effects of cladding material on irradiation performance of...

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EFFECTS OF CLADDING MATERIAL ON IRRADIATION PERFORMANCE OF MONOLITHIC MINI-PLATES

Hakan Ozaltun Idaho National Laboratory

Idaho Falls/ID - USA

ABSTRACT Monolithic, plate-type fuels are the proposed fuel form for the conversion of the research and test reactors to achieve higher uranium densities within the reactor core. This fuel type is comprised of a low enrichment, a high density U-10Mo alloy fuel-foil, which is sandwiched between diffusion barriers and encapsulated in a cladding material. To understand the irradiation performance, fuel-plates are being benchmarked for large number of parameters. In this work, effects of the cladding material were studied. In particular, a monolithic fuel-plate with U7Mo foil and Zry-4 cladding was simulated to explore feasibility of using Zircaloy as a surrogate cladding material. For this, a selected mini-plate from RERTR-7 tests was simulated first with as-run irradiation history. By using same irradiation parameters, a second case, a plate with U10Mo fuel and Al6061 cladding was simulated to make a comparative assessment. The results indicated that the plate with Zircaloy cladding would operate roughly 50 °C hotter compared with the plate with Aluminum cladding. Larger displacement profiles along the thickness for the plate with Zircaloy cladding were observed. Higher plastic strains occur for the plate with Aluminum cladding. The results have revealed that any pre-irradiation stresses would be relieved relatively fast in reactor and the fuel-foil would be essentially stress-free during irradiation. The fuel stresses however, develop at reactor shutdown. The plate with Zircaloy cladding would have higher residual stresses due to higher pre-shutdown temperatures. Similarly, the stresses magnitudes are higher in the foil core for the plates with Zircaloy cladding. Finally, pressure on the fuel is significantly higher for the plates with Zircaloy cladding. Overall, employing a Zircaloy as surrogate cladding material did not provide a better thermo-mechanical performance compared with the Aluminum cladding. Keywords: Mini-plate, U7Mo fuel, Zry4 cladding, Irradiation

1. INTRODUCTION The Office of Material Management and Minimization’s (M3) the Reactor Conversion (RC) and the Fuel Development (FD) Programs aims to develop fuel types that would substitute highly enriched uranium in research reactors with proliferation resistant, low enriched uranium (<20% 235U). Lower enrichment however, requires higher fuel densities either as dispersion fuels at high volume loading, or in a monolithic form to compensate lower fission rates. Within this concept, fuels in monolithic forms are proposed for the conversion of high performance research reactors to low enrichment uranium fuel reactors. These plate type fuels consist of a high density; low enrichment U-Mo alloy based fuel foil encapsulated in Aluminum based cladding material [1]. Current monolithic plate design employs a 0.025 mm thick diffusion barrier which is 99.8% pure annealed Zirconium, between fuel foil (U10Mo) and cladding materials (AL6061). This design modification produced promising irradiation results. Recently, it is questioned, if replacing Aluminum cladding with Zircaloy-4 would provide a better fabrication and irradiation performance. It was postulated that use of Zry-4 instead of AL6061 simplifies the fabrication process, eliminates Zirconium diffusion liner, allows using a thinner cladding, and thus, provides more space for fuel. It is claimed that the plates would be more compliant as Zircaloy and U7Mo have similar properties at high temperatures, even though the large thermal expansion mismatch between Zry-4 and U7Mo is present. To benchmark these claims, two plates with Zircaloy cladding (MZ25 and MZ50 of CNEA - Comisión Nacional De Energia Atómica of Argentina) were irradiated in RERTR-7. In this work, the plate MZ50 was considered and its irradiation behavior was simulated. Simulations were repeated for Al6061 to investigate the feasibility of replacing Al6061 with Zry-4.

Proceedings of the 2016 24th International Conference on Nuclear Engineering ICONE24

June 26-30, 2016, Charlotte, North Carolina

ICONE24-60120

1 Copyright © 2016 by ASME

2. FABRICATION PARAMETERS The plates were fabricated via co-laminating technique First step of plate fabrication is the alloy preparation. The alloy for the fuel meat (U-7Mo) was prepared by melting Uranium lumps and Molybdenum chips in a high frequency induction furnace at 1300 °C. Once melted, a coupon with the dimensions of 2×75×100 mm3 was formed in a vertical mold. Coupon was trimmed to 18×20 mm2 for lamination. The picture-frame technique was used for the hot rolling process. For this, U-7Mo meat is surrounded by a frame and two covers plates made of Zircaloy are assembled. Frame dimensions for the frame are 50×60 mm2 at the outer perimeter and 18×20 mm2 section cut at the center. Thicknesses for the frame and covers are 1 mm and 1.5 mm, respectively. The picture-frame assembly was then hot-rolled at 675 °C in eight passes via 150 mm rolls. After reaching desired thickness for the fuel, the plates were straightened and trimmed to final dimensions. Compared with a mini-plate, MZ50 had a thinner cladding and a slightly shorter foil. Dimensions of the final product and comparison with the nominal dimensions of mini-plates are in Table 1.

Table 1 MZ50 and mini-plate dimensions

Plate ID MZ50 [3] Mini Plate [mm] [mm] Fuel thickness 0.510 0.254 Fuel width 18.600 19.050 Fuel length 71.000 82.550 Cladding thickness 0.250 0.572 Plate length 101.00 101.40 Plate width 25.00 25.40 Plate thickness 1.010 1.398

3. IRRADIATION PARAMETERS

The plate MZ50 in position C4 was irradiated with edge-on flux configuration for 89.9 effective full power days (EFPD). Irradiation tests were carried out in two cycles. Volumetric heat generation, fission density, and local to average ratio (L2AR) of the fission density are summarized in Table 2 and Table 3. Fission power density in Figure 1a was expressed by piecewise linear functions and implemented via a user subroutine. The fission density (fd, [fis/m3]) was expressed as a function of the irradiation time (t, [hours]) and implemented as,

15 3 19 2 249.976 10 8.45( ) 1 10 1.086 10 d tf t t t (1) Local to Average Ratio (L2AR) of the fission density was implemented as a function of the foil width (x, [mm]) as,

6 6 5 5 4 42

3 3 2 2

( ) 0.529 10 3.10 10 7.039 10

7.95 10 5.075 10 0.236 1.658

L ARFD x x x x

x x x (2)

The local fission density in a specific coordinates at a specific time was calculated by the products of L2AR and fd and implemented as,

2, ( () )L ARlocal dFD x t f t FD x (3) Expressions in Eqn.1-3 were called for each material point. Comparison of actual experimental data with the numerical models that were used is shown in Figure 1.

Table 2 Fission and Power Density for MZ50 plate [2] Table 3 Fission rates (L2AR) in transverse direction [2]

RERTR-7A Cycle Breakdown

Fission Density

Fission Power Density

[days] [hours] [fission/cm3] [W/cm3]

136A

15 360 3.81E+20 8493.51 35 840 8.58E+20 7960.10

50.9 1221.6 1.22E+21 7594.75

136B

62.9 1509.6 1.48E+21 7334.79 76.4 1833.6 1.77E+21 7131.69 89.9 2157.6 2.05E+21 6888.12

Distance L2AR Distance L2AR Distance L2AR [mm] [-] [mm] [-] [mm] [-]

0 1.66 7 0.99 14 0.81 1 1.46 8 0.94 15 0.80 2 1.34 9 0.91 16 0.79 3 1.25 10 0.89 17 0.76 4 1.15 11 0.87 18 0.76 5 1.11 12 0.84 19 0.78 6 1.06 13 0.84

Figure 1 Irradiation parameters (a) Volumetric heat generation (b) Fission density (c) Fission profile (L2AR)


4. MATERIAL MODELS Material models that were used in this study are: U7Mo for the fuel, Zircaloy-4 (SRA), AL6061-O for the cladding and light water at 2.52 MPa for the coolant model. 4.1. U7Mo Material Model Conductivity model is based on the experimental data by Beghi [4] and Klein [5],

6 29.2511 10 0.0202 5.3930k T T (4) where k is thermal conductivity in (W/m-K), T is temperature in (°K). Valid temperature range is 294 ≤ T ≤ 1073 °K. Model for the thermal conductivity degradation of the fuel material was adapted from Hayes [6] as,

( 2.14 )0

Ppk k e (5)

where k0 is the thermal conductivity of the fully dense material, P is the porosity factor (valid for P ≤ 0.3) and kp is the thermal conductivity of the porous medium. The porosity factor P is,

0

0

( )

( ) 1g

g

V VP

V V

(6)

where (ΔV/V0)g is volumetric swelling due to gaseous products. The model for gaseous swelling is based on Kim [7].

0

1.0 d

f

Vf

V

fd ≤ 3×1027 fis/m3 (7)

2

0

3.0 2.3 ( 3) 0.33 ( 3)d d

g

Vf f

V

fd > 3×1027 fis/m3 (8)

where (ΔV/V0)g volumetric swelling (%) due to gaseous products, fd is the local fission density in ×1027 (fissions/m3). Gaseous swelling, thermal conductivity and localized conductivity degradation models are shown in Figure 2.

The model for the coefficient of thermal expansion is based on experimental data by Beghi [4],

2-7 -23.0426 10 1.0180 10 8.4696T T (9) where is the thermal expansion (1/°K), and T is temperature (°K). Valid temperature range is 294 ≤ T ≤ 873 °K. Density model is based on the data by Beghi [4] and Klein [5],

17391 0.884 T (10) where is density in (kg/m3), T is temperature in (°K). Valid temperature range for the model is 294 ≤ T ≤ 1083 °K. Specific heat model is based on the data by Beghi [4],

0.074145 114.46pC T (11) where Cp is specific heat in (J/kg-K), T is temperature in (°K). Valid temperature range is 273≤ T≤ 1273 °K. The model for the modulus is based on the data by Beghi [4].

2 50.018718 72.926 1.1084 10T TE (12) where E is the modulus of elasticity in (MPa), T is temperature in (°K). Equation is valid for 294 ≤ T ≤ 873 °K. Poisson’s ratio was adapted from [8] and it is constant 0.324. Plasticity model is based on the data by Beghi [4] and Klein [5].

6 3 3 21.272 10 2.430 10 2.428 1478.6y T T T (13) where y is yield strength in (MPa), and ), T is temperature in (°K). Valid temperature range is 300 ≤ T ≤ 866 °K. The irradiation creep model of the fuel is based on Kim [9],

A f (14)

where, is creep strain rate (1/sec), A is irradiation induced

Figure 2 (a) Gaseous swelling (b) Thermal conductivity model, k(f, T) (c) Normalized conductivity degradation


creep coefficient (500×10-25 cm3/MPa), is the equivalent stress (MPa), f fission density rate (fissions/cm3-sec). The model for the total fuel meat swelling due to fission products is based on the relation given by Perez [10]

2

0

23.87 7.27 ( 3) 0.374 ( 3)

d d

f

Vf f

V

(15)

where (ΔV/V0)f total volumetric swelling in (%) and fd is the local fission density in ×1027 (fissions/m3). The relation is valid for the fission densities below 8.21027 fissions/m3. 4.2. Zircaloy Material Model When available, physical, thermal and mechanical properties of Zircaloy were defined as functions of fast neutron fluence and temperature. Model for the elastic behavior is based on MATPRO [11] as,

11 71 2

3

1.088 10 - 5.475 10 )

T K KE

K

(16)

where E is modulus with random texture in (Pa), T is cladding temperature in (°K). Equation is valid for T ≤ 1090 °K. In equation, K1, K2 and K3 are modification factors. K1 (Pa) is for the effect of oxidation, K2 (Pa) is for the effect of cold work and K3 (unitless) is for the effect of fast neutron fluence. The models for the effects of oxidation, cold work, and fast neutron fluence are,

11 81 (6.61 10 5.912 10 )K T (17)

102 -2.6 10K C

(18)

3 250.880 0.12 exp(- )

10K

(19)

where Δ is change in average oxygen concentration, C is cold work ratio, is fast neutron fluence in (n/m2). For MZ50 model, the cold work ratio is assumed to be zero, as the plate was fabricated via hot rolling in multiple passes. Furthermore, change of oxygen concentration in Zircaloy-4 cladding was neglected as there is no reported experimental data. Various Poisson’s ratios are reported in literature. Whitmarsh [12] reports that Poisson’s ratio is 0.368-0.380 at 27 °C and 0.425-0.460 at 150 °C for annealed Zircaloy. MATPRO [11] reports a constant value of 0.300. Scott [13] reports that Poisson’s ratio changes linearly from 0.296 to 0.243 at 21°C and 400 °C, respectively. Schwenk [14] reports that Poisson’s ratio is 0.406 at room temperature and 0.412 at 316 °C. In this

work, the model for the Poisson’s ratio is based on the data reported by Schwenk [14] as,

-52 10 0.4056v T (20) where, is Poisson’s ratio, T is temperature in (°C). Valid temperature range is 21 ≤ T ≤ 316 °C. The model for the plastic behavior of Zircaloy-4 is based on MATPRO [11] and it was defined as follows,

310

mnK

(21)

where is true effective stress in (Pa), is effective plastic

strain, is rate of change of true effective plastic strain (s-1). Material parameters, K, m and n are defined as:

3 3 2

5 9

1.72752 3.28185 10

4.54859 10 1.17628 10

K T T

T

(T≤750 °K) (22)

10 3 6 2

3 2

9.588 10 1.992 10

1.165 10 9.49 10

n T T

T

(T≤1099 °K) (23)

0.02m ( T≤730 °K) (24)

Model for the thermal expansion was adapted from [12], and implemented as follows,

-6 -95.62 10 3.162 10 T (25) where is thermal expansion in (1/°C), and T is temperature in (°C). Valid temperature range is 26 ≤ T ≤ 1500 °C. Constitutive model for the volumetric swelling of Zircaloy-4 cladding due to fast neutrons was adapted from MATPRO manual [11] and implemented as,

240.8 0.5

(1 3 ) (1 0.02 )Tz

L A e t f CWL (26)

Where ΔL/L is fractional change in the length due to growth, A=1.407×10-16 (n/m2)0.5, T is cladding temperature (°K), is fast neutron flux (n/m2-s), t is time (sec), fz is texture factor (0.05 is typical [11]), CW is coefficient for the cold work. The cold work coefficient was assumed to be 0 for this work, as the plate was fabricated via hot rolling. The relation in Eqn.26 is for the axial growth of a tubular Zry-4 cladding. There is no available data for the growth of Zircaloy-4 for the plate type fuels. For this work, swelling of the cladding was assumed to be isotropic. Hence, the growth from the Eqn.26 was distributed equally into length, width and thickness directions of the cladding.


Creep model for Zircaloy-4 cladding was adapted from FRAPCON [15], which is based on a model given by Limback and Andersson [16]. The model uses a thermal creep model of Matsuo [17] and irradiation creep model based on the data reported by Franklin [18]. Thermal creep of Zry-4 was calculated according to,

sinhn Q

i effth R Tcr

aA e

E

(27)

Irradiation creep of the cladding material due to fast neutrons was calculated in accordance with,

1 20 ( )C Cirr

cr effC f T (28)

Total creep strain rate was calculated by the summation of the thermal creep and irradiation creep rates as follows,

total th irrcr cr cr (29)

In the equations above, thcr is the thermal creep strain rate

(1/hr), irrcr is the irradiation creep strain rate (1/hr), T is the

cladding temperature (°K), eff is the effective stress (MPa), R

is the universal gas constant 0.008314 (kJ/mol-°K), and is the fast neutron flux (n/m2-s). The variables A, E, ai, n, Q, Co, C1, C2, and f(T) are the material parameters [15]. Material parameters vary depending on the cladding type (SRA or RXA). For this work, Zircaloy cladding was assumed to be in Stress Relieved Annealed (SRA) condition. Resultant parameters are shown in Table 4.

Conductivity is based on the database by IAEA [19] as,

4 6 212.767 5.4348 10 8.9818 10k T T (30) where k is thermal conductivity in (W/m-K), T is temperature in (°K). Valid temperature range is 300 ≤ T ≤ 1800 °K. Specific heat is from [19], and expressed as,

-7 2 8 10 0.1015 255.88 pC T T (31)

where Cp is specific heat in (J/kg-K), T is temperature in (°K). Valid temperature range is 273≤ T≤ 1140 °K. Density [19] is,

6595.2 0.1477 T (32) where is density in (kg/m3), T is temperature in (°K). Valid temperature range is 294 ≤ T ≤ 1083 °C. 4.3. AL6061-O Material Model When available, physical, thermal and mechanical properties of Al6061-O were defined as functions the fluence and the temperature. Material model included irradiation hardening and growth due to fast neutrons. The properties for the material model of Al6061-O are discussed elsewhere [20] [21]. 4.4. Coolant Channel Model Models for the thermo-physical properties of the coolant were based on the property data reported by NIST [22]. Mathematical relations were developed for the nominal pressure; and thus, the models are valid for the water at 2.52 MPa. Valid temperature range for the models is 1-100 C.

Density was defined according to

5 3 3 2 31.46 10 5.664 10 3.318 10 1001T T T (33)

where, is density (kg/m3), T is the coolant temperature (C). The model for specific heat is implemented as,

6 4 4 3 2 22.462 10 6.120 10 6.169 10

2.459 4206

pC T T T

T

(34)

where, Cp is specific heat (J/kg-K), T is temperature (C). Thermal diffusivity model in accordance with

12 2 10 72.068 10 5.562 10 1.334 10T T (35)

where, is thermal diffusivity (m2/sec), T is temperature (C).

Table 4 Parameters for creep law for SRA Zircaloy-4 Thermal Creep

A 1.08×109 °K/MPa/hr

ai -27 1.3650 364 1 exp(-1.4 10 ) MPa-1

Fast neutron fluence n/cm2

E 51.149 10 59.9 T MPa

n 2 (-) Q 201 kJ/mol R 0.008314 kJ/mol-°K

Irradiation Creep

C0 4.0985×10-24 (n/m2.s)-C1.MPa-C2 C1 0.85 (-) C2 1 (-)

f(T) -0.7283 -7.0237+0.0136·T -1.4763

T<570 °K 570≤T≤625 °K

T>625 °K (-)


The model for the thermal conductivity is

6 2 39.565 10 2.147 10 0.5609k T T (36) where, k is thermal conductivity (W/m-K), T is temperature of the water (C). Kinematic viscosity was implemented as

14 4 12 3 10 2

8 6

3.009 10 8.433 10 9.291 10

5.321 10 1.758 10

T T T

T

(37)

where, is kinematic viscosity (m2/sec), T is temperature (C). Dynamic viscosity was formulated as

11 4 9 3 7 2

5

2.986 10 8.382 10 9.259 10

5.332 10 0.00176

T T T

T

(38)

where, µ is dynamic viscosity (Pa.s) and T is temperature (C). Prandtl number was calculated via Eqn.39 and represented in a polynomial form given in Eqn.40 as,

pPr Ck

(39)

where Pr is Prandtl Number, Cp is specific heat (J/kg-K), µ is dynamic viscosity (Pa.s), and k is thermal conductivity (W/m-K) and T is the temperature (C). Reynolds Number was calculated according to

Hv DRe

(41)

Where, Re is the Reynolds Number, is the density (kg/m3), v is the velocity (m/sec) and DH is the hydraulic diameter (m). Coolant velocities for the RERTR-7 are, 14.0 m/sec for the

inner channels and 10.8 m/sec for the outer channels. Channel schematics and the plate position are shown in Figure 3a. Hydraulic diameter (DH) was calculated via,

4H

AD P

(42)

where A is the cross sectional area and P is the wetted perimeter of the cross-section. For MZ50 plate in position C4, the channel widths are 2.581 mm for the inner channel (Channel 4), and 1.692 mm for the outer channel (Channel 5). The channel length is 22.555 mm. Nusselt number was calculated by Petukhov, Gnielinski correlation [23]. For fully developed turbulent and transition flow (Re > 2300), the Nusselt number is given by

1

22

3

Re 1000 Pr8

1 12.7 Pr 18

f

Nuf

(43)

where 0.5 ≤ Pr ≤ 2000 and 3000 < Re < 5×106 and f is the friction factor from the first Petukhov equation. Friction factor was calculated according to

20.790 ln( ) 1.64f Re

(44)

Finally, the heat transfer coefficient was calculated by

H

kh Nu

D (45)

where, h is heat transfer coefficient (W/m2-K), k is thermal conductivity (W/m-K), DH is hydraulic diameter (m), Nu is Nusselt Number. The coolant channel temperatures in Figure 3b and the heat transfer coefficient in Figure 3b were used for the definition of surface film condition and heat transfer calculations.

7 4 5 3 3 22.632 10 7.336 10 7.970 10

0.4396 13.13

Pr T T T

T

(40)

Figure 3 (a) Channel schematics and Plate MZ50 in C4 position (b) Coolant temperatures (c) Heat transfer coefficients


5. FINITE ELEMENT MODEL Irradiation process was modeled for 2157.6 hours (89.9 days). Time history was divided into 2 sub-steps for each irradiation cycles (136A and 136B). Irradiation cycle 136A was simulated for 1221.6 hours, and cycle 136B for 936 hours. To reduce the computational time, models took advantage of the symmetry conditions about the x-y plane (mid-plane). C3D8RT element of ABAQUS, an 8-node thermally coupled brick, tri-linear displacement and temperature with reduced integration and hourglass control, was used. Equally spaced 5 layers were used to represent the thickness of the foil. Nodal divisions along the length and width directions are 200 and 60, respectively. A total number element on the foil was 60000 bricks. For the cladding, the thickness was represented by 10 layers. The nodal divisions along its length and width directions are 270 and 80, respectively. The total number element on the cladding was 156000. Meshed model contained 216000 hexahedral and 256322 nodes. Resulted finite element discretization and the plate dimensions that were used are shown in Figure 4. It was assumed that the bonding between the foil and the cladding are ideal and there are no defects prior the irradiation process. It was also assumed that no interfacial debonding occurs during the irradiation. Thus, all nodal points at the foil- cladding interfaces were tied together. On the mid-plane, a symmetry condition was assigned to corresponding nodes. The plate was modeled as free to move in all direction, except on edges. Plate edges along the lengthwise directions were constrained; allowing sliding only motion to simulate the mechanical restrictions resulted by the grooves in the capsule. A single node at the lower right corner of the plate was fixed to prevent rigid body motion. Irradiation parameters, fission profile (L2AR), average fission density, fission power density, fast neutron flux and fast neutron fluence in were implemented via user subroutines.

The utility routine, USDFLD was created to define the local fission density within the fuel foil with respect to the spatial coordinates and the irradiation time as formulated in Eqn.1-3. This subroutine was also used to define the fast neutron flux and fluence and was called in material points to calculate the irradiation hardening behavior of the cladding material. The volumetric heat generation of the fuel foil was defined as a body heat flux in the model. This thermal load was calculated by using the local fission density calculated in USDFLD routine and it was called for each material point of the fuel foil. Thermal conductivity degradation the fuel foil (Eqn.5) was also included in this utility subroutine. For this, gaseous swelling (Eqn.7-8) and the porosity (Eqn.6) was calculated and the conductivity (Eqn.4) of the fuel material was degraded as a function of the local fission density. Constitutive relations for the Creep-swelling-viscoelastic behaviors of the materials were defined in the ABAQUS user subroutine CREEP. In this subroutine, (1) irradiation creep and volumetric swelling of the foil, and, (2) thermal creep, irradiation creep and swelling of the cladding material due to fast neutrons were implemented accordingly. Mathematical relations were discussed previously in Sec.4.1 and Sec.4.2. Heat transfer between the plate surface and the primary coolant were simulated via surface film condition. The film condition was created on the plate surface and reported coolant channel temperatures were used for the sink definition. An interaction property was created by using the calculated film coefficient as formulated in Sec.4.4. A fully coupled temperature-displacement transient solver with swelling-creep behavior was employed. An explicit/implicit scheme was used for the creep/swelling integration. The maximum time increment per step was set to be 24 hours and temperature increment per step was limited with 5 °C to avoid numerical instabilities. Thermal load variation with time was set to be linear ramp over the step.

Figure 4 (a) Model geometry for the plate MZ50 (b) Half symmetric model and discretization


6. RESULTS AND DISCUSSIONS

6.1. Temperature Fields Peak temperatures during the transient are in Figure 5a, and temperature profiles at the mid-plane are shown in Figure 5b. From the figures, the peak is at the fuel centerline and is roughly 190 °C. The results indicate a slight increase in centerline temperature during irradiation. This increase is

caused by conductivity degradation of fuel and a thickness increase caused by swelling. Using a non-linear geometry via fully coupled a thermal-structural interaction is essential for the accuracy. Ignoring the displaced dimensions and using the initial ones may lead to inaccurate temperature predictions. In Figure 6, temperature contours at the end of irradiation (before shutdown, the plates at power) are shown. The peak temperatures are 102 °C at the cladding surface, 158 °C at the interface and 192 °C at the fuel centerline.

Figure 5 (a) Peak temperatures during the irradiation (b) Temperature profile at the mid-plane of the plate for the end of irradiation

Figure 6 (a) Temperature [°K] fields, end of irradiation before shutdown, (Cycle 136B, 89.9 days, at 6888.12 [W/cm3]), contours are showing: (a) Cladding surface temperature (b) Foil-cladding interface temperature (c) Fuel centerline temperature


6.2. Stress and strain fields Simulations indicated presence of large residual stresses due to the fabrication process. The stress magnitudes were 559 MPa in fuel and 535 MPa in Zry-4 cladding. This stresses are significantly greater that those in plates with Aluminum cladding. Because pre-irradiation stresses were significant, fabrication stresses were used to define an initial state for the irradiation

simulations. In particular, residual stresses from the fabrication simulations were applied to the corresponding nodes. Figure 7 shows variation of equivalent stresses during irradiation. In the figure, a sudden stress relief at startup can be seen. This stress reduction is as a result of a temperature increase at the startup. Examination of the results revealed that post fabrication stresses in the fuel material would be relieved quickly and the foil would be essentially stress-free during the irradiation. The stresses however, would develop at shutdown as shown in Figure 7. Unlike fuel material, stresses continue to increase in the cladding material. This increase is caused by the strains as a result of volumetric swelling of the fuel. Additional stresses are also created by the growth and irradiation hardening of Zircaloy. Figure 8 shows equivalent stress fields in the fuel and the cladding materials. End of life stresses of the fuel material is small due to large creep strains (Figure 8a). The peak stress is 6 MPa before the shutdown. The fuel stresses suddenly increase to 168 MPa at shutdown (Figure 8b). The peaks are closer to the fuel edge, where pre-shutdown temperatures are the highest. The shutdown stresses in the cladding material is significantly higher, reaching to roughly 620 MPa (Figure 8c).

Figure 7 Peak equivalent stresses [MPa] during irradiation

Figure 8 Equivalent stress [MPa] fields for the foil and the cladding, contours are showing: (a) Foil, end of irradiation (89.9 days, at 6888.12 [W/cm3],) (b) Foil, end of shutdown (c) Cladding, end of shutdown


6.3. Case studies: Effects of the cladding type To make a comparative evaluation to assess the feasibility of using Zry-4 instead of Aluminum, the simulations were

repeated for Al cladding. Same irradiation parameters and geometric dimensions were used. To assess the performance, four primary variables were comparatively evaluated. In figures 9-12, temperature, displacement, stress and strains are

Figure 9 Temperature profiles at the end of irradiation (a) Foil core (b) Foil-cladding interface (c) Cladding surface

Figure 10 Swelling and displacement profiles (a) Volumetric swelling (b) Final foil thickness (c) Final plate thickness

Figure 11 Stress and pressure profiles (a) Equivalent stress in the foil (b) Pressure on the foil (c) Equivalent stress in the cladding

Figure 12 Strain profiles in cladding (a) Equivalent plastic strain (b) True strain at the interface (c) True strain at the surface


comparatively evaluated. Temperature profiles in Figure 9 indicate that Zircaloy cladding causes the fuel centerline temperatures increase roughly 50 °C. This is due to a lower thermal conductivity of Zircaloy compared with Aluminum. Displacement behaviors of the plates are shown in Figure 10. Even though the swelling profiles are similar, the peak magnitudes in the bulged regions would be slightly greater, if Zircaloy cladding is used. Equivalent stress profiles at mid-plane of the plates are shown in Figure 11. Equivalent stresses at the reactor shutdown are seen in Figure 11a. The results indicate that Zircaloy cladding causes the foil stresses increase significantly at shutdown. The stress magnitudes in the fuel reach to 160 MPa, while they are significantly lower, if Aluminum cladding is used instead. A similar trend is seen for the hydrostatic pressure in the fuel. Pressure magnitudes are greater for the case with Zircaloy cladding. Similarly, stresses in the cladding are considerably lower for the case with Aluminum cladding. Finally, strain profiles for the cladding materials are compared in Figure 12. From figures, higher plasticity was observed for the cases with Aluminum cladding. 7. CONCLUSIONS In this work, effects of the cladding material type were studied. For this, a selected plate with U7Mo foil and Zry-4 cladding was simulated to explore feasibility of using Zircaloy as a surrogate cladding material. In particular, a selected mini-plate from RERTR-7 tests was simulated first by using as-run irradiation history. By using same irradiation parameters, a second case, a plate with U10Mo fuel and Al6061 cladding was simulated to make a comparative assessment. Plates with Zircaloy cladding would operate approximately 50 °C hotter. This is due to the lower thermal conductivity of Zircaloy compared with the conductivity of Aluminum cladding. Zircaloy cladding would also have slightly higher displacements in the thickness direction. In both cases, the equivalent stresses in the fuel material would be negligible during irradiation. The stresses however, would develop at the shutdown stage. The plate with Zircaloy cladding would have higher residual stresses due to higher pre-shutdown temperatures. The stresses are higher in the foil core for the plates with Zircaloy cladding. While the fuel has a compressive stress state, the magnitudes are considerably higher at shutdown if Zircaloy is used as cladding. Higher plasticity would occur for the plates with Aluminum cladding. Overall, employing a Zircaloy as surrogate cladding material did not provide a better irradiation performance compared with the Aluminum cladding, as the plates with Zircaloy cladding resulted higher operating temperatures, higher shutdown stresses and slightly higher displacements.

ACKNOWLEDGMENTS This work was supported by the U.S. Department of Energy, Office of Nuclear Materials Threat Reduction (NA-212), National Nuclear Security Administration, under DOE-NE Idaho Operations Office, Contract DE-AC07-05ID14517. The U.S. Government retains a non-exclusive, royalty-free license to publish or reproduce the published form of this contribution, or allow others to do so, for U.S. Government purposes. REFERENCES [1] J. L. Snelgrove, G. L. Hofman and M. K. Meyer,

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