The number of displaced atoms inside the cascade can be simply estimated using the Kichin — Pease formula9 or the modified Kichin-Pease for­mula (Norgett-Robinson-Torrens model or NRT model).1 , 1 According to this last model, the number of displaced atoms within the cascade in the case of a 22 keV PKA and using a displacement energy of Ed = 40 eV is np = 0.4i7r/Ed ~ 220. Because of the large mean free path of fast neutrons (several
centimeters), it can be considered that only one PKA is created by the incoming neutron going through the Zr cladding used in pressurized water reactors (PWRs) (with a thickness of 0.6 mm). There­fore, if the PKA creation rate per unit volume within the cladding is known for a typical fuel assem­bly in a PWR (with typical fast neutron flux is 5 x 1017 nm-2 s-1 (E > 1 MeV)), the number of dis­placed atoms per unit volume and per second can be computed. From this value, the overall number of displacements per atom (dpa) and per second can be simply computed. This calculation can be achieved, as described by Luneville et at., by taking into account the PWR neutron spectrum as well as the neutron-atom differential cross section. It can be shown that a typical damage rate for a cladding in a PWR core is between 2 and 5 dpa year- , depending on the neutron flux history. This means that each atom of the cladding has been displaced 2-5 times per year! A more accurate correspondence between the fast fluence and the damage for a cladding in a PWR is provided by Shishov et a/.12 These authors evaluate that a fluence of 6 x 102 4 nm 2 (E > 1 MeV) corresponds to a damage of 1 dpa.

This simple approach gives a good description of the number of displaced atoms during the creation of the cascade, but does not consider intracascade elas­tic recombinations that occur during the cascade relaxation or cooling-down phase.11,13,14 In addition, this approach does not give any information on the form of the remaining damage at the end of the cascade, such as the point-defect clusters that can be created in the cascade.

In order to have a better understanding of the created damage in a-zirconium, several authors have

performed MD computations also using different types of interatomic potentials. It is shown that, at the end of the cascade creation (<2 ps), the cascade is composed of a core with a high vacancy concentra­tion, and the self interstitial atoms (SIAs) are concen­trated at the cascade periphery.14-16 The cascade creation is followed by the athermal cascade relaxa­tion that can last for a few picoseconds. During this phase, most of the displaced atoms quickly reoccupy lattice sites as a result of prompt (less than a lattice vibration period, 0.1 ps) elastic recombination if a SIA and a vacancy are present at the same time in the elastic recombination volume (with 200 ^ <V<400 ^, where V is the elastic recombination volume and ^ the atomic volume.17) Wooding eta/.16 and Gao eta/.8 have shown that at the end ofthe cascade relaxation the number of surviving point defects is very low, much lower, only 20% at 600 K, than the number of Frenkel pairs computed using the NRT model. It is also shown that all the point defects are not free to migrate but that small point-defect clusters are created within the cas­cade. This clustering is due to short-range diffusion driven by the large elastic interaction among neighbor­ing point defects and small point-defect clusters. In the case of zirconium, large point-defect clusters, up to 24 vacancies and 25 SIAs (at 600 K), can be found at the end of the cascade relaxation (Figure 1).8 According to Woo eta/.,14 the presence of these small point-defect clusters spatially separated from each other, as well as the different concentrations of single vacancies and SIAs, can have a major impact on the subsequent microstructural evolution. This effect is known as the production bias, which has to be considered when solving the rate equations in the mean-field approach of point-defect evolution.14

The form of these small clusters is also of major importance since it plays a role on the nucleation of dislocation loops. Wooding et a/.16 and Gao et a/.8 have shown that the small SIA clusters are in the form of dislocation loops with the Burgers vector 1/3(1120). The collapse of the 24-vacancy cluster to a dislocation loop on the prism plane was also found to occur.

Historically, the influence of differences in dpa rate across small cores was perceived as an effect of tem­perature on swelling rate rather than a flux effect, primarily because it was difficult to separate the influence ofdpa, dpa rate, and temperature in limited data fields from small cores. While it was recognized for many years that there was some effect of dpa rate to determine the transient duration, until rather recently the full strength of the rate effect was underappreciated.

The new appreciation for the strong influence of dpa rate arises from two categories of studies con­ducted over the past decade. The first type involved direct single variable comparisons of the effect of dpa rate on swelling. The second category involved the examination of components irradiated at very low dpa rates and often at temperatures below the previ­ously perceived lower limit of swelling.

4.02.8.3.5.1 Category I of dpa rate effects

Three examples of the first category of dpa rate studies are presented here. The first experiment by Garner and coworkers involved the examination (density change and microscopy) of five unfueled hexagonal subassemblies constructed of a single heat of annealed AISI 304 stainless steel irradiated for many years in the reflector rows 8, 9, 10, and blanket row 14 of the EBR-II fast reactor.139,140 These com­ponents were chosen because they were made of the same steel used to construct the baffle-former-barrel assembly of PWR internals and the hexagonal sub­assemblies spanned the full range of dpa rates and temperatures found in the most swelling-vulnerable parts of the PWR baffle-former assembly.

The EBR-II experiment isolated the effect of dpa rate by concentrating on a limited range of tempera­tures (373-388 °C), but covering a very large range of dpa rates (0.06-3.8 x 10~7dpas_1), with no sig­nificant difference in He/dpa ratio. The data in Figure 52 clearly shows that the transient regime of swelling is progressively shortened as the dpa rate decreases, such that only 10 dpa is required to reach 1% swelling in row 14. In a previous publication it was shown that 30-50 dpa were required to exceed 1% swelling when data were collected at these tempera­tures from rows 2 to 4 inside the EBR-II core at higher dpa rates.141 In this experiment the swelling rates at the highest doses reached are still far from the 1% per dpa known to be a characteristic of this alloy (Figure 53).

Voids and carbide precipitates were found in all examined specimens with swelling ranging as high as 2.8%. Examples of the void microstructure and its sensitivity to dpa rate are shown in Figure 54.1 2 Universally, it was found that lower dpa rates at a given temperature increased the swelling.

The second series of experiments were reported by Okita and coworkers and involved simple model alloys, ternary Fe15Cr16Ni and quaternary Fe15Cr16Ni-0.25Ti, with very low levels of other solutes.143-145 These alloys have no possibility to be involved in segregation-induced precipitation of Ni-rich phases, so any dependence on dpa rate must involve the evolution only of voids, loops, and dislocations.

These simple austenitic alloys were irradiated in the FFTF fast reactor with actively controlled tem­peratures near 400 °C at seven different dpa rates. Measurement techniques used were density change

and microscopy. Multiple specimens were irradiated side-by-side and the measured swelling was remark­ably reproducible.

Figure 55 shows swelling for five of the seven dpa rates where there was a progressive shortening of the transient regime as the dpa rate decreased. At the lower two dpa rates (not shown here) the transient regime had decreased to less than 1 dpa. Most importantly, the steady-state swelling rate appeared to be approach­ing or to have reached 1% per dpa at all seven dpa rates. The most illuminating observation came from the microscopy, however, showing that the
microstructural feature most prominently associated with attaining the steady-state swelling rate was the loss of all Frank loops and the establishment of a glissile rather than sessile dislocation structure.

In a companion experiment the ternary Fe15Cr16Ni alloy was irradiated over a range of temperatures using nickel ions at three much higher dpa rates; it was shown that while voids can nucleate in a highly sessile microstructure, they cannot grow at a high rate.146 Most importantly, it was confirmed that increases in dpa rate led to a progressive decrease in swelling even in sessile networks.

Whereas most void swelling models focus on the rate dependence of void nucleation and growth, Okita showed by microscopy that the effect of dpa rate was most strongly manifested in the Frank loop population. High dpa rates produced a high density of loops of smaller size, while low dpa rates produced fewer loops at larger size. The latter ensemble is more prone to unfaulting, the first step toward pro­ducing a glissile microstructure. Denser ensembles at smaller sizes resisted unfaulting for a longer period. Thus the dependence of transient duration on dpa rate arose primarily from its influence on the stability against loop unfaulting.

In the third series of experiments, Budylkin prepared two experimental alloy series to be irra­diated in very similar neutron spectra in both the BOR-60 and BN-350 fast reactors at nearly identical temperatures and dpa levels.147 The first four-alloy series was Fe-16Cr-15Ni-3Mo-0.6Nb-0.6Mn-0.06C — 0.008P but varying in silicon content from 0.4 to 1.2 wt%. The second three-alloy series contained the 0.63% silicon variant from the first series and two other alloys where 0.15% titanium either was added to or replaced the 0.6% Nb.

The irradiations proceeded at 5.06 x 10~7dpas_1 and 480 °C in BOR-60 and at 1.58 x 10~6dpas_1 and 490 °C in BN-350. Thus there was approximately a factor of three difference in dpa rate. As shown in Figure 56, significantly higher swelling was uni­formly observed in the lower flux irradiation in BOR-60, regardless of alloy composition.

4.05.4.1 Introduction

The previous section included a description of how the effect of radiation damage on the bulk properties of ferritic steels was established from the 1950s and how critical insight into the important role of Cu arose in the late 1960s and early 1970s. Equivalent advances in mechanistic understanding did not occur for another 10 or 15 years.

The improved mechanistic understanding in the 1980s had its origin in the identification of the con­trolling variables that emerged from the experiments discussed in Section 4.05.3. This stimulated consider­able interest on the possible role of elements such as Cu in the embrittlement process. The other, possibly more important, reason was that in the 1970s there were only a few microstructural techniques available for characterizing irradiation damage. Transmission electron microscopy (TEM), the dominant technique, could not resolve the irradiation-induced damage in steels that resulted in a significant change in mechani­cal properties.14 However, in the mid-1980s there was an explosion of information resulting from the appli­cation of a range of different and improved micro­structural techniques. These techniques have now been applied to PWR, BWR, and Magnox steels irra­diated in surveillance locations of power reactors and to representative materials irradiated in materials test­ing reactors.

A more recent advance that is highly relevant to developing detailed mechanistic insight is the advent of ‘multiscale’ modeling. Here, the power of modern computing tools is such that microstruc­tural development (and the resultant change in mechanical properties) can be modeled across the various length and timescales involved in RPV embrittlement. Such models are subject to intense R&D and the current capability can be seen in Wirth et a/.,42 Soneda et al.,43 Becquart,44 and Domain et a/.45 However, these models have not, as yet, made a direct impact on the development of DDRs and so the current state of multiscale model­ing is not reviewed here.

The irradiation effect on nanoindentation hardness of Rohm and Haas CVD SiC in a fluence range of 0.1-18.7 dpa is summarized in Figure 15. It is interest­ing to note that the nanoindentation hardness exhibits relatively small scatter for the individual experiments, and the trend in data as a function of temperature is uniform. This observation is in contrast to both the flexural strength and the indentation fracture tough­ness data, which indicate a broad peak at an intermedi­ate temperature and a relatively large scatter. It is worth noting that nanoindentation hardness of brittle ceramics is, in general, determined primarily by the dynamic crack extension resistance in the near surface bulk material, and therefore should be more relevant to fracture toughness than to plastic deformation resis­tance. However, surface effects of the original sample affect the nanoindentation hardness less, as the samples are generally polished prior to testing.

4.07.4.2 Fracture Toughness of Monolithic SiC

The effect of irradiation on the fracture toughness of Rohm and Haas CVD SiC is summarized in Figure 16. This compilation plots data using the Chevron notched beam technique, although the bulk of the
data sets report Vicker’s or nanoindentation gener­ated data.55-57 The general trend is that the irradiation-induced toughening seems to be signifi­cant at 573-1273 K for the indentation fracture tough­ness data, in spite of the decrease in elastic modulus, which confirms the increase in fracture energy caused by irradiation. The scatter of the indentation fracture toughness data among different experiments is likely caused by both the condition of the sample surface and the lack ofstandardized experimental procedures. Typ­ically, indentation should be applied on the polished surfaces, but conditions of polishing are not always provided in literature. Moreover, the crack length mea­surements are done using optical microscopy, conven­tional scanning electron microscopy (SEM), or field emission SEM, all of which may give very different crack visibility. In addition, a few different models have been used for derivation of the fracture toughness. In conclusion, indentation fracture toughness techni­ques can be used only for qualitative comparison within a consistent set of experiments. It is noted that the experiment employing the Chevron notched beam technique also indicates the irradiation-induced tough­ening, although scatters of toughness values were even greater. These results lead to the conclusion that, in the intermediate irradiation temperature range, the increase of the fracture toughness of SiC exists.

4.09.1.2.1 Precipitation-induced cracking

Solid-state cracks in welds often occur near the time/ temperature regime of a phase transformation in which the local stress or strain produced from the phase transformation interacts with global stresses in the weldment and results in cracking. This basic phenomenon has several different names based on the alloy system it occurs in and includes ‘ductility

dip’ cracking in low-strength nickel-based alloys and stainless steels,10’18 ‘strain-age’ cracking in precipita­tion hardenable nickel — and iron-based alloys,1 — ‘reheat cracking’ in 2%Cr-1Mo-type steels,2 and ‘subsolidus cracking’ in titanium alloys.23

Ductility dip cracking has been studied in detail by Young and Capobianco, who provide a good example of how this phenomenon occurs.18 The cracking derives its name from the corresponding

loss of tensile ductility in the homologous tempera­ture range (~0.4—0.9 Tm) that corresponds to the time/temperature regime of the precipitation of a partially or fully coherent second phase. In low — strength nickel-chromium alloys, the ductility dip occurs during on-cooling from a peak temperature high enough to solutionize existing carbides and cause intergranular precipitation of the detrimental phase (M23C6 carbides, in this case).

The relationship between the precipitation kinet­ics of the detrimental phase and the macroscopic tensile ductility is shown in Figure 9, which com­pares a calculated TTT plot for M23C6 precipitation in a Ni-29Cr-9Fe-0.01C (wt%) alloy (i. e., an analog to EN52/Alloy 690), with experimental on-cooling tensile ductility data for the alloy.10 As shown, if very rapid cooling suppresses precipitation, there is no ductility loss (region 1). The ductility minimum occurs near the nose of the precipitation curve when the local strain contribution from intergranular carbide precipitation is maximized (region 2). Duc­tility recovery occurs as precipitation progresses because local misfit strains decrease as chromium depletion occurs and as misfit dislocations are gener­ated (region 3). Ductility is restored when precipita­tion is complete (region 4).

In Figure 10, the stages of ductility dip crack formation are outlined, in which (often in reheated weld metal of a multipass weld or in the base metal heat-affected zone) (Cr, Fe)23C6 carbides preferen­tially nucleate during on-cooling on grain boundaries with partial, cube-on-cube coherency (Figure 10(a)). Due to misfit strains, tension develops between the carbides, producing intermittent microscopic cracking (Figure 10(b)). Upon the development of global stres­ses (e. g., from thermal strains on-cooling or applied during hot ductility testing), these cracks often link up
and form the classic ‘ductility dip’ crack (Figure 10(c)), that is, an intergranular crack that typically extends < 1 grain in length. Compared to a solidification-type crack, the fracture surfaces of these solid-state cracks show less evidence of the underlying dendritic struc­ture and are littered with (Cr, Fe)23C6-type carbides.24 Figure 10(d) illustrates how the misfit strain between the carbide and matrix increases with increasing chro­mium concentration in the alloy. In part, this explains why 30 wt% alloys (A690 and EN52) are more sus­ceptible to this defect than their lower chromium counterparts (A600/E-182).

The transient nature of ductility loss with time and temperature, which are important dependencies cannot be explained by other proposed mechanisms for this solid-state cracking.2 -32 Specifically, in the Ni-Cr alloys of interest to nuclear systems, neither impurity segregation (at least at ‘typical’ levels of <50 wt ppm sulfur, <100 wt ppm P in the bulk alloy) nor grain boundary sliding plays a significant role in cracking. For example, if sulfur is migrating to grain boundaries at ^870 °C (1600 °F), ductility would not be expected to recover after short hold times (~10s as shown in Figure 9). Similarly, the temperature dependence of the ductility minimum must be explained, as the effect of embrittling agents

such as sulfur should persist to low homologous

18

temperatures.

Similarly, if grain boundary sliding were contri­buting to the intergranular fracture, the fastest quenched sample in Figure 9 should show the most embrittlement, that is, where sliding would be favored by a microstructure without carbides to pin the grain boundaries.29,30 A relative grain-by-grain map of the plastic strains from samples strained to 5 and 10% in the ductility dip temperature range (Figure 11) shows direct evidence against the

10mil	EB house 1c 1% nital etch
HAZ
Weld
S
1
4
10.0 keV 2.1kX
9/21/104
C
2.1 kX
9/20/104 Ф	10.0 keV
10.0 mm 9/20/104 10.0keV 2.1kX Ф

Figure 8 Illustration of intergranular liquation-type cracks in a low-alloy steel. The cracks occurred in both the partially melted zone and heat-affected zone along prior austenite grain boundaries (top) and subsequent analysis of crack surfaces via Auger electron microscopy identified bands of MnS-type sulfide inclusions (bottom).

notion that solid-state cracking is caused by sliding, that is, the uniformity of slip with some strain accu­mulation (yellow and red areas) near the ductility dip cracks. If grain boundary sliding played a role in ductility dip cracking, there would be less strain contrast near the cracks, not more, as this technique is sensitive only to the diffraction pattern rotation produced by dislocations.

The scenario of weld cracking occurring in the time/temperature regime of precipitation of a par­tially or fully coherent second phase is also well
recognized as controlling strain-age or ‘reheat’-type cracking in y’/y"-strengthened alloys.10,18,20,21,33 While susceptibility to reheat cracking is often plot­ted as a function of the aluminum and titanium content of the alloy, a more fundamental correlation based on the transformation kinetics and precipitate/ matrix mismatch of the alloy is possible.18 As shown in Figure 12, alloys with high susceptibility to strain — age cracking display fast transformation kinetics and a large negative precipitate/matrix mismatch (i. e., tension develops between precipitates).

As transformation stresses are displaced to longer times and precipitation-induced stresses become compressive, weldability is improved. However, while weldability is increased by displacing precipitation — induced stresses to longer times, hot workability is often degraded for the same reasons.

It is notable that some titanium alloys undergo a tensile ductility loss when tested near the p! a tra­nsformation.23,34,35 While the authors do not know of equivalent research on zirconium alloys, these alloys could also be susceptible to this form of precipitation — induced cracking (PIC). Mechanistically, this could be caused by the nucleation of a from the p-phase
if the (110)pk(0001)a is significant, or from some other phase with partial coherency (e. g., HCP Laves on HCP-a).

1. Care must be taken when interpreting graphite data because of the variety of fast neutron dose units used. Older data in particular should be treated with care.

2. ‘Graphite damage’ has been equated to activation of nickel at a standard position in DIDO. This can now be calculated and equated to dpa.

3. ‘Graphite damage’ may also be equated to channel burnup which can also be equated to dpa.

4. ‘Graphite damage’ can also be equated to En > 0.18 MeV.

5. EDT is not applicable to irradiation temperatures above 300 °C; there is some evidence that it may be applicable below 300 ° C.

6.
There are conversion factors between all these units but these are subject to various degrees of uncertainty.

The theory originally developed by Simmons in the 1960s reported in detail by Hall et al61 relat­ing the polycrystalline dimensional change rate and CTE with crystallite dimensional change rate, and CTE has been further developed95 in an attempt to explain the shape of the graphite irradiation creep behavior at high dose. The proposed theory argues that if the dimensional change rate in polycrystalline graphite can be related to the CTE, and because irradiation creep has been observed to modify CTE of the loaded specimen differently to that seen in unloaded specimens, changing the CTE by creep would be expected to change the dimensional change rate and hence, the dimensional change in the loaded specimen. This leads to the introduction of the so-called ‘interaction strain.’ The theory behind this methodology is described below.

Considering two specimens (a crept specimen and an unloaded control) being irradiated under identical conditions; in the unloaded control specimen, by applying the Simmons equations, the bulk dimensional change rate gx and bulk CTE ax can be defined by

g (1 AX)g! ^

ax (1 Ax)aa ^ Axac [58]

Figure 65 High-fluence German and US data.
where ga and gc are crystal dimensional change rate in the a and c directions, respectively, and aa and ac are the crystal CTE in the a and c directions, respec­tively. Ax is referred to as the structure factor and by rearrangement
• Apparent creep = dimensional change in loaded specimen —dimensional change in control Thus, the interaction term gr^—г) is included in the finite element analysis of graphite components. The limited data that exists on irradiated HOPG indicates that the dimensional change rate of graphite crystallites increases with increasing fluence in the ‘c’ direction and decreases in the ‘a’ direction for all measured irradiation temperatures and dose range. For irradiation temperatures of 450 and 600 °C, the data indicates that ac and aa remain invariant to fluence. However, below 300 °C the crystal CTE appears to change. There are no crystal CTE data for higher temperatures. It should also be noted that Simmons equations imply that ^ ax aa gx ga Ax ac —aa gc —ga Close examination of typical graphite irradiation data, say for Gilsocarbon irradiated in the tempera­ture range where crystal data are available (450 and 600 °C), shows that the relationship given above does not hold. In fact, the Simmons relationship and measured data diverge at low dose. This is attributed to Simmons assuming that polycrystalline graphite can be considered as a loose collection of crystallites with no mechanical interactions. Others95 have added an extra ‘pore generation’ term to the Simmons dimensional change relationship to try and reconcile these issues, but again there is no real validation of these models.
	[59]
Thus,
gx = ga + gT 0х—г [60] ac aa where gT is the crystal shape rate factor and is equal to gc —ga. Similarly for the loaded specimen,
or gx = gx+gT(y—a;) 1631 where Aa is the change in CTE under load (aX — ax). This leads to the following definitions:
• The true dimensional change in the loaded specimen = the dimensional change in the control + the interaction term • True creep = dimensional change in loaded specimen — true dimensional change in loaded specimen

The use of this interaction term did not gain wide (international) acceptance as it appeared to be using the Simmons relationship beyond its applicability and did not explain the difference between compres­sive and tensile loading at high fluence.	of stresses caused by dimensional change. However, it is difficult to envisage such a yield and shear mechanism in crystalline graphite. The second model98 suggests that under load, the crystallite basal planes will slide because of a pinning and unpinning mechanism during irradiation. Such a mechanism is described in detail by Was99 with rela­tion to metals and could explain primary creep and secondary linear creep. However, if irradiation creep in graphite is associated with basal plane slip due to pinning-unpinning, it is surprising that in PGA, irradiation creep is less in the WG or parallel to the basal plane direction than it is in the AG or perpen­dicular to the basal plane direction (Figure 57). Another possibility is that stress modifies the crys­tal dimensional change rate itself. In support of this are X-ray diffraction measurements1O° that showed that the lattice spacing in compressive crept speci­mens is less than that in the unstressed control specimens (Figure 66). Such a mechanism would explain the PGA data and could be related to the change in CTE and the observed annealing behavior. However, the data and experimental fluence and creep range given are very limited. It is clear that changes to the lattice spacing in crept graphite would be an area worthy of further investigation in future irradiation creep programs. Irradiation creep in the graphite crystallite will be reflected in the bulk deformations observed in creep specimens and in reactor components. Changes to the bulk microstructure due to radiolytic oxidation would be expected to influence this bulk behavior, as would large crystal dimensional changes at very high fluence (past dimensional change turnaround). It would be expected that at very high fluence the behavior of graphites with differing microstructures would diverge; this appears to be the case from the limited high fluence data available.
4.11.20.6.4 Recent nuclear industry model Recently Davies and Bradford96 have developed a far more complex creep model as given below:
y
1 — exp
y0=O
[65]
where a, 1 esu (where this is defined by s/EO); ki, 0.0857e(163O.4/T); b, 0.15 esu per 102Oncm—2 EDN; k2, 0.0128e(127O.8/T); o, 5 esu; k-, 0.4066e(—13359/T); s, stress (P); EO, unirradiated SYM (Pa) appropriate to the stress applied (O.84 x DYM); S(y, T), struc­ture term representing structural induced changes to creep modulus (a function offluence and temperature); W(x), oxidation term representing oxidation-induced changes to creep modulus (a function of weight loss, x, which is a function of fluence). The lateral strain ratio for the primary and recov­erable terms is assumed to be equal to the elastic Poisson’s ratio. The lateral strain ratio for secondary creep, nsc, is assumed to follow the relationship
VsC = O.5[1 — 3Sc(y)]
Sc is a structural connectivity term that the authors have used in model fits for other graphite property changes.57 This model certainly fits the available inert data better than the previous models, although it cannot be tested against radiolytically oxidized — graphite data as there is none.
4.11.21 Concluding Remark
Nuclear grade graphite has been used, and is still used, in many reactor systems. Furthermore, it pro­vides an essential moderator and reflector material for the next-generation high-temperature gas-cooled nuclear reactors that will be capable of supplying high-temperature process heat for the hydrogen economy. Hence, nuclear graphite technology remains an important topic. Although there is a wealth of data, knowledge, and experience on the design and operation of graphite-moderated reactors,
Read More 22.08.2015   Comprehensive nuclear materials Post-yield deformation: Macroscopic behavior Concerning the mechanical behavior beyond the YS, it is pointed out by several authors97,115,116 that for RXA zirconium alloys, the strain hardening rate is higher after irradiation at the onset of plastic flow but decreases rapidly with the plastic strain, more rapidly than before irradiation, resulting in a low strain hard­ening capability, and therefore in little difference between YS and UTS.2 This strong decrease of the strain hardening rate is believed to be the cause of the early localization of the plastic strain at the specimen scale, observed particularly in RXA zirconium alloys, which leads to a strong decrease of the uniform elon- 92-94,96-98,117 gation, as reported by numerous authors. Several authors112,118-120 have shown that, for RXA zirconium alloys, this apparent or macroscopic loss of ductility is related to the early localization of the plastic strain inside shear bands, the failure mode remaining ductile with dimples.97,112,117,121,122 The material does not become brittle considering the frac­ture mode but localizes all the plastic strain in a limited part of the specimen, which leads, at the specimen scale, to a very low, uniform elongation (Figures 12 and 13). As the irradiation-induced hardening increases with the fluence, the uniform elongation decreases rap­idly with the fluence from 10% to values lower than 1 % for RXA alloys at 350 °C, and saturates from a fluence of 5 x 1024 nm~2.92 As for the irradiation-induced hardening, the SRA and RXA zirconium alloys exhibit similar uniform elongation at saturation.100 Some authors96,117 suggest that there is a minimum of uniform elongation for RXA zirconium alloys for testing tem­peratures between 300 and 400 °C. This loss of ductility could be due to an additional hardening that can occur in this temperature range because of the trapping of oxygen atoms by the loops,117 as already observed using microhardness tests.101 For testing temperatures above 400 °C, the ductility is progressively recovered as shown by Garde.117 Read More 22.08.2015   Comprehensive nuclear materials Radiation Damage of Core Components in Fast Reactors The core components in fast reactors include the following: clad (cylindrical tubes which house the fuel pellets) for the fuel and wrapper (a container which houses fuel elements, in between which the coolant flows) for fuel subassemblies. Figure 3 shows a schematic of clad and wrapper in a typical fuel subassembly. The necessity to develop robust tech­nology for core component materials arises from the fact that the ‘burn-up’ (energy production from unit Head Adaptor B&C shielding Steel shielding Top _ plannet Fuel — Bottom plannet I Coolant entry tube J Discriminator. і і Section-XX Figure 3 Schematic of a typical fuel subassembly. quantity of the fuel) of the fuel depends on the performance of the clad materials. The higher burn — up of the fuel increases the ‘residence time’ of the subassembly in the core, eventually lowering the cost. The core component materials in fast breeder reactors are exposed to severe environmental service conditions. The differences in the exposure condi­tions of the clad and wrapper in a fast reactor core are listed in Table 1. Under such exposure condi­tions, materials in the fast reactor fuel assemblies exhibit many phenomena (Figure 4), specific to fast reactor core: Void swelling, irradiation growth, irra­diation hardening, irradiation creep, irradiation, and helium embrittlement. Another selection criterion, namely the compati­bility of the core component materials with the cool­ant, the liquid sodium, has already been established. Presently, methods are known to avoid interaction of the clad material with the coolant. Detailed books and reviews19,20,21,22,23 are avail­able on all the degradation mechanisms mentioned above, which are related to the production, diffu­sion, and interaction of point defects in the specific lattice of the material. Hence, a brief introduction is presented below (see also Chapter 1.03, Radiation — Induced Effects on Microstructure; Chapter 1.11, Primary Radiation Damage Formation; and Chapter 1. 04, Effect of Radiation on Strength and Ductility of Metals and Alloys). Void swelling in a fast reactor core can change a cube of nickel to increase (20%) its side from 1 cm to 1.06 cm, after an exposure to irradiation of 1022ncm~ . Void swelling is caused by the conden­sation of ‘excess vacancies’ left behind in the lattice after ‘recombination’ of point defects produced dur­ing irradiation. Void swelling is measured using the change in volume (V V/V) of bulk components of the reactor or image analysis of voids observed using transmission electron microscope (TEM). The ‘irradiation growth’ (fluence ^102°ncm~ ) can increase the length of a cylindrical rod of uranium three times and reduce its diameter by 50%, retaining the same volume. This occurs mainly in anisotropic crystals, introducing severe distortion in core compo­nents. It is caused by the preferential condensation of interstitials as dislocation loops on prism planes of type (110) of hcp structures and vacancies as loops on the basal planes (0001), which is equivalent to transfer of atoms from the basal planes to prism planes, via irradiation-induced point defects. Irradiation hardening refers to the increase in the yield strength of the material with a Table 1 Comparison of exposure conditions of clad and wrapper of fast reactor core Criterion Clad tube Wrapper tube Exposure conditions (only trends; exact values depend on core design)   Maximum temperature: 923-973 K Steeper temperature gradient Higher stresses from fission gas pressure Chemical attack from fuel Average neutron energy: 100 keV Neutron flux: 4-7 x 1011 nm~2s Neutron fluence: 2-4 x 1019nm~2 Void swelling Irradiation creep at higher temperatures Irradiation embrittlement Interactions with fuel and fission products Tensile strength Tensile ductility Creep strength Creep ductility Compatibility with sodium Compatibility with fuel Compatibility with fission products   Lower temperature range than clad: 823 K Lower temperature gradient Moderate stresses from coolant pressure Flowing sodium environment Neutron environment similar   Void swelling Irradiation creep Irradiation embrittlement Interaction with sodium Tensile strength Tensile ductility   Major damage mechanisms   Selection criteria: mechanical properties   Corrosion criteria   Compatibility with sodium   General common selection criteria Good workability International neutron irradiation experience as driver or experimental fuel subassembly Availability   concomitant reduction in ductility, under irradiation at temperatures <0.3 Tm. The large number density of defect loops, voids, and precipitates generated during irradiation pins the mobile dislocations and acts as an obstacle to their further movement, requiring addi­tional stress to unpin the immobile dislocations. The irradiation creep, the most important param­eter for design consideration, is the augmentation of thermal creep of the material, under irradiation. This leads to premature failure of the material and restricts the service life. The mechanisms responsible for irradiation creep are identified as the ‘stress — induced preferential absorption’ (SIPA) and the ‘stress-induced preferential nucleation (SIPN)’ of point defects by dislocations, which revolve around the interaction of excess point defects generated dur­ing irradiation with dislocations. Irradiation embrittlement, another frequent observation in ferritic steels exposed to irradiation, refers to the increase in the ductile to brittle transi­tion temperature (DBTT) during irradiation. Drastic loss in ductility at low temperatures results from a lower sensitivity of the fracture stress, sf, due to irradiation and less dependence on temperature than the yield strength sy. Materials with a high value of the Hall-Petch constant are more prone to brittle failure. Such materials like ferritics release more dislocations into the system when a source is unlocked, causing hardening and loss of ductility. Some of the engineering materials contain nickel, an element which undergoes an (n, a) reaction, produc­ing high concentration of helium. The binding energy of helium with a vacancy being very high ^2 eV, the helium atoms stabilize the voids, enhancing their growth rate. Incorporation of helium during irradia­tion into voids along the grain boundaries assists grain boundary crack growth by linking voids causing ‘helium embrittlement.’ Of these many degradation mechanisms, the alloy development programmes have focused mainly on the void swelling, irradiation hardening, embrittle­ment, and the irradiation creep, since these are the major life limiting factors. Read More 22.08.2015   Comprehensive nuclear materials Development of Mechanistically Based DDRs 4.05.5.1 Introduction DDRs are equations that describe the changes in mechanical properties (yield stress, Charpy transition temperature, upper shelf toughness, hardness, etc.) as a function of neutron dose. The purpose of this section is to set out the mechanistic DDRs that have been developed to describe the embrittlement of RPV steels incorporated in the different reactor clas­ses worldwide. However, it is important to note that the earliest DDRs were purely statistical in nature. The formulas were derived in different countries from the analysis of (different) databases. The first prediction formula in the United States that included the effect of residuals (‘residuals’ refers to levels of solutes such as Cu) was published in 1975. It was then followed by the Regulatory Guide 1.99 revision 1.106 This Guide has been particularly influential and presents some important features, such as the exis­tence of thresholds in chemical composition, and an explicit dependence on Cu and Ni. It was followed in 1988 by USNRC Regulatory Guide 1.99 Revision 2.107 Petroquin108 has reviewed and compared the formulas employed for the prediction of irradiation embrit­tlement of reactor vessel materials, including the empirical DDRs developed in France (FIS and FIM formulae109), Germany (KTA110,111), and Japan (Japan Electric Association Code (JEAC) 4201 1991112,113). We focus here on DDRs (or embrittlement corre­lations) that have been developed with the form of the equations reflecting mechanistic understanding of the development of radiation damage in RPV steels, while the exact parameterization has been undertaken through fitting the models to large mechanical property databases arising from the test­ing of irradiated surveillance samples. The major driving force for such developments has been the need to take advantage of the greatly improved understanding of embrittlement mechanisms in DDRs that enable interpolation or extrapolation with improved confidence to a parameter space poorly covered by a given (national) surveillance database. A common feature of such DDRs is that they follow the same mechanistic framework (described in Section 4.05.4), but give different weights to the parametric dependencies of radiation damage that have been described in the previous sections. Properly describing the effect of flux on the embrittlement of both low Cu and Cu-containing steels has been subject to extensive debate (see Section 4.05.6). A further common fea­ture is that the DDRs have been refined as new surveillance data have become available, frequently with changes in the form of the equations in order to accommodate more sophisticated mechanistic under­standing. It is important to note that they have been developed to describe embrittlement under relatively low dose rate conditions that apply to specific steel types, that is, CMn or MnMoNi steels. Two classes of steels have been described by such DDRs, namely, CMn RPV steels employed in Mag — nox reactors and MnMoNi steels used in Western LWRs (primarily in the United States and Japan). The mechanistically based DDRs for CMn steels were developed in the 1980s while it was not before 1998 that the first such DDR was published describing embrittlement in US RPV steels. Read More Календарь Май 2024 Пн Вт Ср Чт Пт Сб Вс   1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31   Рубрики 1 BIOFUELS A Look Back at the U. S. Department of Energy’s Aquatic Species Program: Biodiesel from Algae A. Worrall ABOUT THE AUTHOR ACCELERATOR DRIVEN SUBCRITICAL REACTORS ADVANCED BIOFUELS Advanced Biofuels and Bioproducts Advanced separation techniques for nuclear fuel reprocessing and radioactive waste treatment ADVANCES IN Advances in Biochemical Engineering/Biotechnology Advances in Biofuels Advances in Biorefineries Alcoholic Fuels Algae Energy All alternative energy Alternative transportation An Indispensable Truth An Introduction to Nuclear Materials AN INTRODUCTION. TO THE ENGINEERING. OF FAST NUCLEAR REACTORS ANNEX III. AHWR. Bhabha Atomic Research Centre, India ATOMIC ACCIDENTS BACKGROUND Bioenergy Bioenergy — Realizing the Potential Bioenergy from Wood BIOENERGY. RESEARCH:. ADVANCES AND. APPLICATIONS BIOETHANOL BIOFUEL'S ENGINEERING PROCESS TECHNOLOGY BIOFUELS BIOFUELS 1 Biofuels and Bioenergy Biofuels for Road Transport Biofuels from Agricultural Wastes and Byproducts BIOFUELS FROM ALGAE Biofuels Refining and Performance BIOGAS BIOGAS 1 BIOMASS — DETECTION, PRODUCTION AND USAGE Biomass and Biofuels from Microalgae Biomass Conversion Biomass Gasification and Pyrolysis BIOMASS NOW — CULTIVATION AND UTILIZATION BIOMASS NOW — SUSTAINABLE GROWTH AND USE Biomass Recalcitrance Biomasses identities Biotechnological Applications of Hemicellulosic Derived Sugars: State-of-the-Art Biotechnological Applications of Microalgae Biotechnology. for Fuels and Chemicals Cellulosic Energy Cropping Systems Comprehensive nuclear materials DESIGN FEATURES TO ACHIEVE. DEFENCE IN DEPTH IN SMALL AND. MEDIUM SIZED REACTORS Design of Reactor Containment Systems for Nuclear Power Plants ENERGY Energy Efficiency ENERGY SERVICES IN THE HINDU KUSH HIMALAYAN REGION Energy Storage Estimating Loss-of-Coolant Accident (LOCA) Frequencies Through the Elicitation Process EUROSUN 2008 EuroSun2004 EuroSun2008-10 EuroSun2008-11 EuroSun2008-13 EuroSun2008-2 EuroSun2008-3 EuroSun2008-4 EuroSun2008-5 EuroSun2008-7 EuroSun2008-9 EXAMPLES OF REACTIVITY-CONTROL SYSTEMS Exploitation des creurs REP Fast Breeder Reactor Programs: History and Status Fast Reactor Safety. (Nuclear science. and technology) Fertilization Frequency Response Testing. in Nuclear Reactors Fuels and Chemicals. from Biomass Gebaudetypologie Bayern Geothermal Energy GREEN BIORENEWABLE. BIOCOMPOSITES Handbook Nuclear Terms Handbook of biofuels production Handbook of Small Modular Nuclear Reactors Hydrogen — Fuel Cells Hydropower IAEA RADIATION TECHNOLOGY SERIES No Infrastructure and methodologies for the. justification of nuclear power programmes Innovative Biofibers from Renewable Resources Integral design concepts of advanced water cooled reactors Introduction to Nuclear Power Liquid Biofuels: Emergence, Development and LIQUID, GASEOUS AND SOLID BIOFUELS — CONVERSION TECHNIQUES Management von Biogas-Projekten Materials' ageing and degradation in. light water reactors Microbes and biochemistry of gas fermentation Modern Power Station Practice Natural circulation data and methods for advanced water cooled nuclear power plant designs Natural gas Neutron Scattering Applications and Techniques Nuclear and Radiochemistry Nuclear Back-end and Transmutation Technology for Waste Disposal NUCLEAR CHEMICAL ENGINEERING NUCLEAR ELECTRIC POWER Nuclear energy Nuclear Power and the Environment Nuclear power plant life management processes: Guidelines and practices for heavy water reactors NUCLEAR POWER PLANTS NUCLEAR POWER the PUBLIC Nuclear Reactor Design NUCLEAR REACTOR ENGINEERING Nuclear Reactors 1 NUCLEAR REACTORS 2 Others Particle Image Velocimetry (PIV) Passive Safety Systems and Natural Circulation in Water Cooled Nuclear Power Plants PHYSICS OF. HIGH-TEMPERATURE. REACTORS POWER Pretreatment Techniques for Biofuels and Biorefineries Principles of Fusion Energy PROCESS SYNTHESIS. FOR FUEL ETHANOL. PRODUCTION Production of Biofuels and Chemicals with Ionic Liquids Progress, Challenges, and Opportunities for. Converting U. S. and Russian Research Reactors Pumping Pyrolysis Radioactive waste management and contaminated site clean-up Recycling of Biomass Ashes Renewable Energy Products Rudiger Meiswinkel, Julian Meyer, Jurgen Schnell Second Generation Biofuels and Biomass Small modular reactors (SMRs) the case of Russia solar energy Solar Thermal and. Biomass Energy Sonar-Collecttors SonSolar Springer Series in Materials Science Study on Neutron Spectrum of Pulsed Neutron Reactor Sustainable Biotechnology Switchgrass Technologies for Converting Biomass to Useful Energy The Asian Biomass Handbook The Experimental Analyze Of The Solar Energy Collector The Future of Nuclear Power Thermal biomass. conversion and utilization —. Biomass information. system Thoria-based Nuclear Fuels Type of Membrane Contactor Suitable for CO2-O2 Exchanges in Culture Broth Vereinfachtes Verfahren WAS INTENTIONALLY LEFT BLANK Why We Need Nuclear Power wind power WORKSHOP ON NUCLEAR REACTION DATA AND. NUCLEAR REACTORS:. PHYSICS, DESIGN AND SAFETY Автономное энергообеспечение Альтерантивная энергия Альтернативные источники энергии и энергосбережение Без рубрики Биотопливо Ветровая энергия Ветрогенераторы, солнечные батареи и другие полезные конструк­ции Возобновляемые источники энергии ВОПРОСЫ ТЕОРИИ. И ИННОВАЦИОННЫХ РЕШЕНИЙ. ПРИ ИСПОЛЬЗОВАНИИ. ГЕЛИОЭНЕРГЕТИЧЕСКИХ СИСТЕМ ГЕЛИОЭНЕРГЕТИКА Другая энергия Зарядные станции Источники питания Источники энергии ИСУ Концентраторы солнечного излучения КРЕМНИЕВЫЕ СОЛНЕЧНЫЕ БАТАРЕИ Получение кремниевых пластин для солнечной энергетики Применение солнечной энергии Разное Солнечная электроэнергия Солнечная энергия Солнечная энергия — использование Солнечные батареи Солнечные коллекторы Солнечный ДОМ ТОНКОПЛЕНОЧНЫЕ. СОЛНЕЧНЫЕ ЭЛЕМЕНТЫ. НА ОСНОВЕ КРЕМНИЯ ФОТОЭЛЕКТРИЧЕСКОЕ. ПРЕОБРАЗОВАНИЕ. 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