4.05.1 Introduction

The ferritic steel reactor pressure vessel (RPV) of a light water reactor (LWR) is unique in terms of nuclear plant safety. This is because the RPV is a pressure boundary component whose catastrophic failure by brittle fracture could lead to severe core damage and, potentially, to the widespread release of radioactivity. In addition to the thermal, mechanical, and chemical degradation processes common to all primary circuit components, the ferritic steel RPV, because of its close proximity to the reactor core, also undergoes changes in mechanical properties because of radiation damage from the flux of fast neutrons arising from nuclear reactions in the fuel. The integ­rity of the RPV has to be assured throughout the life of the plant. Irradiation results in hardening and embrittlement processes, the most important effect of which is the rise in the ductile-brittle transition temperature (DBTT) and the decrease in the frac­ture toughness of the RPV. This can be an important issue in the region of the beltline which experiences the highest neutron fluence. These changes in mechanical properties make the RPV more suscepti­ble to brittle fracture as the plant ages. The primary purpose of this chapter is to demonstrate our current understanding of such radiation damage effects in ferritic pressure vessel steels.

Low alloy ferritic steel pressure vessels are employed in all western LWRs (both boiling water reactors (BWRs) and pressurized water reactors (PWRs)), and also in VVER (LWR) reactors in Russia and a number of European countries (see, e. g., Steele and Sterne1). In the past, ferritic pressure vessel steels were also employed in gas-cooled Magnox reactors in the United Kingdom2 (Magnox reactors with steel vessels are now undergoing decommissioning ).

Demonstrating the safe operation of such a plant has led to extensive international research over the last 40-50 years on the aging effects in ferritic steels. The need for such scientific understanding has been raised at the highest level. For example, Sir Alan Cottrell, then UK Government Chief Scientist, in a memorandum concerning the integrity of LWR pressure vessels, dated 22 January 1974, to the UK Parliament Select Committee on Science and Indus­try stated ‘‘The possible gradual growth of small cracks in highly stressed regions, by ageing and corro­sion effects during service needs further scientific

4

investigation.

The discussion here establishes that in the field of radiation damage, it is the direct application of fun­damental research to operating reactors that is signif­icant. This chapter demonstrates that developments in the understanding ofthe damage mechanisms have enabled an improved description of the in-service properties of RPVs of operating reactors. Indepen­dent peer review has been central to the process and particularly important from a regulatory perspective. Frequently, it is not simply the research community directly involved that has to assess any improved description ofthe degradation processes; for example, the safety authorities within the utility, operating the reactor (or fleet), or the national regulator will become involved in the process.

Most importantly it has not always been possible to predict the end of life (EOL) vessel properties from the data obtained from materials irradiated as part of vessel surveillance programs. The vessel sur­veillance programs for commercial nuclear reactors are intended to monitor the irradiation-induced changes in mechanical properties of life-limiting structural materials subjected to significant neutron fluence. Thus, they are designed to provide advance information concerning the state of degradation in the mechanical properties of key structural compo­nents. However, because of the inevitable differences in neutron dose rate between the vessel wall and such surveillance samples (typically a factor of5 or more), the scarcity of such data at the start of plant opera­tion, and complex and unexpected embrittlement dependencies on steel composition, it has become necessary to develop dose-damage relationships (DDRs) on the basis of mechanistic understanding that predict the embrittlement dependence on mate­rial and irradiation variables.

The vast majority of investigations on the aging effects in ferritic steels over the last 40-50 years have been concerned with the effects of neutron irradiation over quite a narrow set of irradiation conditions, for example, irradiation temperatures of ^250-300 °C (although there was interest in irradiation tempera­tures as low as 160 °C) and irradiation doses typical of in-service exposures (<0.1 dpa). Early studies focused, primarily, on the effects of irradiation on mechanical properties, while in the last 20 years such studies have been combined with rigorous investigations of the effects ofmaterials and irradiation variables on the microstructure developed under irradiation. It is this combination that has allowed significant insight into the mechanisms that determine the effect of radiation damage on the bulk properties of ferritic RPV steels. As will be shown, such studies have encompassed simple model alloys, steels with a controlled composi­tion, and commercial steels employed in real vessels. A major outcome in recent years is the development of mechanistically based or guided DDRs that are employed, frequently in a regulatory framework, to predict the behavior of reactor vessels. (Some work­ers refer to DDRs as ‘embrittlement correlations’.) In formulating such DDRs, it has been necessary to encompass not only the irradiation variables such as flux, fluence, and irradiation temperature but also material factors, such as composition, heat treatment, and product form.

In reviewing such a long-standing field, it is neces­sary to provide a focus to enable presentation of a manageable set of data. As stated earlier, the chapter focuses on the mechanisms that control RPV em­brittlement, how such understanding has been incorporated into mechanistically based DDRs, and the limitations or current research issues associated with their development. These mechanistically based DDRs have been developed primarily for LWRs and Magnox reactors located in the West and this chapter gives prominence to such studies; that is, the chapter does not provide an extensive review of studies on the embrittlement of the RPVs of VVER reactors (see Nikolaev et al.,5 Kryukov et al,6 Shtrombakh and Nikolaev,7 and Brumovsky8 for such a review). Its organization reflects the overall focus; first, the chapter provides a description of RPV steels (Section 4.05.2) and then provides an overview of the effects of radiation damage on their mechan­ical properties (Section 4.05.3). Section 4.05.4 describes the status of our mechanistic understanding of embrittlement caused by radiation damage. This understanding has proved pivotal to the development of the DDRs described in Section 4.05.5. Outstand­ing issues, particularly those arising through plant life extension, are outlined in Section 4.05.6.

The neutron-induced swelling of SiC has been well studied for low and intermediate temperatures (^293- 1273 K). Originally, this material was investigated in
support of nuclear fuel coating1-9 and more recently, for various nuclear applications such as structural SiC composites.10 Before proceeding, it is important to distinguish neutron-induced effects on high-purity materials, such as single crystal and most forms of chemical vapor deposited (CVD) SiC, from those on lower purity forms such as sintered with additives, reaction-bonded, or polymer-derived SiC. It is well understood that the presence of significant second phases and/or poorly crystallized phases in these mate­rials leads to unstable behavior under neutron irradia­tion,11-14 as compared to stoichiometric materials, which exhibit remarkable radiation tolerance. Discus­sion and data for this section refer only to high purity, stoichiometric, near-theoretical density SiC, unless otherwise specified. Rohm and Haas (currently Dow Chemicals) CVD SiC is an example of such material.

The irradiation-induced microstructural evolu­tion of CVD SiC is roughly understood and has been reviewed recently by Katoh et a/.15 An updated version of the microstructural evolution map is shown in Figure 1. However, the contribution of the defects themselves to the swelling in SiC is less understood. Below several hundred Kelvin, the observable

Figure 2 Microstructure for CVD neutron irradiated at 573 and 1073 K.

microstructure of neutron-irradiated SiC is described as containing ‘black spots, which are most likely tiny clusters of self-interstitial atoms in various indeterminate configurations. For irradiation tem­peratures less than about 423 K, accumulation of strain due to the irradiation-produced defects can exceed a critical level above which the crystal becomes amorphous. This has been shown in the case of both self-ion irradiation and fast neutron irra- diation.20-22 As shown by Katoh et al.,23 the swelling at 323 K under self-ion irradiation increases logarithmi­cally with dose until amorphization occurs. The swelling of neutron — and ion-amorphized SiC has been reported to be 10.8% for 343 K irradiation.22 However, there is evidence that the density of amor­phous SiC will depend on the conditions of irradiation (dose, temperature, etc.)24

For temperatures above the critical amorphiza­tion temperature (423 K), the swelling increases logarithmically with the dose until it approaches saturation, with a steady decrease in the saturation swelling level with increasing irradiation tempera­ture. The dose exponents of swelling during the logarithmical period are in many cases close to two — thirds, as predicted by a kinetic model assuming planar geometry for interstitial clusters.25 This tem­perature regime is generally referred to as the point — defect swelling regime and can be roughly set between 423 and 1273 K. As an example of how these ‘black spot’ defects mature in the point-defect swelling regime, Figure 2 shows neutron-irradiated microstructures at 573 and 1073 K for doses
consistent with a saturation in density. While these microstructural features are generically classified as ‘black spots,’ the defects formed at 1073 K are clearly coarser compared to those formed under 573 K irradiation.

The approach to saturation swelling is shown for High Flux Isotope Reactor (HFIR) neutron irra­diated Rohm and Haas CVD SiC in Figure 3. In this figure, the swelling is depicted in both logarith­mic (Figure 3(a)) and linear (Figure 3(b)) plots. In addition to the approach to saturation, this figure highlights two other characteristics of neutron — induced swelling of SiC. First, the swelling of SiC is highly temperature dependent. For the data given in Figure 3, the 1 dpa and saturation values of swelling at 473 K are approximately five times that for 1073 K irradiation. This reduced swelling with increasing irradiation temperature is primarily attrib­uted to enhanced recombination of cascade — produced Frenkel defects due to lower interstitial clustering density at higher temperatures. The sec­ond characteristic swelling behavior to note is that the swelling saturates at a relatively low dose. For damage levels of a few dpa (typically months in a fission power core), the swelling in the point-defect recombination range has found its saturation value.

At higher temperatures such as 1173-1673 K,4,18,26 Frank faulted loops of the interstitial type become the dominant defects observed by transmission elec­tron microscopy (TEM). It has also been reported that Frank faulted loops appear for lower tempera­ture neutron irradiation at extremely high doses.27

Tirr=200°C ■ Tirr=300°C ♦ Tirr=400°C Tjrr=500°C a Tirr=600 °C a Tirr=800°C

Figure 3 Swelling of SiC in the intermediate temperature point defect swelling regime. Reproduced from Snead, L. L.; Nozawa, T.; Katoh, Y.; Byun, T-S.; Kondo, S.; Petti, D. A. J. Nucl. Mater. 2007, 371, 329-377.

Under silicon ion irradiation at 1673 K, the develop­ment of Frank loops into dislocation networks through unfaulting reactions at high doses is reported.26 The volume associated with dislocation loops in irradiated SiC has been estimated to be on the order of 0.1%28 At temperatures where vacancies are sufficiently mobile, vacancy clusters can be formed. Three­dimensional (3D) cavities (or voids) are the only vacancy clusters known to commonly develop to large sizes in irradiated SiC. The lowest temperature at which void formation was previously reported under neutron irradiation is 1523 K.4 Senor reported the lack of void production after neutron irradiation to 0.9 dpa at 1373 K, although voids were observed after subsequent annealing at 1773 K for 1 h.18 Under silicon ion irradiation, voids start to form at 1273 K at very low density and become major contributors to swelling at irradiation conditions of 1673 K at >10 dpa.29 Positron annihilation and electron para­magnetic resonance studies have shown that the silicon vacancy in cubic SiC becomes mobile at 1073-1173 K.30,31 Therefore, it would not be sur­prising for void swelling to take place at as low as 1273 K at high doses, particularly for low damage rate irradiations.

As previously mentioned, data on swelling of SiC in the high-temperature ‘void swelling’ regime has been somewhat limited. Recently, however, work has been carried out in the 1173—1773 K range for Rohm and Haas CVD SiC irradiated in HFIR. Of particular significance to that experiment is the confidence in irradiation temperature owing to the melt-wire passive thermometry. 2 Recent TEM imaging by Kondo28 clearly shows the evolution of complex defects. As an example, Figure 4 indicates sparse void formation on stacking faults for material irradiated at 1403 K. Significant growth of voids commences at 1723 K. The well-faceted voids appeared to be tetrahedrally bounded by planes, which likely provide the lowest surface energy in cubic SiC. In many cases, voids appeared to be aligned on stacking faults at all temperatures. However, intra­granular voids unattached to stacking faults were also commonly observed at 1723 K. The evolution of dis­location microstructures at 1403—1723 K is shown in Figure 5. In this temperature range, dislocation loops are identified to be Frank faulted loops of inter­stitial type. Evolution of the dislocation loops into dislocation networks was confirmed for irradiation at 1723 K.

Figure 6 plots both historical data, recently pub­lished, and unpublished data on the swelling behavior of SiC over a wider range of temperature.16,33 This plot is limited to literature data on high-purity CVD SiC. A divergence from point-defect ‘saturated’ swelling to unsaturated swelling is observed in the 1273-1473 K range, although additional data in this temperature range as a function of fluence would be required to precisely define such behavior. Above 1373 K, there exists a clear unsaturated swelling behavior for CVD SiC. The three divergent curves

drawn in Figure 6 represent data taken at nomi­nally 1.75, 5.0, and 8.5 x 1025nm~2 (E> 0.1 MeV) (assumed 1.75, 5.0, and 8.5 dpa). In the 1373-1473 K temperature range, volumetric swelling is apparently at a minimum, although it increases from ^0.2% to ^0.4% to ^0.7% for ~1.75, 5.0, and 8.5 dpa, respectively. Clearly, the swelling in this temperature range has not saturated by 10 dpa. Above this minimum in swelling, the data indicates a continual swelling increase to the highest irradiation temperature of ^1773-1873 K. At 1773 K, measured swelling

was ~0.4, 1.0, and 2.0% for ~1.75, 5.0, and 8.5 dpa, respectively. It was also noted in the study by Snead eta/.33 that at 1773 K, surface reaction between SiC and the graphite holder had taken place. However, a loss of silicon from the surface cannot be ruled out.

Figure 6 includes historical data for swelling above 1273 K.3,4,18,22,34,35 Specifically, Senor eta/.18 report swelling for the same type of CVD SiC irra­diated in this study when irradiated in a water­moderated fission reactor (the ATR) as well. Their maximum dose, irradiation temperature, and swelling data were ^1 dpa, 1373 ± 30 K, and 0.36 ± 0.02%, respectively. The irradiation temperature quoted in Senor et a/.’s work was a best estimate, although the authors also provide an absolute bound of 1073-1473 K for their experiment. The maximum swelling in their work (0.36 ± 0.02% at ^1dpa) is somewhat higher than the ^0.25% swelling at 2 dpa, ^1373 K, of the trend data in Figure 6. This is seen from the rightmost figure of Figure 6. Also seen in the figure is the high-temperature swelling of Price.3,4,34 The Price data, which are in the dose range of about 4-8 dpa, are in fair agreement with the
measured swelling of the Snead data16,33 of Figure 6. The highest swelling material (^ 1523 K, ^6 and 10 dpa) shows the largest discrepancy, although if the temperature error bands quoted by the various authors are taken into account, the data are conceivable more in alignment. It is also noted that the Price material may have had some excess silicon leading to higher swelling as compared to stoichiometric material.

As mentioned earlier, the microstructural evolu­tion of irradiated SiC is roughly understood, at least for temperatures up to 1373 K. The swelling near the critical amorphization temperature (^423 K) is classically described as the differential strain between the single interstitial, or tiny interstitial clusters, immobile vacancies, and antisite defects. As the tem­perature increases above the critical amorphization temperature, the number of defects surviving the postcascade thermally activated recombination is reduced and the mobility of both silicon and carbon interstitials becomes significant. For temperatures exceeding ^1273 K, microstructural studies have noted the presence of both Frank loops and tiny voids, indicating limited mobility of vacancies.

The apparent increase in swelling with dose in the 1373-1873 K range seen in Figure 6 and the observed production of voids are interesting considering that the maximum irradiation temperature (^1773 K) in Figure 6 is ^0.65 of the melting (dissociation) temperature (Tm) for SiC. Here, we have assumed Olesinski and Abbaschian’s36 value of 2818 K where stoichiometric SiC transforms into C + liquid phase. This value of 0.65 Tm is high when viewed in compar­ison to fcc metal systems where void swelling typi­cally begins at ~-0.35 Tm, goes through a maximum value, and decreases to nil swelling by ^0.55 Tm. (It is noted that the melting and dissociation temperatures of SiC are somewhat variable in the literature. How­ever, even considering this variability, the previous statement is accurate). If, as the swelling data seems to indicate, the voids in SiC are continuing to grow in SiC irradiated to 1773 K, the energies for diffusion of either the Si or C vacancy or both must be quite high, as are the binding energies for clustered vacancies. This has been shown through theoretical work in the literature.37-40 However, it is to be noted that the defect energetics obtained from this body of work, and in particular those of the Si and C vacancies within SiC, vary widely. Perhaps, the work of Bockstedte eta/.,39 which follows an ab initio approach, is the most accurate, yielding a ground state migra­tion energy of 3.5 and 3.4 eV for Si and C vacancies, respectively. It was also noted by Bockstedte et a/.41 that the assumed charge state of the vacancy affects the calculated migration energy. Specifically, the car­bon vacancy in the +1 and +2 charge state increases from 3.5 to 4.1 and 5.2 eV, respectively, and that of silicon in the -1 and -2 charge state decreases from 3.4 to 3.2 and 2.4 eV, respectively. Several papers discuss the vacancy and vacancy cluster mobil­ity measured experimentally. The silicon monova­cancy has been shown to be mobile below 1273 K. Using electron spin resonance, Itoh et a/.30 found the irradiation-produced T1 center in 3C-SiC disappear­ing above 1023 K. The T1 center was later confirmed to be an Si vacancy.31 Using electron spin resonance, the carbon vacancy in 6H-SiC is shown to anneal above 1673 K.42 Using isochronal annealing and positron lifetime analysis, Lam et a/.40 have shown a carbon — silicon vacancy complex to dissociate above 1773 K for the same 6H single crystal materials studied here.

From a practical nuclear application point of view, the swelling data for CVD SiC can be broken down into the amorphization regime (<423 K), the saturable point-defect swelling regime (423-1073 K) range, and the unsaturated void swelling regime, which occurs for irradiation temperature >1273 K. From the data of Figure 6, it is still unclear where the actual transition into the unsaturated swelling begins. Furthermore, while there is an increase in swelling in the 1273-1773K range, as the dose is increased from ~1.75, 5.0, and 8.5 x 1025nm~2 (E > 0.1 MeV), swelling is close to linear with neutron doses, and it is unclear how swelling will increase as a function of dose above 10 dpa. For example, swelling by voids estimated from the TEM examina­tion accounts for only relatively small fractions of the total swelling even in the void swelling regime. Analo­gous to the typical swelling behavior in metals, void growth may cause steady-state swelling after a certain transition dose regime. However, dose dependence of the swelling due to the nonvoid contribution remains to be understood. Extrapolation of swelling outside of the dose range of Figure 6 is therefore problematic.

Solidification cracks occur in the mushy zone of a weld bead on cooling, as the strains that develop exceed the ductility of the (solid + liquid) mixture. The modern theory of solidification cracking was developed by Borland,2 who highlighted the impor­tance of the quantity and distribution of the liquid near the terminal phase of solidification, as well as the stresses that act on that liquid. The primary factors that affect hot cracking are summarized in texts by Kou, Messler, and others.3-6 These factors are listed below:

1. The solidification temperature range: The larger the solidification temperature range, the more exten­sive the solid + liquid mushy zone, which is sus­ceptible to cracking. While large solidification temperature ranges may promote crack healing via

Homologous temperature (T/Tmelt)

Environmental degradation

Impurity segregation via diffusion

Ordering reactions/brittle second phases precipitate

Figure 1 Comparison of the typical temperature ranges for the different types of weld cracking (top) and forms of environmental degradation common to nuclear power systems (bottom). All temperature ranges are approximate, based on the homologous temperature of the alloy under consideration.

500 pm

Figure 2 Illustration of the different forms of hot cracking. Liquation cracks occur in the partially melted and/or heat-affected zone (HAZ) of the weld bead being deposited (top). Solidification-type cracks occur in the composite region of the weld during solidification (middle), and hot tears are dominated by mechanical forces and occur at macroscopic notches (bottom). Note that the cracks are all from nickel-chromium alloy welds but are not all from the same weldment.

backfilling, solute-rich ‘backfill’ may have degraded properties relative to the bulk weld metal. The approximate solidification temperature ranges of several alloys used in nuclear construction are shown in Figure 3.

2. The solidification path: Solidification crack suscep­tibility is markedly influenced by the type and distribution of solid phases, for example, initial 8-ferrite formation from the liquid in austenitic stainless steel welds imparts hot crack resistance

by breaking up the solidification structure and by scavenging tramp elements (e. g., sulfur and phosphorous). Conversely, eutectic-type reac­tions during terminal solidification (e. g., liquid! g + Laves in nickel-based alloys) are notably detrimental to solidification cracking resistance.7 Figure 4 illustrates the calculated solidification path and hot cracking resistance of two nickel — chromium filler metals. The more solute-rich filler metal that forms Ni2(Nb, Mo)-type Laves phase is

1900

§ 1600

К

1500

03

0

0 1400

о

сЛ "О

1300

_оЗ

=3

о

О 1200 1100 1000

Figure 3 Comparison of the calculated solidification temperature ranges of some common materials used in nuclear power systems (JMatPro, Version 4.1). For a given alloy class, hot cracking is promoted by larger solidification temperature range and low solidus temperature. Note that the compositions used are ‘typical’ values and significant variability exists within each alloy’s specification range.

much more prone to hot cracking than the Laves — free alloy.

3. The surface tension of the terminal liquid: Low surface tension liquids wet solidification boundaries and promote cracking by increasing the amount of interface incapable of supporting appreciable ten­sile strains.

4. The metallurgical structure of the weld: Large colum­nar dendritic grains are more susceptible to solid­ification cracking than finer equiaxed structures. Coarse solidification structures result in longer crack paths and less grain boundary area to dis­tribute elements that lower the solidus and/or embrittle the boundary. Columnar grains may exacerbate hot cracking by promoting wetting of the grain faces and can result in linear solidifica­tion boundaries near the centerline of the weld bead where tensile stresses are often the highest.

5. The mechanical forces that act on the weld: High tensile strains during the terminal stages of solidification promote cracking.

Given the complexity of the factors that contribute to

solidification cracking, it is difficult to predict its

occurrence in production welds. However, weld­ability tests such as the transvarestraint test enable a quantitative ranking of alloys with respect to solidification cracking susceptibility and offer a standardized methodology to optimize welding para- meters.8-10 Results from transvarestraint tests on sev­eral corrosion-resistant alloys are shown in Figure 5, which compares the maximum crack distance (i. e., the extent of the mushy zone when the crack distance becomes insensitive to the applied strain) and hence the intrinsic susceptibility of the alloy to solidifica­tion cracking. A representative transvarestraint sam­ple is shown in Figure 6, which illustrates the locations of solidification — and liquation-type cracks. Note that solid-state cracks can also be produced in this test.10

In general, alloying additions that are rejected into the liquid (i. e., whose equilibrium segregation coeffi­cient, k, is <1) lower the solidus and increase the solidification temperature range. This increases the extent of the solid + liquid ‘mushy’ zone and increases the susceptibility to solidification cracking. For exam­ple, niobium and molybdenum have segregation

(c)

Figure 4 Illustration of the effect of solidification path on cracking resistance. (a) Two Ni-30Cr filler metals show markedly different hot crack susceptibilities. (b) Scheil modeling predicts that the more solute-rich alloy has a larger solidification temperature range and can form a, Laves and S in the terminal solid and (c) SEM investigation confirms Nb, Mo-rich Laves near solidification cracks.

coefficients <1 in austenitic stainless steels and nickel — based alloys, which explains the longer crack lengths in 347 SS than in 308L SS (see Figures 5 and 7). Similarly, in nickel alloys, the susceptibility to solidification
cracking is Alloy 625 > EN52MSS > EN52i > EN82H > 68HP, which is a direct result of the decreasing alloying content ofthe strong melting point depressants molybdenum and niobium.7,10 15

When designing a nuclear reactor core, a channel ‘rating’ can be related to the reactor power and weight of uranium in a particular channel. This channel ‘rating’ can be related to a rate of change in the graphite properties. The channel rating is given in MW/Atu and over time the channel burnup as mega­watt days per adjacent tonne of uranium (MWd/Atu). Note that this unit is literally the (power in a particular channel) x (number of days) x (weight of uranium in that channel). No account is taken of refueling. However, fuel burnup is a function of reactor design and therefore, the equivalence concept was used and damage was related to a standard position.

In the United Kingdom, the change in graphite property was defined at a standard position in a Calder Hall reactor to give Calder equivalent dose. This was defined as the dose at a position on the wall of a fuel channel in a Calder Hall reactor. In the Calder Hall design, the lattice pitch is 8 in. The stan­dard position was chosen to be in a 3.55-in.-diameter fuel channel at a point on the shortest line between the centers of two fuel channels. The fuel is assumed to be 1.15-in.-diameter natural uranium metal rods. Calder equivalent dose was then used as a function to relate graphite property change to fuel burnup.

Kinchin14 had measured the change in graphite electric resistivity as a function of distance into the BEPO reflector. By normalizing this change, he defined a ‘graphite damage function’; see also Bell eta/.15

Thus, graphite damage at some position in a reac­tor core graphite component could be defined as a function of the following:

• source strength

• distance between position and source

• attenuation in damage with distance through the intervening graphite

The damage function is a measure of the last two bullet points. The source strength is related to fuel burnup. The graphite damage function df is defined as fRg)

R where f(Rg) is the damage absorption curve for an equivalent distance through BEPO graphite ‘Rg’ of density 1.6 gcm~3, and R is the distance through graphite between the source and position of interest. Note that nonattenuating geometric features, that is, holes, need to be accounted for.

Calder equivalent rating Pe can now be defined as

AdfP

ACalder dfCalder

where ‘ACalder’ and ‘A’ are the uranium fuel cross­sectional areas in Calder (1.04 in.2) and in the reactor under consideration, respectively; ‘d/Calder’ and ‘df ’ are the values of the damage at the Calder standard position (1.395) and in the reactor under consider­ation, respectively, and ‘P is the fuel rating in the reactor under consideration.

Thus, a graphite property change in a reactor under assessment can be related to the equivalent graphite property change at the Calder standard position.

However, in a real reactor there is more than one fuel channel. There may also be absorbers or empty interstitial holes, the fuel rating will change with burnup, and the fuel will be replaced from time to time. Therefore, a more complex, multiple source cal­culation is required to take account of the actual chan­nel rating and the geometric features of the core. This is normally done by considering a 5 x 5 lattice array:

[4]

where Bj and B are the accumulated fuel burnup at the jth and reference source, respectively, f(Rg); is the damage absorption function corresponding to thickness Rg for jth source, and Rg is the distance between the jth source and target.

This method was successfully used to design the Magnox reactors. However, because of the higher enriched oxide fuel and more complex fuel design in the AGRs, this approach became less satisfactory and new ‘damage functions’ that accounted for the new fuel and geometry were calculated using Monte Carlo methods (made possible by the introduction of the digital computer). This method was until recently still used in industry codes such as ‘Fairy’ (National Nuclear Company) and ‘GRAFDAM’ (UKAEA).

4.11.5.2.1 Calder effective dose

When only low-dose irradiation graphite property data were available, it was assumed that irradiation damage could be obtained at one temperature and that the property change versus dose (fluence) curves could be adjusted for all other temperatures using the so called R(0) curve:

4.11.20.4.1 Coefficient of thermal expansion

Significant differences have been observed between the unstressed CTE and stressed CTE, as illustrated in Figure 58. Compressive creep strain was found
to increase the CTE, and tensile creep strain to decrease the CTE.

The changes in CTE caused by irradiation creep have similarities to those caused by the applica­tion of stress on unirradiated graphite. Figure 59(a) shows the changes in CTE in irradiated, crept specimens plotted as a function of creep strain92 and Figure 59(b) gives the changes in CTE in unirradi­ated graphite due to stress.93

At room temperature, the average CTE of an isotropic graphite with no porosity should be the average of the crystallite CTEs, that is, the crystallite CTEs are -27.0 x 10-6K-1 and -1.0 x 10-6K-1 in the V and У directions respectively, giving an average

of 8.0 x lO^KT1. From Figure 59(a), which is for Gilsocarbon with an unirradiated CTE of

4.0 x 10~6K~1,itisinterestingto note that the increase in CTE in compression is approaching that value.

In binary Zr-Nb alloys (Zr—1% Nb and Zr-2.5% Nb), the microstructure is usually in a metastable state due to the thermomechanical processing in the upper a range or in the a + p domain. Indeed, at this relatively low temperature (around 580 °C), the atomic mobility is low and the equilibrium state cannot be reached in reasonable time. After cooling, the matrix is therefore supersaturated in Nb and the composition of secondary phases (Nb rich) still corresponds to the high-temperature chemical com­position. It is indeed shown by Toffolon-Masclet eta/.85 that a Zr—1% Nb-O alloy that has undergone a final heat treatment at 580 °C for a few hours can still evolve toward its thermodynamic equilibrium after 10000 h of heat treatment at 400 °C.

Under irradiation, it is observed that the micro­structure of Zr-Nb alloys is not stable and very fine Nb-rich precipitates, with diameter of a few nanometers, are observed in very high density (Figure 11). This precipitation of Nb from the super­saturated matrix is observed in any type of binary alloys: in Zr—1% Nb such as M5™(86) and E110(12,87) as well as Zr—2.5% Nb.88 This needle-like precipita­tion has been studied mainly by TEM, and also by small angle neutron scattering (SANS) analyses.86

Simultaneously, a noticeable decrease of Nb content in the matrix occurs.89

This precipitation is due to an enhanced mobility of Nb atoms under irradiation due to the very high vacancy concentration created by irradiation. This enhances the Nb mobility and allows the rapid evolu­tion of the microstructure toward its thermodynamic equilibrium, leading to precipitation of very fine Nb — rich precipitates in Zr—Nb binary alloys.

In Zr—Nb alloys, the Nb-rich phases also undergo chemical changes under irradiation. Indeed, it is shown that the o phase, obtained in Zr—2.5Nb by transformation of the p-Nb after extrusion, disap­pears and transforms into p-Nb.60 For the p-Nb phase and in the case of M5™ alloys, an evolution of the chemical composition under irradiation has also been observed, but the p-Nb precipitates still remain fully crystalline even after six PWR cycles of irradiation (70 GWd t_ ). Only a decrease in Nb content with a small increase in the size of the precipitates has been noticed86 (Figure 11). The same has been obtained for E110 and E635 Russians alloys, where p-Nb precipitates are altered in com­position to reduce the Nb content from 85—90% to 50%.12

Moreover, for the Zr(Nb, Fe)2 Laves phases with hcp structure found in E635 and E110 alloys, it seems that a release of iron atoms into the matrix from the

precipitates has occurred after irradiation, leading to the transformation into p-Nb particles with bcc

12,89

structure.

Fatigue loading can be very detrimental for situations involving cyclic loading, especially when associated with thermal cycling such as might occur in the first wall of a fusion device. As shown in preceding sections, radiation changes the microstructure and affects the phase stability ofsteels as well as generating deleterious gases such as helium and hydrogen.

Therefore it is not unexpected that fatigue life will be adversely affected by irradiation as shown in Figure 90.192

Fatigue tests are by necessity conducted out-of­reactor and therefore are not fully representative of in-reactor conditions, especially not being subject to the mitigating influence of radiation creep to reduce local stress concentrations. In this sense out-of­reactor results may be conservative. The tests can be conducted in a variety of ways, however, generally using either strain-controlled or load-controlled methods, with the former being more relevant to low cycle fatigue arising from thermal cycling. Guidance on the application of fatigue data is provided by Tavassoli.195

Figure 90 presents the usual engineering curves of total strain versus the number of cycles to failure. In this representation the lifetimes of irradiated and unirradiated materials are not really so dissimilar. The observed difference is the result of competing influences, degradation due to irradiation, and improvement due to hardening. As pointed out by Boutard,196 it is better to isolate the irradiation effect on the lifetime in which the controlling parameter is the plastic strain range.

As shown in Figure 91, there is a significant effect of radiation on the lifetime at a given plastic strain.196,197 The lower the plastic strain, the greater the decrease in lifetime. Under conditions where the crack initiation phase controls the lifetime of the unirradiated material, irradiation will result in much earlier crack formation

and much earlier failure. Other researchers have reached the same conclusion.198

In general it appears that most researchers agree that helium is a contributing but not primary cause of the radiation-induced degradation in lifetime.195-199

4.02.10 Conclusions

In general there are no beneficial aspects of radia­tion on austenitic steels when exposed to neutron

irradiation. Structural components used in various nuclear reactors may have been constructed from alloys with carefully tailored and optimized proper­ties, but there is an inevitable degradation of almost all engineering properties of interest as irradiation proceeds. Even more importantly, having labored to build a device with well-defined dimensions, separations, and tolerances, it must be recognized that these dimensional attributes can also change dramatically, requiring that the design anticipate such changes in order to maximize safe and efficient operation for the longest possible lifetime.

This evolution of properties and dimensions frequently determines the lifetime of any given structural component, a lifetime that will be very specific to each nuclear environment. It is important to recognize that all potential degradation processes may not yet have been identified and that others may lie over the current exposure horizon, espe­cially as light water reactors are being considered for life extension to 60 or 80 years, and as fast reactors are being designed for doses well beyond 200 dpa.

There have also been a number of studies of the effect of alloying on loop formation. These studies have not examined all the alloying elements of interest, but Mn and P have been shown to have an important influence on the cluster distributions observed by TEM in Fe binary or ternary alloys. For example, Ebraimi and coworkers76,77 examined the effects of adding Ni (and P). They found that a higher density of smaller loops was observed in a Fe-Mn alloy (as compared to pure iron irradiated under similar con­ditions), whereas P added to an Fe-Ni alloy caused an increase in loop size.

Phosphorus dissolves substitutionally in iron and the solid solubility is 0.5 at.% (0.27 wt%) at 400 °C.87 Jones and Buswell,88 in reviewing the available micro­structural evidence, concluded that the hardening observed in low Cu steels could be attributable to precipitation hardening by M3P particles produced by the irradiation-induced segregation of phosphorus to defect sinks and the depletion of phosphorus in solid solution, as detected by TEM and AP methods.

Nagai et a/.89 have reported results from a CDB study of Fe-0.3wt% Cu, Fe-0.15wt% Cu, and Fe-0.05 wt% Cu alloys irradiated at 8.3 x 1018 n cm~2, E > 1 MeVat ^300 °C (the irradiation time was 144 h). As a result of CDB and positron lifetime measure­ments on irradiated and annealed samples, the authors reported the formation of microvoids (~10 vacancies), dislocation loops, and Cu-mono-vacancy-Cu com­plexes. They considered that the microvoids were decorated with Cu in all the alloys studied, and that in all cases the microvoids were almost completely coated with Cu. After electron irradiation,90 vacancy clusters and single vacancies surrounded by Cu (v-Cun, where n > 6) were observed in electron — irradiated Fe-Cu, and vacancy clusters were observed Fe-Ni and Fe-P, but no vacancy clustering in Fe-C, Fe-Si, or Fe-Mn was observed.

A recent development of some importance is the observation (primarily using the LEAP) of MnNiSi clusters in irradiated low Cu steels. For example, Miller et a/.91 characterized the irradiation-induced microstructure of low copper (0.05 wt%) high nickel (1.26 and 1.78 wt% Ni) VVER-1000 forging and weld materials that were neutron irradiated to a total flu — ence of 1.38 x 1023 nm~2 (E > 1 MeV). Atom probe tomography revealed ultrafine Ni-Mn-Si-enriched clusters but no CECs. The number density of clusters in the VVER-1000 weld was estimated to be ~1.5 x 1023 m~ , while the number density of clusters in the forging was estimated to be slightly lower at 1 x 1023 m~ . These ultrafine clusters may, or may not, be associated with vacancies. The observa­tions of such clusters may be interpreted as evidence of a mechanism not encompassed by the framework set out in this section. This is further discussed in the next section.

There is strong evidence that interstitial solutes (ISs) such as C and N are attracted to the point defects produced by irradiation. ISs may well add to preexisting SIA clusters, and may even inhibit their growth. Conversely, they appear to encourage the formation of multiple-vacancy complexes. Little and Harries92 further demonstrated that the amount of free nitrogen, indicated by the height of the Snoek internal friction peaks, decreased with increasing irradiation fluence, such that it was zero with fluences of about 2 x 1018ncm~2. This was attributed to trapping of free nitrogen or precipitation of nitrides at point defects or defect clusters.

4.05.4.5.3 MD and hardening

Various scientists have attempted to determine the nature of the defects which result in hardening. Soneda65 quoted evidence from Ortner93 showing that AHv (the change in Vickers hardness) and AS (related to the volume fraction of open-volume defects) increase after irradiation of a low Cu steel EP2, indicating that vacancy-type defects are formed by irradiation. During the postirradiation annealing, AS starts to recover at a lower temperature than AHv. This clearly indicates that the change in AS is unre­lated to the change in AHv, and thus, vacancy-type defects are not solely responsible for the observed irradiation-induced hardening.

Alinger’s results indicate that the mechanically alloyed powder annealed at 700 °C shows the smallest radius and highest density in Y-Ti complex oxide particles,8 as shown in Figure 1. Considering that

Y2O3 particles are decomposed during MA, subsequent annealing results in the formation and precipitation of Y—Ti complex oxide particles at elevated temperatures of 700 °C or higher. Since the reverse transformation of a-g-phase takes place at a temperature over 850 °C, which is higher than the precipitation temperature of Y-Ti complex oxide particles, it is possible that the retention of the residual a-ferrite can be attributed to the presence of Y-Ti complex oxide particles in 9Cr-ODS steels. These particles could block the motion of the a-g interface, thereby partly suppres­sing the reverse transformation from a — to g-phase. This section presents a quantitative evaluation of this process.

The chemical driving force (AG) for the reverse transformation from a — to g-phase in the Fe-0.13C — 2W-0.2Ti system without Y2O3, can be evaluated in terms of Gibbs energy versus carbon content curves at each temperature. These curves were derived using the Thermo-Calc code and the TCFE6 database. The result of the calculation is presented in Figure 8.22,23 The peak value of the driving force for the reverse transformation from a — to g-phase reaches 4 MJ m— at 1000 °C in the case of 0.13 wt% C.

The pinning force (F) against the motion of the a-g interface can be expressed as the following equation, which was derived from the modified Zener equation of Mishizawa et a/.24

8r

where, s(Jm—2) is the interfacial energy between a — and g-phases, and its value was selected to be 0.56J m—225 The character r represents the radius of the oxide particles (m) in the a-phase; its value was determined as 1.5 nm by using TEM observation. The character fp represents the volume fraction of dispersed oxide particles (—), and was derived on the basis of the experimental evidence that oxide particles consist of Y2Ti2O7. By substituting these values into the afore­mentioned equation, the value of pinning force F was determined for 0.1, 0.35, and 0.7 wt% Y2O3, which are also shown in Figure 8.2 , The value of F increases with the amount of Y2O3 added according to the relation off2=3.

The velocity of the a-g interface motion (v) is proportional to the difference between Fand AG, as shown in the following equation:

v = M(AG — F). [4]

M is the mobility of the interface. AG and F are competitive, and AG > Findicates a positive velocity for the interface motion, that is, the reverse trans­formation from a — to g-phase. On the other hand, AG < F indicates that the a-g interface can be

Figure 9 Formation process of residual ferrite in 9Cr-ODS steel (Fe-0.13C-2W-0.2Ti-0.35Y2O3). Reproduced from Yamamoto, M.; Ukai, S.; Hayashi, S.; Kaito, T.; Ohtsuka, S. Mater. Sci. Eng. A 2010, 527, 4418-4423.

pinned by oxide particles so that the a-phase is, thus, retained. The results of the calculation shown in Figure 822 reveal that in the case of Y2O3 con­tents of 0.35 and 0.7 wt%, the pinning force is larger than the driving force for 0.13 wt% C. These results are reasonably consistent with our observation of the retainment of residual ferrite during a—g reverse transformation.

On the basis of the aforementioned discussion, the formation process of the residual ferrite in Fe-0.13C — 2W-0.2Ti-0.35Y2O3 is schematically illustrated in Figure 9. At the AC1 point, the carbide begins to decompose, and a—g inverse transformation takes place in the area of higher carbon content around the decomposed carbide, where the driving force of the reverse transformation exceeds the pinning force because the carbon content may be >0.2 wt% (see Figure 8). The g-phase could be enlarged by these processes. Approaching the AC3 point, the matrix carbon content achieves equilibrium at 0.13 wt%, where the pinning force (0.35Y2O3) exceeds the driving force (0.13C), and the velocity of the a—g interface motion is markedly reduced due to dragging by the oxide particles. Thus, the a-ferrite could be retained even beyond the AC3 point.

The main concerns in austenitic stainless steel weld­ing are solidification, liquation, and PIC. Addition­ally, avoiding grain boundary chromium depletion via carbide precipitation (i. e., sensitization or ‘knife­line’ attack) is critical to maintaining in-service corrosion resistance (Chapter 2.09, Properties of Austenitic Steels for Nuclear Reactor Applica­tions). A key factor in solidification cracking resis­tance is proper control of the weld chemistry to form delta ferrite in the initial solid.98-100 Delta ferrite formation breaks up long, linear solidification bound­aries and acts to scavenge tramp elements from the liquid and prevent their concentration at interden­dritic boundaries during terminal solidification.101,102

Delta ferrite levels are typically controlled to ~5-10% by volume to impart solidification cracking resistance but retain the mechanical properties of a face-centered cubic alloy. Specifically, the body — centered cubic ferrite is susceptible to cleavage at low temperatures and to spinodal decomposition of the ferrite into iron-rich (a) and chromium-rich (a0) phases at intermediate temperatures. Control of delta ferrite levels for different alloys is given in handbooks and can be predicted via the experimen­tally based Schaeffler or Delong diagrams, or com­putationally, by multicomponent phase diagrams, as shown in Figure 21.103-107 As a practical example, it is often difficult to weld over fully austenitic metals (e. g., nickel-based alloys) with austenitic filler metals (e. g., 308), as the increased nickel (from dilution) promotes the primary austenite solidification mode.

As with most fusion welds, liquation cracking can be controlled by minimizing solidification segrega­tion (e. g., faster cooling rates and finer, more equiaxed structures) and by using lower heat input.

As discussed earlier, stainless steels can be susceptible to PIC via partially coherent M23C6 carbide precipita­tion. One distinction relative to nickel-based alloys is that cracking may more likely occur on heating or with longer in-service exposures, as carbon may be in solution as-welded, and precipitation kinetics are usually slower than for high-chromium nickel-based alloys.10