Category Archives: Comprehensive nuclear materials

Fast Neutron Irradiation Experiments

Rowcliffe and Horak86 investigated the tensile prop­erties of Inconel 706 (in a multistep ‘fully aged’ condition) and Inconel 718 (ST condition) following irradiation in EBR-II to fluences of 4-5 x 1026nm~2 (E > 0.1 MeV). Irradiation temperatures (Ti) ranged from 450 to 735 °C, with tensile tests being per­formed at a strain rate of 4 x 10~4 s~3 at temperatures corresponding to Ti and to Ti + 110 °C. Yield stresses and total elongation data for Inconel 706 are shown in Figure 12 and for Inconel 718 in Figure 13. Data for Inconel 706 showed very high (>1000 MPa) yield stresses and ultimate tensile strengths (UTS) in
specimens irradiated at temperatures up to and including 500 °C. This high tensile strength was maintained in a specimen irradiated at 500 °C but tested at 610 ° C. Although there was some reduction in strength in specimens irradiated at 560 °C and above, the UTS remained above 650 MPa in speci­mens irradiated at 625 ° C. The very high tensile strengths exhibited at the lower irradiation tempera­tures were attributed to the instability of the (ordered body-centered tetragonal) g» phase below 525 °C and its consequent dissolution, leading to the reprecipita­tion of nickel and niobium as (ordered face-centered cubic) g’ on dislocation loops. At higher irradiation temperatures, both g’ and g" were stable, but

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800

 

Temperature (°C)

 

precipitate coarsening resulted in lower tensile strength. Elongations to failure for tests carried out at the irradiation temperature were between 1.5% and 3% up to 625 °C, compared to >8% in unirradi­ated material. Irradiation embrittlement was gener­ally more severe in tests at T + 110 °C, particularly at 610-735 °C where the lowest recorded ductility was 0.2%. Fractures in irradiated Inconel 706 were predominantly intergranular, with failure believed to be facilitated by the decohesion of Z phase (hexago­nal Ni3(Ti, Nb)) platelets which were formed at grain boundaries during the initial heat treatment.

Rowcliffe and Horak’s data for ST Inconel 718 showed similar trends to Inconel 706. Precipitation of the g and g" phases occurred during the irradia­tion of Inconel 718, resulting in yield strengths in excess of 1000 MPa at irradiation temperatures up to 560 °C and above 800 MPa at 625 °C. The ductility of Inconel 718 was reduced from more than 30% in the unirradiated condition to 0.2% or less in specimens which were irradiated at 500-560 °C and tested at Ti + 110 °C. In contrast to Inconel 706, failures in irradiated Inconel 718 were reported to be predomi­nantly transgranular. Crack propagation in Inconel 718 appeared to have been via a ‘channel’ fracture mechanism, that is, with deformation occurring by highly localized planar slip and consequent linkage of radiation-induced voids.

Bajaj et al.87 examined the tensile properties of Nimonic PE16 irradiated in EBR-II to neutron fluences up to a maximum of ^7 x 1026nm 2 (E > 0.1 MeV), at temperatures in the range of 450­735 °C. The alloy was in a STA (1 h at 900 °C plus 8 h at 750 °C) condition, and appears to have been the same low-Si heat of PE16 that was subsequently used in the AA-1 swelling experiment described by Garner and Gelles.22 Tensile tests were carried out at 232 °C (to simulate refueling conditions), at the irradiation temperature Ti and at Ti + 110 ° C (to simulate reac­tor transients), at a strain rate of 4 x 10~4s~ and with a small number of tests at 4 x 10~3s~ . Irra­diated specimens tested at 232 °C generally showed a substantial increase in yield stress and a small increase in UTS over the unirradiated values (although samples irradiated at the highest tempera­ture of 735 °C exhibited some softening), and retained good levels of ductility with total elonga­tion values above 10%. Yield stress and total elon­gation data for PE16 at higher test temperatures are shown in Figure 14 for specimens irradiated to a fast neutron fluence of 4.3 x 1026nm~2 (enabling direct comparison with the data for the similarly irradiated Inconel alloys shown in Figures 12 and 13). Speci­mens tested at the irradiation temperature again showed strengthening at temperatures in the range of 450-625 °C and softening at 735 °C, with good

ductility at 450 °C but total elongations reduced to ^3% at 560-625 °C. Tests at T + 110 °C showed fUrther increases in tensile strength (consistent with the greater hardening expected from irradiation at a lower temperature) and more severe embrittlement with ductility levels at 670-735 °C reduced to 0.3% at a fluence of 4.3 x 1026nm~2 and to zero (i. e., failure before yield) in higher dose samples (7.1 x 1026nm~2). Tests at Ti at the higher strain rate resulted in an improvement in ductility by a factor of two or three. Examination of fracture surfaces showed that failures were predominantly intergranular in irradiated sam­ples tested above ^550 °C, transgranular at 232 °C, and mixed mode at 450-550 °C. Bajaj et al. considered that the irradiation embrittlement of PE16 evident at high temperatures could simply be explained by matrix hardening with little or no change in the grain bound­ary fracture strength — evidenced by increases in yield strength but no significant changes in true (as opposed to engineering) UTS values — so that mechanisms relying on the weakening of grain boundaries could be discounted for the test conditions studied.

Sklad et al50 reported tensile data for two aged conditions of Nimonic PE16 which were irradiated in EBR-II to 1.2 x 1026nm~2 (E >0.1MeV) at 500 °C and tested at strain rates from ^3 x 10~5 to 3 x 10~3s~ . There was no significant difference in the postirradiation properties of the two differently aged conditions, although one aging treatment (2 h at 800 °C plus 16 h at 700 °C) resulted in an unirradiated yield stress ^25% higher than the other condition (1 h at 900 °C plus 8 h at 750 °C). No effect of strain rate on tensile properties was evident in tests at the irradiation temperature, where total elongations remained above 10%. Tests at higher temperatures were made only at the lowest strain rate, with failure elongations being reduced to 1.6% at 600 °C and 0.5% at 700 °C. The low ductility failures were associated with an increased tendency toward intergranular fracture, and additional tests, in which samples irradiated to 4 x 1026nm~2 at 500 °C were fractured in situ in an Auger spectrometer, revealed helium release from samples which fractured intergranularly as well as the segregation of Ni, P, and S to grain boundaries. Helium release was estimated at ^0.03 He atoms per grain boundary atom. No grain boundary helium bubbles were observable by TEM, and it was therefore considered that helium either remained in solution as a partial monolayer or was present in unresolved bubbles less than 1-2 nm in diameter.

The presence of grain boundary helium bubbles in Nimonic PE16 was reported by Fisher et a/.88 in sections of AGR (advanced gas-cooled reactor) tie bars irradiated at 512 °C and above. AGR tie bars, which are approximately 10 m long and are under load only during charging and discharging of the fuel element stringers, operate at temperatures from 325 to 650 °C from bottom to top, with peak doses of ^3 dpa occurring at around the 4 m position. Stress-rupture testing at 600 °C at an applied stress of 500 MPa showed a trough in properties (i. e., a minimum in failure times) and intergranular failures in sections of some tie bars which were irradiated at temperatures in the range of 350-400 °C where grain boundary helium bubbles were not generally observed. Even so, grain boundary cavitation was observed in a fractured tie bar section which was irradiated at 360 °C, with the cavities appearing to be nucleated (possibly at submicroscopic helium bubbles) at the intersection of slip bands with the boundary. The trough in stress-rupture properties occurred in tie bar sections which exhibited both high yield strengths (attributable to high concentra­tions of dislocation loops and small voids) and high levels of grain boundary segregation. EDX (energy dispersive X-ray) analyses showed a significant enrichment of Ni and Si, and a depletion of Fe, Cr, and Mo, at the grain boundaries ofsections irradiated at 335-585 °C. In addition, high levels of Si were detected in sections irradiated at 335-512 ° C in the g phase that precipitated at the surface of voids, with the Si content increasing with decreasing irradiation temperature. Although the presence of Si-enriched g phase at grain boundaries could not be confirmed, it was suggested that its formation may have contribu­ted to the minimum in stress-rupture life, which was thought to result from the weakening of the bound­aries relative to the matrix.

Grain boundary helium bubbles were also observed by Boothby and Harries89 and Boothby28 in PE16 irradiated in DFR and EBR-II at 535 °C and above. Tensile testing of DFR-irradiated PE16, exposed to ^20dpa at 465-635 °C, and strained at a rate of 2.5 x 10~6s_1 at temperatures approximating those of irradiation, revealed severe embrittlement with mini­mum elongations of ^0.2% at 550 °C; TEM examina­tion of strained specimens provided evidence of intergranular cavitation, and the ductility data were interpreted using a model for the diffusion-induced growth of cavities nucleated at grain boundary helium

bubbles.89

The postirradiation tensile properties and micro­structure of developmental g (D21, D25, and D66) and g/g’ (D68) strengthened alloys were discussed by Yang et al. The alloys were all irradiated in a ST condition; additionally, D25 was irradiated in an aged (24h at 700°C) condition (STA), and D66 in a 30% cold-worked plus aged (11 h at 800 °C plus 2 h at 700 °C) condition (CWA). Specimens were irradiated at 450-735 °C to a fast neutron fluence of 4 x 1026nm~2 (E > 0.1 MeV) in EBR-II, and were tested at Ti, Ti + 110 °C and 232 °C. Severe irradiation embrittlement was evident in the ST alloys and STA D25, particularly in tests at Ti + 110 °C. Zero ductility was recorded in the lower-Ni alloy D21 (25Ni-8Cr) irradiated and tested at 550 and 600 °C. Severe ductil­ity losses were associated with intergranular failures, which were attributed to irradiation-induced solute segregation and consequent precipitation of brittle g0 layers at grain boundaries. However, reasonable levels of ductility, ranging from 2 to 6%, coupled with trans­granular failures, were obtained at all temperatures in irradiated CWA D66 (45Ni-12Cr). The preirradiation grain boundary structure of this material, comprising a ‘necklace’ of small recrystallized subgrains plus large g0 particles and discrete Laves particles, remained stable with no indication of irradiation-induced g0 layers. Yang etal. considered that the radiation-induced segregation of g0 forming solutes to grain boundaries was inhibited by the introduction of a high density of dislocation sinks by cold working.

Vaidyanathan et al.90 and Huang and Fish91 examined the embrittlement of EBR-II-irradiated, precipitation-hardened alloys, using ring ductility tests. In this test, small sections of tubing are com­pressed and the ductility, defined as the strain at the initiation of cracking, is deduced from the change in the sample radius of curvature at maximum load. Both experiments included Inconel 706 and Nimonic PE16 in ST conditions, while Vaidyanathan et al. also examined the developmental alloys D25 and D68 in ST and STA conditions. Peak fluences in these experiments were around 6-7 x 1026nm~2 (E > 0.1 MeV) and irradiation temperatures were in the range 460-616 ° C. All the materials exhibited low ductility failures at high test temperatures, particu­larly in tests at about Ti + 110 °C where ductilities were generally below 0.1%, though Vaidyanathan et al. found that postirradiation heat treatments (typi­cally of 4 h at 785 °C) produced a moderate recovery in ductility. Based largely on observations reported by Yang81 for irradiated ST PE16, Vaidyanathan et al. and Huang and Fish considered that the irradiation — induced embrittlement of precipitation-hardened alloys could generally be attributed to the formation of brittle g0 layers at grain boundaries. However, the arguments presented were far from conclusive — microstructural examinations of the developmental alloys which were reported by Vaidyanathan et al. showed only weak indications of g0 precipitation in D25 even within the grains, and evidence for g0 pre­cipitation at grain boundaries in D68 was not found in the low ductility tested samples but only in material irradiated to a higher fluence. Yang81 examined the microstructure of a low Si (0.01%) heat of ST PE16, which was irradiated in EBR-II to doses of about 30 and 50 dpa at temperatures from 425 to 650 °C. Grain boundary g0 layers were observed in ST PE16 samples which were irradiated at 510 °C or above but not at 425 °C, and helium bubbles were detected at bound­aries in samples irradiated at 600-650 °C. It was considered by Yang that the irradiation-induced embrittlement of ST PE16 was mainly attributable to the cleavage fracture of grain boundary g0 layers and that any effects of helium were of secondary impor­tance. However, although grain boundary precipitation of g0 was observed by Boothby28 in PE16 irradiated to relatively high doses in EBR-II, there was no evidence for the formation of intergranular g0 layers in the aged conditions of PE16 which exhibited low ductility fail­ures following irradiation in DFR to ^20 dpa.89 Thus, although it remains possible that the formation of grain boundary g0 layers may aggravate the embrittlement, it was considered by Boothby28 that the irradiation embrittlement of PE16 is primarily due to helium.

A breach in solution-annealed Inconel 706 fuel pin cladding, irradiated to 5% burn-up in EBR-II, was reported by Yang and Makenas.92 The rupture occurred from 12.7 to 18.4 cm from the bottom of the pin, corresponding to irradiation at 447-526 °C at a fluence of 6 x 1026nm~2 (E > 0.1 MeV). Microstruc­tural examinations revealed a brittle intergranular fracture, with failure being attributed to a combina­tion of matrix hardening due to g0 precipitation and grain boundary weakening due to the formation of interconnected Ni3(Ti, Nb) Z phase particles. In con­trast to the work of Rowcliffe and Horak86 where grain boundary Z phase was precipitated during a preirradiation aging treatment, this phase formed during the irradiation period in the solution — annealed cladding. Precipitation of Z was considered to be irradiation enhanced because it was not formed in long-term thermal annealing experiments at 480­540 °C. Grain boundary precipitation of Z phase was also observed at the hot (650 °C) end of the fuel pin cladding, with both g0 and g00 in the matrix.

Cauvin et al.93 and Le Naour et al.94 also attributed irradiation embrittlement effects in Inconel 706 cladding to the combined effects of matrix hardening and the precipitation of Z at grain boundaries. Inconel 706 fuel pin cladding, fabricated from four heats with Nb contents varying from 1 to 3% and in two heat-treated conditions (solution annealed or aged), was irradiated in the Phenix fast reactor up to a maximum of 100 dpa. Tensile tests on cladd­ing sections were carried out at a strain rate of 3 x 10-4 s-1. Tensile tests performed at ambient tem­perature showed high UTS (>1000 MPa) along the full length of the pins with peak values of 1500 MPa in sections irradiated near 500 °C; ductility values (uniform elongations only were given) remained low (<2%) for irradiation temperatures up to 550 °C and then increased sharply. In tests carried out at the irradiation temperatures, however, prema­ture failures occurred above about 500 °C, with ten­sile strengths reduced to 300 MPa and ductilities close to zero. All of the materials examined by Cau — vin and Le Naour et al. showed similar properties, with no systematic influence of composition or heat treatment. Plitz et a/.57 listed three fuel pin failures in Inconel 706 cladding in the Phenix reactor, with a further 12 failures in austenitic steel cladding; two of the Inconel 706 failures were associated with long periods of low power operation followed by a rise to full power conditions, resulting in mechanical inter­action between the fuel and the low ductility cladding material.

Irradiated Mechanical Properties of W and W Alloys

Like all other refractory metal alloys, tungsten is sensitive to embrittlement issues following irradi­ation, the causes of which are point defect genera­tion, impurity segregation to grain boundaries, and radiation-enhanced precipitation. The strengthening ofthe metal matrix can raise the deformation stress to levels greater than the cleavage strength of the alloy, resulting in brittle failure. While only a limited num­ber of mechanical property tests have been performed on tungsten and its alloys, the actual composition of the materials reported is not well characterized and therefore may have a significant range of impurity levels that can affect grain boundary cohesion and the mechanical strength of the material. Similarly, preirradiation heat treatments have also shown minor improvements in the postirradiation mechanical
properties,59 likely through the development and coarsening of interstitial impurities into precipitate formations that reduce grain boundary sensitivities.

For the irradiated tensile properties of tungsten, two works are typically referenced that make up the bulk of the data available. In the work of Steichen,1 the properties of wrought tungsten, stress-relieved at 1273 K, irradiated at 658 K to fluences between 0.4 x 1022 and 0.9 x 1022ncm~2 (E > 0.1 MeV), were examined, the results of which are shown in Figure 24. The irradiated yield strength of the material increased to approximately twice that of the unirradiated values,
while significant reduction in ductility was observed. Only in tensile tests well above the irradiation temper­ature did ductility values approach that of the unirra­diated material.

Подпись: Figure 24 Temperature-dependent tensile properties of irradiated and unirradiated tungsten. Reproduced from Gorynin, I. V.; Ignatov, V. A.; Rybin, V. V.; etal. J. Nucl. Mater. 1992, 191-194, 421-425; Steichen, J. M. J. Nucl. Mater. 1976, 60, 13-19.

In the work by Gorynin et al.,59 pure W consoli­dated through powder metallurgy was irradiated at temperatures of up to 1073 K in both a mixed and fast reactor up to 2 x 1022ncm~2 (E > 0.1 MeV). Samples irradiated and tested at temperatures near 573 K showed brittle failures at low stress levels, while some ductility and appreciable hardening were observed for samples tested and irradiated at

Подпись: 1200-Подпись: 1000-Подпись: g 800 1= m 600 Подпись: 400-Подпись: 200-Подпись:Подпись: 0Подпись:image2391073 K. Limited recovery of strength and ductility was observed in postirradiated material annealed at 1473 K for 1 h.

Embrittlement following irradiation due to radia­tion hardening and loss of grain boundary strength due to impurities resulted in increased DBTT for the aforementioned work. The DBTT is dependent on the test conditions in addition to material conditions prior to irradiation and should be used with caution. The DBTT in samples examined by Steichen111 increases from ~-333 K in the unirradiated condition to 503 K, following 1-2 dpa irradiation at ~-653 K, while DBTT values increased from 673 Kunirradiated to 873 K after 1 dpa at 373 K for sintered W.59

Increased DBTT values with irradiation were also reported by Krautwasser et at}42 in powder metallurgy to form W, W-10Re, and Densimet 18 (W-3.4Ni-1.6Fe) bend-test bars irradiated between 525 and 575 Kup to 5.6 x 1021 ncm~2 (E> 0.1 MeV) (see Figure 25). While the addition of Re to W results in improved nonirradiated mechanical properties,1 2 the increased DBTT in the irradiated W-10Re is more severe than in pure W. In the case of the former, the possible development of the w-phase may be responsible for the higher DBTT values and the general increased sensitivity to radiation hardening. The w-phase observed in W-26Re irradiated from 2 to 9.5 dpa at temperatures between 373 and 800 °C141 is reported as precipitating as plate-like particles on the {110} planes of the W matrix, therefore, restricting slip in the material. [2]

It should be noted that due to the limited mechan­ical property data available for W and W-Re alloys, particularly the lack of irradiated data at ele­vated temperatures, accurate determination of the DBTT cannot be made. Nonetheless, increases in DBTT between 200 and 500 K for ~1 dpa of damage reported for the various grades of pure tungsten create limitations on its use, particularly at low irradiation temperatures.59,109,142 Based on irradia­tion data for Mo alloys, the minimum irradiation temperature which avoids severe radiation embrit­tlement is >0.3 Tm or ^1300K for tungsten at neutron fluences >0.03 dpa or 1 x 1021ncm~ (E > 0.1 MeV),3 which correlates with the irradia­tion defect recovery data on tungsten compiled by Keys et a/.127

Recent work in the development of ultra-fine grained tungsten incorporating TiC additions has shown promising results in reducing the sensitivity to radiation-induced degradation of properties.143,144 The grain size refinement, in the range of 50-200 nm, depending on TiC additions and process, theoreti­cally reduces the effective size of weak grain bound­aries that can act as crack initiators. In addition, significant reductions are observed in the density of void formation in the materials relative to pure W at irradiations conducted at 873 K and 2 x 1020n cm~ , though interstitial loop densities are unchanged. While unirradiated room temperature tensile prop­erties still show brittle fracture behavior, the fracture stress is up to four times higher in the W-TiC sam­ples than in pure W in addition to showing 100 K lower DBTT in impact testing. In microhardness measurements following irradiation, the W-TiC samples exhibited no radiation hardening compared with pure W. The change in Vickers hardness follow­ing irradiation for the W-TiC material of Kurishita et a/.143 compared to neutron — and proton-irradiated W and W-Re alloys135 irradiated to similar tempera­tures and doses is shown in Figure 26. The reduced sensitivity of the W-TiC alloy to radiation hardening offers the potential for further development of these alloys for nuclear applications.

12Cr-ODS steel cladding in EBR-II

JAEA manufactured 12Cr-ODS steel cladding (1DK and 1DS) and Argonne National Laboratory in the United States qualified a welding process that employs PRW. Fuel pins composed of 12Cr-ODS steel cladding and MOX fuel pellets were successfully fabricated and qualified, and irradiated up to 35 dpa at EBR-II.73 The ODS cladding with high smear density solid pellet MOX fuel did induce some diametral strain, demon­strating some in-core ductility. This program demon­strated the viability of ODS steel as a potential cladding material for long-life advanced FRs.

4.08.8.3.2 DT2203Y05 in Phenix

Fuel pins with DT2203Y05 cladding were irradiated in an experimental capsule placed in a special subas­sembly in Phenix. The process by which they were manufactured was described in Section 4.08.6. The dose reached at midplane was 81 dpa and the temper­ature along the fuel pin ranged from 400 to 580 °C.

It was observed by TEM that the uniform distribu­tion of fine oxides totally disappeared, and a few large oxides were also fragmented into smaller ones. The recoil resolution of particles is a process where the atoms that compose particles are ballistically ejected by an impinging neutron. Dubuisson63 pointed out that the atoms ejected from oxides by ballistic dissolu­tion depend on radiation-enhanced solute diffusivity and enhanced solubility under irradiation.

A uniform distribution of tiny particles <10 nm in size and with a density higher than the original oxide
density, was observed in the lower part of the fuel pin at temperatures <500 °C. These precipitates were found to be a’-phase, as shown in Figure 43(a).63 At irradiation temperatures above 500 °C, precipita­tion ofw-phase was uniformly distributed throughout all grains, as shown in Figure 43(b). Their chemical composition was slightly different from that of the intergranular w-phase that was present before irradi­ation. At a high temperature and low dose, w-phase is replaced by the thermal precipitation of Laves phase, as shown in Figure 43(c).

From the results of tensile tests at levels corres­ponding to the fissile column, rupture occurred with­out striction, and uniform and total elongations were equal. The elongation values reached 0.2% close to the maximum dose. These results indicate that DT2203Y05 cladding was highly embrittled by irra­diation. At the bottom of the fuel pin, where the temperature is below 500 °C, a’ precipitation, oxide redistribution and dislocation loops are the main features of the microstructure. Dubuisson63 pointed out that dislocation glides on the dislocation denuded bands in the hardened materials, that the deformation is all localized in these bands, and that this heteroge­neous shear could nucleate cracks that then propa­gate along these channels. At higher temperatures, w precipitation induces a loss of ductility.

4.08.7 Summary

The formation process of nanosized oxide particles through decomposition by MA and subsequent pre­cipitation by annealing was reviewed. Based on
information concerning the irradiation embrittle­ment of DT2203Y05 cladding produced by CEN-SCK Mol due to the formation of a0-phase below 500 °C and w-phase above 500 °C, 9Cr-ODS and 12Cr-ODS steels containing low Cr and low Ti were developed. The manufacture of cladding and improvement of the creep rupture strength in the hoop direction were successfully achieved by introdu­cing a—g reverse transformation or recrystallization. 9Cr-ODS steel has a unique structure consisting of tempered martensite and residual ferrite that induces superior strength through finely dispersed oxide par­ticles, which are promising candidates for advanced SFR fuel cladding. 16Cr-4Al-ODS steels present an advantage due to their superior resistance to corro­sion and oxidation in LBE and SCPW environments. There is still uncertainty concerning the irradiation performance of ODS steels, such as the oxide particle dissolution due to their diffusion-based mechanism. In order to substantiate the use of cladding materials as advanced fast reactor fuels, abundant ODS cladding fuel pins should be irradiated, and their results should provide feedback contributing to the further improve­ment of ODS steels.

Microstructure/Property Relationships

The microstructure of a typical nuclear graphite is described with reference to Gilsocarbon. This product was manufactured from coke obtained from a naturally occurring pitch found at Bonanza in Utah in the United States. To understand the microstructural properties, one has to start with the raw coke. The structure of Gilsonite coke is made of spherical parti­cles about 1 mm in diameter as shown in Figure 4. This structure is retained throughout manufacture and into the final product. In Figure 4(b), the spher­ical shaped cracks following the contours of the spherical particles are clearly visible. This coke will be carefully crushed in order to keep the spherical structures that form the filler particles and help to give Gilsocarbon its (semi-) isotropic properties.

At a larger magnification in a scanning electron microscopy (SEM), the complexity of these cracks is clearly visible, Figure 4(c), and at an even larger magnification, a ‘swirling structure’ made up of graphite platelets stacked together is discernable between the cracks. In essence, the whole structure contains a significant amount of porosity.

After graphitization, the Gilsonite coke filler par­ticles are still recognizable (Figure 5(a) and 5(b)). From the polarizing colors, one can see that the main V axis orientation of the crystallites follows the

image394image395(a)

Figure 4 Gilsonite raw-coke microstructure. (a) Photograph of Gilsonite coke, (b) Scanning electron microscopy (SEM) image of polished Gilsonite coke, (c) detail in an SEM image showing the region around cracks that follow the spherical shape of the coke particles, and (d) a higher magnification SEM image showing the intricate, random arrangement of platelets. Courtesy of W. Bodel, University of Manchester.

Подпись: 500 pm200 pm

Figure 5 Polarized optical and scanning electron microscopic images of Gilsocarbon graphite. (a) Optical image, (b) optical image, (c) SEM image, (d) SEM image. Courtesy of A. Jones, University of Manchester.

spherical particles circumferentially, as does the ori­entation of the large calcination cracks. The crystal­lite structures in the binder phase are much more randomly oriented, and this phase contains signifi­cant amounts of gas-generated porosity. There are also what appear to be broken pieces of Gilsonite filler particles contained within the binder phase.

The bulk properties of polycrystalline nuclear graphite strongly depend on the structure, distribu­tion, and orientation of the filler particles.12 The spherical Gilsonite particles and molding technique give Gilsocarbon graphite semi-isotropic properties, whereas in the case of graphite grades such as the UK pile grade A (PGA), the extrusion process used dur­ing manufacture tends to align the ‘needle’ type coke particles. Thus, the crystallite basal planes that make up the filler particles tend to align preferentially, with the ‘c’ axis parallel to the extrusion direction and the V axis perpendicular to the extrusion direc­tion. The long microcracks are also aligned in the extrusion direction. The terms ‘with grain (WG)’ and ‘against grain (AG)’ are used to describe this phe­nomenon, that is, WG is equivalent to the parallel direction and AG is equivalent to the perpendicular direction. Thus, the highly anisotropic properties of the crystallite are reflected in the bulk properties of polycrystalline graphite (Table 1).

A graphite anisotropy ratio is usually defined by the AG/WG ratio of CTE values. For needle coke graphite, this ratio can be two or more, while for a more randomly orientated structure, values in the region of 1.05 can be achieved by careful selection of material and extrusion settings. A more scientific way of defining anisotropy ratio is by use of the Bacon anisotropy factor (BAF).

Other forming methods are usually used to pro­duce isotropic graphite grades such as the Gilsocar — bon grade described above. In this case, it was found that Gilsocarbon graphite produced by extrusion was not isotropic enough to meet the advanced gas — cooled reactor (AGR) specifications. Therefore, a

Table 1 Relative properties-grain direction relationships

Property

With grain (WG)

Against grain (AG)

Coefficient of thermal

Lower

Higher

expansion (CTE) Young’s modulus

Higher

Lower

Strength

Higher

Lower

Thermal conductivity

Higher

Lower

Electrical resistivity

Lower

Higher

‘molding’ method where the blocks were formed by pressing in two directions was used. This had the effect of slightly aligning the grains such that the AG direction was parallel to the pressing direction and the WG was perpendicular to the pressing direc­tion. However, Gilsocarbon has proved to be one of the most isotropic graphite grades ever produced, even in its irradiated condition.

Another approach is to choose an ‘isotropic coke’ crushed into fine particles and then produce blocks using ‘isostatic molding’ process. The isostatic mold­ing method involves loading the fine-grained coke binder mixture into a rubber bag which is then put under pressure in a water bath. In this way, high quality graphite can be produced mainly for use for specialist industries such as the production of elec­tronic components. This type of graphite (such as IG — 110 and IG-11) has been used for high-temperature reactor (HTR) moderator blocks, fuel matrix, and reflector blocks in both Japan and China. However, even these grades exhibit slight anisotropy.

The final polycrystalline product contains many long ‘thin’ (and not so ‘thin’) microcracks within the crystallite structures that make up the coke particles. Similar, but much smaller, cracked structures are to be found in the ‘crushed filler flour’ used in the binder, and in well-graphitized parts of the binder itself. It is these microcracks that are responsible for the excellent thermal shock resistance of artificial polycrystalline graphite. They also provide ‘accom­modation,’ which further modifies the response of bulk properties to the crystal behavior in both the unirradiated and irradiated polycrystalline graphite. Typical properties of several nuclear graphite grades are given in Table 2. One can see that polycrystalline graphite has about 20% porosity by comparing the bulk density with the theoretical density for graphite crystals (2.26 gcm~ ). About 10% of this is open porosity, the other 10% being closed.

Dimensional Change and Irradiation Creep Under Load

Compressive stress increases, and tensile stress decreases, the irradiation-induced dimensional change of graphite as illustrated in Figure 54. In these experiments, two matching graphite samples, a loaded specimen and an unloaded ‘control’ specimen, were irradiated adjacent to each other in an MTR, and dimensional change in the direction of load was measured.

However, as well as change in dimension in the load direction, there are also dimensional changes perpen­dicular to the load direction as shown in Figure 55.

An irradiation creep curve can be simply obtained by subtraction of the unloaded dimensional change curve from the crept dimensional change curve, as illustrated in Figure 56. However, for practical use in assessments, this would require data for a range of temperatures and fast neutron fluences covering all of the expected operating conditions. Also, in the case of carbon dioxide-cooled reactors, the effect of (a)

1

image470

(b) Fluence (1020 ncm-2 EDND)

Figure 54 Dimensional changes of loaded ATR-2E graphite. (a) compression and (b) tension. Modified from Haag, G. Properties of ATR-2E Graphite and Property Changes due to Fast Neutron Irradiation; FZJ, JQl-4183; 2005.

the rate of radiolytic oxidation on creep rates would have to be quantified and understood. In addition, changes to the CTE and Young’s modulus with irra­diation creep have been observed, which further complicate assessment technology.

(c) Component dislocation loops

At the time of the thorough review by Northwood,51 no (c) component loops had been observed yet. The ‘round robin’ work45 also established that up to an irradiation fluence of 1 x 1025 n m~2 no (c) component dislocation loop is observed. As highly irradiated Zircaloy samples became available, for fluence higher than 5 x 1025 nm~2, evidence of (c) component loops arose.46’54’70-73’189 The (c) component loops have been analyzed as being faulted and of the vacancy type. They are located in the basal plane with a Burgers vector
1 /6(2023) having a component parallel to the (c) axis (Figure 6). The (c) component loops are much larger than the (a) loops but their density is much lower. For instance, for recrystallized Zy-2 and Zy-4 irradiated at 300 °C, after5.4 x 1025nm~2, (c) component loops are found with a diameter of 120 nm and with a density between 3 and 6 x 1020 m~ .

Whatever the irradiation conditions, these (c) component loops are always present in conjunction with more numerous and finer (a) loops. The (c) component loops can therefore only be observed edge-on by TEM by using the g = 0002 diffraction vector, which leads to invisible (a) type defects. The (c) loops thus appear as straight-line segments.

There is considerable evidence to show that their formation is dependent on the purity of the zirconium used (Figure б).46,74-76,190 It is also observed that at the beginning of their formation, these dislocation loops appear to be located close to the intermetallic precipi­tates present in the Zircaloy samples46,76 (Figure 7). By using an HVEM on iron-doped samples, it has been possible to prove that iron enhances the nucle — ation of the (c) loops, the loop density increasing as a function ofthe iron content. Moreover, iron was found to have segregated in the plane of the loops.76

Dependence of creep and creep relaxation on neutron spectra

It is sometimes assumed that thermalized neutron spectra can produce more effectively surviving point defects since gamma-recoil events do not pro­duce cascades and therefore there is less in-cascade annihilation. Thus, a larger fraction of thermally pro­duced defects are postulated to survive to contribute to creep or embrittlement.180,181

image128

Foster and coworkers have published three papers over the past several decades where it appeared that irradiation creep indeed occurred at a higher rate in thermal reactors than in fast reactors.182-184 In the last of these papers it was noted that, as proposed by Garner 34 the previously unsuspected 59Ni con­tributions to dpa might account for the apparent but possibly misleading increase in creep rate. The T/F ratio in the experimental test reactors cited by Foster was rather high compared to that in PWRs.

An additional reason for such enhancement of creep probably lies in the large amounts of trans­muted helium and stored hydrogen in thermalized spectra that results from the 59Ni sequence and the stored hydrogen concept, producing bubbles and voids that accelerate the creep rate. Therefore, it does not appear necessary to invoke an enhanced
survivability or displacement effectiveness of gamma recoil events to explain the apparently higher creep rates in thermal reactors.

Development with increasing fluence

The progressive precipitation of the Cu present in solution at the SOL as a result of irradiation has been recognized since the 1980s. There are a large number of studies that show that a high density of small CECs are formed under irradiation, and that the number density, size, and volume fraction are strongly depen­dent on the irradiation fluence, flux, and the material composition.

For MnMoNi steels and Fe-Cu alloys, the number density and volume fraction increase rapidly with increasing fluence, and then there is an appearance of saturation, that is, a pattern of behavior that mir­rors the shape of the curve in Figure 6(a). This is illustrated in Figure 8 from the work of Odette et al. (see data presented in Eason eta/.29 where the volume fraction, fp, and radius have been derived from SANS data). It can be seen that the radius increases with fluence in this example. Auger et a/.62 had found a similar pattern of behavior in SANS and AP data from ten steels and two Fe-Cu alloys with <0.2 wt% Cu. Saturation occurred at a similar fluence to that of Odette et a/., that is, ~1 x 1019 n cm~2 (for irradiation temperatures close to 290 °C).

The rate at which the volume fraction increases with fluence is also strongly dependent on the irradi­ation flux and the composition of other elements such as Ni. Figure 9 shows the SANS measurements of Williams and Phythian63 on MnMoNi SAWs. It shows the effect of dose rate, Cu, and Ni on the development of CEC volume fractions with dose. Decreasing the Cu decreases both the volume fraction and CEC size. In the high Cu welds (seen most clearly at high dose rate), increasing the Ni clearly increases the total volume fraction of CECs formed at all doses. At the same time, the mean CEC diameter is somewhat decreased in the higher Ni weld (thus the volume fraction increase is associated with a large increase in cluster number density). It is also evident that, while the precipitated volume fraction appears to be satur­ating at the highest dose in the low Ni welds, there is no sign that saturation is close in the high Ni welds.

A number of authors have found similar results.29,64,65

image197

Figure 8 SANS data on volume fraction, fp, and, radius, rp, for 0.4 wt% Cu, 1.25 wt% Ni split melt model steel alloys (LD) irradiated at three flux levels between 0.6 and 10 x 1015nm~2s~1 in IVAR at 290 °C, plotted as a function of fluence, ft. Reproduced from Eason, E. D.; Odette, G. R.; Nanstad, R. K.; Yamamoto, T.; EricksonKirk, M. T. A Physically Based Correlation of Irradiation-Induced Transition Temperature Shifts For RPV Steels; Oak Ridge Report ORN L/TM-2006/530, 2007.

 

■ High Cu, High dose rate A High Cu, Medium dose rate

■ High Cu, Low dose rate Low Cu, High dose rate

 

image198

Figure 9 Effect of bulk composition and dose rate on CEC size and volume fraction in MnMoNi SAWs. In (a) data are from low Ni welds, high Cu ~0.08Ni, 0.55Cu; low Ni, low Cu ~0.08Ni, 0.15Cu; and in (b) data are from high Ni welds, high Cu ~1.65Ni, 0.55Cu; high Ni, low Cu ~1.5Ni, 0.05Cu (all wt%). In both figures could be seen high flux ~5.5 x 10~9, medium flux ~6.3 x 10~10, and low flux ~9 x 10-11 (all dpas-1). Reprinted with permission from Williams, T. J.; Phythian, W. J. In Effects of Radiation on Materials, 17th International Symposium, ASTM STP 1270; Gelles, D. S., Nanstad, R. K., Kumar, A. S., Little, E. A., Eds.; American Society for Testing and Materials: Philadelphia, 1996; p 191. Copyright ASTM International.

It is to be noted that Soneda65 found that when com­paring Cu clusters in low-fluence-irradiated steels formed at a flux of 109 and 1010ncm_2s_1 E > 1 MeV, there was significant effect of dose rate on cluster size rather than number density.

The effect of Ni was established early on,66 but it has only just been established that Mn also has an important effect. Odette et al. demonstrated from SANS studies that at constant Cu and Ni, increasing Mn decreased the size of the clusters but increased their number density as illustrated for 0.4 wt% Cu, 0.8 wt% Ni, and 3.4 x 1019 E > 1 MeV in Figure 10. In higher Ni steels, Burke et a/.67 have also demon­strated that removing Mn from a steel significantly lowers the resultant embrittlement and the level of observable solute-related damage.

It was thought for many years (e. g., Jones and Bolton2) that CEC-related hardening would reach a maximum level once all the Cu had precipitated, and remain at this level as the CEC size remained constant — probably as a result of a balance between cluster nucleation and growth, and cluster destruction in cascades, that is, overaging did not occur. Jones and Bolton2 reported measurements of Cu cluster diame­ter using SANS on unirradiated and irradiated C-Mn SMA welds. It was shown that under surveillance conditions, and at temperatures below about 300 °C, Cu clusters grew to about 2 nm in diameter. Even after subsequent accelerated irradiations (of the sur­veillance samples irradiated to the lowest doses) to doses between ^200 x 10~5 and 1200 x 10~5dpa, the mean precipitate diameter was still ^2 nm.

Figure 10 SANS data on cluster radius, rp, number density, Np, and volume fraction, fp for 0.4 wt% Cu split melt model steels irradiated at high IVAR flux at 290 °C. Effects on Mn variations in alloys with ~0.8 wt% Ni. Reproduced from Eason, E. D.; Odette, G. R.; Nanstad, R. K.; Yamamoto, T.; EricksonKirk, M. T. A Physically Based Correlation of Irradiation-Induced Transition Temperature Shifts For RPV Steels; Oak Ridge Report ORNL/TM-2006/530, 2007.

image201

Figure 12 Schematic of the effect of selected material and irradiation variables on CEC volume fraction.

 

image200

Figure 11 Radius of gyration and number density of CRPs for the RPV surveillance test specimens of Doel-1 (△) and Doel-2 (•). Reproduced from Toyama, T.; Nagai, Y.; Tang, Z.; et al. Acta Mater. 2007, 55, 6852-6860.

 

image199

More recent observations at the onset of the pla­teau in CEC formation in a number of commercial steels have shown that only around half of the avail­able Cu had precipitated (Auger etal.)62 This suggests that particle coarsening and overaging could occur in irradiated RPV steels as well as in thermally aged steels, once the precipitation level was high. Particle coarsening has been reported in MnMoNi surveillance material from the Doel-1 and Doel-2 reactors,68,69 as shown in Figure 11. This particle coarsening should result in overaging (i. e., softening) after the hardness reaches a maximum value.

Figure 12 illustrates schematically the influence of selected material and irradiation variables on the

CEC volume fraction (nominally for a Cu-containing MnMoNi steel irradiated at ^290 °C).

The Cu level in the matrix at the SOL is an important parameter as it is the matrix Cu that is available for precipitation of CECs. This has been determined by either thermodynamic modeling or by direct measurement. For example, modeling calcula­tions were performed by Buswell and Jones70 to determine matrix Cu levels in Magnox SMA welds with bulk Cu contents between 0.13 and 0.31 wt%. They found that the precipitation of Cu during the final weld stress-relief heat treatment (at 590-600 ° C), and also during the subsequent extremely slow cooling (5 °Ch-1) of the RPV before reactor operation, reduced the maximum Cu available to precipitate during irradiation to no more than 0.15-0.20 wt%.70 Precipitation during the final weld stress relief also occurs in US steels. Indeed, a consensus has emerged that there is an upper limit to SOL-dissolved Cu, which is dependent on heat treatment. McElroy and

Lowe have shown that even differences of 20-30 °C in the heat treatment temperature can markedly affect the dissolved Cu content,71 as can the slow cooling of real structures from the stress-relief temperature.

Nanoscale Oxide Particle Control

4.08.2.1 Dissociation and Precipitation

The fine distribution of Y2O3 particles, which is essential to improving the high temperature strength of ODS steels, is attained by the dissociation of oxide particles during MA processing.2 The thermodynam­ically stale Y2O3 particles are forcedly decomposed into the ferritic steel matrix during the MA process. Subsequent annealing induces oxide particles to pre­cipitate finely at elevated temperature of around 1000 °C. The co-addition of Ti during MA proces­sing promotes the decomposition of Y2O3 and then the precipitation of Y-Ti complex oxide particles through an annealing heat treatment.3,4 A field emis­sion ion micro-probe (FIM) analysis confirmed that this type of complex oxide is constituted of several nanometer-sized Y-Ti-O compounds.5-7

The precipitation process of the decomposed Y2O3 was investigated by means of a small angle neutron scattering (SANS) experiment.8 The neutron-scattering cross-section (dS/dO) versus scattering vector (q2) plots for the milled U 14YWT(Fe-14Cr-0.4Ti-3W — 0.25Y2O3) are shown in Figure 1(a). They indicate that the hot isostatic pressing (HIP) of U14YWT at 850 °C leads to the precipitation of a high number density of nanoclusters, as designated by Odette. Figure 1(b) shows the effects of HIP (filled symbols) and powder annealing (open symbols) at tempera­tures of 700, 850, 1000, and 1150 °C. The increase in magnitude and decrease in slope of the dS/dO versus q2 curves indicate that the radius of nanoclus­ters decreases and their number density increases with decreasing temperature at HIP and powder annealing. Annealing at 700 °C produces the highest scattering and lowest sloping, which indicates that the smallest-sized nanoclusters precipitate with the high­est number density at lower temperatures. In terms of an X-ray diffraction experiment using Super Photon

ring-8 eV (Spring-8) constructed in Japan, Kim eta/, recently reported that nanoclusters could be in a noncrystalline state and can be transformed to nano­crystalline oxide particles at around 10000C9

4.08.2.2 Structure and Coherency

With regard to ODS steels without Ti, high resolu­tion (HR) TEM investigations were performed by Klimiankou to investigate the structure of Y2O3.10 The crystallographic lattice of the metal matrix cor­responds to a-Fe with a bcc structure and a lattice constant of a0 = 0.287 nm.11 The Y2O3 has a crystal­line bcc structure with a 1.06 nm lattice constant.11 Figure 2 shows an HRTEM image taken from an Y2O3 particle that is surrounded by the matrix (M) lattice. This image was taken from the grain, oriented with [1 1 1]M zone axis to the electron beam. A fast Fourier transformation (FFT) of the image shows the matrix lattice as a hexagonal pattern with diffraction spots of the {110} type and dM(110) = 0.203 nm dis­tance. In the FFT image, the Y2O3 (YO) lattice is rectangular, with diffraction spots of the {2 2 2} type and a corresponding atomic planes distance of dYO(2 2 2) = 0.306 nm. The angle of 70.50 between diffraction spots of the {2 2 2}YO type marked in Figure 2(a) confirms that the Y2O3 particle is oriented with the [110] zone axis, and consequently [1 1 0]YO// [1 1 1]M. The orientation correlation of both lattices is (1 I I)YO//(1 T 0)M. Therefore, the following Kurdjumov-Sachs orientation relationship12 is satisfied:

(111 )yo//(110)m ;

[110] YO//[111]m : I1]

image267

Figure 1 Results of a SANS experiments for as-mechanically alloyed powders and after HIP and annealing in U14YWT (Fe-14Cr-0.4Ti-3W-0.25Y2O3). (a) As-MA, 8500C HIP and annealing and (b) HIP (filled) and annealing (annealing) at 1150,1000, 850, and 7000C. Reproduced from Alinger, M. J.; Odette, G. R.; Hoelzer, D. T. J. Nucl. Mater. 2004,382, 329-333.

 

_ (011)

101)(2^^>.(1T0) _ (2TT)

(222) _

(T10)<^j22?)(101) , (011)

 

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70.5

 

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(a)

 

(b)

 

Figure 2 HRTEM micrograph of the Y2O3 particle with surrounding matrix (a) and FFT image of micrograph (b). The diffraction spots from Y2O3 particle of {2 2 2} type form the rectangle, whereas diffraction spots from the matrix of {1 1 0} type form the hexagon at the [1 1 0] zone axis and [1 1 1] of matrix. Reproduced from Kliniankou, M.; Lindau, R.; Moslang, A. J. Nucl. Mater. 2004, 329-333, 347-351.

 

image380

image268

image269

Figure 3 EFTEM images of Y2Ti2O7 particles. Reproduced from Kliniankou, M.; Lindau, R.; Moslang, A. J. Nucl. Mater. 2004, 329-333, 347-351.

data are equal to the following data calculated from the Y2Ti2O7 structure: d2 2 2 = 0.29 nm and d0 0 4 = 0.25, and an angle between the (0 0 4) and (2 2 2) atomic planes of 54.7°. The analysis of EFTEM results defini­tively shows that Y-Ti-O particles have a Y2Ti2O7 composition.

These findings suggest that nano-oxide particles precipitate from the ferritic matrix, maintaining crys­talline coherency or partial-coherency with a ferritic matrix. In general, the nucleation and growth of pre­cipitates proceeds, as both interfacial and strain ener­gies become minimal. In the case of ODS steels, interfacial coherency could be maintained between thermodynamically stable nanoparticle precipitates and the ferritic matrix in order to decrease the free energy in the system from the extremely high energy state induced by MA. Elucidation of the details of the nanoscale precipitation is important not only as basic materials science research but also as the develop­ment of high-strength engineering materials.

In-Service Performance

4.09.3.1 Environmentally Assisted Cracking

Welds and their heat-affected zones have long been known to be the areas of concern for environmentally assisted cracking (EAC) because of their propensity
for as-fabricated flaws, high residual stresses, ele­vated plastic strains, chemical heterogeneity, and microstructural differences relative to base metals (Chapter 5.04, Corrosion and Stress Corrosion Cracking of Ni-Base Alloys; Chapter 5.05, Corro­sion and Stress Corrosion Cracking of Austenitic Stainless Steels; Chapter 5.06, Corrosion and Environmentally-Assisted Cracking of Carbon and Low-Alloy Steels; Chapter 5.02, Water Chem­istry Control in LWRs; and Chapter 5.08, Irradia­tion Assisted Stress Corrosion Cracking). Common EAC concerns in the nuclear industry include corro­sion fatigue of low-alloy steels, hydride-induced

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cracking of zirconium alloys, and stress corrosion cracking of corrosion-resistant structural alloys. Specifically, stress corrosion of austenitic stainless steel65-68 and nickel-alloy welds and their heat — affected zones has been a topic of considerable research.9,66,6972 In austenitic stainless steels, sensiti­zation — and welding-induced plastic strains are the key factors in stress corrosion resistance.

In nickel-alloy welds, the bulk chromium con­centration, the solidification segregation, and the as-fabricated plastic strain are critical factors for understanding their stress corrosion performance. The stress corrosion cracking growth rate of nickel — alloy filler metals in high-temperature, high-purity water is shown as a function of their bulk chromium concentration in Figure 18(a). Note the strong decrease in stress corrosion crack growth rate at bulk chromium levels near 22 wt%. This decrease is likely associated with a change in crack tip oxide from NiO-type to a more stable spinel (NiCr2O4) or corundum (Cr2O3) structure.73-75 However, the bulk chromium concentration does not explain the extreme resistance of EN52 weld metal compared to other ^30 wt% bulk chromium alloys (Figure 18(a)). Consideration of how solidification segregation affects the grain boundary chromium concentration is critical to understanding the stress corrosion resis­tance of the high-alloy weld metals.76 Specifically, niobium — and molybdenum-bearing alloys tend to deplete the solidification grain boundaries in
chromium, while the Nb — and Mo-free EN52 grain boundaries are enriched in chromium as shown in the graph in Figure 18(b).

In Alloy 600 heat-affected zones, the increased susceptibility to SCC in high-temperature deaerated water is due, in large part, to the lack ofintergranular chromium carbides.77,78 Figure 19(a) shows a cross­section of a stress corrosion crack grown in an Alloy 600 heat-affected zone and the flat grain boundary topography (GBT) in the HAZ, which is an indica­tion of a low degree of intergranular chromium car­bide precipitation.78 Additionally, Figure 19 shows the different chromium concentration profiles in the HAZ and base metal (Figure 19(b)), the increased strain in the weld and HAZ relative to the base metal (Figure 19(c)), and the transmission electron micro­graphs of the grain boundaries in the HAZ (showing sparse (M7C3- and M23C6-type carbides) versus the large continuous Cr7C3 carbides in the unaffected base metal (Figure 19(d)). The diffraction patterns in Figure 19(d) identify the M23C6 (left) and M7C3 (right) carbides.

Stress corrosion crack growth rate predictions for Alloy 600 heat-affected zones are shown in Figure 20, which illustrates the strong temperature dependence as well as the effects of the applied stress intensity factor and the electrochemical potential. Figure 20 is based on eqn [1], which describes the crack growth rate of A600-type alloys exposed to high-temperature, high-purity water,77 in which A0, », m, b, x0, and c are the

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experimentally determined constants, Kj is the stress intensity factor, sYs is the yield strength, AEcP is the electrochemical potential relative to the Ni/NiO phase transition, QEffective is the apparent activation energy, R is the gas constant, and T the temperature. The appropriate parameters for Alloy 600 HAZs are given in Table 3.

a = a0 • • smS