Fuel Behavior under

Abnormal Conditions

Office of Nuclear Regulatory Research

NUREG/KM-0004

Fuel Behavior under 

Abnormal Conditions

NUREG/KM-0004

January 2013

Office of Nuclear Regulatory Research
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owned rights.
Fuel Behavior under Abnormal 

Conditions

Manuscript Completed: April 2009

Date Published: 

Prepared by 

R.O. Meyer

Prepared for

Office of Nuclear Regulatory Research

U.S. Nuclear Regulatory Commission

Washington, DC 20555-0001

NUREG/KM-0004

iii NUREG/KM-0004

ABSTRACT

Under normal operating conditions, cladding and core structural materials operate around 

300 degrees Celsius (C), and fuel pellets experience peak temperatures below 2,000 degrees C 

at the pellet centerline. At these temperatures, fuel cladding integrity is maintained, and fission 

products are contained within the fuel rods. However, under some abnormal conditions, higher 

temperatures and other conditions significantly alter the behavior of these materials. These 

conditions can threaten core coolability and lead to fission product release. This NUREG report 

considers the following two types of accident conditions: (1) reactivity-initiated accidents and

(2) loss-of-coolant accidents. This report describes the fuel behavior of each accident condition

from basic concepts to the current state of the art. It also mentions safety criteria, references

the classic experimental work in each of these areas, and presents equations and figures that 

permit some quantitative evaluations.

v NUREG/KM-0004

CONTENTS

ABSTRACT................................................................................................................................iii

CONTENTS................................................................................................................................v

FIGURES..................................................................................................................................vii

FOREWORD .............................................................................................................................ix

ABBREVIATIONS......................................................................................................................xi

1. INTRODUCTION ................................................................................................................ 1

2. REACTIVITY-INITIATED ACCIDENTS............................................................................... 3

2.1 Reactivity-Initiated Accidents with Fresh Fuel .............................................................. 3

2.2 Reactivity-Initiated Accidents with High-Burnup Fuel ................................................... 9

3. LOSS-OF-COOLANT ACCIDENTS ...................................................................................15

3.1 Loss-of-Coolant Accidents with Fresh Fuel .................................................................16

3.1.1 Phase Change.....................................................................................................16

3.1.2 Ballooning and Rupture .......................................................................................16

3.1.3 Oxidation .............................................................................................................19

3.1.4 Diffusion of Oxygen into the Metal .......................................................................21

3.1.5 Hydrogen Absorption ...........................................................................................25

3.2 Loss-of-Coolant Accidents with High-Burnup Fuel ......................................................26

3.2.1 Effect of Hydrogen ...............................................................................................26

3.2.2 Inside Diameter Oxygen Pickup...........................................................................27

3.2.3 Fuel Relocation....................................................................................................31

4. REFERENCES ..................................................................................................................35

vii NUREG/KM-0004

FIGURES

Figure 1 Dependence of pulse width on energy (fuel enthalpy change) for beginning-ofcycle and end-of-cycle conditions in PWRs (Figure 4 in Ref. 2)....................................4

Figure 2 Enthalpy of UO2 as a function of temperature to 4,000 K (Figure 2-3 in Ref. 3)............5

Figure 3 Linear thermal expansion of UO2 as a function of temperature.....................................5

Figure 4 Significant rise in the cladding temperature after the power pulse (calculated with 

FRAPTRAN, Ref. 4) .....................................................................................................6

Figure 5 High-temperature damage in the cladding of fresh fuel after its exposure to a large 

RIA power pulse (285 cal/g) in the Power Burst Facility test reactor (Figure 73 in 

Ref. 5 and Figure 5 in Ref. 6)........................................................................................7

Figure 6 Photographs of fresh fuel rods after RIA testing in the Special Power Excursion 

Reactor Test (SPERT) reactor (Figure 1 in Ref. 7) .......................................................8

Figure 7 Maximum fuel enthalpy change for an RIA in a PWR at hot zero power for various 

values of delayed-neutron fraction, beta (Figure 15 in Ref. 2).......................................8

Figure 8 (a) Scanning electron microscope image showing the ultrahigh-burnup rim 

structure and (b) elemental distribution as a function of the distance from the 

fuel-to-cladding interface in a fuel rod with a burnup of about 105 GWd/t (Figure 1 

in Ref. 8).....................................................................................................................10

Figure 9 Edge-peaked pellet temperatures early in an RIA transient and center-peaked 

temperatures after significant heat transfer (based on Figures 24 and 25 in Ref. 9) ...11

Figure 10 Thermal expansion algorithms for (a) normal operation (highest temperature at 

pellet centerline) and (b) a zero-power RIA (highest temperature at the edge) in 

high-burnup fuel.......................................................................................................12

Figure 11 Plastic strain measured in nonfailed cladding as a function of maximum fuel 

enthalpy change for tests in the CABRI test reactor and the NSRR (Figure 7 in 

Ref. 2)......................................................................................................................12

Figure 12 Solubility of H in Zr as a function of temperature (based on Ref. 10)........................13

Figure 13 RIA test data for irradiated fuel, plotted as maximum fuel enthalpy change as a 

function of H in the cladding (H content was estimated when data were not 

available); solid symbols indicate cladding failure (based on Figure 3 of Ref. 2)......14

Figure 14 Cladding temperature (solid line) and rod pressure (dashed line) during a 

postulated LOCA (Figure 6 in Ref. 11).....................................................................15

Figure 15 Illustration of temperature progression and associated phenomena during a 

postulated LOCA .....................................................................................................16

Figure 16 Correlations of rupture temperature and corresponding cladding stress for three 

heating rates (degrees Celsius per second) from data for Zircaloy-4 heated in 

steam (Figure 3 in Ref. 12) ......................................................................................17

Figure 17 Maximum circumferential strain as a function of rupture temperature for Zircaloy 

cladding heated in steam (Figure 8 of Ref. 12) ........................................................18

Figure 18 Ballooned and ruptured region of unirradiated Zircaloy-2 after undergoing LOCA 

conditions (Figure 217 in Ref. 13)............................................................................18
NUREG/KM-0004 viii

Figure 19 Linear power generation from the metal-water reaction for cladding with a 

diameter of 1.25 centimeters and various oxide thicknesses (Figure 4-69 in Ref. 

3).............................................................................................................................21

Figure 20 Pseudobinary Zircaloy-oxygen phase diagram (Figure 4 in Ref. 16).........................22

Figure 21 Microscopic image of unirradiated Zircaloy-2 after oxidation in steam at 

1,200 degrees Celsius for 600 seconds at room temperature (Figure 4 in Ref. 13)..23

Figure 22 Qualitative diagram of oxygen concentration in Zircaloy cladding exposed to 

steam at high temperature.......................................................................................23

Figure 23 Diagram of ring-compression test.............................................................................24

Figure 24 Illustration of diffusion mechanisms in Zr-based cladding alloys...............................25

Figure 25 Older E110 cladding showing early breakaway oxidation at 1,000 degrees C 

compared with modern M5 cladding, which is resistant to breakaway oxidation 

(based on Figure 88 in Ref. 13 and on related unpublished figures) ........................26

Figure 26 Embrittlement threshold for cladding specimens exposed to steam at 

1,200 degrees Celsius and quenched after slow cooling to 800 degrees Celsius 

(Ref. 19) ..................................................................................................................27

Figure 27 Interaction bonding layer between UO2 fuel and Zircaloy-4 cladding in a

high-burnup specimen at 83 GWd/t (Figure 10 in Ref. 20) .......................................28

Figure 28 Free energy of formation of oxides of Zr-alloy constituents and some impurities 

(Figure 1 in Ref. 13).................................................................................................29

Figure 29 Oxygen sources for diffusion into cladding metal during a LOCA .............................30

Figure 30 Grain morphology and alpha layer at the OD and ID of a high-burnup fuel rod 

exposed to LOCA conditions (Supplementary Figure 3.5.24 in Ref. 20)...................31

Figure 31 Fuel pellet fragments in PWR fuel rods after normal operation to low and medium 

burnup levels (Figure 30 in Ref. 21).........................................................................32

Figure 32 Cross-section of the rupture region of an irradiated fuel rod after testing under 

LOCA conditions (Figure 13 in Ref. 21) ...................................................................32

Figure 33 Pellet stack reduction as a function of the increase in volume in cladding balloons 

for preirradiated fuel rods (Figure 32 in Ref. 21) ......................................................33

Figure 34 Gamma scan of very-high-burnup (approximately 92 GWd/t) fuel rod showing 

major loss of fuel material after LOCA testing (Figure 15 in Ref. 22)........................34
ix NUREG/KM-0004

FOREWORD

As part of the U.S. Nuclear Regulatory Commission’s (NRC’s) knowledge management effort, 

one of our retiring staff members, Dr. R.O. Meyer, prepared textbook material regarding the 

subjects on which he worked during his entire 35-year career with the NRC. The following 

NUREG report presents this material, which discusses fuel rod behavior during postulated 

accidents that the NRC considers in safety analyses. Fuel behavior under conditions of 

reactivity-initiated accidents and loss-of-coolant accidents are timely subjects because the NRC 

is in the process of revising Regulatory Guide 1.77, “Assumptions Used for Evaluating a Control 

Rod Ejection Accident for Pressurized Water Reactors,” issued May 1974, and Title 10 of the 

Code of Federal Regulations (10 CFR) 50.46, “Acceptance Criteria for Emergency Core Cooling 

Systems for Light-Water Nuclear Power Reactors.” These subjects are discussed 

comprehensively and bring the reader current with the state of the art.

During his career, Dr. Meyer worked extensively in these areas and published more than 

40 related papers and NUREG reports. His effort in documenting some of his knowledge in 

such a readable fashion is greatly appreciated.

xi NUREG/KM-0004

ABBREVIATIONS

B-J Baker-Just

BIGR fast pulse graphite reactor

BWR boiling-water reactor

C Celsius

C-P Cathcart-Pawel

cal/g calories per gram

CFR Code of Federal Regulations

ECR equivalent cladding reacted

FRAPTRAN Fuel Rod Analysis Program—Transient

GWd/t gigawatt day per ton

H hydrogen

H2O water

He helium

ID inside diameter

IGR pulse graphite reactor

J/kg joules per kilogram

K Kelvin

LOCA loss-of-coolant accident

LWR light-water reactor

Nb niobium

NRC U.S. Nuclear Regulatory Commission

NSRR Nuclear Safety Research Reactor

OD outer diameter

PCMI pellet-cladding mechanical interaction

psi pounds per square inch

Pu plutonium

PWR pressurized-water reactor

RIA reactivity insertion accident

Sn tin

SPERT Special Power Excursion Reactor Test

UO2 uranium dioxide

wt.ppm weight parts per million

Zr zirconium

ZrO2 zirconium dioxide

1 NUREG/KM-0004

1. INTRODUCTION

Under normal operating conditions, cladding and core structural materials operate around 

300 degrees Celsius (C), and fuel pellets experience peak temperatures below 2,000 degrees C

at the pellet centerline. At those temperatures, zirconium (Zr) alloys remain in their

low-temperature alpha phase (hexagonal close-packed structure). Furthermore, because the 

vapor pressures of major fuel constituents remain low, most fission products are retained within 

the fuel pellets. However, under some abnormal conditions, higher temperatures and other 

conditions significantly alter the behavior of the materials.

Several of these abnormal conditions are of special interest in addressing the safety of nuclear 

power reactors. Licensing authorities generally require that accidents be postulated, that safety 

equipment be installed to mitigate these accidents, and that analyses be performed to 

demonstrate that the plant would survive these accidents without major releases of radioactivity. 

As a result, a great deal of research has been conducted over the years in the United States as 

well as other nations possessing nuclear power technology, by both regulators and industry 

stakeholders, to study the behavior of fuel materials under abnormal conditions.

From the point of view of fuel behavior, reactivity initiated accidents (RIAs) and loss-of-coolant 

accidents (LOCAs) are the two most challenging types of accidents postulated for light-water 

reactors (LWRs). The RIAs of particular interest are the most severe overpower events, and the 

LOCAs of interest are the most severe undercooling events that seem credible. As such, these 

accidents involve the most limiting conditions that fuel materials may experience.

3 NUREG/KM-0004

2. REACTIVITY-INITIATED ACCIDENTS

A large reactivity excursion initiates the postulated RIA. It is followed, in turn, by a power 

excursion, the expulsion of hot fuel particles into the coolant, and the conversion of that thermal 

energy into mechanical energy resulting in a steam explosion. The RIA is the type of accident 

that occurred at the Chernobyl plant in April 1986; the subsequent steam explosion in this 

accident ejected core materials and started a fire. An RIA would initiate differently in a 

boiling-water reactor (BWR) than it would in a pressurized-water reactor (PWR), but the 

progression of the subsequent events would be similar.

In a BWR, the accident is postulated to occur after a control blade hangs up in the core as the 

drive assembly is withdrawn, and some time later the control blade drops out of the core at its 

maximum velocity. This type of accident is called a rod-drop accident. An accident of this type 

that occurs under cold zero-power conditions produces the largest reactivity excursion. 

Although no rod-drop accidents have occurred in BWRs, the broken and cracked shafts found in

the Oskarshamn and Forsmark plants in 2008 may be considered precursors to this type of 

accident (Ref. 1).

In a PWR, the accident is postulated to occur after a crack develops around an upper head 

penetration (nozzle) that houses a control rod drive, and the drive unit and its attached control

rod cluster are ejected under pressure when the crack fails. This type of accident is called a 

rod-ejection accident. An accident of this type that occurs under hot zero-power conditions

produces the largest reactivity excursion. This type of accident is not possible in a PWR under 

cold conditions because the vessel must be pressurized (and therefore hot) to cause the 

ejection. No rod-ejection accidents have occurred in PWRs either, but a precursor occurred in 

2002 at the Davis-Besse Nuclear Power Station when a control rod drive nozzle remained 

attached only by its stainless steel liner following nozzle cracking and severe corrosion of the 

reactor head.

2.1 Reactivity-Initiated Accidents with Fresh Fuel

Regardless of the speed of a falling BWR control blade or an ejecting PWR control rod, the 

nuclear reaction soon becomes prompt critical. From that point on, the rate of power increase 

and subsequent Doppler-caused decrease depend only on nuclear properties of the core 

design. In general, the resulting pulse has a half-width (i.e., fuel width at half maximum) of only 

a few tenths of a millisecond. Because little heat is transferred from the fuel pellet to the 

cladding during this time, the event can be considered adiabatic. Consequently, a power pulse 

in an RIA is usually characterized by the maximum fuel enthalpy in calories per gram (cal/g) and 

by the pulse half-width in milliseconds. Figure 1 shows the pulse width for typical RIA enthalpy 

additions in a PWR (Ref. 2). For a given energy, the pulse is somewhat broader in a BWR 

because the nuclear coupling in that reactor type is looser than that of a PWR.
NUREG/KM-0004 4

Figure 1 Dependence of pulse width on energy (fuel enthalpy change) for beginning-ofcycle and end-of-cycle conditions in PWRs (Figure 4 in Ref. 2)

Consider a pulse that deposits 200 cal/g (0.84x106 joules per kilogram (J/kg)) in the uranium 

dioxide (UO2) fuel pellets within a Zircaloy-clad fuel rod, which is at zero power and room 

temperature. Assuming that the energy is deposited uniformly in the UO2 pellets, the

temperature of the pellets will rise to 2,600 Kelvin (K) (2,327 degrees Celsius) according to the 

enthalpy relation shown in Figure 2 (Ref. 3). From the thermal expansion relation shown in 

Figure 3 (Ref. 3), the linear thermal expansion of UO2 going from room temperature to 2,600 K 

(2,327 degrees Celsius) is 2.9 percent. For a 15x15 fuel design, the as-fabricated gap between 

the pellets and the cladding is about 2 percent of the cladding diameter. The gap thus 

accommodates much of the pellet expansion, leaving a net strain in the cladding of less than 

1 percent, which fresh Zr-alloy cladding can readily accommodate. Therefore, the mechanical 

interaction between the pellets and the cladding will not lead to cladding failure

(i.e., through-wall penetration or fracture) for fresh fuel; however, the result is very different for 

high-burnup fuel (see Section 2.2).
5 NUREG/KM-0004

Figure 2 Enthalpy of UO2 as a function of temperature to 4,000 K (Figure 2-3 in Ref. 3)

Figure 3 Linear thermal expansion of UO2 as a function of temperature (Equation 2-36 in 

Ref. 3)

However, note that 2,327 degrees C in this example is well above the melting point of Zr

(1,852 degrees C). Although the cladding temperature cannot rise significantly during the 

10-millisecond period of the power pulse, the heat in the pellets eventually goes through the 

cladding into the coolant. During this process, the cladding temperature rises significantly as 

shown in Figure 4, which was calculated with FRAPTRAN (Ref. 4) for a somewhat smaller pulse 

(108-cal/g peak fuel enthalpy) and includes appropriate heat-transfer kinetics.

 

0.000

0.005

0.010

0.015

0.020

0.025

0.030

0.035

0.040

0 500 1000 1500 2000 2500 3000

Temperature (K)

∆L/L0 (unitless)
NUREG/KM-0004 6

Figure 4 Significant rise in the cladding temperature after the power pulse (calculated 

with FRAPTRAN, Ref. 4)

Actual cladding temperatures depend on heat transfer across the pellet-to-cladding gap and 

from the outside of the cladding to the coolant; cladding temperatures also depend on time, 

thermal conductivities, and heat capacities. Because these processes are complicated and

difficult to model, the progression of fuel damage during RIAs is customarily determined 

empirically by testing. Figure 5 shows the result of one such test on a fresh fuel rod. This test 

was performed by the Department of Energy for the Nuclear Regulatory Commission in the 

Power Burst Facility test reactor at an initial temperature of 265 degrees Celsius and resulted in 

a peak fuel enthalpy of 285 cal/g with a pulse width of 13 milliseconds (Ref. 5).

Based on the photomicrograph in Figure 5, very high cladding temperatures were clearly 

achieved. The beta phase seen in the center of the cladding is evidence of temperatures above 

the phase transformation at about 850 degrees C. Also, the large oxide layers on the inside and 

outside surfaces of the cladding could not have developed during the transient unless 

temperatures were well above 1,000 degrees C. Furthermore, the eventual failure (quench 

fracture) is a brittle fracture as deduced from the fracture surface, and oxygen diffusing into the 

bulk metal from the oxide on the surfaces caused cladding embrittlement. This amount of 

embrittlement in such a short time indicates temperatures well above 1,200 degrees C. The 

high-temperature behavior of this Zircaloy cladding is thus similar to that which occurs in a 

LOCA (see Section 3). Finally, the failure clearly occurred at a low temperature during the 

cooldown phase because there is no oxide present on the fracture surface.
7 NUREG/KM-0004

Figure 5 High-temperature damage in the cladding of fresh fuel after its exposure to a 

large RIA power pulse (285 cal/g) in the Power Burst Facility test reactor (Figure

73 in Ref. 5 and Figure 5 in Ref. 6)

The nuclear industry has used a traditional value of 170-cal/g total enthalpy to indicate the level 

at which cladding failure will occur as a result of overheating. Although the technical basis for 

this traditional value is apparently lost, the value is consistent with the test results from the 

pulsed graphite reactor (IGR) and the fast pulse graphite reactor (BIGR) in Russia; these results

indicate that swelling and rupture, rather than a mechanical mechanism, caused cladding failure

(Ref. 2).

Although cladding failure is of some interest in assessing the safety consequences of an RIA 

because of the small releases of fission products, the major consequence of this type of 

accident comes from a possible steam explosion. Merely causing a crack in the cladding will 

not necessarily expel hot fuel particles into the coolant such that a steam explosion could occur. 

However, Figure 2 shows that fuel enthalpies greater than 275 cal/g (1.15x106 J/kg) would result 

in some molten UO2. At some enthalpy higher than this value, the thermal expansion that takes 

place during the phase change would cause the expulsion of molten or hot solid particles of UO2

from the rod into the coolant. MacDonald et al. (Ref. 7) found damage levels for fresh and 

low-burnup fuel in their classic work, as shown in Figure 6, and concluded that a safety limit 

should have been set at about 230 cal/g rather than the 280-cal/g limit that the U.S. Nuclear 

Regulatory Commission (NRC) adopted because of confusion between total energy deposition 

and peak fuel enthalpy (i.e., some energy is lost in the tests even in the first 10 milliseconds).
NUREG/KM-0004 8

Figure 6 Photographs of fresh fuel rods after RIA testing in the Special Power Excursion 

Reactor Test (SPERT) reactor (Figure 1 in Ref. 7)

Fuel enthalpy resulting from an RIA is related to the worth of the ejected control rod, as shown 

in Figure 7 (Ref. 2). Because control rod worth is generally less than $2, Figure 7 shows that 

the fuel enthalpy change would usually be less than about 70 cal/g. If 25 cal/g is added for an 

RIA that starts at about 300 degrees Celsius in a PWR, the total is still less than the 

170-cal/g enthalpy level at which cladding failure would occur and much less than the 

230-cal/g level at which hot fuel particles might be expelled from a fuel rod. Therefore, no 

cladding failure, fuel dispersal, or steam explosion would be expected for fresh LWR fuel in an 

RIA.

Figure 7 Maximum fuel enthalpy change for an RIA in a PWR at hot zero power for 

various values of delayed-neutron fraction, beta (Figure 15 in Ref. 2)
9 NUREG/KM-0004

2.2 Reactivity-Initiated Accidents with High-Burnup Fuel

At the present time, power reactors are achieving fuel burnups as high as a little over 

60 gigawatt day per ton (GWd/t) (rod average), and burnups above 40 GWd/t are considered 

high. Several properties of high-burnup fuel radically alter the evolution of an RIA in both BWRs 

and PWRs. In particular, the fissile atom distribution is changed within the fuel pellets, the 

pellet-to-cladding gap is closed, hydrogen (H) is present in the cladding, and fission gas bubbles 

are found within the fuel pellets, as can be seen in Figure 8(a).

Figure 8(b) shows fissile atom redistribution (Ref. 8) in a fuel rod with a very high burnup. 

Natural shielding suppresses fissions in the center of the fuel pellets relative to that in the 

peripheral regions. This effect becomes greatly enhanced as burnup progresses by the buildup 

of plutonium (Pu), which is largely fissile, near the pellet surface. The concentration of Pu 

atoms in this particular high-burnup fuel rod more than doubles near the pellet surface relative 

to that at the centerline, thus resulting in very high fuel temperatures near the pellet surface 

early in the power transient (Figure 9). This near-surface peak temperature is much higher than 

the peak temperature in a fresh fuel rod.

High fuel surface temperatures substantially enhance the thermal expansion of the pellet. 

Figure 10(a) illustrates a typical thermal-expansion algorithm that is used in most computer 

models, especially for normal operating conditions when the peak temperature is at the pellet 

centerline. In this algorithm, the centerline node expands more than the other nodes do, and 

the expansion of each node is added to the next. Because UO2 has no significant tensile 

strength, each nodal ring cracks, and the incremental expansions adequately add together 

without much sensitivity to the number of rings chosen.

Figure 10(b) shows the thermal-expansion algorithm that must be used for an RIA with 

high-burnup fuel. This figure shows that the outer node expands more than the other nodes do, 

and the expansion decreases from the surface to the center. Conceptually, the outer node 

determines the expansion of the pellet as if the whole pellet were at the peak temperature. This 

algorithm poses two practical problems. First, the temperature that is assigned to the outer 

node will be sensitive to the thickness of that node and hence the number of nodes chosen. 

Second, a very thin outer node will not have the ability to deform the cladding outward without 

some inward deformation of the node itself. Although this makes analysis difficult, a 

high-burnup fuel pellet will apparently expand considerably more than a fresh or low-burnup 

pellet for a given fuel enthalpy in an RIA.

The next factor to consider in high-burnup fuel is the pellet-to-cladding gap. This gap closes as 

a consequence of fuel pellet swelling during normal operation combined with cladding 

creepdown caused by a pressure differential during normal operation. As a result, all expansion 

of the fuel pellet will be transmitted to the cladding without any accommodation as in fresh fuel. 

Referring to an example above, it is seen that a 200-cal/g pulse would result in a cladding strain 

of more than 2.9 percent in high burnup fuel whereas that same pulse would result in a cladding 

strain of less than 1 percent in fresh fuel.
NUREG/KM-0004 10

Figure 8 (a) Scanning electron microscope image showing the ultrahigh-burnup rim 

structure and (b) elemental distribution as a function of the distance from the 

fuel-to-cladding interface in a fuel rod with a burnup of about 105 GWd/t (Figure

1 in Ref. 8)

Because of the difficulties in calculating pellet expansion, gap closure, and cladding strain, 

empirical data can be used to obtain the strain values. Figure 11 shows data from RIA tests 

with high-burnup fuel in the CABRI test reactor in France and the Nuclear Safety Research 

Reactor (NSRR) in Japan (Ref. 2). In general, a trend from higher strain for PWR fuel with the 

largest operating pressure differentials (i.e., greatest cladding creepdown) to BWR fuel with 

modest operating pressure differentials to test reactor fuel with no operating pressure differential

can be seen. The ordinate in Figure 11 shows only the measured plastic strain, so an additional 

elastic strain would exist in each test. Although the data exhibit a great deal of scatter, the total 

strain (plastic plus elastic) would clearly be greater than 2.9 percent for any of these cases at 

200 cal/g in agreement with the above discussion. Although it appears that fresh cladding could 

easily accommodate a 1-percent strain during the power pulse considered, it is not clear that 

irradiated cladding would be so accommodating.
11 NUREG/KM-0004

Figure 9 Edge-peaked pellet temperatures early in an RIA transient and center-peaked 

temperatures after significant heat transfer (based on Figure 24 and Figure 25 

in Ref. 9)
NUREG/KM-0004 12

Figure 10 Thermal expansion algorithms for (a) normal operation (highest temperature at 

pellet centerline) and (b) a zero-power RIA (highest temperature at the edge) in 

high-burnup fuel

Figure 11 Plastic strain measured in nonfailed cladding as a function of maximum fuel 

enthalpy change for tests in the CABRI test reactor and the NSRR (Figure 7 in 

Ref. 2)

During normal operation, corrosion (i.e., slow oxidation) of the Zr-alloy cladding takes place 

according to the following reaction:

Radius

Temp.

Temp.

Radius
13 NUREG/KM-0004

Zr + 2H2O → ZrO2 + 2H2

For each molecule of water (H2O) that reacts with the cladding to form zirconium dioxide (ZrO2), 

two H atoms are liberated. Much of the H is swept away in the flowing coolant, but a fraction of 

the H is absorbed in the cladding because the monoclinic oxide structure is not very protective. 

At burnups around 60 GWd/t, typical cladding materials will contain H ranging from 100 to 

800 weight-parts-per-million (wt.ppm), depending on the cladding alloy. Figure 12 shows that 

only about 50 wt.ppm of that H will be in solution at normal operating temperatures (Ref. 10). 

The remaining H will be in precipitates that will not dissolve during the nearly adiabatic period of 

an RIA power pulse. Like all precipitates, the hydrides will harden the cladding and reduce its 

ductility. The reduction in ductility will lead to cladding failure at lower and lower pulse energies 

as the H concentration increases (Figure 13). This type of failure, which is referred to as 

pellet-cladding mechanical interaction (PCMI) failure, generally starts with crack initiation in the 

brittle hydrided rim near the outside diameter (OD) and proceeds by a mixture of brittle and 

ductile failure modes through the rest of the cladding wall. 

Figure 12 Solubility of H in Zr as a function of temperature (based on Ref. 10)

Two significant comments can be made about Figure 13. First, such data are usually evaluated 

as a function of maximum fuel enthalpy change. This change corresponds to the expansion 

during the transient and does not include any expansion that might take place slowly as the 

temperature increases from room temperature to operating temperatures (e.g., in a PWR). 

Irradiated cladding can usually accommodate expansion that takes place slowly by some 

combination of cladding creepout and realignment of pellet fragments. Second, at very low H 

concentrations, the cladding has enough ductility to survive the period of the power pulse, but 

the high-temperature mechanism described above for fresh fuel ultimately causes it to fail 

around 170 cal/g (total).

0

50

100

150

200

250

300

350

400

450

500

0 100 200 300 400 500

Temperature (oC)

Hydrogen (wppm)
NUREG/KM-0004 14

Figure 13 RIA test data for irradiated fuel, plotted as maximum fuel enthalpy change as a 

function of H in the cladding (H content was estimated when data were not 

available); solid symbols indicate cladding failure (based on Figure 3 of Ref. 2)

Finally, fuel dispersal that could lead to a steam explosion would occur by a totally different 

mechanism in high-burnup fuel than in fresh fuel. In fresh fuel, the fuel must melt to produce a

sudden expansion that could expel hot fuel material. Fission gas bubbles, which accumulate on

grain boundaries (shown as pores in Figure 8(a)), can cause such an expansion in high-burnup 

fuel. The rapid heating of fuel material, especially in the gassy ultrahigh-burnup rim region near 

the pellet periphery, causes the breakup of the fuel pellets and the entrainment of particles in

gas that escapes through the cladding failure. Although data are sparse, most tests with 

high-burnup fuel in which the PCMI mechanism caused the failure experienced fuel dispersal 

that produced significant pressure pulses in the test apparatus. Based on the information 

presented in Figure 6, most fuel rods in a reactor would undergo a fuel enthalphy change of less 

than 70 cal/g during an RIA; however, Figure 13 shows PCMI failures in that range. Therefore,

some irradiated fuel with high H content might experience cladding failure, fuel dispersal, and 

the potential for a steam explosion in an RIA if such fuel were located near high-worth control 

rods.

0

50

100

150

200

250

300

350

0 50 100 150 200 250 300 350 400 450 500 550 600

Estimated Hydrogen Content (ppm)

Fuel Enthalpy Rise (cal/g)

BIGR

CABRI

IGR

NSRR

PBF

SPERT
15 NUREG/KM-0004

3. LOSS-OF-COOLANT ACCIDENTS

A pipe break or a leak in a component can initiate a LOCA. The LOCA at the Three Mile Island 

Nuclear Generating Station (Three Mile Island) in 1979 occurred when coolant was lost through 

a relief valve that did not close after a series of unplanned events. This accident evolved into a 

severe accident when an emergency core cooling pump, which had automatically started, was 

turned off because the operators mistakenly thought that the pressurizer volume was going 

“solid.” The Three Mile Island accident offered many lessons, and improved instrumentation 

and procedures should significantly increase the likelihood that a future LOCA would be 

successfully terminated. This section will address LOCAs up to the point at which they are 

successfully terminated by an emergency core cooling system.

In BWRs and PWRs, a postulated LOCA begins with a blowdown of steam through the pipe 

break or leak as water evaporates rapidly (flashes). The increase in coolant voids shuts down 

the nuclear reaction, but heat stored in the fuel and decay heat from existing radionuclides must

be removed to prevent excessive core temperatures. As the pressure in the vessel drops and 

core temperatures increase, emergency cooling systems are activated to add water to the 

vessel in an attempt to turn this temperature increase around. Figure 14 shows cladding 

temperatures and fuel rod pressures during a typical postulated LOCA that is successfully 

terminated by the emergency core cooling system (Ref. 11).

Figure 14 Cladding temperature (solid line) and rod pressure (dashed line) during a 

postulated LOCA (Figure 6 in Ref. 11)

Emergency core cooling systems are designed to provide enough cooling to limit fuel damage, 

and the extent of predicted fuel damage in a safety analysis determines the adequacy of these 

systems. After a lengthy public hearing, the U.S. Atomic Energy Commission in 1973 

concluded that fuel damage would be adequately limited if the cladding retained some ductility. 

Although limited ductility will not prevent fracturing, even marginal ductility will ensure that the 

cladding will exhibit its full tensile strength and be less susceptible to scratches and flaws than 

brittle material. This criterion was thought to be the best way to avoid fragmentation and keep 
NUREG/KM-0004 16

fuel pellets within fuel rods in a coolable array. The ductility concept was adopted by most 

countries with nuclear power reactors, and cladding ductility under LOCA conditions has been 

extensively studied.

3.1 Loss-of-Coolant Accidents with Fresh Fuel

This discussion considers the events that take place as cladding temperatures rise and then fall 

during a typical postulated LOCA transient. Figure 15 illustrates these events, which the 

following sections discuss.

Figure 15 Illustration of temperature progression and associated phenomena during a 

postulated LOCA

3.1.1 Phase Change

The first event for Zr-alloy cladding (much of this discussion will assume Zircaloy-4) is a phase 

change from the alpha phase (hexagonal close-packed structure) to the beta phase 

(body-centered cubic structure) with the transition beginning at about 800 degrees Celsius and 

completed at about 975 degrees Celsius. The paragraphs below discuss subsequent phase 

transformations.

3.1.2 Ballooning and Rupture

Because fuel rods are pressurized with helium (He) to improve internal heat transfer, fuel rods 

have a high internal pressure when they are at operating temperatures. By design, these fuel 

rod pressures are limited in relation to system pressures (i.e., approximately 2,250 pounds per 

square inch (psi) in PWRs and approximately 1,035 psi in BWRs) to ensure that cladding does 

not creep away from the fuel pellets, thus degrading heat transfer. During a LOCA, system 

pressure is lost, and therefore the differential pressure across the cladding wall is large. 

Because of changes in its lattice structure, the cladding material softens enough to balloon and 

rupture in the same temperature range as the phase transformation. Figure 16 shows the 

temperatures and the corresponding engineering hoop stress at which rupture occurs for 

Zircaloy-4 (Ref. 12). The following equation relates the engineering hoop stress σ to the fuel 

rod pressure:

σ = d ΔP / 2t,

Time (minutes)

Cladding Tempature (C)1200

800

400

Ballooning,

Rupture,

Phase Change

Diffusion,

Oxidation

Quenching,

Phase Change
17 NUREG/KM-0004

where d is the cladding inside diameter (ID), t is the cladding thickness, and ΔP is the pressure 

differential.

Figure 16 Correlations of rupture temperature and corresponding cladding stress for 

three heating rates (degrees Celsius per second) from data for Zircaloy-4

heated in steam (Figure 3 in Ref. 12)

Following a period of uniform outward deformation, a pressurized tube will eventually 

experience some local wall thinning that is triggered by a materials imperfection or, in the case 

of a fuel rod, a random local hot spot. As the wall thins, the local stress increases and the 

deformation will accelerate. This local deformation process is unstable, and the resulting 

balloon will soon burst. Because of the instability, it is not surprising that measured burst strains 

vary considerably from test to test; however, important trends are present. Figure 17 shows a 

large number of measured burst strains that reveal a maximum at around 800 degrees Celsius 

(Ref. 12). For this material (Zircaloy), 800 degrees Celsius marks the beginning of the phase 

transformation from alpha to beta. Thus, strains are apparently the largest when the material 

ruptures in the pure alpha phase, but the strains are reduced substantially when rupture occurs 

with a mixture of alpha and beta phases.
NUREG/KM-0004 18

Figure 17 Maximum circumferential strain as a function of rupture temperature for 

Zircaloy cladding heated in steam (Figure 8 of Ref. 12)

Figure 18 shows an unirradiated fuel rod that has ruptured in a simulated LOCA transient 

(Ref. 13). The size of the cladding balloons at the time of rupture is important for two reasons. 

First, the swollen fuel rods reduce the flow area for coolant during the subsequent course of the 

LOCA. However, the increased surface area for cooling along with the turbulence introduced by

the balloon usually result in a little extra cooling, rather than a temperature increase, in the 

balloon region.

Figure 18 Ballooned and ruptured region of unirradiated Zircaloy-2 after undergoing 

LOCA conditions (Figure 217 in Ref. 13)

Second, cladding balloons will have thinner walls than those of the undeformed cladding, thus 

leading to higher oxidation when measured as a percentage of the wall thickness (equivalent 

cladding reacted (ECR)). In fact, oxidation will also take place on the inside of the cladding as 
19 NUREG/KM-0004

well as on the outside because steam will enter through the rupture opening. This enhanced 

two-sided oxidation plays a significant role in most safety analyses.

3.1.3 Oxidation

When Zr is exposed to steam, it oxidizes at a more rapid rate than it does as a result of 

corrosion during normal operation. As the cladding temperature increases above

1,000 degrees C, the cladding surface oxidizes rapidly enough that more than 10 percent of the 

cladding wall thickness can be consumed during the period of a LOCA before emergency 

systems cool the core. The high-temperature tetragonal oxide structure is normally adherent 

and forms a protective layer on the cladding surface. Thus, H that is liberated in the

high-temperature reaction does not get into the metal and is swept away with the flowing steam.

As the protective oxide builds up on the surface of the metal, it slows down the rate of oxidation 

by increasing the distance that oxygen has to diffuse to reach the metal surface. In the 

important temperature range of 1,000–1,500 degrees C, the amount of oxygen consumed per 

unit time is found experimentally to obey parabolic kinetics, as follows:

dwg/dt = (k2

/2)/wg,

where wg is weight gain in grams per square centimeter of surface area, and k is a 

temperature-dependent coefficient. Under isothermal oxidation conditions, the integration of 

this equation is simply

wg

2

/2 = (k2/2) t,

or

wg = k t

1/2,

which plots as a parabola.

Most chemical reactions and diffusion processes involve movement from one state or location to 

another that is separated by an energy barrier. Such reactions and processes accelerate 

rapidly as temperature increases according to the following equation, which was named after 

the Swedish chemist, Svante Arrhenius (1859–1927):

k = a exp (-Q/RT),

where R is the universal gas constant; T is temperature in Kelvin; and the preexponential factor

and activation energy, a and Q, respectively, are determined experimentally. Combining the 

parabolic equation with the Arrhenius equation gives the following equation:

wg = a t

1/2 exp (-Q/RT)

Baker and Just (Ref. 14) performed an early study on Zr oxidation. Although it was found that 

the Baker-Just (B-J) correlation overestimates oxidation by as much as 30 percent around 

1,200 degrees Celsius, this equation is provided below because it has been so widely used:

wg (B-J) = 2.02 t

1/2 exp (-22,750/RT)
NUREG/KM-0004 20

Cathcart et al. (Ref. 15) performed a more recent and more accurate study of Zircaloy-4 

oxidation. The Cathcart-Pawel (C-P) correlation is as follows:

wg (C-P) = 0.602 t1/2 exp (-19,970/RT)

A related parameter that is often used is ECR, which is defined as the percentage of the 

cladding thickness that would be oxidized if all the oxygen stayed in the oxide layer as ZrO2. 

This parameter is artificial because some of the oxygen diffuses into the metal, but it is useful 

and is directly related to weight gain by simple geometric factors along with factors based on the 

density of Zr (6,500 kilogram per cubic meter = 6.5 grams per cubic centimeter) and on the 

atomic masses of Zr and oxygen. The following equations provide the conversion for one-sided

oxidation and two-sided oxidation:

one-sided oxidation ECR = 43.9 [(wg/h)/(1 - h/do)], and

two-sided oxidation ECR = 87.8 wg/h,

where ECR is a percentage, h is cladding thickness in centimeters, and do is the cladding OD in 

centimeters.

The oxidation reaction of Zr in steam is exothermic with a reaction heat of 140.5 kilocalories per 

mole of Zr (6.45x106 J/kg) (Ref. 3). This reaction heat (also called metal-water reaction heat) 

can be greater than the decay heat from radioactive nuclides at higher temperatures, and the 

reaction heat will then dominate the heat-transfer situation. If dw/dt is the rate of Zr mass that 

reacted with steam, then the power P in kilowatts per centimeter generated by the metal-water 

reaction per centimeter length of cladding is as follows:

P = 20.3 do dw/dt

If all of the oxygen is assumed to form stoichiometric ZrO2, then the mass of Zr that reacted is 

simply the following:

w = 91.2/32.0 wg,

where w is in grams per square centimeter of surface area, 91.2 is the atomic mass of Zr, and 

32.0 is the atomic mass of diatomic oxygen. Therefore, the following equation applies:

P = 57.9 do dwg/dt

Figure 19 provides an example of linear power for various temperatures and various oxidation 

levels.
21 NUREG/KM-0004

Figure 19 Linear power generation from the metal-water reaction for cladding with a 

diameter of 1.25 centimeters and various oxide thicknesses (Figure 4-69 in 

Ref.3)

3.1.4 Diffusion of Oxygen into the Metal

At the same time that oxidation is proceeding rapidly, oxygen from the cladding surface is 

diffusing rapidly into the cladding metal. However, Zr alloys in the beta phase cannot hold much 

oxygen. Therefore, as oxygen pours into the metal, near-surface regions with high oxygen 

concentrations change phase again—this time back to the alpha phase, which oxygen stabilizes

(i.e., the so-called oxygen-stabilized alpha phase). The oxygen solubility limit in the alpha and 

beta phases depends on temperature, as shown in Figure 20 (Ref. 16). For example, at 

1,200 degrees C, the beta phase can hold only about 0.7 weight-percent oxygen.

Finally, the emergency core cooling system will reflood the core, temperatures will begin to 

come down, and all of the cladding metal will return to the alpha phase. The imprint of the 

high-temperature phases can actually be seen microscopically at room temperature as shown in 

Figure 21 (Ref. 13). When the cladding temperature reaches its wetting (Leidenfrost) 

temperature in the range of 600–800 degrees C, the cladding will quench, and the temperature 

will fall quickly to the average water temperature. Because the containment is sealed, the 

containment pressure will rise somewhat, thus elevating the boiling point of water to about 

135 degrees C; therefore, the cladding does not return exactly to room temperature. At this 

lower temperature, oxygen diffusion is effectively stopped and the high-temperature oxygen 

distribution is frozen into the cladding, as illustrated in Figure 22.
NUREG/KM-0004 22

Figure 20 Pseudobinary Zircaloy-oxygen phase diagram (Figure 4 in Ref. 16)
23 NUREG/KM-0004

Figure 21 Microscopic image of unirradiated Zircaloy-2 after oxidation in steam at 

1,200 degrees Celsius for 600 seconds at room temperature (Figure 4 in Ref.13)

Figure 22 Qualitative diagram of oxygen concentration in Zircaloy cladding exposed to 

steam at high temperature

Zircaloy metal containing more than about 0.6 wt-percent oxygen is brittle. Therefore, only the 

low-oxygen material, which was in the beta phase when it was at high temperature, is ductile. 

To determine the LOCA conditions under which fuel rod cladding becomes brittle, mechanical 

tests are usually performed at 135 degrees C on short lengths, or rings, of cladding specimens 

that have been exposed to high-temperature steam for different lengths of time. Figure 23 

shows a ring-compression test that is generally used for this purpose. During compression, 

maximum tensile stresses are generated at the 12 o’clock and 6 o’clock positions on the ID and 

at the 9 o’clock and 3 o’clock positions on the OD. Zero ductility is assumed when failure 

occurs at one of these locations with a very small (1 percent) permanent strain.
NUREG/KM-0004 24

Figure 23 Diagram of ring-compression test

The transition from ductile to brittle failure could then be correlated with time; however, the time 

would strongly depend on the steam temperature. Instead, the ductile-to-brittle transition is 

usually correlated with the calculated (not measured) ECR using either the B-J equation or the 

C-P equation. This is in effect a variable transformation that combines both time and 

temperature. Using this method, the transition from ductile-to-brittle behavior is found at 

approximately 17-percent ECR as calculated with the C-P correlation for modern Zr-alloy 

cladding materials; this result is nearly independent of temperature. In other words, enough 

oxygen diffuses into the metal to cause embrittlement in the same amount of time that it takes 

Zircaloy to oxidize to 17-percent ECR. Because this is just a mathematical transformation, the 

same Zircaloy oxidation equation is used to evaluate embrittlement in all Zr-alloy cladding 

materials.

Interestingly, although the diffusion of oxygen controls the rate of oxidation and embrittlement of 

the cladding materials, the diffusion mechanisms are very different. In one case, oxygen is 

diffusing through the oxide; in the other case, oxygen is diffusing through the metal. Oxides 

such as ZrO2 have crystal structures that are ionic in nature, and local charge neutrality must be 

maintained. Therefore, if an impurity such as niobium (Nb) with a valence of +5 gets into the 

oxide, which normally has Zr cations with a valence of +4, the local lattice defect concentration 

is modified, and the diffusion rate is altered. Impurities like Nb are called aliovalent impurities. 

Note that tin (Sn) has a valence of +4 just like Zr; therefore, Sn impurities do not significantly 

affect diffusion in ZrO2. Consequently, alloys like M5 (Zr-1 percent Nb) oxidize at different rates 

than those of Zircaloy (Zr-1.4 percent Sn).

On the other hand, diffusion of oxygen in Zr metal results from an interstitial mechanism. The 

number of interstitial locations is fixed and not affected by substitutional impurities such as Sn 

and Nb. Therefore, the rate of embrittlement of different Zr-based cladding alloys should not be

sensitive to alloy composition. Figure 24 identifies these diffusion mechanisms and indicates

the oxygen solubility limits in the different phases.
25 NUREG/KM-0004

Figure 24 Illustration of diffusion mechanisms in Zr-based cladding alloys

3.1.5 Hydrogen Absorption

Two special circumstances exist in which H can be absorbed in the cladding metal during a 

LOCA transient. One involves a phenomenon called breakaway oxidation, and the other 

involves ruptured balloons. The significance of H absorption is that H acts like a catalyst and 

accelerates the embrittlement process partly by increasing the rate of diffusion of oxygen in the 

metal.

As stated previously, the reaction of Zr with steam during a LOCA normally produces a 

protective oxide layer on the cladding surface; however, this is not always the case. The normal 

protective tetragonal form can transform to a monoclinic form under some circumstances. The 

monoclinic form of ZrO2 is fragile and contains many cracks that give H access to the metal. 

Very soon after the monoclinic oxide forms at LOCA temperatures, sufficient H enters the metal 

to cause embrittlement long before the 17-percent ECR level is reached.

Several conditions can lead to early breakaway oxidation (Refs. 13 and 17). A rough surface on 

the cladding promotes the formation of a monoclinic oxide by providing alternate compressive 

and tensile stress states for crystal growth. Fluorine, which has been used in some etchants, 

also promotes breakaway oxidation. Impurities in Zr produced by the Kroll process seem to be 

beneficial in preventing breakaway oxidation compared with pure electrolytic Zr. However, the 

origins of breakaway oxidation are not well understood, and other factors may be involved.

Figure 25 shows two cladding materials that have the same nominal composition but were 

fabricated differently. The older Russian E110 alloy experienced breakaway oxidation in a few 

hundred seconds compared with the French M5 alloy, which shows no evidence of breakaway

oxidation after 2,400 seconds. After learning about the factors mentioned above, the Russian 

manufacturer, TVEL, altered the manufacturing process to avoid early breakaway oxidation in 

the E110 alloy (Ref. 18).
NUREG/KM-0004 26

Figure 25 Older E110 cladding showing early breakaway oxidation at 1,000 degrees C

compared with modern M5 cladding, which is resistant to breakaway oxidation

(based on Figure 88 in Ref. 13 and on related unpublished figures)

3.2 Loss-of-Coolant Accidents with High-Burnup Fuel

The same properties of high-burnup fuel that alter RIA behavior (Section 2.2) also alter LOCA 

behavior but in an entirely different manner.

3.2.1 Effect of Hydrogen

All of the H that existed as hydride precipitates in high-burnup fuel during normal operation will 

go into solution at LOCA temperatures, as shown in Figure 12 (off scale). As mentioned above, 

H in the cladding metal increases the rate of oxygen diffusion at LOCA temperatures and

accelerates the embrittlement process so that embrittlement occurs in less time than it takes to 

oxidize Zircaloy to 17-percent ECR. Figure 26 shows this effect for cladding with various H 

concentrations, using the calculated ECR (C-P correlation) as the measure of time at 

temperature. Data points in this figure that are not labeled with burnup values correspond to 

unirradiated cladding samples that were either as-fabricated or artificially charged with H. Each 

point in this figure represents a series of ring-compression tests that were conducted to locate 

the embrittlement threshold. The trend apparently applies equally to all of the Zr alloys, as 

expected (see Figure 24 and related text).
27 NUREG/KM-0004

Figure 26 Embrittlement threshold for cladding specimens exposed to steam at 

1,200 degrees Celsius and quenched after slow cooling to 800 degrees Celsius

(Ref. 19)

3.2.2 Inside Diameter Oxygen Pickup

The pellet-to-cladding gap closes early during the burnup process, and long-term contact 

between the pellet and cladding at operating temperatures results in diffusion welding, or 

bonding. This process occurs earlier in PWRs than it does in BWRs because of the different 

design pressures and cladding thicknesses, and the bonding is fully developed by about 

50 GWd/t in PWRs and 60 GWd/t in BWRs. Bonding can be seen microscopically (Figure 27), 

and technicians who remove fuel from high-burnup specimens for testing purposes have found 

tangible evidence of this bonding. When bonding is present, impact drilling is usually required 

to remove the fuel, and the bonding interaction layer along with attached pieces of fuel remain 

attached to the cladding.
NUREG/KM-0004 28

Figure 27 Interaction bonding layer between UO2 fuel and Zircaloy-4 cladding in a 

high-burnup specimen at 83 GWd/t (Figure 10 in Ref. 20)

The bonding layer is mostly ZrO2. Figure 28 provides insights into this bonding process. This 

Ellingham plot shows the free energy of formation of oxides with various metals that are relevant 

to nuclear fuel materials. Note that the formation energy is nearly the same for Zr, uranium, and 

Pu (prevalent in high-burnup fuel) and that all of these metals form dioxides. Thus, oxygen can 

be exchanged freely among them when the cladding and the fuel are in contact.
29 NUREG/KM-0004

Figure 28 Free energy of formation of oxides of Zr-alloy constituents and some 

impurities (Figure 1 in Ref. 13)

The consequence of fuel-to-cladding bonding for LOCA behavior is that an oxygen source is 

then present on the cladding ID and on the OD, as indicated in Figure 29.

-310

-260

-210

-160

-110

-60

-10

250 500 750 1000 1250 1500

-1300

-1100

-900

-700

-500

-300

-100

3/2Fe + O2 = 1/2Fe3O4

4Cu + O2 = 2Cu2O

4/3Fe + O2 = 2/3Fe2O3

Pu + O2 = PuO2

2Ni + O2 = 2NiO

Zr + O2 = ZrO2

Sn + O2 = SnO2

2Fe + O2 = 2FeO

Cu+ O2 = CuO

4K + O2 = 2K2O

4/3Cr + O2 = 2/3Cr2O3

4/3Al + O2 = 2/3Al2O3 U + O2 = UO2

2Mg + O2 = 2MgO

2Ca + O2 = 2CaO

Temperature (K)

ΔG = RT ln

ρ

O2 (kcal/mole O2)

ΔG = RT ln

ρ

O2 (kJ/mole O2)

4/5Nb + O2 = 2/5Nb2O5

2H2 + O2 = 2H2O

Th + O2 = ThO2

-310

-260

-210

-160

-110

-60

-10

250 500 750 1000 1250 1500

-1300

-1100

-900

-700

-500

-300

-100

3/2Fe + O2 = 1/2Fe3O4

4Cu + O2 = 2Cu2O

4/3Fe + O2 = 2/3Fe2O3

Pu + O2 = PuO2

2Ni + O2 = 2NiO

Zr + O2 = ZrO2

Sn + O2 = SnO2

2Fe + O2 = 2FeO

Cu+ O2 = CuO

4K + O2 = 2K2O

4/3Cr + O2 = 2/3Cr2O3

4/3Al + O2 = 2/3Al2O3 U + O2 = UO2

2Mg + O2 = 2MgO

2Ca + O2 = 2CaO

Temperature (K)

ΔG = RT ln

ρ

O2 (kcal/mole O2)

ΔG = RT ln

ρ

O2 (kJ/mole O2)

4/5Nb + O2 = 2/5Nb2O5

2H2 + O2 = 2H2O

Th + O2 = ThO2
NUREG/KM-0004 30

Figure 29 Oxygen sources for diffusion into cladding metal during a LOCA

During the high-temperature portion of a LOCA, cooling is poor, and the heat flux through the 

cladding is small. As a result, the cladding is nearly isothermal when it is at its highest 

temperatures and when most of the oxygen diffusion is taking place. Therefore, the oxygen 

diffusion rate is the same on the ID and the OD. Furthermore, because the quantity of oxygen 

needed to embrittle the metal is rather small (see Figures 22 and 24), the thicknesses of the OD 

and ID oxide layers are relatively unimportant—usually enough oxygen exists for embrittlement. 

Thus, when a well-developed bonding layer is present, the same amount of oxygen should enter 

the metal from the ID and the OD.

Figure 30 provides confirmation of this process. These micrographs were taken on a 

high-burnup fuel rod after testing under LOCA conditions in the Halden boiling heavy water 

reactor (Figure 27 shows a pretest micrograph). In Figure 30, the microscopist measured and 

labeled the thickness of the oxygen-stabilized alpha layer at the OD and ID at two azimuthal 

locations. In all cases, this alpha layer had the same thickness (about 20 microns) on the OD 

and ID. Because the interior edge of the alpha layer is fixed at an oxygen concentration of 

about 6.7 wt-percent (see Figure 22), the oxygen concentration profile is the same on the ID 

and OD, thus demonstrating that the same amount of oxygen entered from both directions.
31 NUREG/KM-0004

Figure 30 Grain morphology and alpha layer at the OD and ID of a high-burnup fuel rod 

exposed to LOCA conditions (Supplementary Figure 3.5.24 in Ref. 20)

3.2.3 Fuel Relocation

Because UO2 is a brittle ceramic, reactor startup and subsequent power changes cause fuel 

pellets to crack even at moderately low burnups. Figure 31 shows pellet fragments in two such

irradiated fuel rods that have been exposed only to normal operating conditions. If these pellet 

fragments could move axially into the enlarged volume of a cladding balloon during a LOCA, the 

heat generation rate within the balloon caused by radionuclide decay and stored heat would 

increase. This temperature increase would accelerate the embrittlement process in the balloon 

region.
NUREG/KM-0004 32

Figure 31 Fuel pellet fragments in PWR fuel rods after normal operation to low and 

medium burnup levels (Figure 30 in Ref. 21)

As cladding temperatures rise during a LOCA, unstable deformation, ballooning, and rupture will

all occur within a few seconds once the rupture temperature and pressure conditions are met 

(Figure 16). Immediately thereafter, cracked pellet fragments from just above the ballooned 

region move into the enlarged volume of the balloon. Gravity drives this movement, or 

relocation. Figure 32 shows an example of this process.

Figure 32 Cross-section of the rupture region of an irradiated fuel rod after testing under 

LOCA conditions (Figure 13 in Ref. 21)

Randomly oriented granules in a rubble bed or heap are characterized by a packing fraction that 

is less than unity. Figure 32 clearly shows that the fragmented fuel particles that have relocated 

into the balloon have a lower overall density than that of the original fuel pellets from which the 

fragments came. Therefore, a certain minimum balloon size would be required to realize an 
33 NUREG/KM-0004

actual increase in fuel mass within the balloon region. Figure 33 shows that the relative volume 

increase needed to accommodate additional mass in the balloon is about 18 percent for a large 

number of simulated LOCA tests with irradiated fuel rods. This corresponds to a packing 

fraction of about 82 percent on average. A diametral strain of less than 9 percent will give a 

volume increase of 18 percent; therefore, Figure 18 clearly shows that essentially all balloons 

that occur during a LOCA will be large enough to accommodate extra mass by fuel relocation.

Figure 33 Pellet stack reduction as a function of the increase in volume in cladding 

balloons for preirradiated fuel rods (Figure 32 in Ref. 21)

It should be noted here that Figure 8(a) shown in a previous section displays a special case of 

fuel relocation that can occur at very high burnups. Porosity is very high in the rim region 

(22 percent in the case shown), and the pores are filled with fission gas at high pressure. When 

the fuel rod pressure is released at the time of cladding rupture, the unopposed pressure within 

the pores fractures the brittle fuel material, and very small fuel particles are entrained in the 

fission gas and fill gas that escape through the rupture opening. 

Figure 34 shows the gamma scan of a fuel rod segment that had been subjected to LOCA 

conditions in the Halden boiling heavy water reactor. This fuel had a burnup of about 92 GWd/t, 

and more than 40 percent of the fuel volume had the rim structure. In this test, the entire upper 

portion (19 centimeters) of the fuel above the rupture opening was lost during rod 

depressurization. Researchers at Argonne National Laboratory have run similar out-of-pile tests 

on fuel that had a burnup of about 57 GWd/t with the observed loss of fuel amounting to less 

than that in one fuel pellet. Earlier LOCA tests at the Karlsruhe Nuclear Research Center on 

fuel with burnups no greater than 35 GWd/t resulted in no loss of fuel. Thus, very high burnup 

fuel with a well-developed rim structure may be susceptible to significant loss of fuel particles

during a LOCA transient.
NUREG/KM-0004 34

Figure 34 Gamma scan of very-high-burnup (approximately 92 GWd/t) fuel rod showing 

major loss of fuel material after LOCA testing (Figure 15 in Ref. 22)
35 NUREG/KM-0004

4. REFERENCES1

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More recent NRC documents can also be found at www.nrc.gov.
NUREG/KM-0004 36

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Fuel Behavior under

Abnormal Conditions

Office of Nuclear Regulatory Research

NUREG/KM-0004

NUREG/KM-0004

January 2013