Gary L. Stevens

Investigation of Differences in the Finite Element Solution of a Sample Fatigue Cumulative Usage Factor Calculation Problem

In November 2009, the Electric Power Research Institute (EPRI) assembled an Advisory Panel on Environmental Fatigue, consisting of various industry and vendor participants, whose charter is to provide insight and recommendations to EPRI (including the Pressurized Water Reactor (PWR) Materials Reliability Program (MRP), the Boiling Water Reactor Vessel and Internals Project (BWRVIP), and the Advanced Nuclear Technology (ANT) organizations) on conducting additional work and providing guidance associated with environmental fatigue. The goal of the panel is to identify areas in environmentally assisted fatigue (EAF) formulations, or application of the EAF formulations, contained in regulations and the ASME Code that may cause application difficulties, to determine where new research efforts are necessary to provide guidance or alternatives to application of these formulations, and to investigate industry design problems with a goal of identifying solutions to obtain near- and long-term relief. The Advisory Panel consists of various industry and vendor participants that have been engaged in the environmental fatigue topic over the past several years. As a part of the activities investigated by the Expert Panel, in 2010, a sample problem was defined for use in testing the application of proposed ASME Code Cases for evaluation of EAF using the EAF multiplier (Fen ) correction factor methodology. The sample problem was provided to multiple industry organizations and regulators to be solved so that differences in approaches and methods applied to the sample problem could be identified and understood. The intent of this effort was to refine the Fen methodology to clarify issues that have been previously identified and its practical application to typical industry fatigue evaluation problems. NRC staff elected to participate in solving the sample problem and comparing solutions generated by the other participating organizations in order to more fully understand the issues with fatigue calculation methodologies, as well as to provide input and develop consensus on the evaluation approaches. The sample problem represents a simplified form of a traditional reactor pressure vessel-type evaluation for transient thermal stress analysis and fatigue cumulative usage factor (CUF) calculation of a representative piping component evaluated in accordance with ASME Code, Section III, Subarticle NB-3200 methods. This paper describes detailed investigation of differences between two solutions to the Expert Panel sample problem. This investigation involves comparisons of results from the initial finite element solution for thermal and pressure stresses (using different finite element software packages), to the calculation of CUF (both with and without EAF effects). Observations regarding differences in results and the reasons for those differences are identified and discussed. Recommendations for eliminating these differences are also made.Copyright

Additional Improvements to Appendix G of ASME Section XI Code for Nozzles

This paper is the second in a continuing series of papers to highlight additional bases and recommended improvements to Appendix G. In 2008, the authors prepared a paper that reviewed some of the original basis documents for Appendix G for calculating pressure-temperature (P-T) limits and identified recommended areas for improvement. The 2008 paper discussed the fact that the original Appendix G in Section XI of the ASME Code was primarily based on Welding Research Council (WRC) Bulletin 175, and identified the changes that have been made to Appendix G over the past 20 years. However, the nozzle corner solutions have remained the same as those given in WRC 175. Proposed revisions to Appendix G are included in this paper regarding the stress intensity factor (K) calculation procedures for pressure and thermal gradient loading at a nozzle corner based on the various solutions described in the authors’ previous paper and on other more recent investigations. The current paper is focused on incorporating the results of additional studies that have been completed associated with nozzle corner solutions. This additional work has become more important because plants must address the effects of nozzles in the reactor pressure vessel (RPV) as a part of pressure-temperature (P-T) curve development, especially if the nozzles are located sufficiently close to the active core region such that they accumulate significant fluence. In addition, the treatment of operating stresses exceeding the material yield stress is discussed and the basis for the limit of material yield strength to 90 ksi in G-2110(b) is provided. Finally, this paper identifies other areas for future improvements in Appendix G, including those areas remaining to be addressed from prior work.Copyright

Suggested Improvements to Appendix G of ASME Section XI Code

This paper reviews some of the original basis documents for ASME Section XI Nonmandatory Appendix G for calculating pressure-temperature (P-T) limits and recommends areas for improvement. The original Appendix G in Section XI of ASME Code was mainly based on Welding Research Council (WRC) Bulletin 175 (WRC-175). Changes have been made to Appendix G over the past 20 years such as the use of the KIC reference toughness curve instead of KIR . However, aspects of the Appendix G method still refer back to WRC Bulletin 175. The published technical literature since the development of WRC 175 could be used to enhance the Appendix in a number of areas. One such area is stress intensity factor (K) calculation procedures for thermal gradient loading at a nozzle corner. This paper will review and evaluate the available K calculation methods for a nozzle corner crack, and develop closed-form expressions for incorporation into Appendix G. Also, the following areas will be reviewed: (1) treatment of operating stresses exceeding the material yield stress, and (2) fracture toughness criteria typically used for other than reactor pressure vessel (RPV) and piping for protection against non-ductile failure. This paper will also identify areas for future improvements in Appendix G.Copyright

Options for Defining the Upper Shelf Transition Temperature (Tc) for Ferritic Pressure Vessel Steels

This paper evaluates current guidance concerning conditions under which the analyst is advised to transition from a linear-elastic fracture mechanics (LEFM) based analysis to an elastic-plastic fracture mechanics (EPFM) based analysis of pressure vessel steels. Current guidance concerning the upper-temperature (T>c) for LEFM-based analysis can be found in ASME Section XI Code Case N-749. Also, while not explicitly stated, an upper-limit on the KIc value that may be used in LEFM-based evaluations is sometimes taken to be 220 MPa√m (a value herein referred to as KLIM). Evaluations of Tc and KLIM were performed using a recently compiled collection of toughness models that are being considered for incorporation into a revision to ASME Section XI Code Case N-830; those models provide a complete definition of all toughness metrics needed to characterize ferritic steel behavior from lower shelf to upper shelf. Based on these evaluations, new definitions of Tc and KLIM are proposed that are fully consistent with the proposed revisions to Code Case N-830 and, thereby, with the underlying fracture toughness data. Formulas that quantify the following values over the ranges of RTTo and RTNDT characteristic of ferritic RPV steels are proposed:• For Tc, two values, Tc(LOWER) and Tc(UPPER), are defined that bound the temperature range over which the fracture behavior of ferritic RPV steels transitions from brittle to ductile. Below Tc(LOWER), LEFM analysis is acceptable while above Tc(UPPER) EPFM analysis is recommended. Between Tc(LOWER) and Tc(UPPER), the analyst is encouraged to consider EPFM analysis because within this temperature range the competition of the fracture mode combined with the details of a particular analysis suggest that the decision concerning the type of analysis is best made on a case-by-case basis.• For KLIM, two values, KLIM(LOWER) and KLIM(UPPER), are defined that bound the range of applied-K over which ductile tearing will begin to occur. At applied-K values below KLIM(LOWER), ductile tearing is highly unlikely, so the use of the KIc curve is appropriate. At applied-K values above KLIM(UPPER), considerable ductile tearing is expected, so the use of the KIc curve is not appropriate. At applied-K values in between KLIM(LOWER) and KLIM(UPPER), some ductile tearing can be expected, so it is recommended to give consideration to the possible effects of ductile tearing as they may impact the situation being analyzed.These definitions of Tc and KLIM better communicate important information concerning the underlying material and structural behavior to the analyst than do current definitions.Copyright

Probabilistic Fracture Mechanics Evaluations That Consider Nozzles in the Extended Beltline Region of Reactor Pressure Vessels

For many years, ASME Section XI committees have discussed the assessment of nozzle penetrations in various flaw evaluations for reactor pressure vessels (RPVs). As summarized in Reference [1], linear elastic fracture mechanics (LEFM) solutions for nozzle penetrations have been in use since the 1970s. In 2013, one of these solutions was adopted into ASME Code, Section XI, Nonmandatory Appendix G (ASME App. G) [2] for use in developing RPV pressure-temperature (P-T) operating limits. That change to ASME App. G was based on compilation of past work [3] and additional evaluations of fracture driving force [4][5].To establish the P-T limits on RPV operation, consideration should be given to both the RPV shell material with the highest reference temperature as well as regions of the RPV (e.g., nozzles, flange) that contain structural discontinuities. In October 2014, the U.S. Nuclear Regulatory Commission (NRC) highlighted these requirements in Regulatory Issue Summary (RIS) 2014-11 [6].Probabilistic fracture mechanics (PFM) analyses performed to support pressurized thermal shock (PTS) evaluations using the Fracture Analysis Vessels Oak Ridge (FAVOR) computer code [7] currently evaluate only the RPV beltline shell regions. These evaluations are based on the assumption that the PFM results are controlled by the higher embrittlement characteristic of the shell region rather than the stress concentration characteristic of the nozzle, which does not experience nearly the embrittlement of the shell due to its greater distance from the core. To evaluate this assumption, the NRC and the Oak Ridge National Laboratory (ORNL) performed PFM analyses to quantify the effect of these stress concentrations on the results of the RPV PFM analyses. This paper summarizes the methods and evaluates the results of these analyses.Copyright

Models of the Temperature Dependence and Scatter in J-R and J0.1 for Ferritic Reactor Pressure Vessel Steels

At the 2014 ASME Pressure Vessel and Piping Conference, these authors and others presented a paper that drew together a number of models describing the fracture toughness of ferritic reactor pressure vessel (RPV) steels. That paper summarized models of both the temperature dependence and scatter in a number of fracture toughness metrics (i.e., KJc, KIa, JIc, and J0.1). That paper also provided equations that quantify the interrelationships between these toughness metrics, and how these interrelationships are affected by hardening. Significantly, all of these models and interrelationships are linked via a single parameter: the Master Curve index temperature, To, which can be measured as described in ASTM Standard Test Method E1921. Work is currently underway within the ASME Section XI Working Group on Flaw Evaluation (WGFE) to develop a revision to Code Case N-830 that incorporates all of these models, and provides information on how to apply them in a flaw evaluation. As part of that work, an effort was initiated to augment these models by the addition of a model that can be used to predict the temperature variation of, and the scatter in, J-R curve behavior. A J-R curve model is also expected to support on-going WGFE efforts to in development of acceptance criteria for flaws in ferritic components operating in the upper shelf temperature range.The work presented in this paper provides a model of the J-R behavior of ferritic RPV steels. When combined with other fracture toughness models to be published in Code Case N-830-1, this model allows prediction of the mean J-R curve, confidence bounds on the mean, and the temperature dependence of J-R all based only on input of To. The J-R model described herein has equivalent or better accuracy to other models described in the literature, and generally has fewer fitting parameters than those other models. Because the full J-R curve is predicted, this model is also useful for prediction of J0.1.Copyright

Assessment of Fracture Toughness Models for Ferritic Steels Used in Section XI of the ASME Code Relative to Current Data-Based Models

Section XI of the ASME Code provides models of the fracture toughness of ferritic steel. Recent efforts have been made to incorporate new information, such as the Code Cases that use the Master Curve, but the fracture toughness models in Section XI have, for the most part, remained unchanged since the KIc and KIa curves were first developed in Welding Research Council Bulletin 175 in 1972. Since 1972, considerable advancements to the state of knowledge, both theoretical and practical have occurred, particularly with regard to the amount of available data. For example, as part of the U.S. Nuclear Regulatory Commission’s (NRC’s) pressurized thermal shock (PTS) re-evaluation efforts the NRC and the industry jointly developed an integrated model that predicts the mean trends and scatter of the fracture toughness of ferritic steels throughout the temperature range from the lower shelf to the upper shelf. This collection of models was used by the NRC to establish the index temperature screening limits adopted in the Alternate PTS Rule documented in Title 10 to the U.S. Code of Federal Regulations (CFR), Part 50.61a (10CFR50.61a). In this paper the predictions of the toughness models used by the ASME Code are compared with these newer models (that are based on considerably more data) to identify areas where the ASME Code could be improved. Such improvements include the following:• On the lower shelf, the low-temperature asymptote of the KIc curve does not represent a lower bound to all available data.• On the upper shelf, the de facto KIc limit of applicability of 220 MPa√m exceeds available data, especially after consideration of irradiation effects.• The separation between the KIc and KIa curves depends on the amount of irradiation embrittlement, a functionality not captured by the ASME Section XI equations.• The temperature above which upper shelf behavior can be expected depends on the amount of irradiation embrittlement, a functionality not captured in the ASME Section XI equations.Copyright

A Fracture-Toughness Based Transition Reference Temperature for Use in the ASME Code With the Crack Arrest (KIA) Curve

In the early 2000s, ASME adopted Code Cases N-629 and N-631 [1–2], both of which permit the use of the Master Curve reference temperature (To) to define an reference temperature RTTo, as follows (in SI units, as are used throughout the paper):Display FormulaRTTo=To+19.4℃ The Code Cases state that “this reference temperature … may be used as an alternative to [the] indexing reference temperature RTNDTfor the KIcand KIatoughness curves, as applicable, in Appendix A and Appendix G [of Section XI of the ASME Code].” KIa is now only used in Appendix A. The functional form of the ASME KIc and KIa curves dictate that the temperature separation between them remains constant irrespective of the degree of neutron radiation embrittlement, as quantified by ΔRTNDT or ΔRTTo. However, data collected from the literature and new data reported by Hein et al. show that radiation embrittlement brings the KIc and KIa curves closer together as embrittlement increases. As a result, current Code guidance will not produce a bounding KIa curve in all situations when RTTo is used as an reference temperature. To reconcile this issue, this paper summarizes available data and, on that basis, concludes that use of the following reference temperature will ensure that the ASME KIa curve bounds currently available KIa data:Display FormulaRTKIa=RTTo-19.4+44.97×exp⁡−0.00613×RTTo-19.4Copyright

ASME Section III Flaw Tolerance Sample Problem for Fatigue Design of Nuclear System Components

An ASME Section III Task Group (TG) was formed in 2012 to develop alternate rules for the design assessment of Section III Class 1 nuclear components subject to fatigue service with environmental effects. Specifically, a flaw tolerance approach is being investigated based on similar methodology to that found in ASME Section XI Nonmandatory Appendix L. A key initial task of the TG (which reports to the Section III Working Group on Environmental Fatigue Evaluation Methods) was to develop and solve a detailed sample problem. The intent of the sample problem was to illustrate application of proposed rules, which will be documented as a Section III Code Case with a supporting technical basis document. Insights gained from round robin solution of the sample problem are presented and discussed in this paper. The objective of documenting the findings from the sample problem are to highlight the observed benefits and limitations of the proposed procedures, particularly how rules typically associated with in-service experience might be adapted into design methods.The sample problem is based on a heavy-walled stainless steel nozzle that meets cumulative fatigue usage requirements in air (i.e., usage factor, U, without reactor water environment effects less than unity), but fails to meet usage factor requirements when environmental fatigue effects are applied.The sample problem demonstrates that there is a class of problems dominated by severe thermal transients where fatigue initiation is predicted based on elastic methods including environmental effects, but fatigue crack propagation results are acceptable. Preliminary conclusions are drawn based on the results of the sample problem, and the next steps are also identified.Copyright

Treatment of Stresses Exceeding Material Yield Strength in ASME Code Section XI Appendix G Fracture Toughness Evaluations

A previous PVP paper [1] identified suggested improvements to be made to ASME Code, Section XI, Nonmandatory Appendix G, “Fracture Toughness Criteria for Protection Against Failure” [2]. That paper also identified that the current version of Appendix G does not have any provisions for when the calculated operating stress (pseudo stress) exceeds the material yield strength. The treatment of stresses exceeding yield was included in earlier versions of Appendix G, but it was removed via Code Action ISI-94-40 in 1995. The specific reasons for removal of these provisions were not documented.In some Appendix G postulated flaw evaluations for pressure-temperature (P-T) limits, the calculated total linear-elastic (or pseudo) stress (i.e., including the primary stress due to pressure loading and thermal stress) may exceed the material yield stress. The ASME Section XI Working Group on Operating Plant Criteria (WGOPC) decided that this provision needed to be more fully considered, with appropriate benchmarking and possible adjustments to Appendix G made consistent with the current state of knowledge in elastic-plastic fracture mechanics (EPFM) methods. This is appropriate since the state of knowledge in EPFM has significantly advanced since the time the technical basis for Appendix G was established, as documented in Welding Research Council (WRC) Bulletin No. WRC-175, which was published in 1972. Furthermore, EPFM provides an improved method for evaluating the effects of high stresses.This paper describes the results of preliminary investigations of stresses exceeding the material yield stress in fracture toughness assessments associated with Appendix G. Also included in the technical evaluations presented are the temperature conditions for which upper shelf conditions are present and where EPFM methods are applicable.Copyright