DDRs used to predict the embrittlement of the C-Mn steels used in the UK Magnox RPV had been mechanistically based from the 1980s.2 These predict radiation-induced changes in yield stress (hardening) or embrittlement (Charpy impact energy transition temperature or fracture toughness transi­tion temperature) as a function of radiation dose and temperature. The approach adopted has been set out in Jones and Bolton2 and Wootton et al.3,n The advantage of this approach was that the derived rela­tionships could be used with confidence when limited extrapolation was required into regions of neutron dose, dose rate, or irradiation temperatures that were not specifically included in the surveillance database.

It is important to note that it was the advances in understanding that enabled the adoption of a mecha­nistic approach (rather than adopting an empirical approach which had been followed in all other embrit­tlement correlations of this time). More specifically,
the seminal work of Fisher and coworkers in the early 1980s50 assumed that changes in yield stress arose from the combined effects of irradiation damage clusters and copper precipitates. Subsequently,2,3,114 a two-term relationship was finally adopted2 to model both hardening (As) and embrittlement (A T40j) and had the following form:

AT40J

or

As

This relationship follows the model of Fisher and coworkers,50 where Dcopper represents the contribution of nanoscale copper precipitation to the property change and Dmatrix the contribution from matrix hard­ening arising from the production of point defect clus­ters by neutron irradiation. A further simplification was made in developing a DDR that could be applied to operational Magnox reactors. Namely, under the con­ditions of irradiation dose and temperature of interest there was no overaging; that is, the contribution to hardening or embrittlement from Cu cluster formation would reach a peak and then remain constant. Fur­ther, the hardening from Cu clusters could be repre­sented by a constant at all doses of interest, clearly a conservative assumption at doses before which the hardening from Cu clusters had reached a peak. On this basis, mechanistically based DDRs of the form

AT40J 9

or = B V AFtVd [5]

As >

were adopted. In this equation, B represented the material-specific copper precipitate contribution to the property change, with the MD contribution being given by AFtVD. In this term, A is a material specific constant, D is the dpa dose, and Ft is the irradiation temperature dependence factor.2,35 The fact that B is a constant independent of the measured bulk Cu level is consistent with the effect of the low final stress-relief temperature on reducing the variation in the Cumatrix between different materials (see Buswell and Jones70).

DDRs were derived for the different RPV materi­als over the years. They were revised as and when new Charpy impact energy or tensile test data became available or following revisions to the neu­tron doses accrued by the surveillance specimens.114 For example, it was found that SMA welds are much more susceptible to the occurrence of intergranular fracture effects, with manual welds, plates, and forgings
showing minimal effects. DDRs had to be developed that accommodated a nonhardening embrittlement mechanism. In addition, it was established that thermal neutrons could make a significant contribution to the irradiation damage in side-core locations, and that they were not conservatively covered by the DDRs.115,116 This conclusion was reached from an analysis of sur­veillance data from samples irradiated in locations in reactors with different levels of thermal fluxes and also from a well-controlled irradiation in a heavy water moderated reactor in Halden. It was established that to allow for extra displacements from low-energy recoils (^500 eV), a thermal neutron effectiveness fac­tor (k) needed to be introduced to modify the dose term in each material DDR. This meant that the gen­eral form of the two-term DDRs for both embrittle­ment and hardening (eqn [5]) became

AT 9

or = B + AFTJ Df + kDt [6]

As >

In this equation, the definitions of B, A, and FT remained unchanged, but the single dose term, D, was replaced by (Df + kDt), where Df and Dt are the doses of fast dpa (redefined to be from neutrons of energy E > 1 keV) and thermal dpa (from neutrons of energy < 1 keV), respectively; the constant k is the thermal neutron effectiveness factor for the material. The thermal neutron effectiveness factor was found to be material dependent,114 and separate values were estimated for the different RPV materials. It should also be noted that a large-scale sampling and testing program of SMA weld metal removed from a decom­missioned RPV validated the assessment process11 detailed above.

Wotton eta/.114 note that as a result of successfully addressing these and other challenges when the last two steel pressure vessel stations closed in December 2006, they had achieved lifetimes of nearly 40 years. To quote the authors,11 ‘‘This radical approach was subjected to rigorous peer review and its acceptance by the UK Nuclear Installations Inspectorate (NII) regulator was a major achievement.’’ Part of the peer review process may be illustrated by Knott and cow — orkers117,118 which detail the result of independent peer review by the UK Technical Advisory Group on Structural Integrity (TAGSI) of, first, the principles underlying the assessment of mechanical properties of irradiated ferritic RPV steels, and, second, the effects of gamma irradiation dose on the properties of C-Mn steels used in RPVs.

4.05.5.2 US Mechanistically Guided DDRs

In the late 1990s, mechanistically guided correlations were developed to describe the embrittlement of RPV materials employed in the United States.119,120 In common with other mechanistic DDRs, the form of these correlations is determined by current mecha­nistic understanding, but, in this case, the coefficients employed in the various terms in the correlation are determined by fitting to the extensive mechanical property data on the embrittlement of RPV materials acquired in vessel surveillance programs (Charpy V-notch shift at the 41J transition temperature, AT41 J). These correlations are developed to describe a specific fleet of reactors, namely the embrittlement of RPV materials in US boiling water and pressurized water reactors (BWRs and PWRs).

The initial mechanistically based or guided corre­lation models were presented in NUREG/CR-6551, published in November 1998.119 The models dis­cussed incorporated material chemical composition and various exposure variables to enable predictions of TTS and USE changes. Another embrittlement shift model was developed at about the same time on the same mid-2000 database under the auspices of the Electric Power Research Institute (EPRI) and the American Society for Testing and Materials (ASTM) E10.02 subcommittee (the E900 model120), published as E900-02 in 2002. This was a simplified form but did not have a strong dependence on flux.121

The embrittlement shift model in NUREG/CR — 6551 was updated in July 2000 with additional sur­veillance data collected since the earlier work; this is referred to in this report as the Draft 2000 model.122 Significantly, motivation for a new modeling effort came from the fact that 62 additional low flux BWR shifts became available in 2003 (described below). These data were significantly underpredicted by the previous shift models,119,120 so it was necessary to investigate the cause of the underprediction. Addi­tional pressurized water reactor (PWR) data from surveillance reports (about 140 shifts) were also added to the database in 2003 and 2004. Finally, the reliability of the database was improved when all old and new surveillance data were reviewed for com­pleteness, duplicates, and discrepancies, during the summer and fall of 2004, in cooperation with the ASTM Subcommittee E10.02 on Radiation Effects in Structural Materials.123

The DDR that has been incorporated into the latest USNRC Regulatory Guide on screening limits for pressurized thermal shock124 was produced by

Eason eta/.123 This is the most explicitly mechanistic DDR for MnMoNi steels produced to date, referred to as ‘EONY’ for convenience after the authors. The DDR, which is much more complex than the mild steel DDRs discussed above, is

AT = MF + CRP (in°F) [7]

where

MF = A(1 — 0.001718Ti) (l + 6.13PMn2’47) vfe) [8]

and A = 1.140 x 10-7 for forgings, 1.561 x 10-7 for plates, and 1.417 x 10-7 for welds

Ti = irradiation temperature (° F); P = bulk P (wt%); Mn = bulk Mn (wt%)

ft for f > 4.39 x 1010ncm-2s-1 д 0.259

for f < 4.39 x 1010ncm-2s-1

= effective (flux-corrected) fluence

and	80
t T
CRP = B( 1 + 3.77NiL191) f (Cue, P) g(Cue, Ni; fte) [9]

where B = 102.3 for forgings; 135.2 for plates in vessels manufactured by Combustion Engineering (CE); 102.5 for non-CE plates; 155.0 for welds; 128.2 for plates of the standard reference materials (SRMs)

0 for Cu < 0.072wt%

min[Cuactuai, Cumax] for Cu > 0.072wt%

= effective Cu level [10]

in which Cuactual = bulk Cu level (wt%), Cumax = 0.243 for typical (Ni > 0.5) Linde 80 welds, and 0.301 for all other materials. (Equations [7] and [8] are in °F, reflect­ing units in the original reference. It is to be noted that °F are employed in USNRC regulatory guides, rather than SI units.)

0 for Cu < 0.072

[Cue — 0.072]0′[1] for Cu > 0.072 and P < 0.008

[Cu — 0.072 + 1.359(P — 0.008)]0,668 for Cu > 0.072 and P > 0.008

[11]

g (Cue, Ni, fte)

1 1 unit [ log10 (ft) e + 1.139Cue — 0.448Ni — 18.120′ = 2 + 2tan 0.629

20

о

(a)

1016 1017 1018 1019 1020 (b) Fluence (n cm-2) (E> 1 MeV) Figure 16 (a) Schematic of the effect of flux and fluence on the magnitude of the matrix feature term, and (b) schematic of the CRP term showing the effect of key variables (low flux is 109 and all others are 1011 ncm-2s-1).

dependence of both the matrix and CRP term is broadly consistent with the understanding outlined in the previous section. The concept of f te is partic­ularly important as it both provides a means of allow­ing for flux effects and gives a threshold below which flux effects might be expected.63 These trends are further illustrated in Figure 16.

Overall, for a Cu-containing steel (say 0.2-0.3 wt% Cu), the MD becomes a significant fraction of the damage only at doses beyond the plateau in the shift from CRPs. This is consistent with the hardening from MD inferred from microstructural data. Carter et al. examined the effect of irradiation on microstructure on a high copper Linde 80 flux weld BW2 (0.25 wt% Cu, 0.62 wt%Ni,

0. 017 wt% P),125 and concluded that out of a total hardness of DHvtot 40 ± 6 the hardness from MD was

DHvMatrix 5-10 VPN.

In Section 4.05.2, it was described how irradiation also caused a drop in the Charpy USE. It is to be noted that Eason et a/.22 used the US surveillance power reactor database to investigate the dependence of the USE drop (DUSE) on a number of variables. They demonstrated that there was a strong correla­tion between the DUSE and Charpy TTS at 30 ft-lbs. Eason et al. derived a detailed set of equations that allowed the DUSE to be determined from the TTS for a number of product forms.