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| Issue date: | 06/09/2015 |
| From: | State of NY, Office of the Attorney General |
| To: | Atomic Safety and Licensing Board Panel |
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| RAS 27910, ASLBP 07-858-03-LR-BD01, 50-247-LR, 50-286-LR | |
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NYS000520 Submitted: June 9, 2015 Proceedings of PVP2014 2014 ASME Pressure Vessels and Piping Division Conference July 20-24, 2014, Anaheim, CA, USA PVP2014-28540 ASSESSMENT OF FRACTURE TOUGHNESS MODELS FOR FERRITIC STEELS USED IN SECTION XI OF THE ASME CODE RELATIVE TO CURRENT DATA-BASED MODELS 1
Mark Kirk Senior Materials Engineer, Nuclear Regulatory Commission, Rockville, MD, USA, mark.kirk@nrc.gov Marjorie Erickson President, Phoenix Engineering Associates, Inc. Unity, NH, USA, erickson@peaiconsulting.com William Server President, ATI Consulting, Black Mountain, NC, USA, wserver@ati-consulting.com 1
Gary Stevens Senior Materials Engineer, Nuclear Regulatory Commission, Rockville, MD, USA, gary.stevens@nrc.gov Russell Cipolla Principal Engineer, Intertek AIM, Sunnyvale, CA, USA, russell.cipolla@intertek.com ABSTRACT The temperature above which upper shelf behavior can be Section XI of the ASME Code provides models of the fracture expected depends on the amount of irradiation embrittlement, a toughness of ferritic steel. Recent efforts have been made to functionality not captured in the ASME Section XI equations.1 incorporate new information, such as the Code Cases that use the Master Curve, but the fracture toughness models in Section XI have, BACKGROUND AND OBJECTIVE for the most part, remained unchanged since the KIc and KIa curves A key input to assessments of the integrity of operating structures in were first developed in Welding Research Council Bulletin 175 in the presence of real or postulated defects is the fracture toughness of 1972. Since 1972, considerable advancements to the state of the material in question. Various parts of the ASME Code (that is, the knowledge, both theoretical and practical have occurred, particularly Code itself, various Nonmandatory Appendices, and Code Cases) with regard to the amount of available data. For example, as part of provide models of the fracture toughness properties of ferritic steels; the U.S. Nuclear Regulatory Commissions (NRCs) pressurized principally the KIc and KIa curves developed in the early 1970s [1]. The thermal shock (PTS) re-evaluation efforts the NRC and the industry Code has recently been expanded to include procedures to estimate jointly developed an integrated model that predicts the mean trends RTNDT using the Master Curve index temperature To [2-3], and to and scatter of the fracture toughness of ferritic steels throughout the estimate the temperature above which an EPFM-based analysis is temperature range from the lower shelf to the upper shelf. This needed [4]. Since the early 1970s, considerable advancements to the collection of models was used by the NRC to establish the index state of knowledge, both theoretical and practical have occurred, temperature screening limits adopted in the Alternate PTS Rule particularly with regard to the amount of data available and empirical documented in Title 10 to the U.S. Code of Federal Regulations models derived from these data. For example, as part of the U.S.
(CFR), Part 50.61a (10CFR50.61a). In this paper the predictions of Nuclear Regulatory Commissions (NRCs) pressurized thermal shock the toughness models used by the ASME Code are compared with (PTS) re-evaluation efforts, reports from which were issued in early these newer models (that are based on considerably more data) to 2010, the NRC and the industry jointly developed an integrated model identify areas where the ASME Code could be improved. Such that predicts the mean trends and scatter of the fracture toughness of improvements include the following: ferritic steels throughout the complete temperature range from the lower shelf to the upper shelf [5]. This collection of models was used On the lower shelf, the low-temperature asymptote of the KIc by the NRC in the probabilistic fracture mechanics (PFM) Code, curve does not represent a lower bound to all available data. Fracture Analysis Vessels - Oak Ridge (FAVOR) [6], to establish the On the upper shelf, the de facto KIc limit of applicability of 220 index temperature screening limits adopted in the Alternate PTS Rule MPam 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 1
by the ASME Section XI equations. The views expressed herein are those of these authors and do not represent an official position of the NRC. This material is the work of the United States Government and is not subject to copyright protection in the United States. This paper is approved for public release with unlimited distribution.
1
documented in Title 10 to the U.S. Code of Federal Regulations The relationship between transition fracture toughness and upper (CFR), Part 50.61a (10CFR50.61a) [7]. shelf fracture toughness values [24].
The objective of this paper is to compare the predictions of the References [4, 5, 20-24] discuss both the empirical and physical bases toughness models within the ASME Code with the newer models that for these relationships, which were developed from large databases are based on considerably more data to identify areas where the ASME (data numbering in the hundreds) covering a wide range of material Code could be improved. conditions (e.g., different product forms, different irradiation exposures, different material chemistries). These papers provide ASME CODE TOUGHNESS MODELS information demonstrating that, like the Master Curve, these The KIc and KIa curves that appear in Article A-4200 of Nonmandatory relationships can be expected to apply with comparable accuracy to all Appendix A to ASME Section XI [8] (the KIc curve also appears in ferritic steels irrespective of composition, product form, heat Appendix G [9]), are expressed as follows (all equations in this paper treatment, degree of hardening, degree of irradiation damage, etc.
are expressed in SI units): Significantly, all of these models are linked via a single parameter:
To. Once To is determined the mean initiation and arrest toughness (1) behavior, and the scatter about the mean, can be determined from (2) lower shelf through upper shelf using combinations of the models Eqs. (1-2) are intended to represent the lower bounds of KIc and KIa presented in Table 1. Figure 1 shows the curve shapes and data. These estimates of KIc and KIa depend on the index temperature relationships of these models and defines their variables visually.
RTNDT, which is determined per ASME NB-2331 [10]. Where In addition to the models shown in Figure 1, Table 1 includes the appropriate, RTNDT is adjusted to account for the effects of neutron equation for RTTo provided by Code Cases N-629 and N-631 (and now irradiation embrittlement. Neither Appendix A nor Appendix G, place in the ASME Code Section XI, Appendices A and G). RTTo provides an upper-limit on the KIc value that may be estimates using eqs. (1-2). an alternative to RTNDT such that To can be used to index the ASME Nevertheless, a value of 220 MPam has, over time, become a de facto KIc and KIa lower bound curves. RTTo thereby links the data-based limit on KIc despite scarce mention or defense of this value in the models of Table 1 to the ASME models for KIc and KIa. This linkage literature. The basis for this limit and an assessment of its accuracy enables comparison of the ASME lower bound descriptions of relative to data appears in [11]. transition initiation and arrest toughness to the data-based models of CURRENT DATA-BASED TOUGHNESS MODELS initiation and arrest toughness.
In 1984 Wallin and co-workers began publication of a series of papers COMPARISON OF ASME MODELS TO CURRENT DATA-BASED that, collectively, describe what has come to be called the Master MODELS Curve [12-14]. The Master Curve quantifies the temperature The data-based models of ferritic steel toughness summarized in Table dependence and scatter of the fracture toughness (i.e., KJc or Jc values) 1 can be compared with the ASME models for KIc and KIa to identify of ferritic steels in the fracture mode transition temperature region.
situations where the ASME models adequately reflect the data versus Existing work in which large databases were examined demonstrates situations where the ASME models could potentially be improved. In that the temperature dependence and scatter of the Master Curve are the next two subsections [A and B] the comparisons made can be consistent for all ferritic steels [15-16]2. All that needs to be interpreted in two ways: (1) either as an assessment of the accuracy of determined for a particular material is the Master Curve index the ASME models when RTTo (i.e., To) is used as an index temperature (To), which positions the Master Curve on the temperature temperature, or (2) as an assessment of the accuracy of the ASME axis. Using ASTM E1921 protocols it is possible to estimate To using models when the index temperature RTNDT is used and RTNDT exceeds as few as six fracture toughness specimens [19], providing the To by 19.4 °C. Subsection C re-examines these analyses to assess the possibility that To can be directly determined from the specimens effect of the NDT/Charpy-based value of RTNDT being other than already placed in the surveillance capsules of nuclear reactor pressure 19.4 °C above To, which is often the case. Finally, an assessment is vessels.
made in Subsection D of the influence margin terms have on the Over the past fifteen years papers have been published that expand ability of the ASME models to represent, or conservatively bound, the upon and extend the Master Curve concept. These papers describe: fracture toughness data.
The temperature dependence and scatter in crack arrest fracture A. Crack Initiation - KIc and Upper Shelf toughness (KIa) [20]. Figure 2 compares the predictions of the data-based models for KIc /
The temperature separation of the KJc and KIa transition curves, KJc and JIc with the ASME KIc curve augmented by the de facto upper and how this separation changes with the condition of the shelf limiting value of 220 MPam for three RTTo values: -100, 0, and material [20-21] +100 °C (these being chosen to examine a range of hardening that The temperature dependence and scatter in upper shelf fracture could result from, as an example, neutron radiation embrittlement).
toughness data (JIc) [22-23], and These graphs support the following observations:
The ASME model over-estimates the lower shelf fracture toughness at temperatures 60 °C or more below RTTo for all 2
Some studies by Wallin suggest adjustments to the Master Curve lower values of RTTo. For un-irradiated materials such low temperatures bound value on the lower shelf [17], and of the temperature dependence in cannot be achieved during normal operations. However, as the case of extremely high embrittlement [18]. In absolute terms the radiation embrittlement causes the material transition temperature magnitude of these adjustments are minor, having only small effects on the to approach regulatory limits (e.g., the PTS limits of 132 to 149 °C predicted values. These adjustments could be considered as a further in 10CFR50.61 [25]) a temperature 60 °C below these values is improvement to the models suggested herein should the cognizant ASME clearly within the range achievable during a cool-down.
Code groups decide to adopt these models.
2
In the transition regime between lower shelf and upper shelf the differences could affect the outcome of probabilistic assessments, ASME model maintains a consistent location below the data, thus which are more sensitive to changes in the models near the lower providing a conservative estimate of KJc. The well recognized bound, they are not expected to adversely affect deterministic difference between the temperature dependence of the data and assessments performed according to ASME SC-XI Appendix A or that of the ASME model is also evident in these plots. While these Appendix G.
Table 1. Summary of Data-Based Toughness Models for Ferritic Steels.
refs Model Equations Eq. #
Reference temperature for ASME KIc and
[2-3] RTTo (3)
KIa curves based on To K Jc 30 70 exp 0.019T To Temperature dependence of median (4) fracture toughness of a 1T specimen Scatter at a fixed temperature P
K Jcf K min K o 20 ln 1 Pf 1 4 , where (5)
[12- Ko 31 77 exp 0.019T To KJc 14] 1 B
K Jc ( x ) K min K Jc ( o ) K min o b
Size effect Bx (6) where Bx is the thickness of the specimen of interest while Bo is the reference thickness (1-in., or 25.4 mm).
Temperature dependence of mean KIa K Ia 30 70 exp 0.019T TKIa (7a)
[20] KIa Scatter at a fixed temperature Log-normal with a variance () equal to 18% of the mean value. (7b)
J Ic 1.75C1 exp C2TK C3TK ln 3.325 J adj J adj J c (US ) J Ic (US )
J c (US ) 30 70 exp 0.019TUS To 1 2 E 2
J Ic (US ) 1.75 C1 exp C T C T ln 3.325 2 US K
3 US K
Temperature dependence (temperature E 207200 57.1 T (8) is in Kelvin)
= 0.3 Tref = 288C (or 561K)
T USK TUS 273.15 C1 = 1033 MPa C2 = 0.00698/K C3 = 0.000415/K = 0.0004/sec
[22-23]
JIc J A e Ic BT where T T 288 C A 9.03 e1.12P Scatter at a fixed temperature B MIN0,0.0009P 0.0045 (9)
P MIN1, MAX 0, MIN P1 , P2 J Ic ( 288)
P1 0.46 120 J Ic ( 288)
P2 0.51 800
[21, Linkage of KJc and KIa data (10) 34] The standard deviation of ln (TKIa-To ) is 0.383.
[24] Linkage of KJc and JIc data (11)
The accuracy of the de facto ASME upper limit of 220 MPam on limit on KIc should be informed by the upper shelf fracture KIc is strongly compromised by increasing RTTo [11]. Above RTTo toughness. The upper shelf of many ferritic materials falls below of 0 °C 220 MPam exceeds the upper shelf fracture toughness of 220 MPam even when J0.1 is used as the characterizing parameter most RPV steels by a considerable amount, suggesting a practical (see the Appendix for further discussion). TUS, defined in Table 1, 3
can be used to define the upper limit of applicability for the KIc Another paper presented at this conference [34] corrects this situation curve based on data [11].3 by using eq. (10) to adjust RTTo so that it can be used to index the KIa curve.
B. Crack Arrest Figure 3 compares the predictions of the data-based models for KIc / D. Effect of Margins KJc and KIa with the ASME KIc and KIa curves for three RTTo values: - Taken as a whole, the information in subsections [A], [B], and [C]
100, 0, and +100 °C (these being chosen to examine a range of leads to the conclusion that the ASME models are out of date and, in hardening that could result from, as an example, neutron radiation some cases, non-conservative. Especially on the lower shelf, the upper embrittlement). The data-based models show that as RTTo increases transition limit, and for all of the crack arrest transition, the ASME the KIc and KIa curves converge. This convergence is not a feature of models fail to capture trends clearly evident in data now available.
the ASME models, which maintain a constant temperature separation Even the application of large margins implicit to some RTNDT values between them. The result of using a constant temperature separation does not fully ameliorate the non-conservatisms identified here (see to represent the actual material behavior is that the ASME model is Figure 4).
overly pessimistic for high values of RTTo indicative of highly irradiated material and over-estimates KIa at low values of RTTo. Table 2. ASME Code margin terms.
Code Ref. Margin Values Equation C. Sensitivity Study Based on the To - RTNDT Relationship 2 for current practice As described in [2-3], RTTo was defined as To + 19.4 °C so that the KIc Appendix G 1 for risk informed curve indexed to RTTo appropriately bounds available fracture 10 for normal and toughness data. Appropriate bounding was defined in [26] as a IWB-3612/ anticipated loading curve bounding approximately 95% of the data, a finding also Appendix A 2 for emergency and validated by Wallin [27]. The consistent placement of the reference KIc curve enabled by the use of a true fracture toughness measure like faulted loading To ensures that this degree of bounding will occur for all materials.
Thus, the analysis of the previous section [B] applies to situations In view of these observations, the question arises as to how the ASME where RTTo is used as an index temperature, or to materials for which Code models survived for over 40 years without these inaccuracies RTNDT exceeds To by 19.4 °C. However, RTNDT does not always becoming evident. The primary explanation is the margins placed on equal To +19.4 °C. Figure 4 draws together data from two sources loading, flaw size, and the effects of radiation embrittlement. The (one being the source used to establish the epistemic uncertainty in deterministic method described in the ASME Code, Appendix G, uses RTNDT for the PFM computer code FAVOR [6]) to illustrate that the these margins with the expectation that they account for these degree by which RTNDT exceeds (or in one case does not) To varies by discrepancies between the data and the ASME models..Some of the a considerable degree. The following values of (RTNDT -To) were taken specific margins applied are listed below:
from these data and used to re-plot the ASME models in the format of Margin on irradiated RTNDT: The ASME Code states that RTNDT Figure 2 and Figure 3 to assess the degree to which the ASME models should be adjusted to account for the effects of radiation damage.
represent the data for different values of RTNDT: Regulatory Guide 1.99 Revision 2 suggests a margin term that RTNDT = To + 0 °C: This is an extreme case, but nonetheless accounts for uncertainty in the unirradiated value of RTNDT and in possible based on these data and moreover is representative of a the estimated shift of this value due to irradiation damage [29].
worst-case assessment of the conservatism of the ASME models. The value for each of these terms depends on several factors (e.g.,
RTNDT = To + 47 °C: This represents the median of the product form, generic or measured values, credibility of distribution of (RTNDT -To) values shown on Figure 4. surveillance data, etc.). To provide a sense of the magnitude of the margin term the range of values adopted for the various Figure 5 illustrates that the deficiencies of the ASME KIc model in materials in the operating fleet reported in the NRCs RVID2 representing the lower shelf and upper limit of applicability noted in database is provided in Figure 7 [30].
the discussion of Figure 2 are not influenced by the difference between Margin on KI: Table 2 summarizes some of the different margins RTNDT and To. For materials where RTNDT exceeds To by less than 19.4 applied to the value of KI in different parts of the ASME Code.
°C, Figure 5 illustrates that non-conservative predictions of KIc in Margin due to flaw size: This margin is generally coupled with transition can also be expected. the aforementioned margin on KI. For ASME Code Appendix G Figure 6 illustrates that RTNDT would need to exceed To by more than calculations for pressure temperature operating curves, an 47 °C (a value of approximately 65 °C would be needed) to ensure that assumed large flaw size of 1/4-thickness of the vessel wall is used.
the ASME KIa model provides a conservative bound to the KIa data for In IWB-3611/Appendix A where a detected flaw is being the range of RTTo values considered. The data in Figure 4 demonstrate evaluated, the margin on flaw size is a factor of 10 relative to the that such materials make up only 25% of the population of RPV steels. critical flaw size, which is reflected by the value of 10 that Thus, the use of RTTo to index the KIa curve will provide a non- appears in Table 2.
conservative representation for approximately 75% of RPV materials. By way of example Figure 8 illustrates the effect of these margin terms on the situations from Figure 5 and Figure 6 where the ASME models are most in need of margin to be conservative.
3 It should be noted that with the exception of Code Case N-749 [4] the ASME The upper graph in Figure 8 shows that a RTNDT margin of +20 Code does not now explicitly consider the area from the upper transition °C (approximately the median from Figure 7) plus a KI margin of region to the upper shelf. Instead the Code independently assesses 2 is sufficient to make the ASME KIc model bounding on lower cleavage fracture in the transition region using linear elastic fracture shelf and in transition for most steels. However, a larger KI mechanics (LEFM), and on the upper shelf using elastic-plastic fracture margin (=2) would be needed to ensure bounding on the upper mechanics (EPFM), in each case with appropriate margin terms.
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shelf for high RTTo materials. It should be noted that the not measured. Various embrittlement trend curves are available for effectiveness of the Appendix G KI margins, which are just this purpose [29, 31-33] for ASME use in replacing current toughness applied to the K arising due to pressure, are not assessed here. models the equations given in Table 5 could be expressed as a low Since these margins apply only to a portion of K, greater values probability (p) value (e.g., 5%), with the specific p-value perhaps tied (i.e., greater than 2) would be needed to ensure bounding on the to the loading condition as is now the practice in IWB-3612. The upper shelf. appropriate margins to use with this data-consistent approach, beyond The lower graph in Figure 8 shows that a RTNDT margin of +40 the margin associated with this selection of a p-value, merits further
°C (higher than any of the values in Figure 7) plus a KI margin of discussion. Reconsidering the types of margins used currently:
2 is sufficient to make the ASME KIa model bounding on lower Table 3. ASME Code use of models from Table 1.
shelf and in transition for most steels.
ID Summary Accuracy These examples illustrate that in many, but certainly not all, cases N-629 [2] KIc: OK in transition. Need combination of the ASME models and these margin terms results in a conservative characterization of KIc and KIa relative to data now N-631 [3] Use RTTo to index the KIc margin on lower shelf available. Nevertheless, the degree of conservatism is by no means App. A and KIa curves KIa: inconsistent with the consistent across the range of conditions found in the operating fleet. App. G data, but being fixed [34]
The temperature Tc is not CONCLUSIONS Defines a temperature a function of To, which is N-749 [4] (Tc) above which EPFM A. For RTNDT-based Characterizations not consistent with the analysis is needed For RTNDT-based assessments the comparisons of the ASME model data.
predictions to the data demonstrate the necessity of maintaining the Re-defines the KIc curve The constant lower shelf current margins on RTNDT and on KI to compensate for the inaccuracies as a fixed percentile of value follows current Proposed of the ASME models. Maintenance of these margins is expected to the Master Curve in ASME practice but is not enable the ASME models to produce conservative characterizations in N-830 transition and a consistent with the Master most cases. However, the information presented herein demonstrates [35]
constant value on lower Curve bound and fracture that conservatism cannot be guaranteed in all cases. Additionally, the shelf. toughness data.
actual margin achieved by the combination of explicit and implicit margins currently adopted by the Code varies considerably across the Margin on To: With the elimination of the uncertainty on the fleet, and instances can be found where the actual margin achieved is unirradiated value of RTNDT (which, as illustrated here, consumed less than one would wish. In our view, the best remedy to ensure a large part of the existing margin), less margin seems necessary.
consistent and quantifiable margins is the adoption of a To-based It is suggested that two factors be considered: the measurement assessment strategy. Such a goal has been the focus of Code Cases uncertainty on To (see [19]), and the uncertainty in the and various activities within the Code over the past fifteen years. The embrittlement shift prediction (see [29, 31-33]). As is current following section summarizes briefly these past efforts, and goes on to practice a square root sum of squares combination of these two suggest a more integrated approach that could be adopted moving factors can be used. Additionally, should a direct measurement of forward. To in the irradiated condition be made then some reduction of these margin terms would be in order.
B. For To-based Characterizations Margin on K: The values of KIc and KIa on the lower shelf that Existing Code activities address some, but not all, of the needed are exhibited by the data, and are therefore reflected by equations components of a model that is fully consistent with the data and with listed in Table 4 and Table 5, are lower than the values predicted current-day understandings of the fracture toughness behavior of by current ASME models. It is recognized that this presents a ferritic steels. These activities, which are in some cases in accord with particular challenge within the ASME Section XI Appendix G the data and in other cases are not, are listed in Table 3. To augment context of setting P-T limits for normal operation because a these activities and bring them into closer accord with the underlying positive head pressure on the pumps needs to be maintained.
data, this paper summarizes a model of the fracture toughness behavior Figure 8 illustrated that the current ASME models with a 2 across the entire temperature range from lower to upper shelf. This margin term on KI produces KIc and KIa values roughly equivalent model, which can be based on the information summarized herein, to a 2.5th percentile curve of the equations listed in Table 5 In depends only on a value of To and on a selected bounding probability view of the added accuracy associated with a To-based approach value, p, where (for example), p could equal 0.05 as is typical for the use of a bounding p-value and no additional margin on KI many engineering applications. Table 4 summarizes the equations, seems appropriate. Should this not produce a sufficiently wide P-inputs and constants, and limits that fully define this model for T corridor for routine heat-up and cool-down it is suggested that calculation of central tendency (median, mean) values while Table 5 the conservatism inherent to the use of a 1/4t flaw in establishing summarizes the same information for calculation of a bounding value the P-T limits be revisited by the Code.
of fracture toughness. These tables do not present new equations, but rather recast those previously presented in Table 1 in a compact
SUMMARY
format. In 1972 when ASME adopted the KIc and KIa curves and much of the The equations of Table 4 and Table 5 capture the effect of radiation current margin approach, the margins were established based mostly embrittlement (or, equivalently, of To) on the interrelationships of KJc, on engineering judgment. Now, ample data exists to build more KIa, JIc, and J0.1. This feature absent from existing ASME models, and accurate toughness models and to quantify the amount of margin its absence is responsible for many of the inaccuracies of ASME needed to bound the data; this paper addresses both topics. The models noted herein. What remains absent from Table 4 and Table 5 models summarized in this paper are based on To; they produce safety are equations to predict the effects of radiation on To if this effect is margins that are both consistent and quantifiable across the fleet, a benefit that cannot be obtained within the current correlative 5
framework based on RTNDT. Additionally, while the information Experiments, 2006 ASME Pressure Vessel and Piping presented here demonstrates the conservatism of the current RTNDT- Conference, PVP2006-ICPVT11-93652.
based approach in most cases, available data shows it may be non- [6] Williams, P., Dickson, T., and Yin, S., Fracture Analysis of conservative in some situations. It is suggested that the cognizant Vessels - Oak Ridge FAVOR, v12.1, Computer Code:
ASME Code committees consider these models so that the Code can Theory and Implementation of Algorithms, Methods, and achieve the benefits made possible by use of current technology and Correlations, Oak Ridge National Laboratory Report data. ORNL/TM-2012/567, United States Nuclear Regulatory Commission ADAMS Accession Number ML13008A014, REFERENCES (2012).
[1] PVRC Ad Hoc Group on Toughness Requirements, PVRC
[7] 10 CFR 50.61a, Alternate fracture toughness requirements Recommendations on Toughness Requirements for Ferritic for protection against pressurized thermal shock events, Materials. Welding Research Council Bulletin No. 175, http://www.nrc.gov/reading-rm/doc-August 1972.
collections/cfr/part050/part050-0061a.html.
[2] American Society Of Mechanical Engineers, Use of Fracture
[8] ASME Boiler and Pressure Vessel Code, Rules for Inservice Toughness Test Data to Establish Reference Temperature for Inspection of Nuclear Power Plants,Section XI, Appendix Pressure Retaining Materials,Section XI, Division 1, A., Analysis of Flaws ASME Boiler and Pressure Vessel Code Case N-629, ASME, New York (1999). [9] ASME Boiler and Pressure Vessel Code, Rules for Inservice Inspection of Nuclear Power Plants,Section XI, Appendix
[3] American Society Of Mechanical Engineers, Use of Fracture G., Fracture Toughness Criteria for Protection against Toughness Test Data to Establish Reference Temperature for Failure Pressure Retaining Materials Other than Bolting for Class 1 Vessels,Section III, Division 1, ASME Boiler and Pressure [10] ASME NB-2331, 1998 ASME Boiler and Pressure Vessel Vessel Code: An American National Standard, Code Case Code, Rules for Construction of Nuclear Power Plants, N-631, ASME, New York (1999). Division 1, Subsection NB, Class 1 Components
[4] American Society Of Mechanical Engineers, Alternative [11] Kirk, M.T., Stevens, G.L., Erickson, M.A., and Yin, S., A Acceptance Criteria for Flaws in Ferritic Steel Components Proposal for the Maximum KIc for use in ASME Code Flaw Operating in the Upper Shelf Temperature Range, Section and Fracture Toughness Evaluations, 2011 ASME Pressure XI, Division 1, ASME Boiler and Pressure Vessel Code Vessel and Piping Conference, PVP2011-57173.
Case N-749, ASME, New York (2011). [12] Wallin, K., The Scatter in KIc Results, Engineering
[5] EricksonKirk, M.T., and EricksonKirk, M.A., Use of a Fracture Mechanics, 19(6), pp. 1085-1093, 1984.
Unified Model for the Fracture Toughness of Ferritic Steels [13] Wallin, K., The Size Effect in KIc Results, Engineering in the Transition and on the Upper Shelf in Fitness-for- Fracture Mechanics, 22, pp. 149-163, 1985.
Service Assessment and in the Design of Fracture Toughness Table 4. Equations to estimate central tendency (mean, median) fracture toughness values for ferritic steels, and their variation with temperature.
Toughness Equations Eq. # Inputs and Constants Limits Cleavage crack K Jc 30 70 exp 0.019T To To measured as per ASTM T TUS, initiation, lower shelf (4)
E1921 TUS per eq. (11) and transition (10)
K Ia 30 70 exp 0.019T TKIa Cleavage crack arrest To, as above ---
(7a)
(11) To, as above 2
J c (US ) 30 70 exp 0.019TUS To 1 2 E n, from fit to J-R curve of the form
J Ic (US ) 1.75 C1 exp C2TUSK C3TUSK ln 3.325 E 207200 57.1 T (8)
Ductile crack initiation J adj J c (US ) J Ic (US ) T > TUS, on the upper shelf = 0.3 TUS per eq. (11)
J Ic 1.75C1 exp C2TK C3TK ln 3.325 J adj C1 = 1033 MPa C2 = 0.00698/K C3 = 0.000415/K (A1)
= 0.0004/sec Notes: By performing these calculations beginning at the top and moving to the bottom of this table, all variables will be defined in the order that they are needed in later equations.
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Table 5. Equations to estimate bounding fracture toughness values for ferritic steels, and their variation with temperature.
Toughness Equations Eq. # Inputs and Constants Limits To measured as per ASTM Cleavage crack initiation, lower shelf
K Jcp K min K o 20 ln 1 p 1
4 , where (5)
E1921 p is a selected bounding T TUS, and transition Ko 31 77 exp 0.019T To value (e.g., 0.01, 0.025, TUS per eq. (11) 0.05)
(10) To as above p Mp Cleavage crack arrest K Ia 30 70 exp 0.019T TKIa (7a) 0.01 2.33 ---
(7b) 0.025 1.96 0.05 1.64 (11)
J c (US ) 30 70 exp 0.019TUS To 1 2
2 E
J Ic (US ) 1.75 C1 exp C2TUSK C3TUSK ln 3.325 (8)
J adj J c (US ) J Ic (US )
To, as above J Ic 1.75C1 exp C2TK C3TK ln 3.325 J adj n, from fit to J-R curve of J A eBT the form Ic E 207200 57.1 T where Ductile crack initiation T T 288 C = 0.3 T > TUS, A 9.03 e1.12P C1 = 1033 MPa on the upper shelf TUS per eq. (11)
C2 = 0.00698/K B MIN0,0.0009P 0.0045 C3 = 0.000415/K (9)
P MIN1, MAX 0, MIN P1 , P2 = 0.0004/sec J Ic ( 288)
P1 0.46 120 J Ic ( 288)
P2 0.51 800 (8-9) Mp as above (A1) ---
Notes: By performing these calculations beginning at the top and moving to the bottom of this table, all variables will be defined in the order that they are needed in later equations.
[14] Wallin, K., Irradiation Damage Effects on the Fracture [18] Wallin, K., Application of Master Curve to Highly Toughness Transition Curve Shape for Reactor Vessel Irradiated RPV Steels, Presentation to the LONGLIFE Steels, Int. J. Pres. Ves. & Piping, 55, pp. 61-79, 1993 Final Workshop, 15-16 January 2014, Dresden Germany,
[15] EricksonNatishan, MarjorieAnn, Establishing a Physically http://projects.tecnatom.es/webaccess/LONGLIFE/.
Based, Predictive Model for Fracture Toughness Transition [19] ASTM E1921-02, Test Method for Determination of Behavior of Ferritic Steels (MRP-53): Materials Reliability Reference Temperature, To, for Ferritic Steels in the Program (MRP), EPRI, Palo Alto, CA:2001. 1003077. Transition Range, ASTM, 2002.
[16] Kirk, M., Lott, R., Kim, C., and Server, W., Empirical [20] Wallin, K., and Rintamaa, R., Master Curve Based Validation Of The Master Curve For Irradiated And Correlation between Static Initiation Toughness KIc and Unirradiated Reactor Pressure Vessel Steels, Proceedings Crack Arrest Toughness KIa, Proceedings of the 24th MPA-of the 1998 ASME/JSME Pressure Vessel and Piping Seminar, Stuttgart, October 8 and 9, 1998.
Symposium, July 26-30, 1998, San Diego, California, USA. [21] Kirk, M. T., Natishan, M. E., and Wagenhofer, M., A
[17] IAEA TRS-429, Guidelines for application of the master Physics-Based Model for the Crack Arrest Toughness of curve approach to reactor pressure vessel integrity in nuclear Ferritic Steels, Fatigue and Fracture Mechanics, 33rd power plants, International Atomic Energy Agency, Vienna Volume, ASTM STP-1417, W. G. Reuter, and R. S. Piascik, Austria, 2005.
7
Eds., American Society for Testing and Materials, West [29] U.S. Nuclear Regulatory Commission Regulatory Guide Conshohocken, PA, 2002. 1.99 Radiation Embrittlement of Reactor Vessel Materials,
[22] EricksonKirk, Marjorie and EricksonKirk, Mark, An May1988, Upper-Shelf Fracture Toughness Master Curve for Ferritic http://pbadupws.nrc.gov/docs/ML0037/ML003740284.pdf Steels, Submitted to International Journal of Pressure [30] Nuclear Regulatory Commission Reactor Vessel Integrity Vessels and Piping, 83 (2006) 571-583 Database, Version 2.1.1, July 6, 2000.
[23] Materials Reliability Program: Implementation Strategy for [31] Charpy Embrittlement CorrelationsStatus of Combined Master Curve Reference Temperature, To (MRP-101), EPRI, Mechanistic and Statistical Bases for U.S. RPV Steels Palo Alto, CA, and U.S. Department of Energy, Washington, (MRP-45): PWR Materials Reliability Program (PWRMRP),
DC: 2004. 1009543. EPRI, Palo Alto, CA: 2001. 1000705.
[24] EricksonKirk, Marjorie and EricksonKirk, Mark, The [32] Developing an Embrittlement Trend Curve Using the Relationship between the Transition and Upper Shelf Charpy Master Curve Transition Reference Temperature, Fracture Toughness of Ferritic Steels. Fatigue Fract Engng Reliability Program (MRP-289), EPRI, Palo Alto, CA: 2011.
Mater Struct 29, 672-684 (2006). 1020703.
[25] 10 CFR 50.61, Fracture toughness requirements for [33] Kirk, Mark, A Wide-Range Embrittlement Trend Curve for protection against pressurized thermal shock events, Western Reactor Pressure Vessel Steels, Effects of http://www.nrc.gov/reading-rm/doc- Radiation on Nuclear Materials on June 15, 2011 in collections/cfr/part050/part050-0061.html. Anaheim, CA; STP 1547, Takuya Yamamoto, Guest Editor.,
[26] Application of Master Curve Fracture Toughness pp. 1-32, doi:10.1520/STP103999, ASTM International, Methodology for Ferritic Steels (PWRMRP-01): PWR West Conshohocken, PA 2012.
Materials Reliability Project (PWRMRP); EPRI, Palo Alto, [34] Kirk, M., Hein, H., Erickson, M., Server, W., and Stevens, CA: 1999. TR-108930. G., Fracture-Toughness based Transition Index
[27] Wallin, K., and Rintamaa, R., Statistical Definition of the Temperatures for use in the ASME Code with the Crack ASME Reference Curves, Proceedings of the MPA Arrest (KIa) Curve, ASME Pressure Vessel and Piping Seminar, University of Stuttgart, Germany, October 1997. Meeting 2014, PVP2014-28311.
[28] B. Houssin, R. Langer, D. Lidbury, T. Planman and K. [35] Proposed Code Case N-830 (BC 09-182), Direct Use of Wallin, "Unified reference fracture toughness design curves Master Fracture Toughness Curve for Pressure Retaining for RPV steels - Final Report", CEC-DG XI Contract B7- Materials for Vessels of a Section XI, Division 1, Class.
5200/97/000809/MAR/C2, EE/S.01.0163.Rev. B 2001.
Fracture Toughness JIc KJc KIa 100 MPam RTarrest To TKIa Temperature TUS Figure 1. Illustration of the variables used by the models in Table 1 to describe the fracture toughness of ferritic steels.
8
250 Fracture Toughness [MPa*m1/2]
200 150 100 50 RTTo = -100 C 0
250-300 -200 -100 0 100 200 300 Fracture Toughness [MPa*m1/2]
Temperature [oC]
200 150 100 250 Fracture Toughness [MPa*m1/2]
50 RTTo = 0 C 200 0
250-300 -200 -100 0 100 200 300 Fracture Toughness [MPa*m1/2]
150 Temperature [oC]
200 KIc or KJc 2.5-97.5%
data ranges 100 JIc 150 ASME KIc 50 curve 100 0
-300 -200 -100 0 100 200 300 50 Temperature [oC] RTTo = +100 C 0
-300 -200 -100 0 100 200 300 Temperature [oC]
Figure 2. Comparison of ASME KIc curve (truncated at the de facto limit of 220 MPam) to data-based models of KIc / KJc (pink) and JIc (blue). The shaded regions depict the 97.5% / 2.5% confidence bounds for the data-based models. Within the overlap of the shaded regions there is competition between cleavage and ductile fracture.
9
250 Fracture Toughness [MPa*m1/2]
200 150 100 50 RTTo = -100 C 0
250-300 -200 -100 0 100 200 300 Fracture Toughness [MPa*m1/2]
Temperature [oC]
200 150 100 250 Fracture Toughness [MPa*m1/2]
50 200 RTTo = 0 C 0
250-300 -200 -100 0 100 200 300 Fracture Toughness [MPa*m1/2]
150 KIc or KJc Temperature [oC]
2.5-97.5%
200 data ranges 100 KIa 150 ASME KIc 50 curve ASME KIa 100 curve 0
-300 -200 -100 0 100 200 300 50 Temperature [oC]
RTTo = +100 C 0
-300 -200 -100 0 100 200 300 Temperature [oC]
Figure 3. Comparison of ASME KIc and KIa curves (truncated at the de facto limit of 220 MPam) to data-based models of KIc / KJc (pink) and KIa (green). The shaded regions depict the 97.5% / 2.5% confidence bounds for the data-based models.
10
60 NUREG-1807 Houssin et al.
40 1:1 To + 19.44 C 20 RTNDT [C]
0
-20
-40
-60
-80
-140 -120 -100 -80 -60 -40 -20 0 To [C]
1.0 Cumulative Probability 0.8 0.6 0.4 0.2 0.0
-20 0 20 40 60 80 100 120 140 RTNDT - To [C]
Figure 4. Combination of data from [6] and [28] where measurements of RTNDT and To are available for the same materials to illustrate the considerable range by which RTNDT can exceed To.
11
250 Fracture Toughness [MPa*m1/2]
200 RTNDT = To RTNDT = To + 19.44 C (RTTo) 150 RTNDT = To + 47 C 100 50 RTTo = -100 C 0
250-300 -200 -100 0 100 200 300 Fracture Toughness [MPa*m1/2]
Temperature [oC]
200 150 100 250 Fracture Toughness [MPa*m1/2]
50 RTTo = 0 C 200 0
250-300 -200 -100 0 100 200 300 Fracture Toughness [MPa*m1/2]
150 Temperature [oC]
200 KIc or KJc 2.5-97.5%
data ranges 100 JIc 150 ASME KIc 50 curve 100 0
-300 -200 -100 0 100 200 300 50 Temperature [oC] RTTo = +100 C 0
-300 -200 -100 0 100 200 300 Temperature [oC]
Figure 5. Comparison of ASME KIc curve (truncated at the de facto limit of 220 MPam) to data-based models of KIc / KJc (pink) and JIc (blue). The shaded regions depict the 97.5% / 2.5% confidence bounds for the data-based models. The ASME KIc curve is shown for various temperature differentials between To and RTNDT.
12
250 Fracture Toughness [MPa*m1/2]
200 RTNDT = To RTNDT = To + 19.44 C 150 RTNDT = To + 47 C 100 50 RTTo = -100 C 0
250-300 -200 -100 0 100 200 300 Fracture Toughness [MPa*m1/2]
Temperature [oC]
200 150 100 250 Fracture Toughness [MPa*m1/2]
50 200 RTTo = 0 C 0
250-300 -200 -100 0 100 200 300 Fracture Toughness [MPa*m1/2]
150 KIc or KJc Temperature [oC]
2.5-97.5%
200 data ranges 100 KIa 150 ASME KIc 50 curve ASME KIa 100 curve 0
-300 -200 -100 0 100 200 300 50 Temperature [oC]
RTTo = +100 C 0
-300 -200 -100 0 100 200 300 Temperature [oC]
Figure 6. Comparison of ASME KIa curve (truncated at the de facto limit of 220 MPam) to data-based models of KIc / KJc (pink) and KIa (green). The shaded regions depict the 97.5% / 2.5% confidence bounds for the data-based models. The ASME KIa curve is shown for various temperature differentials between To and RTNDT.
13
1.0 Forging Cumulative Probability 0.8 Plate Weld 0.6 0.4 0.2 0.0 0 10 20 30 40 Reg. Guide 1.99 Rev. 2 Margin [C]
Figure 7. Values of RTNDT margin reported in RVID2 [30].
250 Fracture Toughness [MPa*m1/2]
KIc or KJc 200 RTNDT = To JIc (no margins) on RTNDT +20 C Margins 150 on K 2 100 on RTNDT +20 C Margins on K 2 50 RTTo = +100 C 0
250-300 -200 -100 0 100 200 300 Fracture Toughness [MPa*m1/2]
Temperature [oC]
KIc or KJc 200 KIa on RTNDT +20 C 150 Margins on K 2 RTNDT = To (no margins) 100 on RTNDT +40 C Margins on K 2 50 RTTo = -100 C 0
-300 -200 -100 0 100 200 300 Temperature [oC]
Figure 8. Comparison of ASME models (curves) with various margin terms applied to data-based models of KIc / KJc (pink), JIc (blue),
and KIa (green). The ASME models are all truncated at the de facto limit of 220 MPam. The shaded regions depict the 97.5% / 2.5% confidence bounds for the data-based models.
14
The J-R curve data in NUREG/CR-5729 exhibit a clear relationship APPENDIX: RELATIONSHIP BETWEEN J0.1 AND JIc between the ratio of J0.1/JIc and the J-R curve exponent n (see Figure A2), as follows:
Background
Nonmandatory Appendix K of the ASME Code, Assessment of Reactor Vessels with Low Upper Shelf Charpy Impact Energy (A1)
Levels, [A1] adopts an elastic-plastic fracture mechanics assessment method based on the J-R curve. Appendix K does not use JIc as a This relationship can be used to convert the JIc-based KIc limit parameter characterizing ductile crack initiation, but rather adopts the proposed by Kirk et al. [A4]:
parameter J0.1, with the subscript denoting that this is the value of J at 0.1 inches (2.5 mm) of stable ductile crack growth. JIc is determined (A2) at the onset of ductile crack growth [A2]; since the J-R curve is rapidly increasing for most reactor materials at loading levels around JIc values of JIc can exhibit considerable scatter. The ASME Code to one based on J0.1:
therefore adopted J0.1 as an engineering measure of ductile crack initiation; it generally exhibits less scatter than does JIc.
(A3)
J0.1 Model In NUREG/CR-5729 Eason et al. assembled from the literature a Figure A3 compares the limit of eqn. (A2) to that of eqn. (A3), and to considerable collection (over 500 specimens) of J-R curve data, the de facto ASME limit of 220 MPam for different values of the J-including both unirradiated and unirradiated RPV materials, welds as R curve exponent n. For high values of n and low values the RTTo well as base metal, and also nuclear grade piping materials [A3]. reference temperature the ASME limit is appropriate or conservative.
Figure A1 shows all of these data, plotted as a function of However, in view of the tendency for irradiation damage to increase temperature, where upper shelf is characterized using both JIc and RTTo and also reduce n, it seems that the continued use of a 220 J0.1. As previously reported by Kirk et al. [A4], the JIc MPam upper limit on KI be re-examined. Figure A4 provides an characterization demonstrates that in virtually every case ASMEs de illustrative example of the elevation of J0.1 above JIc for two different facto upper limit on KIc of 220 MPam is non-conservative. values of n.
Conversely, the J0.1 characterization of upper shelf shows that for many, but certainly not all, materials ASMEs de facto upper limit on KIc of 220 MPam is appropriate or conservative. 9 J = C(a)n 8 J 900 high n JIc - Unirradiated 7 800 JIc - Irradiated 6 low n J0.1 / JIc 700 600 5 a JIc [kJ/m2]
500 4 400 3 300 220 MPam 2 y0.1= e2.0141x 200 1 = 2 R2 = 0.85 R²= 0.8531 100 0
0 0 0.2 0.4 0.6 0.8 1 900 0 50 100 150 200 250 300 800 Test Temperature [oC] J0.1 - Unirradiated n 700 J0.1 - Irradiated Figure A2. Data from [ref] showing a clear relationship between the ratio J0.1/JIc (top) and the J-R curve exponent n.
J0.1 [kJ/m2]
600 500 400 300 220 MPam 200 100 0
0 50 100 150 200 250 300 Test Temperature [oC]
Figure A1. Data from [ref] plotted in terms of both JIc (top) and J0.1 (bottom). The de facto ASME limit on KIc of 220 MPam, converted to J units, is shown on each graph.
15
500 K Limit based on JIc References K Limit based on J0.1, n = 0.2 450 Limit on KIc above which Upper K Limit based on J0.1, n = 0.4 [A1] ASME Boiler and Pressure Vessel Code, Rules for 400 K Limit based on J0.1, n = 0.6 Inservice Inspection of Nuclear Power Plants,Section XI, 350 K Limit based on J0.1, n = 0.8 Limit for n = 0.5 Appendix G., Assessment of Reactor Vessels with low 300 Upper Shelf Charpy Impact Energy Levels Shelf Behavior is Expected 250 [A2] ASTM E1820, Standard Test Method for Measurement of 200 Fracture Toughness, ASTM International, West 150 Conshohocken, Pennsylvania, USA.
[A3] Eason, E.D., Wright, J.E., and Nelson, E.E., Multivariable
[MPa*m0.5]
100 Conditions in the shaded region 50 have proposed limits below the de facto limit of 220 Mpam Modeling of Pressure Vessel and Piping J-R Data, 0 NUREG/CR-5729, United States Nuclear Regulatory
-150 -50 50 150 250 Commission, 1991.
RTTo [oC] [A4] Kirk, M.T., Stevens, G.L., Erickson, M.A., and Yin, S., A Figure A3. Illustration of the effect of J-R curve exponent n on the Proposal for the Maximum KIc for use in ASME Code Flaw KIc upper shelf limit supported by upper shelf toughness as and Fracture Toughness Evaluations, 2011 ASME characterized by J0.1. The KIc limit based on JIc was proposed in Pressure Vessel and Piping Conference, PVP2011-57173.
[A4].
400 Fracture Toughness [MPa*m1/2]
Cleavage Initiation 2.5% LB Cleavage Initiation Median JIc 2.5% LB JIc Mean 300 J0.1 Mean J0.1 2.5% LB 220 200 100 n = 0.8 0
400-300 -100 100 300 Fracture Toughness [MPa*m1/2]
Cleavag e In itiation 2.5% LB Temperature Cleavag e In itiation Median [oC]
JIc 2.5% LB JIc Mean 300 J0.1 Mean J0.1 2.5% LB 220 200 100 n = 0.2 0
-300 -100 100 300 Temperature [oC]
Figure A4. Illustration of the effect of J-R curve exponent n (n=0.8 top, n=0.2 bottom) on the magnitude of upper shelf toughness characterized by J0.1 for a material having RTTo = 102 C.
16