4.02.2.1 Atomic Displacements
What are the nature and origins of neutron-induced phenomena in metals? The major underlying driving force arises primarily from neutron collisions with atoms in a crystalline metal matrix. When exposed to displacive irradiation by energetic neutrons, the atoms in a metal experience a transfer of energy, which if larger than several tens of eV, can lead to displacement of the atom from its crystalline position. The displacements can be in the form of single displacements resulting from a low-energy neutron collision with a single atom or a glancing collision with a higher energy neutron. More frequently, however, the ‘primary knock-on’ collision involves a larger energy transfer and there occurs a localized ‘cascade’ of defects that result from subsequent atom-to-atom collisions.
There are several other contributions to displacement of atoms from their lattice site, but these are usually of second-order importance. The first of these processes involve production of energetic electrons produced by high-energy photons via the photoelectric effect, Compton Effect, or pair production.18 These electrons can then cause atomic displacements, but at a much lower efficiency than that associated with neutron-scattering events. The second type of process involves neutron absorption by an atom, its subsequent transmutation or excitation, followed by gamma emission. The emission-induced recoil of the resulting isotope often is sufficient to displace one or several atoms. In general, however, such recoils add a maximum of only several percent to the displacement process and only then in highly thermalized neutron spectra.4 One very significant exception to this generalization involving nickel will be presented later.
For structural components of various types of nuclear reactors, it is the convention to express the accumulated damage exposure in terms of the calculated number of times, on the average, that each atom has been displaced from its lattice site. Thus, 10 dpa (displacements per atom) means that each atom has been displaced an average of 10 times. Doses in the order of 100-200 dpa can be accumulated over the lifetimes of some reactor components in various high-flux reactor types. The dpa concept is very useful in that it divorces the damage process from the details of the neutron spectrum, allowing comparison of data generated in various spectra, providing that the damage mechanism arises primarily from displacements and not from transmutation.
The use of the dpa concept also relieves researchers from the use of relatively artificial and sometimes confusing threshold energies frequently used to describe the damage-causing portion of the neutron spectrum. Neutrons with ‘energies greater than
X MeV,’ where X is most frequently 0.0, 0.1, 0.5, or 1.0 MeV, have been used for different reactor concepts at different times in history. The threshold energy of 0.1 MeV is currently the most widely used value and is most applicable to fast reactors where large fractions of the spectra lay below 0.5 and 1.0 MeV. Many older studies employed the total neutron flux (E > 0.0) but this is the least useful threshold for most correlation efforts. Caution should be exercised when compiling data from many older studies where the neutron flux was not adequately identified in terms of the threshold energy employed.
There are rough conversion factors for ‘displacement effectiveness’ for 300 series austenitic steels that are useful for estimating dpa from >0.1 MeV fluences for both in-core or near-core spectra in most fission spectra. Examples are ^7 dpa per 1022 n cm~ (E > 0.1) for most in-core light water spectra with lower in-core values of ^5 dpa per 1022 n cm~2 (E > 0.1) for metal fueled fast reactors and ^4 dpa per 1022 n cm~2 (E > 0.1) for oxide-fueled fast reactors.4 Such conversion factors should not be trusted within more than (10-15%), primarily due to spatial variations across the core resulting from neutron leakage. For fast reactor spectra, E > 1.0 conversion factors are completely unreliable.
When E > 1.0 fluxes are employed in light water reactor studies, the conversion factor increases from ^7 dpa per 1022 n cm~2 (E > 0.1) to ~14 dpa per 1022 n cm~2 (E > 1.0). In Russia, a threshold energy of >0.5 MeV is popular for light water
reactors with ^9 dpa per 1022 n cm~2 (E > 0.5). All of these conversion factors assume that within several percent pure iron is a good surrogate for 300 series alloys. Note that other metals such as Cu, Al, W, etc. will have different conversion values arising from different displacement threshold energies and sometimes different displacement contributions.
A standard procedure for calculating dpa has been published,19 although other definitions of dpa were used prior to international acceptance of the ‘NRT model’ where the letters represent the first letter of the three author’s last name (see Garner1 for details on earlier models). Caution must be exercised when compiling doses from older studies where displacement doses were calculated using other models (Kinchin-Pease, Half-Nelson, French dpa, etc.) sometimes without clearly identifying the model employed. Conversion factors between the NRT model and various older models of dpa are provided in Garner,1 but all models agree within ^23%.
 |
While sometimes controversial with respect to how far the dpa concept can be stretched to cover the full range of spectral differences for neutron and especially for charged particle environments, it appears that the dpa concept is very efficient to stretch over light water, heavy water, fusion, and spallation spectra, providing that all energy deposition and displacement processes are included. Note in Figure 1 how well the dpa concept collapses the data on neutron-induced strengthening of stainless steel into one response function for three very different spectra (light water fission, pure D-T fusion and ‘beam-stop’ spallation).20
An ambitious target of increasing the temperature and pressure of steam in many power plants has provided a high impetus for the development of steels with better high temperature properties. Very often, the weld joints play a crucial life limiting role in these components. One of the recurrent problems is the frequent failure of weldments due to Type IV cracking (see below), in weldments of ferritic steels subjected to creep loading. Another problem encountered during service exposure of joints of dissimilar ferritic steels is the failure due to the formation of hard brittle zone at the heat-affected zone (HAZ). Both these issues are discussed below.
The modified 9Cr-1Mo steel fusion weld joint (Figure 14) consisting of base metal, deposited weld metal, and the HAZ produces a complex heterogeneous microstructure due to thermal cycle. The base metal and weld metal consist of a tempered martensite structure, with columnar grains in the weld metal.
The HAZ comprises coarse prior-austenitic grain martensite, fine prior-austenitic grain martensite and an intercritical structure, as one traverses from the weld fusion interface toward the unaffected base metal. This is dictated by the peak temperatures experienced by the base metal during weld thermal cycle and the phase transformation characteristics of the steel. It has been established that the localized microstructural degradation in the intercritical region of HAZ is mainly responsible for the premature creep-rupture strength of Cr-Mo weld joint and can be overcome if residual stresses of the weld are adequately relieved by PWHT
The lower creep-rupture strength of weld joint than the base metal is due38,77 to the different types of cracking developed during creep exposure. Four types of cracking have been identified (Figure 15) in Cr-Mo steel weld joint. They have been categorized as Type I, Type II, Type III, and Type IV. The Type I and Type II cracks originate in the weld metal, propagate either through the weld metal itself (Type I) or cross over in the HAZ (Type II). The Type III cracking occurs in the coarse grain region of HAZ and can be avoided by refining the grain size. Type IV cracking nucleates and propagates in the intercritical/fine grain region of HAZ. Type IV failure occurs at longer creep exposure and higher test temperature, by coalescence of fine cavities leading to microcracks (Figure 16(a)) and their eventual propagation to the surface.
|
Weld metal
Figure 15 Locations77 of different types of failure in weld geometry of the ferritic steels: (a) schematic representation and (b) experimental observation in creep tested weldment of 9Cr-1Mo steels.
|
|
Figure 16 Type IV cracking in same sample as in Figure 15. (a) cavities in the intercritical region and (b) Z-phase77 in creep-tested 9Cr-1Mo steel. The inset shows the microchemistry of the Z-phase.
|
The type IV cracking susceptibility, defined as the reduction in creep-rupture strength of weld joint compared to its base metal, depends on the type of ferritic steel. 2.25Cr-1Mo steel is most susceptible to type IV cracking; whereas the plain 9Cr-1Mo steel is the least susceptible. At higher test temperature, the type IV cracking susceptibility is higher in modified 9Cr-1Mo steel than the plain steel. This is related77 to the precipitation of Z-phase (Figure 16(b)), a complex Cr (V, Nb) N particle, in the modified steel. The Z-phase grows rapidly at elevated temperatures during long term exposure, by dissolving the beneficial
MX types of precipitates. This promotes the recovery of the substructure with associated decrease in strength in the intercritical region of HAZ.
Although it is difficult to completely eliminate Type IV cracking, several methods are being adopted to improve type IV cracking resistance. It is more severe in thick sections due to the imposed geometrical constraint. A design modification can be adopted to decrease the variation in tensile stresses across the welded section of the component or avoid joints in critical regions having high system stresses and relocate them in the less critical region. Strength homogeneity across the weld joint can also be improved by a suitable PWHT. An increase in width of the HAZ can reduce the stress triaxiality such that the soft intercritical region deforms with less constraint with the consequence of reduced creep cavitation, to minimize type IV cracking tendency. The width of the HAZ can be increased both by changing preheat and heat-input during welding. Another contrasting approach to overcome type IV cracking is to avoid or minimize the width of the HAZ, to eliminate the intercritical zone. This is being attempted by employing advanced welding techniques such as laser welding. The resistance against intercritical softening can also be improved by increasing the base strength of the steel with the addition of solid solution hardening elements such as W, Re, and Co and also by microalloying the steel with boron. Microalloying with boron retards the coarsening rate of M23C6 by replacing some of its carbon. The boron content needs to be optimized with the nitrogen content to avoid BN formation. Addition of Cu is also found to be beneficial. Copper is almost completely insoluble in the iron matrix and when added in small amounts, precipitates as nanosize particles to impart creep resistance. A suitable adjustment of the chemical composition of steel within the specification range also reduces the large difference in creep strength between the softened HAZ, the base metal, and the coarse grain HAZ of the joint. A weld joint of modified 9Cr-1Mo steel with low carbon, nitrogen, and niobium has been reported to possess creep strength comparable to that of the base steel.
It is expected that a judicious combination of changes in chemistry and process variables would reduce the failures due to type IV cracking in weldments of ferritic steels subjected to creep loading.
Another frequent problem78-81 is the formation of ‘hard brittle zone’ during service exposure of dissimilar joints between ferritic steels, leading to failures. The formation (Figure 17(a)) of microscopic layer of
  hard, brittle zone along the HAZ in dissimilar weldments of steels is known to be responsible for the cold cracking, stress corrosion cracking, and higher frequency of failures of the weldments. This is one of the cases where modeling has enabled an in-depth understanding of the problem, in addition to providing an industrial solution to prevent the formation of brittle zone.
The brittle layer at the interface between 9Cr-1Mo weld and 2.25Cr-1Mo base metal is shown77 to be a manifestation of a number of synergistic factors: (a) microstructural changes in regions close to the heat source during welding (b) migration of carbon during PWHT, driven by the gradient in its activity and (c) formation (inset in Figure 17(a))
 |
of series of fine carbides when there is a local supersaturation of carbon. It has been possible to use modeling methods like Finite Difference Methods to predict the carbon profile across the weld region of 9Cr-1Mo and the base metal of 2.25Cr — 1Mo (Figure 17(b)), which were in good agreement with the profiles obtained using electron probe microanalysis. These calculations could be refined using Thermo-Calc and diffusion-controlled transformations (DICTRA) to take into account the simultaneous precipitation of carbides and diffusion ofcarbon. These computational methods were instrumental in predicting the methods to prevent the formation of hard zone in dissimilar joints of ferritic steels. Three elements which would repel carbon
atoms, that is, with the positive interaction energy were chosen for this purpose. Figure 17(c) shows78 the comparison of three different metals, Ni, Cu, and Co in preventing the formation of hard zone. Experimental confirmation was obtained79 using interlayer between the two dissimilar ferritic steels. Further insight could also be arrived81 at in the diffusion behavior (Figure 17(d)) of carbon interstitial in the lattices of bcc iron and fcc nickel using molecular dynamics. These calculations could demonstrate that the activation energy for diffusion of carbon in a fcc nickel lattice is higher than bcc iron. This sluggish diffusion kinetics is due to the repulsive potential of nickel toward carbon, which is the main reason for the choice of nickel as the most effective diffusion barrier between the two ferritic steels. Thus, an industrial solution to prevent the formation of brittle zone in joints of dissimilar ferritic steels after service exposure could be arrived at, based on an in-depth understanding of the interaction between the lattice potentials of atoms.
It has been demonstrated in the above studies that modeling methods could be used most effectively to reduce the experimental time required for overcoming an industrial problem. Experimental benchmarking was required only for final confirmation of the predictions. These trends are becoming more common in almost all problems in materials technology, in recent years, be it atomistic mechanisms or fabrication technologies or prediction of life of components. It is hoped that this approach of knowledge — based design of materials would gradually replace the time consuming empirical methods of today.
4.03.7 Summary
Future trends in the global fast reactor industry are toward higher operating temperatures, higher burn — up (250 GWdt~ ), higher breeding ratios (~1.4) and longer lifetime for reactor (60-100 years). These goals require several developments in materials science and technology across all components ofnuclear plants, especially for core component materials.
Ferritic steels have a much better void swelling resistance compared to currently used austenitic stainless steels and are capable of enhancing the burn-up of the fuel up to about ^200GWdt~ Ferritic-martensitic steels based on 9-12% Cr compositions exhibit the highest swelling resistance and a number of commercial swelling resistant materials have been marketed. The principles behind the design of swelling resistant ferritic steels for core components of fast reactors have been discussed. However, their use is rendered difficult due to their poorer creep strengths at temperatures higher than ~-873 K. Improvement of higher temperature tensile and creep strengths in these alloys will enable us to achieve higher temperatures, in addition to higher burn-up, thus improving the economics of nuclear power production. Presently, the reduced creep strength of 9-12Cr ferritic steels at temperatures above 798 K, has restricted their use to certain low stressed components such as subassembly wrappers. Another crucial problem is ‘embrittlement’ in ferritic steels. The mechanisms and methods which are being attempted to overcome embrittlement problems are discussed.
Alloy development programmes are in progress to explore ferritic-martensitic oxide dispersion strength variants, for higher target burn-up of 250 dpa, with enhanced high temperature (^973 K) capability, by improving mechanical properties. Conventional alloy melting routes will have to be abandoned in favor of powder metallurgy techniques of ball-milling, hot isostatic pressing, and hot extrusion for the synthesis of these ODS steels. Process optimization for the development of 9Cr-based ferritic-martensitic steels strengthened by a fine dispersion of yttria nanoparticles has been completed. The major concerns in this family of ferritic or ferritic-martensitic steels are the anisotropy of properties in ferritic 12Cr steels or oxidation resistance in 9Cr steels, fabrication procedure, microstructural stability under irradiation, and dissolution during back-end technologies.
Materials science, engineering, and technology have become an integral part of the aspiration of the nuclear community to improve the economic viability of fast reactors. One of the major concerns in the alloy development programmes has been the unacceptably long time taken to launch newer materials. It is expected that the current trends in materials development, through intense international collaborations and increased role of modeling in materials behavior, would certainly reduce the time and cost of alloy development programmes for future reactors.
Little coverage of the changes in mechanical properties following irradiation has been given to Nb and Nb alloys, with the majority of the data for temperatures below 800 K. Some preliminary experimental work on the irradiated mechanical properties of Nb alloys Cb-752 (Nb-10W-2.5Zr)30 and FS-85 (Nb — 10W-28Ta-1Zr)31 is available. However, these alloys are not commercially produced and have shown indications of thermal aging instabilities, leading to grain boundary embrittlement.12,32,33 The irradiated mechanical properties of these alloys show similar radiation hardening as in the pure metal, but with mechanical properties more sensitive to thermal aging conditions. The bulk of the irradiated mechanical properties data is for the Nb-1Zr alloy as well as the pure metal, and is covered in this review.
The irradiated mechanical properties of Nb and Nb-1Zr are strongly governed by irradiation temperature, determining whether the mechanical properties are controlled by dislocation loops or a combination of loops and voids in the microstructure. As cavity formation can be delayed or suppressed by higher irradiation temperatures in Nb-1Zr, mechanical property comparisons between the alloy and the base metal will reflect their irradiated microstructure. For Nb and Nb-1Zr irradiated to 3 x 1022ncm~2 at ^728 K, the pure metal contains both dislocation loops and voids, while the alloy exhibits no void formation.19 A comparison of the tensile properties of Nb and Nb-1Zr irradiated under similar conditions is shown in Figure 3. The irradiated strength of both materials shows an increase in tensile strength above the unirradiated
 |
condition, with Nb-1Zr showing a greater sensitivity to irradiation. As the mechanical properties of Nb-1Zr are dominated by the dislocation loop structures, yield instability is observed in the material, leading to the early onset of necking. This results in <0.2% uniform elongation, though total elongation near 10% is still achieved. The yield instability is associated with dislocation channeling, in which deformation dislocations will create defect-free channels along their slip plane, following the annihilation of the loop structures. This occurs only after enough applied stress is achieved to overcome the obstacles, but the net effect is a nonuniform plastic deformation through channels that allow for the movement of deformation dislocations at reduced stress.
The irradiated Nb samples whose properties are shown in Figure 3 contain, in addition to dislocation loops, voids that limit dislocation channeling by providing added obstacles to deformation, resulting in some measure of uniform elongation and work hardening upon yielding. The microstructure dependence on the tensile properties can best be illustrated by the comparison shown in Figure 4 of Nb irradiated at 328 and 733 K. The higher irradiation temperature results in the development of microstructural voids and thus the significant differences in the tensile curves. The lower irradiation temperature results in dislocation channeling following yield and the
|
Elongation (%)
Figure 4 Comparison of tensile curves between Nb irradiated at 328 and 733 K. Yield instability is seen at 328 K due to channeling of deformation dislocations through the irradiated dislocation loop structures. The higher irradiation temperature resulted in the development of small voids providing a barrier to dislocation movement. Reproduced from Wiffen, F. W. In Refractory Alloy Technology for Space Nuclear Power Applications, CONF-8308130; Cooper, R. H., Jr, Hoffman, E. E., Eds.; Oak Ridge National Laboratory: Oak Ridge, TN, 1984; pp 252-277.
|
associated work softening during necking to failure at around 11% total elongation. While the higher irradiation temperature sample was irradiated to a higher total fluence, the effect of dose is observed only on the
relative strength increase over the unirradiated condition. The higher irradiation temperature produced voids in the microstructure, providing additional obstacles to deformation and higher uniform elongations and modest work hardening.
Little is known with regard to the aging properties of Nb-1Zr or the combined thermal and radiation effects. The addition of 1 wt% Zr to Nb creates a dispersion-strengthened alloy, in which the Zr combines with interstitial impurities creating fine precipitates throughout the material. The development of these fine precipitates on aging at 1098 K can increase the tensile strength between 50 and 100 MPa over the annealed condition and provide an effective strengthening greater than that observed through modest irradiation31 (Table 1).
Irradiation of Nb-1Zr to 0.9 dpa at 1098 K showed a modest increase in yield and ultimate tensile strength to 135 and 192 MPa, respectively, over the annealed condition. This increase in tensile strength either through aging or irradiation results in a corresponding decrease in uniform elongation from 15% to 3.5% and total elongation from 25% to 15%. Aging at temperatures above 1098 K produces little effective hardening as the precipitates coarsen in the microstructure.33 Irradiation to 0.9 dpa at 1248 and 1398 K of Nb-1Zr showed only a modest increase in the yield strength over the aged and annealed specimens, though ultimate tensile strength and elongation were unchanged or less. Irradiation to 1.88 dpa at 1223 K resulted in weaker tensile properties
compared to the 0.9 dpa sample, believed to be due to further precipitate coarsening. The time under irradiation conditions for the 1.88 dpa sample was near 1100 h and produced similar tensile properties as that of the aged-only material.
As discussed in the preceding paragraphs, the irradiated properties of Nb and Nb-1Zr are governed by their microstructure and are influenced by temperature, displacement damage rate, and neutron spectrum. The tensile properties of neutron-irradiated Nb-1Zr for damage levels between 0.1 and 5 dpa (Horak et al.34 and Wiffen35) summarized by Zinkle and Wiffen3 are shown in Figure 5. At temperatures below 800 K, a large increase in the tensile strength from irradiation is observed with the corresponding low uniform elongations. At higher temperatures, uniform elongation increases because of the presence of voids in the microstructure. However, the data plotted in Figure 5 show uniform elongations remaining low up to 1100 K, while radiation hardening is relatively moderate, suggesting that impurities are the source of the reduced elongation values.
No irradiated fracture toughness data exist for Nb or Nb-1Zr, though comparisons can be made from the larger irradiated vanadium alloy database, in which fracture toughness embrittlement becomes a concern when tensile strength exceeds 600-700 MPa and therefore at temperatures below 400 K for Nb-1Zr.36 However, if a conservative value is assigned to the critical stress to induce cleavage fracture of ^400 MPa (40% lower than that observed in vanadium alloys),
fracture toughness becomes a concern at temperatures below 800 K for Nb-1Zr.3 While irradiated tensile strength above 800 K is close to the unirradiated values, uniform elongation values remain low until irradiation temperatures >1000K. Therefore, a conservative approach towards engineering design needs to be taken with this alloy.
The mechanical properties ofirradiated refractory alloys can be influenced by the formation of He developed through the (n, a) reactions, leading to the grain boundary formation of bubbles and the eventual embrittlement of the material. Some scoping investigations on the effect of He on the irradiated mechanical properties of Nb-1Zr have been performed. Wiffen37 investigated the high-temperature mechanical properties of 50MeV a-irradiated Nb—1Zr. In tensile tests conducted at 1273 and 1473 K, no significant effect of He on the strength or ductility of Nb-1Zr was observed for samples containing 2-20 appm He. Later analysis of the creep ductility reductions was found to be dependent on the observed precipitate phase development through the pick-up of oxygen during implantation.38 He-implanted Nb-1Zr through 100 MeV a-irradiations at 323 and 873 K by Sauges and Auer39 found no significant effect on ductility up to 80 appm He. Wiffen19 observed that uniform elongations stayed around 1% between test temperatures of 723 and 1073 K on 130 appm 10B doped Nb-1Zr irradiated in a fast reactor between 723 and 1223 K up to 6 x 1022 n cm~2. These were slightly higher than those observed in undoped material; this is believed to be due to the formation of He bubbles in the grains of the material
acting similar to voids in generating obstacles to dislocation channeling. In general, no detrimental effects on mechanical properties were reported for accelerator-injected He between 1273 and 1473 K for He concentrations <200 appm.37,40
The addition of Al to ODS ferritic steels sometimes softens their creep and tensile properties. Figure 2544 shows the effects of Al addition and Cr content on the
|
Figure 24 Aging embrittlement of high Cr-ODS steels with respect to Cr content. Absorbed fracture energy was measured at room temperature with the use of miniaturized Charpy V-notch (CVN) specimen which measures 1.5 mm square with 20 mm length. Reproduced from Kimura, A.; Kasada, R.; Iwata, N.; et al. In Proceedings of ICAPP ’09, Tokyo, Japan, May 10-14, 2009; Paper 9220.
|
tensile strength of high Cr-ODS steels. A decrease in UTS versus Al content is obvious in 16Cr-ODS steels; this dependency becomes weaker at higher temperature. The effect ofCr concentration on the UTS is not so obvious between 13.7 and 17.3 wt% at 450 and 700 °C.
In the case of 9Cr-12Cr-ODS steels, high — temperature strength is considerably enhanced by the uniform dispersion of Y-Ti complex oxide (Y2Ti2O7) particles. In Al-added high Cr-ODS steels, however, Y-Al complex oxides and/or Al oxides are formed rather than Y-Ti complex oxides, which leads to larger oxide particles, causing a degradation of high — temperature mechanical strength. Therefore, Hf or Zr, which form thermodynamically stable oxides, were added to form Y-Hf or Y-Zr complex oxide particles rather than Y-Al complex oxide. The process of manufacturing these materials is exactly the same as that used for 9Cr-ODS ferritic steels: MA by an attrition type ball mill and hot extrusion at a nominal temperature of 1150 °C. The extruded bars were provided for mechanical tests. The creep rupture properties of Al-added high Cr-ODS steels are summarized in Figure 26.44 The creep strength of the standard steel is generally lower than that of Al-free steel. On the other hand, the addition of Zr and Hf induces an improved creep strength which approaches that of Al-free steel. Furthermore, it was found that their
|
Figure 26 Creep rupture strength of various Al added high Cr-ODS steels in hoop direction by using pressurized specimens at 700°C. Reproduced from Furukawa, T.; Ohtsuka, S.; Inoue, M.; et al. In Proceedings of ICAPP ’09, Tokyo, Japan, May 10-14, 2009; Paper 9221.
|
fracture elongation and reduction of area are slightly higher than those of Al-free steel. Under microstructural observation by TEM, oxide particles consisting of Y3A5O12, YAlO3, and Al2O3, were observed in typical Al-added ODS steel, whereas this Y-Al complex oxide can be changed to Y2Hf2O7 in Hf-added ODS steel. The improved creep rupture strength in Hf-added ODS steel could be attributed to the nanosize dispersion of the Y2Hf2O7 complex oxide.
The Kelly and Burchell50,51 model recognizes that creep produces significant modifications to the dimensional change component of the stressed specimen compared to that of the control and that this must be accounted for in the correct evaluation of creep strain data.
The rate of change of dimensions with respect to neutron dose g(n cm-2) in appropriate units is given by the Simmons’ theory2 for direction x in the unstressed polycrystalline graphite:
dXT + + F
ac — a, dg Xa dg
where ax is the thermal expansion coefficient in the x-direction, and ac and aa are the thermal expansion coefficients of the graphite crystal parallel and perpendicular to the hexagonal axis, respectively, over the same temperature range. The term Fx is a pore generation term that becomes significant at intermediate doses when incompatibilities of irradiation — induced crystal strains cause cracking of the bulk graphite.67 For the purposes of their analysis, Kelly and Burchell ignored the term Fx. The parameters (1/Xc)(dXc/dg) and (1/Xa)(dXa/dg) are the rates of change of graphite crystallite dimensions parallel and perpendicular to the hexagonal axis, and
dXT _ 1 dXc 1 dXa
dg Xc dg Xa dg 19
The imposition of a creep strain is known to change the thermal expansion coefficient of a stressed specimen, increasing it for a compressive strain and decreasing it for a tensile strain compared to an unstressed control. Thus, the dimensional change
component of a stressed specimen at dose g(n cm 2) is given by
К—a, «г + і gX + f:
ac — a, dg X, dg
where a0x is the thermal expansion coefficient of the crept sample, and Fx0 is the pore generation term for the crept specimen. The difference between these two equations is thus the dimensional change correction that should be applied to the apparent creep strain (the pore generation terms Fx and Fx0 were neglected):
[21]
The true creep strain rate can now be expressed as
de_ de0 a’x — Kx dXT
dg dg ac — a, dg 2
where e is the true creep strain and Є is the apparent creep strain determined experimentally in the conventional manner. Thus, the true creep strain (ec) parallel to the applied creep stress is given by
g. …
ec = e’c
0
where ec is the induced apparent creep strain, (ax — ax) is the change in CTE as a function of dose, (ac — aa) is the difference of the crystal thermal expansion coefficients of the graphite parallel and perpendicular to the hexagonal axis, XT is the crystal shape change parameter given above, and g is the neutron dose. The apparent (experimental) creep strain is thus given by
g
ec = ec +
0
Substituting for ec from eqn [13] gives the apparent (experimental) creep strain ec as
g.
ec = ES+ksg
with the terms as defined above.
The Kelly-Burchell model is unique in that it does take account of the sign of the applied stress in
|
predicting creep strain through changes in the CTE of the stressed graphite. While the model gave good agreement between the predicted H-451 graphite apparent creep strain and the experimental data at low doses and high temperatures51 (Figures 19-22), the creep model was shown to be inadequate at doses >0.5 x 1022ncm~2 [E>50keV] (—3.4dpa) at an irradiation temperature of 900 °C (Figure 23).50
As previously discussed, Gilsocarbon graphite for the AGRs was manufactured by molding (or pressing) the spherical filler particles and blocks, resulting in a semi-isotropic graphite with an anisotropy ratio of ~1.01 (based on the ratio of the orthotropic CTE values). Dimensional change MTR data for Gilsocarbon over a wide range of temperatures is given in Figure 35. There are two sets of data at each temperature; one WG and one AG. This illustrates how isotropic the properties of Gilsocar — bon are, even when irradiated. In Figure 35, it is also clearly illustrated that the higher the irradiation
 |
|
|
|
|
Figure 34 High-fluence irradiation dimensional change in pile grade A graphite irradiated at 600 °C. Reproduced from Brocklehurst, J. E.; Kelly, B. T. Carbon 1993, 31(1), 155-178.
|
|
|
♦
|
430 °C
|
|
■
|
600 °C
|
|
A
|
900 °C
|
|
•
|
940 °C
|
|
О
|
1240 °C
|
|
□
|
1430°C
|
|
|
|
|
|
|
|
|
|
|
|
Figure 35 Dimensional change in Gilsocarbon graphite. Modified from Birch, M.; Brocklehurst, J. E. A review of the behaviour of graphite under the conditions appropriate for the protection of the first wall of a fusion reactor; UKAEA, ND-R-1434(S); 1987; Brocklehurst, J. E.; Kelly, B. T. Carbon 1993, 31(1), 155-178.
|
|
 
 50 100 150
Fluence (1020 ncm-2 EDND)
temperature, the sooner the turnaround is reached. At very low fluence, semi-isotropic graphite swells. This swelling can be quite significant as demonstrated by the irradiation of semi-isotropic NBG — 10 at 294 and 691 ° C.67 This behavior has been attributed to the annealing out of residual machining stresses or shrinkage strains, but there are no microstructural or other experimental observations to validate this reasoning.
When graphite is irradiated past turnaround and reaches its original volume, sometimes referred to
as ‘critical fluence,’ the structure of the graphite begins to break down, as illustrated in Figure 36.
4.11.14.1 Effect of Radiolytic Oxidation on Dimensional Change
When designing the UK AGRs, irradiation experiments in a carbon dioxide atmosphere were carried out in BR-2 at Mol, Belgium. These experiments were designed to obtain high radiolytic weight loss (~35%) in a very short time, and hence, a low fast
|
♦ NA
|
■ NA oxidized, x<9
|
* NA oxidized, 9<x<12
|
|
• NA oxidized, 12<x<21
|
О NA oxidized, 21<x<22
|
□ NA oxidized, 22<x<33
|
|
Д PV (NA unimpregnated, x~8)
|
-©- Simmons (curve A)
|
|
Figure 37 Dimensional changes in preoxidized samples. Modified from Brocklehurst, J. E.; Edwards, J. The fast neutron-induced changes in dimensions and physical properties of near-isotropic graphites irradiated in DFR; UKAEA, TRG Report 2200(S); 1971.
neutron fluence. Some of these specimens, referred to as ‘preoxidized,’ were reirradiated in an inert atmosphere in other MTRs, including DFR, with some achieving reasonably high irradiation fluence. Figure 37 gives the dimensional change behavior of some of these experiments.68
The results show a clear correlation between preoxidized weight loss and dimensional change behavior, indicating an increased dimensional change and delay in turnaround with increased preoxidized weight loss. This has clear implications for the AGRs and required further investigation. Unfortunately, the
graphite MTR experiments designed to carry out simultaneous radiolytic oxidation and fast neutron damage under power reactor conditions were abandoned because of the closure of the UKAEA MTRs at Harwell in 1990. It is therefore unclear how significant this behavior is for the AGRs. However, there are now MTR experiments being undertaken in HFR (High Flux Reactor) at Petten, the Netherlands to try and address this.
4.11.14.2 Dimensional Change Rate
The constitutive models used to predict stresses in polycrystalline components often do not use dimensional change directly but use dimensional change rate. The dimensional change rate and dimensional change of Gilsocarbon graphite irradiated at 550 °C are compared in the schematic shown in Figure 38. The turnaround in dimensional change rate occurs earlier than turnaround in dimensional change. In channel-type reactors such as an AGR or Magnox reactor, it is the turnaround in rate that is associated with the peak inbore stress. Thus, when planning a nuclear graphite MTR experiment, it is important to obtain data in the low to medium fluence range, as well as at high fluence.
One of the conditions of all operating licenses for water-cooled power reactors in the United States is that the primary reactor containments shall meet the containment leakage test requirements set forth in Appendix J, Primary Reactor Containment Leakage Testing for Water-Cooled Power Reactors, to 10 CFR Part 50.21 These test requirements provide for preoperational and periodic verification by tests of the leak-tight integrity of the primary reactor containment as well as systems and components that penetrate containment of water-cooled power reactors and establish the acceptance criteria for such tests. The purpose of these tests is to ensure that (1) leakage through the primary reactor containment and the systems and components penetrating primary reactor containment shall not exceed allowable leakage-rate values as specified in the technical specifications or associated bases and (2) periodic surveillance of reactor containment penetrations and isolation valves is performed so that proper maintenance and repairs are made during the service life of the containment as well as systems and components that penetrate primary containment. Contained in this regulation are requirements pertaining to Type A, B, and C leakage- rate tests that must be performed by each licensee as a condition of their operating license. Type A tests are intended to measure the primary reactor containment overall integrated leakage rate (1) after the containment has been completed and is ready for operation and (2) at periodic intervals thereafter. Type B tests are intended to detect local leaks and to measure leakage across each pressure-containing or leakage-limiting boundary for primary reactor containment penetrations (e. g., penetrations that incorporate resilient seals, gaskets, or sealant compounds and air lock door seals). Type C tests are intended to measure containment isolation valve leakage rates. Requirements for system pressure testing and criteria for establishing inspection programs and pressure-test schedules are contained in Appendix J.
Appendix J to 10 CFR Part 50 also requires a general inspection of the accessible interior and exterior surfaces of the containment structures and components to uncover any evidence of structural deterioration that may affect either the containment structural integrity or leak tightness. Subsection IWL of ASME Section XI addresses reinforced and post — tensioned concrete containments (Class CC). Two examination categories are provided in Subsection IWL. Examination Category L-A addresses accessible concrete surfaces and examines them for evidence of damage or degradation, such as cracks. The concrete is examined at 1, 3, and 5 years following the containment structural integrity test and every 5 years thereafter. The primary inspection method of Category L-A is visual examination (general or detailed). Examination Category L-B addresses the unbonded post-tensioning system. The unbonded post-tensioning system examination schedule is the same as for the concrete. For post-tensioned concrete containments, tendon wires are tested for yield strength, ultimate tensile strength, and elongation. Tendon corrosion protection medium is analyzed for alkalinity, water content, and soluble ion concentrations. Prestressing forces are measured for selected sample tendons. Subsection IWL specifies acceptance criteria, corrective actions, and expansion of the inspection scope when degradation exceeding
the acceptance criteria is found. Additional requirements for inaccessible areas are specified in 10 CFR 50.55a(b)(2)(viii). The acceptability of concrete in inaccessible areas is to be evaluated when conditions that could indicate the presence or result in degradation to such inaccessible areas exist in accessible areas. Information on aging management programs for masonry walls22,23 and water-control structures24 is available. Inspection requirements for steel containments and liners of concrete containments are contained in Subsection IWE of ASME Section XI. Editions and addenda of the ASME Code acceptable to the USNRC are identified in 10 CFR 50.55a.
The duration of the transient regime of austenitic and nickel-base alloys depends to the first-order on major element composition, primarily on the Fe, Cr, and Ni content.1,57,120 Increases in chromium content decrease the effective vacancy diffusion coefficient and thereby increase the vacancy supersaturation, increasing void nucleation, and decreasing the transient duration. Increases in nickel initially increase the effective vacancy diffusion and thereby the transient, but behavior reverses at some mid-nickel level (40-60%), reflecting the nonmonotonic dependence of both the effective vacancy diffusion coefficient and the dislocation bias on nickel content.55,128,129
With respect to minor solutes, the most important elements influencing swelling are P and Si.57,130 On a per atom basis phosphorus has the most pronounced effect on the transient duration, followed by silicon. Additions of small amounts of silicon and phosphorus initially increase swelling, but then strongly decrease it at higher content, producing a nonmonotonic swelling behavior. This response reflects the two competing roles of these elements on solute — interstitial binding at low concentration and their much stronger enhancement of vacancy diffusion at higher content. Very small differences in silicon between two otherwise identical heats of steel can produce quite different transient duration and therefore swelling, as shown in Figure 51.130
Looking back at the FFTF fuel assembly in Figure 16, it can be seen that there are three clusters
|
Figure 51 Top of a fuel assembly from the BN-600 fast reactor showing larger swelling-induced elongation of annealed EI-847 steel in pins with lower (0.09 vs. 0.20%) silicon content, with both heats having concentrations below the specified maximum of 0.4%. Reproduced from Porollo, S. I.; Shulepin, S. V.; Konobeev, Yu. V.; Garner, F. A. J. Nucl. Mater. 2008, 378, 17-24.
|
of pins that also extend above their neighbors. The pins in these clusters were made from a nominally similar heat with differences in phosphorus level, 0.002 versus 0.009 wt%, both below the maximum specification of 0.04wt%. In both the silicon and phosphorus examples shown here, the compositions fell under the specified maximum value, indicating the necessity to specify both the upper and lower limits of active elements when attempting to control swelling.131
Other common solute additions such as boron, carbon, manganese, molybdenum, niobium, vanadium, and others have some impact on diffusion, but appear to exert their greatest influence on the formation of various precipitates that remove the more active elements from solution.
| | | |
