The first embrittlement correlation for the TTS of the Japanese RPV materials, JEAC 4201, was issued in 1991. Additional surveillance data have been com­piled since 1991 and in 2002 the Japanese electric power utilities started a project with CRIEPI to develop a new mechanistically based embrittlement correlation.126

Soneda and coworkers have adopted a two — step approach to developing a new correlation method.6 , ,7 In the first step, the microstructural

effects due to radiation damage are modeled, and the mechanical property changes engendered by such change are detailed. The microstructural changes, namely, the formation of solute atom clusters and MD features, due to irradiation are modeled using the following equations:

bulk chemical contents of Cu and Ni, DCu is the Cu diffusivity, f is the dose rate, t is the irradiation time, and tr is the relaxation time, respectively.

Equations [13 and 14] represent the time evolu­tion of solute atom clusters and the MD clusters, respectively (see Hiranumu eta/.126 for a full descrip­tion of the equations). In eqn [13], it is to be noted that solute atom clustering occurs with MD features as the nuclei. This process can occur without Cu atoms but is accelerated by their presence. In eqn [14], the formation of MD features is affected by the irradiation temperature and also the bulk Ni content. Equation [15] models the depletion of the matrix Cu content because of the formation and growth of Cu-enriched solute atom clusters. Note that the depletion of the matrix Cu reduces the formation rate of Cu-enriched solute atom clusters. Equation [19] gives an expression for the diffusivity of Cu atoms, which combines terms from both irradiation — induced vacancies and thermal vacancies.

Mechanical property changes are correlated with the microstructural changes using the following equations:

ATSC = Х1бРЦ~

= X1^Xf^+f PffiC [20]

f (CCT, Csc) = X11 CCu~ ^ + X12 [21]

CSC

g (CNi) = (1 + X13 (cNi)X14 У [22]

h(ft) = X9(1 + X10DSC)f t DSC ~ DCu [23]

ATmd = X17P Cmd [24]

AT = J (ATSc)2 + (ATmd)2 [25]

where A Tsc and ATmd are the contributions of solute atom clusters and MD features, which are calculated using eqns [20 and 24] as functions of Csc and CMD, respectively. In calculating the contri­bution ofsolute atom clusters, an empirical model, in which the TTS is proportional to the square root of the volume fraction of solute atom clusters, is used. The average volume per cluster, which is necessary for calculating the volume fraction, is modeled using eqns [21-23], which take into account the effect of chemical composition and the growth of the clusters during irradiation. The Greek characters in the above equations are coefficients, and were optimized using

the surveillance database of Japanese commercial reactors.126,127 The partitioning of the total embrit­tlement between that due to copper clusters and MD features is shown in Figure 17. It can be seen that the MD has a weak dependence on the Cu level of the steel.

Figure 18 shows a comparison between the calcu­lated and measured TTS. The standard deviation of the prediction error is smaller than that of the other correlation equations used in Japan and in the United States, as shown in Figure 10. When a plant-specific adjustment is applied to the initial transition temper­ature, the standard deviation of the prediction error becomes much smaller and is as low as 6 °C. A practical output of this approach is the develop­ment of a new embrittlement correlation method for Japanese RPV steels, and this method has been adopted in theJEAC 4201-2007. Thus, this study is a good example of how the understanding of a funda­mental mechanism can be applied in a real-world engineering application.

4.05.5.3 Summary

It is clear from the discussion above that there has been successful development of mechanistically based DDRs for both CMn and MnMoNi steels.

Different DDRs have been developed in different countries to describe the hardening and embrittle­ment of the various RPV steels. The inevitably approximate nature of the DDR expressions, the lim­ited variation of different parameters in each surveil­lance database, and the limited amount ofsurveillance data mean that the effects ofmany parameters must be implicit. Different irradiation and compositional var­iable ranges in different surveillance schemes may contribute significantly to the forms of the DDRs and the strength of different dependences. The lim­itations in the form of the DDRs and the R&D into outstanding issues are the subject of the next section.