Intergranular fracture of unrestructed UO2 fuel, during film-boiling operation

Journal of Nuclear Materials 84 (1979) 295-318 0 North-Holland Publishing Company

INTERGRANULAR FRACTURE OF UNRESTRUCTED UO2 FUEL, DURING FILM-BOILING OPERATION A.W. CRONENBERG and T.R. YACKLE Thermal Fuels Behavior Progrum, EG&G Idaho, Inc., P.O. Box 1625. Idaho Falls, ID 83401, USA Received 28 December 1978

Extensive grain-boundary separation has been found to occur within the unrestructured region of UOs fuel pellets as a result of in-pile testing of nuclear fuel rods to elevated temperatures at which fiim boiling occurs. Since, in general, the grain size in the unrestructured region is only about 5 microns in diameter, unrestructured fuel experiences grain-boundary separation has been commonly referred to as powdering fuel. Because fuel in such a condition will result in a loss of pellet stmctural integrity, an understanding of the cause of powdering is of interest to the overall assessment of thermal fuel behavior under postulated accident conditions, where film boiling leading to high fuel temperatures occurs. This paper examines the experimental conditions under which grain-boundary separation of fine-grained umestructured fuel has been observed and presents calculations demonstrating that such gram-boundary separation (intergranular fracture) can be explained by the combination of a severe loss of grain-boundary strength at the elevated temperatures experienced during film boiling and the high tensile stresses induced by requenching of fuel rods from such a high-temperature condition; thus, resulting in a desintering of unrestructured fuel to a powdery form.

1. Introduction

event of cladding rupture, an understanding of the factors influencing powdery fuel formation is of interest to the overall assessment of fuel behavior under accident conditions where film boiling may occur. The purpose of this paper is to review the metallurgical nature of such powdery fuel, the experimen tal conditions under which it has been observed, and the factors considered to be the cause of such grainboundary failure in previously sintered fine-grained U02 fuel.

In-pile fuel behavior experiments for off-normal heat-transfer conditions are being performed by EG&G Idaho, Inc., in support of the Nuclear Regulatory Commission’s Water Reactor Safety Research Fuel Behavior Program. Assessment of fuel rod mechanical performance and metallurgical changes, as a consequence of testing at elevated temperatures at which film boiling occurs, is a part of this program. One of the fuel behavior phenomena that has been observed during film-boiling testing of pressurized water reactor (PWR)-type fuel rods, is extensive grain-boundary separation (intelgranular fracture) within the inner portion of the unrestructured fuel region; as illustrated in fig. 1 [ 11. Since the grain size of the tested fuel, in the unrestructured region is approximately 3 to 5 m in diameter,.unrestructured fuel experiencing extensive grain-boundary separation has been referred to as powdery fuel [2]. Because such finely-fragmented fuel has limited structural integrity and may relocate from its original position, including washout into the coolant stream in the

2. Experimental findings Extensive grain-boundary fracture in unrestructured fuel has been observed in several fuel rods tested under various simulated power or coolant accident conditions during which film boiling occurs. The rods were tested singularly or four at a time in the power burst facility (PBF) within an in-pile tube, with each rod contained in its own coolant flow shroud. Seven power-cooling-mismatch (PCM) tests 295

296

A. W. Cronenberg,

T.R. Yackle / Intergranular fracture of unrestructured Unrestructured fuel -

I-

,,s pollshed

Final molten fuel boundary

L

Initial

High density,

Fig. 1. Metallographic illustration of a typical fuel microstructure powdering of unrestructured fuel.

were run in the PBF, all with unirradiated fuel rods. In addition, six irradiation effects (IE) tests were run with both previously irradiated and unirradiated fuel rods. The results of such experiments indicate that extensive grain-boundary separation is sometimes observed at the interior annulus of unrestructured fuel or both previously irradiated and unirradiated fuel. Although transgranular or intragranular fracture * (across or through grains) usually occurs during normal power cycling of reactor fuel elements, extensive intergranular fracture (at or around grain boundaries) in the unrestructured region of U02 fuel elements has not been observed, to the knowledge of the present investigators, for fuel elements operated under normal conditions, except at relatively high burnup levels (i.e., in excess of 3 at%) where fission gas bubble accumulation at grain boundaries has been shown to result in grain-boundary separation [3]. However, the only evidence known for the occurrence of grain-boundary failure for unirradiated fuel is that resulting from in-pile testing of fuel rods under film* Although the usual mode of fracture is transgranular, intergranular fracture often accompanies such transgranular (also called intragranular) fracture.

molten

(102 fuel

I

fuel boundary

200 pm

large grain fuel

for unirradiated fuel which experienced film boiling and

boiling conditions in the PBF test series. To determine whether grain-boundary separation in unrestructured U02 is peculiar only to the fuel tested in the PBF test series, or whether it might be a general consequence of U02 fuel rods subjected to film-boiling operation, several factors are addressed. Such factors include fuel-fabrication characteristics, microstructure and irradiation history, and experimental requenching conditions. Such effects are discussed in this section; however, a description of the nature of powdery fuel is first presented. 2.1. Nature of powdery fuel Fig. 2 [4,5] illustrates that powdery fuel is essentially unrestructured fuel which has undergone extensive grain-boundary separation. The fragmentation size is approximately 3 to 5 pm * in diameter, which is characteristic of the grain size of as-fabricated, un-

* Remnant fuel from the powdery zone indicates, that aggregates of sintered unrestructured fuel are also found, such that complete grain-boundary separation does not always occur, although an extensive amount of fines (individual granular fuel) is found. However, no population assessment with respect to size has been made.

A. W. CronenbeB, TX. Yacklef Inter~anu~r

291

fractureof u~esr~e~red UC+fire1

grains exhibiting intergranular fracture, epoxy does not penetrate between grains; thus, resulting in fallout during metallographic-mount preparations. This residue fuel from the unrestructured region has been given the name powdery [1,2,5 J or disintered fuel and is the subject of this paper [6]. In summary, powdery fuel is characterized as finegrained unrestructured fuel exhibiting extensive grain-boundary separation with an eroded surface indicating a grain-boundary sliding mode of fracture. However, because no population assessment with respect to size has been performed to date, exact size characterization of the powdery fuel can not be made. Although aggregates are found to accompany powdery fuel, a significant amount of such fuel is fragmented to an as-fabricated grain size of about 3 to 5 pm in diameter. 2.2. Effect of fuel fabrication process The fuel used in the PCM test series was unirradiated enriched UOZ, fabricated by Gulf United Nuclear Fuel Corporation [7] (GUNFC) to rigid Polished Fig. 2. Unrestructured-powdery

fuel interface.

Table 1 Fuel rod characteristics for the PCM and IE test series GUNFC-fuel [S ] (PCM-series)

restructured fuel. A similar fragmentation size is found for previously irradiated rods. However, because similar grain-boundary separation occurs for previously unirradiated fuel, subject to equivalent film-boiling testing conditions, fission-gas bubble release does not appear to primarily influence the observed intergranular separation. Fig. 2 [4,5] also illustrates the fact that the grain boundaries of powdery fuel have rounded or eroded surfaces in comparison with the sharp-edged boundaries for unrestructured fuel in an as-frabricated condition, indicat~g a ~id~g-ductiIe mode of failure at the grain boundaries. For film-boiling operation, similar intergranular fracture is also noted in the equiaxed region. However, since the average grain size is approximately 30 to 40 pm in this region, and since the epoxy used in metallograp~c-mount preparation can penetrate the space between these larger grains, equiaxed fuel which has undergone extensive intergranular fracture has not been referred to as powdery fuel. However, for smaller

Saxton-fuel [6] (IE-series)

Fuel: Uoz.o Fabrication process Oxygen/uranium ratio Density Pellet diameter (cm) Moisture (ppm) Impurities (ppm)

Average fuel grain size (unrestructured zone) @m)

Sintered 2.002 f 0.0002 (10.10 f 0.17)g/cm3 0.929 i 0.0013 1.4 385

3.0 to 4.0 a)

Sintered 2.00 * 0.003 94% theoretical density 0.853 i 0.005 5 Depending on irradiation l&tory 3.5 to 5.3

Cladding: Zircaloy-4 Inside cladding radius (cm) Outside cladding radius (cm) a) Unpublished data.

0.4750

0.4375

0.5360

0.4997

A. W. Cronenberg, T.R. Yackle / Intergranular fracture of unrestructured

298

(102 fuel

Table 2 Summary of fuel behavior results for IE and PCM tests Test

Rod number

Powdering

Previous irradiation history

Fuel type

Peak’power in filmboiling

Time *) in fdm-boiling (s)

Mass flux in filmboiling (kg/m2 *s)

Rod failure during experiment

67

288

2090

b)

55 61 61 61

None None 60 90

-

No No

1280 1414

bNp

68 63 64 64

72 60 60 60

2520 1600

b) 4

2030

No

65 65 62 61

90 90 90 90

2550 2650 2750 2750

No No No No

71 65 71 62

70 70 70 70

2110 2160 2290 2100

b) No No No

62 68 63 69

70 70 70 80

1190 1210 1100 1265

d No

bN,”

80

660

1383

b)

60

1397

No

W/m) IE-ST-l

IE-001

Yes

No

IEST-2

IE-002 IE-004 IE-005 IE-006

No No No

No No

No

No

IE-1

IE-2

Ie-007 IE-008 IE-009 IE-010

No

Yes

Yes

No No

Yes Yes Yes

No

Saxton

Yes

No

No

No

No No

No No

IE-015 IE-016 IE-017 IE-018

Yes Yes No

Yes Yes

IE-019 IE-020 IE-021 IE-022

Some dl Some N/A f) N/A

No No No

”

PCM 8-l RS

UTA-0004

Yes

No

UnitedNuclear

PCMCHF-ST

UTA-0005

No

No

63

PCM 8-1 RF

UTA-0006

No

No

61

30

407

No

PCM-2A

UTA-0007

No

No

58

210

827

No

PCM-2

UTA-0008 UTA-0009 UTA-0010 A-0014

No No No No

No

50 53 51 50

105 52 50 50

775 920 980 905

No No No No

UTA-00 11 UTA-0013 A-0015 A-0021

No No No No

49 51 53 49

60 None 60 60

855 880 779 1000

No No

UTA-0014 UTA-0015 UTA-0016 A-0017

No No No No

71 67 68 70

115 160 130 120

1862 1848 2027 2044

No No No No

IE-3

IE-5

PCM-3

PCM-4

*) b, c) d, e, f) g)

IE-011 IE-012 IE-013 IEXtl4

Yes

Yes Yes

No

No No

No No No

No No No No

No No

Time that the indicated cladding surface temperature exceeded 730 K. Failed after shutdown. Hydride faihue during test. Highly irregular fallout, such that no radius of powdering was assessed. Rod failed during departure from nucleate boiling. Fuel analysis not available. Rod failed during test.

ii?

A. W. Cronenberg, T.R. Yackle / Intergranular fiacture of unrestructured UOz fuel

specifications to assure controlled fuel pellet characteristics during the entire series of the PCM experiments. The fuel pellets used in the IE test series were either unirradiated or irradiated enriched UOZ Saxton fuel [8] which was designed by Westinghouse Electric Corporation for use in a small prototype, pressurized water reactor located at Saxton, Pennsylvania. Table 1 lists the appropriate fuel pellet data for both test series. Since powdering occurred for both fuel types, fragmentation is apparently independent of some peculiarity of the fabrication process. 2.3. Effect of microstructure and irradiation history The as-fabricated gram size is generally uniform across the fuel-pellet radius and characteristically about 3 to 5 pm in diameter. However, some fuel restructuring occurs rapidly for fresh fuel at the elevated temperatures experienced during film boiling, whereby well-developed, equiaxed and sometimes. columnar grain-growth regions form. Such’iapld“’ restructuring has been observed for fresh UOZ fuel operated in film boiling for about 75 s [4]. Table 2 presents a summary of all fuel rods tested under film-boiling conditions in the PCM and IE test series. Comparison of columns three (powdering) and four (previous irradiation history), reveals that both previously unirradiated and irradiated fuel rods exhibited powdering, indicating that irradiation history may not primarily influence such powdering. However, it should be noted that voids or fission-gas bubbles would tend to weaken grain boundaries and, therefore, somewhat enhance the formation of powdery fuel. Indeed grain-boundary separation in unrestructured irradiation UOz fuel has been observed in the direct electrical transient heating experiments conducted at Argonne [9]. 2.4. Effect of power level during film boiling Inspection of table 2 indicates that, in general, fuel operated in a film-boiling condition at relatively high power levels exhibits powdering, whereas, for low power film boiling operation such powdering is not observed. Therefore, it is hypothesized that the inner annulus of the unrestructured fuel region, during high-power operation in film boiling, reaches elevated temperatures at which significant loss of grain-bound-

299

ary strength results, such that extensive intergranular fracture occurs, the initiator for such fracture being thermal stresses upon requenching *. Although requenching thermal stresses are also significant at the outermost radius of the fuel pellet, this region remains intact since the temperatures are sufficiently low such that the intergranular cohesive strength is high enough to resist thermal-stress-induced failure at the grain boundaries. To quantify the hypothesis of thermally-induced loss of grain boundary strength and the generation of requenching thermal stresses which exceed such grain-boundary strength, specific factors are assessed, including: (1) general strength characteristics for fine-grained UOZ fuel; (2) grain boundary strength of sintered UOZ fuel as a function of temperature; (3) principal stresses within the fuel during requenching from film boiling; (4) radial temperature distribution and corresponding local fracture mode within the fuel pellet during film boiling. The general strength characteristics for fine-grained UO? fuel and the grain-boundary strength of sintered UOZ fuel as a function of temperature are addressed in the following section while an assessment of the requenching stresses and radial temperature distribution during film boiling and the resultant local temperature-dependent fracture mode are presented in the analysis and calculational results section.

3. Fuel strength and fracture characteristics Before the hypothesis can be assessed that extensive grain-boundary fracture occurs at the interior annulus of unrestructured fuel due to a combination of high temperatures and thermal stresses upon requenching, the effects of temperature and the strength characteristics of UOZ must be quantified. First, however, an

* Althoughother stressinitiators such as cladding restraint during fuel expansion, cladding collapse, and differential fuel expansion or contraction during power cycling can lead to to stressing of the fuel pellet during various stages of fiiboiling testing, the requenching stresses are probably the most severe over the film-boiling testing sequence.

300

A. W. Cronenberg, T.R. Yackle / Intergranular frccture of unrestructured IJO fuel

Equicohesive temperature \I

i

Iemperarure Fig. 3. Illustration of grain strength (intragranular) versus grain-boundarystrength(intergranular)as a function of temperatures, fo; typical polycrystiine metal; and ceramics.

overview of the general strength characteristics of polycrystalline ceramics is presented. 3.1. General strength chamcteristics of polycrystalline ceramics The normal mode of fracture for ceramic materials at low temperatures is transgranular. However, as is true with polycrystalline metals, ceramic strength properties are likewise increasingly influenced by grain-boundary conditions at elevated temperatures where the strength of grain boundaries is decreased. At temperatures higher than the recrystallization temperature (normally defined as the temperature at which a cold-worked ahoy completely recrystallizes in about one hour [lo]), the interior forces holding an individual grain intact exceed those at the grain boundaries; thus; fracture at elevated temperatures is generally intewanular, whereas at low temperatures it is intragranular. The nature of fracture with respect to temperature is illustrated in fig. 3, the temperature of intersection often called the “equicohesive temperature ” [ 111. To assess the nature of grain-boundary strength, a comparison of metals with ceramics is meaningful.

As would be expected, the bonding of atoms in crystals depends very strongly on interatomic spacing. Since the atomic spacing at grain boundaries is disturbed, the strength at the grain boundaries can be expected to be less than the strength within the more compact crystal itself. This effect is small in metals because the cohesive energy is insensitive to exact atomic arrangement, (since metals have loosely bonded electrons which results in longer range interactions), whereas covalent-bonded ceramic crystals (with shorter range forces) are more sensitive to atomic arrangement. Such an effect may account for the fact that ceramic materials fracture intergranularly more commonly than metals. However, the effects of plastic flow and impedement of dislocation movement at grain boundaries also have a pronounced influence on the strength of ceramics. Such effects as porosity (e.g., fission-gas bubbles for irradiated fuel *), gram size, stoichiometry, strain

* As discussed in refs. [ 31 and [ 91, grain-boundary separation for irradiated fuel in excess of 3% bumup has been observed due to fusion-gas bubble migration to grain boundaries, resulting in a-weakening of grain strength and resultant intergranular fracture.

301

A. W. Cronenberg, T.R. Yackle / Intergranular fracture of unrestructured 1102 fuel

3.2. Fracture strength of UO, versus temperature

rate, temperature and impurity type, content, and location, are all known to affect the fracture strength in addition to fabrication mfluences. A discussion of these factors, as they relate to the general strength characteristics of ceramics, can be found in refs. [ 12-151. However, because such influences cannot be easily quantified, an a priori quantitative assessment of material strength from an atomic view has, to date, not proven successful for engineering applications. As a result, the study of material strength is, at present, essentially empirical in nature. An assessment of the fracture strength and mode, for fmegrained unrestructured UOz, is therefore, based on experimental evidence and is presented in the following section.

16OC

I

The effects of temperature, grain size, and strain rate on the fracture strength of UOz [ 161 and mixed U-F’u oxides [ 17,181 have been investigated using the four-point bending technique. The general characteristics of sintered ceramic fuel fracture are as indicated in fig. 4. At low temperatures, fracture is characteristically brittle and intragranular, whereas fracture at high temperatures is ductile and intergranular, with brittle-to-ductile transition occurring at approximately 1900 K for the stated gram size and strain-rate conditions. Fractography for U--F%oxide fuel [ 17,181 is illustrated in fig. 5, indicating that transition from

I

I

I

14oc

-Brittle - mgranular c~DuctiIef;a~~ranuIar-

fracture

i 200 ogb>“g

ag>“gb

\ \ \

\ \ Strain rate 2 9.2/h Grain size z 8 pm -

-

-

-

Extrapolated

TransItIon or equicohesive temperature

\ I

1300

I

‘1600 Temperature

\r 1900 (K)

I 2200

IO

Fig. 4. Ultimatetensilestrengthof sinteredUO2 as a function of temperatureillustrating that low-temperature fracture is introgranular while high-temperature

fracture is intergranular (where uab is grain boundary strength and oB is intragranular strength).

A. W. Cronenberg, T.R. Yackle / Intergranularfracture of unreetructured UO2 firer

302

a Fig. 5. Factography of a mixed-oxide fuel, illustrating the effect of temperature on fracture mode (courtesy of Argonne National Laboratory). (a) 14.5 urn GS, T = 500°C (i.e.
b

Table 3 Ultimate tensile strength and fracture mode of UO2 fuel at a grain size of 8 pm and a strain rate of 9.2/h Ultimate tensile strength (lo6 kg/m2)

Temperature (K)

14.0 14.2 14.3 14.4 14.5 12.0

1473 1573 1673 1773 1873 1973

11.0

10.0 9.0 7.5 6.0 4.5 4.0

__m______..___

-2073

Fracture mode

T Brittle

(intmgrmular) Trar?? ____________

Ex~ap,-&&d ___.-------:

2173 2273 2373 2473 2573 2673

Ductile (intergranular)

” a) Estimated from fa. 11.

_-_----

I

-v-m-

A. W. Cronenberg, T.R. Yackle /Intergranular fracture of unrestructured iJO fuel

brittle-to-ductile failure can be correlated with a change in fracture mode. Similar fractography is expected for U02, which has similar strength characteristics. Fracture below TEc is transgranular, as evidenced by the random distribution of cleavage steps, with no obvious signs of plastic deformation. Above TEC, the fracture is intergranular with an eroded and rounded grain surface, indicating grain boundary sliding and plastic flow. Table 3 summarizes the estimated fracture strength and mode versus temperature, where the highest experimental strain rate (9.2/h) data were used [ 16,171 since the fuel strain rates upon requenching are estimated to be approximately 29th. [ 191. To assess whether or not fracture can be expected, the ultimate tensile strength is compared with the tensile thermal stresses estimated to occur as a result of requenching from film boiling, whereas the mode of fracture is assessed from a knowledge of the actual temperatures experienced within the fuel. In the following section estimates of the thermal requenching stresses and fuel-rod temperature conditions (for film boiling) defining the fracture mode are presented.

4. Analysis and calculational results To assess the temperature histories (and resultant thermal stress conditions) experienced by the PCM and IE test fuel rods during high-temperature filmboiling operation and requenching upon termination of film boiling, the FRAP-T4 [20] code for light water reactor oxide-fuel transient analysis was used. The analysis is essentially divided into two sections. The radial tem~rature profiles calculated by the FRAP-“14code, during requenching from film boiling, are first evaluated and used as initial conditions for assessment of the resultant thermal stresses, based upon elastic stress theory. Such radially dependent thermal stresses are then compared with the temperature-dependent strength properties of UOZ, (which are also radially dependent due to the high thermal gradient experienced by ceramic fuel), in order to identify the fracture mode. The radial temperature profile is determined for each individual test fuel rod, based upon a knowledge of the film-

303

boiling thermal conditions for that particular rod. ~ter~~ular ductile-type fracture is predicted for fuel radii assessed to experience both temperatures in excess of TEC and tensile stresses greater than the ultimate tensile strength. However, for fuel radii assessed to experience low temperatures, transgranular brittle-type fracture is predicted (if the tensile stresses upon requench~g are greater than the ultimate tensile strength of the fuel). Such predictions of the fracture mode are finally compared with the experimentally observed fracture characteristics of the various test fuel rods. 4. I, Assessmen f of thermal stresses during req~en~~~ng In the present analysis, film-boiling operation is assumed to be sufficiently long (one minute or greater) and fuel pellet temperatures sufficiently high (at or near melting at the centerline), that plastic flow results in significant stress relief during fern-boiling operation. This situation is justified by calculations in which the time for stress relief by creep flow is estimated to be approximately one minute [ 191, which is similar to the film-boiling times for most of the experiments. The tem~rature profile during fnm boiling, just prior to requenching, is thus considered to be an unstressed state of the fuel pellet. Upon coolant requenching of the fuel rod, the radial, tangential and axial stress components in the fuel and cladding due to differential shrinkage are computed, under the normal assump tion of an ~isymmetric stress field about the central, axis. At high temperatures, inelastic behavior is expected for ceramic materials [21-231. However, it has been demonstrated that for rapid strain rates (due here to sudden temperature changes), the elastic limit can be increased by 100% or more [24], thus increasing the range of elastic behavior. The strain rates due to requenching from a ffim-boiling condition are of sufficient magnitude that such an increase in the elastic range can be expected. In addition, it has been shown 12%281 that stress calculations based on elastic analysis with tem~rature-dependent properties normally correspond to the upper value of inelastic stresses due to finite viscoplastic flow of materials at elevated temperatures. Thus, elastic analysis with temperaturedependent properties appears reasonable for order-ofmagnitude estimates of the thermal stresses, where the

304

A. W. Crone&erg, T.R. Yockle / Intergmnular fracture of unrestructured UOs fuel

Table 4 Mechanical properties of UOz and zircaloy used in thermal-stress calculations Property

Relation

Symbol

UO2 fuel Poisson’s ratio

”

Modulus of elasticity (Psi)

E

0.4

Zircaloy cladding 0.3 14.57 x lo6 - 6.85 XlO’T(K)

Coefficient of thermal expansion (1PF)

elastic modules, E(T), and the coefficient of expansion, a(T), are taken to be temperature dependent (table 4) and Poisson’s ratio (u) is taken to be constant. The analysis of thermal stress in a cylinder in which

/

” t

Fig. 6. Model for principal thermal stresses in a cylindrical shell.

material properties and temperature vary radially is simplified by considering the cylinder to be a composite of subcylinders. An illustration of the model is shown in fig. 6 while the relevant stress equations are presented in appendix A. To numerically estimate the thermal stresses generated due to requenching from film boiling, the temperature history experienced by a typical test-fuel rod must be assessed. The temperatures predicted by the FRAP-T4 [20] code for the IE-3-16 fuel rod during film boiling and requenching are considered typical of temperatures experienced by the various fuel rods tested in film boiling. A listing is presented in table 5 of such estimated temperatures. Considering the last time step for film boiling, predicted by the FRAP-T4 code, as an unstressed state and assuming no stress relief over the entire requenching period, the stress conditions can be estimated at various time intervals after commencement of requenching. Fig. 7 illustrates the resulting estimated stresses for three time intervals after commencement of requenching, that is, 50 ms (Ti to T2), 1.12 s (Ti T3), and 2.7 s (Tr - T4). As can be seen, the outer portion of the fuel radius is initially subjected to tensile stresses in both the axial and tangential directions and are predicted to be on the order of about lo8 kg/m2 for the initial 50 ms time period chosen (Ti to Tz). If a one-second period is chosen (that is going from temperature Ti to T3), the location of maximum tensile stress moves radially inward due to thermal penetration of the requenching front. However, the stresses remain high (80 X lo6 kg/m2) assuming negligible stress relief after this time period.

305

A. W. Cronenberg, T.R. Yackle / Intergranular fracture of unrestructured UOQfiel

do t

i

I I

I

-12eo

’

’

1

’

’

2

’

’

Radiw ,mm2

’

’

.

1’

Fig. 7. Illustration of principal stresses predicted upon requenching from an unstressed fdm-boiling condition, assuming no stress relief over the requenching period.

i I

s

A. W. Cronenberg, T.R. Yackle / Intergranularfracture of unrestructured UOz fuel

306

Table 5 Radial temperature distributions calculated from the FRAP-T4 code, as a function of requenching time for a typical IE fuel rod requenched from film boiling by power reduction Region

Fuel Fuel Fuel Fuel Fuel Fuel Fuel Fuel Fuel Fuel Fuel

Fuel Fuel Fuel Fuel Fuel Fuel Cladding Cladding Cladding

Radius (mm)

0

1 2 3 3.102 3.203 3.305 3.406 3.508 3.609 3.711 3.812 3.914 4.015 4.117 4.218 4.320 4.366 4.666 4.966

Last time in film boiling

First node time after requenching

Later time after requenching

tr= 150.01 s

t2= 150.06 s

ts= 151.13 s

3160 3110 2890 2520 2470 2420 2360 2300 2240 2180 2100 2040 1960 1880 1810 1730 1650 1610 1600 1580

t4= 152.70 s

ts=155.70 s

i-2

T3

TS

(K)

(K)

W

3150 3100 2880 2510 2460 2410 2350 2290 2230 2160 2080 1990 1890 1770 1620 1430 1190 1090 940 640

3140 3080 2810 2270 2180 2090 1990 1880 1770 1660 1550 1440 1330 1230 1140 1050 970 710 660 620

As the thermal requenching front penetrates into the interior of the fuel pellet, the radial position at which the maximum temperature reduction occurs shifts to the interior of the fuel pellet, resulting in compressive tangential and axial stresses at the fuel surface and maximum tensile stresses at the interior. The requenching process results in a moving tensile stress front which is initially maximum at the fuel surface and progresses radially inward. However, the temperatures in the outer portion of the fuel pellet are below 1900 K such that transgranular facture is expected (see the discussion on fracture mode versus temperature presented in the previous section) while intergranular fracture is expected in the higher temperature region of the fuel pellet, at radii less than about 3.9 mm. For the calculations presented in fig. 8, stress relief

3110 2940 2650 2070 1990 1910 1830 1750 1670 1590 1520 1450 1370 1290 1230 1160 1090 680 650 620

2760 2670 2390 1900 1840 1770 1720 1650 1590 1530 1470 1420 1360 1300 1240 1190 1140 670 640 620

t6= 160.70 s

2360 2290 2070 1690 1650 1610 1560 1520 1480 1440 1400 1350 1310 1270 1220 1180 1140 660 640 620

over the entire requenching period is neglected. However, since thermal stresses in a structure are coupled, stress relief due to initial cracking at the fuel surface and viscoplastic flow in the interior high-temperature region of the fuel can occur, relieving stresses within an annulus of fuel bounded by these stress-relief regions. Due to such boundary stress relief, interior fuel might also be relieved of thermal stresses even though a temperature gradient exists. However, fig. 8 illustrates the fact that even if stress relief by fracture is accounted for, the requenching process is such that significant interior tensile stresses can be expected as the thermal requenching front propagates radially through the fuel pellet. The fact that significant thermal stresses are predicted is due to the high transient-temperature gradients that exist for low conductivity U02 fuel. Albeit

A. W. Cronenberg, T.R. Yackle / Intergranular fracture of unrestructured UO2 fuel

307

i

Radius (mm)

Radius (mm)

Fig. 8. Illustration of principal stresses predicted upon requenching from an unstressed film-boiling condition, assuming stress relief by fracture during the previous requenching time.

Table 6 Comparison of thermal stresses with temperature-dependent Reference temperature difference, AT

TI -

T2

Tr - Ts

TI -

T4

T2

-

T3

T3

-

T4

fracture strength and experimentally

observed fracture mode

Thermal stress values, o (at R) (IO” kp/m2)

Radial position R of maximum tensile stress (mm)

Temperature atR (K)

Fracture strength of(T) (Wm2)

Fracture mode

Ot

= 110 = 100 =8 = 80 = 50 =- 15 ot = 4.5 oa= 30 a, =- 15

R ~4.3

1420 a)

214

Brittle (transgranular)

Yes

0, or ot oa or

R -3.9

1650 8)

Z-14.4

Brittle (transgranular)

Yes

R 23.5

1960 (T4)

z-14

Ductile (intergranular)

Yes

Transition (intergranular and transgranular) Ductile (intergranular)

Yes

at = Oa = or=-

85 80 5

R = 3.7

1810 (T3)

r15

q

20 35 15

R = 3.0

2170 (2-4)

210.5

=

a, = or=

Failure criterion

Experimental observation

ot ’ Of

a) Computed as average temperature over the stress interval, for example, Tave = d(Tr + T2).

Yes

Transgranular cracking -1

T

Intergranular fracture (grain boundary separation)

308

A. W. Cronenberg, TX. Yackle / Intergmnular fracture of unrestructured UOz fuel

such stress predictions can only be considered orderof-magnitude estimates, they do illustrate the fact that the requenching process results in a dynamic stress field which propagates through the fuel as the thermal effects of requenching are felt within the interior of the fuel. Such an effect is clearly illustrated

on comparing figs. 7 and 8, where it can be seen that at a particular outer radial position, the tangential and axial stresses are tnesile initially while the radial component is compressive, while at later times the stress vectors are reversed at the same radial position. A summary of such behavior is presented in table 6.

Table 7 Summary of test data in order of Increasing cladding surface temperature, estimated from the oxide layer thickness formed due to steam-zircaloy interaction Test

Rod

Elevation from bottom of fuel stack (ml

Linear power (kW/ml

Effective cladding surface temperature in film-boiling W

IE-1 PCM CHF-ST IE-ST-2 IE-2 IE-2

IE-009 UTA-0005 IE-005 IE-012 IE-014

0.565 0.567 0.794 0.559 0.598

56 55 27 54 51

1270 1410 1410 1440 1440

60 39 37 34 91

No No No

PCM 8-l RF PCM-2 PCM-4 PCM-4 PCM-4

UTA-0006 A-0014 UTA-0014 UTA-0016 A-0017

0.768 0.623 0.600 0.667 0.629

30 38 57 46 55

1450 1450 1476 1491 1506

78 57 55 136 116

No

IE-2 IE-1 IE-3 PCM3 PCM-2

IE-013 IE-008 IE-017 A-002 1 UTA-0008

0.592 0.559 0.578 0.441 0.533

58 56 58 44 41

1520 1540 1540 1584 1600

87 20 71 26 101

No No

IE-3 PCM4 PCM3 IE-1 IE-5

IE-018 UTA-0015 A-0015 IE-010 IE-019

0.597 0.607 0.483 0.559 0.571

55 54 46 59 60

1620 1624 1637 1640 1650

78 67 17 79 44

IE-3 IE-ST-1 PCM-2A IE-5 PCM 8-l RS

IE-015 IE-001 UTA-0007 IE-020 UTA-0004

0.584 0.482 0.590 0.568 0.581

56 64 47 53 43

1670 1691 1700 1700 1740

84 70 3 56 362

IE-2 IE-5 IE-3 IE-5 IE-1

IE-011 IE-021 IE-016 IE-022 IE-007

0.592 0.527 0.539 0.495 0.532 0.501

55 58 56 60 62

1760 1840 1920 1940 2000

94 44 47 54 74

aJ Some = highly irregular fallout, such that no radius of powdering was assessed. bl N/A = fuel analysis not available.

Time in boiling (sl

Powdering

No No No No No

No

No

No No Yes

No No No

Some a) Yes Yes No Some Yes Yes N/A bl Yes N/A Yes

A. W. Cronenberg, T.R. Yackle / Intergranular fracture of unrestructured UOz fuel

As indicated in all cases, the calculated thermal stresses are sufficient to cause fracture. For the lower temperatures at the fuel surface, the fracture mode is predicted to be transgranular, while for the interior regions of the fuel pellet above 7’~~)intergranular fracture is predicted. As indicated in the last column

Previous irradiation

FRAP-T4 calculation of the dimensionless radial position at given temperature R(T)/Rf T= 1900K

Tmp = 3113 K

No No No No No

0.820 0.865 0.676 0.878 0.868

No No No No No

melting melting melting melting melting

No No No No No

0.735 0.817 0.891 0.865 0.903

No No No No No

No Yes Yes No No

0.909 0.912 0.915 0.903 0.895

No No No No No

Yes No No Yes No

309

of table 6, the experimentally observed fracturemode regions compare favorably with the predicted fracture-mode regions. It is also interesting to note that Bellamy and Rich [3] likewise indicate that the initiator for fracture is due to thermal stresses. They proposed, however, that fission gas bubble migration

Metallurgical observation Dimensionless radius of outer edge of central void

Dimensionless radius of final melt/column interface

Dimensionless radius of columnar/ equiaxed interface

Dimensionless radius of equiaxed/ unrestructured interface

No void

0.16

0.34

0.80

0.31

0.75 0.44

Not available Unrestructured No void 0.12

-

melting melting melting melting melting

No void No void 0.15 0.03

-

melting melting melting melting melting

0.932 0.932 0.922 0.942 0.946

Yes No No No No

0.946 0.958 0.945 0.95 1 0.954

No No Yes No Yes

0.970 0.992 >l.O >l.O >l.O

-

0.34

0.73 0.75 0.77 0.73

0.28 0.19 No void No void No void

0.25 0.46 -

0.47 0.45 0.55 -

0.86 0.83 0.91 0.64 0.86

No melting No melting No melting 0.232 0.353

0.01 No void No void 0.12 0.08

0.27 0.46 0.56

0.36 0.67 0.77

0.83 0.80 0.81 0.90 0.98

0.200 0.397 No melting No melting No melting

0.06 0.07 No void 0.13 0.11

0.49 0.44 0.41 -

0.60 0.52 0.55 0.25

0.64 0.77 0.63 0.82 0.71

0.286 0.374 0.415 0.513 0.548

0.15

0.29

0.48

0.93

0.60

0.64

0.72

0.71

Not available 0.002

0.51 Not available

No void

0.52

310

A. W.Cronenberg,T.R. Yackle! Intergranular fractureof unrestructuredUO2fuel

(for fuel previously irradiated to a burnup condition in excess of 3 at%) to grain boundaries primarily causes a loss of grain-boundary strength, rather than by thermally induced loss of grain-boundary strength as proposed here, the initiator for fracture being thermal stresses in both cases. The fact that at a particulat time and radial location, the tangential and axial stresses are tensile while the radial stress component is compressive but of a much lower magnitude, indicates that for the majority directions oblique to the normal axis the stresses should be tensile. This is clearly indicated in a qualitative manner using a Mohr’s circle analysis presented in fig. 9, where the stress condition presented in fig. 8a (that is for the thermal stresses resulting from a temperature change from T2 to T3 at a fuel radius of 3.5 mm) is considered characteristic of the stress field felt by the fuel zone which undergoes grain-boundary fracture. As discussed in ref. [29], the normal stresses for oblique planes lie inside the shaded area; thus, as indicated in fig. 9, the majority of grain-boundary planes oblique to the principle axis are subject to tensile stresses. Although assessment of the thermal stresses indicates, in a qualitative manner, whether or not fracture can be expected, the mode of fracture is dependent upon the temperature experienced by the fuel. For low temperatures, a transgranular fracture mode occurs while for temperatures in excess of the equicohesive temperature, TEE, intergranular fracture is expected. To assess whether such a criterion is satis-

or = -7 x 106 kg/d

fied, a heat transfer analysis is performed in the following section for each fuel rod of the PCM and IE test series to determine the radial position at which TEC is predicted to occur. A comparison is then made with the experimental radial dimension at which serve grain-boundary fracture is observed for unrestructured fuel and the radius at which TEC is predicted to occur. 4.2. Assessment of the radial temperature distribution within fuel during filmboiling and the corresponding local temperature-dependent fracture mode To assess the radial temperature profile, thus the temperature dependent fracture strength characteristics, across the fuel rod section experiencing film boiling, the FFUP-T4 [20] code is used assuming a steady-state heat transfer condition within the fuel rod for stable film-boiling operation. The assumption that the fuel approaches a steady-state condition during film boiling is based on the fact that typical thermocouple readings for test fuel rods indicate a relatively steady temperature reading during tilmboiling operation for times longer than approximately 20 s. A 20 s time period establishment of a quasisteady thermal condition is also consistent with a simple diffusional assessment of the thermal conduction relaxation time (T) of the fuel rod, which, for fuel-cladding contact found in film boiling, can be approximated as r = R)/4cq + X;2/4a, ,

+75x

106kg/m2--/

Fig. 9. Mohr’s circle for three-dimensional

stress.

A. W. Cronenberg, T.R. Yackle / Intergmnular fracture of unrestructured UOz fuel

where Rf = fuel radius = 0.46 cm, X, = cladding thickness = 0.06 cm, cq = fuel thermal diffusivity = 0.0042 cm2/s, (Y,= cladding thermal diffusivity = 0.069 cm2/s. For the properties and dimensions given, which are characteristic of the test fuel rods, T = 13 s. Since powdering phenomena have been observed for film-boiling times in excess of one minute, a steadystate analysis is thus justified. To estimate the radial temperature profile using

311

the FRAP-T4 code, a temperature boundary condition and local power level must be specified. A summary of such information is presented in table 7 for each fuel rod tested in the PCM and IE test series. The temperature-boundary condition used is the claddingsurface temperature at the axial position of peak power which is estimated from measurements of the alphazircaloy and Zr02 layers formed at the cladding surface during zircaloy-steam reaction over the fdm-

Table 8 Summary of test data in order of increasing FRAP-T4 prediction of the timeless dimensionless radius at which TEC is reached Test identification radiation

Rod number

FRAP-T4 prediction dimensionless radius (R/Rf) at which TEC = 1900 K occurs

Observed powdering

Previous irradiation

IE-ST-2 PCM-8-l-RF PCM-2 IE-1 PCM-CHF-ST PCM-4 IE-2 IE-2 PCM4 PCM-2 PCM-4 PCM-3 IE-2 IE-1 IE-3 PCM-3 IE-3 PCM-4 IE-1 IE-5 IE-3 PCM-2A IE-5 PCM-8-l-RS IE-ST-1 IE-2 IE-5 IE-3 IE-5 IE-1

IE-005 UTA-006 A-0014 IE-009 UTA-0005 UTA-0016 IE-014 IE-012 UTA-0014 UTA-008 A-0017 A-0021 IE-013 IE-008 IE-017 A-0015 IE-018 UTA-0015 IE-010 IE-019 IE-015 UTA-0007 IE-020 UTA-0004 IE-001 IE-011 IE-021 IE-016 IE-022 IE-007

0.676 0.735 0.817 0.820 0.865 0.865 0.868 0.878 0.890 0.895 0.903 0.903 0.909 0.912 0.915 0.925 0.932 0.932 0.942 0.946 0.946 0.948 0.951 0.954 0.958 0.970 0.992 1.00 1.00 1.00

No No No No

No No

No No

No No No No No No

No

No

No

No

No No

No No

No

No

No

Yes Yes No

No

No

No No Yes

Yes

No

No

No Some a) Yes No bI Some a) Yes Yes Yes N/A cI Yes N/A c) Yes

Yes No Yes No No

No No

No No Yes No Yes

aI Highly irregular fallout, such that no radius of powdering was assessed. bI Time in film boiling is 3 s, while the thermal response time of the fuel element is approximately prediction is not valid in this case and is overestimated. ‘I Post-test metallographic examination not available.

13 s; thus, the fuel temperature

41

78

IE-016

IE-018

PCM8-1 RS W-A-0004

84

IE-015

IE-3

362 362

74

IE-007

0.663 0.622

No

0.539

Yes 0.498

0.584

Yes

Yes

0.501

Yes

0.686

70

IE-1

58.0

0.597

IO

63.0 66.0

61.0

61.0

58.0

66.0

48.0

63.0

No

&W/m)

Power at axial location of powdering Outside

0.57 0.67 0.63

0.32 0.30

0.64

0.28 0.25

0.64

0.28

0.57

0.25

0.71

0.85

0.37

0.31

0.75

0.33

0.43 0.40

0.39

0.41

0.41

0.40

0.33

0.41

0.37

0.90 0.84

0.89

0.94

0.94

0.91

0.75

0.94

0.85

R RI& R RlRf (cm) (cm)

Inside

Observed radii of powdery fuel zone

1690 1590 1580 1620 1550 1630 1510 1270 1450 1340 1920 1870 1590 1640 1750 1670 1640 1430 1360 1340 1390 1430

(185”), (275”) (S”), (95”) (185% (275”) (5”), (95”) (185”). (290”) (180”), (195”) CO”), (270”) (go”), (180”) (180”), (270”) (0”) CO”), (90°) (180”)

Effective isothermal outer-cladding surface temperature (K) (at various angular orientations)

calculations for test fuel rods exhibiting powdering

0.482

70

IE-001

IE-ST-1

Table 9 Summary of experimental conditions and FRAP-T4 temperature Axial Rod Time Irradiated Test fuel location iu film boiling of sample from (s) bottom of fuel stack (m)

1350 (0”) 1390 (average)

1430 (270”)

1750 (90”)

1620 (average)

1900 (average)

1400 (240”)

1600 (average)

1640 (average)

Approximate effective isothermal outercladding surface temperature a) laverage, or at approprfate angular orientation)

-

IE-OO1

IE-ST-1

IE-007 IE-015 IE-016 IE-018 PCM 8-l RS UTA-0004

III-1 IR-3

Rod

Test

Table 9 (continued)

0.947 0.931 0.840 1.142 0.936 0.970 0.890 0.869 0.886

TEC = 1900 K

0.397 0.227 Nomelting 0.550 0.227 0.395 Nomelting No melting No melting

Tmp = 3113 K

FRAP-T4 calculation of the dimensionless radial position RVlIRf

7 5 1 9 6 8 4 2 3

Test data nomenclature for fig. 10

iR/R f>

tR/Rfl

CR/Rd 0.07 0.44 0.52 Inside thermocouple Equlaxed Inside thermocouple Equiaxed w Not distinguishable 0.06 0.49 0.60 0.002 0.51 0.60 0.08 0.48 0.50 Equiaxed EqUiaxed No void Drilled hole Equiaxed Rqulaxed ---

Columnar/ l?qulaxed interface

Final melt/columnar interface

Outer edge of central void

0.75 0.85 0.57 0.7 1 0.64 0.64 0.57 0.67 0.63

U?/Rd

Equiaxed/ umestructured interface

observation of dimensionless radii position

Me~ur~~

. B

3 &

$ 3 P

B

314

A. W. Cronenberg, T.R. Yackle / Intergranularfracture of unrestructured UOz fuel

boiling time period [30]. Values of cladding surface temperature estimated in such a manner are considered to be the most reliable determination of the actual cladding-surface temperature experienced during film-boiling operation *. The power levels used in the code are as quoted, considering a flux depression factor across the fuel radius as predicted by the FRAP-T4 code for UOZ zircaloy-clad fuel rods. It should be mentioned here that the FRAPT4 temperature estimates should be considered in a qualitative sense only, since such factors as restructuring, stress-induced transgranular and intergranual fracture, and changes in bond-gap thickness all influence fuel thermal performance. Such factors are not easily quantified; thus, fuel-rod temperature predictions under highly transient conditions, where significant changes in fuel properties can occur, should be considered approximate estimates only. The calculated dimensionless radii at which the estimated equicohesive temperature ( TEC Y 1900 K) are and melting point (Tmp =3113K)oftheUOs given in the last two columns of table 7 for each of the quoted fuel-rod experimental conditions. A relisting of experiments in order of increasing radius at which TEc is predicted, is presented in table 8. As indicated for low power-low cladding-surface temperature conditions, TEC is reached only within the inner portion of the fuel pellet; therefore, the temperatures predicted for the outer unrestructured fuel zone are lower than the temperature considered necessary for fracture by grain-boundary separation such that powdering is not predicted. This result is consistent with the experimental results, in which powdering is not observed for the low power-low film-boiling cladding temperature experiments. HOWever, brittle-type transgranular cracking can be expected for such low-power experiments if unrestructured

* As discussed in ref. [ 301,the film-boiling time for a particular test-fuel rod is assumed to be the same at all axial and circumferential locations within the film-boiling zone; thus, variations in thickness measurements are assessed in terms of temperature difference only. In reality, however, the film-boiling process may be somewhat unstable, particularly where the coolant-flow stream is heavily instrumented; thus, circumferential and axial variations in the oxide-layer thickness may be due to variations in film boiling times rather than nonuniform temperatures.

fuel is subject to significant requenching stresses below TEc, which is indeed observed. It is also noted in table 8, that for high power-high cladding temperature experiments, TEc is reached within the outer radial portions of the fuel, which are normally in an unrestructured condition. Thus, fracture by grain-boundary failure is expected, which corresponds to the observed trend of powdering for such high power-high temperature experiments. A close inspection of table 8 indicates that several high thermal-condition fuel rods did not exhibit a characteristic annulus of powdery fuel, that is rods 19 and 20 of the IE-5 experiment and the PCM-2A fuel rod. In the case of the PCM-2A test, the filmboiling time was only approximately 3 s; thus, the steady-state temperature profde prediction is incorrect. As discussed previously, the temperature predictions are valid only for fuel rods operated in film boiling in excess of about 13 s, which corresponds to the thermal relaxation time of the fuel rod. Therefore, the PCM-2A temperature estimate is overpredieted. It is also noted that fuel rods IE-019 and IE-020, for the IE-5 experiment, indicated highly irregular fallout; thus, such fuel was not included in the quantitative comparison presented in table 8 of the observed radius of powdery fuel versus the predicted radius at which TEc is estimated. The values for the inner and outer radius of the fuel exhibiting powdering are presented in table 9, as well as the power levels and cladding surface temperatures. The information given in table 9 is illustrated graphically in fig. 10, where the various fuel restructuring and powdery region versus dimensionless fuel radii are depicted. In addition the predicted dimensionless radii is given at which TEE = 1900 K occurs (based upon the local power level and the cladding-surface temperature assessed from metallurgical examination of the oxide layer formed during film boiling). With respect to powdering, it can be seen that the threshold temperature, TEC, for grainboundary fracture in unrestructured fuel appears to correlate the observed outer extent of the powdery fuel zone. It should be noted that the inside radius of the powdery zone corresponds, in all cases, to the approximate outer radial position at which equiaxed grain growth diminishes. However, a definitive outer boundary for equiaxed grain growth can not be asses-

A. W. Cronenberg, T.R. Yackle / Intergranular fracture of unrestructured UOz fuel

-a Cold

fuel region

+F \;,\ f :.?:$+

\4 7

>

p

1,

ksi

\

\

444

0.8

444

\\ \

444

444

444

444

444

444

ttt

444

444

444

ttt

TTT

ttt

444

iii

444

ttt

ttt

ttt

444

to

ttt

ttt

ttt

ttt

ttt

MM_

ttt

ttt

to

1900 K

ttt

ttt

to

444

444

t +

444

B cu s ._

g

444

0.5

2 6;

444

444

444

0.6

Equiaxed fuel grains

\\ \ iii3

0.7

444

i 5 2 5 2

p-J

444

444 \

;-

Columnar fuel grains

v b

t %

I,trl

!b\

\,‘\\

2’; \\ ~\ ,~:\

Void

ttt

444

444 TTT

444

ttt

444

ttt

444

ttt

444

ttt

444

ttt

to

to

ttt

444

ttt

ttt

ttt

ttt

444

ttt

ttt

ttt

ttt

444

to ttt ttt

ttt

ttt

to

ttt

ttt

ttt

ttt

ttt

ttt

444

ttt

ttt

444

LLL

ttt

444

on

)))

0.4

444 444

2

iii ttt ttt

4

Unrestructured sintered fuel grains

Unrestructured powdered fuel

ttt

6

8

Test5data I

1 48

I 63

1

I

1400

I

70

No

I

I 362

I

I

I

1360 i390 1430 Outside cladding I

I

I I I 66LineZlpowe5rBlevel

362 I

No

No

I

I

I $h/my3 I

61 I

1600 1620 1640 surface temperature

I I I 78 70 84 70 Film boiling time (s) I I I I Yes No Yes No Previous irradiation

I

I

I 66

I

1750 (K)

I

I

1900

I 47

I

I 74

I Yes

I Yes

Fig. 10. Illustration of fuel restructuring regions, powdery fuel zone, and radius at which TEC = 1900 K is predicted to occur using the FRAP4T code, baaed upon input power levels and estimated cladding surface temperatures during film boiling.

315

316

A. W. Cronenberg, T.R. Yackle / Intergranularfracture of unrestructured UOz fuel

sed here, since fuel fallout (that is powdery fuel) in metallographic sample preparation most likely contains some fraction of equiaxed fuel. An a priori prediction of the radius of the outer boundary of the equiaxed grain-growth region (thus, the inner radius of the previously unrestructured or powdery fuel zone) is beyond the scope of the present study, since little is known of the kinetics of grain growth at the elevated temperature applicable to film-boiling condition. As illustrated in fig. 10, such factors as power level and cladding-surface temperature inducing stable fdm boiling, under various coolant thermal-hydraulic conditions influence the fuel-rod thermal response, and therefore the kinetics of fuel restructuring, in addition to film-boiling times and previous irradiation history. 5. conclusions Although intergranular fracture in unrestructured fuel can be accounted for by a combination of loss of grain-boundary strength above the brittle-to-ductile transition temperature (4900 K for UOa) and tensile stresses upon requenching, such a mechanism is based on limited experimental evidence of fuel powdering found during in-pile testing of fuel rods to a film-boiling condition. To properly assess the phenomena associated with grain-boundary fracture, controlled metallurgical experiments would be necessary to evaluate the influence of such factors as stoichiometry, impurity content, sintering characteristics, strain rate, temperature and void concentration on grain-boundary strength. Since such metallurgical analysis is not available under controlled out-of-pile conditions the arguments presented here must be considered preliminary. Nevertheless, the analysis presented indicates that the experimentally observed extent of powdering can be directly correlated with a severe loss of tensile strength at the elevated temperatures experienced during film-boiling operation, and that requenching thermal stress are sufficient to account for extensive grain-boundary fracture. In addition, irradiation history does not appear to significantly alter the nature or threshold conditions for grain-boundary fracture in unrestructured sintered UOa fuel at the elevated temperatures experienced by fuel during high-power level film-boiling operation. However, as discussed in refs. [3] and [9], for previ-

ously irradiated fuel rods, in excess of approximately 3% burnup, fission gas bubbles at grain boundaries may play on increasingly important role in grainboundary separation for both restructured and unrestructured fuel. Based upon comparison of experimental observations and the analysis presented, the following factors are considered important to the powdering or desintering process of unrestructured fuel during film-boiling testing, and are listed in order of importance: (1) Relatively high thermal conditions during film boiling, resulting in temperatures within the unrestructured fuel zone in excess of the equicohesive temperature, which is estimated for UOz to be in the range of 1900 K. (2) Significant thermal stresses, which are primarily tensile in the majority of stress planes, and exceed the ductile fracture strength of UOa. (3) Weakening of grain boundaries due to precipitates, voids and fission-product impurities located a grain-boundary interfaces. With respect to LWR safety, fuel powdering can lead to loss of pellet structural integrity with an attendant increased possibility of washout into the coolant stream, if cladding failure occurs. Indeed, as discussed in ref. [l] and [2], small amounts of micron-sized fuel particles from the powdery zone appeared to have been released to the coolant stream, for cladding in a fractured condition. However, many of the fuel rods exhibiting powdering remained intact. For these rods, a change in heat transfer characteristics of fuel pellets which experienced significant grain-boundary separation, is expected, particularly if sintering upon return to normal reactor operating conditions does not occur. Robertson’s [31,32] conclusion that sintering of UOz powder compacts can occur at temperatures as low as 1100 K in an irradiation environment, indicates that post film-boiling operation may result in similar resintering of powdery fuel. However, the burnup for such resintering [3 1,321 was reported to be 2200 MWd/ton U; thus, upon return-to-normal reactor operating conditions, powdery fuel may not resinter until after similar prolonged irradiation exposure. Upon a more comprehensive understanding of the powdery fuel phenomena, alteration of such properties as thermal conductivity and mass diffusion characteristics, in fuel behavior codes for light-water reactor safety assessment, should be considered.

A. W.Oonenberg, T.R. Yackle/ Intergrandar fracture of unrestructuredUO2fuel Appendix A Thermal-stress equations The code TSTRESS *, available from the Applied Mechanics Division of EG&G Idaho, is used to numerically evaluate the elastic radial (Us), tangential (a& and axial (03 stress components resulting from surface cooling of a composite cylinder with a solid outer annulus and an inner molten core. The relevant stress equations are:

(1)

(2)

Oa=2VD+Ee,

--

orE(AT) (1 -v) ’

with the radial displacement

+(l

E j@rHr) -v)r2p

given by:

dd - u&} ,

where u = Poission’s ratio, o = coefficient of linear thermal expansion, E = modulus of elasticity, AT = temperature increase over the stress-free reference temperature, ez = unit elongation in the axial direction, p = constant equal to the inner radius of the cylinder (that is, the liquid-solid radius), r = radial distance to a point in the cylindrical increment, D and F = constants.

Acknowledgements The authors thank Mr. Richard Rahl for the computer-generated thermal stress estimates and Drs. S.L. * Developed by R.C. Guenzler of the Applied Mechanics Division of EC&G Idaho, Inc.

317

Seiffert and R.R. Hobbins, and Mr. A.S. Mehner for their helpful discussions on the genera1 aspects of the problem. In addition, the authors gratefully acknowledge a critical review of this work by Prof. D.P.H. Hasselman of the Virginia Polytechnic Institute and Prof. D.R. Olander of the University of California, Berkeley.

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318

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