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| number = ML15160A220
| number = ML15160A220
| issue date = 06/09/2015
| issue date = 06/09/2015
| title = NYS000520 - Kirk, M. Et Al., Assessment of Fracture Toughness Models for Ferritic Steels Used in Section Xi of the ASME Code Relative to Current Data-Based Model, PVP2014-28540, Proceedings of PVP2014, 2014 ASME Pressure Vessels and Piping  
| title = NYS000520 - Kirk, M. Et Al., Assessment of Fracture Toughness Models for Ferritic Steels Used in Section XI of the ASME Code Relative to Current Data-Based Model, PVP2014-28540, Proceedings of PVP2014, 2014 ASME Pressure Vessels and Piping
| author name =  
| author name =  
| author affiliation = State of NY, Office of the Attorney General
| author affiliation = State of NY, Office of the Attorney General
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{{#Wiki_filter:Proceedings of PVP2014 2014 ASME Pressure Vessels and Piping Division Conference July 20-24, 2014, Anaheim, CA, USA 1                                                  PVP2014-28540  
{{#Wiki_filter: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


ASSESSMENT OF FRACTURE TOUGHNESS MODELS FOR FERRITIC STEELS USED IN SECTION XI OF THE ASME CODE RELATIVE TO CURRENT DATA-BASED MODELS Mark Kirk 1 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 Gary Stevens 1 Senior Materials Engineer, Nuclear Regulatory Commission, Rockville, MD, USA, gary.stevens@nrc.gov Russell Cipolla Principal Engineer, Intertek AIM
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].
, Sunnyvale, CA, USA, russell.cipolla@intertek.com    ABSTRACT 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 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:
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.
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 22 0 irradiation effects. The separation between the KIc and KIa curves depends on the amount of irradiation embrittlement, a functionality not captured
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


by the ASME Section XI equation
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.
: s. 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.
Table 1. Summary of Data-Based Toughness Models for Ferritic Steels.
1 BACKGROUND AND OBJECTIVE A key input to assessments of the integrity of operating structures in the presence of real or postulated defects is the fracture toughness of the material in question. Various parts of the ASME Code (that is, the Code itself, various Nonmandatory Appendices, and Code Cases) provide models of the fracture toughness properties of ferritic steels
refs                          Model                                                                        Equations                                  Eq. #
; principally the KIc and KIa curves developed in the early 1970s [1]. The Code has recently been expanded to include procedures to estimate
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


RTNDT using the Master Curve index temperature To [2-3], and to estimate the temperature above which an EPFM-based analysis is needed [4]. Since the early 1970s, considerable advancements to the state of knowledge, both theoretical and practical have occurred, particularly with regard to the amount of data available and empirical models derived from these data. For example, as part of the U.S.
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.
(PTS) re-evaluation efforts, reports from which were issued in early 2010, 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 complete temperature range from the lower shelf to the upper shelf [5]. This collection of models was used by the NRC in the probabilistic fracture mechanics (PFM) Code, Fracture Analysis Vessels  Oak Ridge (FAVOR) [6], to establish the index temperature screening limits adopted in the Alternate PTS Rule 1  The views expressed herein are those of these authors and do not represent an official position of the NRC.
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]
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.
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.
2  documented in Title 10 to the U.S. Code of Federal Regulations (CFR), Part 50.61a (10CFR50.61a) [7].
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).
The objective of this paper is to compare the predictions of the toughness models within the ASME Code with the newer models that are based on considerably more data to identify areas where the ASME Code could be improved. ASME CODE TOUGHNESS MODELS The KIc and KIa curves that appear in Article A-4200 of Nonmandatory Appendix A to ASME Section XI [8] (the KIc curve also appears in Appendix G [9]), are expressed as follows (all equations in this paper are expressed in SI units):
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.
  (1)  (2)  Eqs. (1-2) are intended to represent the lower bounds of KIc and KIa data. These estimates of KIc and KIa depend on the index temperature RTNDT, which is determined per ASME NB-2331 [10]. Where appropriate, RTNDT is adjusted to account for the effects of neutron irradiation embrittlement. Neither Appendix A nor Appendix G, place an upper-limit on the KIc value that may be estimates using eqs.
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.
(1-2). Nevertheless, a valde facto limit on KIc despite scarce mention or defense of this value in the literature. The basis for this limit and an assessment of its accuracy relative to data appears in [
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:
11]. CURRENT DATA-BASED TOUGHNESS MODELS In 1984 Wallin and co-workers began publication of a series of papers that, collectively, describe what has come to b-14]. The Master Curve quantifies the temperature dependence and scatter of the fracture toughness (i.e., KJc or Jc values) of ferritic steels in the fracture mode transition temperature region.
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.
Existing work in which large databases were examined demonstrates that the temperature dependence and scatter of the Master Curve are consistent for all ferritic steels [15-16]2. All that needs to be determined for a particular material is the Master Curve index temperature (
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].
To), which positions the Master Curve on the temperature axis. Using ASTM E1921 protocols it is possible to estimate To using as few as six fracture toughness specimens [19], providing the possibility that To can be directly determined from the specimens already placed in the surveillance capsules of nuclear reactor pressure vessels. Over the past fifteen years papers have been published that expand upon and extend the Master Curve concept. These papers describe:
worst-case assessment of the conservatism of the ASME models.                 The value for each of these terms depends on several factors (e.g.,
The temperature dependence and scatter in crack arrest fracture toughness (
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].
KIa) [20]. The temperature separation of the KJc and KIa transition curves, and how this separation changes with the condition of the material [20-21]  The temperature dependence and scatter in upper shelf fracture toughness data (
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.
JIc) [22-23], and Some studies by Wallin suggest adjustments to the Master Curve lower bound value on the lower shelf [
°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.
17], and of the temperature dependence in the case of extremely high embrittlement [
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.
18]. In absolute terms the magnitude of these adjustments are minor, having only small effects on the predicted values. These adjustments could be considered as a further improvement to the models suggested herein should the cognizant ASME Code groups decide to adopt these models. The relationship between transition fracture toughness and upper shelf fracture toughness values [24
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.
]. References [
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.
4, 5, 20-24] discuss both the empirical and physical bases for these relationships, which were developed from large databases (data numbering in the hundreds) covering a wide range of material conditions (e.g., different product forms, different irradiation exposures, different material chemistries). These papers provide information demonstrating that, like the Master Curve, these relationships can be expected to apply with comparable accuracy to all ferritic steels irrespective of composition, product form, heat treatment, degree of hardening, degree of irradiation damage, etc. Significantly, all of these models are linked via a single parameter:
4
To. Once To is determined the mean initiation and arrest toughness behavior, and the scatter about the mean, can be determined from lower shelf through upper shelf using combinations of the models presented in Table 1.
Figure 1 shows the curve shapes and relationships of the se models and defines their variables visual ly. In addition to the models shown in Figure 1, Table 1 includes the equation for RTTo provided by Code Cases N-629 and N-631 (and now in the ASME Code Section XI, Appendices A and G).
RTTo provides an alternative to RTNDT such that To can be used to index the ASME KIc and KIa lower bound curves.
RTTo thereby links the data-based models of Table 1 to the ASME models for KIc and KIa. This linkage enables comparison o f the ASME lower bound descriptions of transition initiation and arrest toughness to the data-based models of initiation and arrest toughness. COMPARISON OF ASME MODELS TO CURRENT DATA-BASED MODELS The data-based models of ferritic steel toughness summarized in Table 1 can be compared with the ASME models for KIc and KIa to identify situations where the ASME models adequately reflect the data versus situations where the ASME models could potentially be improved. In the next two subsections [A and B] the comparisons made can be interpreted in two ways: (1) either as an assessment of the accuracy of the ASME models when RTTo (i.e., To) is used as an index temperature, or (2) as an assessment of the accuracy of the ASM E models when the index temperature RTNDT is used and RTNDT exceeds To -examines these analyses to assess the effect of the NDT/Charpy-based value of RTNDT being other than To, which is often the case. Finally, an assessment is made in Subsection D of the influence margin terms have on the ability of the ASME models to represent, or conservatively bound, the fracture toughness data. A. Crack Initiation  KIc and Upper Shelf Figure 2 compares the predictions of the data-based models for KIc / KJc and JIc with the ASME KIc curve augmented by the de facto upper RTTo values: -100, 0, and +100 °C (these being chosen to examine a range of hardening that could result from, as an example, neutron radiation embrittlement). These graphs support the following observations:
The ASME model over-estimates the lower shelf fracture RTTo for all values of RTTo. For un-irradiated materials such low temperatures cannot be achieved during normal operations. However, as radiation embrittlement causes the material transition temperature to approach regulatory limits (e.g., the PTS limits of 132 to 149 °C in 10CFR50.61 [25]) a temperature 60 °C below these values is clearly within the range achievable during a cool-down.
3  In the transition regime between lower shelf and upper shelf the ASME model maintains a consistent location below the data, thus providing a conservative estimate of KJc. The well recognized difference between the temperature dependence of the data and that of the ASME model is also evident in these plots. While these differences could affect the outcome of probabilistic assessments, which are more sensitive to changes in the models near the lower bound, they are not expected to adversely affect deterministic assessments performed according to ASME SC-XI Appendix A or Appendix G.
Table 1. Summary of Data-Based Toughness Models for Ferritic Steels. refs Model Equations Eq. # [2-3] RTTo Reference temperature for ASME KIc and KIa curves based on To  (3) [12-14] KJc Temperature dependence of median fracture toughness of a 1T specimen (4) Scatter at a fixed temperature
, where  (5) Size effect  where Bx is the thickness of the specimen of interest while Bo is the reference thickness (1
-in., or 25.4 mm).
(6) [20] KIa Temperature dependence of mean KIa  (7a) Scatter at a fixed temperature Log-normal with a variance () equal to 18% of the mean value.
(7b) [22-23]  JIc Temperature dependence (temperature is in Kelvin)
        = 0.3 Tref = 288C (or 561K)
C1 = 1033 MPa C2 = 0.00698/K C3 = 0.000415/K   
= 0.0004/sec (8) Scatter at a fixed temperature where                (9)  [21, 34]  Linkage of KJc and KIa data  The standard deviation of ln (
TKIa-To ) is 0.383.  (10) [24] Linkage of KJc and JIc data  (11)  The accuracy of the de facto ASME upper limit of on KIc is strongly compromised by increasing RTTo [11]. Above RTTo exceeds the upper shelf fracture toughness of most RPV steels by a considerable amount, suggesting a practical limit on KIc should be informed by the upper shelf fracture toughness.
The upper shelf of many ferritic materials falls below J0.1 is used as the characterizing parameter (see the Appendix for further discussion).
TUS, defined in Table 1, 4  can be used to define the upper limit of applicability for the KIc curve based on data [11].
3  B. Crack Arrest Figure 3 compares the predictions of the data-based models for KIc / KJc and KIa with the ASME KIc and KIa curves for three RTTo values: -100, 0, and +100 °C (these being chosen to examine a range of hardening that could result from, as an example, neutron radiation embrittlement). The data-based models show that as RTTo increases the KIc and KIa curves converge. This convergence is not a feature of the ASME models, which maintain a constant temperature separation between them. The result of using a constant temperature separation to represent the actual material behavior is that the ASME model is overly pessimistic for high values of RTTo indicative of highly irradiated material and over-estimates KIa at low values of RTTo. C. Sensitivity Study Based on the To - RTNDT Relationship As described in
[2-3], RTTo was defined as To + 19.4 °C so that the KIc curve indexed to RTTo toughn[26] as a curve bounding approximately 95% of the data, a finding also validated by Wallin [27]. The consistent placement of the reference


KIc curve enabled by the use of a true fracture toughness measure like To ensures that this degree of bounding will occur for all materials. Thus, the analysis of the previous section [B] applies to situations where RTTo is used as an index temperature, or to materials for which RTNDT exceeds To RTNDT does not always equal To +19.4 °C. Figure 4 draws together data from two sources (one being the source used to establish the epistemic uncertainty in  
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           


RTNDT for the PFM computer code FAVOR [6]) to illustrate that the degree by which RTNDT exceeds (or in one case does not)
==SUMMARY==
To varies by a considerable degree. The following values of (
RTNDT -To) were taken from these data and used to re-plot the ASME models in the format of Figure 2 and Figure 3 to assess the degree to which the ASME models represent the data for different values of RTNDT:  RTNDT = To + 0 °C:  This is an extreme case, but nonetheless possible based on these data and moreover is representative of a worst-case assessment of the conservatism of the ASME models. RTNDT = To + 47 °C:  This represents the median of the distribution of (
RTNDT -To) values shown on Figure 4. Figure 5 illustrates that the deficiencies of the ASME KIc model in representing the lower shelf and upper limit of applicability noted in the discussion of Figure 2 are not influenced by the difference between RTNDT and To. For materials where RTNDT exceeds To by less than 19.4
°C, Figure 5 illustrates that non-conservative predictions of KIc in transition can also be expected.
Figure 6 illustrates that RTNDT would need to exceed To by more than 47 °C (a value of approximately 65 °C would be needed) to ensure that the ASME KIa model provides a conservative bound to the KIa data for the range of RTTo values considered. The data in Figure 4 demonstrate that such materials make up only 25% of the population of RPV steels. Thus, the use of RTTo to index the KIa curve will provide a non-conservative representation for approximately 75% of RPV materials.
3  It should be noted that with the exception of Code Case N-749 [4] the ASME Code does not now explicitly consider the area from the upper transition region to the upper shelf. Instead the Code independently assesses cleavage fracture in the transition region using linear elastic fracture mechanics (LEFM), and on the upper shelf using elastic-plastic fracture mechanics (EPFM), in each case with appropriate margin terms. Another paper presented at this conference [34] corrects this situation by using eq. (10) to adjust RTTo so that it can be used to index the KIa curve. D. Effect of Margins Taken as a whole, the information in subsections [A], [B], and [C] leads to the conclusion that the ASME models are out of date and, in some cases, non-conservative. Especially on the lower shelf, the upper transition limit, and for all of the crack arrest transition, the ASME models fail to capture trends clearly evident in data now available.
Even the application of large margins implicit to some RTNDT values does not fully ameliorate the non-conservatisms identified here (see Figure 4). Table 2. ASME Code margin terms.
Code Ref.
Margin Values Equation Appendix G 2 for current practice 1 for risk informed IWB-3612/ Appendix A anticipated loading  faulted loading In view of these observations, the question arises as to how the ASME Code models survived for over 40 years without these inaccuracies becoming evident. The primary explanation is the margins placed on loading, flaw size, and the effects of radiation embrittlement. The deterministic method described in the ASME Code, Appendix G, uses these margins with the expectation that they account for these discrepancies between the data and the ASME models..Some of the specific margins applied are listed below:
Margin on irradiated RTNDT:  The ASME Code states that RTNDT should be adjusted to account for the effects of radiation damage. Regulatory Guide 1.99 Revision 2 suggests a margin term that accounts for uncertainty in the unirradiated value of RTNDT and in the estimated shift of this value due to irradiation damage [29]
. The value for each of these terms depends on several factors (e.g.,
product form, generic or measured values, credibility of surveillance data, etc.)
. To provide a sense of the magnitude of the margin term the range of values adopted for the various


database is provided in Figure 7 [30]. Margin on KI:  Table 2 summarizes some of the different margins applied to the value of KI in different parts of the ASME Code. Margin due to flaw size
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
:  This margin is generally coupled with the aforementioned margin on KI. For ASME Code Appendix G calculations for pressure temperature operating curves, an assumed large flaw size of 1/4-thickness of the vessel wall is used. In IWB-3611/Appendix A where a detected flaw is being evaluated, the margin on flaw size is a factor of 10 relative to the critical flaw sizeappears in Table 2. 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.
The upper graph in Figure 8 shows that a RTNDT margin of +20 °C (approximately the median from Figure 7) plus a KI margin of KIc model bounding on lower shelf and in transition for most steels. However, a larger KI margin (=2) would be needed to ensure bounding on the upper 5  shelf for high RTTo materials. It should be noted that the effectiveness of the Appendix G KI margins, which are just applied to the K arising due to pressure, are not assessed here. Since these margins apply only to a portion of K, greater values (i.e., greater than 2) would be needed to ensure bounding on the upper shelf. The lower graph in Figure 8 shows that a RTNDT margin of +40 °C (higher than any of the values in Figure 7) plus a KI margin of KIa model bounding on lower shelf and in transition for most steels.
These examples illustrate that in many, but certainly not all, cases combination of the ASME models and these margin terms results in a conservative characterization of KIc and KIa relative to data now available. Nevertheless, the degree of conservatism is by no means consistent across the range of conditions found in the operating fleet. CONCLUSIONS A. For RTNDT-based Characterizations For RTNDT-based assessments the comparisons of the ASME model predictions to the data demonstrate the necessity of maintaining the current margins on RTNDT and on KI to compensate for the inaccuracies of the ASME models. Maintenance of these margins is expected to enable the ASME models to produce conservative characterizations in most cases. However, the information presented herein demonstrates that conservatism cannot be guaranteed in all cases. Additionally, the actual margin achieved by the combination of explicit and implicit margins currently adopted by the Code varies considerably across the fleet, and instances can be found where the actual margin achieved is less than one would wish. In our view, the best remedy to ensure consistent and quantifiable margins is the adoption of a To-based assessment strategy. Such a goal has been the focus of Code Cases and various activities within the Code over the past fifteen years. The following section summarizes briefly these past efforts, and goes on to suggest a more integrated approach that could be adopted moving forward. B. For To-based Characterizations Existing Code activities address some, but not all, of the needed components of a model that is fully consistent with the data and with current-day understandings of the fracture toughness behavior of ferritic steels. These activities, which are in some cases in accord with the data and in other cases are not, are listed in Table 3. To augment these activities and bring them into closer accord with the underlying data, this paper summarizes a model of the fracture toughness behavior across the entire temperature range from lower to upper shelf. This model, which can be based on the information summarized herein, depends only on a value of To and on a selected bounding probability value, p, where (for example),
p could equal 0.05 as is typical for many engineering applications.
Table 4 summarizes the equations, inputs and constants, and limits that fully define this model for calculation of central tendency (median, mean) values while Table 5 summarizes the same information for calculation of a bounding value of fracture toughness.
These tables do not present new equations, but rather recast those previously presented in Table 1 in a compact format. The equations of Table 4 and Table 5 capture the effect of radiation embrittlement (or, equivalently, of To) on the interrelationships of KJc, KIa, JIc, and J0.1. This feature absent from existing ASME models, and its absence is responsible for many of the inaccuracies of ASME models noted herein. What remains absent from Table 4 and Table 5 are equations to predict the effects of radiation on To if this effect is not measured. Various embrittlement trend curves are available for this purpose [29, 31-33] for ASME use in replacing current toughness models the equations given in Table 5 could be expressed as a low probability (p) value (e.g., 5%), with the specific p-value perhaps tied to the loading condition as is now the practice in IWB-3612. The appropriate margins to use with this data-consistent approach, beyond the margin associated with this selection of a p-value, merits further discussion. Reconsidering the types of margins used currently: Table 3. ASME Code use of models from Table 1. ID Summary Accuracy N-629 [2] N-631 [3] App. A App. G Use RTTo to index the K Ic and KIa curves KIc: OK in transition. Need margin on lower shelf KIa: inconsistent with the data, but being fixed [34]
N-749 [4] Defines a temperature (Tc) above which EPFM analysis is needed The temperature Tc is not a function of To, which is not consistent with the data. Proposed N-830 [35] Re-defines the KIc curve as a fixed percentile of the Master Curve in transition and a constant value on lower shelf. The constant lower shelf value follows current ASME practice but is not consistent with the Master Curve bound and fracture toughness data.
Margin on To:  With the elimination of the uncertainty on the unirradiated value of RTNDT (which, as illustrated here, consumed a large part of the existing margin), less margin seems necessary. It is suggested that two factors be considered: the measurement uncertainty on To (see [19]), and the uncertainty in the embrittlement shift prediction (see [29, 31-33]). As is current practice a square root sum of squares combination of these two factors can be used. Additionally, should a direct measurement of To in the irradiated condition be made then some reduction of these margin terms would be in order.      Margin on K:  The values of KIc and KIa on the lower shelf that are exhibited by the data, and are therefore reflected by equations listed in Table 4 and Table 5, are lower than the values predicted by current ASME models. It is recognized that this presents a particular challenge within the ASME Section XI Appendix G context of setting P-T limits for normal operation because a positive head pressure on the pumps needs to be maintained. Figure 8 margin term on KI produces KIc and KIa values roughly equivalent to a 2.5th percentile curve of the equations listed in Table 5 In view of the added accuracy associated with a To-based approach the use of a bounding p-value and no additional margin on KI seems appropriate. Should this not produce a sufficiently wide P-T corridor for routine heat-up and cool-down it is suggested that the conservatism inherent to the use of a 1/4t flaw in establishing the P-T limits be revisited by the Code. SUMMARY In 1972 when ASME adopted the KIc and KIa curves and much of the current margin approach, the margins were established based mostly on engineering judgment. Now, ample data exists to build more accurate toughness models and to quantify the amount of margin needed to bound the data; this paper addresses both topics. The models summarized in this paper are based on To; they produce safety margins that are both consistent and quantifiable across the fleet, a benefit that cannot be obtained within the current correlative 6  framework based on RTNDT. Additionally, while the information presented here demonstrates the conservatism of the current RTNDTbased approach in most cases, available data shows it may be non-conservative in some situations. It is suggested that the cognizant ASME Code committees consider these models so that the Code can achieve the benefits made possible by use of current technology and data. REFERENCES  [1] Recommendations on Toughness Requirements for Ferritic August 1972. [2] American Society Of Mechanical Engineers, Use of Fracture Toughness Test Data to Establish Reference Temperature for Pressure Retaining  Materials, Section XI, Division 1, ASME Boiler and Pressure Vessel Code Case N-629, ASME, New York (1999). [3] American Society Of Mechanical Engineers, Use of Fracture Toughness Test Data to Establish Reference Temperature for Pressure Retaining Materials Other than Bolting for Class 1 Vessels, Section III, Division 1, ASME Boiler and Pressure Vessel Code: An American National Standard, Code Case N-631, ASME, New York (1999). [4] American Society Of Mechanical Engineers, Alternative Acceptance Criteria for Flaws in Ferritic Steel Components Operating in the Upper Shelf Temperature Range, Section XI, Division 1, ASME Boiler and Pressure Vessel Code Case N-749, ASME, New York (2011
).  [5] Unified Model for the Fracture Toughness of Ferritic Steels in the Transition and on the Upper Shelf in Fitness-for-Service Assessment and in the Design of Fracture Toughness Conference, PVP2006-ICPVT11-93652. [6] Williams, P., DicksonVessels  Oak Ridge FAVOR, v12.1, Computer Code: Theory and Implementation of Algorithms, Methods, and ORNL/TM-2012/567, United States Nuclear Regulatory Commission ADAMS Accession Number ML13008A014, (2012). [7]
http://www.nrc.gov/reading-rm/doc-collections/cfr/part050/part050-0061a.html
.  [8] ASME Boiler and Pressure Vessel Code, Rules for Inservice Inspection of Nuclear Power Plants, Section XI, Appendix


A [9] ASME Boiler and Pressure Vessel Code, Rules for Inservice Inspection of Nuclear Power Plants, Section XI, Appendix Failure [10] ASME NB-2331, 1998 ASME Boiler and Pressure Vessel Code, Rules for Construction of Nuclear Power Plants, Division 1, Subsection NB, Class 1 Components [11]
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.
Proposal for the Maximum KIc for use in ASME Code Flaw Vessel and Piping Conference, PVP2011-57173.  [12] WallKIc Fracture Mechanics, 19(6), pp. 1085-1093, 1984. [13] KIc Fracture Mechanics, 22, pp. 149-163, 1985.Table 4. Equations to estimate central tendency (mean, median) fracture toughness values for ferritic steels, and their variation with temperature.
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:
Toughness Equations Eq. # Inputs and Constants Limits Cleavage crack initiation, lower shelf and transition (4) To measured as per ASTM E1921 US,  TUS per eq. (11)
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).
Cleavage crack arrest (10) To, as above
[1]        PVRC Ad Hoc Group on Toughness Requirements, PVRC
--- (7a) Ductile crack initiation on the upper shelf (11) To, as above n, from fit to J-R curve of the form      = 0.3 C1 = 1033 MPa C2 = 0.00698/K C3 = 0.000415/K    
[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.
  = 0.0004/sec T > TUS,  TUS per eq. (11)
collections/cfr/part050/part050-0061a.html.
  (8)    (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.
[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.
6


Table 5. Equations to estimate bounding fracture toughness values for ferritic steels, and their variation with temperature.
Table 5. Equations to estimate bounding fracture toughness values for ferritic steels, and their variation with temperature.
Toughness Equations Eq. # Inputs and Constants Limits Cleavage crack initiation, lower shelf and transition
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
, where (5) To measured as per ASTM E1921 p is a selected bounding value (e.g., 0.01, 0.025, 0.05) US,  TUS per eq. (11)
4 , where               (5)
Cleavage crack arrest (10) To as above ---  (7a) (7b) p Mp 0.01 2.33 0.025 1.96 0.05 1.64  Ductile crack initiation on the upper shelf (11) To, as above n, from fit to J
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)
-R curve of the form     = 0.3 C1 = 1033 MPa C2 = 0.00698/K C3 = 0.000415/K    
(10)     To as above p          Mp Cleavage crack arrest          K Ia  30  70  exp 0.019T  TKIa                                (7a)             0.01       2.33           ---
  = 0.0004/sec T > TUS,  TUS per eq. (11)
(7b)              0.025       1.96 0.05       1.64 (11)
  (8)     where                (9)  (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.
J c (US )  30  70  exp 0.019TUS  To  1 2
  [14] Toughness Transition Curve Shape for Reactor Vessel Int. J. Pres. Ves. & Piping, 55, pp. 61-79, 1993 [15] Establishing a Physically Based, Predictive Model for Fracture Toughness Transition Behavior of Ferritic Steels (MRP-53): Materials Reliability Program (MRP), EPRI, Palo Alto, CA:2001. 1003077. [16] Validation Of The Master Curve For Irradiated And of the 1998 ASME/JSME Pressure Vessel and Piping Symposium, July 26-30, 1998, San Diego, California, USA. [17] IAEA TRS-curve approach to reactor pressure vessel integrity in nuclear Austria, 2005. [18] Final Workshop, 15-16 January 2014, Dresden Germany, http://projects.tecnatom.es/webaccess/LONGLIFE/. [19] ASTM E1921- Reference Temperature, To, for Ferritic Steels in the Transition Range. [20] Master Curve Based Correlation between Static Initiation Toughness KIc and Crack Arrest Toughness KIas of the 24 th MPA-Seminar, Stuttgart, October 8 and 9, 1998. [21] Kirk, M. T., Natishan, Physics-Based Model for the Crack Arrest Toughness of Fatigue and Fracture Mechanics, 33 rd Volume, ASTM STP-1417, W. G. Reuter, and R. S. Piascik, 8  Eds., American Society for Testing and Materials, West Conshohocken, PA, 2002. [22] Upper-Shelf Fracture Toughness Master Curve for Ferritic International Journal of Pressure Vessels and Piping
2 E
, 83 (2006) 571583 [23] Materials Reliability Program: Implementation Strategy for Master Curve Reference Temperature, T o (MRP-101), EPRI, Palo Alto, CA, and U.S. Department of Energy, Washington, DC: 2004. 1009543
J Ic (US )  1.75 C1  exp C2TUSK  C3TUSK  ln    3.325 (8)
. [24] Relationship between the Transition and Upper Shelf Fatigue Fract Engng Mater Struct 29, 672684 (2006). [25]
J adj  J c (US )  J Ic (US )
http://www.nrc.gov/reading-rm/doc-collections/cfr/part050/part050-0061.html
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)
.  [26] Application of Master Curve Fracture Toughness Methodology for Ferritic Steels (PWRMRP-01): PWR Materials Reliability Project (PWRMRP); EPRI, Palo Alto, CA: 1999. TR-108930. [27] Seminar, University of Stuttgart, Germany, October 1997. [28] B. Houssin, R. Langer, D. Lidbury, T. Planman and K. Wallin, "Unified reference fracture toughness design curves for RPV steels - Final Report", CEC-DG XI Contract B7-5200/97/000809/MAR/C2, EE/S.01.0163.Rev. B 200
C2 = 0.00698/K B  MIN0,0.0009P  0.0045                                        C3 = 0.000415/K (9)
: 1. [29] U.S. Nuclear Regulatory Commission Regulatory Guide 1.99 Radiation Embrittlement of Reactor Vessel Materials
P  MIN1, MAX 0, MIN P1 , P2                                    = 0.0004/sec J Ic ( 288)
, May1988, http://pbadupws.nrc.gov/docs/ML0037/ML003740284.pdf [30] Nuclear Regulatory Commission Reactor Vessel Integrity Database, Version 2.1.1, July 6, 2000. [31] Charpy Embrittlement CorrelationsStatus of Combined Mechanistic and Statistical Bases for U.S. RPV Steels (MRP-45): PWR Materials Reliability Program (PWRMRP),
P1                  0.46 120 J Ic ( 288)
EPRI, Palo Alto, CA: 2001. 1000705. [32] an Embrittlement Trend Curve Using the Reliability Program (MRP-289), EPRI, Palo Alto, CA: 2011. 1020703. [33] -Range Embrittlement Trend Curve for Radiation on Nuclear Materials on June 15, 2011 in Anaheim, CA; STP 1547, Takuya Yamamoto, Guest Editor.,
P2                  0.51 800 (8-9)     Mp as above (A1)                     ---
pp. 132, doi:10.1520/STP103999, ASTM International, West Conshohocken, PA 2012. [34] Kirk, M., Hein, H., Erickson, M., Server, W., and Stevens, Fracture-Toughness based Transition Index Temperatures for use in the ASME Code with the Crack Arrest (KIa) Curvessure Vessel and Piping Meeting 2014, PVP2014-28311. [35] Proposed Code Case N-830 (BC 09-182)
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.
, Direct Use of Master Fracture Toughness Curve for Pressure Retaining Materials for Vessels of a Section XI, Division 1, Class.
[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


Figure 1. Illustration of the variables used by the models in Table 1 to describe the fracture toughness of ferritic steels.
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,
9   Figure 2. Comparison of ASME KIc curve (truncated at the de facto lto 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.  
[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


10  Figure 3. Comparison of ASME KIc and KIa curves (truncated at the de facto 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.  
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


11  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.
250 Fracture Toughness [MPa*m1/2]
12  Figure 5. Comparison of ASME KIc curve (truncated at the de facto 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.
200 150 100 50 RTTo = -100 C 0
13  Figure 6. Comparison of ASME KIa curve (truncated at the de facto -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.
250-300      -200        -100              0          100        200        300 Fracture Toughness [MPa*m1/2]
14  Figure 7. Values of RTNDT margin reported in RVID2 [30].
Temperature            [oC]
Figure 8. Comparison of ASME models (curves
200 150 100 250 Fracture Toughness [MPa*m1/2]
) 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 97.5% / 2.5% confidence bounds for the data-based models.  
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


15  APPENDIX: RELATIONSHIP BETWEEN J0.1 AND JIc Background Nonmandatory Appendix K of the ASME Code, Reactor Vessels with Low Upper Shelf Charpy Impact Energy  [A1] adopts an elastic-plastic fracture mechanics assessment method based on the J-R curve. Appendix K does not use JIc as a parameter characterizing ductile crack initiation, but rather adopts the 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.
60 NUREG-1807 Houssin et al.
JIc is determined at the onset of ductile crack growth [A2]; since the J-R curve is rapidly increasing for most reactor materials at loading levels around
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


JIc values of JIc can exhibit considerable scatter. The ASME Code therefore adopted J0.1 as an engineering measure of ductile crack initiation; it generally exhibits less scatter than does JIc. J0.1 Model  In NUREG/CR-5729 Eason et al. assembled from the literature a considerable collection (over 500 specimens) of J-R curve data, including both unirradiated and unirradiated RPV materials, welds as well as base metal, and also nuclear grade piping materials [A3].
250 Fracture Toughness [MPa*m1/2]
Figure A1 shows all of these data, plotted as a function of temperature, where upper shelf is characterized using both JIc and J0.1. As previously reported by Kirk et al. [A4], the JIc characterization demonstrates de facto upper limit on KIc of 220 MPa-conservative. Conversely, the J0.1 characterization of upper shelf shows that for de facto upper limit on KIc    Figure A1. Data from [ref] plotted in terms of both JIc (top) and J0.1 (bottom). The de facto ASME limit on KIc to J units, is shown on each graph. The J-R curve data in NUREG/CR-5729 exhibit a clear relationship between the ratio of J0.1/JIc and the J-R curve exponent n (see Figure A2), as follows:
200 RTNDT = To RTNDT = To + 19.44 C (RTTo) 150 RTNDT = To + 47 C 100 50 RTTo = -100 C 0
  (A1)  This relationship can be used to convert the JIc-based KIc limit proposed by Kirk et al. [A4
250-300      -200        -100            0          100        200        300 Fracture Toughness [MPa*m1/2]
]:  (A2)  to one based on J0.1:  (A3)  Figure A3 compares the limit of eqn. (A2) to that o f eqn. (A3), and to the de facto J-R curve exponent
Temperature        [oC]
: n. For high values of n and low values the RTTo reference temperature the ASME limit is appropriate or conservative.
200 150 100 250 Fracture Toughness [MPa*m1/2]
However, in view of the tendency for irradiation damage to increase RTTo and also reduce n, it seems that the continued use of a 220 KI be re-examined. Figure A4 provides an illustrative example of the elevation of J0.1 above JIc for two different values of n. Figure A2. Data from [ref] showing a clear relationship between the ratio J0.1/JIc (top) and the J-R curve exponent
50 RTTo = 0 C 200 0
: n.   
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


16  Figure A3. Illustration of the effect of J-R curve exponent n on the KIc upper shelf limit supported by upper shelf toughness as characterized by J0.1. The KIc limit based on JIc was proposed in
250 Fracture Toughness [MPa*m1/2]
[A4].       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.  
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


References
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]
[A1] ASME Boiler and Pressure Vessel Code, Rules for Inservice Inspection of Nuclear Power Plants, Section XI, Assessment of Reactor Vessels with low Upper Shelf Charpy Impact Energy [A2] ASTM E1820, Standard Test Method for Measurement of Fracture Toughness, ASTM International, West Conshohocken, Pennsylvania, USA. [A3] Eason, E.D., WrightModeling of Pressure Vessel and Piping J-NUREG/CR-5729, United States Nuclear Regulatory Commission, 1991. [A4] Proposal for the Maximum KIc for use in ASME Code Flaw Pressure Vessel and Piping Conference, PVP2011-57173.}}
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}}

Latest revision as of 11:13, 5 February 2020

NYS000520 - Kirk, M. Et Al., Assessment of Fracture Toughness Models for Ferritic Steels Used in Section XI of the ASME Code Relative to Current Data-Based Model, PVP2014-28540, Proceedings of PVP2014, 2014 ASME Pressure Vessels and Piping
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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.

4

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.

6

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.

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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.

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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