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Examples of Creep Behavior

Various aspects of behavior resulting in irradiation creep can be illustrated with some examples pre­sented in Figures 68-75.

4.02.9.2 Creep Disappearance

The previous figures demonstrate the swelling-creep correlation at its simplest when swelling is either zero or just beginning, but not yet provoking the next shift in quasi-equilibrium. When looking across a wider

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Figure 68 Creep-induced deflections of helical springs constructed from two steels with different composition that were irradiated in DMTR at 100 °C, normalized to the elastic deflection, showing that both the transient and steady-state creep rate B0 are proportional to the stress level. While the transients are different in the two steels, the posttransient creep rate is independent of composition. Reproduced from Lewthwaite, G. W.; Proctor, K. J.

J. Nucl. Mater. 1973, 46, 9-22. The maximum dose is ~0.5dpa.

 

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Figure 67 Linear stress dependence of total diametral strain (creep and swelling) for 20% cold-worked PCA (Ti-modified 316 stainless) pressurized tubes irradiated in FFTF at 400°C. Reproduced from Garner, F. A.; Puigh, R. J. J. Nucl. Mater. 1991, 179-181, 577-580. Stress-free swelling is approximately three times the Y-intercept value with the largest swelling at ~8%.

 

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Figure 73 Swelling and creep strains observed in two French steels irradiated as pressurized tubes in PHENIX, showing strong correlation between the two types of strain as the swelling rate increases. Reproduced from Dubuisson, P.; Maillard, A.; Delalande, C.; Gilbon, D. D.; Seran, J. L. In Effects of Radiation on Materials:

15th International Symposium; STP 1125; 1992; pp 995-1014.

Подпись: Figure 71 Acceleration of irradiation creep in two carbon variants of a stainless steel by a low rate of swelling at 350 and 420°C. Reproduced from Neustroev, V. S.; Shamardin, V. K. In Effects of Radiation on Materials: 16th International Symposium; 1993; pp 816-823. The lower carbon steel has a longer transient regime of swelling. The height of the plateau is determined by the swelling rate. B0 was determined to be ~1 x 10-6 (MPa dpa)-1 and D to be 0.6 x 10-2MPa-1.
Подпись: Figure 72 Temperature-independent creep strains observed in 20% cold-worked 316 and 25% cold-worked PCA during irradiation in the ORR test reactor at a high He/ dpa ratio. Reproduced from Grossbeck, M. L.; Horak, J. A. J. Nucl. Mater. 1988, 155-157, 1001-1005. Note that the two steels have very similar values of creep modulus B and are independent of irradiation temperature over a wide range. The creep modulus B is about three times that of B0 = 1 x 10-6 (MPa dpa)-1, however, probably arising from observed high densities of helium bubbles to produce bubble-enhanced creep. range of swelling behavior some unusual behaviors are often observed. An example is shown in Figure 76 where the two-peaked swelling behavior frequently observed in 300 series steels is mirrored in the creep strains, but the relative proportions of the two strains are distorted.172 This is one manifestation of the creep disappearance phenomenon in which the attainment of significant swelling causes irradiation creep to strongly drop in rate or even to disappear under some conditions as seen in Figures 77 and 78.

In early fuel pin studies it was often observed that irradiation creep strains would increase and then abruptly decrease and sometimes stop entirely, even though fission gas pressures continued to increase.173,174 These results were interpreted as evi­dence of fuel swelling very quickly to meet and thereby put stress on the cladding but later the onset of swelling in the clad caused it to out-swell the fuel and break contact. Actually, the driving force

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Figure 74 (left) Diametral strains resulting from void swelling at 400 °C in neutron-irradiated stress-free tubes constructed from nine titanium-modified 316 stainless steels, (right) Stress-normalized midwall creep strains observed in three of these steels, showing a strong correlation of swelling and irradiation creep rates in each steel. Reproduced from Toloczko, M. B.; Garner, F. A.; Eiholzer, C. R. J. Nucl. Mater. 1992, 191-194, 803-807.

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Figure 75 Creep modulus measured for six austenitic steels irradiated in BOR-60 fast reactor at 420 °C, showing an enhancement of creep versus Ni-equivalent. Reproduced from Neustroev, V. S.; Shamardin, V. K.

J. Nucl. Mater. 2002, 307-311, 343-346. This behavior corresponds to the known effect of nickel on void swelling, indicating swelling-enhanced creep.

was primarily increasing levels of fission gas but irradiation creep had disappeared by ~7% burn-up.

Several features of creep disappearance are noteworthy.

1. The combined creep and swelling strain rate in a fuel pin or pressurized tube cannot exceed 0.33%

per dpa or one-third of the eventual steady-state swelling rate.

2. As swelling approaches 1% per dpa the creep rate backs down proportionately to maintain this max­imum rate as shown in Figures 78-80.

3. The limit of 0.33% per dpa is reached before swelling gets to a significant fraction of 1% per dpa, as shown in Figure 80. Some tubes had already reached the maximum strain rate limit, but then lost their gas pressure and continued to swell at less than 1% per dpa.

4. As the creep cessation process gets underway the creep strain loses its responsiveness to the magnitude of the stress. Note in Figures 79 and 80 that doubling the hoop stress did not double the strain rate in the tube.

5. The coupling coefficient D tends to fall to zero rather quickly when swelling-before-creep occurs but falls more slowly in creep-before-swelling scenarios (fuel pins vs. pressurized tubes).175

A consensus explanation ofthe creep disappearance phenomena has not yet been reached. Various models have been proposed involving voids acting to erase the anisotropy of dislocation Burgers vector176,177 and the involvement of precipitate sinks to serve as strong sinks that compete with dislocations.175