technical report on the master curve. · currently, the asme kic and kir curves, indexed to the...
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NOTE
In 2002 staff from the NRC’s Office of Nuclear Regulatory Research (RES) completed this report. It was transmitted to the Office of Nuclear Reactor Regulation (NRR) at the time and reviewed by NRR staff. The technical information contained in the report was used to (a) support NRR assessments of industry submittals based on the Master Curve, and to (b) support the technical basis development for the alternative PTS rule.However, due to other matters arising of higher priority (e.g., the PTS rule, Davis Besse) this report was never finalized.
Finalization of this report in some matter is necessary to address an item identified in NRR User Need Request 2007-001. In discussion between the RES and NRR staff it was agreed to publish the report and post it into the ADAMS document management system “as is.” In doing so it is recognized that the information in this report provides an accurate and thorough assessment of the technology as it existed in 2002, however updating the report to reflect developments of the last seven years is not warranted at this time.
Mark Kirk USNRCRockville, Maryland 18th December 2009 [email protected]
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The Technical Basis for Application of the Master Curve to the Assessment of Nuclear Reactor Pressure Vessel Integrity
Manuscript Completed: October 2002
Prepared by Mark T. Kirk
Prepared for Division of Engineering Office of Nuclear Regulatory Research U.S. Nuclear Regulatory Commission Washington, DC 20555-0001
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ABSTRACT
The fracture toughness of the reactor pressure vessel (RPV) steel in a nuclear plant provides a key input to calculations that commercial licensees perform to demonstrate the fracture integrity of the vessel during both normal operations and postulated accident conditions (e.g. pressurized thermal shock, or PTS). Currently, the ASME KIc and KIR curves, indexed to the RTNDT of the material, describe the fracture toughness of the RPV and its variance with temperature. These curves were adopted in 1972 as a lower bound representation of a set of 173 linear elastic fracture toughness (KIc) values and 50 linear elastic arrest toughness (KIa) values for 11 heats of RPV steel. The use of RTNDT to normalize temperature was intended to account for the heat-to-heat differences in fracture toughness transition temperature, thereby collapsing the fracture toughness data onto a single curve. However, RTNDT is not always successful in this regard, often providing a conservative characterization of fracture toughness.
Developments since 1972 set the scene for substantial improvements to the KIc / RTNDT characterization of fracture toughness. In 1980 Landes and Schaffer noticed a weakest link size effect for specimens failing by transgranular cleavage. They demonstrated that larger specimens fail at lower toughness values. Beginning in 1984, Wallin and co-workers from VTT in Finland combined this weakest link size effect with micro-mechanical models of cleavage fracture. Wallin developed a model that accounts successfully for size effects, and provides a means to calculate statistical confidence bounds on cleavage fracture toughness data. These concepts, combined with the observation that ferritic steels exhibit a common variation of cleavage fracture toughness with temperature, gave birth to the notion of a “master” fracture toughness transition curve for all ferritic steels.
Recently Master Curve technology has been incorporated into ASTM and ASME codes and standards. In 1997 ASTM adopted standard E1921 that describes how to measure an index temperature for the Master Curve, To. To locates the Master Curve on the temperature axis for the steel of interest. E1921 incorporates a modern understanding of elastic-plastic fracture mechanics, and so permits determination of To using specimens as small as a precracked Charpy V-Notch (CVN). In 1998 ASME published Code Cases N-629 and N-631. These Code Cases permit use of a Master Curve-based index temperature (RTTo�To+35�F) as an alternative to RTNDT. Because RTTo is calculated from fracture toughness data, it consistently positions bounding KIc and KIR curves relative to fracture toughness data for all material and irradiation conditions encountered in nuclear RPV service. Such consistency cannot be achieved via the correlative RTNDT techniques used currently.
Motivation for a More Accurate Fracture Toughness Characterization
Price deregulation of the electric power industry in the United States fundamentally changes the economics of continued of nuclear power plant (NPP) operation. Before deregulation NPPs, which provide primarily baseload, were paid based on capacity. Now NPPs must compete with other energy sources, so utility executives are considering new operational scenarios, some of which were unheard of as little as five years ago: extending the licensed life of the plant beyond 40 years, removal of flux reduction, up-rating of the reactor, etc. These actions all increase the rate of embrittlement, causing current licensing limits to be approached at an earlier date. Also, the lead time needed to bring
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replacement power sources on-line push back by nearly a decade from the end of license (EOL) the date on which utilities, and consequently the NRC, must make the decisions that decide the future of a nuclear power plant (NPP). In combination, these factors suggest that the fate of nearly 30% of currently operating pressurized water reactors (PWRs) will be decided between 2005 and 2010. Consequently, both the industry and the NRC are now considering refinement of the procedures used to estimate of RTNDT at EOL with an eye to reducing known over-conservatisms while adequately protecting the public safety. Use of the Master Curve is but one of these refinements
In addition to these economic motivations for change, regulatory motivations exist as well. The perception, based on RTNDT, of a lower toughness RPV steel than actually exists can unnecessarily restrict the permissible pressure-temperature (P-T) envelope for routine heat-up and cool-down operations, and this can reduce overall plant safety. For example, an unnecessarily narrow P-T envelope increases the possibility of damaging pump seals due to insufficient cooling water pressure. Considering that pump seal failure produces a small-break loss of coolant accident (a potential pressurized thermal shock initiator), this situation is clearly undesirable. Additionally, the current perception of low RPV toughness (based on high RTNDT values) produces the need for flux suppression systems to maintain an acceptable P-T envelope. Flux suppression produces higher fuel peaking and, consequently, less margin against fuel damage if an accident were to occur. The risk to the plant and the public associated with these situations can be mitigated by replacing the conservative RTNDT-based characterization of fracture toughness with the more accurate characterization provided by the Master Curve.
The use of Master Curve-based approaches is consistent with the NRC’s goal of moving toward a risk informed framework for rule and decision-making. This framework, and the probabilistic risk assessment (PRA) methodologies that support it, require the use of best estimate values rather than bounding values whenever possible. The Master Curve provides best estimates of fracture toughness and features an explicit consideration of uncertainty. Conversely, RTNDT technology provides bounding values, suggesting that the Master Curve fits better within a risk informed framework than does RTNDT.
The Master Curve
In this document, we examine the technical basis for the Master Curve, and for its application to the assessment of nuclear RPV integrity against fracture. The discussion includes an examination of the technical basis for the Master Curve itself, and for its use in ASTM and ASME codes and standards. We also examine issues that arise when Master Curve technology is applied to assess the integrity of nuclear RPVs against fracture. We discuss recent progress concerning these issues and examine how close they are to resolution. Key findings presented in this document are summarized below.
1. Technical Basis for the Master Curve: The Master Curve includes two key features: a statistical model of cleavage fracture, and a temperature dependency of fracture toughness common to all ferritic steels. An examination of the physical reasons for why these features exist, and of the empirical evidence provided by fracture toughness data suggests that the Master Curve characterizes well the conditions for fracture of all nuclear grade RPV steels. The Master Curve characterization applies equally well to all product forms, all chemistries, all strength grades, and all irradiation conditions encountered in nuclear RPV service. In its present form, the Master Curve applies rigorously only when failure occurs under conditions of small scale yielding. However, this limitation does not restrict the application of Master Curve techniques to assess the fracture integrity of a nuclear RPV.
2. The ASTM E1921 Master Curve Testing Standard: In 1997 the American Society for Testing and Materials (ASTM) adopted standard E1921-97, “Test Method for Determination of Reference Temperature, To, for Ferritic Steels in the Transition Range.” Based on physical rationale and justified by considerable empirical evidence, the Master Curve prescribes the temperature
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dependency of toughness, the scatter of toughness at a given temperature, and the minimum observable toughness value. With all of these parameters prescribed, E1921 provides a procedure to estimate the median fracture toughness value based on very small data sets (6 specimens), a value that establishes the position of the Master Curve on the temperature axis (i.e., To). E1921 protocols produce estimates of To that are unbiased and have appropriate statistical confidence bounds, with one exception. Evidence drawn from the literature and presented herein suggests that To values determined using fatigue precracked Charpy V-notch specimens systematically underestimate To values determined using larger specimens, with the level of deformation at fracture correlating with the amount of underestimation. It is important that this information be reviewed, discussed, and resolved by ASTM committee E08 due to the interest of nuclear licensees in using precracked CVN specimens to estimate To.
3. The ASME Code Cases: ASME Code Cases N-631 and N-629 provide a methodology to establish an RTNDT-like quantity from a To value via the relationship RTTo�To+35�F. This appeal to RTNDT / KIc technology suggests that RTTo should provide an “implicit margin” (i.e. the amount of separation between the KIc curve and measured fracture toughness data) functionally equivalent to the implicit margin historically accepted for RTNDT approaches. The information presented herein suggests that this goal has been achieved. The relationship RTTo�To+35�F is defensible as it bounds a reasonable percentage of all fracture toughness data now available (97.5%) for a crack front length (2.1-in.) that exceeds the great majority of flaws found in RPV fabrication.
4. Application of the Master Curve to the Assessment of Nuclear RPVs: Procedures beyond the scope of both ASTM E1921 and ASME N-629 require further development to enable the application of Master Curve technology to the assessment of nuclear RPV integrity. These include procedures to estimate the fracture toughness for future irradiation conditions (e.g. EOL), and the use of these procedures in a probabilistic fracture mechanics (PFM) calculation to establish the level of fracture toughness needed to ensure vessel integrity during a pressurized thermal shock event. Such procedures would need to account for the following: uncertainty in To,irradiation damage effects on To, the effect of crack front length on To for semi-elliptical and buried flaws, and the effect of loading rate on To. In this report, we review recent progress in accounting for each of these factors, and suggest a process by which issues surrounding each factor can be resolved.
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CONTENTS
PageABSTRACT ................................................................................................................................................. iv CONTENTS ................................................................................................................................................ vii List of Tables ............................................................................................................................................... ix List of Figures ............................................................................................................................................... x 1 BACKGROUND AND OBJECTIVE ............................................................................................... 13 2 CURRENT PROCEDURES TO ESTIMATE THE FRACTURE TOUGHNESS OF NUCLEAR
RPV STEELS .................................................................................................................................... 15 2.1 Procedure Description ............................................................................................................. 15 2.2 Conservatism of Procedure ..................................................................................................... 16
2.2.1 Due to the LEFM Representation of Fracture Toughness ........................................... 16 2.2.2 Due to the Use of RTNDT to Normalize Temperature ................................................... 16 2.2.3 Quantification of Conservatism ................................................................................... 17
3 COMMERCIAL AND REGULATORY MOTIVATION TO UPDATE FRACTURE TOUGHNESS PROCEDURES ........................................................................................................ 193.1 Technical ................................................................................................................................. 19 3.2 Economic ................................................................................................................................. 20 3.3 Summary ................................................................................................................................. 20
4 HISTORY OF THE MASTER CURVE ........................................................................................... 22 4.1 Wallin, Sarrio and Törrönen (WST) Cleavage Fracture Model .............................................. 22 4.2 Generalizations Made Based on WST Cleavage Fracture Model ........................................... 26
4.2.1 Weibull Distribution of Fracture Toughness at a Fixed Temperature ......................... 26 4.2.1.1 Two Parameter Weibull Distribution ........................................................... 26 4.2.1.2 Three Parameter Weibull Distribution ......................................................... 27
4.2.2 Size Effects and a Weakest-Link Description of Cleavage Fracture ........................... 28 4.2.2.1 Landes and Schaffer: Early Experimental Evidence Supporting a Weakest-
Link Description of Cleavage Fracture ........................................................ 29 4.2.2.2 Relationship Between Crack Front Length and Fracture Toughness .......... 30
4.2.3 A “Master” Fracture Toughness Transition Curve for Ferritic Steels ......................... 30 4.3 Master Curve Testing Standard, ASTM E1921-97 ................................................................. 31 4.4 Master Curve Application Standard, ASME Code Cases N-629 and N-631 .......................... 33
5 TECHNICAL BASIS OF THE MASTER CURVE ......................................................................... 35 5.1 Physical Basis .......................................................................................................................... 35
5.1.1 Statistical Model .......................................................................................................... 35 5.1.2 Curve Shape ................................................................................................................. 36
5.1.2.1 Work by Natishan and Co-Workers ............................................................ 36 5.1.2.2 Work by Odette and Co-Workers ................................................................ 39 5.1.2.3 Summary ...................................................................................................... 41
5.2 Empirical Evidence ................................................................................................................. 42 5.2.1 Database ....................................................................................................................... 42 5.2.2 Statistical Model .......................................................................................................... 42
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5.2.2.1 Distribution of Fracture Toughness at a Fixed Temperature ....................... 43 5.2.2.1.1 A Fixed Shape Parameter of 4 ................................................. 43 5.2.2.1.2 Fixed Minimum Value, Kmin = 20 MPa�m ............................... 43
5.2.2.2 Effect of Specimen Size (Crack Front Length) on Fracture Toughness ...... 44 5.2.3 Temperature Dependency of Fracture Toughness ....................................................... 46
6 TECHNICAL BASIS OF THE E1921-97 TESTING STANDARD ................................................ 55 6.1 Degree of Data Replication ..................................................................................................... 55 6.2 Permissible Range of Test Temperatures ................................................................................ 55 6.3 Deformation / Constraint Limits ............................................................................................. 56
6.3.1 General ......................................................................................................................... 56 6.3.2 For PC-CVN Specimens .............................................................................................. 59
7 TECHNICAL BASIS FOR CODE CASES N-629 AND N-631 ...................................................... 61 7.1 Comparison of Margins Implicit to the RTNDT and RTTo Methodologies ................................. 62 7.2 Summary ................................................................................................................................. 63
8 APPLICATION OF THE MASTER CURVE IN PTS CALCULATIONS ..................................... 66 8.1 Plant-Specific Applications of Master Curve Technology ...................................................... 68 8.2 Progress Toward a Generic Master Curve Methodology ........................................................ 68
8.2.1 Generic Values of To and/or RTTo ................................................................................ 71 8.2.2 Estimate of Irradiation Damage Effects on To ............................................................. 73 8.2.3 The Effect of Crack Front Length on To ...................................................................... 74 8.2.4 The Effect of Loading Rate on To ................................................................................ 75
9 SUMMARY ...................................................................................................................................... 78 10 REFERENCES .................................................................................................................................. 79 Appendix A – Description of Empirical Database ...................................................................................... 88 Appendix B - Multi-Temperature Approach for To Determination ............................................................ 90 Appendix C – Assessment of Master Curve Goodness of Fit to Individual Datasets ................................. 91 Appendix D – Data Sets that do not Statistically Match the Master Curve Temperature Dependence ...... 92
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LIST OF TABLES
PageTable 4.1. Input variables used by WST in their prediction of the transition fracture toughness curve for
HSST Plate 02. .......................................................................................................................... 25 Table 5.1. Summary of data sets used to assess ¼-power exponent on thickness in Eq. 5-11. ................. 45 Table 5.2. Summary of data sets that deviate from Master Curve assumed temperature dependency (see
Appendix D for plots). .............................................................................................................. 53 Table 5.3. Summary of experimental assessment of Master Curve temperature dependence. .................. 54 Table 6.1. Replication requirements and estimated standard deviation for To from E1921-97. ................ 55 Table 6.2. M Coefficients determined by Dodds and co-workers .............................................................. 57 Table 6.3. Data sets used in the analysis of the potential bias in To values estimated from KJc tests
performed on precracked CVN specimens. .............................................................................. 60 Table 7.1. Data sets used in to assess the margin implicit to use of RTNDT as an index temperature for
fracture toughness data. ............................................................................................................. 64 Table 8.1. Codes, Standards, and Regulations that Govern the Assessment of Fracture Toughness for Use
in a PTS Analysis. ..................................................................................................................... 67 Table 8.2. Generic RTTo values for different classes of nuclear RPV materials ........................................ 73
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LIST OF FIGURES
PageFigure 1.1. Illustration of the inconsistency with which RTNDT positions the KIc curve relative to measured
fracture toughness data. ........................................................................................................... 14 Figure 2.1. Comparison of original KIc data (top) and the original crack arrest (KIa) data (bottom) to the
bounding KIR curve [Marston 87]. ........................................................................................ 16 Figure 2.2. Placement of LEFM (ASTM E399) valid data relative to the overall population of
cleavage fracture toughness data for nuclear RPV steels. All values are plotted as-measured, and are normalized relative to an ASME NB-2331 value of RTNDT. ............................................................... 18
Figure 2.3. Procedure for defining the conservatism inherent to a KIc curve located based on RTNDTrelative to measured KIc data for the same steel [Bass 00]. The RTNDT-located KIc curve is translated toward the dataset until it intersects the first KIc value in transition. The amount of translation defines �RTLB. .................................................................................................................................... 18
Figure 2.4. Conservatism inherent to a KIc curve located based on RTNDT quantified by applying the procedure illustrated in Figure 2.3 [Bass 00] to a set of LEFM valid data assembled by the Oak Ridge National Laboratory (ORNL) [Bowman 00]. .......................................................................... 18
Figure 3.1. Licensing status of commercial power reactors in the United States [NRC RVID] relative to the current PTS screening criteria. ..................................................................................................... 19
Figure 3.2. Variation of �RTTo with fluence, and comparison with Reg. Guide 1.99 Rev. 2 fluence function developed to describe trends in Charpy V-Notch data [Kirk 99]. ........................................ 20
Figure 3.3. Distribution of differences between RTNDT and RTTo for a variety of un-irradiated domestic RPV steels. ......................................................................................................................................... 21
Figure 4.1. Relationship between the crack-tip stress field and applied-K values used in the original WST model [Wallin 84a]. .................................................................................................................. 24
Figure 4.2. Distribution of carbide sizes used in the original WST model [Wallin 84a]. ........................ 24 Figure 4.3. The prediction of the original WST model compared with experimental fracture toughness
data for HSST Plate 02 [Wallin 84b]. ................................................................................................ 24 Figure 4.4. Empirical basis for a Kmin value of 20 MPa�m [Wallin 84c]. ............................................... 28 Figure 4.5. The prediction of a three parameter Weibull model compared with experimental fracture
toughness data for HSST Plate 02 [Wallin 84b]. ............................................................................... 28 Figure 4.6. Fracture toughness data reported by Landes and Schaffer that show a weakest-link size
effect [Landes 80]. .............................................................................................................................. 29 Figure 4.7. Incorrect transition fracture toughness behavior predicted using a constant value for �s+wp=9
[Wallin 84a]. ...................................................................................................................................... 31 Figure 4.8. Data used to establish the temperature dependence of the Master Curve [Wallin 93a]. ....... 31 Figure 4.9. Illustration of the process used by E1921-97 to establish the Master Curve index
temperature, To. .................................................................................................................................. 32 Figure 4.10. A comparison of RTNDT and the To (here called T100) values unirradiated RPV steels
[Sokolov 98]. ...................................................................................................................................... 34 Figure 5.1. Demonstration that materials having a temperature dependence of the flow stress
characteristic of a BCC lattice also have fracture toughness data that matches the Master Curve while non-BCC materials do not [Kirk 00b]. ..................................................................................... 40
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Figure 5.2. Prediction of transition curve shapes using and RKR-type model with a constant cleavage fracture stress [Odette 00]. ................................................................................................................. 41
Figure 5.3. Prediction of transition curve shapes using and RKR-type model with a non-constant cleavage fracture stress [Odette 00]. .................................................................................................. 42
Figure 5.4. Comparison of the room temperature (engineering) tensile properties of the various steels in the fracture toughness database. ......................................................................................................... 42
Figure 5.5. Comparison of Weibull slopes calculated from fracture toughness data with 5%/95% confidence bounds on the expected slope of 4. .................................................................................. 44
Figure 5.6. Comparison maximum likelihood estimates of Kmin with the customary value of 20 MPa�m. ............................................................................................................................................................ 44
Figure 5.7. Comparison of fracture toughness data with the ¼-power trend on thickness assumed by Master Curve technology. .................................................................................................................. 46
Figure 5.8. Comparison of the range of specimen sizes tested by Rathbun with those characteristic of the remainder of the database. .................................................................................................................. 47
Figure 5.9. Effect of ligament dimension with specimen thickness held constant for an A533B Cl. 1 plate (ex-Shoreham) [Rathbun 00]. ............................................................................................................. 47
Figure 5.10. Effect of specimen thickness on lower shelf fracture toughness. .......................................... 47 Figure 5.11. Procedure for evaluating Master Curve shape relative to fracture toughness data.. .............. 49 Figure 5.12. Effect of eliminating invalid data on KJC residual plot.. ........................................................ 50 Figure 5.13. Deviation of KJC data from the Master Curve for an un-irradiated RPV steel tested at quasi-
static loading rates [Joyce 00, Rathbun 00]. ....................................................................................... 50 Figure 5.14. Deviation of KJC data from the Master Curve for an irradiated RPV steel tested at quasi-
static loading rates [Nanstad 96]. ....................................................................................................... 51 Figure 5.15. Deviation of KJC data from the Master Curve for a non-RPV steel tested at quasi-static
loading rates [Sorem 89]. ................................................................................................................... 51 Figure 5.16. Deviation of KJC data from the Master Curve for an un-irradiated RPV steel tested at a high
loading rate [Ishino 88] . .................................................................................................................... 52 Figure 5.17. Deviation of KJC data from the Master Curve for a non-RPV steel tested at elevated loading
rates [Joyce 97]. ................................................................................................................................. 52 Figure 6.1. Comparison of uncertainty in To estimates determined by Monte Carlo simulation (points)
with the recommendation of E1921-97 (curves). ............................................................................... 56Figure 6.2. Effect of test temperature on the bias of an E1921-97 estimate of To relative to a multi-
temperature (MT) estimate of To. MT To estimates must have at least three times as many KJC values as E1921 To estimates. ........................................................................................................................ 57
Figure 6.3. Comparison of fracture toughness data with the M=30 deformation limit of E1921. ............. 58 Figure 6.4. Variation of To bias with deformation level (quantified as ) for To values determined from
precracked CVN specimens. Error bars shown are 95% confidence bounds on the To difference between precracked CVN specimens larger specimens. The line labeled “prediction” is determined based on finite element analysis of a precracked CVN specimen with n=10, �ys = 60ksi [Ruggeri 98] ............................................................................................................................................................ 59
Figure 7.1. Illustration of how the difference between RTNDT and To quantifies the separation between a RTNDT indexed KIc curve (solid curve) and the fracture toughness data it is intended to represent (5%-95% confidence bounds). The influence of crack front length on this separation is also illustrated 63
Figure 7.2. The range of margins (defined as RTNDT – the 100 MPa�m fracture toughness transition temperature To) implicit to current practice. The different horizontal axes correspond to the crack front length indicated (in inches)........................................................................................................ 64
Figure 7.3. The size of fracture toughness specimens tested in the original KIc dataset [Marston 87]. ..... 65 Figure 7.4. Comparison of a KIc curve (positioned based on RTTo) with as-measured fracture toughness
values for irradiated RPV steels [EPRI 98]. ....................................................................................... 65 Figure 8.1. Root cause diagram illustrating the methodology used currently to estimate the fracture
toughness of a reactor pressure vessel steel after irradiation [Li 00]. ................................................ 72
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Figure 8.2. Use of fracture toughness data for A533B Cl. 1 (left) and for Linde 80 (right) to establish generic values of RTTo. ....................................................................................................................... 73
Figure 8.3 Comparison of irradiation induced CVN and To shifts for nuclear RPV welds and base materials [Sokolov 96]. ...................................................................................................................... 74
Figure 8.4. Comparison of data for part through surface cracks to a 1T equivalent Master Curve [Joyce 97, Porr 95]. ........................................................................................................................................ 75
Figure 8.5. Separation between the KIc and KIR curves [Yoon 99]. ........................................................... 77 Figure 8.6. Crack arrest Master Curve proposed by Wallin [Wallin 98b]. . ............................................. 77 Figure 8.7. Illustration of the largest shift between a static initiation toughness curve (Master Curve) and
a crack arrest toughness curve that will be bounded by a KIR curve located using RTTo. ................... 77 Figure 8.8. The shift in transition temperature between a static initiation toughness curve (Master Curve)
and a crack arrest toughness curve [Wallin 98b]................................................................................ 77
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1 BACKGROUND AND OBJECTIVE
The fracture toughness of steels used to fabricate nuclear reactor pressure vessels (RPV) provide a key input to calculations that commercial licensees perform to demonstrate the fracture integrity of the RPV during both normal operations and postulated accidents. These calculations include the following:
� 10CFR50.61: Resistance of the RPV to fracture during postulated pressurized thermal shock events [10CFR50.61].
� ASME Section XI Appendix G: Resistance of the RPV to fracture during the heat-up and cool-down cycles that occur during normal operations [10CFR50 APPG, ASME XI-G].
� ASME Section XI (IWB-3500, IWB-3600):Resistance of the RPV to fracture from a specific flaw detected during in-service inspection.
In each of these calculations, the ASME KIc or KIR curve, indexed to the RTNDT of the material, is used currently to describe the fracture toughness of the RPV, and how fracture toughness varies with temperature. The KIc and KIR curves were adopted in 1972 as lower bound curves to a set of 173 valid linear elastic fracture toughness (KIc) data for 11 heats of RPV steel [WRC 175, Marston 78]. The use of RTNDT to normalize temperature was intended to account for the heat-to-heat differences in the fracture toughness transition temperature, thereby collapsing all of the fracture toughness data onto a single curve [ASME NB2331]. This description of fracture toughness must beconservative relative to actual fracture toughness data for two reasons. First, the KIc curve was established using only fracture toughness data deemed to be “valid” by linear elastic fracture mechanics (LEFM) criteria [ASTM E399]. Consequently, only the lower range of cleavage
fracture toughness values were used to position of the KIc curve. Second, the ASME NB-2331 definition of RTNDT ensures that reported values upper-bound the range of RTNDT values possible for the material tested [ASME NB2331]. However, the degree of conservatism provided by the KIc / RTNDT description of fracture toughness is inconsistent from material to material. The transition temperature indices used to determine RTNDT (i.e. Charpy V-Notch (CVN) and nil-ductility (NDT) transition temperatures) only correlate with the fracture toughness. CVN and NDT transition temperatures do not and cannot establish the fracture toughness transition temperature for the simple reason that CVN and NDT do not measure fracture toughness. These characteristics of RTNDT result in inconsistent placement of the KIc curve relative to fracture toughness data, as illustrated in Figure 1.1. This inconsistency has motivated research aimed at the development of more direct methods to quantify the fracture toughness transition temperature.
Developments since 1972 set the scene for substantial improvements to the KIc / RTNDTcharacterization of fracture toughness. In 1980 Landes and Schaffer noticed a statistical “size” effect for specimens failing by transgranular cleavage [Landes 80]. They demonstrated that large specimens fail at lower toughness values than small specimens. Beginning in 1984, Wallin and co-workers from VTT in Finland [Wallin ALL] combined this “weakest link” size effect with micro-mechanical models of cleavage fracture proposed by Curry, Knott, Smith, Ritchie, Rice and others [Smith 66, Knott 66, Smith 68, Ritchie 73, Curry 76, Curry 78, Curry 79]. Wallin developed a model that accounts successfully for these size effects [Wallin 84d], and provides a means to calculate
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statistical confidence bounds on cleavage fracture toughness data [Wallin 84c]. These concepts combined with the observation, made first in 1984 and reinforced in 1991 [Wallin 84a, Wallin 93a], that all ferritic steels exhibit a common variation of cleavage fracture toughness with temperature gave birth to the notion of a “master” transition curve for all ferritic steels. ASTM recently adopted a standard (E1921-97) that describes how to measure the Master Curve index temperature, To, based on limited replicate testing [ASTM E1921]. E1921-97 incorporates a modern understanding of elastic-plastic fracture mechanics [EPFM], and so permits determination of To using specimens as small as a precracked CVN provided limits on the deformation preceding fracture are satisfied. The potential for characterizing transition region fracture toughness using specimens already in surveillance programs has sparked considerable interest within the commercial nuclear power community. Potential uses of the Master Curve include the opening of operating windows for plant heat-up and cool-down, and providing part of the technical justification to demonstrate RPV integrity through extended (60 year) licensing periods. This interest led to publication of ASME Code Cases N-629 and N-631 in 1998
[ASME N629, ASME N631]. These Code Cases permit use of a Master Curve-based index temperature (RTTo�To+35�F) as an alternative to RTNDT. This development represents a necessary first step toward application of Master Curve technology to the assessment of RPV integrity.
In this document, we examine the technical basis for the Master Curve, and for its application to the assessment of nuclear RPV integrity against fracture. To provide a background for this discussion, we begin with by examining the current methods for estimating the fracture toughness of RPV steel (Section 2), the industrial and regulatory motivation to improve these methods (Section 3), and the historical development of Master Curve technology (Section 4). We then examine the technical basis for the Master Curve itself (Section 5), and also discuss the technical basis for existing Master Curve testing and application standards, E1921-97 (Section 6) and N-629 (Section 7), respectively. The report concludes (Section 8) with an examination of issues that arise when Master Curve technology is applied to assess the integrity of nuclear RPVs against fracture. We discuss recent progress concerning these issues and examine how close they are to resolution.
Midland Beltline WeldUNIRRADIATED[McCabe, 1994]
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HSST Plate 02[Marston, 1987]
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Midland Beltline WeldUNIRRADIATED[McCabe, 1994]
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Figure 1.1. Illustration of the inconsistency with which RTNDT positions the KIc curve relative to measured fracture toughness data.
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2 CURRENT PROCEDURES TO ESTIMATE THE FRACTURE TOUGHNESS OF NUCLEAR RPV STEELS
2.1 Procedure Description
In all calculations performed to assess the integrity of a nuclear RPV against fracture, an estimate of the fracture toughness of the vessel after neutron embrittlement is needed. Practical limitations regarding the volume of material that can be irradiated as part of a surveillance program restrict both the quantity and size of the material samples used to obtain this estimate.Currently the fracture toughness of RPV steel is estimated by the following procedure:
� The transition temperature of the material before irradiation (RTNDT(u)) is determined using either ASME NB-2331 procedures [ASME NB2331], or alternative procedures intended to be conservative to NB-2331 [NRC MTEB5.2].
� RTNDT(u) is shifted to account for the effects of neutron irradiation. The shift added is increase in the CVN 30 ft-lb transition temperature (�T30) produced by irradiation. �T30 may be either based on shift measurements (from a ASTM E185 qualified surveillance program) or on shifts calculated from chemical composition using an embrittlement trend curve [NRC RG199R2].
� Margins are added to account for uncertainties in the state of knowledge of the material, and for uncertainties in the calculational process [NRC RG199R2, Randall 87].
� The estimated transition temperature of the vessel after some amount of irradiation (now RTNDT(u) + �T30 + Margin) is used as an index temperature for the ASME KIcand/or KIR curves, thus establishing the lower bound above which the actual
fracture toughness of the material is expected to lie.
It should be noted that nowhere in this process is the fracture toughness of the material actually measured, rather it is inferred through a series of correlations. The components of this procedure began to be established as early as 1972, and the procedure was solidified in concept as early as 1977 (NRC RG199R1). Two state-of-knowledge limitations that existed in this timeframe necessitated adoption of a correlative approach:
� Linear Elastic Characterization of Fracture Behavior: Between 1972 and 1977, the only mathematical description of fracture behavior sufficiently well developed for ASME codification was one premised on a linear elastic characterization of material constitutive behavior. At temperatures in fracture mode transition, large fracture toughness specimens (minimum lineal dimension of 2-in.) of nuclear RPV steels need to be tested to meet the validity requirements of a linear elastic fracture theory [ASTM E399]. It is not practical to use specimens of this size as part of a surveillance program.
� Need to Determine the Entire Transition Curve: Calculations of the fracture integrity of a nuclear RPV require as input the complete variation of toughness with temperature through transition, not just the toughness at a fixed temperature. Between 1972 and 1977 there was no procedure available from which such a comprehensive description of transition fracture toughness behavior could be inferred based on tests of a limited number of specimens.
16
While approximate, the KIc / RTNDT procedure is believed to be, and indeed must be, conservative (i.e. always underestimate the measured fracture toughness of the material in question) due to factors discussed further in the following section.
2.2 Conservatism of Procedure
2.2.1 Due to the LEFM Representation of Fracture Toughness
In 1972, ASME adopted the KIc and KIR curves to describe the variation with temperature of the static and dynamic/arrest (respectively) fracture toughness of nuclear RPV steels [WRC 175, Marston 87]. These curves were hand-drawn as lower bounds to a set of fracture toughness data valid according to the requirements of ASTM E399 [ASTM E399]. Figure 2.1 illustrates the original datasets, and the KIc and KIR curves.
ASTM E399 restricts on the size of the plastic zone at fracture relative to the overall size of the specimen to ensure that a linear elastic description of material flow behavior is not violated significantly. The E399 size requirement is as follows:
Eq. 2-1 Error! Objects cannot be created from editing field codes.
where a is the crack length, b is the length of the uncracked ligament, B is the specimen thickness, Kq is the stress intensity factor at fracture, and �yis the yield strength at the test temperature. Considering that the diameter of the plastic zone ahead of a deforming crack in a thick structure can be expressed as follows:
Eq. 2-2 2
31
�
�
�
��
y
Iplastic
Kd
��
one concludes that E399 requires that the smallest specimen dimension (a, b, or B) must exceed the size of the plastic zone by a factor of approximately 25 (=2.5�3��). This restriction admits only the lowest part of the population of cleavage fracture toughness values to further
analysis, as illustrated in Figure 2.3. Since the KIc and KIR curves are based on these low fracture toughness values, the requirement for LEFM validity forces establishment of a low bounding curve.
Figure 2.1. Comparison of original KIc data (top) and the original crack arrest (KIa) data (bottom) to the bounding KIR curve [Marston 87].
2.2.2 Due to the Use of RTNDT to Normalize Temperature
17
When using fracture toughness data to establish the bounding KIc and KIR curves, the fracture toughness values were not plotted vs.temperature, but rather vs. the difference between the test temperature and an index temperature called RTNDT [WRC 175, Marston 78]. RTNDT is determined from Charpy V-Notch (CVN) and nil-ductility temperature (NDT) data as per ASME NB-2331, as follows:
Eq. 2-3 � �60, 50/35 �� TTMAXRT NDTNDT (in �F)
where TNDT is the nil-ductility temperature determined by testing NDT specimens as per ASTM E208, and T35,50 is the transition temperature at which Charpy-V notch (CVN) specimens tested as per ASTM E23 exhibit at least 35 mills lateral expansion and 50 ft-lbs absorbed energy. RTNDT is intended to account for the heat-to-heat differences in fracture toughness transition temperature, and thereby collapse all of the transition toughness curves for specific heats of steel onto a single curve [ASME NB2331, ASTM E208, ASTM E23]. This procedure of using RTNDT to normalize temperature conservatively places the KIc curve relative to measured fracture toughness data for the following reasons:
1. The NB-2331 Procedure for Determining RTNDT: This procedure requires first that TNDT be established, and that three CVN tests be conducted at 60�F above TNDT to demonstrate that the minimum CVN energy exceeds 50 ft-lbs, and that the minimum lateral expansion exceeds 0.035-in. NB-2331 does not require the user to either bracket the NDT temperature (i.e. achieve both break and no-break results), nor does it require determination of the temperature at which the 50 ft-lbs / 35 mil criteria is just exceeded. Consequently, the NB-2331 procedure forces reported values of RTNDTtoward the upper end of all RTNDT values for a particular heat of steel.
2. The Procedure by which the Relationship Between the ASME KIc curve and RTNDTwas Established: In the early 1970’s an ASME task group established the following
relationship between RTNDT and the KIccurve:
Eq.2-4 Error! Objects cannot be created from editing field codes.(K in ksi�in, T in �F)
This equation (a hand-drawn curve at the time) was constructed in 1972 such that no existing measured KIc value in transition (i.e. at T-RTNDT > 100�F) fell below the KIccurve†. This empirical approach to developing a transition toughness curve was needed because at the time no theoretical basis existed to account for the differences in loading, loading rate, crack geometry, and specimen thickness between NDT and CVN tests and the conditions of interest in nuclear RPV service (i.e. a sharp crack in a thick structure).
The substantial collection of fracture toughness data available today (Figure 2.2) testifies to the bounding characteristics achieved through the use of the ASME NB-2331 definition of RTNDTalong with the ASME KIc curve‡. It is important to recognize that the combined effects of these two factors produce a bounding curve. Neither the ASME NB 2331 definition of RTNDT nor the ASME KIc equation acting individually ensures bounding.
2.2.3 Quantification of Conservatism
Because the index temperature RTNDT is determined with complete independence from the fracture toughness data it represents there is no guarantee that a KIc curve positioned with respect to RTNDT will always under-estimate KIcdata by the same amount. In fact, quite the
† The ASME committee did not enforce this bounding requirement on the lower shelf, as evidenced by the considerable number of KIc values that fall below the 33.2 ksi�in asymptote in Fig. 2(a).
‡ Only one KIc value falls below the KIc curve in transition. A KIc value of 98¼ ksi�in measured using a 6T C(T) of HSST Weld 72W falls 0.9 ksi�in below the ASME KIc curve at T-RTNDT = +59.4�F.
18
contrary is true, as illustrated previously in Figure 1.1. Recently, Bass et al. [Bass 00] quantified the range of possible conservatism inherent to a KIc curve positioned using RTNDT by the procedure illustrated in Figure 2.3. Figure 2.4 shows the results of this analysis, which demonstrate that a definition of the transition
temperature that consistently positions a bounding curve relative to fracture toughness data can fall below RTNDT by up to 200�F,illustrating the conservatism inherent to the RTNDT process.
0
100
200
300
400
-400 -300 -200 -100 0 100
T-RT NDT [oF]
KJc
[ks
i*in0.
5 ]
Cleavage (Invalid) EPFM (E1921 Valid) LEFM (E399 Valid) ASME KIC Curve
Figure 2.2. Placement of LEFM (ASTM E399) valid data relative to the overall population of cleavage fracture toughness data for nuclear RPV steels. All values are plotted as-measured, and are normalized relative to an ASME NB-2331 value of RTNDT.
0
50
100
150
200
-250 -150 -50 50 150
T-RT NDT [oF]
KIC
[ks
i*in0.
5 ]
KIC Data Shifted 68F Indexed to RTNDT
�RTLB = +68oF
0
50
100
150
200
-250 -150 -50 50 150
T-RT NDT [oF]
KIC
[ks
i*in0.
5 ]
KIC Data Shifted 68F Indexed to RTNDT
�RTLB = +68oF
Figure 2.3. Procedure for defining the conservatism inherent to a KIc curve located based on RTNDT relative to measured KIc data for the same steel [Bass 00]. The RTNDT-located KIc curve is translated toward the dataset until it intersects the first KIc value in transition. The amount of translation defines �RTLB.
0%
20%
40%
60%
80%
100%
-50 0 50 100 150 200
�RTLB [oF]
Cum
ulat
ive
Prob
abili
ty
Data5%P95%
Figure 2.4. Conservatism inherent to a KIccurve located based on RTNDT quantified by applying the procedure illustrated in Figure 2.3 [Bass 00] to a set of LEFM valid data assembled by the Oak Ridge National Laboratory (ORNL) [Bowman 00].
19
3 COMMERCIAL AND REGULATORY MOTIVATION TO UPDATE FRACTURE TOUGHNESS PROCEDURES
In the United States, the Nuclear Regulatory Commission (NRC) licenses utilities to operate nuclear reactors for a 40-year term. During this time, the fracture toughness of pressurized water reactors (PWRs) must be adequate to maintain vessel integrity during postulated pressurized thermal shock (PTS) events. The United States Code of Federal Regulations Part 10§50.61 expresses the current procedures used to assess the fracture integrity of a nuclear RPV during a PTS event. This assessment is performed by estimating the fracture toughness transition temperature following irradiation to end of license (EOL) conditions of the materials in the RPV beltline region. This estimate is expressed as a value of RTNDT at the clad-to-base metal interface at EOL adjusted for the effects of neutron irradiation and uncertainty. A comparison of this transition temperature to a screening criterion of 300�F for circumferential welds and of 270�F for longitudinal welds, plates, and forgings [10CFR5061, SECY82465] establishes the suitability of the RPV for continued operation through EOL.
Figure 3.1 shows that the current licensing values of RTPTS [NRC RVID] are generally lower for newer plants, a trend that reflects the lessons learned regarding material effects on irradiation sensitivity during the initial years of commercial RPV construction. While no RTPTS
values currently exceed the 300�F / 270�Fscreening limits, the values for several plants lie close to these limits. Both technical and economic factors make being “close” to the screening limit an untenable position for a commercial utility.
3.1 Technical
o Estimates of RTPTS are sensitive to their input values. Small changes to an input value can dramatically alter the estimate of RTPTS, moving it from just under to just over the screening limit.
o Formulas used to estimate of RTPTS can be revised to reflect additional data and/or a better understanding of an underlying physical process. For example, the NRC is currently engaged in an effort to revise the equation used to predict the increase in Charpy transition temperature due to irradiation [Eason 87]. Such revisions cannot be expected to result in systematically lower values of RTPTS for all plants.
0
20
40
60
80
2000 2010 2020 2030 2040
Year
Num
ber o
f PW
Rea
ctor
s
0
50
100
150
200
250
300
AR
T at
EO
L [o F]
License Expires Limit = 270F Limit = 300F
RT P
TS[o
F]
0
20
40
60
80
2000 2010 2020 2030 2040
Year
Num
ber o
f PW
Rea
ctor
s
0
50
100
150
200
250
300
AR
T at
EO
L [o F]
License Expires Limit = 270F Limit = 300F
RT P
TS[o
F]
Figure 3.1. Licensing status of commercial power reactors in the United States [NRC RVID] relative to the current PTS screening criteria.
20
3.2 Economic
o Deregulation of the United States electric power industry fundamentally changes the economic factors that govern the continued operation of nuclear power plants (NPPs). Before deregulation NPPs, which provide primarily baseload, were paid based on capacity. Now NPPs must be cost competitive with other energy sources, so utility executives are considering new operational scenarios, such as extending the licensed life of the plant beyond 40 years, removal of flux reduction, and up-rating of the reactor. Some of these scenarios were unheard of as little as five years ago. These actions all increase the amount of embrittlement that the RPV will experience over the operating life of the plant, causing 10CFR50.61 screening limits to be approached at an earlier date.
� As NPPs approach the end of their 40-year operating licenses utilities must consider options for replacement power sources. These sources can include gas turbines, coal, or license renewal of the NPP for an additional 20 years. All of these options require between four and eight years of lead time to address adequately all engineering, procurement, and regulatory considerations. These factors push back by nearly a decade from EOL the date on which utilities, and consequently the NRC, must make the decisions that decide the future of a NPP.
3.3 Summary
In summary, both technical and economic factors point toward the possible increase of licensing values of RTPTS in the coming years. Additionally, the lead-time needed to plan for replacement power suggests that the fate of nearly 30% of currently operating PWRs will be decided between 2005 and 2010 (see Figure 3.1), with many of these being early construction plants having high copper content welds and, therefore, high RTPTS values. These factors are forcing both the industry and the NRC to
consider refinement of the procedures used to estimate of RTNDT at EOL with an eye to reducing known over-conservatisms while adequately protecting the public safety.
One potential refinement to this procedure is the use of Master Curve technology to assess the state of RPV embrittlement by direct measurement of fracture toughness rather than through the use of currently accepted correlative approaches. Empirical evidence suggests that the effects of irradiation on both CVN and fracture toughness are similar [Kirk 98, Sokolov 96]; Figure 3.2 summarizes some of these results. Consequently, the potential change in the estimate of RTNDT at EOL can be estimated, to the first order, as the simple difference between RTNDT (estimated as per NB-2331) and RTTo (estimated as per Code Case N-629) for a RPV material in the unirradiated condition. A comparison of these values (Figure 3.3) suggests that Master Curve technology could provide a basis for reducing the estimated RTNDT at EOL for approximately three out of every four operating PWRs, and that the average reduction for a particular plant would be on the order of 50�F.
All �RTTo ValuesNormalized to CF = 100oF
0
50
100
150
200
0 1 2 3 4 5 6
Fluence (x 1x1019) [n/cm2]
�R
TTo
* 10
0 / C
F[o F]
80 weld 0091 weld 0124 weld Plate CF = 100F
A
Fluence (/ 1x1019) [n/cm2]
Figure 3.2. Variation of �RTTo with fluence, and comparison with Reg. Guide 1.99 Rev. 2 fluence function developed to describe trends in Charpy V-Notch data [Kirk 99].
21
0%
20%
40%
60%
80%
100%
-100 -50 0 50 100 150
RTNDT - RTTo [oF]
Cum
ulat
ive
Prob
abili
ty Forging Plate Weld
Figure 3.3. Distribution of differences between RTNDT and RTTo for a variety of un-irradiated domestic RPV steels.
In addition to these economic motivations for change, regulatory motivations exist as well. The perception, based on RTNDT, of a lower toughness RPV steel than actually exists can unnecessarily restrict the permissible pressure-temperature (P-T) envelope for routine heat-up and cool-down operations, and this can reduce overall plant safety. For example, an unnecessarily narrow P-T envelope increases the possibility of damaging pump seals due to insufficient cooling water pressure. Considering
that pump seal failure produces a small-break loss of coolant accident (a potential pressurized thermal shock initiator), this situation is clearly undesirable. Additionally, the current perception of low RPV toughness (based on high RTNDT values) produces the need for flux suppression systems to maintain an acceptable P-T envelope. Flux suppression produces higher fuel peaking and, consequently, less margin against fuel damage if an accident were to occur. The risk to the plant and the public associated with these situations can be mitigated by replacing the conservative RTNDT-basedcharacterization of fracture toughness with the more accurate characterization provided by the Master Curve.
The use of Master Curve-based approaches is consistent with the NRC’s goal of moving toward a risk informed framework for rule and decision-making. This framework, and the probabilistic risk assessment (PRA) methodologies that support it, require the use of best estimate values rather than bounding values whenever possible. The Master Curve provides best estimates of fracture toughness and features an explicit consideration of uncertainty. Conversely, RTNDT technology provides bounding values, suggesting that the Master Curve fits better within a risk informed framework than does RTNDT.
22
4 HISTORY OF THE MASTER CURVE
Wallin, working in collaboration with Sarrio and Törrönen, began to publish papers that would become the basis for what is now referred to as the “Master Curve” as part of his doctoral research work in 1984 [Wallin, all citations]. This work includes two components: a statistical model of cleavage fracture, and a temperature dependency of fracture toughness common to all ferritic steels.
The statistical model of cleavage fracture proposed by Wallin, Sarrio and Törrönen (WST) has important progenitors dating to the 1950s. The idea that cleavage fracture of ferritic steel occurs when a critical tensile stress is exceeded evolves from the work of Hendrickson, et al., McMahon and Cohen, Curry and Knott, and Smith, among others [Curry 76, Curry 78, Curry 79, Knott 66, McMahon 65, Smith 66, Smith 68]. In the 1970s, Ritchie, Knott, and Rice (RKR), and Curry and Knott incorporated these observations into models that predict, respectively, how toughness changes with temperature, and the scatter of fracture toughness at a single temperature [Ritchie 73, Curry 76, Curry 78, Curry 79]. The WST model begins with the notion, most commonly attributed to RKR, that cleavage fracture will initiate and propagate to failure when a critical opening mode stress is exceeded over some critical distance ahead of the crack tip. WST combined an RKR-type model with Curry and Knott’s idea that cleavage fracture is controlled by a “statistical competition between crack nuclei of varying sizes and frequencies in the rapidly changing stress gradient ahead of a {sharp} crack tip” [Curry 80]. The most significant contribution of the WST model is not the introduction of a new understanding of cleavage fracture, but rather the important generalizations WST made concerning the
cleavage fracture behavior of all ferritic steels. This section includes a review of the WST model, a discussion of these generalizations, and a description of recent activities within ASTM and ASME that have used Master Curve technology.
4.1 Wallin, Sarrio and Törrönen (WST) Cleavage Fracture Model
Four separate publications from 1984 describe the WST model [Wallin 84a, 84b, 84c, 84d]. The model presumes that a statistically distributed volume of carbides (later generalized to “cleavage initiators”, see [Merkle 98]) controls cleavage fracture, and thus the fracture toughness in the transition regime. WST adopt a Griffith instability criteria for a round carbide in a ferrite matrix to relate local stresses and the dimension of crack initiators that cause failure [Griffith 20]:
Eq. 4-1 � �
� � 2212 yy
psCRIT
wEr
�����
��
Where rCRIT is the radius of a particle that would lead to cleavage fracture for the loading and material conditions described by Eq. 4-1, E is Young’s modulus, � is Poisson’s ratio, �s is the surface energy of the matrix, wp is the plastic work needed for crack propagation, and�yy is the applied opening mode stress ahead of the crack tip. �yy is itself a function of the flow properties of the material (�yield, n), the elastic properties of the material (E, �), the applied loading (KI), and the distance ahead of the crack tip (X). In 1984 WST used curve fits to crack-tip solutions [McMeeking 77, Rice 70, Tracy 76] to define
23
�yy, however in principal any sufficiently detailed crack tip solution can be used.
Eq. 4-1 can be used to formulate the following deterministic failure criteria: cleavage failure will occur if a candidate cleavage crack initiator, which is located at a certain position ahead of the crack tip, has a radius that exceeds the critical value expressed by Eq. 4-1. However, the inherently statistical nature of cleavage fracture [Curry 76, Curry 78, Curry 79] motivated WST to express this criterion probabilistically instead:
Eq. 4-2 � �� ���
���������plasticr
X
XdXBFNcritf rrPP
0
sin11 �
where Pf is the probability of cleavage fracture, X is the distance ahead of the crack tip, r is the radius of a cleavage crack initiation site (carbide), rplastic is the distance from the crack tip to the elastic/plastic interface, N is the number of cleavage crack initiation sites (carbides) per unit volume, F is the fraction of crack initiation sites (carbides) taking part in the fracture process, Bis the specimen thickness, dX is the width if the summation volume, X�sin� is the height of the summation volume, and � is an angle measured counter-clockwise from the crack plane. �characterizes the volume of material that might affect the fracture process. WST assumed a constant value of for �, however this value was never specified in any of their papers.
Several features of this formulation should be noted:
1. Use of rplastic as the summation limit in Eq. 4-2 recognizes that plastic deformation is a necessary condition for cleavage fracture [Low 54, Smith 66].
2. Use of the specimen thickness (B) in Eq. 4-2 gives the WST model a three dimensional aspect by recognizing that the critical conditions for cleavage crack initiation could be achieved at any location along the crack front. However, this model ignores certain recognized 3D effects, namely the loss of plane strain constraint where the crack front intersects the free
surface of the specimen. Under the conditions of small scale yielding to which the WST model is intended to apply, the effect of this approximation is expected to be minimal.
Eq. 4-1 for rcrit is substituted into Eq. 4-2 to capture all of the factors that govern the probability of cleavage fracture according to the WST model in a single equation:
Eq. 4-3
� �� �
�
����
��sin
022 ,,,,,12
11
�����
��
��
��
�!
�"#
$$$
%
&
'''
(
)
�
�����
XdXBFNr
XIyieldyy
psf
plastic
KXEn
wErPP
Eq. 4-3 is evaluated in the following manner. First load is “applied” by establishing a KI value, and calculating �yy from the crack-tip stress distribution (Figure 4.1). rcrit is then calculated from this value of �yy and deterministically established material variables according to Eq. 4-1. The plastic zone is divided into volume elements (width=dX, height=Xsin�) that are small enough that they can be considered to exist under a state of uniform stress. For each volume element, a carbide radius, r, is randomly selected from a distribution of values (Figure 4.2). The inequality in Eq. 4-2, r � rcrit, is evaluated to determine the contribution of this dX x Xsin� volume to the overall probability of failure (Pf) for this applied load (KI) level. The contribution of all volume elements to the total probability of failure establishes a pair of values (Pf, KI(applied)) that characterizes a particular load level. Repeating this calculation for progressively higher applied-K values defines a statistical distribution of KI at a fixed temperature. WST took KIc as the mean value (Pf = 0.5) of this distribution.
In their 1984 paper, WST provide an example evaluation of Eq. 4-3, complete with input values for all material variables, to predict the variation of fracture toughness with temperature for HSST Plate 02 [Wallin 84b]. The input variables used to generate this prediction are summarized in Table 4.1, while Figure 4.3 demonstrates that the original WST model
24
predicts the scatter in fracture toughness and the variation of fracture toughness with temperature reasonably well.
Figure 4.1. Relationship between the crack-tip stress field and applied-K values used in the original WST model [Wallin 84a].
Figure 4.2. Distribution of carbide sizes used in the original WST model [Wallin 84a].
Figure 4.3. The prediction of the original WST model compared with experimental fracture toughness data for HSST Plate 02 [Wallin 84b].
25
Tab
le 4
.1.
Inpu
t var
iabl
es u
sed
by W
ST in
thei
r pr
edic
tion
of th
e tr
ansi
tion
frac
ture
toug
hnes
s cur
ve fo
r H
SST
Pla
te 0
2.
Var
iabl
e So
urce
of t
his V
aria
ble
Var
iabl
e co
ntrib
utes
to K
JC. .
.
Form
ula
Dat
a Su
ppor
ting
Form
ula
Mag
nitu
deSc
atte
r Te
mpe
ratu
re
Dep
ende
nce
E N
one
give
n.
X
X
*
Non
e gi
ven.
X
� yy
Fit t
o fin
ite e
lem
ent r
esul
ts, s
ee F
igur
e 4.
1.
[McM
eeki
ng 7
7, R
ice
70, T
racy
76]
X
� yie
ld
Yar
oshe
wic
h-R
yvki
na M
odel
fit t
o Te
nsile
Dat
a �
�+
,�
�K
T�
��
��
0126
.0ex
p45
016
7745
0K
otila
inen
79
X
X
nA
ctua
l pro
perti
es u
nkno
wn,
n��
yiel
d = 7
0 M
Pa a
ssum
ed
XX
(by
link
to
� yie
ld)
� s +
wp
Act
ual p
rope
rties
unk
now
n,
+,
��
KT
��
��
0126
.0ex
p17.0
8.5as
sum
ed a
s a fi
tting
par
amet
er
X
X
r�
��
�$$ %&
'' ()�
� $ %&' () �
��
�
rr
crr
acr
po
oa
o/
exp
!21
a=10
, c=8
, r-b
ar =
0.11
-m (S
ee F
igur
e 4.
2)
[Wal
lin 8
4a, W
allin
84b
]
X
N
��
30
235
.0rf
drrr
pN
o
o�
�./
whe
re f,
the
volu
me
fract
ion
of th
e ca
rbid
es, =
0.
04 a
s ev
alua
ted
from
che
mic
al
com
posi
tion
[Ash
by 6
6, R
awal
77]
X
X(b
ecau
sea
func
tion
ofr)
FA
ssum
ed =
10-4
bas
ed o
n th
e id
ea th
at 0
.1 to
1%
of t
he c
arbi
des
brea
k an
d 1%
to 1
0% o
f the
se a
re o
rient
ed o
n th
e cr
ack
plan
e so
as
to e
nabl
e cr
ack
grow
th.
X
BP
resc
ribed
X
�
Hel
d co
nsta
nt, n
o re
fere
nce
or v
alue
giv
en
X
Rel
atio
nshi
p:
��
��
��
��
�
��
sin
,,
,,
,1
21
10
22
��
��
�� � �� �
� !� "#
$$$ %&
''' ()
�
��
��
�� �
XdX
BF
NK
XE
nwE
rP
Ppl
astic
r XI
yiel
dyy
ps
f
26
4.2 Generalizations Made Based on WST Cleavage Fracture Model
In the years that followed the publication of the WST cleavage fracture model, Wallin and co-workers published a number of other papers in which they made two important observations concerning the cleavage fracture behavior of allferritic steels:
1. The distribution of cleavage fracture toughness values at a single temperature is well described by a 3-parameter Weibull distribution having 2 parameters fixed (a minimum value (Kmin) of 20 MPa�m and a shape parameter (b) of 4). This distribution applies to all ferritic materials that can be considered to have a random distribution of cleavage initiations sites spread homogeneously throughout the material [Wallin 84c]. Thus, the only material dependent quantity needed to establish the distribution of cleavage fracture toughness values at a single temperature is the Weibull location parameter, Ko. Another consequence of this finding is that the effect of specimen size (i.e. crack front length) on fracture toughness scales with the ¼-power of thickness [Wallin 84d, Wallin 91, Wallin 93b].
2. The alloying, heat treatment and irradiation conditions characteristic of a particular ferritic material influence only the position of the transition fracture toughness curve on the temperature axis, while the variation of cleavage fracture toughness with temperature follows a common form, i.e. a “Master Curve,” irrespective of these factors [Wallin 84a, Wallin 93a].
The basis for these generalizations is examined in greater detail in the following sections.
4.2.1 Weibull Distribution of Fracture Toughness at a Fixed Temperature
4.2.1.1 Two Parameter Weibull Distribution
Wallin notes that eqs. (5) and (6) can be represented approximately in the following integral format [Wallin 84c]:
Eq. 4-4 � ���
��
�!
�"#
��������0 .�
plasticX
Xcritf XdXrrPBFNP
0
sinexp1 �
Under conditions of small scale yielding (SSY), the crack-tip stress fields scale in proportion to KI. This permits establishment of the following non-dimensional length scale in the vicinity of the crack-tip:
Eq. 4-5 2ˆ
$%&
'()
�
yield
IKXX
�
Use of this non-dimensional length scale in Eq. 4-4 produces the following relationship:
Eq. 4-6
� ���
��
�!
�"#
���$$%
&''(
)������0 .
�
plasticX
X
crityield
If XdXrrPKBFNP
ˆ
0ˆ
4
ˆˆsinexp1�
�
Because the integral expression is a constant, Eq. 4-6 simplifies to the following form:
Eq. 4-7 � �4exp1 If KBP ����0 C
where
Eq. 4-8 � ���
��
�!
�"#
����
� .�
plasticX
Xcrit
yieldXdXrrPFN
ˆ
0ˆ4
ˆˆsin�
�C
Thus, after making the following assumptions:
1. That plastic deformation is needed for cleavage fracture to occur [Low 54, Smith 66],
27
2. That SSY conditions prevail at the crack tip§, and
3. That the material has a random distribution of cleavage initiations sites spread homogeneously throughout the material.
the WST model suggests that the distribution of cleavage fracture toughness values follows a 2-parameter Weibull distribution [Wallin 84c]. Most significantly, this development of Eq. 4-7, which follows that of [Wallin 84c], demonstrates that the scatter of these fracture toughness values (i.e. the exponent of 4 on KI in Eq. 4-7) does notdepend on the cleavage initiator distribution (i.e. r in Eq. 4-8). This material independence of the scatter in fracture toughness data follows directly from use of the similarity length scale in Eq. 4-5, which in turn follows directly from the assumption of SSY conditions at the crack tip. Once this substitution is made in Eq. 4-6, and the relationship simplified, Eq. 4-7, the material dependent variables are completely subsumed into a constant C (Eq. 4-8) that only scales the probability of failure. Consequently, the factors in Eq. 4-8 that describe the cleavage initiator distribution effect only the mean value of fracture toughness, whereas the distribution (or scatter) in the probability of failure depends onlyon the applied-value of the stress intensity factor raised to the 4th power (i.e. it is feature common to all ferritic steels).
4.2.1.2 Three Parameter Weibull Distribution
Use of a 2-parameter Weibull distribution produced the prediction of HSST-02 transition behavior illustrated in Figure 4.3. This prediction agrees reasonably well with the fracture toughness data, however the tolerance bounds seem in general too wide, and the lower tolerance bound too low. Based on this observation Wallin argued that using a more physically realistic Weibull distribution would
§ It should be noted that “small-scale yielding” does not imply LEFM valid conditions as outlined by ASTM Standard E399. Small-scale yielding places less severe restrictions on the crack-tip deformation state than does LEFM, as will be discussed in Section 6.3 in additional detail.
provide a better fit to the distribution of fracture toughness data. This more physically realistic distribution has a lower bound (Kmin) value below which cleavage fracture is impossible (i.e. Pf� 0 when KI(applied) < Kmin). A three-parameter Weibull distribution can be constructed in the spirit of Eq. 4-7 as follows [Wallin 91]:
Eq. 4-9 ��
��
�!
�"#
$$%
&''(
)��
���4
min
minexp1KKKK
BBP
o
I
of
where Kmin is a value of applied KI below which cleavage fracture is not possible, i.e. Pf � 0, B isa normalization thickness. It can be set equal to any thickness of interest, and Ko is a normalization toughness that corresponds to a 63.2% probability of failure.
In addition to Eq. 4-9 providing a more “physically realistic” model of cleavage fracture because it does not permit an infinitesimal KI(applied) value to produce a finite probability of failure, Wallin advanced several physical rationale for a non-zero value of Kmin [Wallin 91]:
1. At very small KI values, the volume of material at the crack tip subjected to plastic flow could be smaller than the size of the cleavage initiator, thereby violating the requirement that cleavage fracture must be preceded by plastic flow [Smith 68].
2. In most situations of engineering relevance for modern steels having even a modest level of fracture toughness, cleavage fracture requires a pre-existing crack from which to initiate. When cracks grow sub-critically in fatigue, warm pre-stress effects establish a Kmin value equal to the maximum-K value applied during fatigue crack growth. Consequently, the fatigue crack growth threshold for steels suggests that Kmin should be on the order of 10 to 20 MPa�m.
While physically plausible, Wallin nevertheless relied on empirical evidence to support a Kmin
value of 20 MPa�m (see. Figure 4.4). Figure 4.5 illustrates that use of a 3-parameter Weibull
28
distribution with Kmin = 20 MPa�m, Eq. 4-9, indeed captures the behavior of the HSST-02 data much better than the 2-parameter Weibull distribution.
Kmin = 0 MPa�m
(Kmin = 10 MPa�m
Kmin = 20 MPa�m
Figure 4.4. Empirical basis for a Kmin value of 20 MPa�m [Wallin 84c].
Figure 4.5. The prediction of a three parameter Weibull model compared with experimental fracture toughness data for HSST Plate 02 [Wallin 84b].
4.2.2 Size Effects and a Weakest-Link Description of Cleavage Fracture
The correspondence between the failure probability equation derived by Wallin, Eq. 4-7, and a Weibull distribution [Weibull 51] itself offers evidence, but not proof, that the physical phenomena described by Eq. 4-7 may be driven by a weakest-link mechanism wherein failure of one material volume signals failure of the entire component. In a review of statistical models of cleavage fracture initiation Wallin points out that the literature includes two different models of the conditions required for cleavage fracture to initiate [Wallin 91]. Weakest-link models have been advocated by WST, and by many others [Landes 80, Beremin 83, Slatcher 86, Tyson 88, Anderson 89a, and Anderson 89b]. The other model requires that the critical conditions for cleavage initiation be achieved over a certain (substantial) percentage of the crack front [Evans 83, Lin 86, Godse 89]. The weakest link models all suggest that the fracture toughness should decline with increasing crack front length, while models requiring that the critical conditions for cleavage fracture be met over some finite percentage of the crack front predict no such effect. The weight of experimental evidence clearly supports the weakest link description [Kirk 98a, Lott 98, Rathbun 00].
29
In this section, we begin by reviewing the information presented by Landes and Schaffer, which the early WST papers cited as “experimental verification” that a weakest-link mechanism controls cleavage fracture. We then go on to derive the specific relationship between fracture toughness and crack front length suggested by the three-parameter Weibull characterization of fracture toughness, Eq. 4-9.
4.2.2.1 Landes and Schaffer: Early Experimental Evidence
Supporting a Weakest-Link Description of Cleavage Fracture
Landes and Schaffer reported that small specimens failing by transgranular cleavage exhibit a higher mean toughness than larger specimens, as illustrated by their data in Figure 4.6 [Landes 80]. Landes and Schaffer considered two possible explanations for this observed difference in toughness values:
Figure 4.6. Fracture toughness data reported by Landes and Schaffer that show a weakest-link size effect [Landes 80].
� Loss of Constraint: At some deformation level the crack tip plastic zone becomes large enough to interact with the free surfaces of the specimen. When this occurs the triaxial constraint that localizes plastic flow to the crack-tip region begins to diminish. This loss of constraint produces the need for disproportionately large increases in applied deformation to elevate the driving force to fracture, thereby elevating the toughness value observed at fracture. Obviously loss of constraint more easily affects small specimens than large specimens because the plastic zone interacts with the free boundaries of a small specimen at lower applied deformation
levels. Thus, loss of constraint tends to elevate the toughness measured by small specimens relative to that measured by large specimens.
� Statistical Sampling of Fracture Initiation Sites: Landes and Schaffer proposed a model having two main premises: that the toughness of a material depends on the local microstructure (and is therefore variable throughout the material), and that the toughness measured by a particular specimen is controlled by the location of lowest toughness along the crack front.The first premise is true for any polycrystalline material, whereas the latter is particular to the fracture of ferritic
30
materials by transgranular cleavage in fracture mode transition. The fracture surfaces of specimens tested in fracture mode transition provide clear physical evidence supporting this weakest link model of cleavage fracture. Ferritic materials tested in transition characteristically exhibit a single, or extremely limited number of, initiation site(s), suggesting that the notion of the toughness value being controlled by one localized region is correct. Such fractographic evidence was provided by Landes and Shaffer.
Landes and Schaffer also found evidence in fracture toughness data to support their statistical model over the loss of constraint model. Landes and Schaffer argued that the loss of constraint argument leads to the conclusion that the toughness values of small specimens should always exceed those of larger specimens. Referring to Figure 4.6, this is clearly not the case. Conversely, a small specimen sometimes exhibiting a lower toughness than a large specimen (as shown in Figure 4.6) is fully consistent with, and indeed anticipated based on, the statistical model because it is possible that, with sufficient sampling, a small specimen may contain a region of lower toughness than any of the large specimens tested.
4.2.2.2 Relationship Between Crack Front Length and Fracture Toughness
Having established Eq. 4-9 as an appropriate description of the distribution of cleavage fracture toughness at a fixed temperature, the relationship between cleavage fracture toughness and crack front length (B in Eq. 4-9)) can be derived directly with no additional assumptions. Taking the natural logarithm of Eq. 4-9 and re-arranging terms leads to:
Eq. 4-10 � �4
min
min1ln $$%
&''(
)��
���KKKK
BBP
o
I
of
Raising each side to the ¼ power produces the following relationship:
Eq. 4-11
� �� � $$%
&''(
)��
$$%
&''(
)���
min
min4/1
4/11lnKKKK
BBP
o
I
of
Comparing two toughness values from different thickness specimens, Eq. 4-11 becomes:
Eq. 4-12
� �� � $$%
&''(
)�
�$$%
&''(
)�$$
%
&''(
)�
�$$%
&''(
)���
min
min)2(4/1
2
min
min)1(4/1
14/11lnKK
KKB
BKK
KKB
BPo
SizeI
o
Size
o
SizeI
o
Sizef
Since B0, K0 and Kmin are constants, Eq. 4-12 reduces to the following relationship:
Eq. 4-13
� �4/1
1
2min)2(min)1( $$
%
&''(
)���
Size
SizeSizeJcSizeJc B
BKKKK
Eq. 4-13 quantifies the effect of crack front length on fracture toughness at any fixed fracture probability, or even for individual specimens.
4.2.3 A “Master” Fracture Toughness Transition Curve for Ferritic Steels
The temperature dependent variables in the original WST model, Eq. 4-3, include E, �yield, n(through an assumed dependence on �yield), and the quantity �s+wp. WST found that assuming temperature independence of the quantity �s+wpproduced incorrect predictions of fracture toughness data, as illustrated in Figure 4.7 [Wallin 84a]. Consequently, WST adopted an exponential form, i.e. �s+wp =
+ ,� �KT ���� 0126.0exp17.08.5 , as an empirically motivated fitting parameter to bring their model’s prediction into agreement with the fracture toughness data of HSST Plate 02 [Wallin 94b]. WST attributed the temperature-dependence of this surface energy / plastic work
31
term to the temperature-dependence of the Peierls-Nabarro stress (the stress that resists dislocation motion through the crystal), but provided no theoretical linkage between (�s+wp)and the Peierls-Nabarro stress.
In 1993 Wallin published a paper examining the effects of irradiation on transition curve shape [Wallin 93a] that established the equation now known as the “Master Curve,” i.e.:
Eq. 4-14� �+ ,omedianJc TTK ���� 019.0exp7030)(
Equation (17) is an empirical fit to transition fracture data for 10 heats of well-characterized nuclear reactor pressure vessel steels and weldments (see Figure 4.8). Thus, in its present form the temperature dependence of the Master Curve, while having considerable empirical support, lacks a rigorous physical basis.
Figure 4.7. Incorrect transition fracture toughness behavior predicted using a constant value for �s+wp=9 [Wallin 84a].
Figure 4.8. Data used to establish the temperature dependence of the Master Curve [Wallin 93a].
4.3 Master Curve Testing Standard, ASTM E1921-97
Since the Master Curve establishes both the statistical distribution of toughness values at a particular temperature, and the variation of toughness with temperature, all that remains for estimation from test data is the position of the toughness vs. temperature curve on the temperature axis. In 1997 the American Society for Testing and Materials (ASTM) adopted standard E1921-97, “Test Method for Determination of Reference Temperature, To, for Ferritic Steels in the Transition Range,” as a methodology to establish an index temperature (To) that locates the Master Curve on the temperature axis for the particular steel of interest. This standard was the result of efforts undertaken by ASTM Committee E08.08 on Elastic-Plastic fracture between 1994 and 1997. The standard provides a method to establish the temperature at which the median Master Curve for a 1-inch thick specimen passes through 100 MPa�m based on testing of 6 or more replicate fracture toughness (KJc) specimens at a single temperature. The technical basis for the provisions of E1921-97 are addressed in Section 6, and discussed in detail elsewhere [Merkle 98].
32
Here we overview briefly the E1921-97 procedure for determining To, and illustrate where and how components of Master Curve technology influence the standard. A four step procedure for To determination is illustrated in Figure 4.9, and described below:
0
50
100
150
200
-100 -50 0 50 100
T - T o [oF]
1T E
qu
iv. K
Jc [
ksi*
in0.
5 ]
To
1
2
4
3
Figure 4.9. Illustration of the process used by E1921-97 to establish the Master Curve index temperature, To.
1. Test 6-10 toughness specimens at one temperature: To begin the E1921-97 process, one must test at least 6 specimens (generally 6-12 specimens are needed to obtain a valid data set) at a single temperature. The median toughness of these specimens must exceed 50 MPam. Additionally, any specimens exhibiting ductile crack extension before cleavage fracture that exceeds 5% of the remaining ligament length are regarded as invalid and are not used to estimate To. These two data validity requirements recognize that the Master Curve accounts only for deformation by dislocation glide. Other deformation mechanisms, such as twinning on the lower shelf and ductile hole growth in the upper transition / upper shelf, are not treated by the Master Curve, and so are eliminated from consideration by these validity requirements.
2. Convert to 1T equivalence: As discussed in Section 4.2.2, the Master Curve recognizes that cleavage in fracture mode transition fracture is modeled by a weakest link process, with failure at a single cleavage initiation site signaling failure of the entire specimen. The next step in calculating To is therefore to adjust the measured KJC values to a common size (1T, or 1-inch thick) using Eq. 4-13, which is repeated below for clarity:
Eq. 4-15
4/1
minmin)1( 1
BKKKK JcTJc
where KJc is the toughness measured using a specimen of thickness B (units=inches), and Kmin = 18.18 ksiin (or 20 MPam). As reviewed in more detail in Section 4.2.1 and 4.2.2, Eq. 4-15 makes the following assumptions:
a) Cleavage fracture occurs under small-scale yielding conditions [Low 54, Smith 66],
b) There is a random distribution of cleavage initiations sites spread homogeneously throughout the material, and
c) Cleavage fracture cannot occur (i.e. the probability of fracture is defined as zero) below an applied-K of 20 MPam.
3. Calculate median 1T equivalent KJc and plot it: First the KJc limit is calculated for each specimen according to the following formula
Eq. 4-16
If the specimen is of size other than 1T the KJC(limit) is scaled to 1T equivalence using Eq. 4-15. The values KJC(1T) and KJC(limit)(1T) are then used in the following equation to estimate KJC(median)(1T):
33
Eq. 4-17
20
3068.0
20,9124.0
4
1
1
4
)1)((lim)1(
1)(
r
KKMinK
N
iTitJcTJc
TmedJc
where N is the total number of specimens tested, and r is the number of specimens that satisfy the ASTM E1921-97 maximum deformation criteria, Eq. 4-16.
Eq. 4-17 is a maximum likelihood estimate of KJC(median)(1T). The derivation of this relationship from Eq. 4-9 is detailed elsewhere [Merkle 98]. Since Eq. 4-17 also finds its origin in a three parameter Weibull distribution, Eq. 4-9, the same assumptions noted in Step 2 (above) also apply to Eq. 4-17.
4. Determine the temperature at which the 1T equivalent KJC is 100 MPam. This temperature is To: To is determined from the following equation:
Eq. 4-18
70
30ln
019.0
1 )(medJc
Testo
KTT
This relationship is a simple algebraic re-expression of Eq. 4-14. It mathematically extrapolates KJC(median)(1T) along the Master Curve until its value becomes 100 MPam. The temperature at which this occurs is called To. The assumption made here is that the temperature dependence of toughness for the material of interest is well described by the Master Curve. As discussed in Section 4.2.3, in its current form the temperature dependency of the Master Curve is justified as an empirical fit to fracture toughness data.
4.4 Master Curve Application
Standard, ASME Code Cases N-629 and N-631
The Pressure Vessel Research Council (PVRC) Task Group on Master Curve Applications
developed a phased strategy for incorporation of Master Curve concepts into the ASME Code [EPRI 98]. In the short term this strategy advocates developing a Master Curve-based index temperature for the ASME KIc and KIR curves to use as an alternative to RTNDT. In the long term the group envisions eliminating the KIc and KIR curves and, instead, employing a methodology that uses the Master Curve directly. While work toward the long-term goal is only just beginning, ASME Sections XI and III accomplished the short-term goal with the adoption of Code Cases N-629 and N-631, respectively [ASME N629, ASME N631]. These Code Cases provide the following formula for RTTo, a Master Curve-based index temperature: Eq. 4-19 F35o
oTo TRT Here To is the value established by testing in accordance with E1921. An ASME committee developed the technical basis for Code Case N-629 for application to RPV steels both before and following irradiation [EPRI 98]. This document points out that even though there is no direct correlation between RTNDT and To (as illustrated in Figure 4.10 based on work by Sokolov [Sokolov 98]), an approach that ensures that RTTo continues to perform the same function as RTNDT can be used to relate the two quantities. Historically, a KIc curve indexed to RTNDT has provided an appropriate lower bound to available fracture toughness data. The challenge in selecting the numeric value of 35F in Eq. 4-19 therefore involved agreeing on and quantifying the degree of margin implicit to a lower bound KIc curve indexed to RTNDT. As illustrated in Figure 1.1, the level of implicit margin (defined here as the separation between fracture toughness data and a RTNDT-indexed KIc Curve) varies considerably. Because of this, the committee decided that in the past one could only rely on the level of margin implicit to the most limiting material (i.e. the material having fracture toughness data closest to the bounding curve). Maintaining the margin historically associated with HSST Plate 02 therefore became the mark for RTTo to achieve. The committee
34
determined that the 35F value used in Eq. 4-19 achieves this goal.
T100 (oF)
-200 -150 -100 -50 0 50 100
RT
ND
T
(o F)
-200
-150
-100
-50
0
50
100
T100 (oC)
-125 -100 -75 -50 -25 0 25
RT
ND
T
(oC
)-125
-100
-75
-50
-25
0
25
HSST-01 subarc weldA533B class 1 subarc weldA533B class 1 weldA533B weld HAZ
A533B class 1HSST-01HSST-02HSST-03
A508 class 2A508 class 2A508 class 2
1:1
Figure 4.10. A comparison of RTNDT and the To (here called T100) values unirradiated RPV steels [Sokolov 98].
35
5 TECHNICAL BASIS OF THE MASTER CURVE
As described in Section 4, the Master Curve includes two key features: a statistical model that characterizes cleavage fracture as a weakest link process, and a single temperature dependency of fracture toughness common to all ferritic steels. In the following sections we review both the physical basis for these features as well as the empirical evidence available to support them. Empirical evidence is needed to validate the Master Curve description of fracture toughness in the transition regime and demonstrate its applicability, both before and after irradiation, to the plates, forgings, and weldments used in nuclear RPV fabrication. However, because empirical evidence only speaks with certainty to the conditions for which data is available, empirical evidence alone is insufficient to demonstrate the adequacy of the Master Curve for use in RPV applications. Only arguments founded in the fundamental physics of deformation and fracture can speak with certainty to the breadth of conditions to which the Master Curve can be expected to apply. For this reason we first review the physical basis for the Master Curve (Section 5.1). This information establishes both a framework within which to view available empirical evidence, reviewed in Section 5.2, as well as an expectation for what this evidence should show.
5.1 Physical Basis 5.1.1 Statistical Model In the development of the WST statistical model of cleavage fracture, the following three assumptions are made at the outset:
a. That plastic deformation is a necessary precursor of cleavage failure,
b. That the crack tip stress state at the time of failure is characterized by conditions of small scale yielding, and
c. That there exists a random distribution of cleavage initiation sites spread uniformly throughout the material.
The first assumption is a necessary condition for cleavage fracture of a BCC solid [Low 54, Smith 66]. All RPV steels are ferritic (i.e. BCC), so this assumption in no way limits the applicability of the Master Curve in RPV applications. The derivation presented in Section 4.2.1.1 demonstrated that, subject to the second assumption, the median fracture toughness is influenced by the distribution of cleavage initiation sites throughout the material. However, the scatter of toughness about this value is independent of the cleavage initiator distribution, indeed it is independent of all material variables. This understanding suggests that the second assumption also places no material dependent limits on Master Curve applicability to RPV applications. The third assumption requires only that the material exhibit a uni-modal distribution of cleavage initiation sites over the size scale of the plastic zone at crack initiation (i.e. a sub millimeter size scale). This assumption creates complications when applying the Master Curve to welded structures having a weld bead size on the order of the thickness of the material, as is characteristic of some offshore and pipeline applications [Pisarski 99]. However, the high degree of grain refinement and re-tempering characteristic of the small beaded welds suggests that this difficulty should not limit RPV applications. In summary, subject only to a requirement for conditions of small scale yielding at the time of
36
fracture, the statistical description of fracture toughness adopted by the Master Curve is expected to be appropriate. The information in Sections 4.2.1.1 and 4.2.1.2demonstrate that a three parameter Weibull distribution with two parameters fixed (Kmin = 20MPam and slope = 4) well describes cleavage fracture toughness data. Physically, a Weibull distribution describes a weakest link processes wherein failure of a single component signals failure of the entire structure. Physical evidence that this model properly describes cleavage fracture in transition abounds in scanning electron micrographs of cleavage fracture surfaces. These photos invariably demonstrate that the macroscopic fracture of the component or specimen traces back to a single initiation site. 5.1.2 Curve Shape Despite the strong empirical evidence for a universal Master Curve shape in transition [Sokolov 96, Kirk 98], the lack of a physical understanding for why such a remarkably uniform temperature dependency should exist gives rise to concerns about applying the Master Curve beyond it’s range of applicability [Mayfield 97, Kirk99, Kirk 00a]. This is especially true in nuclear reactor applications, where of necessity judgments must be made concerning reactor vessel integrity years in advance of having material samples for the actual irradiation conditions of interest. These practical concerns have motivated work to identify the underlying physical basis for a single “master” curve shape as a means to ensure that the applicability bounds of Master Curve technology are not violated when the Master Curve is applied in the assessment of reactor pressure vessel integrity. Two research groups have focused in this area: one led by Natishan [Natishan 98, Natishan 99a, Natishan 99b, Wagenhofer 00a, Wagenhofer 00b, Kirk 00b] and another led by Odette [Odette 00]. The research activities of both groups are still on going. In the following sections we summarize the current findings of both groups.
5.1.2.1 Work by Natishan and Co-Workers
Work by Natishan and co-workers has focused on development of a physical basis for a universal Master Curve shape that would enable one to establish, a priori, those steels to which the Master Curve should apply, and those to which it should not [Natishan 98, Natishan 99a, Natishan 99b, Wagenhofer 00a, Wagenhofer 00b, Kirk 00b]. These investigators employ dislocation-based deformation models to describe how various aspects of the microstructure of a material control dislocation motion, and, thus, the energy absorbed to fracture, and how these effects vary with temperature and strain rate. The microstructural characteristics of interest include both short- and long-range barriers to dislocation motion.
o Short Range Barriers: The lattice itself provides short-range barriers that effect the atom-to-atom movement required for a dislocation to change position within the lattice.
o Long Range Barriers: Long-range barriers include point defects (solute and vacancies), precipitates (semi-coherent to non-coherent), boundaries (twin, grain, etc), and other dislocations. Long-range barriers have an inter-barrier spacing several orders of magnitude greater than the short-range barriers provided by the lattice spacing.
Classifying microstructural features by their inter-barrier spacing is key to establishing the microstructural features responsible for the temperature dependency of the flow behavior, and thus for the shape of the Master Curve. Thermal energy acts to increase the amplitude of vibration of atoms about their lattice sites, consequently increasing the frequency with which an atom is out of its equilibrium position in the lattice. Since the activation energy for dislocation motion depends on the energy needed to move one atom past another, this energy is reduced when an atom is out of position. Increased thermal energy therefore decreases the resistance of these short-range barriers to dislocation motion. Conversely,
37
increased thermal energy is not effective at moving dislocations past long-range obstacles because no matter how large the amplitude of atomic vibration, the height of the energy barrier required to move the dislocation past these large obstacles is orders of magnitude larger. The flow stress of a material includes contributions from both the thermally activated short-range barriers, as well as from the non-thermally activated long-range barriers. In their 1984 paper, WST [Wallin 84a] suggest a link between the micro-mechanics of cleavage fracture and the observation of a “master” fracture toughness transition curve. WST use a modified Griffith equation to define the fracture stress, i.e.:
Eq. 5-1 0
2 )1(2 r
Eeff
fail
where E is the elastic modulus, is Poisson’s ratio, r0 is the size of the fracture-causing microstructural feature, and eff is the effective surface energy of the material, i.e. the sum of the surface energy and the plastic work absorbed to crack initiation (s + wp). In the transition region, eff is dominated by the plastic work consumed in moving dislocations. WST showed that values of KIc computed based on a temperature dependent expression for the plastic work fit experimental KIc values much more accurately than KIc values calculated using a temperature independent eff value of 14 J/m2 [Curry 76, Curry 78] (see Figure 4.7). WST therefore proposed the following empirically motivated temperature dependence of wp: Eq. 5-2 TCBAw
p exp
Natishan, et al. [Natishan 98] proposed that the empiricism represented by Eq. 5-2 is unnecessary, and provided the following dislocation-mechanics based description of the plastic work term: Eq. 5-3 d
eff
Here the integrand is a measure of the strain energy density, and is the length scale ahead of the crack over which this strain energy density is applied. The choice of a constitutive model based on dislocation mechanics to define the stress value in Eq. 5-3 establishes a physically based method of computing fracture toughness while simultaneously accounting for the uniform temperature dependence of fracture toughness for ferritic steels. These investigators used the following constitutive model derived by Zerilli and Armstrong based on dislocation mechanics considerations [Zerilli 87]:
Eq. 5-4
lnexp'4315TCTCCC
l
k n
GAZ
where G
’ quantifies strengthening due to solute atoms and precipitates, k is the grain boundary strength specific to a particular material, l is the grain diameter, is strain, n is the strain hardening coefficient, and C1, C3, C4 and C5 are material constants. More recently, Wagenhofer, et al. proposed that, given the local nature of Eq. 5-1, the appropriate length scale by which to multiply the strain energy density of Eq. 5-3 to determine the plastic work value for final fracture is the dimension of the microstructural feature that produces the critical microcrack [Wagenhofer 00b]. Consequently, Eq. 5-3 represents the plastic work per unit area of microcrack surface created when is approximately the size of a carbide or of a ferrite grain, depending on which microstructural feature controls cleavage fracture. Based on this idea, Eq. 5-3 becomes: Eq. 5-5 oAZeff rd
Combining Eq. 5-5 and Eq. 5-1 eliminates of the size of the critical microstructural feature from the local failure criteria. Making this substitution, and further modifying Eq. 5-5 to account for the combination of triaxiality, strain, and stress needed to promote cleavage fracture based on a model proposed by Chen, et al. [Chen 91, Chen 92, Chen 93] (see [Wagenhofer 00b] for the full details of this derivation), produces
38
the following physically-based criteria for cleavage failure in fracture mode transition:
Eq. 5-6 212
SED
fail
E
where E is Young’s modulus, is Poisson’s ratio, SED is the strain energy density, m is the mean stress, is the von Mises effective stress in plane strain, crit is the strain at crack initiation, p is the plastic strain, and
Eq. 5-7 pAZfail
mSED d
crit
0
The temperature dependency of the Master Curve is captured by the temperature dependency of Eq. 5-6, which contains the following three temperature dependant terms: E, crit, and Z-A. The population of steels to which a single Master Curve shape applies can therefore be assessed by examining the population of steels that share a common variation of E, crit, and Z-A with temperature:
o Elastic Modulus: The consistent temperature dependence of the elastic modus (E) exhibited by all ferritic steels is well documented, and is therefore not further addressed here.
o Critical Strain: Several investigators have reported an exponential increase in the strain at crack initiation (crit) with temperature [Chen 92, Koide 94]. The microstructural dependency of crit is a topic of continuing investigation, but due to the relationship between stress and strain Natishan et al. use the Zerilli-Armstrong constitutive model to define crit, thereby suggesting that all ferritic steels will exhibit the same temperature dependency of crit.
o Flow Stress: Natishan et al. therefore focus on the flow stress as quantified by the Zerilli-Armstrong constitutive relation (Z-
A) as a property that can distinguish the population of steels to which a single Master Curve shape applies. Since the lattice structure alone controls the temperature dependence of the flow stress
[Zerilli 87, Natishan 98], Eq. 5-6 and Eq. 5-7 suggest that the temperature dependence of fracture toughness also depends only on the lattice structure. This understanding supports the following proposal: 1. The Master Curve should model the
temperature dependence of fracture toughness for pearlitic, ferritic, bainitic, and tempered martensitic steels because all of these steels have a BCC matrix phase lattice structure.
2. The Master Curve should not apply to un-tempered martensite, which has a body-centered tetragonal (BCT) lattice structure, or to austenite, which has a FCC lattice structure. All BCT materials will also exhibit a common Master Curve, albeit a different one that that proposed by Wallin for BCC materials. FCC materials cannot have a “master” variation of toughness with temperature because strain history influences the temperature dependency of the flow curve for these materials [Wagenhofer 00b].
Figure 5.1 shows recently published experimental evidence that validates this proposal [Kirk 00b]. Thus, while Natishan et al. continue to work on a fully predictive model, their rationale that the short-range barriers to dislocation motion are the sole factor influencing the temperature dependency of fracture toughness in the fracture mode transition of ferritic steels appears to be correct. Consequently, the Master Curve can be expected to describe the transition fracture behavior of all steels having a body centered cubic (BCC) iron lattice structure. Other factors that vary with steel composition, heat treatment, and irradiation (e.g., grain size/boundaries, inclusions, precipitates, and dislocation substructures) all provide long-range barriers to dislocation motion, and so only influence the position of the transition curve on the temperature axis (i.e. To as determined by E1921-97), but not its shape. This understanding suggests that concerns of extending the Master Curve beyond its applicability limits when applying it to the
39
assessment of irradiated RPV steels are without technical merit. 5.1.2.2 Work by Odette and Co-
Workers Odette et al. [Odette 00] begin by considering the transition curve shape predicted by the critical-stress critical-distance criterion proposed by Ritchie, Knott and Rice (RKR) [Ritchie 73] and similarly posed models [Dodds 91, Odette 94]. These criteria suggest that cleavage fracture will occur when the opening mode stresses ahead of a deforming crack tip exceed the “cleavage fracture stress,” which is typically taken as temperature invariant. Odette et al. shows that such a model produces a Master Curve-like temperature dependence when the fracture toughness transition temperature occurs at low temperatures (as it does for unirradiated steels) because in this regime there is a strong exponential dependence of flow stress on temperature (see for example the upper curves in Figure 5.1). However, when the fracture toughness occurs at higher temperatures (as it does for irradiated steels) where there is hardly any variation of flow stress with temperature, the RKR-type models predict a transition curve shape that does not agree well with experimental data. Figure 5.2 illustrates this problem.
40
-300
-150
0
150
300
450
600
-200 -100 0 100 200 300 400
Temperature [oC]
sy -
sy(
ref)
[M
Pa
]
Forging/Un-Irr For ging/Pow er Forging/Test
Plate/Un- Irr Plate/Power Plate/Test
Weld/Un- Irr Weld/Power Weld/Test
Prediction
0
50
100
150
200
250
300
-150 -100 -50 0 50 100
Temperature [oC]
1T E
qu
iv.
KJc
[M
Pa*
m0.
5 ]
5.5x1018 N/cm2, Sys = 52 MPa
To = +53oC
1.0x1019 N/cm2, Sys = 103 MPa
To = +73oC
5.3x1019 N/cm2, Sys = 151 MPa
To = +126oC
Un-Irrad., Sys = 464 MPa
To = -43oC
-300
-150
0
150
300
450
600
-200 -100 0 100 200 300 400
Temperature [oC]
sy
- s
y(re
f)
[MP
a]
HY-130 Plate
Maraging Steel Plate
HY-130 Weld
Predict ion
0
50
100
150
200
250
300
-200 -150 -100 -50 0 50
Temperature [oC]
1T E
qu
iv.
KJ
c
[MP
a*m
0.5
] 18Ni (250) Maraging, Sy=1696 MPa(Shoemaker & Rolfe)
To = -74C
Ferritic Steel (BCC) Martensitic Steel (HCP)Yi
eld
Dat
a Co
mpa
red
to
Zeril
li-Ar
mst
rong
Toug
hnes
s D
ata
Com
pare
d to
M
aste
r Cu
rve
Match
No Match
Match
No Match
sy(ref) = room temperature yield strength
-300
-150
0
150
300
450
600
-200 -100 0 100 200 300 400
Temperature [oC]
sy -
sy(
ref)
[M
Pa
]
Forging/Un-Irr For ging/Pow er Forging/Test
Plate /Un- Irr Plate /Power Plate /Test
Weld/Un- Irr Weld/Power Weld/Test
Prediction
0
50
100
150
200
250
300
-150 -100 -50 0 50 100
Temperature [oC]
1T E
qu
iv.
KJc
[M
Pa*
m0.
5 ]
5.5x1018 N/cm2, Sys = 52 MPa
To = +53oC
1.0x1019 N/cm2, Sys = 103 MPa
To = +73oC
5.3x1019 N/cm2, Sys = 151 MPa
To = +126oC
Un-Irrad., Sys = 464 MPa
To = -43oC
-300
-150
0
150
300
450
600
-200 -100 0 100 200 300 400
Temperature [oC]
sy
- s
y(re
f)
[MP
a]
HY-130 Plate
Maraging Steel Plate
HY-130 Weld
Predict ion
0
50
100
150
200
250
300
-200 -150 -100 -50 0 50
Temperature [oC]
1T E
qu
iv.
KJ
c
[MP
a*m
0.5
] 18Ni (250) Maraging, Sy=1696 MPa(Shoemaker & Rolfe)
To = -74C
Ferritic Steel (BCC) Martensitic Steel (HCP)Yi
eld
Dat
a Co
mpa
red
to
Zeril
li-Ar
mst
rong
Toug
hnes
s D
ata
Com
pare
d to
M
aste
r Cu
rve
Match
No Match
Match
No Match
sy(ref) = room temperature yield strength
Figure 5.1. Demonstration that materials having a temperature dependence of the flow stress characteristic of a BCC lattice also have fracture toughness data that matches the Master Curve while non-BCC materials do not [Kirk 00b].
41
200
400
600
800
1000
1200
-200 -100 0 100 200
T(°C)
Un-Irradiated
KJc
y
KJcy
Irradiated
y
(MP
a) &
KJ
c(M
Pa
m) 6
200
400
600
800
1000
1200
-200 -100 0 100 200
T(°C)
Un-Irradiated
KJc
y
KJcy
Irradiated
y
(MP
a) &
KJ
c(M
Pa
m) 6
200
400
600
800
1000
1200
-200 -100 0 100 200
T(°C)
Un-Irradiated
KJc
y
KJcy
Irradiated
y
(MP
a) &
KJ
c(M
Pa
m) 6
200
400
600
800
1000
1200
-200 -100 0 100 200
T(°C)
Un-Irradiated
KJc
y
KJcy
Irradiated
y
(MP
a) &
KJ
c(M
Pa
m) 6
200
400
600
800
1000
1200
-200 -100 0 100 200
T(°C)
Un-Irradiated
KJc
y
KJcy
Irradiated
y
(MP
a) &
KJ
c(M
Pa
m) 6
200
400
600
800
1000
1200
-200 -100 0 100 200
T(°C)
Un-Irradiated
KJc
y
KJcy
Irradiated
y
(MP
a) &
KJ
c(M
Pa
m) 6
Figure 5.2. Prediction of transition curve shapes using and RKR-type model with a constant cleavage fracture stress [Odette 00]. Odette et al. suggest a number of candidate reasons for why the RKR-type models fail to accurately predict experimentally observed trends in fracture toughness data for steels having high transition temperatures: Irradiation induced damage decreases in the
strain hardening rates reduce the amplitudes of the crack tip stress fields and also enhances constraint loss, or
Reductions in ductile tearing resistance could mask a decrease in cleavage toughness, or.
The cleavage fracture stress could increase at higher temperatures rather than remaining constant.
These effects would in general vary from steel to steel and so do not rationalize a universal Master Curve common to all ferritic steels. However, Odette et al. suggest that a RKR-type model could be reconciled with empirical evidence provided the intrinsic micro-arrest toughness (Kmicro) of the ferrite matrix increases with temperature, thereby signaling an increase with temperature of the cleavage fracture stress. Odette notes that the Kmicro at micro-cleavage is sensitive to the local dislocation mobility and, therefore, to the temperature and strain rate. Since this dislocation motion is local to the microcrack tip, the lattice friction, or Peierl’s,
stress controls dislocation mobility. Consequently, the temperature dependence of Kmicro (and therefore the cleavage fracture stress) should be related to the thermally activated component of the flow stress which, as demonstrated by Natishan et al. and illustrated in Figure 5.1 (upper right hand graph), is a feature common to all ferritic steels. Figure 5.3 illustrates that by assuming a modest increase in the cleavage fracture stress above 0C Odette et al. were able to predict an exponential increase of toughness with temperature across a wide spectrum of absolute transition temperatures, in qualitative agreement with the Master Curve. Thus, this work suggests a means by which a Master Curve temperature dependence common to all ferritic steels can be rationalized. However, a direct linkage between toughness values and the micro-scale physical parameters, and a demonstration that these micro-scale parameters are indeed a common feature to all ferritic steels is currently lacking. 5.1.2.3 Summary The work recently advanced by both Natishan and Odette suggests that an understanding of the physical basis for a universal Master Curve shape may be close at hand. While differing in details of the model and the method of explanation, both investigators point to the temperature dependence of the lattice friction (Peierl) stress (i.e. the temperature dependent part of the flow stress) as the factor that explains a temperature dependence of transition fracture toughness common to all ferritic steels. The method Natishan et al. use to build their model is useful from an application perspective. In starting from basic dislocation mechanics and incorporating empirical evidence only as a validation these investigators provide a clearly theoretical model untainted by empiricism. Ultimately this approach offers the best promise of allaying fears of applying the Master Curve beyond its applicability limits. Odette et al. employ empiricism much earlier in the model development process, thereby raising questions regarding the predictive capabilities of their model. Nevertheless, demonstration of a Master Curve-type trend of toughness vs. temperature by this method provides an encouraging
42
indicator of the ultimate success of these research activities.
0
50
100
150
200
-200 -100 0 100 200 300
T(°C)
KJc
(MP
am
)
y
Increasing
y / 5.7
CFS/20
0
50
100
150
200
-200 -100 0 100 200 300
T(°C)
KJc
(MP
am
)
y
Increasing
y / 5.7
CFS/20
Figure 5.3. Prediction of transition curve shapes using and RKR-type model with a non-constant cleavage fracture stress [Odette 00].
5.2 Empirical Evidence 5.2.1 Database When ASME adopted the KIc curve in 1973, the data basis consisted of 173 quasi-static fracture toughness experiments ranging in size from 1T to 11T performed on 11 heats of unirradiated RPV steel and welds [Marston 78]. Considerably more toughness data for a broader range of material conditions is now available. Appendix A summarizes the contents of a database assembled to validate the Master Curve description of fracture toughness in the transition regime**. The database includes a total of 6,534 fracture toughness records. It contains information on welds, plates, and
** The author began development of this database
under EPRI funding while he was employed by the Westinghouse Electric Company (1998-1999). The database has been expanded upon since that time, to include both recently developed information as well as information obtained from the literature. The author is indebted to EPRI for permitting use of the database for the purpose of preparing this report.
forgings used in the fabrication of nuclear RPVs. These include tests conducted both before and after neutron irradiation. Furthermore, cognizant that breadth of conditions represented by these data may not capture the full diversity of conditions in the operating nuclear fleet, we also examine available data for ferritic non-RPV steels in this analysis. These non-RPV steels can differ more from each other, and from RPV steels, than any two heats of RPV steel differ from one another. Consequently, use of data for non-RPV steels supports a more comprehensive examination of Master Curve applicability than would be possible otherwise. Figure 5.4 demonstrates that the non-RPV steels both cover and extend the range of tensile properties of the nuclear RPV steels, both before and after irradiation.
0
25
50
75
100
125
150
0 25 50 75 100 125 150
Ambient Yield Strength [ksi]
Am
bie
nt
Ult
ima
te S
tre
ng
th [
ks
i]
RPV Steel, Un-Irradiated
RPV Steel, Irradiated
Non RPV Steel
Figure 5.4. Comparison of the room temperature (engineering) tensile properties of the various steels in the fracture toughness database.
5.2.2 Statistical Model The Master Curve includes two relationships that describe the distribution of fracture toughness values at a single temperature, Eq. 4-9, and the effect of specimen size (crack front length) on fracture toughness, Eq. 4-13. As detailed in Section 4.2.2.2, Eq. 4-13 derives mathematically from Eq. 4-9 without any assumptions. In this section we compare available fracture toughness data to the mathematical form of these relationships.
43
5.2.2.1 Distribution of Fracture
Toughness at a Fixed Temperature
The three-parameter Weibull probability distribution included as part of the Master Curve is as follows:
Eq. 5-8 p
o
Jcf KK
KKp
min
minexp1
The minimum and shape parameters of this distribution, Kmin and p, are fixed at 20 MPam and 4, respectively, leaving testing to determine only the location parameter, Ko. Here we assess how well these fixed Kmin and p values represent available fracture toughness data 5.2.2.1.1 A Fixed Shape Parameter
of 4 Eq. 5-8 can be represented graphically as a straight line having a slope of 4 on a plot of ln{ln(1 – Pf)} vs. ln{KJc – 20} (KJC in MPam). To determine how well a fixed slope of 4 represents available fracture toughness data, a Weibull slope was fit to available data for comparison with the theoretically expected value of 4. The procedure used to establish this fit is as follows:
1. A data set is identified that includes at least three KJc values satisfying ASTM E1921-97 validity requirements (eq. (19)) measured at a single temperature and a single loading rate using a single specimen size. The data set must have a median fracture toughness above 50 MPam.
2. The KJc values are rank ordered and assigned the following value as an estimate of the median rank probability:
Eq. 5-9 4.0
3.0
N
iPf
where i is the order of the KJc value and N is the total number of KJC values.
3. The (Pf, KJC) data pairs are used to calculate (X*,Y*) data pairs, where X*= ln{KJc – 20} and Y*= ln{ln(1 – Pf)}. A line is fit through the (X*,Y*) data using the method of least squares. This best fit slope is compared with the theoretical value of 4.
The result of this analysis is presented in Figure 5.5, and compared with the confidence bounds reported by Wallin [Wallin 84c]. Of the 399 calculated slope values, 6.8% fall outside of the 5%/95% confidence bounds. Thus, the assumption of an underlying distribution having a Weibull shape parameter of 4 is consistent with experimental evidence taken from a wide variety of ferritic steels. 5.2.2.1.2 Fixed Minimum Value, Kmin
= 20 MPam The analysis of the preceding section presumes a Kmin value of 20 MPam. Wallin established this Kmin value in 1984 by inspection of the plots shown in Figure 4.4, which showed a Kmin value of 20 MPam to bring the expected confidence bounds (calculated by Monte Carlo simulation using the assumed distributional form) into best accord with the experimental evidence then available. Figure 5.5 demonstrates that this same conclusion remains justified today. More recently Wallin has published a method to estimate Kmin from an experimental dataset using the method of maximum likelihood [Wallin 98], as follows: Eq. 5-10
(a)
01
ˆ
ˆˆ
4
3
1
3
min
1 1
4
minmin
N
ii
N
i
N
ii
i
i
KKr
KKKK
(b)
min
4/1
1
4
minˆ
2ln1
ˆ
Kr
KK
K
N
iI
o
(c) 1
ˆmin
min
r
KKrK o
44
where r is the number of KJC values that satisfy Eq. 4-16. A value of minK̂ is selected to satisfy eq. Eq. 5-10 (a). Kmin is then determined by solving eqs. Eq. 5-10 (b) and (c).
Note: 1. Only E1921 Valid Data Used to Determine the Best Fit Weibull Slope. 2. 6.8% of 399 datum outside of confidence bounds.
1
10
100
1 10 100
r , Number of E1921 Valid K Jc Tests
Be
st
Fit
We
ibu
ll S
lop
e
RPV, Unirradiated
RPV, Irradiated
Non-RPV
Dynamic
95% UB
5% LB
Slope=4
Figure 5.5. Comparison of Weibull slopes calculated from fracture toughness data with 5%/95% confidence bounds on the expected slope of 4.
-100
-80
-60
-40
-20
0
20
40
60
80
100
-150 -100 -50 0 50 100 150
T-To [oC]
Km
in [
MP
a*m
0.5 ]
Figure 5.6. Comparison maximum likelihood estimates of Kmin with the customary value of 20 MPam.
The confidence bounds on this estimate of Kmin depend on both r and on the ratio of Ko to Kmin [Wallin 98]. In practical terms, only large datasets obtained at temperatures below To provide any meaningful commentary on the value of Kmin. Therefore, in our empirical evaluation of Kmin we restricted attention to data sets having at least 20 measured KJC values. Figure 5.6 summarizes the Kmin values calculated from these data using Eq. 5-10. This analysis suggests that a fixed Kmin value of 20 MPam is appropriate for analysis of ferritic steels in fracture mode transition.
5.2.2.2 Effect of Specimen Size (Crack Front Length) on Fracture Toughness
In Section 4.2.2.2 we demonstrated that, having established a three-parameter Weibull distribution with a fixed Kmin and slope as an appropriate characterization of the distribution of fracture toughness at a fixed temperature, the ¼-power relationship between specimen “size” (i.e. crack front length) and fracture toughness follows mathematically without further approximation. Thus, the good agreement established between experimental data and a slope of 4 (Section 5.2.2.1.1) and a Kmin of 20 MPam (Section 5.2.2.1.2) suggests that experimental data should also agree well with the form of Eq. 4-13, i.e. Eq. 5-11
4/1
min)(min)(
x
y
yJcxJc B
BKKKK
Previously both Rathbun et al. and Kirk et al. have examined the appropriateness of the ¼-power scaling rule by comparing the predictions of Eq. 5-11 with fracture toughness data [Rathbun 00, Kirk 98a]. While differing in some analytical details, both investigations concluded that Eq. 5-11 represents the trends in available fracture toughness data well. We do not repeat a similar analysis herein because it is exceedingly difficult to resolve the rather weak ¼-power thickness dependence against the background of scatter characteristic of cleavage fracture in transition. Alternatively, we have identified the most substantial data sets in the database for analysis (i.e. widest range of specimen sizes tested with the highest number of replicate tests and all KJC values below the E1921-97 deformation limit, Eq. 4-16. Table 5.1summarizes the results of this analysis, and Figure 5.7 includes four of the largest data sets in for inspection. While a “best fit” exponent through these data sometimes deviates from the ¼-power of Eq. 5-11, both a statistical test and inspection of the data show these differences to be statistically insignificant. Thus, available fracture toughness data does not provide any compelling evidence that the exponent on
45
thickness in Eq. 5-11 should be anything other that the value of ¼ derived by Wallin from theoretical considerations for failure under small scale yielding conditions. It is appropriate to note two other findings here. First, during development and after the adoption of ASTM standard E1921-97 there was a question regarding if the ¼-power exponent was purely the result of a statistical size effect, or if this effect might also be attributed in part to loss of constraint in small specimen sizes. In a recent investigation Rathbun et al. varied ligament and thickness independent of each other [Rathbun 00]. This contrasts with the conventional practice of scaling all specimen dimensions in geometric proportion to one another (see Figure 5.8). Rathbun et al.
generated a data set capable of differentiating statistical size effects (various thicknesses with ligament dimension held constant) from loss of constraint effects (various ligament lengths with thickness held constant). Their data, already presented in Figure 5.7, demonstrates that the effect of specimen thickness (with ligament dimension held constant) does indeed scale with a ¼-power on thickness, as demonstrated by the much larger body of data on proportionally sized specimens. Of equal importance, these investigators found no significant effect of ligament dimension on cleavage fracture toughness with thickness held constant (see Figure 5.9), demonstrating that within the bounds of E1921-97 validity there is no competing loss of constraint effect for the ¼ power size effect to be confused with.
Table 5.1. Summary of data sets used to assess ¼-power exponent on thickness in Eq. 5-11.
Author Prod. Form
RPV Steel?
Material Test
Temp. [oF]
To [oF]
T-To [oF]
# of Geom.
# KJc Values
(r)
Fit Exponent on Thickness
Exp. Std.
Error,
# of between fit exponent & 1/4 power
Rathbun, H.J.
Plate Yes
A533B Cl. 1 (Shoreham)
-132 -134 2 3 24 0.167 0.123 0.67
Rathbun, H.J. A533B Cl. 1 (Shoreham)
-132 -134 2 6 49 0.266 0.050 0.32
McCabe, D.E. A533B Cl. 1 (Plate 13A)
-103 -110 7 4 64 0.197 0.076 0.70
Chaouadi, R. A533B Cl. 1 -13 47 -60 4 46 0.295 0.084 0.53
Joyce, J. A533B Cl. 1 (Shoreham)
-180 -121 -59 3 24 0.065 0.248 0.74
Sorem, W.A. No A36 -105 -65 -40 4 44 0.292 0.073 0.58
McCabe, D.E.
Weld
Yes
Linde 80, Heat 72105
-58 -70 12 3 17 0.206 0.113 0.39
Nanstad, R.K. Linde 0124, Heat 87984
-58 -70 12 3 13 0.262 0.115 0.11
Nanstad, R.K. Linde 0124, Heat 87986
-58 -78 20 3 13 0.198 0.142 0.37
Wallin, Kim Forging
22NiMoCr37 -132 -124 -8 4 110 0.174 0.039 1.95 Iwadate, T. A508 Cl. 3 -76 -54 -22 3 39 0.178 0.100 0.73 Alexander, D.J. A508 Cl. 2 0 -2 2 3 19 0.203 0.165 0.28
46
[Rathbun, b=0.5-inch]
0
50
100
150
200
0.0 0.5 1.0 1.5 2.0
B max [inches]
KJc
[k
si*
in0.
5 ] Valid
Theory: 0.25 Power
Fit: 0.17 Power
[Rathbun, b=1-inch]
0
50
100
150
200
250
0 2 4 6 8 10
B max [inches]
KJc
[k
si*
in0.
5 ]
Valid
Theory: 0.25 Power
Fit: 0.27 Power
[Wallin, 22NiMoCr37 Forging]
0
50
100
150
200
0 1 2 3 4 5
B max [inches]
KJc
[k
si*
in0.
5 ]
Valid
Theory: 0.25 Power
Fit: 0.174 Power
[McCabe, Plate 13A]
0
50
100
150
200
0 1 2 3 4 5
B max [inches]
KJc
[k
si*
in0.
5 ]
Valid
Theory: 0.25 Power
Fit: 0.197 Power
Figure 5.7. Comparison of fracture toughness data with the ¼-power trend on thickness assumed by Master Curve technology. Finally, it is often noted in descriptions of the Master Curve methodology that the weakest link effect “disappears” on lower shelf [Merkle 98, Wallin 98]. In this temperature regime the resistance to crack initiation is sufficiently low that the cleavage initiators (carbides) crack almost instantly upon application of load, making the controlling event for macroscopic fracture propagation of these initiated microcracks into the surrounding grains. Propagation controlled fracture on the lower shelf is not expected to exhibit a weakest-link size effect, and for this reason E1921-97 does not apply below a median (1T equivalent) fracture toughness of 50 MPam. In identifying large data sets to which the ¼-power scaling rule could be compared, we also located several lower shelf data sets. These data, summarized in Figure 5.10, suggest that the restrictions placed on Master Curve technology and on the
applicability of the E1921-97 standard with regard to the characterization of lower shelf are appropriate. 5.2.3 Temperature Dependency of
Fracture Toughness As discussed in Sections 4.2.3 and 5.1.2, the Master Curve assumes that the median fracture toughness of a steel (when normalized to 1T size) varies with temperature according to the following relationship: Eq. 5-12 omedianJc TTK 019.0exp7030)(
47
0
2
4
6
8
10
0 2 4 6 8 10
Specimen Thickness [in]
Sp
ecim
en W
idth
[i
n]
Rathbun
Others
W=B
W=2B
Figure 5.8. Comparison of the range of specimen sizes tested by Rathbun with those characteristic of the remainder of the database.
[Rathbun, B max =0.313-inch]
0
50
100
150
200
250
0.00 0.25 0.50 0.75 1.00
Ligament (b ) [inches]
KJc
[k
si*
in0.
5 ]
B=0.313, Valid
B=0.313, Not Valid
[Rathbun, B max =0.625-inch]
0
50
100
150
200
250
0.00 0.25 0.50 0.75 1.00
Ligament (b ) [inches]
KJc
[k
si*
in0.
5 ]
B=0.625, Valid
B=0.625, Not Valid
[Rathbun, B max =1.25-inch]
0
50
100
150
200
250
0.00 0.25 0.50 0.75 1.00
Ligament (b ) [inches]
KJc
[k
si*
in0.
5 ]
B=1.25, Valid
B=1.25, Not Valid
Figure 5.9. Effect of ligament dimension with specimen thickness held constant for an A533B Cl. 1 plate (ex-Shoreham) [Rathbun 00].
Wallin22NiMoCr 37 Forging
-245oF
0
10
20
30
40
50
60
0 1 2 3
Thickness [inches]
KJc
[k
si*
in0.
5 ]
McCabeA533B Cl. 1 - Plate 13A
-238oF
0
10
20
30
40
50
60
0 1 2 3
Thickness [inches]
KJc
[k
si*
in0.
5 ]
Figure 5.10. Effect of specimen thickness on lower shelf fracture toughness.
48
where K is in MPam and T is in C. If this functional form provides an appropriate description of a particular data set, the variation of the fracture toughness residuals (i.e., the deviation of an experimental KJC value from the prediction of Eq. 5-12) with temperature will have zero slope and zero y-intercept, as illustrated in Figure 5.11. In this section, the goodness-of-fit of the Master Curve to available experimental data is assessed relative to this criteria. The following analytical procedure is employed:
1. A data set having KJC values measured for at least two temperatures is identified.
2. All cleavage fracture toughness data are considered irrespective of if they satisfy ASTM E1921-97 validity requirements (Eq. 5-12) or not. As illustrated in Figure 5.12, censoring the KJC values per ASTM biases the KJC residuals toward negative values. Such a bias inappropriately penalizes this assessment of the Master Curve temperature dependence, making use of “invalid” cleavage fracture toughness values necessary for this comparison.
3. A To value is calculated for the data set using the multiple temperature technique, see Appendix B
4. All measured toughness values are converted to 1T equivalence Eq. 5-11and are plotted along with the Master Curve (Eq. 5-12).
5. The KJc -residual (i.e., the vertical distance from a datum to the Master Curve) is calculated and plotted on a second graph at the same T- To value.
6. A best fit slope and intercept is estimated from the variation of KJc -residual vs. T- To using the method of least squares. If properly describes the variation of toughness with temperature, these slope and intercept values should be statistically indistinguishable from zero. We test for this condition by applying Student’s T-test at a 99% confidence level.
The tables in Appendix C summarize the results of these analyses for 222 separate data sets, divided into the following categories:
Table Matl. Loading
Rate Irradiation Figure
C-1 RPV
Static
Unirradiated Figure 5.13
C-2 RPV Irradiated Figure 5.14
C-3 Non-RPV
Unirradiated
Figure 5.15
C-4 RPV High
Figure 5.16
C-5 Non-RPV
Figure 5.17
The figures listed above illustrate some of the largest data sets from each category in the database; all show statistically insignificant variations from the Master Curve shape. The results of this statistical assessment of curve shape, summarized in Appendix C, demonstrate that the great majority of available data do not differ from the Master Curve in a manner that suggests that another temperature dependence would be more appropriate. Table 5.2 summarizes the 28 data sets from that exhibit a statistically significant deviation from the Master Curve shape. Plots of all of these data in the format suggested by Figure 5.11 are included in Appendix D for completeness. Here we examine a number of different reasons why statistically significant deviations from the Master Curve temperature dependence occur: Data on the Upper Shelf: As detailed in
Sections 4.1 and 5.1.2, the Master Curve assumes that deformation prior to fracture occurs by dislocation glide. This assumption limits use of the Master Curve method to the transition regime since upper shelf is hole-growth dominated. If a data set has too many KJc values on the upper shelf the statistical assessment illustrated in Figure 5.11 will identify a significant difference between the Master Curve temperature dependence and that of the data being examined. Inclusion of upper shelf data caused five data sets to show statistically significant deviations from the Master Curve temperature dependence. Consequently, these data do not indicate
49
that a different temperature dependency from that of the Master Curve is needed; rather they provide a means to define an upper temperature limit for Master Curve applicability. Examination of these data (see Appendix B) demonstrates that at temperatures more than 150F (83C) above To significant deviations from the Master Curve shape occurs. Previous discussions in ASTM Committee E08 have suggested a limit of 90F (50C) above To. These data suggest that the ASTM limit may be unnecessarily restrictive.
Data on the Lower Shelf: As detailed in
Sections 4.1 and 5.1.2, the Master Curve assumes that deformation prior to fracture occurs by dislocation glide. This assumption limits use of the Master Curve
method to the transition region since the lower shelf is twinning dominated. If a data set has too many, or all, KJC values on the lower shelf the statistical assessment illustrated in Figure 5.11will identify a significant difference between the Master Curve temperature dependence and that of the data being examined. Inclusion of lower shelf data caused seven data sets to show statistically significant deviations from the Master Curve temperature dependence. Consequently, these data do not indicate that a different temperature dependency from that of the Master Curve is needed.
T - To
KJc
KJc
Residual
DataBounds
MasterCurve
T - To
KJ
c R
esid
ua
l
KJc residuals which suggestthat the Master Curve hasanappropriate shape.
T - To
KJc
Res
idu
al
KJc residuals which suggestthat a different shape thanthe Master Curve.
T - To
KJc
KJc
Residual
DataBounds
MasterCurve
T - To
KJc
KJc
Residual
DataBounds
MasterCurve
T - To
KJ
c R
esid
ua
l
KJc residuals which suggestthat the Master Curve hasanappropriate shape.
T - To
KJ
c R
esid
ua
l
KJc residuals which suggestthat the Master Curve hasanappropriate shape.
T - To
KJc
Res
idu
al
KJc residuals which suggestthat a different shape thanthe Master Curve.
T - To
KJc
Res
idu
al
KJc residuals which suggestthat a different shape thanthe Master Curve.
Figure 5.11. Procedure for evaluating Master Curve shape relative to fracture toughness data..
50
All Data
-300
-200
-100
0
100
200
300
-300 -150 0 150 300
T - T o [oF]
KJc
| 1T
- K
Jc| M
edia
n [
ksi*
in0.
5]
Only ASTM Valid Data
-300
-200
-100
0
100
200
300
-300 -150 0 150 300
T - T o [oF]
KJc
| 1T
- K
Jc| M
edia
n [
ksi*
in0.
5]
All Data
-300
-200
-100
0
100
200
300
-300 -150 0 150 300
T - T o [oF]
KJc
| 1T
- K
Jc| M
edia
n [
ksi*
in0.
5]
Only ASTM Valid Data
-300
-200
-100
0
100
200
300
-300 -150 0 150 300
T - T o [oF]
KJc
| 1T
- K
Jc| M
edia
n [
ksi*
in0.
5]
Figure 5.12. Effect of eliminating invalid data on KJC residual plot..
A533B Cl. 1 PlateShoreham Vessel
Tests by Joyce and Rathbun
-200
-100
0
100
200
-150 -75 0 75 150
T-T o [oF]
De
via
tio
n f
rom
M
ed
ian
Ma
ste
r
Cu
rve
[k
si*
in0.
5 ]
Invalid
Valid
Figure 5.13. Deviation of KJC data from the Master Curve for an un-irradiated RPV steel tested at quasi-static loading rates [Joyce 00, Rathbun 00].
51
NanstadLinde 0124 Weld (72W)
Irradiated to 1.5E19
-200
-100
0
100
200
-200 -100 0 100 200
T-T o [oF]
De
via
tio
n f
rom
M
ed
ian
Ma
ste
r
Cu
rve
[k
si*
in0.
5 ]
Invalid
Valid
Figure 5.14. Deviation of KJC data from the Master Curve for an irradiated RPV steel tested at quasi-static loading rates [Nanstad 96].
SoremA36
-150
-75
0
75
150
-300 -200 -100 0 100
T-T o [oF]
De
via
tio
n f
rom
M
ed
ian
Ma
ste
r C
urv
e
[ks
i*in
0.5 ]
Invalid
Valid
Figure 5.15. Deviation of KJC data from the Master Curve for a non-RPV steel tested at quasi-static loading rates [Sorem 89].
52
IshinoGeneric RPV Plate
KDOT=90,900
-200
-100
0
100
200
-150 -100 -50 0 50 100 150 200
T-T o [oF]
De
via
tio
n f
rom
M
ed
ian
Ma
ste
r
Cu
rve
[k
si*
in0.
5 ]
Invalid
Valid
Figure 5.16. Deviation of KJC data from the Master Curve for an un-irradiated RPV steel tested at a high loading rate [Ishino 88] .
JoyceA515 Gr. 70
(open points invalid per E1921)
-75
-50
-25
0
25
50
75
-300 -250 -200 -150 -100 -50 0
T-T o [oF]
De
via
tio
n f
rom
M
ed
ian
Ma
ste
r
Cu
rve
[k
si*
in0.
5 ]
Static
70
9089
61971
Figure 5.17. Deviation of KJC data from the Master Curve for a non-RPV steel tested at elevated loading rates [Joyce 97].
53
Table 5.2. Summary of data sets that deviate from Master Curve assumed temperature dependency (see Appendix D for plots).
Upper Shelf
Lower Shelf
MartesiticAcceptable on
InspectionA Few Highly
Influencial DataUnknown
92 39 Wallin, Kim Forging 22NiMoCr37 "EURO" 636 X3 1 Marston, T.U. Forging A508 Cl. 2 13 X
26 10 Iwadate, T. Forging A508 Cl. 3 153 X27 11 Lidbury, D. Forging A508 Cl. 3 119 X10 1 Marston, T.U. Plate A533B Cl. 1 Plate 02 70 X15 7 Ingham, T. Plate A533B Cl. 1 217 X17 6 McCabe, D.E. Plate A533B Cl. 1 Plate 13A 121 X66 26 Chaouadi, Rachid Plate A533B Cl. 1 JSPS Plate 164 X69 31 Ishino, S. Plate Generic Plate 25 X
30 18 CEOG WeldShoreham Weld 20291/12008
Linde 1092 31 X
65 20 Hawthorne, J.R. Weld Linde 0124 8 X70 31 Ishino, S. Weld 26 X
19 13 Nanstad, R.K. WeldWeld, Midland Beltine
Linde 80 50 X X
20 13 Nanstad, R.K. WeldWeld, Midland Nozzle
Linde 80 28 X X
122 52 Krabiell, Armin Plate St E 47 18 X107 44 Shoemaker, A.K. Plate 18Ni(250) 17 X105 44 Shoemaker, A.K. Plate HY-130 6 X147 60 Hasson, D.F. Plate HY-130 8 X113 46 Fujii, E. (KDOT=83) Forging A508 Cl. 3 9 X113 46 Fujii, E. (KDOT=16,526) Forging A508 Cl. 3 9 X10 40 Shabbits, W.O. Plate A533B Cl. 1 Plate 02 8 X91 38 Link, Richard Plate A533B Cl. 1 Plate 14A 8 X
Yes 69 31 Ishino, S. Plate Generic Plate 12 X115 48 Holtmann, M. Plate 2.25Cr-1Mo 13 X101 44 Shoemaker, A.K. Plate ABS-C 12 X121 52 Krabiell, Armin Plate St 52-3 18 X122 52 Krabiell, Armin Plate St E 47 7 X122 52 Krabiell, Armin Plate St E 47 11 X
Welding FluxM
AT
Yes
No
Reason for Deviation of Data from Master Curve Temperature Depencence
Sta
tic?
Irra
d?
RP
V?
# SampleAuthor ProductMaterial
Specification
NoNo
CIT Special
Designation
Yes
No
Yes
Yes
No
No
54
Martensitic Steels: As detailed in Section
5.1.2, the Master Curve temperature dependency is expected to apply only to ferritic materials, i.e. to materials having a FCC lattice structure. Other materials that exhibit cleavage but have a different inter-atomic spacing present a different barrier distance to dislocation motion, and therefore are expected to exhibit a different temperature dependency. Three data sets for martensitic steels were identified as having statistically significant deviations from the Master Curve shape. Martensitic steels have a HCP lattice structure, and consequently are not expected to exhibit the same variation of fracture toughness with temperature as ferritic steels. Therefore, these data do not indicate that the Master Curve should have a different temperature dependency, but rather help to validate the theoretical limits on Master Curve applicability detailed in Section 5.1.2.
Data Anomalies: Two data sets that failed the statistical test for similarity with the Master Curve temperature dependence nevertheless failed to visually show any significant differences between the data and the Master Curve. Also, in four data sets the reason for the statistically significant difference between the data and the Master Curve could be traced to a very few highly influential KJC values.
These rationale explain the statistical deviation of 19 out of the 28 data sets that showed a statistically deviation from the Master Curve shape, leaving only 9 data sets having no readily apparent reason for being at variance with the Master Curve. Table 5.3 summarizes the results of this analysis, and demonstrates that the great preponderance of available data (over 96%) supports the existence of a universal transition curve shape for ferritic steels, and validates that the Master Curve, Eq. 5-12, well represents the numerical expression of this relationship.
Table 5.3. Summary of experimental assessment of Master Curve temperature dependence.
RPV Steel? Irradiated? Static? Table # Data
Sets
# of Data Sets that Don't Match the
Master Curve Temperature Dependence
% Conforming to Master
Curve Temperature Dependence
Yes No Yes 3 74 2 97% Yes Yes Yes 4 68 2 97% No No Yes 5 (19-3) 0 100% Yes No No 6 30 4 87% Yes Yes No 6 5 1 80% No No No 7 (26-1) 0 100%
218 9 96%
Note: Entries having a (xx-y) notation indicate that y data sets were removed from the total because they are for martensitic steels.
55
6 TECHNICAL BASIS OF THE E1921-97 TESTING STANDARD
In this section we examine the technical basis for various aspects of the ASTM E1921-97standard, which is used to estimate the Master Curve index temperature To. Specifically we examine the followings factors: Requirements on the degree of data
replication, and guidelines on uncertainty bounds for To values.
The permissible range of test temperatures Deformation / constraint limits
A previous NUREG by Merkle et al. discussed in detail statistical methods for estimating the Master Curve parameters Ko and To [Merkle 98]. These aspects of the testing standard are therefore not considered further herein.
6.1 Degree of Data Replication E1921-97 requires that a minimum of six valid fracture toughness samples be tested to estimate To provided the test temperature for the specimens is close to To. At lower test temperatures more replication is needed to compensate for the reduced sensitivity of fracture toughness to test temperature, which increases uncertainty in the estimated To value. Table 6.1 outlines the degree of data replication required by E1921. Regardless of the test temperature, the accuracy of any To determination obviously depends on the number of specimens tested. The requirements of E1921-97 for data replication expressed in Table 6.1 therefore reflect an engineering judgment regarding how well To should be estimated. Consequently, the replication requirements of E1921-97 are not nearly as important as how accurately E1921-97 procedures estimate the standard deviation of a To value (also summarized in Table 6.1). In Figure 6.1 we
compare these estimates to the standard deviation of 1,000 To values simulated by randomly drawing KJC values from a 3 parameter Weibull distribution having a slope of 4, and a minimum of 20 MPam over a range of Ko (and thereby To) values. These comparisons suggest that the E1921-97 estimate of To standard deviation is conservative (too high) by between one and two degrees centigrade.
6.2 Permissible Range of Test Temperatures
ASTM E1921-97 employs KJC values to determine To provided two conditions are satisfied: The estimated median KJC value exceeds 50
MPam, and Between 6 and 10 of the measured KJC
values satisfy the size requirement of ASTM E1921-97, Eq. 4-16.
Table 6.1. Replication requirements and estimated standard deviation for To from E1921-97.
A 1T-Equivalent KJC (Median) of at least (MPam) …
… must be determined based on at least this many valid specimens.
The Standard Deviation of this To Estimate will be [C]
84 6 18/r 66 7 18.8/r 58 8 20.1/r 53 9 21.4/r 50 10 22.7/r Below 50 Not valid per E1921-97
56
0
2
4
6
8
10
12
14
0 5 10 15
Number of Samples Used to Determine To
Sta
nd
ard
De
via
tio
n o
f 1
00
0 T
o
De
term
ina
tio
ns
[oC
] E1921 @ T-To > -25C
T-To = 0C
T-To = -25C
T-To = +25C
T-To = +50C
0
2
4
6
8
10
12
14
0 5 10 15
Number of Samples Used to Determine To
Sta
nd
ard
De
via
tio
n o
f 1
00
0 T
o
De
term
ina
tio
ns
[oC
]
E1921 @ T-To = -50C
T-To = -50C
Figure 6.1. Comparison of uncertainty in To estimates determined by Monte Carlo simulation (points) with the recommendation of E1921-97 (curves). This latitude of permissible test conditions has led to concerns regarding the possibility of a systematic variation of To with temperature [Mayfield 97]. It should, however, be noted that a systematic variation is not anticipated. Such a variation would only exist if the shape of the Master Curve varied from material to material within the limits imposed by E1921-97. As discussed in Section 5.1.2, these limits restrict the test temperature to the transition regime where deformation prior to fracture occurs by deformation glide. Within these limits the theoretical basis for a single Master Curve for all ferritic steels is sound, so the material dependence of the Master Curve shape needed to produce a systematic variation of To with test temperature is not expected to occur. In this section we attempt to validate this theoretical expectation by examining the database for evidence of any systematic bias with test temperature in To values determined as per E1921-97. We quantify this bias as the difference between a To value estimated using
data from a fully developed transition curve using a multi-temperature (MT) approach (see Appendix C) and a To value estimated in accord with E1921-97 protocols based on KJC data taken at a single test temperature. While both of these To values are estimates, the To value determined from the full transition curve is regarded as a better experimental estimate because it is based on a larger data set than an E1921-97 To (To bias was only calculated if the number of KJC values used for the MT To estimate exceeded the number of KJC values used for the E1921-97 To estimate by a factor of 3 or greater). Figure 6.2 demonstrates that the difference between these two To estimates shows no systematic bias or trend with test temperature, confirming the theoretical expectation that To values do not depend on the temperature at which the KJC experiments were conducted provided all of the requirements of E1921-97 are satisfied. These data also suggest that the need for a proposed revision of E1921-97 to further limit the range of permissible test temperatures to To 50C (dashed vertical lines on Figure 6.2) is not justified based on currently available data.
6.3 Deformation / Constraint Limits
6.3.1 General As discussed in Section 4.2.2, the Master Curve approach applies only to conditions of small-scale yielding, i.e. that deformation state for which the crack-tip stress fields at fracture are not influenced by the finite size of the specimen used to make the measurement. During development of the E1921-97 standard, candidate deformation limits were initially assessed based on the results of three-dimensional finite element (FE) analysis conducted by Dodds and co-workers [Nevalenin 95, Ruggeri 98]. These investigators modeled both SE(B) and C(T) specimens using a number different combinations of yield strength and hardening exponent. They used the FE models to quantify the non-dimensional deformation level, M, at which the crack-tip stress fields in a finite size specimen deviate by 20% from the
57
crack-tip stress fields characteristic of an infinite body. Stress fields provided the metric of comparison because the failure mode of interest for Master Curve testing is cleavage fracture which, in simple terms, occurs when a critical stress is achieved ahead of the crack tip [Ritchie 73]. M is determined by finite element analysis as follows:
Eq. 6-1 CTOD
b
J
bM
applied
flow
As suggested by Eq. 6-1, M carries the physical interpretation of the ratio of the unbroken ligament to the CTOD at the time of fracture. Eq. (35) can also be expressed as a deformation limit on KJc in the manner employed in E1921-97 (i.e., Eq. 4-16):
Eq. 6-2 M
EbK y
itJc
)(lim
Table 6.2 summarizes M-values determined by Dodds and co-workers based on their finite element analysis. These results suggest candidate M-limits of between 20 and 100 depending on the material flow characteristics. Some ambiguity inherently exists in a fully analytic determination of the appropriate deformation limit (M-value) to use in Eq. 6-2 because one must assume both a mathematical model of cleavage fracture and an appropriate characterization of the material on the micro-scale to make these calculations. Recognizing that questions regarding the appropriateness of such assumptions are not fully resolved, it is possible to gain additional evidence concerning an appropriate M-value by inspection of the Weibull probability plots for large data sets. As summarized in Section 4.2.1.1, a Weibull probability plot will exhibit a fixed slope of 4 provided the material at the crack tip is deforming in a state of small scale yielding [Wallin 84c]. When small-scale yielding conditions are violated the plastically deformed volume at the crack tip no longer scales in proportion with K4, which changes the slope on a Weibull probability plot. We use this change
in slope to assess the appropriateness of the M=30 deformation limit adopted within E1921-97 by examining Weibull probability plots for all data sets having at least 24 KJC values, at least a fourth of which are valid per the E1921-97 deformation limit (Eq. 4-16). Attention is restricted to large data sets so that the “break” point on the Weibull probability plot can be determined by inspection and compared with the E1921-97 deformation limit. Examination of probability plots for data sets meeting these criteria (Figure 6.3) demonstrate that the E1921-97 deformation limit of M=30 is appropriate for these materials and is, if anything, overly restrictive.
-80
-40
0
40
80
-150 -100 -50 0 50 100 150 200
T - T o [oF]
E1
92
1 T
o -
MT
To [
oF
]
RPV Un-Irradiated RPV Irradiated Dynamic Non-RPV Proposed Limits for E1921 Revision
Figure 6.2. Effect of test temperature on the bias of an E1921-97 estimate of To relative to a multi-temperature (MT) estimate of To. MT To estimates must have at least three times as many KJC values as E1921 To estimates.
Table 6.2. M Coefficients determined by Dodds and co-workers
Ref.Specimen
TypeSide
Groovea/W W/B n E/YS
M Value for 20%
Deviation from SSY
ND, 95 SE(B) 0% 0.5 1 5 500 25ND, 95 SE(B) 0% 0.5 2 5 500 25ND, 95 C(T) 0% 0.6 2 5 500 20
RDW, 98 SE(B) 0% 0.5 1 5 800 29RDW, 98 SE(B) 0% 0.5 1 10 500 66-125RDW, 98 SE(B) 20% 0.5 1 10 500 76-143ND, 95 SE(B) 0% 0.5 1 10 500 60ND, 95 SE(B) 0% 0.5 2 10 500 55ND, 95 SE(B) 20% 0.5 2 10 500 65ND, 95 C(T) 0% 0.6 2 10 500 45ND, 95 C(T) 20% 0.6 2 10 500 55
RDW, 98 SE(B) 0% 0.5 1 20 300 87-117RDW, 98 SE(B) 20% 0.5 1 20 300 97-105ND, 95 SE(B) 0% 0.5 1 20 500 115ND, 95 SE(B) 0% 0.5 2 20 500 115ND, 95 C(T) 0% 0.6 2 20 500 90
58
Va n De r Sluys - 1T C(T)
A508 Cl. 3 Forging a t -58oF
-6
-5
-4
-3
-2
-1
0
1
2
3
4
3 4 5 6 7
ln (K Jc - K m in )
ln(-
ln(1
-Pf)
) Da ta
Slope =4
E1921 KJc Lim it
Lidbury - 3.15T SE(B)
A508 Cl. 3 Forging at +5oF
-5
-4
-3
-2
-1
0
1
2
3
4
4 4.5 5 5.5 6 6.5 7
ln (K Jc - K min )
ln(-
ln(1
-Pf)
)
Data
Slope=4
E1921 KJc Limit
Wallin - 1/2T C(T)
22NiMoCr37 Forging at -76oF
-6
-5
-4
-3
-2
-1
0
1
2
3
4
3 3.5 4 4.5 5 5.5 6
ln (K Jc - K min )
ln(-
ln(1
-Pf)
)
Data
Slope=4
E1921 KJc Limit
Wallin - 1/2T C(T)
22NiMoCr37 Forging at -40oF
-6
-5
-4
-3
-2
-1
0
1
2
3
4
3 4 5 6 7
ln (K Jc - K min )
ln(-
ln(1
-Pf)
)
Data
Slope=4
E1921 KJc Limit
Wallin - 1T C(T)
22NiMoCr37 Forging at -4oF
-5
-4
-3
-2
-1
0
1
2
3
4
4.5 5 5.5 6 6.5
ln (K Jc - K min )
ln(-
ln(1
-Pf)
)
Data
Slope=4
E1921 KJc Limit
Wallin - 2T C(T)
22NiMoCr37 Forging at +32oF
-5
-4
-3
-2
-1
0
1
2
3
4 4.5 5 5.5 6 6.5 7
ln (K Jc - K min )
ln(-
ln(1
-Pf)
)
Data
Slope=4
E1921 KJc Limit
Wallin2.25Cr 1Mo Steel
-6
-3
0
3
4.0 4.5 5.0 5.5 6.0 6.5
ln (K Jc - K min )
ln(-
ln(1
-Pf)
)
Data
Slope=4
E1921 KJc Limit
Figure 6.3. Comparison of fracture toughness data with the M=30 deformation limit of E1921.
59
6.3.2 For PC-CVN Specimens One area of particular concern occurs when To is determined using precracked CVN specimens. This is an application of considerable interest to the commercial nuclear community because CVN specimens are part of existing surveillance programs. When tested as small fracture toughness specimens precracked CVNs can provide a direct measurement of To. However, the small physical size of the CVN specimen has led to concerns that To values determined using PC-CVNs could be biased low relative to To values determined using larger specimens due to loss of constraint [Mayfield 97]. Work by Dodds and co-workers [Ruggeri 98] predict the magnitude of the bias introduced to To by data sets containing specimens, particularly precracked Charpy specimens, that challenge the Eq. 4-16 limit. Experimental assessments show the bias to have a similar functional form to that predicted by Dodds, but a smaller magnitude [Kirk 00c]. To experimentally assess the potential for a To bias related to use of precracked CVN specimens we identified materials in the database having a sufficient data to support the following two independent estimates of To: A valid To value estimated using E1921-97
procedures based only on KJC data determined from precracked CVN specimens, and
A To value estimated using the multi temperature procedure of Appendix C based only on KJC data determined from larger fracture toughness specimens.
Table 6.3 summarizes data sets meeting these criteria. Figure 6.4 illustrates how the difference between the estimate of To obtained from
precracked CVNs and the estimate obtained from larger specimens varies with Mo (a value calculated from Ko using Eq. 6-2). Mo provides a measure of the deformation level characteristic of the precracked CVN data set, with lower Mo values indicating more deformation prior to fracture. The data in Figure 6.4 suggest that To values determined using precracked CVN specimens systematically underpredict To values determined using larger specimens, and that the magnitude of this underprediction increases in proportion to the level of deformation at fracture. However ,the experimental data do not show as large a bias as predicted by Dodds, et al . [??].
-60
-40
-20
0
20
40
60
0 50 100 150 200 250
M o for PC-CVN Dataset
To P
C-C
VN
- T
o R
ef.
[oF
]
Ref. is all 1/2T
Ref is 1/2T to 1T
Ref. is 1/2T to bigger than 1T
Ref. Is 1T or bigger
Prediction
Figure 6.4. Variation of To bias with deformation level (quantified as ) for To values determined from precracked CVN specimens. Error bars shown are 95% confidence bounds on the To difference between precracked CVN specimens larger specimens. The line labeled “prediction” is determined based on finite element analysis of a precracked CVN specimen with n=10, ys
= 60ksi [Ruggeri 98]
60
Table 6.3. Data sets used in the analysis of the potential bias in To values estimated from KJc tests performed on precracked CVN specimens.
~- - - --- ------ ------------for the Precracked CVN Data for the Multi Temperature Data
~ ~ ~ Product ASH.4 Material Fluence Temp. T" T"
Bias (CVN-U ~ Author Date Special Designation
[n/cmz] "" Bmin Bma. 2 Form Specification N , (J [oF] N , (J [oF] MT) [oF] ["F] ["F] (H) ["F] [in] [in]
67 27 3 Miranda, Carlos 1999 Forging A508 CI.3 0 ~130 10 8 -135 10 50 24 23 -140 6 0.5 0.5 6
34 18 3 CEOG 1998 Linde 0091 Farley Unit 1 0 -140 10 8 -140 10 58 9 9 -126 10 1 1 ~14
19 13 12 Nanstad, R.K. 1997 Linde 80 Weld, Midland Beltine 1E+19 71.6 10 8 79 10 64 32 30 84 6 0.5 1 ~5
67 27 3 Miranda, Carlos 1999 Forging A508 CI.3 0 -159 6 6 -149 13 66 24 23 -140 6 0.5 0.5 ~9
30 18 3 CEOG 1998 Linde 1092 Shoreham 0 ~200 17 16 -197 8 66 7 7 -187 12 1 1 ~10
66 26 3 Chaouadi, Rachid 1997 Plate A533B CI.1 JSPS Plate 0 32 10 9 20 10 74 118 115 47 3 0.5 4 ~27
30 18 3 CEOG 1998 Linde 1092 Shoreham 0 ~200 7 7 -185 12 79 7 7 -187 12 1 1 2
31 18 3 CEOG 1998 Linde 1092 0 ~22O 7 6 ~200 12 82 6 6 ~186 12 1 1 ~14
1125 54 3 Onizawa, Kunio 1999 Plate A533B CI.1 0 -112 22 21 -114 7 97 24 24 ~98 6 1 1 ~16
47 19 3 Williams, James F. 1998 Linde 1092 Kewaunee 1 P3571 0 ~200 7 7 -154 13 98 7 7 -145 12 0.5 0.5 ~9
1126 54 3 Onizawa, Kunio 1999 Plate A533B CI.1 0 ~166 10 9 -175 10 101 24 24 -152 6 1 1 ~23
20 13 14 Nanstad, R.K. 1997 Linde 80 Weld, Midland Nozzle 1E +19 77 9 9 113 11 104 19 21 135 7 0.5 1 ~22
47 19 3 Williams, James F, 1998 Linde 1092 0 ~200 8 8 -149 12 105 7 7 -145 12 0.5 0.5 ~3
31 18 3 CEOG 1998 Linde 1092 0 ~22O 6 6 -178 14 110 6 6 ~186 12 1 1 8
46 19 3 Williams, James F, 1998 Plate A533B CL 1 Beaver Valley Unit 1 0 ~200 9 9 -144 11 125 12 13 -133 8 1 1 ~ 11
46 19 3 Williams, James F, 1998 Plate A533B CL 1 Beaver Valley Unit 1 0 ~200 8 8 -139 12 134 12 13 -133 8 1 1 ~5
19 13 12 Nanstad, RK 1997 Linde 80 Weld, Midland Beltine 1E +19 32 8 8 104 13 154 32 30 84 6 0.5 1 21
67 27 3 Miranda, Carlos 1999 Forging A508 CL 3 0 -159 8 8 -133 11 165 24 23 -140 6 0.5 0.5 7
66 26 3 Chaouadi, Rachid 1997 Plate A533B CL 1 JSPS Plate 0 ~13 10 10 39 11 191 118 115 47 3 0.5 4 ~8
1125 54 3 Onizawa, Kunio 1999 Plate A533B CL 1 0 -148 10 10 ~86 11 247 24 24 ~98 6 1 1 12
Sokolov, M, 2000 Linde 0124 Weld73W 0 ~83 82 ~78 ~5
Sokolov, M, 2000 Linde 0124 Weld73W 0 ~92 31 ~78 ~14
Sokolov, M, 2000 Linde 0124 Weld73W 0 ~87 78 ~78 ~9
Sokolov, M, 2000 Linde 0124 Weld72W 0 ~105 49 ~71 ~34
Sokolov, M, 2000 Linde 0124 Weld72W 0 ~83 36 ~71 ~13
Sokolov, M, 2000 Linde 0124 Weld72W 0 ~87 79 ~71 ~16
Sokolov, M, 2000 Plate A533B CL 1 Plate 02 0 ~9 60 ~9 0
Sokolov, M, 2000 Plate A533B CL 1 Plate 02 0 ~15 33 ~9 ~5
Sokolov, M, 2000 Plate A533B CL 1 JRQ 0 -107 72 ~78 ~29
Sokolov, M, 2000 Plate A533B CL 1 JRQ 0 ~89 90 ~78 ~ 11
Sokolov, M, 2000 Plate A302B 0 162 69 140 22
Sokolov, M, 2000 Linde 80 Midland Nozzle 0 ~90 31 ~36 ~54
Tregoning, R 2000 Plate A533B CL 1 Shoreham 0 8 8 ~100 13 156 94 93 -122 3 22
Tregoning, R 2000 Plate A533B CL 1 Shoreham 0 16 11 -119 10 59 94 93 -122 3 4
Tregoning, R 2000 Plate A515 Gr. 70 0 6 6 ~7 16 113 24 24 16 7 ~24
Tregoning, R 2000 Plate A515 Gr. 70 0 13 9 ~7 11 44 24 24 16 7 ~23
Tregoning, R 2000 Plate A515 Gr. 70 0 11 8 26 12 52 24 24 16 7 9
Tregoning, R 2000 Plate A533B CL 1 Plate 14 0 9 9 ~39 14 207 39 35 ~55 5 16
Tregoning, R 2000 Plate A533B CL 1 Plate 14 0 7 6 -101 13 63 39 35 ~55 5 A7
Tregoning, R 2000 Plate A533B CL 1 Plate 14 0 7 5 ~52 14 50 39 35 ~55 5 2
61
7 TECHNICAL BASIS FOR CODE CASES N-629 AND N-631
ASME Code Cases N-631 and N-629 provide a methodology to establish a RTNDT-like quantity from a To value via the relationship RTToTo+35F. As noted in Section 4.4, this appeal to RTNDT / KIc technology suggests that the new index temperature RTTo should provide an “implicit margin” (i.e. the amount of separation between a bounding KIc curve and fracture toughness data) that is functionally equivalent to the margin implicit to current RTNDT approaches [EPRI 98, Lott 99]. In this section we examine the margin implicit to current practice and compare it to the margin achieved through the use of Code Cases N-629 and N-631. Implicit margins could not be assessed with any degree of accuracy when RTNDT and KIc technology was first introduced into ASME code due to lack of fracture toughness data. This situation has changed in the past 20 years. Now considerable data and a better understanding of transition fracture mechanisms exist. These factors combine to permit an assessment of the margin implicit to current technology. To perform this assessment, materials are identified that have both a NB-2331 RTNDT value, and also have sufficient fracture toughness data to permit determination of To. By virtue of its definition based on fracture toughness data, To quantifies the position of the fracture toughness transition curve on the temperature axis in a consistent manner for every heat of ferritic steel. Consequently, the difference between RTNDT and To quantifies the separation between a RTNDT -indexed KIc curve and the fracture toughness data it is intended to represent. Figure 7.1 illustrates schematically how this separation varies depending upon the combinations of RT ( = RTNDT - To) and crack front length used.
The following procedure is used to establish values of RT for RPV steels:
1. A data set is identified for which both a NB-2331 RTNDT value and sufficient fracture toughness data to permit determination of To exist.
2. To is calculated using a multi-temperature technique described by Wallin (see Appendix C). A minimum of 6 specimens having deformation values at or below the E1921-97 validity limit, but above 50 MPam, are required to admit a data set to this analysis. All KJC values are converted to 1T equivalence before calculation of To, so the To values reported here represent the temperature at which the median fracture toughness of a 1-inch thick fracture toughness specimen is 100 MPam. This definition of To is consistent with that of ASTM E1921-97.
3. The quantity (RT = RTNDT - To) is calculated for each data set. These values are separated by product form / irradiation condition, ordered from lowest to highest, and assigned median rank probabilities to produce the cumulative distribution function illustrated in Figure 7.2.
4. The different horizontal axes in Figure 7.2 quantify the separation between a RTNDT-indexed KIc curve and the temperature at which the median fracture toughness is 100 MPam for specimens of different sizes. The various axes are positioned based on the weakest-link scaling relationships provided in ASTM E1921-97, Eq. 5-11.
Table 7.1 summarizes the data sets that met the criteria of step 1. Figure 7.2 quantifies what Figure 1.1 suggested: that the spacing between a RTNDT -indexed KIc curve and the fracture
62
toughness data, the so-called “implicit margin,” varies over a considerable range. Figure 7.2 also shows that any attempt to quantify the margin implicit to current technology must also consider the specimen “size” or, more accurately, the crack front length of interest. These factors are discussed in the following section where the margin implicit to current RTNDT-based procedures is compared to the margin implicit to RTTo (i.e. ASME Code Case N-629 and N-631) based procedures.
7.1 Comparison of Margins Implicit to the RTNDT and RTTo Methodologies
As just discussed, any quantification of implicit margin must consider the following factors: The separation between a bounding curve
and fracture toughness data, and The crack front length of interest.
Code Cases N-629 and N-631 define a Master Curve-based index temperature as RTToTo+, and state that =35F provides an adequate separation between the bounding curve and fracture toughness data. These Code Cases use Master Curve technology to establish a To value, which (as per ASTM E1921-97) carries with it a “size,” or crack front length, or 1-inch. The “crack front length of interest” for the Code Cases is defined by the data set(s) used to establish the appropriateness of the =35F value. A number of data sets have been proposed as candidates for this role:
1. The data set that has the minimum implicit
margin in current, RTNDT based, technology (It has been suggested that this data set is HSST-02, but Figure 7.2 reveals that this is not the case),
2. The original WRC Bulletin 175 KIc dataset illustrated in Figure 2.1.
3. An absolute bound to all available fracture toughness data for RPV steels.
Proposals #1 and #3 both depend on the currently available data, making them susceptible to change over time. For example,
future testing may reveal either a data set that is so un-conservatively predicted by RTNDT that Proposal #1 produces a lower value of implicit margin than previously accepted, or a data set that is so conservatively predicted by RTNDT that Proposal #3 produces a higher value of implicit margin than previously accepted. These proposals are therefore not considered an appropriate basis for regulations, and attention is therefore focused on Proposal #2. Based on Proposal #2, the equivalence of implicit margin, or lack thereof, between RTNDT and RTTo-based methodologies is quantified as follows: Calculate the mean sum of squares of KIc residuals between a KIc curve indexed to RTNDT and the data set. Vary (in To+) until the mean sum of squares of KIc residuals between a KIc curve indexed to (To+) and the data set becomes equivalent to the value calculated in Step 1. The value of established in Step #2 is 33F; it represents the value needed to achieve parity between RTNDT and RTTo-based procedures when the original KIc dataset is used as the reference dataset. On this basis it might be said that RTTo-based procedures that use the =35F from Code Cases N-629 and N-631 include 2F of margin that RTNDT based procedures do not. However, it should be noted that the spread in residuals calculated in steps 1 and 2 more than obscure this 2F difference, suggesting that the difference between values of 33F and 35F is statistically un-resolvable due to the scatter in fracture toughness data. Figure 7.3 documents the crack front length associated with the original KIc dataset. It should be noted that adoption of Proposal #2 offers a number of advantages: Use of the WRC Bulletin KIc dataset as the “reference” dataset maintains a linkage with what has historically been accepted as an adequate degree of separation between the fracture toughness data and the bounding curve, and with what has historically been accepted as
63
adequately large specimens. Continued use of these historical data eliminates the arbitrariness in selection of a “reasonable” tolerance level and an “appropriate” crack front length. The tolerance bound associated with the use of a value of 35F would be considered “reasonable” by most individuals. Wallin presents a statistical analysis showing that a KIc curve indexed to RTNDT corresponds very closely to a 97.5% tolerance bound curve for the original WRC Bulletin 175 KIc dataset [Wallin 97]. The analysis presented in this section suggests that this tolerance bound is maintained, and not changed significantly, for a RTTo indexed KIc curve when RTTo is defined as per ASME N-629 and N-631. The average crack front length associated with the WRC Bulletin KIc dataset (2.1-inches) can be considered “reasonable” for use in the fracture assessment of nuclear RPVs. A 6:1 flaw having this total crack front length would have a depth of approximately 0.3-in., a depth exceeding that of the great majority of flaws found in RPV fabrication [Schuster 99].
7.2 Summary In summary it should be noted that it is fundamentally impossible to achieve a fully technical reconciliation of the margin implicit to existing RTNDT-based approaches and new proposals to define RTTo using the Master Curve because of the wide range of differences between RTTo and RTNDT illustrated in Figure 7.2. The relationship between RTTo and To used in ASME Code Cases N-629 and N-631, i.e. RTToTo+35F, is defensible as it bounds a reasonable percentage of all fracture toughness data now available (97.5%) for a crack front length (2.1-in.) that exceeds the great majority of flaws found in RPV fabrication. Furthermore, application of this proposal to a large collection of irradiated fracture toughness data demonstrates that RTTo will position a bounding KIc curve appropriately relative to measured fracture toughness data (see Figure 7.4).
Separation Distance, RT = RTNDT - To
Cra
ck F
ron
t L
eng
th
1 in
ch2
inch
es
RT = -25F
0
50
100
150
200
250
0 100 200 300 400
Temperature [oF]
KIC
[k
si*i
n0.
5 ]
0
50
100
150
200
250
0 100 200 300 400
Temperature [oF]
KIC
[k
si*i
n0.
5 ]
RT = 0F
0
50
100
150
200
250
0 100 200 300 400
Temperature [oF]
KIC
[k
si*i
n0.
5 ]
0
50
100
150
200
250
0 100 200 300 400
Temperature [oF]
KIC
[k
si*i
n0.
5 ]
RT = +75F
0
50
100
150
200
250
0 100 200 300 400
Temperature [oF]
KIC
[k
si*i
n0.
5 ]
0
50
100
150
200
250
0 100 200 300 400
Temperature [oF]
KIC
[k
si*i
n0.
5 ]
RT = +150F
0
50
100
150
200
250
0 100 200 300 400
Temperature [oF]
KIC
[k
si*i
n0.
5 ]
0
50
100
150
200
250
0 100 200 300 400
Temperature [oF]
KIC
[k
si*i
n0.
5 ]Separation Distance, RT = RTNDT - To
Cra
ck F
ron
t L
eng
th
1 in
ch2
inch
es
RT = -25F
0
50
100
150
200
250
0 100 200 300 400
Temperature [oF]
KIC
[k
si*i
n0.
5 ]
0
50
100
150
200
250
0 100 200 300 400
Temperature [oF]
KIC
[k
si*i
n0.
5 ]
RT = 0F
0
50
100
150
200
250
0 100 200 300 400
Temperature [oF]
KIC
[k
si*i
n0.
5 ]
0
50
100
150
200
250
0 100 200 300 400
Temperature [oF]
KIC
[k
si*i
n0.
5 ]
RT = +75F
0
50
100
150
200
250
0 100 200 300 400
Temperature [oF]
KIC
[k
si*i
n0.
5 ]
0
50
100
150
200
250
0 100 200 300 400
Temperature [oF]
KIC
[k
si*i
n0.
5 ]
RT = +150F
0
50
100
150
200
250
0 100 200 300 400
Temperature [oF]
KIC
[k
si*i
n0.
5 ]
0
50
100
150
200
250
0 100 200 300 400
Temperature [oF]
KIC
[k
si*i
n0.
5 ]
Figure 7.1. Illustration of how the difference between RTNDT and To quantifies the separation between a RTNDT indexed KIc curve (solid curve) and the fracture toughness data it is intended to represent (5%-95% confidence bounds). The influence of crack front length on this separation is also illustrated
64
Table 7.1. Data sets used in to assess the margin implicit to use of RTNDT as an index temperature for fracture toughness data.
0%
20%
40%
60%
80%
100%
RT = RTNDT - To [oF]
Cu
mila
tive
Pro
bab
ility Forging
Plate
Weld
Irradiated
-50 0 50 100 150 200
-50 0 50 100 150 200
-50 0 50 100 150 200
-50 0 50 100 150 200
1T
2T
4T
8T
0%
20%
40%
60%
80%
100%
RT = RTNDT - To [oF]
Cu
mila
tive
Pro
bab
ility Forging
Plate
Weld
Irradiated
-50 0 50 100 150 200
-50 0 50 100 150 200
-50 0 50 100 150 200
-50 0 50 100 150 200
1T
2T
4T
8T
Figure 7.2. The range of margins (defined as RTNDT – the 100 MPam fracture toughness transition temperature To) implicit to current practice. The different horizontal axes correspond to the crack front length indicated (in inches).
HSST-02
65
Average Crack Front Length = 2.1T
0
20
40
60
80
100
120
1T 2T 4T 6T 8T 10T 11T
Specimen Size
Nu
mb
er
of
Sp
ec
ime
ns
Te
ste
d
Figure 7.3. The size of fracture toughness specimens tested in the original KIc dataset [Marston 87].
Figure 7.4. Comparison of a KIc curve (positioned based on RTTo) with as-measured fracture toughness values for irradiated RPV steels [EPRI 98].
66
8 APPLICATION OF THE MASTER CURVE IN PTS CALCULATIONS
Table 8.1 summarizes the codes, standards, and regulations that concern estimation of fracture toughness values used in nuclear RPV integrity calculations. The first two steps identified in Table 8.1include a standard to measure toughness, and a procedure that uses this information to position a reference toughness curve on the temperature axis. ASTM E1921-97 and ASME Code Cases N-629 and N-631 fulfill these roles for the Master Curve. Questions raised previously by the Staff regarding the use of Master Curve technology in these codes and standards [Mayfield 97, Kirk 00a] have received considerable attention over the past few years, and are now largely resolved [Kirk 00e]. These questions, and the resolution status of each, are as follows: 1. ASTM E1921-97
a. Is the single temperature dependence of the Master Curve appropriate for all RPV steels of interest, even after irradiation?: On-going research activities performed by both Natishan (and co-workers) [Natishan 98, Natishan 99a, Natishan 99b, Wagenhofer 00a, Wagenhofer 00b, Kirk 00b] and Odette (and co-workers) [Odette 00] provide encouraging evidence that questions regarding the theoretical limits on the universal Master Curve shape will soon be resolved. These results provide guidance on two related questions: i. Breadth of Applicability: Research
focused on establishing the physical basis for a universal Master Curve shape reveals that the lattice structure alone controls the temperature dependence of fracture toughness. Thus, the Master Curve will model
well the temperature dependence of fracture toughness for all pressure vessels steels of any product form both before and after irradiation because all of these steels have a BCC matrix phase lattice structure.
ii. Effect of Test Temperature: To values determined as per E1921-97 do not show a systematic bias or trend with test temperature, nor is this expected due to the common dependence of fracture toughness on temperature for all ferritic steels. Revisions to E1921-97 propose further restriction to the range of temperatures within which one is permitted to perform toughness tests to estimate To. Available empirical evidence suggests that this additional restriction is not necessary.
b. Does the ¼-power scaling rule adopted within the Master Curve reflect appropriately the effect of specimen size on fracture toughness?: Provided the material has a random distribution of cleavage initiation sites spread homogeneously throughout its volume, the Weibull model of cleavage fracture toughness in transition relies only on the existence of a state of small scale yielding to ensure its theoretical applicability. As the micro-scale inhomogeniety needed to violate the assumption of a random distribution of cleavage initiation sites is not characteristic of RPV steels, applicability of the Master Curve statistical fracture model can be assessed based on a calculation of the deformation state at fracture. Under small scale yielding conditions, fracture
67
toughness will scale with thickness raised to the ¼-power. This result is anticipated theoretically and is well confirmed experimentally.
c. Are To values determined using precracked CVN specimens equivalent to To values determined using larger specimens?: To values determined using precracked CVN specimens show a systematic bias relative to To values determined using physically larger samples. This bias depends on the deformation level at fracture. Information is presented herein that can be used to correct for this bias. It is important that such a correction be reviewed and balloted by ASTM committee E08 due to the interest of nuclear licensees in using precracked CVN specimens removed from surveillance to estimate To.
2. ASME Code Cases N-629 and N-631 a. Will KIc and KIR curves indexed using To
provide an equivalent implicit margin to current approaches?: These Code Cases provide a Master Curve-based index temperature for the KIc and KIR curves that produce implicit margins
functionally equivalent to those historically accepted for RTNDT. The relationship between RTTo and To, i.e.
F35o
oTo TRT , is defensible as it bounds a reasonable percentage of all fracture toughness data now available (97.5%) for a crack front length (2.1-in.) that exceeds the great majority of flaws found in RPV fabrication.
In contrast to this substantial progress, Steps 3 and 4 in Table 8.1 have received little focus to date. Nevertheless, plant-specific Master Curve submittals have moved / are moving forward. In the next section we summarize these submittals, and discusses how each submittal has addressed Steps 3 and 4 in Table 8.1, both of which go beyond the scope of ASTM and ASME codes and standards. This discussion is followed by a section concerning the essential characteristics a general framework to estimate the fracture toughness at EOL. Finally, we discuss recent progress, or lack thereof, toward developing the various components of such a general framework.
Table 8.1. Codes, Standards, and Regulations that Govern the Assessment of Fracture Toughness for Use in a PTS Analysis.
Step Current Technology Master Curve Technology
1 Measure a Material Property CVN: ASTM E23 NDT: ASTM E208
To: ASTM E1921
2 Establish an Index Temperature and Define a Reference Toughness Curve
RTNDT ASME NB-2331
RTTo ASME N-629 and N-631
3 Estimate the Toughness of Some Future Irradiation Condition (e.g., at EOL)
Expressed in: 10CFR50.61, 10CFR50 APPG, ASME XI-G
Not Yet Established Based on: SECY 82-465, NRC MTEB5.2, NRC MEMO 82, Randall 87
4 Establish a Screening Criteria for PTS Expressed in: 10CFR50.61 Not Yet Established Based on: SECY 82-465
68
8.1 Plant-Specific Applications of Master Curve Technology
To date the commercial nuclear power industry has brought two submittals before the NRC that use the Master Curve to estimate the fracture toughness of the RPV at EOL and assess compliance with 10CFR50.61 (i.e., with the PTS Rule). These submittals concerned / concern the licenses of the Zion [Yoon 95] and Kewaunee [Lott 99, Lott 00, Server 00] NPPs:
o Zion: In the Zion submittal the licensee sought to use Master Curve technology and fracture toughness data on the limiting vessel material (Linde 80 weld WF-70) to establish a new un-irradiated value of RTNDT [Yoon 95]. The protocols of 10CFR50.61 were then used to estimate the effects of both irradiation and uncertainties on this value, and to establish a PTS screening criteria to compare this value to. The Zion submittal did not modify 10CFR50.61 protocols to account for the use of Master Curve technology to estimate RTNDT.
o Kewaunee: In a series of papers concerning the Kewaunee submittal, Lott, et al. outline several strategies to use measured values of To, both un-irradiated and irradiated, to estimate a RTNDT-like quantity at EOL [Lott 99, Lott 00, Server 00]. In developing these estimation strategies, the authors sought to use To to estimate a RTNDT-like quantity in a manner that parallels and satisfies the intent of current regulations (i.e. 10CFR50.61). In the Kewaunee submittal this RTNDT-like quantity was compared to the current PTS screening criteria [10CFR50.61]
Lacking any established alternative approach, the Zion and Kewaunee submittals both align closely with current procedures to estimate the toughness for some future irradiation condition, and to assess the adequacy of this toughness during a postulated PTS event. This approach invariably leads to assignment of burdensome margins to account for mis-fits, both real and
perceived, between Master Curve technology and the 10CFR50.61 framework. We examine the potential for moving away from this paradigm in the next section.
8.2 Progress Toward a Generic Master Curve Methodology
The information presented in Table 8.1 points out that factors exist beyond those considered thus far by ASTM and ASME that need to be addressed to bring Master Curve technology to the point that it can be applied routinely to assess nuclear RPV integrity:
1. Procedures to estimate the toughness at EOL: These procedures would predict To and/or RTTo for future irradiation conditions from available information (i.e. mechanical properties, chemical properties, fluence), and adjust these estimates to account for various uncertainties. Toughness is determined through the association of these index temperatures with fracture toughness transition curves. Reg. Guide 1.99 Rev. 2 describes the procedures used currently to this end [NRC RG199R2]††. No parallel rule or guidance exists currently for Master Curve-based methodologies.
2. A PTS screening criteria: This would be a value / values to which a Master Curve-based estimate of To and/or RTTo at EOL would be compared to assess the suitability of the reactor for operation through EOL. SECY-82-465 establishes the technical basis for the current criteria (300F for circumferential welds, 270F for longitudinal welds, plates, and forgings) of
†† These procedures find their origins in the work that
led up to and provided the technical basis for the current PTS screening criteria [NRC MTEB5.2, NRC MEMO 82, Randall 87, SECY 82-456]. Nevertheless, the procedures are applied to estimate toughness not only for use in a PTS assessment (where 10CFR50.61 adopts Reg. Guide 1.99 Rev. 2 procedures and applies them at EOL fluence), but also as part of the calculations that establish heat-up and cool-down limits for routine operation [10CFR50 APPG, ASME XI-G].
69
10CFR50.61 [SECY 82465, 10CFR5061]. No parallel rule or guidance exists for the Master Curve.
In this section we examine the current RTNDT-based procedure to estimate the fracture toughness at EOL and discuss its role in establishing the current PTS screening criteria. This discussion provides a perspective on the obstacles that plant-specific Master Curve applications have encountered in attempts to parallel current procedures. In the following sections we turn attention toward the future research and development achievements needed to eliminate these obstacles. The model used to estimate toughness in the PFM calculations that established the current PTS screening criteria is as follows [SECY 82465]: Eq. 8-1 )()()( fNDTuNDTfNDT RTRTRT
where RTNDT(f) is the estimated RTNDT of the vessel
material after irradiation to the fluence f. Toughness is determined from RTNDT(f) through its use as an index temperature for the KIc and KIR curves
RTNDT(u) can represent either of the following values: o A value of RTNDT in the unirradiated
condition based on testing a specific vessel material in accordance with ASME NB-2331, or, if such measurements are unavailable, For Welds: A generic mean value
determined from a data set relevant to the material class of interest. Currently accepted generic mean values include -56F for welds made with Linde 0091, 1092, 0124, and ARCOS B-5 welding fluxes, and -5F for welds made with Linde 80 flux.
For Plates: If only CVN data are available, as is sometimes the case for plate materials, MTEB-5.2 provides procedures to estimate
RTNDT values that are intended to be conservative to (i.e. higher than) RTNDT values determined using ASME NB-2331 [NRC MTEB52].
RTNDT(f) is the mean value of the irradiation induced transition temperature shift, and is calculated as follows:
Eq. 8-2 )log1.028.0(
)()( f
fNDTfCFRT
RTNDT(f) can represent either of the following values:
o It is the mean value of the of this shift for the material samples tested as part of the credible surveillance program, or, if the surveillance data is not deemed to be credible,
o It is the mean value of this shift for a material having the composition (Cu and Ni) corresponding to the heat average for the entire heat of material in question.
In the former case, when credible surveillance data is used to establish RTPTS, the value adjusts RTPTS to account for differences between the chemical composition of the surveillance material and the heat average chemical composition. represents the “ratio procedure” as described in 10CFR50.61(2)(ii)(B). is defined as the chemistry factor (CF) for the best estimate composition of the heat divided by the chemistry factor for the specific composition of the surveillance weld. Tables in 10CFR50.61 define chemistry factors based on material product form, Cu, and Ni.
Natishan and co-workers have recently developed a diagrammatic representation of eq. (37), Figure 8.1, which illustrates how the value of an input parameter (e.g. Cu, Ni, t, CVN, NDT, etc.) “flows” through Eq. 8-1 to produce an estimate of the value of RTNDT after irradiation to EOL fluence [Li 00]. Thus, in addition to its use in determining the PTS screening criteria, Eq. 8-1 also establishes the variability in estimates of RTNDT(f) that are compared to this screening criteria. This amount of variability, often called a “Margin,” is
70
traditionally added to the estimate of RTNDT(f) as follows [NRC RG199R2]: Eq. 8-3 MRTRTRT fNDTuNDTfNDT )()()(
Eq. 8-4 222 IM
where
I is the standard deviation in the value of
RTNDT(u). It can represent either of the following values:
o I is “determined from the precision of
the test method” if RTNDT(u) is established either (a) by testing the specific vessel material in accordance with ASME NB-2331, or (b) by MTEB-5.2 procedures. While not explicitly stated in 10CFR50.61, a value of I = 0F is used in this situation.
o If a measured value of RTNDT(u) is not available, I is the standard deviation of the data set used to establish the generic mean value of RTNDT(u). The most common value of in this situation is 17F [NRC MEMO 82]. This value applies to welds made with Linde 0091, 1092, 0124, ARCOS B-5, and Linde 80 welding fluxes. Other values, like 26.9F for B&W plate materials have also been established and are recorded in RVID.
In both cases the sum {RTNDT(u) + 2I} represents a bounding value of RTNDT before irradiation. When RTNDT is determined according to ASME NB-2331 or MTEB-5.2, these protocols produce a bounding estimate, so I can be zero. However, when a mean value of RTNDT is used then 2I =34F needs to be added to produce a bounding estimate. is the standard deviation in the value of RTPTS. It can represent either of the following values: o If credible surveillance data is not
available, the values are 28F for welds and 17F for plates
o If credible surveillance data is available, the values are 14F for welds and 8.5F for plates.
These observations illustrate that the main difficulty faced by plant specific Master Curve applications has been the lack of an accepted framework by which to estimate the irradiated fracture toughness of the vessel from To data (i.e. a version of Eq. 8-1 for To), and the fact that this framework was never used to establish a PTS screening criteria for To. Consequently, there is currently no To-based PTS screening criteria, and there is no To-based margin term (i.e. an Eq. 8-4 for To) that can be traced to uncertainty in the input variables. Beyond these general difficulties, the Zion and Kewaunee submittals have encountered the following concerns in their attempts to parallel eqs. (37) and (38):
1. Zion: If an un-irradiated To is used and shifted using the Reg. Guide 1.99 Rev. 2 fluence function, concerns have arisen regarding the appropriateness of applying a CVN-based shift to fracture toughness data.
2. Kewaunee: With the current methodology, the toughness after irradiation can only be estimated from the sum of an un-irradiated reference temperature and an irradiation-induced shift in the reference temperature. Direct measurement of the irradiated transition temperature was not considered when the calculations that support the current PTS rule were adopted. Consequently, this approach currently lacks an established basis to account for differences between the composition of the surveillance samples and the composition of the material in the vessel. The existing Ratio procedure operates on the irradiation-induced shift in the transition temperature, not on its absolute value, making the proper application of this procedure to an irradiated transition temperature unclear.
Beyond these specifics, there is also the concern that forcing Master Curve-technology into the current, non-Master Curve, framework may
71
produce systemic “lack of fit” uncertainties, thereby resulting in the need for higher margins. The only way to alleviate this concern is to establish a Master Curve framework to estimate toughness at EOL, and use this framework as part of the PFM calculations to establish a PTS screening criteria applicable specifically to Master Curve-based estimates of fracture toughness. Work on the development of such a framework for the Master Curve has only recently begun [Natishan 00]. In the following sections we review recent progress in the developing some of the components of such a framework, including:
1. Generic values of To for use when plant specific data is unavailable
2. Irradiation damage effects on To (Irradiation trend curves)
3. Treatment of the linkage between fracture toughness and crack front length.
4. Treatment of the loading rate effect on fracture toughness to establish the position of the crack arrest curves used in establishing the PTS screening criteria.
8.2.1 Generic Values of To and/or RTTo Current RTNDT-based procedures provide generic values of un-irradiated RTNDT for use when material specific information is not available. Similar generic values of RTTo may be needed for a Master Curve methodology that is usable by all plants. Here we use a large collection of fracture toughness values [Rosinski 99] to establish candidate generic RTTo values by the following procedure:
1. The database is queried to identify all fracture toughness data available for a particular class of RPV materials. Here we consider classes defined by flux type (for welds) and by ASTM material specification (for plates and forgings).
2. The fracture toughness values are normalized to a 2.1-in. thickness using the following weakest-link relationship included in ASTM E1921-97:
Eq. 8-5 4/1
min)(min)1.2( 1.2
BKKKK measuredJcTJc
A “size” of 2.1-in. is selected to maintain consistency with the average size associated with the original KIc database used to establish the relationship between KIc data and RTNDT for the current ASME KIc curve [Marston 87].
3. These size-normalized fracture toughness values are plotted vs. test temperature. A KIc curve, i.e.
Eq. 8-6
1000198.0exp81.22.33 )( genericToIC RTTK
(K in ksiin, T in F)
is then plotted, and the value of RTTo(generic) is adjusted position the curve so that it bounds 97.5% of the fracture toughness values in fracture mode transition. While in principal any tolerance bound can be selected, we selected a 97.5% value to maintain consistency with how a RTTo positioned KIc curve bounds the original KIc data set [Wallin 97].
Figure 8.2 illustrates this procedure for A533B Cl. 1 plate and for Linde 80 welds, while Table 8.2 summarizes RTTo(generic) values for the different RPV material classes. This procedure to establish generic values of RTTo incorporates the material uncertainty within the class into the value of RTTo(generic) by basing the position of the 97.5% tolerance bound curve on fracture toughness data for a number of different heats from the same material class. Consequently, if these values of RTTo(generic) are used in a plant assessment, a non-zero uncertainty term (equivaluent to I in the current methodology) should not be used.
72
Relationship Types
Equation, w/ Uncertainty
Choice
Comparison
Equation, Exact
Relationship Types
Equation, w/ Uncertainty
Choice
Comparison
Equation, Exact
KICUncertainty
RTNDTIrradiated
RTNDTUnirrad.
T30see below
TCV35/50
TNDT
NB 2331Ductile or
Brittle
T
welds
notchKIC
In FAVOR[Bowman 00]
Matl. inhomo.
2
3
11
Epistemic
Aleatory
Base level of quantification
EpistemicEpistemic
AleatoryAleatory
Base level of quantificationBase level of quantification
1
T-control
T-measure
12
Limited RTNDT dataas per NB-2331
( -5F)Generic
Flux type10 Limited RTNDT data
as per NB-2331( -56F)
Linde 80
Linde 0091Linde 0124Linde 1092
ARCOS B-5
MTEB5.2
(CVN Only)
Matl?4
SA533B Gr.A Cl.1
SA508Cl. II
T30
0FTUPPER SHELF
60F
T100
Data at OneTemp. to Confirm T30
T45 Minimum
TTest+20F
TransverseSpecimens
Not Tested
T(CV)35/50+20F9
Any
Calculate 65%*CVE,then Determine T(CV)35/50
F60,MAX )50,35( CVNDTNDT TTRT
5MAX
6MIN
8MAX
7
T30 @ EOLBest
Estimate
Ratio Adjustment
CF HeatBest Est.
CF Surv.
IrradiationTemperatureAdjustment(TIrradiation)
EOL Fluence
TRPV(of int.)
Tsurv
Cu
Ni
Cu
Ni
T30
Product Form
13Surveillance
?
14
15
16
19
Cu
Ni19
Yes, andCredible
No, orSurveillance not credible
n Pairs of (T30, Fluence)
EOLFluence
T30Un-Irradiated
n IrradiatedT30 Measurements
17-
15
16
19
14 )log1.028.0(30 )( ttCFT
CF tables from 10CFR50.61
& 19
)log1.028.0(30 ttT
nIrradiatioEstimateBest TTT |303015
16
19
14 )log1.028.0(30 )( ttCFT
CF tables from 10CFR50.61
& 19
)log1.028.0(30 ttT
nIrradiatioEstimateBest TTT |3030
20-
18/
Figure 8.1. Root cause diagram illustrating the methodology used currently to estimate the fracture toughness of a reactor pressure vessel steel after irradiation [Li 00].
73
Table 8.2. Generic RTTo values for different classes of nuclear RPV materials
Material Class
RTTo(Generic) [oF]
Total # of KJc Values
# of KJc
Values not
Bounded
% Bounded
A508 Cl. 2
-14 38 0 100.0%
A508 Cl. 3
-42 606 15 97.5%
A302B 14 58 1 98.3% A302B Mod.
-39 26 0 100.0%
A533B Cl. 1
18 1481 36 97.6%
Linde 0091
2 71 1 98.6%
Linde 0124
-25 178 4 97.8%
Linde 1092
-151 148 3 98.0%
Linde 80 -34 213 5 97.7%
0
100
200
300
400
500
-400 -250 -100 50 200
Temperature [oF]
2.1
-T E
qu
iva
len
t K
Jc [
ks
i*in
0.5 ]
KIC with RTTo = -34oF
Linde 80
Figure 8.2. Use of fracture toughness data for A533B Cl. 1 (left) and for Linde 80 (right) to establish generic values of RTTo.
8.2.2 Estimate of Irradiation Damage Effects on To
As expressed by Eq. 8-1, the current technique for estimating the transition temperature after irradiation is to add an irradiation shift to an un-irradiated transition temperature value. The shift in the CVN transition temperature at 30 ft-lbs is currently calculated from fluence and composition using the following formula [RG 199R2]: Eq. 8-7 )log1.028.0(
30 )( ffCFT
Here the CF (chemistry factor) expresses the aggregate effect of Cu, Ni, and product form on irradiation sensitivity. Reg. Guide 1.99 Rev. 2 includes tables of CF values for a range of compositions. The form of the fluence function in Eq. 8-7, i.e. )log1.028.0( ff , was established by curve-fitting a database of 177 T30 values [Randall 87]. In Master Curve-based applications, a question arises regarding the appropriate form of the shift equation for To. Since the irradiation shifts in both Charpy and fracture toughness transitions are largely controlled by increases of material flow strength produced by irradiation, it seems reasonable that the fluence function for shifts of Charpy transition temperature might model shifts in the fracture toughness transition temperature (i.e. To) as well. Sokolov and Nanstad compared irradiation shifts of both CVN energy and fracture toughness transition [Sokolov 96]. This comparison (see Figure 8.3) showed a 1:1 correlation for welds (42 data points). Conversely, examination of 47 plate materials shows that irradiation shifts the fracture toughness transition temperature 16% more than it does the CVN transition temperature. In both cases the relationship between the two transition temperatures was linear. More recently, Kirk et al. compared available data on To shifts produced by irradiation to the functional form of Eq. 8-7 (see Figure 3.2 in Section 3). Figure 3.2 and Figure 8.3 both suggest that the Reg. Guide 1.99 (Rev. 2) fluence function provides a reasonable description of the shift in To produced by irradiation.
0
100
200
300
400
500
-400 -250 -100 50 200
Temperature [oF]
2.1
-T E
qu
iva
len
t K
Jc [
ks
i*in
0.5 ]
KIC with RTTo = 18oF
A533B Cl. 1
74
These results are encouraging. However, the high cost of irradiated material testing will likely preclude development of a sufficiently well populated database of To shift values to either directly develop a To-based irradiation trend curve, or even to test empirically the appropriateness of Eq. 8-7 for the conditions of interest. Consequently, resolution of this issue could rest with establishing a sound basis for why To and CVN shifts should be the same, or at least related. Existence of such a rationale, which is not currently being investigated, would pave the way for establishing the appropriate functional form for To shifts based on extensive databases of CVN shifts values that are now available [Eason 98].
Figure 8.3 Comparison of irradiation induced CVN and To shifts for nuclear RPV welds and base materials [Sokolov 96]. 8.2.3 The Effect of Crack Front Length
on To As discussed in Sections 4.2.2 and 5.2.2.2, the Master Curve incorporates a relationship between fracture toughness and the length of the crack front based on a weakest-link model of
cleavage fracture under small scale yielding conditions. While relationship predicts a decline in fracture toughness with increasing crack front length, a prediction in accord with considerable experimental evidence for fracture toughness test specimens (see Section 5.2.2.2), it also represents a perceived departure for the current ASME Code practice that treats toughness and crack front length as independent variables. However, the ASME practice of positioning a bounding curve relative to fracture toughness data addresses implicitly the effect of crack front length on toughness. This practice implicitly links to the bounding curve the crack front length(s) characteristic of the fracture toughness data used to establish its position. Thus, both RTNDT and RTTo indexed KIc curves have the same implied crack front length because the original KIc data set [Marston 87] provided the basis for positioning both curves. To develop a fracture assessment methodology used the Master Curve directly rather than just using To to position a bounding curve, explicit procedures to determine the effect of crack front length on fracture toughness will be needed. This methodology will need to treat crack front length effects, and address their interaction with loss of constraint effects, for the embedded elliptical flaws or semi-elliptical surface breaking flaws found in RPVs. Figure 8.4(a) compares cleavage fracture toughness data for semi-elliptical surface cracks in A515 steel with a Master Curve for this material [Joyce 97b, Porr 95]. This comparison illustrates that the relationship between crack front length and fracture toughness that works so well for straight fronted cracks in fracture toughness specimens places data for part-through surface cracks too high relative to the standard Master Curve. In Figure 8.4(b) these data are brought into agreement with the Master Curve by using only 20% of the total crack front length of the past-through surface cracks when calculating their equivalent 1T fracture toughness. The analysis presented in Figure 8.4 is very rudimentary. It fails to discriminate between the variable-KI field around the crack front or loss of full constraint where the crack front intersects the free surface as the cause of this change in the
75
scaling relationship. Nevertheless, the analysis does suggest that, whatever the cause, only a small fraction of the crack front length in a non-straight fronted crack contributes significantly to the probability of cleavage fracture. To enable application of the Master Curve to structures, a form of Eq. 4-13 that addresses non-straight fronted fatigue cracks, and can treat both statistical size effects and constraint effects, is needed. Several on-going research programs address this goal using Weibull models coupled with 3D elastic-plastic finite element analysis to predict fracture the conditions for crack initiation from semi-elliptical surface cracks [Gao 99, Bass 00b]. Ultimately, these efforts will need to both provide a predictive model and assess the breadth of material / irradiation / loading conditions to which the model applies. Non-straight fronted cracks are considered in reactor pressure vessel integrity analysis in the following three areas:
1. Flaw specific-assessments performed according to ASME Section XI (IWB-3500, IWB-3600),
2. PTS analysis as described in 10CFR50.61 and performed in accordance with Regulatory Guide 1.154, and
3. Calculation of permissible limits on heat-up and cool-down performed in accordance with ASME Section XI Appendix G.
In the first two cases, the flaws used in the calculations represent flaws that exist, or could exist in an operating RPV. Thus, a technical resolution of the effect of crack front length on fracture toughness should provide an appropriate analysis methodology for these calculations. Conversely, heat-up and cool-down curves are calculated for a postulated flaw that penetrates one-quarter of the way through the reactor pressure vessel wall and has a 6:1 ratio of surface breaking length to depth. This size of this flaw exceeds considerably that observed in any operating RPV (an 8-in. thick vessel this flaw would have a crack front length of 14-in.), making the flaw size a conservatism implicit to this analysis methodology. Thus, before the Master Curve can be used for Appendix G analyses, a reconciliation of the ¼-T flaw
methodology and the Master Curve approach is needed.
Surface crack K Jc values scaled to 1T using the total crack front length.
0
50
100
150
200
250
-100 -50 0 50 100T-T o [oF]
1T
Eq
uiv
. KJc
[k
si*
in0.
5 ]
Link, Bending, 0.25 x 1.4
Link, Tension, 0.25 x 1.4
Porr, Bending, 0.5 x 3.0
Porr, Bending, 0.5 x 1.4
1T Master Curve w /5%/95% Bounds
Surface crack K Jc values scaled to 1T using 20% of the
total crack front length.
0
50
100
150
200
250
-100 -50 0 50 100T-T o [oF]
1T E
qu
iv K
Jc [
ksi*
in0
.5]
Link, Bending, a=0.25 x 2c=1.4
Link, Tension, 0.25 x 1.4
Porr, Bending, 0.5 x 3.0
Porr, Bending, 0.5 x 1.4
1T Master Curve w / 5%/95%Bounds
2c
a
2c
a
Surface crack K Jc values scaled to 1T using 20% of the
total crack front length.
0
50
100
150
200
250
-100 -50 0 50 100T-T o [oF]
1T E
qu
iv K
Jc [
ksi*
in0
.5]
Link, Bending, a=0.25 x 2c=1.4
Link, Tension, 0.25 x 1.4
Porr, Bending, 0.5 x 3.0
Porr, Bending, 0.5 x 1.4
1T Master Curve w / 5%/95%Bounds
2c
a
2c
a
Figure 8.4. Comparison of data for part through surface cracks to a 1T equivalent Master Curve [Joyce 97, Porr 95]. 8.2.4 The Effect of Loading Rate on To Because the postulated failure of a RPV would likely involve a rapidly propagating crack, the fracture integrity assessment methodology needs to account for the effect of loading rate on fracture toughness. Rate effects enter the methodology via the separation between the static and dynamic fracture toughness curves. This separation (Figure 8.5) is currently fixed irrespective of either the loading rate differential between the two curves, or the strength level /
76
degree of irradiation of the material in question. Nevertheless, empirical evidence abounds that both loading rate and material strength influence the fracture toughness transition temperature [Barsom 87]. Currently the ASME KIR curve represents the lower-bound toughness for both crack initiation at an elevated loading rate, and for crack arrest. In a PTS calculation, a vessel is not considered to have “failed” unless an initiated crack cannot be arrested [Dickson 95]. Absent a change in this definition of vessel failure, treatment of crack arrest will be part of any comprehensive RPV integrity assessment strategy. While crack initiation at elevated loading rates fits well within the Master Curve framework, the same weakest link model used to characterize crack initiation clearly cannot describe crack arrest. Crack arrest will not occur until the local driving force for continued crack propagation falls below the local material arrest toughness over a significant portion of the propagating crack front [Wallin 98b]. The requirements for crack arrest are therefore controlled by a distributed process on the micro-scale, in contrast to crack initiation, which is controlled by local properties. This simple model suggests that the scatter in crack arrest toughness values should be less than for crack initiation toughness values, and that crack arrest toughness should not exhibit a statistical size effect. A recent analysis by Wallin bears out these expectations. In an examination of nine different sets of crack arrest data (seven drawn from HSST/HSSI program records) Wallin demonstrated that crack arrest data are distributed log-normally about a mean curve that has the same temperature dependence as the Master Curve (see Figure 8.6). This similarity between the temperature dependence of initiation and arrest toughness suggests the possibility of describing the position of the arrest toughness curve in terms of a shift from the position of static initiation toughness curve, e.g. as a shift relative to To. Wallin examined this possibility using 55 sets of data for ferritic steels that included a variety of product forms, strength grades, and irradiation conditions [Wallin 98b]. Based on a statistical
analysis of these data Wallin developed the following shift equation: Eq. 8-8
868.0915.0
0)()()( 4.5722.119
27398.4exp y
arrestostaticoarrestoT
TTT
where To is in C and y is the static room temperature yield strength in MPa. ASME Code Cases N-629 and N-631 propose using RTTo as an index temperature for both the KIc and KIR curves, thereby maintaining the fixed separation between these curves illustrated in Figure 8.5. Figure 8.7 demonstrates that this procedure will produce a bounding estimate of crack arrest toughness provided the separation between the median curves for static initiation and crack arrest toughness falls below 95F. In Figure 8.8 we use Eq. 8-8 to determine the conditions for which separations of less than 95F occur. This comparison is made over the range of To values observed for irradiated and un-irradiated RPV steels using mean yield strength values for these conditions (un-irradiated = 69 ksi, irradiated = 90 ksi) taken from the database (Appendix A). While only cursory in nature, this analysis suggests that the Code Case N-629 proposal provides a bounding curve for plants approaching their end of license (i.e. To > 140F). Thus, the Code Case proposal appears to provide an adequate approach for assessment of EOL conditions (and thereby PTS). While the correlations presented in this section provide a useful summary of the trends exhibited by available data, they cannot replace a more fundamental, physically based, understanding of why such trends should occur. The absence of such an understanding raises questions regarding the limits of applicability of these relationships, thereby impeding progress in the application of Master Curve concepts in nuclear RPV integrity assessment.
77
0.0
50.0
100.0
150.0
200.0
-150 -100 -50 0 50 100 150 200
T - RTNDT, F
TEMPERATURE SHIFT, F
KI,
ksi
in
KIa
KIcKIc - KIa
Figure 8.5. Separation between the KIc and KIR curves [Yoon 99].
-150 -100 -50 0 500
50
100
150
200
250
95 %5 %
72W TKIa
=-13 oC
72W Irr. TKIa
=+76 oC
73W TKIa
=-14 oC
73W Irr. TKIa
=+70 oC
PTSE 1 TKIa
=+108 oC)
PTSE 2 TKIa
=+70 oC
15X2MØA TKIa
=+17 oC
18X2MØA TKIa
=+47 oC
HSST 02 TKIa
=+24 oC
KIa [
MP
am
]
T-TKIa [C]
= 18 %
Figure 8.6. Crack arrest Master Curve proposed by Wallin [Wallin 98b]. .
0
50
100
150
200
-150 -75 0 75 150 225 300
T - T o [oF]
KIC
[k
si*i
n0.
5 ]
0
50
100
150
200
KIC
[k
si*i
n0.
5 ]
KIC Curve Positioned
with a N-629 RTTo Value
5%/95% Tolerance
Bounds on 1T Master Curve
KIR Curve Positioned
with a N-629 RTTo Value
5%/95% Tolerance Bounds on Crack Arrest Curve
Shifted 95oF
from To
0
50
100
150
200
-150 -75 0 75 150 225 300
T - T o [oF]
KIC
[k
si*i
n0.
5 ]
0
50
100
150
200
KIC
[k
si*i
n0.
5 ]
KIC Curve Positioned
with a N-629 RTTo Value
5%/95% Tolerance
Bounds on 1T Master Curve
KIR Curve Positioned
with a N-629 RTTo Value
5%/95% Tolerance Bounds on Crack Arrest Curve
Shifted 95oF
from To
Figure 8.7. Illustration of the largest shift between a static initiation toughness curve (Master Curve) and a crack arrest toughness curve that will be bounded by a KIR curve located using RTTo.
0
25
50
75
100
125
150
-250 -150 -50 50 150 250
T o (Static) [oF]
To
Sh
ift
[oF
]
Arrest, Sy = 69 ksi (Un-Irr)
Arrest, Sy = 90 ksi (Irr)
Arrest predicted conservativelyBy ASME N-629 / N-631
0
25
50
75
100
125
150
-250 -150 -50 50 150 250
T o (Static) [oF]
To
Sh
ift
[oF
]
Arrest, Sy = 69 ksi (Un-Irr)
Arrest, Sy = 90 ksi (Irr)
Arrest predicted conservativelyBy ASME N-629 / N-631
Figure 8.8. The shift in transition temperature between a static initiation toughness curve (Master Curve) and a crack arrest toughness curve [Wallin 98b].
78
9 SUMMARY
The information provided in this paper demonstrates that substantial progress has been made recently concerning the adoption of a Master Curve testing standard, and the use of the To-index temperature measured by this standard to position bounding fracture toughness curves for use in vessel integrity calculations. Questions raised previously by the Staff regarding the use of Master Curve technology in these codes and standards are now largely resolved. The main difficulty faced when using the Master Curve to assess RPV integrity is now the lack of an accepted framework by which to estimate the irradiated fracture toughness of the vessel from To data, and the fact that this framework was never used to determine a PTS screening criteria for To. Consequently, there is currently no To-based PTS screening criteria, and there is no To-based margin term to account for uncertainty in the input variables. Ultimately these deficiencies fuel a concern that forcing Master Curve-technology into the current, non-Master Curve, framework may produce systemic “lack of fit” uncertainties, thereby resulting in the need for higher margins. The only way to alleviate this concern is to establish a Master Curve framework to estimate toughness at EOL, and use this framework as part of PFM calculations to establish a PTS screening criteria applicable specifically to Master Curve-based estimates of fracture toughness. Work on the development of such a framework for the Master Curve has only recently begun. In this paper we reviewed recent progress in the developing some of the components of such a framework, including the following:
Generic values of RTTo are provided for use when plant- or material-specific values of RTTo are not available. Data is provided that demonstrates a 1:1 correlation between the irradiation shift of the Charpy-V and To transition temperatures. This information suggests the possibility of applying embrittlement trend curves developed from CVN data to estimate the effect of irradiation on To. Available data suggests that weakest link scaling models developed for straight fronted cracks in test specimens systematically under-predict the fracture resistance of the semi-elliptical and buried cracks found in reactor pressure vessel service. ASME Code Case N-629 uses RTTo to position both the KIc and KIR curves with a fixed temperature separation between them. Information presented in this paper demonstrates that this fixed separation under-estimates the crack arrest toughness of RPV steels in some circumstances, and over estimates it in others. This finding suggests that a revision of the Code Case is needed to ensure that the KIR curve provides an appropriate degree of bounding to crack arrest data for all material conditions of interest. These findings provide cause for optimism that the issues surrounding application of Master Curve-based methodologies to the assessment of nuclear reactor vessel safety can be favorably resolved providing focused efforts continue in a number of key areas.
79
10 REFERENCES
10CFR5061 Code of Federal Regulation 10CFR50.61, “Fracture Toughness
Requirements for Protection Against Pressurized Thermal Shock Events.”
10CFR50 App. G Code of Federal Regulation 10CFR50 Appendix G, “Fracture Toughness Requirements {for Normal Operation}.”
Anderson 89a Anderson, T.L., “A Combined Statistical and Constraint Model for the Ductile-Brittle Transition Region,” Nonlinear Fracture Mechanics II – Elastic-Plastic Fracture, ASTM STP-995, J.D. Landes, A. Saxena, and J. G. Merkle, Eds., pp. 563-583, American Society for Testing and Materials, Philadelphia, PA, 1989.
Anderson 89b Anderson, T.L. and Stienstra, A.D., “A Model to Predict the Sources and Magnitude of Scatter in Toughness Data in the Transition Region,” JTEVA, 17, pp. 46-53, 1989.
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ASME NB2331 ASME NB-2331, 1998 ASME Boiler and Pressure Vessel Code, Rules for Construction of Nuclear Power Plants, Division 1, Subsection NB, Class 1 Components
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80
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Appendix A – Description of Empirical Database
This Appendix summarizes the contents of a MS-Access database assembled to validate the Master Curve description of fracture toughness in the transition regime and demonstrate its applicability, both before and after irradiation, to the plates, forgings, and weldments used in nuclear RPV fabrication‡‡. The database includes a total of 6,534 fracture toughness records. It contains information on welds, plates, and forgings used in the fabrication of nuclear RPVs. These include tests conducted both before and after neutron irradiation. Furthermore, cognizant that breadth of conditions represented by these data may not represent the full diversity of conditions in the operating nuclear fleet, we also examine available data for ferritic non-RPV steels through these analysis. These non-RPV steels can differ more from each other, and from RPV steels, than any two heats of RPV steel differ from one another. Consequently, these data for non-RPV steels support a more comprehensive examination of Master Curve applicability than would be possible otherwise. The following Tables summarize the contents of the database:
Table A1: List of data sources Table A2: List of materials Table A3: List of To values determined as
per the multi-temperature
‡‡ The author began development of the database
used in this assessment began under EPRI funding while he was employed by the Westinghouse Electric Company. The database has been expanded upon since that time, to include both recently developed information as well as information obtained from the literature. The author is indebted to EPRI for permitting use of the database for the purpose of preparing this report.
procedure outlined in Appendix C.
Table A4: List of To values determined as per the single-temperature procedure of E1921-97.
To assess the validity of KJC values and calculate To values from them an estimate of both the yield strength and the modulus, and how these quantities vary with temperature is needed. The 0.2% offset yield stress in ksi (ys) is calculated from the test temperature of the fracture specimen in degrees Kelvin (T) as follows [4]:
6.49lnexp895.6
1321)( TCTCCAmbientysys
(A.1)
Here, ys(Ambient) is the 0.2% offset yield strength at room temperature, C1 = 1033, C2 = 0.00698, C3 = 0.000415, and the strain rate is 0.0004 / second. This variation of strength with temperature was derived from a physics basis by Zerilli and Armstrong [A1.1]. Eq. (A1.1) models the temperature dependence of yield strength in all ferritic steels extremely well [A1.2], as evidenced by Figures A.1 and A.2.
Elastic modulus (in MPa) is estimated using the following equation [A.3]:
][1.57207200 CTE (A.2)
References [A1.1] Zerilli, F.J. and R.W. Armstrong,
“Dislocation-Mechanics-Based Constitutive Relations for Material Dynamic Calculations,” J of Appl. Phys., V61, N5 (1987) 1816-1825.
[A1.2] Kirk, M.T., Natishan, M.A.E., M. Wagenhofer, “Microstructural Limits of
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Applicability of the Master Curve,” 32nd Volume, ASTM STP-1406, R. Chona, Ed., American Society for Testing and Materials, Philadelphia, PA 2001.
[A1.3] Sokolov, M., HSST Program Files, personal communication.
-300
-150
0
150
300
450
600
-200 -100 0 100 200 300 400
Temperature [oC]
sy -
sy(
ref)
[M
Pa
] Forging/Un-Irr Forging/Power Forging/Test
Plate/Un-Irr Plate/Power Plate/Test
Weld/Un-Irr Weld/Power Weld/Test
Prediction
Figure A.1: Comparison of 0.2% offset yield strength data for nuclear RPV steels to the Zerilli / Armstrong constitutive relation.
-300
-150
0
150
300
450
600
-200 -100 0 100 200 300 400
Temperature [oC]
sy -
sy(
ref)
[M
Pa
]
HSLA Plate
C -M n Plate & We ld
Q&T Marte ns it ic Plate
Pre diction
Figure A.2: Comparison of 0.2% offset yield strength data for ferritic non-RPV steels to the Zerilli / Armstrong constitutive relation.
90
Appendix B - Multi-Temperature Approach for To Determination
To values are calculated from data sets that include KJC values determined using tests of different size specimens conducted at different temperatures by iteratively solving the following equation:
(B.1) where
n is the number of toughness specimens tested Ti is the test temperature KJC is the lower of the measured KJC value and the E1921-97 KJC(limit) value. These KJC values
are converted to 1T equivalence. a = 28.179 ksiin b = 69.993 ksiin c = 0.0106 Kmin = 18.18 ksiin I is 1 if E1921-97 size requirements, eq. (19), are met is 0 if E1921-97 size requirements, eq. (19), are not met
In no case is To calculated from less than 6 KJC values that satisfy the E1921-97 validity criteria. Other studies have demonstrated that To values calculated by this technique agree well with To values calculated as per ASTM E1921-97 protocols.
91
Appendix C – Assessment of Master Curve Goodness of Fit to Individual Datasets
This section contains the results of a dataset by dataset comparison of experimental KJc data to the temperature dependence assumed by the Master Curve. This information is organized into the following tables:
Table Matl. Loading
Rate Irradiation
C-1 RPV
Static
Unirradiated C-2 RPV Irradiated
C-3 Non-RPV
Unirradiated C-4 RPV High
C-5 Non-RPV
92
Appendix D – Data Sets that do not Statistically Match the Master Curve Temperature Dependence
Reference (from Table A1): [39] Reason for Statistical Deviation: Inclusion of data at too high a temperature (upper shelf).
Wallin22NiCrMo37
-600
-300
0
300
600
-150 -50 50 150 250
T-T o [oF]
De
via
tio
n f
rom
M
ed
ian
Ma
ste
r C
urv
e
[ks
i*in
0.5 ]
Invalid
Valid
Reference: [1] Reason for Statistical Deviation: Unknown.
MarstonA508 Cl. 2 Forging
-100
-75
-50
-25
0
25
50
75
100
-250 -200 -150 -100 -50 0 50
T-T o [oF]
De
via
tio
n f
rom
M
ed
ian
Ma
ste
r C
urv
e
[ks
i*in
0.5 ]
Invalid
Valid
Reference: [10] Reason for Statistical Deviation: Data looks OK.
IwadateA508 Cl. 3 Forging
-100
-50
0
50
100
-200 -150 -100 -50 0 50 100
T-T o [oF]
De
via
tio
n f
rom
M
ed
ian
Ma
ste
r C
urv
e
[ks
i*in
0.5 ]
Invalid
Valid
93
Reference: [11] Reason for Statistical Deviation: Inclusion of data at too high a temperature (upper shelf).
LidburyA508 Cl. 3
-500
-250
0
250
500
0 50 100 150 200 250
T-T o [oF]
De
via
tio
n f
rom
M
ed
ian
Ma
ste
r C
urv
e
[ks
i*in
0.5 ]
Invalid
Valid
Reference: [1] Reason for Statistical Deviation: Five data points above upper 95% tolerance bound for 10T and
11T specimens.
MarstonA533B Cl. 1
(HSST Plate 02)
-150
-75
0
75
150
-300 -200 -100 0 100
T-T o [oF]
De
via
tio
n f
rom
M
ed
ian
Ma
ste
r
Cu
rve
[k
si*
in0.
5 ]
Invalid
Valid
Reference: [7] Reason for Statistical Deviation: Looks OK.
InghamA533B Cl. 1
-500
-250
0
250
500
0 50 100 150 200 250
T-T o [oF]
De
via
tio
n f
rom
M
ed
ian
Ma
ste
r C
urv
e
[ks
i*in
0.5 ]
Invalid
Valid
94
Reference: [6] Reason for Statistical Deviation: Three data points at the highest test temperature.
McCabeA533B Cl. 1
HSST Plate 13A
-300
-150
0
150
300
-200 -100 0 100 200
T-T o [oF]
De
via
tio
n f
rom
M
ed
ian
Ma
ste
r
Cu
rve
[k
si*
in0.
5 ] Invalid
Valid
Reference: [26] Reason for Statistical Deviation: Inclusion of data at too low a temperature (lower shelf).
ChaouadiA533B Cl. 1
-100
-75
-50
-25
0
25
50
75
100
-250 -200 -150 -100 -50 0 50
T-T o [oF]
De
via
tio
n f
rom
M
ed
ian
Ma
ste
r C
urv
e
[ks
i*in
0.5 ]
Invalid
Valid
Reference: [31] Reason for Statistical Deviation: Inclusion of data at too high a temperature (upper shelf).
IshinoGeneric RPV Plate
-400
-300
-200
-100
0
100
200
300
400
-200 -100 0 100 200 300
T-T o [oF]
De
via
tio
n f
rom
M
ed
ian
Ma
ste
r C
urv
e
[ks
i*in
0.5 ]
Invalid
Valid
95
Reference: [18] Reason for Statistical Deviation: Unknown.
CEOGShoreham Linde 1092 Weld
-100
-50
0
50
100
-50 -25 0 25 50 75 100
T-T o [oF]
De
via
tio
n f
rom
M
ed
ian
Ma
ste
r C
urv
e
[ks
i*in
0.5 ]
Invalid
Valid
Reference: [23] Reason for Statistical Deviation: Inclusion of data at too high a temperature (upper shelf).
HawthorneLinde 0124 Weld
-1200
-800
-400
0
400
-200 -100 0 100 200 300
T-T o [oF]
De
via
tio
n f
rom
M
ed
ian
Ma
ste
r C
urv
e
[ks
i*in
0.5 ]
Invalid
Valid
Reference: [31] Reason for Statistical Deviation: Inclusion of data at too high a temperature (upper shelf).
IshinoGeneric RPV Weld
-1500
-1000
-500
0
500
-600 -400 -200 0 200 400
T-T o [oF]
De
via
tio
n f
rom
M
ed
ian
Ma
ste
r C
urv
e
[ks
i*in
0.5 ]
Invalid
Valid
96
Reference: [13] Reason for Statistical Deviation: Unknown.
NanstadMidland Beltline Weld
Irradiated to 1E19
-200
-100
0
100
200
-200 -100 0 100 200
T-T o [oF]
De
via
tio
n f
rom
M
ed
ian
Ma
ste
r
Cu
rve
[k
si*
in0.
5 ] Invalid
Valid
Reference: [13] Reason for Statistical Deviation: Unknown.
NanstadMidland Nozzle Weld
Irradiated to 1E19
-100
-75
-50
-25
0
25
50
75
100
-100 -50 0 50 100
T-T o [oF]
De
via
tio
n f
rom
M
ed
ian
Ma
ste
r
Cu
rve
[k
si*
in0.
5 ]
Invalid
Valid
Reference: [52] Reason for Statistical Deviation: Data at too low a temperature (lower shelf).
KrabiellSt E 47 - Static
-100
-75
-50
-25
0
25
50
75
100
-300 -250 -200 -150 -100 -50 0
T-T o [oF]
De
via
tio
n f
rom
M
ed
ian
Ma
ste
r C
urv
e
[ks
i*in
0.5 ]
Invalid
Valid
97
Reference: [44] Reason for Statistical Deviation: Martensitic steel.
Shoemaker18Ni(250) Maraging
-400
-200
0
200
400
-250 -125 0 125 250
T-T o [oF]
De
via
tio
n f
rom
M
ed
ian
Ma
ste
r C
urv
e
[ks
i*in
0.5 ]
Invalid
Valid
Reference: [44, 60] Reason for Statistical Deviation: Martensitic Steel.
HY-130
-100
-50
0
50
100
-150 -75 0 75 150
T-T o [oF]
De
via
tio
n f
rom
M
ed
ian
Ma
ste
r C
urv
e
[ks
i*in
0.5 ]
Valid, Shoemaker
Valid, Hasson
Reference: [53] Reason for Statistical Deviation: Unknown.
FujiiA508 Cl.3
-100
-75
-50
-25
0
25
50
75
100
-100 -50 0 50 100
T-T o [oF]
De
via
tio
n f
rom
M
ed
ian
Ma
ste
r C
urv
e
[ks
i*in
0.5 ]
Valid, KDOT=16,526
Valid, KDOT=83
98
Reference: [40] Reason for Statistical Deviation: Unknown.
ShabbitsA533B Cl. 1 (Plate 02)
KDOT=31
-100
-50
0
50
100
-100 -50 0 50 100
T-T o [oF]
De
via
tio
n f
rom
M
ed
ian
Ma
ste
r
Cu
rve
[k
si*
in0.
5 ] Invalid
Valid
Reference: [38] Reason for Statistical Deviation: Unknown.
LinkA533B Cl. 1
KDOT=104853
-90
-60
-30
0
30
60
90
0 25 50 75 100
T-T o [oF]
De
via
tio
n f
rom
M
ed
ian
Ma
ste
r
Cu
rve
[k
si*
in0.
5 ]
Invalid
Valid
Reference: [31] Reason for Statistical Deviation: Unknown.
IshinoGeneric RPV Plate (Irradiated)
KDOT=90,900
-200
-150
-100
-50
0
50
100
150
200
-200 -100 0 100 200
T-T o [oF]
De
via
tio
n f
rom
M
ed
ian
Ma
ste
r
Cu
rve
[k
si*
in0.
5 ]
Invalid
Valid
99
Reference: [48] Reason for Statistical Deviation: Data at too low a temperature (lower shelf).
Holtmann2.25Cr-1Mo
KDOT=5,289
-50
-25
0
25
50
-300 -200 -100 0 100
T-T o [oF]
De
via
tio
n f
rom
M
ed
ian
Ma
ste
r
Cu
rve
[k
si*
in0.
5 ] Invalid
Valid
Reference: [44] Reason for Statistical Deviation: Data at too low a temperature (lower shelf).
ShoemakerABS-C
KDOT=136,336
-20
-15
-10
-5
0
5
10
15
20
-500 -400 -300 -200 -100
T-T o [oF]
De
via
tio
n f
rom
M
ed
ian
Ma
ste
r
Cu
rve
[k
si*
in0.
5 ]
Invalid
Valid
Reference: [52] Reason for Statistical Deviation: Data at too low a temperature (lower shelf).
KrabiellSt 52-3
KDOT=24,788
-50
-25
0
25
50
-400 -300 -200 -100 0
T-T o [oF]
De
via
tio
n f
rom
M
ed
ian
Ma
ste
r
Cu
rve
[k
si*
in0.
5 ]
Invalid
Valid
100
Reference: [52] Reason for Statistical Deviation: Data at too low a temperature (lower shelf).
KraibellSt E 47
KDOT=2,479
-50
-25
0
25
50
-400 -300 -200 -100 0
T-T o [oF]
De
via
tio
n f
rom
M
ed
ian
Ma
ste
r
Cu
rve
[k
si*
in0.
5 ] Invalid
Valid
Reference: [52] Reason for Statistical Deviation: Data at too low a temperature (lower shelf).
KraibellSt E 47
KDOT=413,141
-50
-25
0
25
50
-400 -300 -200 -100 0
T-T o [oF]
De
via
tio
n f
rom
M
ed
ian
Ma
ste
r
Cu
rve
[k
si*
in0.
5 ]
Invalid
Valid