Remarks to the Upper Shelf Master Curve Concept

2008 ◽  
Author(s):  
Jiri Novak
Keyword(s):  
Fracture Toughness ◽  
Temperature Dependence ◽  
Ductile Fracture ◽  
Master Curve ◽  
Critical Strain ◽  
Peierls Stress ◽  
Transition Curve ◽  
Dislocation Slip ◽  
Ferritic Steels ◽  
Deformation Work

Recently, several works appeared in which temperature dependence of ductile fracture toughness of ferritic steels on the upper shelf of brittle-ductile transition curve was analyzed and Upper Shelf Master Curve concept was formulated. Generally, fracture toughness at different temperatures characterized by JIc or dJ/da should be proportional to the deformation work of unit volume evaluated from zero to the critical strain for ductile fracture. As in many other cases, critical strain for ductile fracture initiation may be identified with critical strain for initiation of shear bands, calculated for hyperelastic material with the corresponding stress-strain curve. This concept is successful, among others, in determination of the temperature dependence of fracture toughness of ferritic steels on the upper shelf. Two most important physical mechanisms controlling temperature dependence of constitutive behaviour of ferritic steels in the corresponding temperature range, hence the temperature dependence of both deformation work to initiation of ductile fracture and fracture toughness, are friction resistance to dislocation slip (Peierls stress) and dynamic recovery (dislocation annihilation). Predicted Upper Shelf Master Curve shape based on temperature dependence of constitutive parameters of different ferritic steels corresponds well to the published data.

Addressing NRC Concerns Regarding Proposed CC N-830: Direct Use of Fracture Toughness for Flaw Evaluations of Pressure Boundary Materials in Class 1 Ferritic Steel Components

2019 ◽  
Author(s):  
Marjorie Erickson ◽  
Mark Kirk
Keyword(s):  
Fracture Toughness ◽  
Temperature Dependence ◽  
Pressure Vessel ◽  
Master Curve ◽  
Crack Arrest ◽  
Nuclear Regulatory Commission ◽  
Ferritic Steels ◽  
Class 1 ◽  
Regulatory Commission ◽  
Linkage Models

Abstract Section XI of the ASME Boiler and Pressure Vessel Code provides KIc and KIa fracture toughness models for ferritic steels. These models are based on linear elastic fracture mechanics methods and were initially developed in the 1970s; they remain largely unchanged since that time. Recently, a modification to Code Case (CC) N-830 has been proposed to provide alternative fracture toughness models for use in the flaw evaluation methodologies of ASME Section XI Nonmandatory Appendices A and K. The integrated models contained in proposed Code Case revision predict the mean trends and scatter of the fracture toughness behavior of ferritic steels throughout the temperature range from the lower shelf to the upper shelf. These models include the transition fracture toughness Master Curve and crack arrest master curve approaches that describe the temperature dependence and scatter in KJc and KIa, respectively in the lower transition temperature region. Also included is a model describing the temperature dependence and scatter of JIc on the upper shelf. Finally, linkage models quantify the inter-relationships between these toughness metrics and how they change due to the irradiation-induced hardening. Together, these models describe the temperature dependence and scatter of fracture toughness initiation and arrest behavior for all ferritic reactor pressure vessel (RPV) steels from lower shelf through transition to the upper shelf, all indexed to a single parameter: T0. In late 2017 the Electric Power Research Institute (EPRI) published a report, MRP-418, providing the technical basis for these revisions to CC N-830. Nuclear Regulatory Commission (NRC) staff review of the revised Code Case and MRP-418 resulted in substantive questions regarding validation and range of applicability of the various toughness models. An on-going effort addresses these concerns, and a revision to MRP-418 scheduled for publication later in 2019 will summarize that work. This paper describes the efforts of the WGFE CC-N-830 group to respond to the NRC’s comments, and summarizes responses to some of the comments.

Validity of the Master Curve Temperature Dependence Assumption for Highly Embrittled RPV Materials: Results From the IAEA Coordinated Research Project (CRP-8)

2009 ◽  
Author(s):  
Tapio Planman ◽  
Kunio Onizawa ◽  
William Server
Keyword(s):  
Fracture Toughness ◽  
Temperature Dependence ◽  
Master Curve ◽  
Shape Change ◽  
Transition Curve ◽  
Curve Shape ◽  
Topic Area ◽  
Material Inhomogeneity ◽  
Realistic Description ◽  
Definition Of

The fracture toughness temperature dependence (transition curve shape) has been discussed almost since the original empirical definition of the curve in 1991. The data sets showing anomalous fracture behaviour of highly irradiated VVER-1000 pressure vessel steels presented in 2000’s have further enhanced this discussion and even a special model has been proposed for highly irradiated steels, including a mathematical definition of the curve shape change. Although in most cases the standard Master Curve (MC) approach, assuming a constant transition curve shape, has proven to give a realistic description for also highly irradiated ferritic steels, there are grades which show for example abnormally weak temperature dependence. In these cases, however, an obvious reason for the behaviour may be that the material does not fail by the mechanism assumed in the MC model. The fracture toughness data collected and analysed in the CRP-8 Topic Area 3 supports the validity of the curve shape assumption of ASTM E1921 also in case of irradiated steels and gives no rise to change the present definition. The Master Curve C-parameter (the shape parameter) estimation is proposed as an appropriate analysis method when there is need to estimate also the temperature dependence, whereas the SINTAP procedure is recommended for ensuring conservative lower bound estimates when material inhomogeneity is suspected. The results show that irradiation may slightly lower the fracture toughness in the upper transition region in relation to that predicted by ASTM E1921, but the effect after moderate T0 shift values (up to about 100°C) seems to be negligible. The investigated steels exhibit no or very weak correlation between the C-parameter and T0.

Statistical Analyses for Probabilistic Assessments of the Reactor Pressure Vessel Structural Integrity: Building a Master Curve on an Extract of the “Euro” Fracture Toughness Dataset, Controlling Statistical Uncertainty for Both Mono-Temperature and Multi-Temperature Tests

2006 ◽  
Author(s):  
Florent Josse ◽  
Yannick Lefebvre ◽  
Patrick Todeschini ◽  
Silvia Turato ◽  
Eric Meister
Keyword(s):  
Fracture Toughness ◽  
Temperature Dependence ◽  
Pressure Vessel ◽  
Master Curve ◽  
Structural Integrity ◽  
Ferritic Steels ◽  
Statistical Uncertainty ◽  
Master Curve Method ◽  
Curve Method ◽  
Reactor Pressure

Assessing the structural integrity of a nuclear Reactor Pressure Vessel (RPV) subjected to pressurized-thermal-shock (PTS) transients is extremely important to safety. In addition to conventional deterministic calculations to confirm RPV integrity, Electricite´ de France (EDF) carries out probabilistic analyses. Probabilistic analyses are interesting because some key variables, albeit conventionally taken at conservative values, can be modeled more accurately through statistical variability. One variable which significantly affects RPV structural integrity assessment is cleavage fracture initiation toughness. The reference fracture toughness method currently in use at EDF is the RCCM and ASME Code lower-bound KIC based on the indexing parameter RTNDT. However, in order to quantify the toughness scatter for probabilistic analyses, the master curve method is being analyzed at present. Furthermore, the master curve method is a direct means of evaluating fracture toughness based on KJC data. In the framework of the master curve investigation undertaken by EDF, this article deals with the following two statistical items: building a master curve from an extract of a fracture toughness dataset (from the European project “Unified Reference Fracture Toughness Design curves for RPV Steels”) and controlling statistical uncertainty for both mono-temperature and multi-temperature tests. Concerning the first point, master curve temperature dependence is empirical in nature. To determine the “original” master curve, Wallin postulated that a unified description of fracture toughness temperature dependence for ferritic steels is possible, and used a large number of data corresponding to nuclear-grade pressure vessel steels and welds. Our working hypothesis is that some ferritic steels may behave in slightly different ways. Therefore we focused exclusively on the basic french reactor vessel metal of types A508 Class 3 and A 533 grade B Class 1, taking the sampling level and direction into account as well as the test specimen type. As for the second point, the emphasis is placed on the uncertainties in applying the master curve approach. For a toughness dataset based on different specimens of a single product, application of the master curve methodology requires the statistical estimation of one parameter: the reference temperature T0. Because of the limited number of specimens, estimation of this temperature is uncertain. The ASTM standard provides a rough evaluation of this statistical uncertainty through an approximate confidence interval. In this paper, a thorough study is carried out to build more meaningful confidence intervals (for both mono-temperature and multi-temperature tests). These results ensure better control over uncertainty, and allow rigorous analysis of the impact of its influencing factors: the number of specimens and the temperatures at which they have been tested.

About Relation Between Irradiation Hardening of Ferritic Steels and Ductile Fracture Toughness Decrease

2009 ◽  
Author(s):  
Jiri Novak
Keyword(s):  
Fracture Toughness ◽  
Temperature Dependence ◽  
Ductile Fracture ◽  
Stress Level ◽  
Deformation Theory ◽  
Strain Curve ◽  
Stress Strain Curve ◽  
Stress Strain ◽  
Irradiation Hardening ◽  
Ductile Fracture Toughness

We showed recently that temperature dependence of the ductile fracture toughness can be predicted on the base of two assumptions: 1) assumption of constant characteristic length, 2) assumption of proportionality between J-R curve slope and deformation work in unit volume, evaluated from zero to critical strain for initiation of deformation bands determined in plane strain geometry for material modeled by deformation theory of plasticity. Temperature dependence of ductile fracture toughness results simply from temperature dependence of the stress-strain curve. Irradiation hardening changes stress-strain behavior in a qualitatively different way: It is observed that irradiation hardening to certain yield stress level changes the stress-strain curve of the material in the same way as prestraining of the unirradiated material to the same flow stress level does. Equivalence of irradiation and prestraining concerns all key properties of deformation theory; namely the secant modulus should be taken from the stress-strain curve of unirradiated material. With exception of this specific feature, the task of finding relative fracture toughness decrease by irradiation is the same as prediction of relative decrease of fracture toughness by temperature change. In the frame of the corresponding theory, relative decrease of ductile fracture toughness expressed by J-R curve slope can be obtained from the stress-strain curve of unirradiated material and irradiation hardening level. Quantitative results are presented for the weld metals 72W and 73W, studied in the Fifth Irradiation Series in the Heavy-Section Steel Irradiation Program, and compared with experimental data.

Use of Large Databases to Identify Trends in the Behavior of Ferritic Steels

2009 ◽  
Author(s):  
Mark T. EricksonKirk ◽  
MarjorieAnn EricksonKirk ◽  
Charles Rose ◽  
Xian J. Zhang
Keyword(s):  
Master Curve ◽  
Physical Models ◽  
Irradiation Damage ◽  
Transition Curve ◽  
Ferritic Steels ◽  
Systematic Effect ◽  
Mode Transition ◽  
Large Databases ◽  
Curve Model ◽  
New Evidence

In this paper we explore the crucial role played by the use of large databases in the identification, development, and refinement of models that describe the toughness behavior of ferritic steels. Specifically, we seek to emphasize and illustrate the point that when physical models are calibrated using large databases this process can reveal trends not previously seen, or foreseen. In support of this idea two examples are cited. First, the evidence for a CVE master curve in fracture mode transition is reviewed, as a counterpoint to the commonly held belief that each Charpy tanh transition curve is unique, with little commonality even within specific alloys, let alone across all ferritic steels. Second, new evidence is presented that the degree of prior hardening experienced by a ferritic steel has a systematic effect on the scatter exhibited by KJc data. This evidence suggests that the KJc Master Curve model, in which the scatter of KJc follows a Weibull distribution having a Kmin = 20 MPa√m and a slope (scatter magnitude) of 4, requires refinement, especially for the higher To values characteristic of steels that have been hardened by, for example, neutron irradiation damage.

On the Use of the Notch Master Curve for Apparent Fracture Toughness Predictions of Notched Ferritic Steels Operating Within the Ductile-to-Brittle Transition Zone

2015 ◽  
Author(s):  
Sergio Cicero ◽  
Tiberio Garcia ◽  
Virginia Madrazo
Keyword(s):  
Fracture Toughness ◽  
Transition Zone ◽  
Fracture Resistance ◽  
Master Curve ◽  
Ferritic Steels ◽  
Brittle Transition ◽  
Apparent Fracture Toughness ◽  
Different Temperatures ◽  
Fracture Tests ◽  
Ductile To Brittle Transition

This paper presents the Notch-Master Curve as a model for the prediction of the apparent fracture toughness of ferritic steels in notched conditions and operating at temperatures corresponding to their ductile-to-brittle transition zone. The Notch-Master Curve combines the Master Curve of the material in cracked conditions and the notch corrections provided by the Theory of Critical Distances. In order to validate the model, the fracture resistance results obtained in fracture tests performed on notched CT and SENB specimens are presented. The results gathered here cover four ferritic steels (S275JR, S355J2, S460M and S690Q), three different notch radii (0.25 mm, 0.50 mm and 2.0 mm) and three different temperatures within the corresponding ductile-to-brittle transition zone. The results demonstrate that the Notch Master Curve provides good predictions of the fracture resistance in notched conditions for the four materials analyzed.

Assessment of the Temperature Dependence of Ferritic Steel Fracture Toughness on or Near the Lower Shelf

2015 ◽  
Author(s):  
Mark Kirk ◽  
Marjorie Erickson
Keyword(s):  
Fracture Toughness ◽  
Temperature Dependence ◽  
Cleavage Fracture ◽  
Master Curve ◽  
Companion Paper ◽  
Structural Factors ◽  
Temperature Trends ◽  
Current Guidance ◽  
American Society ◽  
Current Code

Within the American Society of Mechanical Engineers (ASME) the Section XI Working Group on Flaw Evaluation (WGFE) is currently working to develop a revision to Code Case N-830. This revision incorporates a complete and self-consistent suite of models that describe completely the temperature dependence, scatter, and interdependencies between all the fracture metrics (i.e., KJc, KIa, JIc, J0.1, and J-R) from the lower shelf through the upper shelf. A paper presented at the 2014 ASME Pressure Vessel and Piping Conference described most of these models; a companion paper at this conference describes the J-R model. This paper also supports the WGFE effort by performing an assessment of the appropriateness of Wallin’s Master Curve model to represent toughness data on the lower shelf, and by comparing the Master Curve with the current Code KIc curve on the lower shelf. The work presented in this paper supports the following conclusions: 1. The Master Curve provides a reasonable representation of cleavage fracture toughness (KJc) data at lower shelf temperatures. A statistical evaluation of a large database demonstrates that the Master Curve works well to temperatures approximately 140 °C below To or, equivalently, approximately 160 °C below RTTo. 2. The percentile of cleavage fracture toughness data falling below a KIc curve indexed to RTTo varies considerably with temperature. At lower shelf temperatures as much as half of the data lie below the KIc curve, while at temperatures close to RTTo this percentage falls to approximately ≈ 1.5%. The current guidance of Nonmandatory Appendix A to Section XI to use structural factors of √10 or √2 is one means of addressing this inconsistency. 3. The inconsistent degree to which the KIc curve, with or without structural factors, bounds fracture toughness data cannot be fixed within the current Code framework for two reasons: the KIc curve does not reflect the actual temperature dependence shown by the fracture toughness of ferritic RPV steels, and the ratio of a mean or median toughness curve to a fixed percentile bound is not a constant value. It is for these reasons that in the next revision of Code Case N-830 the ASME WGFE is moving away from use of the KIc curve coupled with structural factors and, instead, is adopting models of fracture toughness that represent both the temperature trends and the scatter in the data with high accuracy.

Sign in / Sign up

Export Citation Format

Share Document