Applicability Of Dose-Damage Relations To Operating Reactors

Transcription

1 Applicability Of Dose-Damage Relations To Operating Reactors S. R. Ortner and C. A. English National Nuclear Laboratory, B168 Harwell Oxford Science Campus, Didcot, Oxfordshire OX11 0QT, UK Introduction It is essential for the safe operation of a nuclear power plant (NPP) that the reactor pressure vessel (RPV) should possess adequate toughness to resist the growth of any flaws introduced during manufacturing or service. The changing condition of the RPV during service is predicted using Dose-Damage Relationships (DDRs) *, many of which have been developed over time for different classes of RPV steel. There is currently general agreement concerning the main mechanisms contributing to RPV embrittlement at neutron doses characteristic of currently-operating nuclear power plant. Nonetheless, the DDRs used in different regulatory regimes, vary significantly both in the material factors, or aspects of the irradiation environment, considered to dominate damage development, and in the functional forms of the expressions describing their contributions. This variety arises from: 1) the progressive development of mechanistic understanding of the causes of RPV embrittlement, and the extent to which this is incorporated in the formulation; 2) the difficulty of extracting trends from collections of surveillance data in which variables are confounded and measurements are subject to significant uncertainty; 3) the complexity of transferring data from better-controlled single-variable experiments in Materials Test Reactors to the surveillance or vessel conditions. The variations in the DDRs lead to variability in predictions of the current state of plant and, more especially, in the anticipated state of plant likely to operate for >40 years. The variability is present in both mean predictions and the uncertainty associated with predictions under particular conditions. The ASTM E10.02 sub-committee is in process of updating the ASTM standard method for predicting the radiation-induced change in a RPV steel s ductileto-brittle transition temperature, as measured using Charpy impact tests (T 41J ) [1]. A working group has been set up to compare the DDRs currently available for MnMoNi steels under surveillance conditions, to ensure that the expression(s) contained within the updated standard are of most use to the engineering community. In this paper we present the results * also known as embrittlement trend curves.

2 of contributory investigations carried out at NNL, with particular reference to long term operation. It describes the relation of the DDRs to the databases from which they were derived, and compares this with their ability to predict data from a wider range of sources. (The wider range of sources is found in a database of internationally-acquired surveillance and test reactor data compiled by M. Kirk of the US NRC, identified as the wide-ranging database, WRD, which is used by the ASTM working group). We also consider the contributory factors which are required for a DDR to cover data from a wide range of sources in terms of functional forms and input variables. The DDRs The DDRs under consideration are The predictive trend currently found the US NRC Regulatory Guide 1.99 Revision 2 [2], which was based on statistical analyses of US surveillance data in the 1980s. A number of trend curves based on progressively more recent analyses of US surveillance data, namely: The DDR found in ASTM standard E900, as of 2002 (E900-02) [3], that produced by Eason, Odette, Nanstad and Yamamoto (EONY) in 2006 [4], and that produced by Erickson (Erickson Fit 6) [5] in E and EONY were derived from statistical analyses of US surveillance T 41J data, using functional forms deliberately based on the mechanistic understanding available at the times of development. Erickson Fit 6 was intended to have a simpler mathematical form, in particular involving fewer product form terms, than the previous US DDRs. Of these, EONY has been accepted by the US Regulator. The US surveillance materials include steels with range of Cu, reaching to >0.35wt.%, and this is reflected in the forms of the US DDRs. A DDR developed by Todeschini et al [6], intended for use in EDF s 900MW NPPs, and based on a statistical analysis of French surveillance T 41J data, supplemented by a small amount of materials test reactor (MTR) data. This has been accepted for use by the French regulator. Since French surveillance steels are predominantly low in Cu, this DDR was derived from steels with <0.13wt.% Cu. More specifically, only 6 out of the 362 surveillance data points were from steels with >0.10wt.%Cu, and the DDR is intended to apply to low-cu materials only.

3 The DDR in the Japanese standard JEAC (accepted by the Japanese regulator) is based on a mechanistic model of damage development by Soneda et al [7], with the parameters fixed by fitting to the Japanese surveillance T 41J database. As with the French surveillance database, the Japanese database is dominated by low-cu steels. For JEAC , most fitting was to data from steels with Cu<0.19wt.%. The RR/UCSB DDR [8] was derived primarily from yield stress increment data acquired on low-cu model steels within the UCSB IVAR experiment, with adaptations and additional fitting to hardness increment data within the Rolls-Royce database, and T 41J data acquired from publicly-available sources. The DDR is intended to describe the development of hardening from stable matrix damage, and therefore applies only to steels with Cu<0.075wt.%, and irradiations at fluxes <10 16 n.m -2 s -1 and fluences <2x10 23 n.m -2. The RADAMO DDR [9] was derived from yield stress increments () in a number of model and commercial steels irradiated in surveillance and MTR locations, and applies to a wider range of material and environmental conditions than the previous DDRs. The comparisons with T 41J data given here are made via :T 41J conversions used in the E10.02 working group [10]. WR-C(5) Rev 1 [11] was developed from the statistical analysis of the WRD. It thus derives from specimens with a much wider range in compositions, product forms and irradiation exposure conditions than the DDRs derived from predominantly surveillance data. The details of the different DDRs are to be found in the references given and, for brevity, are not reproduced here. The variables found to contribute in a statistically significant manner to hardening / embrittlement and, therefore, included in the different DDRs are summarised in Table 1. All incorporate effects of neutron fluence, Cu and Ni, and the more modern DDRs include the irradiation temperature explicitly. The major differences lie in whether other elements (P, Mn, Si, C) and flux (or time) are considered to be of importance, and in the number of product form categories, which varies from one (i.e. all forms are treated together) to six. All fluxes ad fluences are given for neutron energies >1MeV.

4 Table 1. Variables Contributing To Embrittlement In DDRs Assessed. DDR Contributing Variables Standard Deviation (1) for different product forms ( C) Product form 1 Reg. Guide Fluence, Cu, Ni, Product Form (base base metal, Rev. 2 metal and weld) weld 15.6 E Fluence, Irradiation Temperature, Cu, all 15.6 Ni Product Form (CE plate, other plate, Linde 80 weld, other weld, forging) EONY Fluence, Flux, Irradiation Temperature, low- (high-) Cu 9.7 (10.9) Cu, Ni, P, Mn Product Form (CE plate, other plate, standard reference plate, Linde 80 weld, other weld, forging) forging low- (high-) Cu plate 8.3 (11.8) low- (high-) Cu weld 10.3 (14.7) Erickson Fit 6 EDF 900MW JEAC RR/UCSB RADAMO WR-C(5) Rev.1 Fluence, Irradiation Temperature, Cu, all 19 Ni, P, Mn Fluence, Irradiation Temperature, Cu, base metal 9.3 Ni, P, Product Form (base metal, weld) weld 13.3 Fluence, Flux, Irradiation Temperature, all 9.4 * Cu, Ni Fluence, Flux, Irradiation Temperature, base metal 8.1 Cu, Ni, Mn, P, C, Si, Product Form (weld, base metal) weld 10.4 Fluence, Time, Irradiation Temperature, all 27.5 # Cu, Ni, P Fluence, Irradiation Temperature, Cu, all ! Ni, P, Mn, Product Form (weld, plate, forging) * without offset correction, # based on ±25 C for Y uncertainty plus 10% for uncertainty in input variables.! for range x10 23 n.m -2. The product form term enters in the conversion from hardening to T 41J.

5 Table 1 also includes the standard deviations (1) found by the DDR developers. For the DDRs derived from US surveillance data, it is evident that decreasing the number of product forms and simplifying the mathematical forms of the dependences (Erickson Fit 6 versus EONY) results in a increase in the standard deviation of the fit between the DDR predictions and the surveillance data, even when the database from which the DDR is derived has expanded. It is also worth noting that JEAC contains fewer input variables than other modern DDRs. It does, however, involve more complex mechanistically-based functions, such that the number of adjustable parameters is similar to that in EONY. Again the increase in complexity (when that complexity is based on mechanistic understanding) is associated with a decrease in 1. The extent to which the differences in the DDRs affect prediction depends on the conditions assessed. Figure 1 illustrates the progression of embrittlement predicted by the different DDRs for a plate with moderate levels of the more significant embrittling elements. The Figure shows that, in these circumstances, the variability in prediction of the mean shift is around 20 C near 2x10 23 n.m -2, rising above 30 C by n.m -2. (These fluences are chosen as they span typical end-of-life fluences for beltline steels in current MnMoNi RPVs and the RPVs of new generation NPP with extended lives.) The extent of the variability is sufficient for the choice of DDR to have a significant effect on a structural integrity assessment. Of equal importance, however, is the uncertainty associated with the prediction. DT41J Measured [oc] Log {Fluence [n/cm2]} Model (P) - E (P) - 10CFR50.61a (EONY) (P) - Kirk, WR-C(5)Rev.1 (P) - Todeschini, EdF 900 MW Erickson, Fit 6 JEAC (P) - RR/UCSB Low Cu (P) - Reg Guide 1.99 Rev. 2 RADAMO Figure 1. Predictions of hardening in a MnMoNi plate containing 0.15Cu, 0.80Ni, 1.3Mn, 0.008P and 0.20Si, irradiated at 285 C and n.m -2 s -1.. This Figure and similar Figures following was produced using the Plotter spreadsheet associated with Kirk s (US NRC) wide-ranging database of

6 Measurement And Prediction Uncertainty The databases from which the DDRs are derived are not ideal for statistical analysis since the variables are generally correlated, and the data are scattered. The strongest correlation is between flux and fluence, but there are also correlations between flux and temperature when the database includes data from BWRs (lower temperatures and fluxes) and PWRs (higher temperatures and fluxes), and between Cu, P and fluence, when the database contains data from older plants manufactured from steels with less tightly controlled levels of Cu and P, and newer plants with lower Cu and P. In addition, the relation between levels of different elements differ in different product forms [6]. The first source of scatter lies in the nature of the measurements themselves (see e.g. [12]), which lead to an expectation of uncertainties of the order ±10 C in the transition temperature, with the uncertainty in the shift measurement correspondingly higher. This uncertainty is associated equally with every datum in a shift database. It affects the extent to which a significant trend curve may be derived from the database, and also affects the reliability of a derived DDR s predictions beyond the most populated parts of the variable space covered by the database. One would expect that prediction uncertainties associated with contributions of this kind to be greatest at the extremes of variable space e.g. at very high or low Cu, temperature, fluence etc. Variations in the measurements of T 41J for the US A533B test plate HSST02 [13] illustrate the variability which may be expected in the start-of-life measurements for a plate steel manufactured in the 1960s US A533B Class HSST-01 T 41J, T 44J data at 1/4t 15 Av = ( o F) sd = ( o F) Count 4 Count T 41J ( o C) a) b) T 30ft-lb ( o F) Figure 2. (a) Measurements of T 41J at the quarter-thickness position at different locations along the length of HSST02 plate. (b) Range of T 30ft.lb (T 41J ) seen in US A5533B Class 1 plate.

7 Some of the variation seen in Figure 2 relate not just to measurement uncertainty, or to the effects of local thermal history, but also to local chemistry variations. These are quantified in Table 2, where they are compared with composition variations seen in a more recent, deliberately low-cu, forging. Table 2. Comparison between composition ranges seen in different RPV steels. Source Approx. Date Composition Range (wt.%) Of Cu Ni Mn P Manufacture Comment JFL Data from through- Japanese thickness variation 0- hollow 1T. ingot Very small variation, forging not systematic with thickness HSST02 Late 1960s Systematic through US plate thickness variation Compositional uncertainties in a datum affect the extent to which compositional dependences may be derived. In addition, they have a strong effect on the predictability of the state of a given RPV. In DDRs, part or all of the shift prediction is of the form: T= (irradiation temperature term)(composition term) (Fluence term) As a result, the prediction uncertainty due to uncertainties in the composition of the material under consideration must increase with increasing neutron dose, even above the level to be expected simply from high fluence representing an extreme of the fluence variable. The overall effect of the all the input uncertainties (in the measurement of T 41J, composition and exposure conditions, and in the relation of the material used for the start of life measurements to that used for surveillance measurements or for vessel manufacture [4, 6]) on the development of the DDRs themselves and their subsequent ability to predict data, are

8 illustrated in Figure 3. Comparing this with Figure 1 shows that the prediction uncertainty associated with each DDR is greater than the variation in the mean predictions between DDRs. The expansion in the range of the residuals, rather than the mean predicted shift, is likely to dominate assessments at the higher fluences. For this reason, it is important for a DDR to be as accurate as possible. Although the influence of certain terms on the mean prediction may not be marked, if their inclusion reduces the prediction uncertainty, then they offer a significant benefit. Predicted - Measured T41J [oc] Log {Fluence [n/cm2]} Figure 3. Expansion of the range of the residuals when the DDR predictions are compared with the data in M. Kirk s Wide-Ranging Database. (Different coloured points refer to residuals produced by the application of different DDRs.) DDR Comparisons In this section, we compare the predictions of different DDRs with the surveillance T41J data in the WRD, in order to assess the importance of including dependences on different variables in accurate prediction. Table 3 shows the residuals for the fits between the DDR predictions and the shift measurements in the WRD for the mechanistically simple situation of low Cu ( 0.075wt.%) moderate Ni ( 1.2wt.%) and moderate flux ( 4x1016n.m2 ;E>1MeV). In this situation, there is not much difference in the behaviours of the different DDRs. The bias in the mean prediction (i.e. the mean value of the residual between datum and predicted shift) is smallest for JEAC , as is the overall RMSD (root mean square deviation).

9 Table 3. Statistical Parameters Showing Fit Between DDRs And WRD Measurements Of Surveillance T 41J In Commercial Steels With Cu0.075wt.%, Ni1.2wt.%, flux4x10 16 n.m -2. DDR Mean Residual (Predicted-Measured, C) RMSD ( C) E EONY WR-C(5) Rev EDF 900MW Erickson Fit JEAC RR/UCSB R.G Rev RADAMO The details of how these values are achieved are illustrated in Figure 4. For this and similar Figures following, the relevant data (i.e. within the defined composition and flux ranges) in the WRD were divided into 10 equally-populated sub-sets, with increasing fluence. Not all data points in the WRD are associated with the same information e.g. not all have Mn or Si measurements. Different DDRs require different input variables, thus the sub-sets associated with different DDRs are not of the same size. In particular, those associated with RR/UCSB are smaller than those associated with the other DDRs. As a result, the precise fluence ranges for each sub-set differ. The x-axis indicates the fluence at the mid-point of the range within which the residuals were calculated for each DDR. Figure 4a shows that WR-C(5) Rev.1, EDF 900MW, Erickson Fit 6 and RR/UCSB progressively over-predict the mean embrittlement, while E900-02, EONY and R.G Rev.2 progressively under-predict it. Even in the highest fluence range, however, the biases for E900-02, EONY, Erickson Fit 6 and RADAMO lie within ±10 C, which is less than the uncertainty in a given shift measurement. There is no clear effect of fluence for RADAMO

10 and JEAC On this basis one would select JEAC or RADAMO for accurate highfluence predictions, or the over-predicting DDRs for slight conservatism, but the differences are not great. Mean Residual (Predicted-Measured, C) 15 E EONY WR-C(5)R1 EdF 900 MW 10 E-Fit 6 JEAC RG1.99 Rev2 RADAMO 5 RR/UCSB E E E E a) Mid-Range Fluence Value (n.cm -2 ) RMSD ( C) E E E E+20 E EONY WR-C(5)R1 EdF 900 MW E-Fit 6 JEAC RG1.99 Rev2 RADAMO Power (E900-02) Power (EONY) Power (WR-C(5)R1) Power (EdF 900 MW) Power (E-Fit 6) Power (JEAC ) Power (RG1.99 Rev2) Power (RADAMO) b) Mid-Range Fluence Value (n.cm -2 ) Figure 4. Behaviour of (a) mean residual and (b) RMSD for low Cu, medium-ni surveillance data. The trend lines are power-law best fits to the data. Figure 4b shows that the prediction uncertainty also increases with fluence. Again JEAC performs best in this aspect, but the behaviour of the other DDRs is less consistent

11 with the behaviour of the mean residual. Lower uncertainties are associated with EONY than with the more conservative DDRs. For prediction at high fluences, therefore, the more heavily-parameterised DDRs are offering a better combination of accuracy in the mean prediction, with lower prediction uncertainty. Table 4 and Figure 5 show similar analyses for higher Cu steels. Since the EDF 900MW and RR/UCSB DDRs do not apply to these steels, they are not included in the Table and Figure. The Cu limit here is 0.25wt.% since, this is the highest level to which JEAC is expected to apply. Now the DDR from Regulatory Guide 1.99 Revision 2 shows the smallest bias over the entire fluence range, but this is offset by the large uncertainty. EONY combines a small overall bias and uncertainty. The behaviour of the RADAMO DDR is surprisingly poor. This may relate to the conversion from yield stress increments to T 41J values used in the ASTM working group s assessment rather than the intrinsic characteristics of the DDR. If so, this caveat may also apply to the behaviour of the RR/UCSB DDR. Table 4. Statistical Parameters Showing Fit Between DDRs And WRD Measurements Of Surveillance T 41J In Commercial Steels With 0.075<Cu0.25wt.%, Ni1.2wt.%, flux4x10 16 n.m -2. DDR Mean Residual (Predicted-Measured, C) RMSD ( C) E EONY WR-C(5) Rev Erickson Fit JEAC R. G Rev RADAMO

12 20 15 Mean Residual (Bias, C) E EONY Kirk, WR-C(5)Rev.1 Erickson, Fit 6 JEAC Reg Guide 1.99 Rev a) E E E E E+21 Fluence in mid-range of sub-set (ncm -2 ;E>1MeV) RMSD ( C) E EONY Kirk, WR-C(5)Rev.1 Erickson, Fit 6 JEAC Reg Guide 1.99 Rev. 2 b) E E E E E+21 Fluence in mid-range of sub-set (ncm -2 ;E>1MeV) Figure 5. Behaviour of (a) mean residual and (b) RMSD for medium-high Cu, medium- Ni surveillance data. Figure 5a shows that the remaining DDRs exhibit low mean residuals for these 0.075<Cu<0.25 steels, up to around 2x10 23 n.m -2. At higher fluences, a bias develops progressively in all DDR predictions except those of EONY. The bias remains less than ±10 C in EONY, WR-C(5) Rev 1 and JEAC even at the highest fluence range.

13 The scatter shown in Figure 5b is higher than in the low-cu steels, and becomes very high for Reg. Guide 1.99 Rev. 2. This is to be expected, since the database from which this DDR was derived was dominated by lower-fluence data, so that the high fluences represent relatively more extreme conditions for this DDR. The scatter is lower for JEAC , EONY, E and WR-C(5) R1 than for the other DDRs. These are thus the preferred DDRs for use with moderately high-cu steels. There are limited numbers of measurements available for steels with Cu>0.25, but the predictions of these data are described in Table 5 and Figure 6. The biases become more conservative with increasing fluence, remaining below ±10 C for EONY and E The scatter is similar for all the DDRs, showing no trend with fluence. For this material range, the US DDRs are all similar, with EONY being slightly more appropriate than the others. Table 5. Statistical Parameters Showing Fit Between DDRs And WRD Measurements Of Surveillance T 41J In Commercial Steels With Cu>0.25wt.%, Ni1.2wt.%, flux4x10 16 n.m -2. DDR Mean Residual (Predicted-Measured, C) RMSD ( C) E EONY WR-C(5) Rev Erickson Fit RADAMO

14 20 Mean Residual (Predicted-Measured, C) E E E E E EONY WR-C(5)R1 E-Fit 6-15 Fluence in mid-range of sub-set (ncm -2 ;E>1MeV) a) RMSD E EONY WR-C(5)R1 E-Fit 6 5 b) E E E E+20 Fluence in mid-range of sub-set (ncm -2 ;E>1MeV) Figure 6. Behaviour of (a) mean residual and (b) RMSD for high Cu, medium-ni surveillance data. National Effects The RMSDs presented in Table 3 - Table 5 are mostly high in comparison with the 1 values reported by the DDRs developers. This is particularly evident when the RMSD values for the entire compositional range are considered, as illustrated in Table 6. This may be because the individual DDRs were developed using limited, or national, data sets, and are being

15 applied to data with greater variable ranges. If that were the only reason for the increased scatter, then the scatter should be smaller for those DDRs developed from large data sets including wide ranges of input variables, i.e. the last three DDRs in Table 6. This is not the case. Investigations of data sets from different countries clarify this point. Table 6. Summary of residuals for surveillance T 41J data in the WRD. DDR Product Form RMSD from relevant sub-set of WRD R.G Rev 2 Base metal 20.3 Weld 25.1 E All 18.0 EONY Low (High) Cu Forging 14.8 (16.1) Low (High) Cu plate 9.9 (13.4) Low (High) Cu weld 19.4 (24.0) JEAC All 16.3 EDF 900MW Base Metal 13.5 Weld 20.5 Erickson Fit 6 All 19.3 RR/UCSB Low Cu base metal 12.1 Low Cu weld 22.0 RADAMO All 29.6 WR-C(5) Rev 1 All 17.2

16 a) US data b) Japanese data c) French data Figure 7. Distribution of residuals when low-cu data from different countries are compared with a selection of DDRs. Red points and linear trend through the points = EONY, blue =WR-C(5) Rev 1, pink = JEAC , purple = EDF 900MW, green = RADAMO.

17 d) German data e) Belgian data Figure 7. Distribution of residuals when low-cu data from different countries are compared with a selection of DDRs. Contd. Figure 7a shows the trends of the residuals when a selection of DDRs is used to predict the low-cu US data in the WRD. The trend lines for EONY (red) and JEAC (pink) lie close to the x-axis, crossing it in opposite directions. EDF 900MW (purple) and WR-C(5) Rev.1 (blue) cross the x-axis in the upward direction with a higher slope, as does RADAMO (green), which is shifted downwards with respect to these two DDRs. A similar effect is observed with the Japanese data (Figure 7b). For the French data, most of the trend lines are rotated clockwise, except for the RADAMO line, which retains its original orientation. As a result, the mean residuals for EDF 900MW and WR-C(5) Rev.1 are reduced, while those for EONY are increased. A similar rotation is seen for fits to the German data (except that the trend in the RADAMO residuals has now rotated). For the Belgian data, the rotation has

18 gone further, with EONY now producing a very marked trend in the residuals. RADAMO now provides a better fit. These trends are likely to be informative in themselves, but here we focus only on the fact that the trends change when data from different countries are considered. If such changes are due to the effect on national DDR development of different distributions of the input variables, then the data in sets showing the most marked differences (i.e. the Belgian versus the US data) should fall in different parts of variable space. In fact, the variable ranges (Cu, Ni, Mn, P, C, Si, flux, fluence, temperature) for the Belgian data fall in well-populated parts of the ranges exhibited by the US data. Any effect of the ranges of the currently-used input variables on the effective parameterisation of the DDRs must, therefore, be subtle enough to require a more sophisticated analysis of the WRD to be identified (and form the basis of deriving a more widely-applicable DDR). Alternatively, it is possible that there remain factors which are not included in any of these DDRs, and exert an influence on embrittlement which can only be discerned when a database includes data from different countries. Despite the number of variables already included in DDRs, there are several factors not included which are known to affect embrittlement. Of these, the most well-known are: 1. Soluble N and C levels (rather than the bulk C level) [14]; 2. Initial hardness [15, 16]; 3. Ratio of fluence to displacements per atom (dpa); 4. Capsule temperature relative to coolant input temperature. Of these, the first two factors will be affected by the thermo-mechanical treatments used by the manufacturer (especially welding procedure when considering N), which could vary from country to country. The third reflects the fact that hardening and embrittlement occur as a function of dpa rather than fluence. The use of fluence is reasonable when the ratio of dpa to fluence is constant. There will, however, be some variations in the ratio between the two depending on the placement of the surveillance capsule (e.g. on the RPV wall or the outside of the baffle), and the extent of the water gap (larger in BWRs than in PWRs). This capsule position can also have an effect on the relation between the capsule temperature and inlet water temperature [17]. Factors 3 and 4 will therefore be affected by the precise reactor design, and the proportion of BWRs in the fleet. Again these factors could vary from country to country. In addition to these relatively well-known factors, it is possible that currently unknown factors have small effects on embrittlement. For example, elements other than those currently consider could affect hardening. If so, the concentrations of these elements

19 may well depend on the origin of the steel. Another indeterminate possibility lies in operational effects, i.e. whether load following, rates of heat-up and cool-down, or outage frequency, influence the embrittlement from a given fluence. While these factors are clearly less influential than e.g. Cu and Ni concentrations, it remains important to investigate their roles for new generation NPP. For RPVs in such plant, the steel supplier may differ from that used traditionally, the thermo-mechanical history of the vessel may differ, and the design and operational procedures will differ from those used in the past. Until the cause of nation-to-nation variation in DDR applicability is determined, it will be difficult to determine which DDR is the most appropriate to use in new generation NPP. It may be argued that current DDRs contain so many input variables that they are overcomplex or over-parameterised already, and that searching for additional variables is not justified. Radiation damage is, however, a complex process, and a direct mechanistic justification may be made for all of the variables included to date, except for product forms. Even for product forms, however, there is evidence that the terms are simplifying surrogates for (less well-known) thermo-mechanical heat treatments, and modifications to the nominal composition terms, both of which are justifiable. As has been shown in this paper, the more complex DDRs, and those incorporating effects of more variables, provide a better combination of accuracy and prediction certainty, and it is the combination of these factors which is of importance in structural integrity assessments. Conclusions The predictive behaviours of a number of DDRs for MnMoNi steels have been investigated against the data from RPV steels in Kirk s (US NRC) wide-ranging database. It has been shown that prediction uncertainty increases with increasing fluence such that, for extended operation, it may be more life-limiting than the mean predicted shift. Considering data over the full range of Cu levels, the more complex DDRs performed better than simpler DDRs, when both mean shift prediction and prediction uncertainty at higher fluences are taken into account. This, together with mechanistic understanding, indicates that even the more complex of the current DDRs are not over-parameterised. The prediction uncertainties were greater than would have been expected from the 1 values found during the development of many of the DDRs. This may relate to the more limited ranges of input variables in the development databases used in different countries. It may

20 also indicate that there are variables affecting embrittlement which are not yet included explicitly in DDRs, and which may (on average) differ from country to country. A number of candidate variables have been suggested. The current association of these variables with particular countries is unlikely to be repeated for new generation NPP. It will, therefore, be advisable to identify their roles before judging which DDR will be most appropriate for a given country s new reactor fleet. Acknowledgments The authors wish to thank the UK s Office of Nuclear Regulation and Rolls-Royce plc for supporting this work. References 1. ASTM Standard E (2007) Standard Guide for Predicting Radiation-Induced Transition Temperature Shift in Reactor Vessel Materials, E706 (IIF). 2. U. S. Nuclear Regulatory Commission Regulatory Guide 1.99 Radiation Embrittlement Of Reactor Vessel Materials Revision 2, May Charpy Embrittlement Correlations Status of Combined Mechanistic and Statistical Bases for U.S. RPV Steels (MRP-45): PWR Materials Reliability Program (PWRMRP), EPRI, Palo Alto, CA: E. D. Eason, G. R. Odette, R. K. Nanstad, and T. Yamamoto, A Physically Based Correlation of Irradiation Induced Transition Temperature Shifts for RPV Steel, Oak Ridge National Laboratory, ORNL/TM-2006/530, ADAMS ML M. Erickson,, "Development of a Charpy Master Curve-Based Embrittlement Trend Curve," proceedings of Fontevraud 7, Paper # A105-T01, September 2010, Avignon, France. 6. P. Todeschini, Y. Lefebvre, H. Churier-Bossennec, N. Rupa, G. Chas, and C. Benhamou, Revision of the irradiation embrittlement correlation used for the EDF RPV fleet, proceedings of Fontevraud 7, Paper # A084-T01, September 2010, Avignon, France.

21 7. N. Soneda, K. Dohi, A. Nomoto, K. Nishida, and S. Ishino, "Embrittlement Correlation Method for the Japanese Reactor Pressure Vessel Materials," Journal of ASTM International, Vol. 7, No. 3, Paper ID JAI (2010). 8. T. J. Williams, K. Wilford, G. R. Odette, T. Yamamoto, "A new model of irradiation hardening in low copper RPV steels from stable matrix damage," IAEA Technical Meeting on Irradiation Embrittlement and Life Management of Reactor Pressure Vessels in Nuclear Power Plants, Znojmo, Czech Republic, October R. Chaouadi, An Engineering Radiation Hardening Model For RPV Materials SCK- CEN Report R-4235, September M. Kirk and M. Natishan, Shift in Toughness Transition Temperature Due To Irradiation: T 0 versus T 41J. A Comparison and Rationalization of Differences IAEA specialists meeting held Prague, Czech Republic, M. Kirk, A Wide-Range Embrittlement Trend Curve for Western RPV Steels, in ASTM Symposium on Effects of Radiation on Nuclear Materials, 25th Volume, ASTM STP-1547, Eds. T. Yamamoto, M. Sokolov, and B. Hanson, Eds., American Society for Testing and Materials, West Conshohocken, PA, J. F. Knott,Cleavage Fracture In Heterogeneous Steel Microstrutures Solid State Mechanics & Applications, 97 (2002) Manufacturing History and Mechanical Properties of Japanese Materials provided by the International Atomic Energy Agency. Japan Engineering Society, October E. A. Little and D. R. Harries, Radiation Hardening and Recovery in Mild Steels and the Effects of Interstitial Nitorgen, Metal Sci., 4 (1970) A. J. E. Foreman and R. J. McElroy, Modelling of RPV Embrittlement, AEA Technology Report AEA-TSD-0067, G. R. Odette et al., "Development of superposition rules for hardening in alloys containing multiple defect populations." Fusion Materials Semiann. Prog Rep. for period ending Dec 31 (1998): A. L. Lowe, Role And Experience With Thermal Monitors In Reactor Vessel Surveillance Capsules in Effects of Radiation on Materials: 18th Int. Symp., ASTM STP Eds., Nanstad et al., pub. ASTM, West Conshohocken, PA, USA (1999) pp