY, despite other evidence that would support their inclusion. As noted above, other parts of the EONY model are likely unphysical, or not even necessary, particularly if some leeway had been given to the statistical fit criteria. The EONY equations can be found in [22e24] and are shown in Appendix A. As illustrated by the example for a 0.2 Cu, 0.7 Ni, 0.6 Mn, 0.010P weld in Fig. 5, the EONY model has SMF (at all Cu) and a CRP (for > 0.072 wt% Cu) terms, where DTc ¼ DTm þ DTp (note the temperature unit in EONY is  F). The SMF DTm increases with the √4te and linearly with decreasing Ti as, DTm ¼ PFm(1e0.00172Ti) (1 þ 6.13PMn2.47)√4te. The MnP term is weak, but DTm also depends on a product form factor (PFm) that differs significantly for plates, forgings and welds, with systematically different Mn contents. Notably the EONY DTm term does not depend on Ni. The EONY CRP DTp term increases rapidly at low 4te and generally saturates above z 1023 n/m2, due to Cu depletion from the matrix. The DTp at saturation (DTps) depends on the PF and the steel Cu (actually Cue, which is the effective dissolved Cu) and Ni contents as: CFp ¼ PFp(Cue-0. 072 þ 1.36(P-0.008))0.67(1 þ 3.77Ni1.19)

(2)

The PFp are different for plates (3 PF for plates and special reference steels), forgings and welds with >0.4 wt% Ni. The effective Cue is the nominal bulk value up to a maximum of 0.24 wt% for Linde 80 welds, or 0.3 wt% for all other welds. The EONY FFp is a sigmoidal tanh function, varying between 0 and 1 (saturated). The FFp ¼ 0.5 is indexed at a reference 4t0.5, which is affected by increasing Cu (shifting 4t0.5 lower), Ni (shifting 4t0.5 higher) and 4 (shifting 4t0.5 higher). The EONY 4 effect is represented by an effective 4te ¼ 4t(4r/4)0.26, where 4r is a reference 4 ¼ 4.4
1014 n/ m2-s and p z 0.26 is a best fit value. However, the EONY 4 effect is limited to <4.4
1014 n/m2-s; at higher 4, 4te ¼ 4t. The EONY DTp term is athermal and independent of Ti. Fig. 6 shows the EONY predicted versus measured DTc for Cu bearing steels. The filled symbols are randomly selected data points that were not used in the fitting. The quality of the fits varies for the different product forms, but the overall predicted minus measured standard deviation (SD) is ±14  C (±27  F). Thus the EONY MBC model provides a good representation of DTc within the limits of the US PREDB that it was fit to. However, EONY is severely limited by: a) the embrittlement variable range, particularly 4t, that it encompasses; b) uncertainties in the key variables that are also not well distributed, and are often highly covariant; and, c)DTc measurement scatter.

4.2. Comparison of EONY model predictions with IVAR data The objective of the UCSB IVAR program was to measure Dsy, as surrogate for DTc, for a large number of RPV steels and irradiation conditions in order to provide a high-resolution map of the individual and combined effects of controlled variations in all key embrittlement variables (Ti, 4, 4t, alloy composition and PF).5 Note,

Fig. 5. Example of an EONY DTc prediction for a 0.2Cu, 0.7Ni, 0.6Mn, 0.01P weld showing the DTm and DTp contributions.

5 Not counting a large number of simple model alloy and a large steel heat treatment matrix, IVAR contained 57 steels distributed among 13 welds, 3 plates and 41 base metals. Forty one alloys were small heat split melt steels with controlled variations in Cu (0.0e0.8%), Ni (0.0e1.6%), Mn (0.0e1.6%) and P (0.005e0.040%) along with Mo, N, C, B, Mo, As þ Sn þ Sb variants for one Cu, Ni and Mn base composition. The irradiation variable ranges were 4 between 0.07e0.98
1016 n/m2-s, 4t between 0.01e3.32
1023 n/m2 (depending on the 4) and Ti between 270 and 310  C. There are a total of 1537 metallurgical-irradiation variable combinations in the core IVAR database. Note the IVAR Dsy database is tabulated in the PLOTTER tool [28] taken from the UCSB final report [172]. A significant subset of IVAR data is also tabulated in [22 and 171].

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G.R. Odette et al. / Journal of Nuclear Materials 526 (2019) 151863

Fig. 6. Predicted EONY versus measured DTc including all calibration and validation data with Cu > 0.072 wt % for: a) BWR and b) PWR TTS databases [24].

the PF presumably acts as a surrogate for an average (by PF class) of the unirradiated steel microstructure and matrix Cu and Mn contents, which are affected by the fabrication and thermal mechanical processing history. Other IVAR objectives were to characterize embrittlement microstructures, to explore high 4t phenomena, like late-blooming MNSP phases, and to develop a better understanding of deformation and fracture micromechanics in irradiated RPV steels. Here, the IVAR results are compared to the EONY predictions, revealing both the MBC model’s strengths and limitations. The comparison involved converting the EONY model DTc to Dsy estimates based on the semi-empirical model shown in Fig. 26 in Section 6. Consistency with IVAR trends lends strong support to the EONY DTc model, especially with respect to the key mechanisms that underpin embrittlement. Inconsistencies indicate parts of the EONY model, which may not be fully physical; or that reflect limits of the PREDB and the corresponding statistical analysis. Clearly, some inconsistencies are to be expected, for the reasons cited above. The examples in Fig. 7aef shows IVAR data and the corresponding EONY model predictions converted to Dsy plotted against √4t for six submerged-arc surveillance welds irradiated at z 290  C at low, medium, and high IVAR 4. Five of the welds (MW, 62W, 63W, 65W and BWA) in Fig. 7aee contain more than 0.2 wt% bulk Cu; the weld (BWC) shown in Fig. 7f contains only z 0.08 wt% Cu, which is near the 0.072 wt% EONY threshold for CRP contributions to DTc. Fig. 7geh shows similar plots for A302B and JRQ reference correlation monitor steel plates, with z0.2 and 0.14 wt% Cu and z0.2 Ni and 0.80 wt% Ni, respectively. Fig. 7i is for a low Cu, high 1.65 wt% Ni submerged-arc weld, WP. Except in the latter case, the EONY model predictions are generally in remarkably good agreement with the independent IVAR low 4 Dsy data, especially considering the DTc to Dsy conversion uncertainty. The large discrepancy in the case of WP is due to the fact that high Ni does not affect the SMF DTm term in the EONY model. However, a strong Ni effect in low Cu steels is well established, including in the IVAR database. The composition dependence of DTm derived from the IVAR database, which is shown in Section 6 (see Equation (11)), predicts the dashed line in Fig. 7i. Fig. 7 also shows that, in all cases, higher 4 shifts the Dsy data to higher 4t. As discussed further in Section 5 to 7 this shift occurs mainly at low 4t. Good agreement between EONY predictions was also observed for

essentially all the other Cu bearing alloys. The agreement is not as good between the EONY model predictions and the IVAR data for low Cu steels, with either higher or lower than average Ni, again due to the lack of its effect on DTm. Specifically, the Dsy are over predicted by EONY at low Ni, while at high Ni the IVAR Dsy are under predicted. Note, however, that the magnitude of SMF Dsy in medium Ni steels is relatively small at z 40 MPa, up to the maximum IVAR 4t, so in most cases the absolute error is not very significant. Fig. 8a compares the 290  C EONY model predictions of the effect of Cu on Dsy at 1.6
1023 n/m2 to the corresponding IVAR Dsy data for z0.8 wt% Ni steels irradiated at z 3
1015 n/m2-s. Fig. 8b shows a similar comparison for Ni variations in steels with a bulk Cu z 0.4 wt%; notably, the curve for Cumax ¼ 0.24 provides the best fit. Fig. 8c shows the EONY versus IVAR comparison for Mn; in this case the Mn effect in the EONY model is expressed in terms of a lower PF for forgings, with less Mn (z0.8 wt%), than is typical in plates (z1.4 wt%). In all the cases shown in Fig. 8, the observed Dsy trends are in good general agreement with the EONY model predictions for the Cu bearing steels. Fig. 8d plots Dsy for steels with similar Mn and Ni contents versus the √Cu. Least square fits to the IVAR data extrapolate to Cu z 0.057 wt% at Dsy ¼ 0, which is reasonably consistent with the Cu ¼ 0.072 wt% EONY minimum for CRP contributions to hardening. While the predicted versus measured agreement is generally good at 290  C, the EONY model generally predicts a significantly stronger Ti effect in low Cu steels than observed in the IVAR database. Indeed the IVAR data clearly shows that both the SMF and CRP Dsy contributions decrease with increasing Ti, while the CRP term in EONY is athermal. The effect of P is stronger in the low Cu IVAR data than predicted by the EONY model. However, the effect of P is reduced in an IVAR steel with slightly higher 0.1 wt% Cu, consistent with a number of other observations (see Chapter 2 in [22] for a discussion of P effects). An exception to this general trend include results recently reported by Chaouadi, who found higher Dsy for both low Cu and Cu bearing steels at very high P (0.020e0.029 wt%) and high 4t [173]. Note, the smaller P contribution to DTm in the EONY model is counter balanced by a small P contribution to the CRP term. However, the net effect of more than 0.008 wt% P in the EONY model is a larger DTc in Cu bearing compared to low Cu steels, which is unphysical. Possible reasons for the complex effects of P are discussed in Section 6.

G.R. Odette et al. / Journal of Nuclear Materials 526 (2019) 151863

13

Fig. 7. EONY predictions compared to the IVAR Dsy data plotted against the square root of fluence for five Cu bearing welds (aee), two low-Cu (f and i) welds and two base metals (g and h) [22,23]. The IVAR HF, MF and LF 4 are z8, 3 and 0.8
1015 n/m2-s, respectively.

4.3. Flux effects revealed in IVAR data One of the main objectives of the IVAR irradiation was to precisely quantify the effects of 4 on Dsy [22e24,198] and the corresponding microstructural evolutions. In summary, IVAR 4 effects on the 4t dependence of CRP and SMF hardening (and the precipitate f) are consistently systematic and significant. Specifically, the Dsy are shifted to higher 4t with increasing 4, as seen in Fig. 9. The 4 effect is strongest in CRP Dsy contribution, which rapidly increases at low 4t. While the 4 effects look small on an expanded √4t scale, the average low 4 (z8
1014n/m2-s) Dsy is z 23% higher than the medium 4 (z3
1015 n/m2-s) hardening; and the high 4 (z8
1015n/m2-s) hardening is z 14% lower. Thus, for a 4 variation of only a factor of z10, there is, on average, a net 37% difference

between low and high 4 IVAR Dsy. It is again important to emphasize that these 4 effects are primarily observed at low 4t. Note, these effects are much larger for other even higher 4 MTR irradiations and extend to higher 4t, than in the IVAR database. The EONY model includes the same 4 effect in both of the CRP and SMF hardening terms as 4te ¼ 4t(4r/4)p, with a fitted p ¼ 0.26. However, an important difference between EONY and IVAR is that the 4 effect in the calibrated EONY model occurs only at < 4.4
1014 n/m2-s, while it exists over the entire range of the IVAR data. Note, above the EONY 4 threshold, a residual trend with 4 can be detected in some surveillance data sets, in the same direction that is shown by the IVAR data. However, the magnitude of the 4 effect in the EONY model residuals is not sufficiently large relative to the scatter in the DTc to be statistically significant. Notably,

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G.R. Odette et al. / Journal of Nuclear Materials 526 (2019) 151863

Fig. 8. Comparisons of EONY model predictions (lines) to IVAR Dsy (filled triangles) at 1.56
1019 n/m2 and 290  C, plotted against: a) Cu; b); Ni; c) Mn. The vertical arrows show the average compositions of these elements in the EONY plate and forging database, while the horizontal solid and dashed lines are the range of Mn in plates and forgings, respectively; (d) Dsy versus the square root of Cu, where the arrow indicates the EONY Cumin [22].

Williams also found a p z 0.25 4 scaling between about 1015 and 1018 n/m2-s [22,68]. Thus the IVAR and other data suggest that 4 effects in EONY and IVAR are similar, but extend to well above the limit found in fitting the PREDB. The IVAR database also shows weaker 4 effects at 310  C, as expected for the solute trap recombination mechanism [22, 198 and Section 6]. While the EONY limit is adequate for predicting DTc for most vessel service conditions, 4 effects are an issue for interpreting embrittlement data from accelerated test reactor irradiations. A broadly similar 2-feature model was developed by M. E. Kirk at the US NRC, which was adopted as the ASTM E900 Standard Practice for predicting DTc [28]. Kirk also created a very powerful Excel tool called PLOTTER, which can be used to compare various DTc models to various PLOTTER databases. The E900 DTc model was based on very extensive statistical analyses in fitting a large number of trial models to an updated US surveillance database. The trial models were also compared to a large number of other databases,

including IVAR. The E900 DTc predictions are generally similar to those for EONY for typical medium Ni RPV steels; but they provide a slightly better fit to the updated database. An exception is the large over prediction of the ATR-2 Dsy by the E900 MBC for higher Ni steels (see below). In summary, the IVAR and related databases provided tremendous new insights on the effects of key embrittlement variables, and variable combinations; and generally lend strong and independent support to the predictive capability of the EONY model. However, both EONY surveillance and IVAR databases are limited in the 4t range they cover. For example, the EONY database only had 9 and 6 data points above 5 and 6
1023 n/m2, respectively. And the highest 4t in the IVAR database is z 3.6
1023 n/m2. Thus, it is particularly notable that the EONY (and E900) model increasingly under predict higher 4 test reactor DTc data with increasing 4t [199,200]. The specified limit for the application of the EONY model is 5
1023 n/m2. Extension of embrittlement predictions to z 1024

G.R. Odette et al. / Journal of Nuclear Materials 526 (2019) 151863

15

Fig. 9. Precipitate volume fractions (f) for medium Ni low (LG filled symbols) and high (LC unfilled symbols) Cu steels versus: a) √4t; and, b) √4te. Note 4te with p ¼ 0.25 collapses the precipitate f data into a narrow trend band. The Low Flux, Medium Flux and HF 4 are z < 8, 8e30 and 20-2000
1015 n/m2-s, respectively.

n/m2, for extended vessel life, is discussed in Section 7, focusing on the contributions of MNSP LBP and diminution of 4 effects at high 4t. We next discuss embrittlement microstructures. 5. Summary of major microstructural observations 5.1. CRPs and MNSPs This section summarizes the evolution of CRPs and MNSPs as a function of 4, 4t, Ti and alloy composition. The microstructural data is primarily a representative subset of a much larger matrix of alloys in previous and ongoing UCSB irradiation experiments (IVAR, ATR1, ATR-2 and BR2); and, with one exception, the data was generated by UCSB. Here we primarily focus on 6 core alloys with systematic controlled variations in Cu and Ni, as examples, but include several others steels as needed. The compositions and irradiation conditions of these steels are summarized in Tables 1 and 2. The nanoscale precipitates described here were primarily characterized by APT, in terms of their composition (Xi), number density (N), mean diameter (d), and volume fraction (f). Note that these (and other) alloys have also been extensively characterized by SANS. Important

Table 1 The nominal bulk compositions of steels discussed in this section (wt.%). Alloy

Cu

Ni

Mn

Si

P

Fe

LB LC LD LG LH LI CM6 MW 62W 63W 65W BWA BWC JRQ A302B

0.40 0.41 0.38 0.01 0.11 0.20 0.02 0.27 0.23 0.30 0.22 0.21 0.08 0.14 0.14

0.18 0.86 1.25 0.74 0.74 0.74 1.68 0.57 0.60 0.69 0.60 0.63 0.62 0.82 0.20

1.35 1.44 1.38 1.37 1.39 1.37 1.50 1.61 1.61 1.65 1.45 1.69 1.30 1.40 1.20

0.22 0.23 0.23 0.22 0.24 0.24 0.17 0.62 0.59 0.63 0.48 0.45 0.54 0.25 0.28

0.005 0.005 0.005 0.005 0.005 0.005 0.007 0.017 0.020 0.016 0.015 0.014 0.009 0.019 0.015

Bal. Bal. Bal. Bal. Bal. Bal. Bal. Bal. Bal. Bal. Bal. Bal. Bal. Bal. Bal.

Also contains some Mo, C, Cr, S, and other trace elements. See [22] for heat treatments.

findings are summarized as follows. As noted previously, the total dissolved Mn þ Ni þ Si content of typical RPV steels is > 2 at.%, compared to < z 0.3 at.% Cu. Thus, while they grow much more slowly, MNSPs ultimately reach much larger f, compared to rapidly forming and saturating CRPs. A large MNSP f is observed in all the core alloys at the ultra-high ATR-1 4t (z1.1
1025 n/m2); the maximum precipitate Cu content in this condition is less than 15%, and the total precipitate f is z 0.85(2Ni þ Cu). In the medium Ni steels at the high ATR-2 4t (z1.4
1024 n/m2), the Mn þ Ni þ Si contents average z 80 ± 20% of a smaller total f z 0.46(3Cu þ Ni). The average MNSP f is z 0.23% in low Cu steels in the ATR-2 condition. In isolation, f ¼ 0.23 results in sp z 240 MPa strength contribution, which produces a net Dsy z 160 MPa following superposition (see below). Thus, MNSPs are very significant at the high, extended life ATR-2 4t. The total MNSP f grows slowly in low Cu steels, first as precursor defect-solute cluster complex SMF, that are initially formed in displacement cascades; the SMF subsequently convert to wellformed MNSPs, that reach a large volume fraction, f, at high 4t. This is illustrated by the filled symbols in Fig. 9a for a Cu-free, medium 0.74 wt% Ni alloy (LG) steel. The open symbols in Fig. 9a are for a high, nominally 0.41 wt% bulk Cu and medium 0.86 wt% Ni steel (LC). In this case the CRPs first grow rapidly up to a nearly saturated f plateau due to depletion of dissolved matrix Cu, but MNSPs subsequently continue to grow slowly by adding Mn, Ni and Si, ultimately forming an appendage to a CRP region, as seen in Fig. 10. As illustrated in Figs. 11 and 12 [145,147], CRPs and MNSPs nucleate heterogeneously on dislocation loops, network dislocations (and grain boundaries not shown); these features are also the sites of significant solute segregation. It is not possible to distinguish homogeneous from heterogeneous precipitation on very small loops. As seen in Fig. 12, the precipitate number density, N, decreases with increasing Ti (270e320  C) and decreasing Cu (0.2 in LI to 0.1 in LH). Heterogeneous nucleation on network dislocations is an increasingly the dominant mechanism at higher temperature and lower Cu and other solute contents. X-ray diffraction (XRD) revealed that the MNSPs in 5 out of the 6 of the ATR-1 core alloys are consistent with an intermetallic Gphase as illustrated in Fig. 13 [201]. The G2 phase is observed in the Cu free, high 1.6 wt% Ni steel.

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Table 2 The irradiation conditions discussed in this section. Irradiation

4 (n m2s1)a

4t (n m2)a

BR2-G1 BR2-G2 BR2-G3 BR2-G4 BR2-G5 BR2-TU ATR-1 ATR-2 IVAR-T6 IVAR-T11 IVAR-T12 IVAR-T13 IVAR-T14 IVAR-T15 IVAR-T16 IVAR-T21 IVAR-T22 IVAR-T23 IVAR-T24 IVAR-K2 IVAR-Piggyback

1.0
1018 1.0
1018 1.0
1018 1.0
1018 3.0
1016 2.3
1017 2.3
1018 3.6
1016 9.7
1015 2.6
1015 3.2
1015 3.1
1015 3.2
1015 2.6
1015 3.0
1015 1.0
1015 1.0
1015 8.4
1014 8.4
1014 7.7
1015 7.7
1015

1.3
1024 6.6
1023 1.7
1023 3.3
1023 2.1
1023 2.1
1024 1.1
1025 1.4
1024 3.3
1023 3.5
1021 1.0
1022 2.4
1022 4.8
1022 8.5
1022 1.6
1023 3.1
1021 1.1
1022 2.4
1022 4.0
1022 5.1
1022 1.0
1023

a

E > 1 MeV, Tt ¼ 290  C.

The ultra-high 4t ATR-1 irradiation results in nearly full precipitation. Fig. 14a shows that, as noted above, the total CRP þ MNSP f z 0.85(2Ni þ Cu) in this case. Some excess solutes remain in solution governed by the phase diagram modified as modified by the Gibbs-Thomson effect at small precipitate sizes. In contrast, Fig. 14b shows that for the high, RPV extended life relevant 4t ATR-2 condition, the CRP þ MNSP f is z 0.46(3Cu þ Ni). APT shows that the MNSP phases are not completely stoichiometric. However, the average Ni composition is z 49 ± 4 at.% in the core alloys in ATR-1 and 2, reasonably consistent with nominal G (T3) (55 at.% Ni) and G2 (50% at.% Ni) stoichiometric phases in the Gibbs triangle Mn-Ni-Si projection of the Fe-Mn-Ni-Si system

shown in Fig. 15 for the ATR-1 core alloys [145]. The corresponding Si þ Mn constitute z51%. Note Mn and Si trade-off with one another in response to variations in the dissolved alloy contents [147]. Fig. 16 shows that for both the ATR-1 (a) and 2 (b) conditions d and f increase between 0.11 and 0.42% Cu (nominal bulk) in the core alloys with medium Ni, while N is approximately constant [145,147]. The N and f increase with Ni, while d is approximately constant in both Cu-free and Cu-bearing steels. The effect of nominal 0.8 to 1.6 wt% Mn increases on increasing f in low Cu steels in the ATR-2 condition is z 0.14 at.% measured by SANS and 0.23 at.% by APT. The corresponding effect of nominal 0.8 to 1.6 wt% Mn variations on f in high Cu steels is z 0.27 at.%. The total f is only slightly sensitive to smaller variations in Si due to its trade-off with Mn. 5.2. Phosphides In low Cu, high P steels, M(Mn)3P alloy phosphide precipitates formed under IVAR irradiations that cause significant hardening [22]. However phosphides are suppressed in Cu bearing steels, presumably due to P association with CRPs (rather than separate alloy phosphides). It is likely that P lowers the CRP interface energy, thus increasing the CRP N while reducing the corresponding d, at least at lower 4t, with little systematic effect on f [88]. However, higher N indirectly leads to larger Dsy in most cases. Thus the role of P is complex, and depends on many other embrittlement variables. Perhaps most notably, the overall effects of typical variations in P for the high ATR-2 4t condition are modest resulting in Dsy differences of 30 MPa in low Cu steels, compared to the total Dsy  160 MPa for low P and Cu, medium Ni steels (see Section 7). 5.3. Dislocation loops and network dislocations However, there is another significant microstructural evolution

Fig. 10. APT maps showing typical precipitates in a high 0.38 wt% Cu, high 1.25 wt% Ni steel (LD) at: a) high 1.4
1024n/m2; and b) ultra-high 1.1
1025n/m2 4t; and, c) and d) are corresponding blow ups of core shell and core-appendage co-precipitates, respectively.

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Fig. 11. APT maps showing: a) segregation at and precipitates heterogeneously nucleating on dislocation loops and network dislocations in a high 0.40 wt% Cu, low 0.18 wt% Ni steel (LB) in the ATR-2 irradiation; and, b) a corresponding blowup of a large individual loop.

associated with dislocations that is increasingly important at high 4t. At larger sizes (>z 3 nm) weak beam TEM techniques can identify discreet dislocation loops [142,155,156,204e207], which again are sites of solute segregation and heterogeneous MNSP nucleation (see Fig. 11). The average visible loop diameters (d) range from z4 to 12 nm, depending on the particular study (alloy, irradiation condition including ions, and the TEM technique and its interpretation). Visible loops are typically not observed, or their number density is low, up to a 4t < z 5
1023n/m2, and are generally within about a factor of 2 of 7
1021/m3 at the high ATR-2 4t z 1.4
1024 n/m2. Notably, however, a recent weak beam STEM study found z3.4
1022/m3 z 4 nm diameter loops, if the smallest black dot type features are included [158]. The authors concluded that at high 4t, the loops contribute to a significant increment of Dsy, assuming a rather high loop strength factor (see Section 6). The effect of high 4t on the pre-existing network dislocation density is even more unsettled; unfortunately, this has been largely ignored previously. Odette and co-workers recently observed that there is a large range of pre and post irradiation inhomogeneous network dislocation densities (r), ranging from r z 1013 to 1015/m2 in various plates and welds; and considerable variability was observed even in the same TEM specimen. Screw dislocations dominate the pre-exiting network structures in bcc Fe. Screw dislocations are weaker sinks for point defects than edge dislocations; and, indeed, the former are biased for vacancies [208,209]. The excess vacancy flux to the screw dislocations causes them to climb into quasi-helical configurations, with an edge component, thus increasing their sink strength and the corresponding line length. The network dislocations are often associated with rafts of loops. The dislocation density (r) and the character affect the pre and post irradiation strength of the alloy, and the strength superposition

effects (see section 6). The dislocation evolution also modifies the defect sink strength, which mediates RED and 4-effects. The overall effect of increasing sink strength expected to result in a corresponding decrease in both RED and the effect of 4 between low and high 4t (see Section 7). Finally, it is noted that the CRP and MNSP themselves may be defect sinks. If so, the effective sink strength at high 4t could be huge, on the order of 1016/m2. Further discussion of this critical emerging topic is beyond the scope of this paper, but we will consider sink strength effects parametrically in Sections 6 and 7. 6. Embrittlement mechanisms and models 6.1. Overview As noted previously, irradiation hardening and embrittlement of RPV steels depend on the combination of a large number of metallurgical and irradiation variables [1]. Physical models and experimental insight on the underlying mechanisms are helpful in identifying functional relations between DT and these variables and variable combinations, for developing simplified reduced order model equations that can be fitted to large databases. The basic mechanisms of irradiation embrittlement are illustrated in the flow chart in Fig. 17. What follows describes the key embrittlement mechanisms in more detail. At the atomic level, aged, neutron-induced displacement cascades create excess populations of vacancy and self-interstitial atom (SIA) defects, and small features like defect clusters. The excess defects that are mobile accelerate the diffusion of solutes, aka radiation enhanced diffusion (RED), and create extended defect-solute cluster complexes, such as small segregated dislocation loops. RED and radiation induced solute segregation (RIS) also

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Fig. 13. X-ray diffraction (XRD) 2q spectra for low (CM6) and high (LD) Cu steels for the ATR-1 ultra-high 4t irradiation. Partial or no known crystal structure (PONKS) simulations of the two spectra based on the nm-scale precipitates sizes and number densities characterized by Small Angle X-ray Scattering (SAXS), showed the presence of: a) G phase (found in in 5 out of the 6 core L-series alloys); and, b) G2 phase in the Cu free high Ni steels CM6). G-phase was observed. The SAXS measurements are also consistent with SANS and APT results [201]. Fig. 12. APT maps showing that the CRP N increases with decreasing Ti (320e270  C) and increasing Cu (0.1 in LH to 0.2 in LI). The APT was carried out by N. Soneda as part of a CRIEPI-UCSB collaboration. The IVAR irradiations were to a 4t z 1.6
1023 n/m2 at 3.3
1015 n/m2-s and 290  C.

lead to enhanced, or induced, formation of precipitates. RIS and RED depend on 4 if vacancy and interstitial recombination is significant. The precipitates and defect-solute cluster complexes impede the glide of dislocations, resulting in Dsy Internal triaxial stresses near a blunting crack tip increase the principal normal crack plane stress (sn) to z 3-5sy. Cleavage occurs at a critical condition, when an internal sn acting on a vulnerable (large) trigger particle, such as a grain boundary carbide, that is oriented to access a cleavage crystallographic system in Fe (like {100} [110]), reaches a microstructurally dependent microcleavage fracture stress (s*) over a critical statistically stressed volume (V*) ahead of a notch or crack tip. The s*- V*, which are classically assumed to be temperature independent for Charpy tests,6 determine a steel’s local

6 Note DT is generally used to denote either DTc or DTo. It is well established that s*(T) is a function of temperature in the case of fracture toughness, mediating the shape of the MC, To and DTo. However, this temperature independent s*may be a

better approximation for Charpy tests.

micromechanical cleavage fracture toughness. Since, sy decreases with increasing temperature, Dsy results in achieving the critical internal stress conditions at a higher test temperature (DT). 6.2. Cascade defect-solute cluster complexes and mobile defect production in aged cascades The initiating embrittlement event is neutron interactions with atomic nuclei that create a spectrum of energetic primary recoil atoms (PRAs), up to tens of keV [210,211]. The PRAs displace other atoms from their lattice sites in displacement cascades. Cascade defects include isolated and small clusters of vacancies and SIA. A significant fraction of the SIA cluster to form small prismatic dislocation loops during the z100 ps hot cascade generation event. However, a cascade remains a spatially and time correlated entity for much longer times while it reconfigures, or ages. During cascade aging, the SIA continue to locally recombine, or join previously formed cascade SIA clusters; but most SIA quickly migrate longer distances away from the cascade [95,115]. Over longer periods, some vacancies locally migrate to form small nanovoid clusters, while others also migrate away from the cascade. Both the small SIA loops and vacancy clusters are mobile, and are quickly complexed with the alloy solutes (Mn, Ni, Si, Cu), both initially, and during the

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Fig. 14. a) The CRP þ MNSP f correlation with 2Ni þ Cu for the ultra-high 4t ATR-1 irradiation condition; and, b) the corresponding f correlation with z 3Cu þ Ni for the high 4t ATR-2 irradiation condition. Note, the APT and adjusted SANS data are filled and unfilled symbols, respectively.

Fig. 15. A Mn-Ni-Si Gibbs triangle projection for the Fe-Mn-Ni-Si system, showing the measured APT MneNieSi MNSP compositions (filled symbols) at the ultra-high ATR-1 4t. The corresponding thermodynamic predictions are shown as unfilled symbols [145,202,203].

much longer period of cascade ageing [42,116,120,121,212]. The ratio of surviving defects to dpa (h) is estimated to be z 1/3 [211]. Thus the generation rate of migrating defects is Gv,i z h4sdpa, where sdpa is the spectral average dpa cross section, which is prototypically z1.5
1025 m2/atom, for 4 (E > 1 MeV). The solutes thermally stabilize the vacancy clusters, and reduce their mobility of both vacancy and SIA clusters. However, the vacancy clusters eventually dissolve, leaving solute cluster remnants. The dissolved vacancies also undergo long-range migration to sinks, or recombine with SIA. Some SIA clusters remain intact, acting as sites for additional solute segregation. Thus the ultimate products of displacement cascades include migrating vacancies and SIA, as well as solute cluster defect complexes. While most of these defect complexes are too small to survive, a fraction evolve into

SMF in both low Cu and Cu bearing steels by acquiring additional solutes by long-range diffusion. The SMF are preferred nucleation sites for CRPs and MNSPs [202,213,214]. CRPs can nucleate homogeneously given the high supersaturation of even small amounts of Cu [22,120,121]. However, cascade defect complexes, and network dislocations are the preferred sites for the heterogeneous nucleation of CRPs at lower Cu or higher temperature (see Fig. 12). The production of the SMF can be represented by a neutron cross section, which is estimated to be z 6
1030 m2/atom for typical low Cu RPV steel compositions (this is a generation-survival rate of z1 per 100 cascades). The volume fraction of SMFs increases with higher trace amounts of Cu and increasing dissolved Ni, Mn and Si.

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Fig. 16. Core alloy precipitate f, N, d for the irradiation conditions in: a) the ultra-high 4t ATR-1; and, b) high 4t ATR-2 conditions.

Fig. 17. A simplified flow chart showing the primary mechanisms leading to RPV steel embrittlement.

6.3. Excess defect fluxes, RED and RIS Substitutional solutes primarily diffuse by a vacancy exchange mechanism. Thus the excess vacancies created by irradiation greatly accelerate solute diffusion rates (RED). At steady state, ignoring sink and source bias, the diffusion coefficient (D) and defect concentration (X) product is given by [22,120,198 and see Appendix B] DvXv z DiXi z gsh4sdpa/kt

(3)

Here, gs  1 accounts for SIA-vacancy recombination during long-range defect diffusion to sinks. In the simplest approximation the RED coefficient (D*), considering only vacancy transport D*, is given by D* z Ds[Xv/Xve] z Ds[DvXv/DvXve] ¼ gsh4sdpa[Ds/Dsd]/kt ¼ K4 (4) Here, Ds is the solute thermal diffusion coefficient, Xve is the equilibrium vacancy concentration, Dsd is the steel Fe self-diffusion coefficient (zDvXve, neglecting a correlation factor z 1). It is useful

to cast D* in this form since it eliminates Dv, and accounts for Ds/Dsd > 1, typical of solutes with binding energies to vacancies. Without recombination gs ¼ 1. Taking h ¼ 0.33, kt ¼ 2
1014/m2, sdpa ¼ 1.5
1025 m2/atom and Ds/Dsd z 10, gives a K ¼ 2.5
1039 m4, or D* z 1.25
1024 m2/s for a nominal service 4 ¼ 5
1014 n/m2-s. Empirical estimates of K are higher, at z 1037 to 1038 m4. For a nominal value of K ¼ 5
1038 m4 and 4 ¼ 5
1014 n/m2-s, the corresponding D* is z 2.5
1023 m2/s. Based on an estimate of the thermal Cu Dcu z 1025 m2/s, which is on the high side of a wide range of estimates, the RED D*/Ds z 250. The corresponding one year diffusion distances, √D*t, is z 28 nm, which is consistent with typical CRP spacing in irradiated steels of z18 nm. 6.4. Flux effects on RED The gs(4) term represents the fraction of vacancies escaping recombination, thus reaching sinks, hence, contributing to RED [22,120,198]. For sink dominated conditions gs ¼ 1, and K is independent of 4. In the recombination dominated regime K and D* scale as 1/√4 and √4, respectively. That is, an increase in 4 by a

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factor of 10 increases D* by the same amount if sinks are dominant, while if recombination is dominant, D* increases only by the √10. Thus, DTc data can be plotted on an effective fluence (4te) scale, where 4te ¼ gs4t. In unalloyed Fe recombination is important only at very high 4, beyond that which is experienced even in most highly accelerated MTR conditions. However, solutes like Cu, Mn, Ni and Si have a positive binding energy to vacancies (that is, the vacancy energy decreases near the solute) [215]. The resulting vacancy trapping at alloy solutes increases the recombination rate, reducing gs and 4te/4t. An analytical expression for gs ¼ h(4, Ti, kt, Es, Xs) is given in Appendix B, where Es and Xs are the solute vacancy binding energy and concentration, respectively. Fig. 18a plots for 4te/4t at 290  C for some nominal values Es, Xs and kt. Above a low 4 plateau, where gs ¼ 1 in the sink dominated regime, 4te/4t (and gs) decrease with increasing 4, due to the corresponding increasing rate of recombination. Fig. 18b plots 4 at 4te/4t ¼ 0.5 as a function of kt and Ti, for typical recombination model parameters. However, a much simpler power law approach has been adopted to analyze large sets of embrittlement data for irradiations over a wide range of 4 [22,198]. The power law scaling assumes that the effect of 4 can be approximately represented as: 4te/4t z 4t(4r/4)p

(5)

Here 4r is an arbitrary reference 4 and p is the fitted scaling exponent used to adjust embrittlement data over a range of 4. For solute trap recombination and sink dominated conditions p z 0.5, while p z 0 for sink dominated conditions. Fitted p values may also approximately account for unmodeled mechanisms other than recombination. For example, the total number of displacement cascades, which is independent of 4 at a given 4t, is likely to influence embrittlement. Fig. 9 showed the effect of 4 on the 4t dependence for a 0.4 wt% Cu, 0.8 wt% Ni core alloy (LC) for both p ¼ 0 (no 4 effect) and p ¼ 0.25. As noted previously, p z 0.25e0.4 4te scaling generally collapses the Dsy(4t) data into a single narrow band at low 4t. This picture of solute transport under irradiation is greatly oversimplified [215]. First, differential coupling of solute and matrix Fe atoms with persistent defect fluxes, leads to RIS at defect sinks or recombination centers; for vacancies this is called the inverse Kirkendall effect. Further, binding energy between vacancies and

21

solutes, and the corresponding effects on local jump frequencies, can result in so-called vacancy drag effects, where vacancies and solutes (Cu, Ni, Si) flow in the same direction, making RED highly efficient, and driving RIS. Further, some solutes can diffuse as stable SIA complexes (P, Mn), further increasing RED and RIS. Note the amount of RIS at defect sinks and recombination centers is affected by thermal back fluxes of the solutes; thus the magnitude of RIS increases with increasing 4. The amount of segregation also depends on the binding energies of the solutes with the segregated feature and between the segregated solutes themselves; this enhances RIS, and results in some thermal segregation in the unirradiated condition. The combined effects of this complex set of interacting solute transport mechanisms have not been modeled. The importance of RIS is clearly demonstrated by MNSP-type cluster formation in highly subsaturated systems in Fe-Cr alloys. This has been modeled in terms of the dislocations acting as a favorable heterogeneous nucleation site in a locally segregated, solute-enriched micro alloy region [213]. Fig. 19 shows the examples of segregation and precipitation on network dislocations, which are a dominant site for MNSPs and CRPs at lower Cu concentrations (also see Figs. 11 and 12). However, as discussed below, models based simply on RED and computational thermodynamics, treating nucleation parametrically, are sufficient to capture to dominant thermo-kinetics of precipitation under irradiation, this will be the focus for further discussion. 6.5. Precipitation mechanisms and models Irradiation hardening and embrittlement of RPV steels is due to the evolution of precipitates, defect cluster-solute complexes, and at high 4t, visible dislocation loops. Precipitates are the dominant hardening feature, while the defect cluster-solute complexes, or SMFs, add a smaller hardening component at lower 4t in both Cu bearing and free steels. More importantly, SMFs act as heterogeneous nucleation sites for MNSPs that develop at high 4t. CRPs also heterogeneously nucleate on loops and network dislocations at lower Cu levels (but still > 0.07% Cu - see Fig. 19). As noted previously, the first embrittlement models proposed by Odette [44], and independently by Fisher [48], treated Cu precipitation hardening. The equilibrium solvus for bcc Cu in Fe, as a function of temperature in Fig. 20a shows that even at dissolved

Fig. 18. Solute trap recombination model f predictions of 4 effects: a) 4te/4t at 290  C as a function of 4 for nominal parameter values of Es ¼ 15 kJ/mol, Xs ¼ 0.02 and kt ¼ 2
1014m2; and, b) the 4 at 4te/4t ¼ 0.5 showing the strong effect of kt and Ti.

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Fig. 19. APT tip and blown up examples of solute maps showing segregation and precipitation on network dislocations for ATR-2 irradiation (4t ¼ 1.4
1024n/m2).

impurity levels of z0.1 at.%, Cu is highly supersaturated at z 290  C. Note, the bulk content may be higher, but Cu excess of z0.25 to 0.3 wt% pre-precipitates during typical tempering and stress relief heat treatments. Most of the remaining dissolved Cu quickly precipitates at low 4t, nearly saturating by about z 1023 n/ m2, typically leaving z0.06 wt/% dissolved in the matrix. CRP precipitation has often been modeled by Cluster Dynamics (CD) and Kinetic Lattice Monte Carlo (KLMC) methods, as illustrated in Figs. 20b and 21a, respectively. CD models represent the number of clusters (N) at each number of cluster atoms (n), N(n), from the mobile monomer species n ¼ 1, up to a maximum number of atoms n ¼ nmax, with a set of ordinary differential Master Equations. In the simplest form [22,94,95,120,202,213,214]. dN(n)/dt ¼ b(n-1)N(n-1) þ a(nþ1)N(n þ 1) - [a(n) þ b(n)] N(n) þ G(n) n ¼ 1 to nmax

(6)

The a and b coefficients are the rates at which a cluster emits or absorbs a mobile monomer species, respectively. The G(n) is the rate of generation of clusters of size n due to heterogeneous nucleation. In the case of homogeneous precipitate nucleation G(n) ¼ 0. In this formulation at n > 1 clusters are assumed to be immobile; however, diffusion and coalescence of clusters can be simply accounted for by additional reaction terms. The a(n) accounts for the Gibbs-Thomson effect, governed by the precipitate Fe interface energy gpm. Fig. 20b plots the , N and f for an Fe0.34 wt% Cu alloy as a function of 4t for a K ¼ 1038 m4/s, showing overlapping stages of nucleation, growth and coarsening. At low 4t, nucleation dominates, as seen in the rapid increase in N. Nucleation rates are dominated by the Cu supersaturation Xcu/Xcue and gpm. At intermediate 4t, growth dominates, as manifested by a more rapid increase in r and f and a peak in N. At still higher 4t, Cu precipitates coarsen, with a slowly decreasing N and increasing r. The gpm¼ 0.375 J/m2 was estimated using a simple pair bond model [121] and Xcue is shown in Fig. 20a. Thus the only adjustable parameter in the

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Fig. 20. a) The solubility of Cu in a-Fe (in equilibrium with bcc Cu) as a function of temperature, also showing typical bulk composition ranges and illustrating the effects of preprecipitation during vessel heat treatments at higher temperature; and, b) an example of a CD model of the nucleation-growth and coarsening Cu precipitates in an Fe 0.3 wt % Cu alloy irradiated at 300  C with only one independent adjustable RED parameter K to set the absolute 4t scale.

Fig. 21. (a) A Kinetic Lattice Monte Carlo simulation of Cu precipitation in an Fe-0.3Cu alloy at 300  C; and, (b) a KLMC simulation of MNSP evolution, based on modified Calphad calibrated pair bond (regular solution) energies evolving from core-shell (left) to core-appendage (right) morphologies;, where the MNSP phase is dominant in the later case [216].

CD model is the RED K, which sets the absolute 4t scale. KLMC tracks precipitation based on statistically weighted vacancy exchanges with solutes and solvent atoms on a rigid lattice. Fig. 21a shows snapshots for a KLMC simulation of Cu precipitation in a highly supersaturated Fe-0.3 at.% Cu alloy [22,95]. Thus the supersaturated system naturally evolves by vacancy exchanges to lower free energy, through overlapping stages of nucleation, growth and coarsening. In multi-constituent steels, CRPs are composed of a Cu rich core and, initially, a Mn-Ni-Si rich shell that typically contains as much or more of the other solute atoms than in the core. MNSPs are found in steels at all Cu levels at ultra-high 4t. In low Cu steels, MNSPs primarily evolve from SMF defect cluster solute complexes, as well as nucleating heterogeneously on loop and network dislocations before growing to large f at high 4t. In Cu bearing steels, MNSPs primarily form as a separate ordered appendage phase on the CRPs at high 4t, as illustrated in Fig. 21b, which is based on a KLMC simulation [216]. Odette first modeled Mn-Ni precipitates (no Si at that time) in the early to mid-1990s based on Calphad thermodynamics [22,118e121]. As illustrated in Fig. 22a, his approach was to calculate the chemical potentials (mi) of Cu, Mn, Ni and Fe (i) in the matrix (mmi) and in the MnNi rich precipitate (mpi). Initially the solute mmi is > mpi; thus Mn and Ni flow into the precipitate until the equilibrium mmi ¼ mpi condition is achieved. Note, the model included the GibbsThomson effect on the nm-scale precipitates, including a

composition dependent gpm; the composition dependent interface energy effect further increases the mean field precipitate Mn and Ni contents. CD was also to calculate steady state homogeneous Mn-Ni nucleation rates, which were found to be negligible without Cu; heterogeneous nucleation was not treated at that time. Hence, the MNPs were called late blooming phases (LBP). Even small amounts of Cu greatly enhanced the MNP nucleation rates, which also increases with higher Ni and Mn and lower Ti. This early work was soon extended to rigid lattice Kawasaki Monte Carlo (LMC) simulations of the Fe-Mn-Ni-Si system based on regular solution type pair bond energies, estimated from Calphad binary alloy heat of mixing data [122]. In LMC simulations atom pairs are swapped based on probabilities determined by the exchange energy difference, but without vacancies. The system again evolves to minimize free energy. As shown in Fig. 22b, the LMC simulations predict precipitates with Cu rich core with Mn-Ni-Si rich shells, which actually show a tendency to order as nascent appendages in the lower left high Ni case [122]. However, the mechanism for the growth of large f of MNSPs has been a matter of considerable debate. Some have argued that the precipitates are non-equilibrium solute clusters formed as a result of RIS [212]. Here, we define RED enhanced precipitation as phases that would form thermally given sufficient time. In contrast, RIS induced phases would not form thermally. A corollary is that RED enhanced precipitates are thermally stable under post irradiation thermal annealing at the irradiation temperature, while RIS

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Fig. 22. a) A schematic illustration of the 1990s UCSB Cu-Mn-Ni precipitation model based on modified Calphad thermodynamic evaluation of the constituent chemical potentials in the matrix and precipitate phases that result in solute flows until equilibrium (the dashed line) is reached. The model accounts for the composition dependent interface energy [22,120]; b) Kawasaki LMC simulations, based on a Calphad calibrated pair bond (regular solution) energies, showing precipitates with Cu rich core with Mn-Ni-Si rich shells [122].

induced clusters would dissolve given sufficient time. Of course, these definitions describe limiting cases; and in reality, both RED and RIS are likely to be involved in precipitate evolution. For example, in many cases, RIS to cascade dislocation loops and network dislocations is an important CRP and MNSP heterogeneous nucleation mechanism; and the compositions of and f of precipitates may be somewhat modified RIS. However, even in the absence of RIS small precipitates cannot be expected to be stoichiometric even if they are as a bulk intermetallic phase [147]. First, the Gibbs-Thomson effect modifies nm-scale precipitate chemistry due to composition dependent gpm effects, and thermal segregation. Further, if an alloy is not fully decomposed (thus the matrix is still supersaturated) a range of precipitate compositions are thermodynamically accessible, that results in a reduction in the system free energy [147]. Finally, precipitate composition varies with the chemical potential of the individual dissolved solutes as governed by Henry’s law. That is, more dissolved/supersaturated matrix Ni would lead to more precipitate Ni (or Mn or Si that trade off with one another). The thermodynamic character of MNSPs G and G2 phases has been demonstrated by: a) XRD measurements (see Fig. 13) [201]; b) computational thermodynamics [203]; c) high temperature, long time thermal annealing [146]; and, d) precipitation under thermal aging [217]. For example, a soon to be published post irradiation annealing (PIA) study at 425  C for 52 weeks was carried out on a high 1.6% Ni, Cu free alloy (CM6) in two Fe-ion irradiation conditions both at z 104 dpa/s. One condition was a 400  C irradiation to 3 dpa to produce larger MNSPs; the second condition was a 1.5 dpa irradiation at 330  C, to nucleate a higher number of MNSPs, followed by a 1.5 dpa increment at 400  C, to grow them to full precipitation [218]. Fig. 23 shows that precipitates formed by the 400  C irradiation are thermally stable, and begin to coarsen, since their as irradiated size (d z 3.3 nm) exceed an evolving critical radius criteria. In contrast, larger number of smaller (d z 2.2 nm), precipitates nucleated in the 330  C and grown at 400  C, largely dissolve, consistent with their size which is below the critical radius criteria. 6.6. Advanced precipitation thermo-kinetics models Modern tools of computational thermodynamics and kinetics are available to model solute clustering and precipitation for both RED (enhanced near equilibrium phases) [202,214] and RIS (induced non equilibrium phases) mechanisms [213]. These models

use empirical thermodynamic databases, like Calphad, to calculating free energy curves, and solute product supersaturations, for specified phases, like G and G2. The thermodynamic parameters are coupled to mean field CD kinetic models [202,214]. KLMC can also be used to model precipitate evolutions given a proper Hamiltonian [122,216,219,220]. Recently the most rigorous treatment of the initial stages of solute clustering was based on cluster expansion evaluation of multi-element interaction energy Hamiltonian [220]. First principles KLMC showed rapid thermal (no RIS) clustering of Mn, Ni, Cu, Si and P on a bcc lattice at 300  C, in spite of the very small cluster sizes, and a correspondingly large Gibbs-Thomson interface energy effect, that promotes cluster dissolution. S. Shu et al. used KLMC to explain the formation of MNSP appendages on previously grown CRPs (see Fig. 21b) [216], and to simulate 425  C long-term PIA effects on medium and high Ni steels previously neutron irradiated at 320  C to form G and G2 phases [218]. The PIA results were also simulated by the Ke (see below) CD model in a paper by N. Almirall [146]. Fig. 24 shows example CD model predictions of the formation of G (Ni16Mn6Si7) and G2 (Ni3Mn2Si) phases, compared to APT and SANS data [202,215]. Fig. 24a shows the f predictions of the model of Ke [202] for medium 0.8 wt% Ni (LG) and high 1.6 wt%Ni, Cu free steels (CM6) [202]. The data points are for multiple APT tips and the calculated bands reflect variations in the actual bulk solute tip compositions, as well as different 4 conditions in the various irradiations included in the plot. Ke’s CD model includes a parametric treatment of a heterogeneous nucleation of MNSPs on defect-solute cluster complexes formed in displacement cascades. M. Mamivand extended the CD model to treat precipitation in Cu bearing steels [214]. Fig. 24b compares his CD model predictions of f (blue diamonds) to measured values (red circles) for a high bulk z 0.41 wt % Cu, medium z 0.86 wt% Ni alloy (LC) irradiated over a wide range of 4, 4t and Ti; the solid blue curve connects points for the various irradiation conditions. In this case MNSPs primarily grow on CRPs, although precipitation on segregated loops (SMF) and network dislocations is also treated. Both the data and CD model show a Cu precipitation plateau followed by a rapid upswing, marking the onset of rapid MNSP growth. Fig. 24c shows the corresponding predicted versus measured f for a number of steels modeled in these studies at 4t up t0 3
1024 n/m2. The predictions are generally reasonable, but in both cases the model underpredicts the ultrahigh 4 and 4t ATR-1 data, especially for the medium Ni, low Cu steel (LG). Otherwise, the predicted versus measured f differences are mainly associated with relatively modest 4t indexing errors in

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25

Fig. 23. Energy dispersive spectrum (EDS) x-ray maps of smaller as-irradiated (AI) precipitates in a high Ni, Cu free steel (CM6) ion irradiated at 1
104 dpa/s at 330  C (to nucleate) and 400  C (to grow) MNSPs (top left), showing MNSP dissolution and coarsening after a 425  C 52 week anneal (bottom left). In contrast, the larger as irradiated precipitates in a 400  C ion irradiated condition (top right) are stable during the 425  C 52 week anneal (bottom right). These results demonstrate the thermodynamic stability of the MNSPs that remain above the critical size during annealing [218]. Of course the precipitates would be far more stable at a much lower neutron irradiation temperature, Ti z 290  C.

the region of the rapid upswing of the predicted f(4t) curves (near the onset of MNSPs). The CD models also predict the precipitate number N, size distributions and average d as a function of the alloy composition (Cu, Ni, Mn, Si, Ti, 4 and 4t). In summary, while not perfectly quantitatively predictive, the CD models provide powerful insight on irradiation enhanced precipitation mechanisms. Finally, as noted above, Ke’s CD model has been successfully applied to CRP and MNSP evolution during PIA [146]. 6.7. Avrami based models While these detailed CD based precipitation models described above provide physical insight, simpler reduced order models are more useful fitting large databases. Notably, the precipitate f(4t) can be modeled with simple Johnson-Mehl-Avrami-Kolmogorov (JMAK) equations, which we simply refer to here as Avrami models [22,198,221]. Basically, Avrami models account for the solutes that have already precipitated, thus are no longer available for further CRP or MNSP growth, in the general form df/dt z C(1-f)

(7)

Eq. (7) is integrated up to the maximum fmax. The Avrami

equation can be expressed as f/fmax ¼ 1 e exp[-(4t/4to)b]

(8)

Here 4to is the indexing 4t at f/fmax ¼ 0.632. The Avrami model also can be related to the physics of precipitation. For diffusion controlled growth of N pre-existing precipitates b ¼ 3/2 and f/fmax z 1 eexp[-4.19js(Xso/Xsp)1/2N(D*t)3/2] ¼ 1 e exp[-4.19js(Xso/ Xsp)1/2N(K4t)3/2] (9) Here Xso is the initial concentration of the controlling solute (e.g., Cu), ts z ln(X/Xse) is a thermodynamic term to account for the solute activity coefficient in terms of its equilibrium solubility (Xse), and Xsp is the fraction of rate controlling solute in the precipitate. Note, Eq. (9) ignores the Gibbs-Thomson effect, and the Xs at the precipitate interface is taken as being negligible; and the RED K is assumed to be constant. The physical factors governing 4to are 4to ¼ [4.19jsXso/Xsp)1/2NK3/2]1

(10)

The Avrami model in Eq. (8) can be generalized for other types of precipitation kinetics. The exponent b controls the shape of the Avrami curve, as mediated by the underlying physics. For example,

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G.R. Odette et al. / Journal of Nuclear Materials 526 (2019) 151863

Fig. 24. Examples of CD predictions of G (Ni16Mn6Si7) and G2 (Ni3Mn2Si) phase f, compared to APT and SANS data for various irradiation conditions: a) the 4t dependence of f for Cu free medium 0.74 wt% and high 1.68 wt% Ni core steels (CM6 and LG) [202]; b) the 4t dependence of f for 0.1 to 0.4 wt% Cu (nominal bulk), medium 0.8 ± 0.06 and high 1.25 wt% Ni core steels (LH, LI, LC and LD) [214]; and, c) the corresponding predicted versus measured for both the Cu free and bearing steels. These results are for 4t < 3
1024 n/m2 (that is, they do not include the ultra-high 4t ATR-1 condition where the f are significantly under predicted by the CD models).

b ¼ 5/2 for a constant continuous nucleation rate, rather than the 3/ 2 for diffusional growth of pre-existing precipitates. Other Avrami model complications are that the Gibbs-Thomson effect is important at small d, the RED K decreases with 4t due to the build up of defect sinks, and precipitation of solute vacancy traps (see Section 7). Thus in practice b, 4to and fmax are fitting parameters that give some indication of the underlying precipitation mechanisms. Further, as an alternative to simple analytical Avrami model forms, the precipitate f/fmax growth equations can be numerically integrated to include all of the physics noted above, including 4tdependent processes. The precipitate fmax and composition and can be measured or computed from Calphad [147] thermodynamic data, modified for the Gibbs-Thomson effect. A single Avrami equation is needed to model the evolution of the MNSP f in low Cu steels. Two Avrami equations are needed to model the precipitate CRP þ MNSP evolutions in Cu bearing steels, since the b, fmax and 4to are different for CRPs and MNSPs. Fig. 25 shows Avrami model fits to CRP and MNSP f in the 6 core alloys [222]. Since the data are for a wide range of 4 and 4t the results are plotted on an √4te scale, for p ¼ 0.25. The f can be used to calculate the corresponding Dsy and DT (see below). The SMF also cause hardening and embrittlement in both low and Cu-bearing steels. The role of alloy composition in SMF hardening has been assessed by least square fitting low Cu steel Dsy in the IVAR experiment with a simple linear chemistry factor (CFm) function of the alloy solute concentrations Xi (at.%) as [22].

Dsymf z CFm√4t (1023 n/m2)

(11a)

CFm ¼ 279.2*(Cu < 0.072))þ 20.89*Niþ7.07*Mnþ690.9*P9.91*Cþ9.20*Si231.2*Ni*P11.775 (11b) Note, the ratio of Mn/Ni/Si coefficients in Eq. (11b) z 62/21/27, are similar to the composition ratios of G phase. The generation rate of SMF is proportional to the CFm, thus deceases with increasing 4t due to solute depletion; and Nmf peaks at an intermediate-high 4t due to the SMF transformation due into growing MNSPs. 6.8. Irradiation hardening and DTc The SMFs and precipitates act as obstacles to dislocation glide, increasing the critical resolved shear stress for plastic yielding. The precipitate f and d can be related to Dsy, which, in turn, can be related to DTc and DTo. A classical dispersed barrier (DB) hardening model is used to calculate the precipitates contribution, sp. Since the model has been described in many publications [223e227], this will not be repeated here. Combining various terms in the DB model, sp z 7.0
104√fap(d)/d, where ap(d) is the precipitate obstacle strength factor. Fig. 26a shows a plot of CRP f paired sp/√f data points from tensile tests and SANS measurements plotted as a function of r (¼d/2). The curve is an adjusted Russell-Brown model [44] fitted to the data with a peak of z4200 MPa at r z 1.25 nm. The variation in sp/√f with d z 0.75e2 nm is not large. The

G.R. Odette et al. / Journal of Nuclear Materials 526 (2019) 151863

27

Fig. 25. Avrami model fits to CRP and MNSP f (SANS and APT) versus 4te data (p ¼ 0.25) for the 6 core matrix alloys for a wide range of IVAR, ATR-1 and ATR-2 irradiation conditions. The 4 units are n/m2-s.

Fig. 26. a) An experimentally calibrated Dsy/√f versus r hardening curve for CRPs; b) an example of predicted versus measured Dsy data based on the dispersed barrier hardening and superposition models as described in the text; and, c) generic curves used to convert DT to Dsy and vice versa.

corresponding ap(d)/d z 0.236 ± 0.022 (nm1). Thus a sp/ √f z 4200 MPa can be used in modeling precipitation hardening. Note the value for MNSP (þCRP) hardening is z 5200 MPa. These sp/√f corresponds to average ap z 0.17 and 0.21, respectively. Eq. (11) gives the SMF hardening contribution. The individual hardening contributions from various irradiation-induced dislocation obstacles must be combined with one another (superimposed), and with the unirradiated contribution to DB hardening, su [22,120,182e184,228]. The limiting

superposition rules are linear sum (LS) and root square sum (RSS). Superposition of the si contributions of features with different medium and high strength (am and ah) falls between LS and RSS, while very weak barriers (aw) superimpose with a LS rule. Computer simulations were used to evaluate the net Dsy for populations of obstacles with different ai [22,120,228]. The resulting computational database was fitted with a simple analytical model for the net Dsy, based on the individual si contributions and the a for weak (aw < 0.05), medium (0.1 < am < 0.6) and strong (as > 0.6)

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G.R. Odette et al. / Journal of Nuclear Materials 526 (2019) 151863

obstacles. The net Dsy is given by

Dsy z swþ (1-S)(s2m þ s2s )1/2 þ S(sm þ ss)  ss

(12a)

The superposition factor S (0) is given by S z as - am(5.0e3.3as)

(12b)

Typical ap ¼ am ¼ 0.17 (cutting after limited bowing), au ¼ as ¼ 0.8 (when the obstacles are bypassed by Orowan bowing) and smf ¼ sw ¼ 0.04 (bypass with little bowing). As an example, assuming sp ¼ sm ¼ 150 MPa, su ¼ ss ¼ 200 MPa and sw ¼ smf ¼ 30 MPa, the net Dsy is z 110 MPa, rather than z180 MPa (pure LS) or z 51.8 MPa (pure RSS). Fig. 26b shows that the combined hardening and superposition model predictions are in good agreement with measured Dsy data [145]. One significant caveat to the DB hardening approach to modeling Dsy is that for a variety of reasons, such as solute segregation and local precipitate pinning as well as their sessile quasi-helical character, pre-existing dislocations may not be mobile following irradiation. Notably, segregation effects have been modeled by G. Monnet [227], but further experimental verification of the corresponding consequences is needed. The micromechanics model for the DTc ¼ CcDsy conversion is described in detail in [22,120] and will not be repeated here. The micromechanical models show that the hardening to shift coefficient, Cc, increases Dsy and the unirradiated CVN curve temperature at 10J, and decreases in CVN upper-shelf energy. However, fine tuning Cc for modeling large databases is not possible. Thus generic

Dsy(DTc) curves for the plates and welds, shown in Fig. 26c, have typically been used for the conversion [22]. For the relevant hardening range, from z175 to 300 MPa, pertinent to high 4t irradiations, Cc averages z0.7 ± 0.1  C/MPa. Notably, a similar value of Co z 0.7 ±0.1C/MPa has been found for the master curve DTo ¼ C0Dsy conversion for RPV steels [229e232], which generally experience a minimal loss of strain hardening following irradiation. In cases where the strain hardening is reduced significantly, the flow stress between 0 and 10% plastic strain, Dsfl, should be used instead of Dsy [229e231]. The preceding discussion of mechanisms and models provides a robust physical framework for predicting DTc and DTo. First fitted Avrami CRP and MNSP f(4te) models are combined with the empirical model of the SMF smf contribution in Eq. (11). While it is beyond the scope of this paper to discuss, note that the key MNSP Avrami model parameters (fmax, 4to and b) dependence on Cu and Ni have been established by a combination of a simple thermodynamic model and fits to the 6 core alloy database. The 4t dependence of Dsy is modeled as follows. The SMF contribution initially increases with the √4t. However, the SMFs convert to MNSPs at higher 4t, and as solutes are depleted from the matrix, thus decreasing the SMF generation rate. This results in an intermediate 4t peak in the SMF hardening. Adding a SMF term to Avrami-based CRP and MNSP hardening contributions requires numerical integration of the precipitation equations. Note, including a SMF term significantly improves the fits to the low 4t Dsy data. The SMFAvrami model predictions for the core alloys are shown in Fig. 27. The SMF contribution is shown as the heavy black dashed line, while the orange and blue lines show the CRP and MNSP

Fig. 27. Fitted SMF-Avrami model Dsy versus 4te (p ¼ 0.25) predictions for the core alloys for a wide range of IVAR, ATR-1 and ATR-2 irradiation conditions.

G.R. Odette et al. / Journal of Nuclear Materials 526 (2019) 151863

contributions, respectively. The solid red curve is the total Dsy(4te) based on the superposition rules described in Equation (12). The 4te is based on a p ¼ 0.25 scaling. The predicted Dsy can be used to estimate the corresponding DTc and DTo based on the best global estimate for Cc and Co as z 0.7 ± 0.05  C/MPa in both cases. Note, integrated Avrami curves can also treat the effect of an increasing sink strength with 4t on D* (or K) and the corresponding 4 effect. 7. The UCSB ATR-2 experiment and the Odette, Wells, Almirall, Yamamoto (OWAY) DT model 7.1. Overview The EONY model provides robust predictions of DTc up to z 4
1023 n/m2, which was the effective limit for the then US surveillance database, as discussed in Section 4. However, for 80-year (or more) vessel extended life, it is necessary to make reliable predictions DTc up to z 1024 n/m2, or higher. Thus the main objective of the UCSB ATR-2 irradiation and PIE program was to develop a new high 4t-low 4 predictive DTc model for extended life, including the effect of Ti, 4, 4t and alloy composition [222]. The ATR-2 irradiation of a large number of alloys (172) covered a range of Ti from 238 to 319  C, 4 from 1.2 to 3.7
1016 n/m2s and 4t from 0.42 to 1.4
1024 n/m2. To date PIE has focused on the highest 4t ¼ 1.38
1024 n/m2, 290  C capsules (7 and 8) at a peak 4 z 3.64
1016 n/m2-s. Special emphasis is on MNSPs, which are observed in essentially all of the ATR-2 steels. The ATR-2 database has been used to derive a preliminary CF ¼ Dsy ¼ f(Cu, Ni, Mn, Si, P) for this high 4t irradiation condition [233]. The 4 in ATR-2 is z 92 times higher than for a 4 of z 4
1014 n/m2-s, which reaches 4t z 1024 n/m2 in 80 full power years of operation. Thus a second major objective of ATR-2 is to evaluate 4 effects at high 4t. As shown in Fig. 28a, ATR-2 is intended to bridge a variety of other databases covering a wide range of 4-4t irradiation conditions, including the IVAR and the PREDB. Details will be described in future publications, but the major conclusions to date of the preliminary analysis, and corresponding model, can be summarized as follows. 7.2. An ATR-2 CF MNSPs, that contribute significantly to Dsy, are observed by APT and SANS in both low and Cu bearing steels, particularly those with

29

medium to high Ni contents. Thus a different CF is required for the high, extended vessel life relevant ATR-2 4t, compared to that for EONY for lower 4t irradiations pertinent to 40-year service. The ATR-2 CF also differs from that for the ultra-high 4 and 4t ATR-1 irradiation condition that led to nearly full precipitation. Fig. 28b shows predicted versus measured Dsy based on a preliminary ATR2 CF. The general CF form was derived from cross plots of Dsy data points as a function of Cu at constant Ni and Ni at constant Cu; both showed simple linear relations. The ATR-2 CF was calibrated by least square fitting various simple analytical forms, including trial Mn, Si and P terms. The fits were restricted to ATR-2 tensile data. The preliminary best CF is given by CFATR2 ¼ 128 þ (Cu - Cumin)*570 þ [(Cu - Cumin)*504 þ 82.8](Ni 0.75) þ 21.4*Mn þ 21.1*Si þ 1471[P-Pmin][1e3.4(Cue e Cumin)] (MPa) (13) for Cumin ¼ 0.04, Cumax ¼ 0.239 and Pmin ¼ 0.004 Including two clear outliers, the SD is 18.9 MPa and excluding them it is 16.3 MPa. There are no significant residual trends [233]. 7.3. Intermediate to high 4t dependence Analysis of the ATR-2 data combined with the IVAR and other databases indicated that the 4t dependence of Dsy for a wide variety of steels is approximately linear between z4 (EONY and IVAR) and 14
1023 n/m2 (ATR-2) conditions, as illustrated by one example in Fig. 29a. Note this is only one of many examples of a linear 4t trend. The filled symbols are measured Dsy while the open symbols are predictions of the EONY (lower 4t) and ATR-2 (high ATR-1 4t) models. The observed linear 4t trend line is in contrast to the 4t dependence, found in previous ETC and MBC studies, with DT scaling with 4tp, where p z 0.3 to 0.6. However, a linear increase in DT at higher 4t is consistent with the SMF-Avrami model discussed previously, and has been more recently reported in the literature for a number of steels irradiated to high 4t [158,205,234e237]. On average, Dsy increases by z 100 ± 30 MPa over 4t increment from 0.4 to 1.4
1024 n/cm2, in medium 0.75 wt% Ni steels. The ATR-2 CF can be used to calculate the Dsy at 1.4
1024 n/cm2 and, based on a Cc z 0.7, the corresponding DTc for the ATR-2 condition can be determined. This DTc can be used with the lower 4t DT data (z 4
1023 n/m2) to linearly interpolate the DTc at

Fig. 28. a) A 4-4t map for various UCSB irradiations along with the surveillance database analyzed in this work (the 4 units are n/cm2-s and the 4t units are n/cm2); and, b) predicted versus measured Dsy based on a preliminary CF fit to the ATR-2 tensile data [233].

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G.R. Odette et al. / Journal of Nuclear Materials 526 (2019) 151863

Fig. 29. a) an example of a linear fit to the Dsy versus 4t for a high Cu, medium Ni weld extrapolated to the 1.38
1024 n/m2 ATR-2 condition for comparison to the ATR-2 data. The open symbols are the predicted EONY (lower 4t) and ATR-2 CF Dsy (higher 4t), respectively. ATR-2 data (or CF predictions) falling below, versus on or above, the extrapolated curve indicate either a possible, or no, 4eeffect, respectively. Similar analysis of large number of datasets suggest that, at high 4t, there is little or no effect of 4, that is 4te z 4t; and, b) A 4te/4t solute trap recombination model curve indexed by Dsy data at 4 between 0.368 and 2.3
1017 n/m2-s that align along a calibrated 4t dependence curve, with an average p z 0.163 ± 0.1.

intermediate 4t; alternatively the lower 4t DT can be estimated using the EONY, or other, shift models.

7.4. The ATR-2 4te and a diminished 4 dependence at high 4t However, the ATR-2 irradiation was at a 4 z 3.64
1016 n/m2-s to a 4t z 1.38
1024 n/m2 at z 290  C. This 4 is z 92 times higher than for a low in-service 4 z 4
1014 n/m2-s, that reaches an end of extended life 4t z 1024 n/m2 in 80 full power years. In the simplest terms, the 4 effect is mainly due to increased recombination of vacancy and SIA defects created by displacement damage. The higher ATR-2 4 results in a lower 4te/4t compared to sink dominated conditions where 4te/4t z 1. An empirically normalized rate theory based solute trap enhanced recombination model was used to estimate the 4te for the ATR-2 4 z 3.6
1016 n/m2-s [198]. The recombination model calculates the fraction of vacancies that escape recombination to reach permanent sinks, gs(4)  1 and drive RED. The gs ¼ 4te/4t solute trap recombination model curve was indexed the 4-scale by data at 4 ¼ 0.364 (ATR-2) and 2.3
1017 n/ m2-s (BR2-TU) that align along the calibrated the Dsy 4t dependence line, with a Ni dependent slopes, which is 100 MPa/1020 n/m2 for 0.75 wt% Ni. The alignment requires and an average p z 0.163 ± 0.1. The black dashed line in Fig. 29a illustrates this indexing. The gs z 1 at the low service 4 and the corresponding 1/ gs(3.64
1016) z 0.931. Thus a reasonable estimate of the ATR-2 is 4te z 1.27
1024n/m2. Another approach to assessing possible 4 effects was to linearly fit lower 4t Dsy data without the ATR-2 Dsy. An extrapolated line that falls below or on the measured ATR-2 Dsy (green square) indicates that there is no 4 effect. An extrapolated line that falls above the measured Dsy, is consistent with a possible 4 effect. The corresponding p brings the extrapolation and measured Dsy into alignment. This procedure is illustrated in Fig. 29a, which, in this case, is consistent with little or no 4 effect. The predicted Dsy at (by EONY) 0.4 and 1.38
1020 n/m2 (by the ATR-2 chemistry factor) are also shown as unfilled symbols. Analysis of a number of alloys using this second procedure suggests that there is little or no significant and systematic effect of 4 at high 4t. Thus a reasonable estimate of the ATR-2 4te is 1.25 ± 0.15
1024 n/ m2.

7.5. Low 4 high 4t DT model predictions Following past tradition, we call the procedure to predict DT the Odette, Wells, Almirall, Yamamoto (OWAY) model. Fig. 30a and b compare OWAY ATR-2 CF based DT predictions for the steel compositions in the US PREDB to predictions of the EONY and E900 models at 1.25
1024 n/m2. Clearly the existing models are nonconservative at higher 4t. Fig. 30c and d plot the corresponding predicted irradiated Tci (Tcu þ DTc) for the steel compositions and irradiation conditions in the US RPV fleet at 1 and 1.25
1024 n/m2, based on the linear interpolation method described above. The significance of these new results to RPV integrity assessments should be a high priority. The estimated application range of the model is shown in Table 3. 8. Concluding remarks and outstanding issues This paper melds an overview of the 60-year history of RPV embrittlement research, focusing on predicting ductile-to-brittle transition temperature shifts, DT (DTc and DTo), with an assessment of the current status of these efforts, especially for extended vessel life. This review shows remarkable progress on a very complex and challenging problem that has been, for several decades, a paradigm for a ‘science in service of engineering’ approach to a critical technological challenge. The fundamental research has laid the foundation for properly analyzing modestly accelerated MTR data to make robust DT predictions beyond the current power reactor surveillance database. Our analysis revealed that most current models, that are accurate at lower 4t, systematically and significantly underpredict DT at high 4t, largely owing to the currently unaccounted for contribution of late blooming MNSPs. We propose a simple empirical approach to predicting DT for extended life between 4te from 0.4 (the approximate current limit) to z 1.25
1024 n/m2 (ATR-2), which is shown to be robust, and is supported by independent physical models. In addition to quantifying the role of MNSPs, important high 4t observations include an approximately linear DT dependence on dose (versus the previous z √4t trend) and a diminution of the effect of 4. The decreased 4 effect at high 4t has very important implications for the use of accelerated MTR data to predict service relevant DT. However, the underlying mechanisms of decreased DT

G.R. Odette et al. / Journal of Nuclear Materials 526 (2019) 151863

31

Fig. 30. a) and b) Comparisons of ATR-2 CF predictions of Dsy for steel compositions in the US surveillance data base with EONY (a) and E900 (b) predictions; and, c) and d) predictions of in-service surveillance Tci at the estimated ATR 4te z 1.25
1024 n/m2 (c) and 1024 n/m2 (d) based on a linear interpolation, where Tu is the unirradiated 41-J Charpy transition temperature.

Table 3 Estimated application range of the model. Variable

Value

Ti ft f Cu Ni Mn Si P

285 -295 ( C) 0 - 1.5x1024 n/m2 2x1014 - 2x1015 n/m2-s 0 - 0.4 wt.% 0.2 - 1.3 wt.% 0.4 - 2.0 wt.% 0.15 to 0.7 wt.% 0.003 - 0.025 wt.%

sensitivity to 4 are not yet well understood in detail. One important component of such understanding is characterization of the evolution of dislocation structures under irradiation (both loops and pre-existing network) needed to properly model both defect sinks and constitutive behavior. Questions include the mobility of highly segregated, precipitate pinned dislocations that may also have a significant degree of sessile helical character. Additional research is needed to extend the new MBC DT models to the worldwide

embrittlement database. Finally, higher 4t surveillance is needed to further evaluate the reliability of the new low 4-high 4t DT model. The clear objective of RPV regulations, and their almost 60 year record of unmatched success, is to demonstrate large safety margins that ensure exceedingly low failure probabilities. However, even when they are highly accurate and reliable, predictive DT models are only one part of the multidisciplinary process of RPV integrity assessment, which now includes powerful tools of statistical propagation of uncertainties, along with prudent engineering judgment regarding appropriate safety margins. Thus, it is important that the implications of the new results, reported in this paper, be carefully examined within this well-established framework. However, further discussion of this, and the other vessel integrity assessment challenges, in particular the quantification of uncertainties from unknowns, are beyond the scope of this paper.

Acknowledgements It is impossible for the lead author (GRO) to properly acknowledge all the people and institutions that have contributed to the

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G.R. Odette et al. / Journal of Nuclear Materials 526 (2019) 151863

content of this paper. First, I thank my coauthors for their incredible contributions to the RPV field (collectively representing z 170 years of experience), and especially for their institutional memory and wisdom, that was crucial in preparing Sections 1 to 3. They have all been wonderful collaborators and colleagues for more than 30 years. Special thanks goes to the graduate students and post docs who carried out RPV research at UCSB, spanning a period of nearly 4 decades, including Peter Lombrozo, Jeff Fint, Bing Ling Chao. Eric Mader, Brian Wirth, Howard Rathbun, Matt Alinger, Nicholas Cunningham, Peter Wells, Nathan Almirall and many others. Special thanks go to Peter and Nathan whose research results dominate Sections 5 to 7. The efforts of Nathan and MD Alam in helping to prepare and edit this manuscript have been very important. And without the long-standing partnership with my UCSB colleague Gene Lucas, none of this would have been possible. Our group’s development engineers Bill Sheckherd, Doug Klingensmith, Kirk Fields and David Gragg contributed to this work in countless ways, both intellectually and physically, with their tremendous hands-on skill and ingenuity. Over the years, our research has been sponsored by EPRI (Karl Stahlkopf and Ted Marston), NRC (Al Taboada, Mike Vassilaros and Carolyn Fairbanks), DOE-ORNL (Jeremy Busby and Keith Leonard), EDF (Jean Claude van Duysen), CRIEPI (Naoki Soneda), British Energy (Bob Priest and Katherine Chivers), Rolls-Royce (Tim Williams and Keith Wilford) and others. In recent years, the major support for this research, and especially the ATR-2 program, has been provided by the DOE Light Water Reactor Sustainability Program (LWRSP) Materials Pathway led by Jeremy Busby, Keith Leonard and Tom Rosseel in sequence. Without their support, encouragement and wise advice the development of a robust low flux, high fluence shift model would not have been possible. The core of UCSBs RPV studies has been large scale experiments, especially the NRC sponsored IVAR irradiation, built and operated by ORNL, through the tireless efforts and remarkable talents of Ken Thoms and Dennis Heatherly; and the NSUF sponsored ATR-2 program carried by a very talented team of INL engineers under the remarkable leadership of Mitch Meyer. We have also greatly benefitted from world class characterization and mechanical testing facilities at UCSB, and access to almost the all major US National nuclear and materials science user facilities, like CAES (APT and FIBing) and NIST (SANS), and many others; as well as a number of facilities abroad, including Tohoku U. IMR-Oarai (BR2 irradiation and PIE). We have also enjoyed a large number of very productive collaborations over the last 40 years, that are far too numerous to mention. However we must note the extremely productive collaborations we have enjoyed with Brian Wirth, after he finished at UCSB; and, more recently, with Dane Morgan’s computational modeling group at the University of Wisconsin. Finally, we gratefully acknowledge the critical role that IGRDM has played in our RPV research for over 30 years. Appendix A. The EONY model EONY model consists of the following set of equations:

TTS ¼ MF term þ CRP term pffiffiffiffiffiffiffi
4te MF term ¼ Að1  0:001718Ti Þ 1 þ 6:13PMn2:47 8 9 < 1:140
107 for forgings = 7 A¼ for plates 1:561
10 : ; 1:417
107 for welds

(A1.1) (A1.2a)

(A1.2b)


 CRP term ¼ B 1 þ 3:77Ni1:191 f ðCue ; PÞgðCue ; Ni; 4te Þ 8 9 102:3 for forgings > > > > > > > < 102:5 for plates in non  CE mfg: vessels > = B¼ 135:2 for plates in CE mfg: vessels > > > > 155:0 for welds > > > > : ; 128:2 for SRM plates  Cue ¼

0 for Cu  0:072wt% min½Cu; MaxðCue Þfor Cu > 0:072 wt% 

MaxðCue Þ ¼

(A1.3a)

(A1.3b)



0:243 for typical ðNi > 0:5Þ Linde 80 welds 0:301 for all other materials

(A1.3c)  (A1.3d)

9 0 for Cu  0:072 > > = for Cu > 0:072 and P  0:008 ½Cue  0:072 f ðCue ; PÞ ¼ 0:668 > > ½Cue  0:072 þ 1:359ðP  0:008Þ > > ; : for Cu > 0:072 and P > 0:008 8 > > <

0:668

(A1.3e) 1 gðCue ; Ni; 4te Þ ¼ 2   1 log10 ð4te Þ þ 1:139Cue  0:448Ni  18:120 þ tanh 2 0:629 (A1.3f) The effective fluence form in Eq. (A1.4) applies to both the MF and CRP terms, Eq. (A1.2) and (A1.3).

9 4t for 4  4:39
1010 > > = !0:259 4te ¼ 10 4:39
10 > > > for 4 < 4:39
1010 > ; : 4t 4 8 > > <

(A1.4)

Appendix B. The solute trap recombination model gs (4) Considering only vacancies and SIA undergoing lattice recombination (the second term) and annihilation at fixed sinks (the third term) neglecting bias, the defect balance equations at steady-state are: Gi - RrXiXv - DiXikt ¼ 0

(B1a)

Gv - RrXiXv - DvXvkt ¼ 0

(B1b)

Gi ¼ Gv ¼ h4sdpa

(B1c)

Rr z 4prr(Di þ Dv)/Ua z 4prrDi/U a, for Di [ Dv

(B1d)

Here, Gi ¼ Gv is the total SIA/vacancy defect generation rates, sdpa is dpa cross-section and h is the fraction of defects per dpa; Xi/v and Di/v are the SIA/vacancy concentration and diffusion coefficients, respectively; Rr and rr are the recombination coefficient and radius, respectively; and the Ua is the atomic volume of Fe. It is convenient to express general solutions to Equation (B1) in terms of the fraction of vacancies and SIA that escape recombination and reach sinks, thus are available to produce microstructural changes, gs, as: gs ¼ [XvDvkt]/Gv

(B2)

G.R. Odette et al. / Journal of Nuclear Materials 526 (2019) 151863

The solution to Equation (B1) yields gs ¼ [2/l][(1 þ l)1/2 -1],

Table B1 Parameters Used in Rate Theory Recombination Models

(B3a)

where (B3b)

In the low 4-high Dv (and high Ti) regime, with negligible recombination, gs z 1 and DvXv ¼ Gv/kt is proportional to 4. In the high 4 recombination dominated regime gs z 2/√4, hence, DvXv is proportional to √4. A nominal set of model parameters for low alloy steels is given in Table B1. Using the baseline values, it is easily shown that matrix recombination rates are minimal (gs z 1) for 4 < 5
1017n/m2-s. However, recombination is greatly enhanced if vacancies are strongly bound to a sufficiently high concentration (Xt) solute trapping sites, which is called solute trapping recombination (STR). Assuming that a solute trap is limited to one bound vacancy, and that a small fraction of traps is occupied (Xt [ Xtv), the approximate steady-state defect balance equations are modified as: Gv þ Xtv/tt - RrXiXv - DvXv(kt þ RtXt) ¼ 0

(B4a)

Gi - RrXiXv - DvXv(kt þ RtXtv) ¼ 0

(B4b)

DvXvRtXt - Xtv/tt - DvXvRtXtv ¼ 0

(B4c)

The solute trapping time is tt is

tt z b2/[Dvexp(-Hb/RT)]

(B4d)

and the recombination rate at trapped vacancies is Rt ¼ 4prtXt/Ua

(B4e)

Here rt is the trap vacancy capture radius, Hb is the trap-vacancy binding energy (or more formally enthalpy) and b is the atomic spacing. Solute vacancy binding energies are typically in the range of about 5e30 kJ/mol. The corresponding gs(4, Ti, St, Xt, rt, Hb) in this case is found by solving Equation (B4a) and B4b for Xv and Xtv, while assuring that Equation (B4c) is obeyed. An approximate solution that ignores higher order terms, resulting in a second-order equation that can be analytically solved for gs as:

gs ¼

1 þ

rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi . ffi 1 þ 4A B2 2A=B

2

1 B

(B5a)

Here,



4prr =Ua ð4prt tt = Ua Þ þ kt Dv kt

 4prt Xt =Ua ð4prt tt = Ua Þ þ kt

A¼

h4sdpa

B¼1 

Parameter

Value

rc & rt

0.57 nm 1.5
1025 m2 0.33 0.5exp(125,000/RT) cm2/s Variable 15 kJ/mol Variable 2
1014 m2 1.17
1023 cm3 0.248 nm Variable 0.02

sdpa h

l ¼ 16prrGv/UaDvk2t

h4sdpa kt



ð4prt tt = Ua Þ

33

(B5b)

(B5c)

Note, that B5a can be seen just as a slight modification of the lattice recombination case (Eq. (B3a)) by re-defining l ¼ 2A/B2 and assuming 1/B z 1. Thus, Eq. (B3a) can be viewed as a reduced order model with l as a fitting parameter for analyzing databases for the effect range of 4 on DvXv.

Dv Hb (base) kt (base)

Ua

b Xt (base)

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G. Robert Odette joined the UCSB faculty after receiving a PhD from MIT in 1970. He retired from his teaching position in the Mechanical Engineering and Materials Departments in 2014. As a Distinguished Emeritus Research Professor, he continues to lead the UCSB Materials Reliability and Performance Group, focusing on developing robust methods for predicting the performance and lifetime limits of materials and structures in extremely hostile service environments; and developing new, high performance materials, especially for nuclear fission and fusion energy systems. Professor Odette's honors include fellow rank in ANS, TMS, ASM and AAAS as well as the 1998 ANS Mishima Award and the 2014 TMS Structural Materials Division Distinguished Scientist of the Year Award. Special Symposia to honor his many important contributions to materials research were held at the Annual TMS Meeting in 2009 and at the 19th International Conference on nusion Reactor Materials in 2019.

Takuya Yamamoto is a Professional Research Engineer in the Engineering Department at the UC Santa Barbara. His research areas center on the development and performance characterization of the structural and functional materials for advanced nuclear device application. Most recently his efforts have focused on understanding and modeling the synergistic effect of radiation damage and helium production in the first wall of thermo-nuclear fusion devices and the radiation embrittlement of light water reactor pressure vessel steels. The efforts also involve understanding of the specimen size effects in fracture toughness evaluation to develop a physically based model of the size effects.

Colin English has over 40 years experience working in R&D within the nuclear industry for UKAEA, AEA Technology and the National Nuclear Laboratory (NNL). He has worked in the field of microstructural characterisation, radiation effects in solids and in-service degradation of structural components. He is internationally recognised as an expert in reactor pressure vessel embrittlement and was the first chairman of the International Group for radiation damage mechanisms in reactor pressure vessels (IGRDM). He was also Scientific Advisor to the European Ames Network and is currently Senior Fellow (Materials) at NNL.

Randy K. Nanstad joined ORNL in 1974, following an M.S. Degree in Nuclear Engineering and a PhD in Metallurgical Engineering from the University of Wisconsin, Madison. He served as the Group Leader of the Fracture Mechanics Group from 1980-2000 and Nuclear Materials Science and Technology Group from 2006-2013. His research has focused primarily on experimental investigation of fracture behavior and radiation effects in materials, including irradiation-induced microstructural evolution and embrittlement in reactor pressure vessel steels and other structural materials. He is a Fellow of the American Nuclear Society, ASM Int. and ASTM Int. and was ORNL Distinguished Engineer for 2013.

Tim Williams was awarded a degree in Materials Science at the University of Cambridge, UK, in 1967 and joined Rolls-Royce plc. There he was responsible for the development of engineering models for the prediction of the toughness of RPV steels through reactor life, and for justifying their use in structural integrity evaluations, actively participating in several international collaborations and networks. Outside RR he has been involved in consultancies and independent expert groups related to RPV safety issues. He is a fellow of the Institute of Materials, Minerals and Mining and was awarded its Colclough Medal and Prize.