RESULTS AND DISCUSSION

With the code just described the six FUMEX experiments were simulated. The real power histories were conveniently simplified to save calculation time. Figures 1-6 show the input data and the results obtained with the code for the central line temperature, the internal rod pressure and the fractional release. The comparison between some results of our calculations and the coresponding data presented in the final report of the FUMEX experiment [19] are summarized in Table II.

The values shown in Table II reveal that the results obtained with our code fit quite well to the experimental results and in all the cases, except the final ramp of experiment 6S, fall within the range of values obtained with the other codes. As it was expected, the fitting is better in the cases of constant or nearly constant power.

The calculation time required to simulate these experiments, with power histories simplified to about 50 power steps, was about 10 minutes in a personal computer with a 330 MHz, Pentium II processor.

FIG.1. Simplified power history and calculation results corresponding to FUMEX 1.

FIG.2. Simplified power history and calculation results corresponding to FUMEX 2.

FIG.3. Simplified power history and calculation results corresponding to FUMEX 3 rod 2

FIG.4. Simplified power history and calculation results corresponding to FUMEX 4 rod B.

FIG.5. Simplified power history and calculation results corresponding to FUMEX 5.

FIG.6. Simplified power history and calculation results corresponding to FUMEX 6F.

TABLE II. COMPARISON BETWEEN DATA OF THE FUMEX EXPERIMENT AND THE PRESENT CALCULATIONS

experimental other codes this code FUMEX 1 central temperature at 20MWd/kgUO2, °C 740 508–800 734

FGR at EOL, % 1.8 0.05–2.18 1.47

FUMEX 2 central temp. at 5MWd/kgUO2 and 40kW/m,

°C

1210–1820 1584

FGR at EOL, % 3 1.2–28.8 3.69

internal rod pressure at power and EOL, bar 20.3 20.1–50 22.9 FUMEX 3 central temp. before power ramp, °C 1040 865–1365 1042

rod 2 FGR before power ramp, % 0.6–44 42.3

FGR after power ramp, % 5.3–50.5 50.4

FUMEX 4 central temp. at start–up and 30 kW/m, °C 1020 876–1398 1067 rod A central temp. during power ramp, °C 1125 792–1533 1161

central temp. at EOL, °C 1225 1035–2246 1610

FRG before power ramp, % 0.3–10.6 7

FGR during power ramp, % 0.7–26.1 7.1

FGR at EOL, % 15.4–53.8 38.6

FUMEX 4 central temp. at start–up, °C 1065 953–1522 957

rod B central temp. at the top of the ramp, °C 1260 1200–1593 1445

central temp. at EOL, °C 1290 1213–2203 1482

FGR at EOL, % 27.5–50 40.3

pressure at hot standby after power ramp, bar 23.9 3–45.3 19.9

FUMEX 5 FGR before period of high power, % 0 0–43.1 0

FGR at EOL, % 5.8 1–21.7 2.3

pressure at start–up, bar 2.3 2.7–66.6 1

pressure at EOL, bar 9.4 3.9–82.6 12.1

FUMEX 6 FGR at end of base irradiation, % 16.4 7–20.2 19.1 pressure at end of base irradiation, bar 7.6–79.5 15.7

FUMEX 6F FGR at EOL, % 45 8.9–38.2 51.2

pressure at EOL, bar 84.6 40.4–102 44.9

FUMEX 6S FGR at EOL, % 50 14–50.4 80.6

pressure at EOL, bar 92.3 40.4–106.7 69.1

5. CONCLUSIONS

Although the results shown above are quite acceptable, the code requires further improvement. For instance, a gas mixing model needs to be included. The code doesn’t contain an adequate treatment of the power ramps, which are averaged. The description in the axial direction has to be modified in order to simulate rod elongation. It is expected that these modifications will improve the performance of the code.

ACKNOWLEDGEMENTS

The authors wish to acknowledge Ing. L. Álvarez and Lic. A. Marino for the provision of the data with which the calculations were performed.

REFERENCES

[1] MATHEWS, J.R., The quantitative description of deformation and stress in cylindrical fast reactor fuel pins, in Advances in Nuclear Science and Technology, Vol.6 (1972), Academic Press.

[2] CAILLOT, L., LINET, B., LEMAIGNAN, C., Pellet clad interaction in PWR fuel.

Analytical irradiation experiment and finite element modelling, (Proc. SMIRT 12, Stuttgart, Germany, 1993)

[3] DELETE, G., CHARLES, M., “Thermal conductivity of fully dense unirradiated UO2: a new formulation from experimental results between 100°C and 2500°C and associated fundamental properties”, Water Reactor Fuel Element Modelling at High Burnup and its Experimental Support, IAEA–TECDOC–957, IAEA (1997) 203–216.

[4] TIMOSHENKO, S., Theory of elasticity, McGraw Hill, 1951.

[5] PENNY, MARRIOT, Design for creep, McGraw Hill, 1971.

[6] HARRIAGUE, S., COROLI, G., SAVINO, E., BACO, a computer code for simulating a reactor fuel rod performance, Nucl. Eng. and Design 56 (1980) 91–103.

[7] SEGERLIND, L.J., Applied finite element analysis, 2^nd Ed., Wiley (1984).

[8] Handbook of materials properties for use in the analysis of light water reactor fuel behavior, MATPRO version 11, NUREG/CR-0497, TREE–1280 (1979).

[9] DENIS, A., PIOTRKOWSKI, R., Simulation of isothermal fission gas release, J. of Nucl. Mater. 229 (1996) 149–154.

[10] DENIS, A., PIOTRKOWSKI, R., A fission gas release model, Water Reactor Fuel Element Modeling at High Burnup and Experimental Support, IAEA-TECDOC-957, IAEA (1997) 455–465.

[11] TURNBULL, J.A., WHITE, R., WISE, C., The diffusion coefficient of Fission Gas Atoms in UO2, IAEA TC 659/3.5 (1987) 174–181.

[12] WHITE, R., TUCKER, M., A new fission gas release model, J. of Nucl. Mater. 118 (1983) 1–38.

[13] ITO, K.,IWASAKI, R:,IWANO, Y., Finite element model for analysis of fission gas release from UO2 fuel, J. of Nucl. Sci. and Technol. 22 (2) (1985) 129–138.

[14] NAKAJIMA, T., A comparison between fission gas release data and FEMAXI–IV code calculations, Nucl. Eng. And Design 101 (1987) 267–279.

[15] STAUFFER, D., Introduction to percolation theory, Taylor & Francis, London ans Philadelphia, 1985.

[16] MALDOVÁN, M., DENIS, A., PIOTRKOWSKI, R., Simulation of isothermal fission gas release. An analytical solution, Nucl. Eng. and Design 187 (1999) 327–337.

[17] OLANDER, D., Fundamental aspects of nuclear reactor fuel elements, Technical Information Center, USDOE, 1976.

[18] FRANKLIN, D., ROBERTS, J., LI, C., Low temperature swelling and densification properties of LWR fuels, J. of Nucl. Mater. 125 (1984) 96–103.

[19] MARINO, A., SAVINO, E., HARRIAGUE, S., BACO code version 2.20: a thermomechanical description of a nuclear fuel rod, J.Nucl. Mater. 229 (1996) 155–168.

[20] INTERNATIONAL ATOMIC ENERGY AGENCY, Fuel Modeling at extended burnup, IAEA–TECDOC–998.

.

MODELLING OF STRESS CORROSION CRACKING IN ZIRCONIUM ALLOYS

O. FANDEUR^1,2, L. ROUILLON¹, P. PILVIN², P. JACQUES³, V. REBEYROLLE⁴

1 CEA, Centre de Saclay, Gif-sur-Yvette, France

2 École Centrale Paris, Châtenay-Malabry, France

3 EDF Septen, Villeurbanne, France

4 FRAMATOME, Lyon, France

Abstract

During normal and incidental operating conditions, PWR power plants must comply with the first safety requirement, which is to ensure that the cladding wall is sound. Indeed some severe power transients potentially induce Stress Corrosion Cracking (SCC) of the zirconium alloy clad, due to strong Pellet Cladding Interaction (PCI). Since, at present, the prevention of this risk has some consequences on the French reactors manoeuvrability, a better understanding and forecast of the clad damage related to SCC/PCI is needed. With this aim, power ramp tests are performed in experimental reactors to assess the fuel rod behaviour and evaluate PCI failure risks. To study in detail SCC mechanisms, additional laboratory experiments are carried out on non-irradiated and irradiated cladding tubes. Numerical simulations of these tests have been developed aiming, on the one hand, to evaluate mechanical state variables and, on the other hand, to study consistent mechanical parameters for describing stress corrosion clad failure. The main result of this simulation is the determination of the validity ranges of the stress intensity factor, which is frequently used to model SCC. This parameter appears to be valid only at the onset of crack growth, when crack length remains short. In addition, the role of plastic strain rate and plastic strain as controlling parameters of the SCC process has been analysed in detail using the above mechanical description of the crack tip mechanical fields.

Finally the numerical determination of the first-order parameter(s) in the crack propagation rate law is completed by the development of laboratory tests focused on these parameters. These tests aim to support experimentally the results of the FE simulation.

1. INTRODUCTION

During normal and incidental operating conditions, PWR power plants must comply with the first safety requirement, which is to ensure that the cladding wall is sound. Indeed some severe power transients potentially induce Stress Corrosion Cracking (SCC) of the zirconium alloy clad, due to strong Pellet Cladding Interaction (PCI) [1]. Since, at present, the prevention of this risk has some consequences on the French reactors manoeuvrability, a better understanding and forecast of the clad damage related to SCC/PCI is needed.

With this aim, power ramp tests are performed in experimental reactors to assess the fuel rod behaviour and evaluate PCI failure risks. However these tests give a global answer whereas a detailed analysis of stress corrosion cracks would be needed. Moreover, Finite Element (FE) simulations of fuel rod behaviour during a power transient show that an accurate evaluation of the clad mechanical state depends on the modelling of phenomena involved in PCI. Thus, to study in details SCC mechanisms, additional laboratory experiments are realised on non-irradiated and non-irradiated cladding tubes; these internal pressurisation tests are performed with well-defined geometry and boundary conditions.

Numerical simulation of these tests has been developed aiming, on the one hand, to evaluate mechanical state variables and, on the other hand, to study consistent mechanical parameters for describing stress corrosion clad failure. The development of new laboratory tests helps to

validate experimentally the results of these FE simulations and to determine the first-order mechanical parameters in the crack growth law.

2. MATERIAL DESCRIPTION

The material investigated in this study is a Stress-Relieved (SR) low-tin content Zircaloy-4, which is commonly used for fuel claddings in Pressurised Water Reactor (PWR).

Its chemical composition in weight percent, in agreement with the ASTM B 350.90 specification, is given in Table I.

Table I. WEIGHT COMPOSITION OF SR ZIRCALOY-4 Alloying elements (%)

Sn 1.30 Fe 0.22 Cr 0.12 O 0.130 Zr balance

The cladding tube geometry is defined by a 9.5-mm outside diameter and a 0.57-mm thickness. The irradiated specimens were cut from fuel rods which have been irradiated during one or two operating cycles in a French PWR. Table II summarises the three studied Zircaloy-4 batches.

Table II. INVESTIGATED MATERIALS

Batch reference Fluence

(neutrons/m²)

Burnup (GWd/t U)

A 0 0

B 1.7 10²⁵ 10.0

C 4.3 10²⁵ 23.1

Due to its fabrication processing, SR Zircaloy-4 exhibits a pronounced crystallographic texture, as shown on Figure 1. This texture does not seem to be significantly modified by irradiation [2]. The microstructure of the stress-relieved metallurgical state is characterised by elongated grains along the rolling direction, which corresponds to the axial direction of cladding tubes. The grain size is 20 µm long in the rolling direction and 2 µm wide in the transverse direction.

FIG. 1. Cladding tube pole figures (a) (0002) basal plane, (b) (10 1 0) prismatic plane [2].

The texture and the hexagonal close-packed lattice imply a strong mechanical anisotropy.

Assuming that the anisotropic axis and the texture axis are the same, Zircaloy-4 tubes have an orthotropic behaviour whose directions correspond respectively to the radial, hoop, and axial directions. In spite of a pronounced anisotropy, the elastic behaviour can be considered isotropic and the elastic parameters (Young modulus E and Poisson coefficient n) are only temperature dependant and not burnup dependant.

3. EXPERIMENTAL PROCEDURE

All the tests performed are internal pressurisation tests, because of commercial product geometry (thin-walled tube) and availability, especially for irradiated material. The working temperature is 623 K (350°C). The inert gas is high purity helium and the aggressive environment is gaseous iodine created by introducing bisublimated iodine (in general 75 mg) inside the tube.

The principal stages of a test are the following:

(i) Sample preparation: metrology, Gyrolock^TM seal system, steel end-plugs.

(ii) Iodine preparation: weighting, putting into a Zirconium melting pot.

(iii) Setting up the sample tube into the pressurisation test installation with the iodine carrier inside. To avoid iodine pollution by room air, stages (ii) and (iii) have to be done in about five minutes.

(iv) After air evacuation (primary vacuum), specimens are pressurised up to 5 bars to detect eventual leaks and then heated to the temperature test (iodine crystals vaporise). This step lasts one hour.

(v) Tube pressurisation with a constant pressure-loading rate of 2 bar.s^-1. (vi) Sample examination: metrology, SEM examinations…

Temperature and internal pressure are continuously recorded during each test.

The sample tubes whose length is 135 mm are closed during the test. Hydrostatic end effect must be taken into account and, on the inner tube surface, the hoop, axial and radial stresses are respectively equal to:

2i

where p is the internal pressure, Re and Ri are the outside and inside radius respectively.

Two different types of tests can be achieved (see Figure 2):

(1) The “conventional” test, frequently used [1, 3, 4]. The hoop stress (pressure) is increased to the test stress sqqM and maintained until clad failure.

(2) The “discriminating” test. The hoop stress is increased to an “high” stress sqqH and kept constant during a predetermined duration TS, which can be called “dwell time”, then the hoop stress is decreased to a “low” stress sqqL and kept constant with time up to failure.

All the pressure transients are done with a constant pressure rate of 2 bar.s^-1.

0

FIG. 2. Description of the different internal pressurisation tests:

(left) “conventional” test, (right) “discriminating” test.

4. EXPERIMENTAL RESULTS

4.1. “Conventional” test results on irradiated ZIRCALOY-4

Tables III and IV gather the results of "conventional" tests performed on both irradiated materials (batches B and C). In order to evaluate SCC susceptibility with irradiation, a normalised hoop stress ||sqq|| has been defined. It corresponds to the ratio between the test hoop stress sqqM and the hoop conventional yield stress sqq0.2% determined elsewhere. The evolution of ||sqq|| versus time to failure is reported on Figure 3.

Table III. INTERNAL PRESSURE TESTS ON IRRADIATED ZIRCALOY-4 (BATCH B) Ref. test Atmosphere Hoop stress

sqqM (MPa)

Table IV. INTERNAL PRESSURE TESTS ON IRRADIATED ZIRCALOY-4 (BATCH C) Ref. test Atmosphere Hoop stress

sqqM (MPa)

Time to failure (h)

C_1 Helium 506 73.90 Burst C_2 Iodine 506 0.60 SCC-burst C_3 Iodine 402 0.84 SCC-burst C_4 / C_5 / C_6 Iodine 207 / 206 / 207 0.55 / 0.96 / 1.75 SCC pinhole

C_7 / C_8 Iodine 167 / 168 1.46 / 3.95 SCC pinhole

C_9 Iodine 143 2.98 SCC pinhole

0 20 40 60 80 100 120

0,1 1 Lifetime (h) 10 100

Normalised hoop stress ( %

non-irradiated Zy-4 helium non irradiated Zy-4 iodine irradiated Zy-4 (batch B) helium irradiated Zy-4 (batch B) iodine irradiated Zy-4 (batch C) helium irradiated Zy-4 (batch C) iodine 200 MPa

400 MPa 350 MPa 430 MPa

FIG. 3. Normalised hoop stress versus time to failure evolution. Burnup effect on SCC susceptibility.

It is shown that irradiation has an important effect on SCC susceptibility. In particular, time to failure reduction upon irradiation occurs at low stress levels. Moreover no susceptibility change is notable when burnup increases from 10 to 23 GWd/t U.

4.2. “Discriminating” test results on irradiated ZIRCALOY-4

“Discriminating“ test validation

During a "discriminating" test, decreasing pressure implies partial internal gas evacuation and a loss of iodine with the pressurisation installation used. To simulate this loss, "conventional"

tests have been conducted at a low stress level (sqqM = 350 MPa) on non-irradiated material with various initial iodine concentrations. The results of the validation tests are reported on Table V.

Table V. INFLUENCE OF INITIAL IODINE CONCENTRATION ON SCC SUSCEPTIBILITY OF NON-IRRADIATED MATERIAL (BATCH A)

Initial iodine concentration

(mg)

Time to failure

(h) Average hoop

plastic strain Number of tests performed

30 4.6 ± 0.5 0.34 ± 0.03 % 5

75 3.9 ± 1.6 0.31 ± 0.05 % 4

120 3.7 ± 0.7 0.34 ± 0.05 % 4

It is shown that the initial iodine concentration has almost no influence on the time to failure and on the hoop plastic strain measured after testing. It is therefore assumed that iodine loss following pressure decrease will not explain eventual differences between times to failure in

"discriminating" tests and those measured in "conventional" tests.

"Discriminating" test results

The conditions for the "discriminating" tests are the following:

(i) Initial iodine concentration of 75 mg.

(ii) The "high" and "low" stresses are sqqH = 430 MPa and sqqL = 350 MPa.

(iii) Various "dwell time" TS equal to 0, 20 and 60 minutes have been tested.

The experimental results are gathered on Table VI.

Table VI. "DISCRIMINATE" TEST RESULTS. INFLUENCE OF "DWELL TIME".COMPARISON WITH "CONVENTIONAL" TESTS

Test ref. Hoop stress sqqM (MPa)

Time to failure

(h) Average hoop

Plastic strain Intergranular crack

depth (µm) Number of tests performed

"Conventional" tests (using as reference)

A_Cl_1 350 3.9 ± 1.6 0.33 ± 0,05 % 60 5

A_Cl_2 430 1.8 1.1 % Non measured 1

Test ref. "Dwell time"

TS (h)

Time to failure (h)

Average hoop Plastic strain

Intergranular crack depth (µm)

Number of tests performed

"Discriminate" tests (sqqH = 430 MPa, sqqL = 350 MPa)

A_D_1 0 4.5 ± 0.3 0.38 ± 0.03 % 130 (*) 2

A_D_2 0.33 4.3 ± 0.2 0.55 ± 0.05 % 150 (*) 2

A_D_3 1 3.9 ± 0.1 0.77 % 150-200 (*) 2

(*) Important oxidation of fracture surfaces.

An important oxidation of fracture surfaces makes difficult the observation and measurement of intergranular crack growth. (An example can be shown on Figure 4). By observing other SCC sites inside the tube, it can be deduced that oxidation follows clad failure.

oxidation

(a) (b)

FIG. 4. "Discriminating" test with a 20-minute "dwell time" (SEM observations):

(a) fracture surface with important oxidation, (b) intergranular propagation domain.

In "discriminating" tests, times to failure are close to each other. In contrast with

"conventional" test results, overload pressure ("high" stress during "dwell time") has no influence on clad lifetime. Hoop plastic strain increases when "dwell time" increases and

appears not to be a controlling parameter of SCC clad failure. Conversely intergranular crack size increases with "dwell time" increments. In this case, it wonders whether the identical lifetimes are the results of compensating opposite effects: faster crack propagation during

"dwell time" at "high" stress than in "conventional" tests and these longer cracks propagate slower at "low" stress than in "conventional" tests conducting to identical times to failure.

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