Graphite component temperature depends on radia­tion and convection (and conduction in the case of light-water gas-cooled reactors) heat transfer from the fuel and heat generated in the graphite by neu­tron and g-heating, that is, energy deposition as dis­cussed above. Therefore, a detailed knowledge of the coolant flow is important.

Thermohydraulic codes such as Panther (http:// www. sercoassurance. com/answers/) are used to cal­culate heat generated in graphite blocks. These codes estimate the following:

1. The heat generated in the fuel.

2. The coolant flow.

3. The heat transfer to the graphite.

4. The heat ‘energy deposition’ in the graphite.

The calculations take account of graphite weight loss and change in thermal conductivity of the graph­ite due to fast neuron damage and radiolytic oxida­tion. The largest uncertainty is probably associated with the size of flow bypass paths and flow resistance.

In an AGR, the temperature at the outside of the brick is lower than the temperature at the inside because of the interstitial flow, whereas in an Reaktor Bolshoy Moshchnosti Kanalniy (RBMK) the temper­ature is hotter at the brick outside.

Using the brick ‘boundary conditions’ including energy deposition temperatures calculated by the thermohydraulic code, a standard finite element code such as ABAQUS can easily be used to calculate the spatial distribution of temperature with the graphite component. Thermal transient tempera­tures can also be calculated using a standard finite element code. Often, the temperature distribution is calculated for a central brick, and the temperatures in the bricks in the rest of the core are calcu­lated using interpolation/extrapolation, that is, form factors as described in Section 4.11.9. The calculated

 

temperatures are compared with the few brick ther­mocouples that are installed in the moderator. The codes are also fine-tuned to these. In conclusion, the calculation of graphite tem­peratures is complex and involves the calculation of heat transfer flow to the fuel and flow calculations. Graphite temperature predictions should be com­pared to measurements taken from thermocouples located in most graphite cores.

 

Read More 22.08.2015   Comprehensive nuclear materials Fundamental Study on Impurity Effects Effects ofC, O, and N on the property ofvanadium are a long-standing research subject. However, research into the effects of C, O, and N on V-4Cr-4Ti is limited. Research with model V-4Cr-4Ti alloys doped with O and N provided information on the partition­ing of O and N into the precipitates and matrix. The density of the blocky precipitates and thin pre­cipitates increased with N and O levels, respectively. Figure 9 shows hardness as a function of N and O levels in V-4Cr-4Ti after melting and annealing at 1373 K for 1 h.2 Hardness after annealing at 1373 K, where only the blocky precipitates were observed in the matrix, increased to a certain extent with O level (~4.5 Hv/100 wppm O), but only very weakly with N level (~0.9 Hv/100 wppm N). These data suggest that, after the annealing, most of the N is included in the blocky precipitates and stable to ~-1373 K. On the other hand, O exists in the matrix, the blocky and the thin precipitates, and the partition­ing changes with the heat treatment. Thus, for the purpose of the property control of V-4Cr-4Ti, the level of N before the heat treatment is not so impor­tant but that of O is crucial. It is to be noted, however, that N contamination during the operation can influ­ence the properties of vanadium alloys seriously. Fundamental information on the impurity dis­tribution and interaction with solutes and dislocations is obtained by serrated flow in tensile deformation as shown in Figure 10. Temperature and stain rate depen­dence of the flow showed that the serrated flow above 673 K is related to C and O and above 773 K to N. Small serration height at 673 K for NIFS-HEAT-1 (1-3 MPa) relative to that of US-832665 (^9MPa) was observed and attributed to the difference in O level.23 Read More 22.08.2015   Comprehensive nuclear materials Radiation Damage in Austenitic Steels 4.02.1 Introduction Austenitic stainless steels are widely used as struc­tural components in nuclear service in addition to being employed in many other nonnuclear engineering and technological applications. The description of these steels and their as-fabricated properties is covered in Chapter 2.09, Properties of Austenitic Steels for Nuclear Reactor Applica­tions. This chapter describes the evolution of both microstructure and macroscopic property changes that occur when these steels are subjected not only to prolonged strenuous environments but also to the punishing effects of radiation. While various nuclear environments involve mixtures of charged particles, high-energy photons and neutrons, it is the latter that usually exerts the strongest influence on the evolution of structural steels and thereby determines the lifetime and continued functionality of structural components. To describe the response of austenitic stainless steels in all neutron environments is a challenging assignment, especially given the wide range of neutron spectra characteristic of various neutron devices. This review of neutron-induced changes in properties and dimensions of austenitic stainless steels in all spectral environments has therefore been compiled from a series of other, more focused reviews directed toward particular reactor types1-8 and then augmented with material from a recently published textbook9 and journal articles. It should be noted, however, that many of the behavioral char­acteristics of iron-based stainless steels following neutron irradiation are also observed in nickel — based alloys. Whenever appropriate, the similarities between the two face-centered-cubic alloy systems will be highlighted. A more comprehensive treat­ment of radiation effects in nickel-base alloys is provided in Chapter 4.04, Radiation Effects in Nickel-Based Alloys. This review is confined to the effects of neutron exposure only on the response ofirradiated steels and does not address the influence of charged particle irradiation. While most of the phenomena induced by neutrons and charged particles are identical, there are additional processes occurring in charged par­ticle studies that can strongly influence the results. Examples of processes characteristic of charged par­ticle simulations are the injected interstitial effect,10, strong surface effects,12,13 dose gradients,14,15 and atypical stress states.16,17 Chapter 1.07, Radiation Damage Using Ion Beams addresses the use of charged particles for irradiation. Austenitic stainless steels used as fuel cladding or structural components in various reactor types must often withstand an exceptionally strenuous and chal­lenging environment, even in the absence of neutron irradiation. Depending on the particular reactor type, the inlet temperature during reactor operation can range from ^50 to ~-370 °C. The maximum temper­ature can range from as high as 650 to 700 °C for structural components in some reactor types, although most nonfueled stainless steel components reach maximum temperatures in the range of 400-550 °C. During operation, the steel must also withstand the corrosive action of fission products on some surfaces and flowing coolant on other surfaces. The coolant especially may be corrosive to the steel under operating conditions. Some of these environmental phenomena are synergized or enhanced by the effect of neutron irradiation. Dependent on the nature of the component and the length of its exposure, there may also be sig­nificant levels of stress acting on the component. Stress not only influences cracking and corrosion (see Chapter 5.08, Irradiation Assisted Stress Cor­rosion Cracking) but can also impact the dimen­sional stability of stainless steel, primarily due to thermal creep and irradiation creep, and also from the influence of stress on precipitation, phase stabil­ity, and void growth, some of which will be discussed later. However, it will be shown that neutron irradia­tion can strongly affect both the microstructure and microchemistry of stainless steels and high-nickel alloys, with strong consequences on physical proper­ties, mechanical properties, dimensional stability, and structural integrity. Stainless steels are currently being used or have been used as structural materials in a variety of nuclear environments, most particularly in sodium — cooled fast reactors, water-cooled and water-moderated test reactors, water-cooled and water-moderated power reactors, with the latter subdivided into light water and heavy water types. Additionally, there are reactor types involving the use of other coolants (helium, lithium, NaK, lead, lead-bismuth eutectic, mercury, molten salt, organic liquids, etc.) and other moderators such as graphite or beryllium. The preceding reactor types are based on the fission of uranium and/or plutonium, producing neutron energy distributions peaking at ^2 MeV prior to moderation and leakage effects that produce the operating spectrum. However, there are more energetic sources of neutrons in fusion-derived spectra, with the source peaking at ^14 MeV and especially from spallation events occurring at ener­gies of hundreds of MeV, although most spallation spectra are mixtures of high-energy protons and neutrons. It is important to note that in each of these various reactors, there are not only significant differences in neutron flux-spectra but also signifi­cant differences in neutron fluence experienced by structural components. These differences in fluence arise not only from differences in neutron flux characteristic of the different reactor types but also the location of the steel relative to the core. For instance, boiling water reactors and pressurized water reactors have similar in-core spectra, but stainless steels in boiling water reactors are located much farther from the core, resulting in a factor of reduction of ^20 in both neutron dose rate and accumulated dose compared to steels in pressurized water reactors. Read More 22.08.2015   Comprehensive nuclear materials Development of Advanced ODS Ferritic Steels In recent years, an attempt to increase the high tem­perature creep life of ferritics to 973 K and target burn-up of the fuel to 250 dpa, has enabled a ‘revisit’ to the concept of strengthening the steel using 5 nm particles of yttria (see Chapter 4.08, Oxide Disper­sion Strengthened Steels), leading to the ODS fer­ritic steels. ODS ferritic steels are prospective candidate materials for sodium cooled fast reactors with peak burn-up of 250 dpa as well as GenlV and fusion reactors. Earliest developments ofODS steels can be traced to the efforts65 of Belgium in 1960s, followed by Japan66 since 1987, and France67 in the last decade. The ODS steels for fast and fusion reac — tors68,69 are in the R&D stage. The design of ODS steels for fast and fusion reactor applications is based on Fe-Cr-W-Ti — Y2O3, either the martensitic 9 or 12Cr or the ferritic 12Cr steels. The dispersoids which confer the high temperature creep life to the ferrite matrix are70 Figure 13 Z-contrast in the high angle annular dark field (HAADF) micrograph of dispersoids in oxide dispersion strengthened (ODS)-9Cr-1 M0 ferritic steels, which are responsible for the superior high temperature creep behavior. (Figure 13) in the size range of around 5 nm with a volume fraction around 0.3%. The yttria dissolves in it some amount oftitanium, leading to the formation of mixed, complex oxide, namely TiO2Y2O3. The rationale for the choice of the matrix compo­sition is as follows: Chromium: Choice of 9% Cr and 0.1% C ensures 100% martensite, during normalization ofthe steel. It is possible to ensure 100% martensite in 12% chro­mium steel by ensuring the carbon content to be above 0.1%. Ferritic ODS steels can be obtained in 12% chromium steels by lowering the carbon content to be less than 0.03%. Higher chromium provides the corrosion and decarburization resistance in sodium at 973 K, with acceptable oxidation resistance. Carbon. Addition of 0.1% carbon ensures 100% martensite in 9% Cr steels, thus ensuring absence of anisotropy during g! a transformation. Higher amount of carbon would promote precipitation of M23C6, thus reducing the toughness. On the other hand, M23C6 along the lath boundaries offers the long-term microstructural stability of the lath structure. Nitrogen: The solubility of nitrogen in ferrite is very low. This is useful in non-ODS ferritic steels like T91, due to enhanced creep resistance by forma­tion of V or Nb carbides/carbonitrides. But, in ODS steels, Ti is used for refining yttria. Hence, nitrogen content is restricted to 0.01%, preventing the forma­tion of deleterious TiN compound. Tungsten-. Tungsten is a more effective solid solution strengthener than Mo, but at the cost of ductility. Tungsten stabilizes 8-ferrite and accelerates formation of Laves phase, both of which cause reduc­tion in toughness. Hence, it is optimized to 2.0%. Yttria — The most important constituent of ODS steels is the yttria, which enhances high temperature creep strength by pinning mobile dislocations and delays void swelling by acting as sinks for point defects produced during irradiation. The strength increase is accompanied by a concomitant loss of ductility and saturates around 0.4% yttria. Hence, it is optimized to 0.35%. Titanium — The major role of titanium in ODS steels is to refine the yttria particles (20 nm after mechanical alloying) to ultra-fine (2-3 nm) particles. The complex Y-Ti-O particle imparts the necessary high temperature creep strength. The beneficial effect of titanium saturates around 0.2%. Further increase introduces manufacturing problems of the tubes and hence titanium is chosen as 0.2%. Excess oxygen — Oxygen is present during processing of the ODS steels. The oxygen present in excess of the amount required for formation of required amount of Y-Ti-O complex leads to increase in tensile and creep strength. The Y-Ti-O complex oxides requires about 0.07 + 0.01% excess oxygen. Argon — A strict control of argon (<0.002%) during processing of ODS steels is essential to avoid embrit­tlement due to formation of argon bubbles during irradiation. Minor elements — Nickel and manganese are to be reduced to maintain the A1 (a! g on heating) tem­perature higher than the anticipated hot spot temper­ature. This enables the tempering temperature to be as high as possible. Silicon, phosphorous, and sulfur undergo RIS and cause embrittlement. Silicon also accelerates formation of deleterious phases like the Laves phase. Hence, their amounts are reduced to 0. 05 and less. The processing route used worldwide is the powder metallurgy route of mechanically alloying prealloyed powders of Fe-Cr-W-Ti-C + Ti2O3, followed by hot extrusion and rolling or hipping with final heat treatments. Commercial ODS steels (Table 7) have been developed demonstrating the standardizing of fabrication technologies. The ferritic-martensitic ODS steels have been developed by adjusting the contents of chromium and carbon. The ferritic ODS steels, with 12% chro­mium and carbon content less than 0.02%, derive71 their high temperature creep strength basically from Table 7 List of few commercial ODS ferritic steels and their chemistry Commercial name Chemistry MA956 Fe-20Cr-4.5Al-0.5Y2O3 MA957 Fe-14Cr-0.3Mo-Ti-0.27Y2O3 M11 Fe-9Cr-Mo-0.37Y2O3 M92 Fe-9Cr-Mo-0.30Y2O3 PM2000 Fe-20CrAlTi-0.5Y2O3 the dispersoids. The ferrite matrix offers72 superior resistance against oxidation and corrosion while the major challenge appears to be the anisotropy73 of properties. The martensitic steels based on either 12% chromium with 0.1—0.2% carbon or the 9% chromium, derive their strength from the martensitic matrix and the dispersoids. The 9% chromium steel displays isotropic properties while it suffers from inferior corrosion resistance. The conventional joining technologies pose sig­nificant problems leading to coalescence of oxide particles. Hence, solid state bonding techniques74 like the pressurized resistance welding have been developed for joining the clad tube with the end plug of a fast reactor. Postweld heat treatments (PWHT) have also been developed to match the strength levels of the clad and the end plug. The in-service performance of ODS steels in flowing sodium has been found to be satisfactory, despite the formation of austenite layer on the sur­face of the clad tube due to the deposition of nickel. The thickness of the oxide layer in 12%Cr ODS steel was found to be only 50% of that in 9Cr ODS steels. Reactor irradiation experiments have been per — formed75,76 on ODS ferritic steels. The dispersoids were found74 to be stable up to a dose of 10 dpa in JOYO. The mechanical properties at 573 K after neutron irradiation were reported to be same as con­ventional ferritic martensitic steels. The studies on long-term in-service behavior and postirradiation behavior are being studied. Presently, the main challenges in this variety of ODS steels are the anisotropy observed in steels with chromium more than 12%, less oxidation resistance in steels with 9% chromium, fabrication procedure with cost-effectiveness, uniformity of dispersoids in all regions of the clad tube, stability of the dispersoids under irradiation, and the joining technologies. It is hoped that the above problems would be overcome in the near future and the ODS ferritic steels can be used in fast reactor core as clad and wrapper, for burn-up beyond 250 dpa, at temperatures exceeding 973 K. Additionally, ODS ferritic steels are also being consid­ered for fusion reactor applications. The rich experi­ence in the development of fast reactor materials would enable launching the advanced ferritic steels for fusion technology, in a shorter time span. Read More 22.08.2015   Comprehensive nuclear materials Radiation-Induced Swelling of Nb and Nb-Base Alloys Like all group V transition metals, the affinity of Nb for, and its ability to dissolve, high concentrations of interstitial atoms such as hydrogen, oxygen, nitrogen, and to a lesser extent, carbon can strongly influence the properties of the metal through defect-impurity interactions. Hydrogen, carbon, and oxygen impurities have a strong effect on the tensile Ductile-brittle transition temperature (DBTT) of pure Nb (reviewed by Hahn et a/.13), with hydrogen levels near 10 ppm increasing the DBTT to 173 K and over 273 K at levels >100 ppm (DBTT of high purity Nb and Nb alloys is near 73 K14,15). The effects of oxygen and carbon were less severe, but influential at levels of 100 ppm and greater. The effect of nitrogen on embrittlement also appears to be as severe as that of oxygen, though some uncertainty exists as to whether solubility limits have been exceeded in the data.1 The effect of interstitial impurities on the irradiated properties of Nb and Nb-base alloys is significant and has been examined, though the overall database for irradiated properties is limited. The interplay between the radiation-created defects and the interstitial impurity elements was investi­gated by Igata et a/.16 for pure Nb (70 wppm oxygen and 30 wppm nitrogen) irradiated to 3.4 x 1020 n cm-2 (E > 1 MeV) at temperatures below 413 K and post­irradiation annealed up to 973 K. Increases in yield strength over the as-irradiated values following annealing were measured at 473 and 673 K, attrib­uted to the interplay of the defect clusters trapping oxygen and nitrogen atoms, respectively. Above 773 K, no difference between the annealed and as-irradiated yield stress was observed. Hautojarvi eta/.17 and Naidu eta/.18 examined the interaction between vacancies and interstitial impurities in irradiated Nb through positron annihi­lation studies. In high-purity Nb, vacancy clustering within the collision cascades is observed, starting as low as 160 K, with vacancy migration peaking around 250 K, but in materials with higher hydrogen content, the vacancy migration stage shifts to temperatures close to 400 K.17 The irradiation exposure at inter­mediate temperatures (0.3—0.6 Tm) can lead to void swelling, irradiation creep, and helium embrittlement through processes involved in (n, a) reactions or impurity gas atoms. Naidu eta/.18 examined the effect of He and its interaction with vacancies in pure Nb, leading to the development of bubbles through a-irradiated specimens. At temperatures between 623 and 1023 K, bubble growth occurs through the addition of He atoms and vacancies, followed by migration and coalescence at higher temperatures, eventually leading to the annealing out of the He bubbles and vacancy complexes above 1173 K.18 The irradiation-induced swelling of pure Nb gen­erally appears at temperatures between 673 and 1323 K with peak swelling near 873 K (0.32 Tm), though these limits are not clearly defined and are based on the very limited data available, compiled by Wiffen19 and Pionke and Davis.1 A maximum swelling of 4.8% fol­lowing irradiation to 2.5 x 1022ncm~2 at 858 K was reported.1 However, the magnitude of swelling shows considerable scatter in the literature, possibly reflect­ing the influence of impurity concentrations and dif­ferences in irradiation conditions and microstructural interpretation of the materials.19 Fischer20 reported that void concentration increased four to seven times for a fourfold increase in flux for the same total fluence. This produced a reduction in void size with flux and therefore a reduction in the total swelling. Loomis and Gerber21-23 examined the influence of oxygen and substitutional binary alloy additions on the swelling of 3 MeV 58Ni+ ion-irradiated Nb up to ^50 dpa. Void formation and characteristics in size and morphology were found to be dependent on temperature, oxygen concentration, and the type of substitutional alloy addition. The average void diam­eter was found to increase with temperature as well as oxygen up to 0.02 at.%. Higher oxygen concentra­tions resulted in a decrease in void diameter to 0.1 at.% O, above which void diameters showed no significant changes. The number density of voids was found to decrease with temperature, but increase with oxygen concentration to ^0.06 at.%, above which the number density showed no significant change. As the volume fraction of swelling (А V/ V) is propor­tional to both the void number and the cube of the void diameter, the volume fraction is observed to increase with temperature and oxygen concentration to ^0.04 at.%, followed by a decrease and plateau of the volume fraction above 0.1 at.%. The dependence of А V/ V on temperature and oxygen concentration is illustrated in Figure 1. Microstructural examina­tion revealed an ordering of the voids into a lattice — type structure in the material irradiated at 1050 K to ^40 dpa and oxygen concentration >0.039 at.% oxygen. The higher temperature of the maximum swelling as compared to the neutron irradiation data is believed to be associated with the higher displace­ment damage rate of the ion-bombarded material,19 though the higher impurity levels may also provide an influence. The effect of dilute (^2.4 at.%) substitutional alloy addition on the swelling of 0.06 at.% oxygen — doped Nb was also examined for 3 MeV 58Ni+ ion irradiation at 1225 K. The AV/V was determined to increase through the addition of Ta, but decreased with increasing effectiveness by the addition of Ti, Zr, V, and Hf. The addition of the reactive alloying elements to Nb suppresses void formation through the gettering of interstitial impurities that act as void nucleation sites. The AV/V was determined to be unaffected by the addition of Ni or Fe. The depen­dence of AV/V on temperature, oxygen, and substitu­tional addition is also shown in Figure 1. • Nb + 2.4at.%Ta « Nb + 2.4at.%Zr Nb + 2.4at.%Ni Nb + 2.4at.%V ■ Nb + 2.3at.%Fe л Nb + 2.4at.%Hf Nb + 2.3at.%Ti Nb + 2.4at.%Mo Figure 1 The dependence of void volume fraction (AV/V) in 3 MeV 58Ni+ ion-irradiated Nb on the concentration of oxygen and dilute solute additions. Reproduced from Loomis, B. A.; Gerber, S. B. J. Nucl. Mater. 1983, 17, 224-233. Swelling in Nb-1Zr has been examined, though only scattered data are available in the examination of temperature and flux dependence. The available swelling data on Nb—1Zr, compiled by Powell eta/.24 and Watanabe eta/.25 presented in Figure 2, show the lack of data on the temperature range in which peak swelling appears. The swelling data shown in the figure were measured through electron microscopy, with the exception of the data by Powell et a/.24 and Wiffen26 Alloy impurity chemistry, in addition to interpretation and measurement error, may account for the scatter associated with the lower tempera­tures. The work of Watanabe et a/.25 and Garner et a/.27 indicates that irradiation-induced swelling is dependent on the thermomechanical history of the material. In that material, cold-working followed by solution anneal and aging exhibited swelling, while material not given the preirradiated cold-working showed some densification. The changes in density of the material are dependent on the phase-related transformations involving precipitation. Swelling in Nb-1Zr appears to be centered over a more narrow temperature range than in Nb, with a peak near 1073 K that is higher than that of the pure metal. While the addition ofZr to Nb appears to delay nucleation of voids to higher temperatures, the voids that form are of larger size than those appearing in pure Nb under comparable conditions. For example, Figure 2 Swelling as a function of irradiation temperature and dose for neutron-irradiated Nb-1Zrfrom available literature compiled by Powell etal.24 and Watanabe etal.25 following irradiation to 2.5 x 1022ncm~2 (E > 0.1 MeV) at 1063 K, the diameter, concentration, and volume fraction of voids in Nb-1Zr was 57.5 nm, 1.8 x 102°m~3, and 2.2%, respectively,1 whereas under similar conditions, the same void parameters in pure Nb were 18.6 nm, 2.8 x 1021 m~3, and 1.04%. While void formation and swelling in Nb and Nb-1Zr occurs, the total swelling is generally <5% and within engineering limits, even for high neutron exposures >10 dpa.3 The addition of Ti to Nb was found to increase void resistance and has been found to suppress void formation in V at concentrations as low as 3%.29 The combination of reactive alloy ele­ments and Nb in the C-103 alloy may suggest a greater void formation resistance than in pure Nb and Nb—1Zr. Read More 22.08.2015   Comprehensive nuclear materials Thermal Aging Embrittlement Due to High Cr Content High Cr concentration often increases susceptibility to aging embrittlement through the formation of Cr-rich secondary phases. The trade-off between cor­rosion resistance and aging embrittlement caused by increasing Cr content is one of the critical issues facing the developers ofhigh-Cr ODS steels. The aging effects of ODS steels with different Cr content were investigated by measuring their impact fracture energy at RT after aging at 500 °C up to 10 kh. The results are shown in Figure 24.43 The fracture energy decreases with increasing Cr content before aging. Aging, then, causes a reduction in the fracture energy. ODS steels with a Cr content >18 wt% show a significant reduc­tion in fracture energy after aging for 100 h. In contrast, 16Cr-4Al ODS steel showed a small reduction in frac­ture energy even after aging for 10 kh. Microstructure observation by TEM revealed that fine secondary phases were formed in high density after aging for 1000 h at 500 ° C. These secondary phases are consid­ered to be Cr-rich phases. In order to reduce suscepti­bility to aging embrittlement, the Cr content could be <16 wt%. Read More 22.08.2015   Comprehensive nuclear materials Review of Prior Creep Models 4.10.6.3.1 Linear viscoelastic creep model Irradiation-induced (apparent) creep strain is con­ventionally defined as the difference between the dimensional change of a stressed specimen and an unstressed specimen irradiated under identical con­ditions. Early creep data was found to be well described by a viscoelastic creep model1,58-63 where total irradiation creep (ec) = primary (transient) creep + secondary (steady-state) creep. ec = ^[1 — exp(-by)] + kay [12] E0 where ec is the total creep strain; a, the applied stress; E0, the initial (preirradiated) Young’s modulus; y, the fast neutron fluence; a and b are constants (a is usually = 1); and k is the steady-state creep coefficient in units of reciprocal neutron dose and reciprocal stress. Equation [13] thus conforms to the Kelly-Foreman theory of creep with an initially large primary creep coefficient, while the dislocation pinning sites develop to the equilibrium concentration, at which time the creep coefficient has fallen to the steady-state or secondary value. Early creep experiments in several

 

countries showed the primary creep saturated at approximately one elastic strain (a/E0) so that the true creep may be represented as a r і ec = + kay [13] E0 This is often normalized to the initial elastic strain and written as ec = 1 + kEog [14] in elastic strain units (esu) (esu is defined as the externally applied stress divided by the initial static Young’s modulus), or creep strain per unit initial elas­tic strain; kE is the creep coefficient in units of recip­rocal dose [United Kingdom ~ 0.23 x 10-20cm2n-1 EDN up to Tirr ~ 500 °С]. (EDN — equivalent DIDO nickel dose, a unit of neutron fluence used in the United Kingdom and Europe.)

 

where a is the applied stress; (dec/dy)0, the initial secondary creep rate; y, the fast neutron fluence; S(y), the structure factor, given by S(y) = Eg/Ep the ratio of the Young’s modulus at dose y to the Young’s modulus after the initial increase due to dislocation pinning. The structure factor, S(y), thus attempts to sepa­rate those effects due to dislocation pinning occurring within the crystallites and structural effects occur­ring ex-crystal through changes in the Young’s modulus. However, the effect of creep strain (tensile or compres­sive) on modulus is not considered when evaluating the structure term. The unstressed Young’s modulus changes are used to establish the magnitude of S(y).

 

4.10.6.3.3 The Kennedy model Kennedy et al66 replaced the structure term in the UK model with a parameter based on the volume change behavior of the graphite: ec = S + k'(y)ay [16] E0

 

where

 

У Г k'(g) = 4 1 0

 

/ DV /V0 ^ (DV / Vq )m

 

dy

 

[17]

Here, m is an empirical constant equal to 0.75 and k0 is the steady-state creep coefficient established from low dose creep experiments.

Although the Kennedy et al66 model was shown to perform well in the prediction of high-dose tensile creep data, it did not predict the compressive data nearly as well. Moreover, as with the UK model, the sign of the applied stress is not considered when evaluating the influence of structure change (as reflected in volume changes). The quotient in eqn [17] is evaluated solely from unstressed (stress — free) samples irradiation behavior. As discussed by Kelly and Burchell,51 the term (AV/Vmax) does not exist at low irradiation temperatures where graphites expand in volume.

The blocks of PGA were manufactured by extrud­ing needle-shaped filler particles mixed with a pitch binder. During the extrusion process, the needle-shaped filler particles tended to align with the V axis parallel, and the V axis perpendicular, to the extrusion direction. Thus, the final product (or block) had two orthotropic directions: parallel to the extrusion direction (WG) and perpendicular to the extrusion direction (AG). This strong ori­entation in direction is reflected not only in the unirradiated properties but also in the irradiation properties and dimensional changes. Dimensional

X X Graphite grade

(c)

Figure 28 Relative position and ratio of /(D/G) by graphite grade and condition. (a) Normalized position of G-Peak, (b) Normalized position of D-Peak, (c) Ratio of the D-peak and G-peak intensities. Courtesy of A. Jones, University of Manchester.

о

60

x

Э

40

0

0 0,2 0,4 0,6 0,8 1 1,2 1,4

(b) I(D/G)

(a)

Figure 30 Schematic of the irradiation-induced changes in Gilsocarbon graphite irradiated at 550 °C (note that there will be a similar set of curves for each irradiation temperature). (a) Dimensional change, dimensional change rate, and coefficient of thermal expansion and (b) Factorial change in Young’s modulus (E/E0-1) and thermal conductivity (K0/K-1), and irradiation creep (elastic strain units, esu).

(c) CTE (10-6 K-1)

180 °C

Figure 31 Correlation between initial growth rate and unirradiated coefficient of thermal expansion. Modified from Simmons, J. Radiation Damage in Graphite; Pergamon: London, 1965.

change MTR data for PGA is given in Birch and Brocklehurst64 for both the parallel (WG) and per­pendicular (AG) directions. In the parallel direc­tion and below 300 °C, the large dimensional

be compared to that of HOPG, as given in Figure 33. If PGA is irradiated to a higher fluence, the shrinkage rate reduces until the graphite begins to expand or ‘turns around,’ as illustrated in Figure 34.

‘Turnaround’ is associated with the closure of the Mrozowski cracks; see Figure 32. When all of the accommodation provided by the cracks has been taken up, the larger ‘C crystallite dimensional change rate would be expected to dominate the V axis shrinkage rate. This behavior has been used, with some success, to model the dimensional change behavior in PGA, Gilsocarbon, and Russian GR-280 graphite.48,65,66

Of the PWR plants that have been licensed for commercial operation in the United States, ^80% utilize either reinforced or prestressed concrete pri­mary containments. In meeting the same basic func­tional and performance requirements as noted for BWR containments, the concrete containments in PWR plants are of three different functional designs: subatmospheric (reinforced concrete), ice condenser (reinforced concrete), and large/dry
(reinforced and prestressed concrete). The primary differences between these containment designs relate to volume requirements, provisions for accident load — ings/pressures, and containment internal structures layout. The PWR containment structure generally consists of a concrete basemat foundation, vertical cylindrical walls, and dome. The basemat may consist of a simple mat foundation on fill, natural cut, or bedrock or may be a pile/pile cap arrangement. Most of the plants have utilized the simple mat on fill or bedrock design. Interior containment surfaces are lined with a thin carbon steel liner to prevent leakage. Exposed surfaces ofthe carbon steel liner are typically painted to protect against corrosion and to facilitate decontamination should it be required. Depending on the functional design, the concrete containments can be on the order of 40-50 m in diameter and 60-70 m high, with wall and dome thicknesses from 0.9 to 1.4 m and base slab thicknesses from 2.7 to 4.1 m. Two of the PWR plants (Bellefonte and Ginna) have rock anchor systems to which the post-tensioning tendons are attached. Figure 3 presents a cross-section for a prestressed concrete, large, dry containment.

The containment internal structures in PWR plants are typically constructed of conventionally reinforced concrete and tend to be more massive in nature than the internal structures in BWR plants, because they typically support the reactor pressure vessel, steam generators, and other large equipment and tanks. In addition, these structures provide shielding of radiation emitted by the NSSS. Some of the specific functions that these structures (typically floor slabs, walls, and columns) are required to per­form include the following:

1. provision of human accessibility;

2.

support and separation of various plant equipment;

3. resistance to emergency loading conditions;

4. transfer of containment loads to containment foundation;

5. missile protection; and

6. channeling/routing steam and air through ice condensers (PWR ice condenser containments).

PWR plants that utilize a metallic primary contain­ment (large dry and ice condenser designs) are usually contained in reinforced concrete ‘enclosures’ or ‘shield’ buildings that, in addition to withstanding environmen­tal effects, provide radiation shielding and particulate collection and ensure that the freestanding metallic primary containment is protected from the natural environment. The secondary containment consists of a vertical cylinder wall with shallow dome and is often supported by the containment basemat.

Except for differences in the spent — and new-fuel storage pools, structures that fall into the other struc­tures category are essentially the same at the PWR and BWR plants. The spent — and new-fuel storage pools for PWR plants are typically located in an auxiliary building proximate to the containment. These reinforced concrete wall and slab structures are generally massive in cross-section to support a large pool of water and the fuel elements and are lined on the water side with stainless steel. The pools are connected to the reactor/refueling cavity (inside containment) via a transfer channel that is also a safety-related structure since it must provide radia­tion shielding and support for the fuel transport mechanism and fuel.

The duration of the transient regime of swelling in austenitic and high-nickel steels is known to be exceptionally sensitive to irradiation parameters but also to be very sensitive to fine details of composition, heat treatment, and mechanical processing. It would require a very long article to review all of the para­metric sensitivities of the transient duration to such a wide array of variables, so only a brief summary will be presented here. The reader is referred to Garner1,116 for a more detailed description.

4.02.8.3.1 Stress state

The dependence of void swelling on stress state is an example of a second-order sensitivity mentioned at the beginning of this section. If a material swells rather easily, stress has only a small or unnoticeable effect on swelling. If the transient regime is large, however, stress can shorten the transient significantly. The effect of stress during irradiation is almost always to increase swelling. One significant exception arises if an annealed steel is subjected to a load above its yield stress during the rise to power. This often leads to a decrease in swelling relative to that pro­duced at a stress below yield. In effect, the steel is plastically deformed and warm-worked during the rise to power, raising the dislocation density.

Applied stresses have been shown to participate in the evolution of Frank loop and dislocation evolution and to produce the anisotropy of Burger’s vector distribution that is important to the operation of irradiation creep.123 Since shear stresses also assist in the unfaulting of Frank loops and in the evolution toward quasi-equilibrium network densities, it is not surprising that applied stress accelerates the onset of swelling. Although most previously reported experi­ments involved only tensile stress states, some experi­ments suggested that both tensile and compressive stress states shortened the transient regime.1 Two recent studies have convincingly shown that the hydro­static component of stress is relatively unimportant and that it is the deviatoric component or shear stress that accelerates swelling.12 ,125 This is especially evi­dent for loads applied to springs where there is a pure shear stress state without a hydrostatic component. In this case stress-enhanced swelling is also observed.124

Until recently it was not known if the stress — enhanced increment of swelling during constantly applied stress was distributed isotropically or not. A recent publication by Gilbert and Garner showed that both the stress-free and stress-enhanced incre­ments of swelling were distributed isotropically.126

The history of the stress state is as important as its magnitude and relative contribution of shear and hydrostatic components. In fuel pins, for instance, the stress is initially low and builds up slowly. In this case, swelling is usually in progress long before stress can participate. In pressurized tubes, however, creep starts long before swelling begins. The loop and dislocation microstructures of the swelling-before­creep and creep-before-swelling scenarios are differ­ent and therefore the swelling and creep behaviors are also somewhat different.1

Stress can also leave a memory in a component after the stress is removed and irradiation continues.123,127 Garner and coworkers recently showed that when stress was removed from previously stressed tubes they continued for a short time to distribute mass in the directions dictated by irradiation creep in response to the stress state characteristic of a pressur­ized tube, although the memory faded as irradiation continued.127 The memory is thought to reside in the stress-induced anisotropic distribution of Burger’s vec­tors, which was eventually replaced with an isotropic distribution.