Annals of Nuclear Energy 46 (2012) 97–105

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Annals of Nuclear Energy

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The effect of beam interruptions on the integrity of ADSR fuel pin cladding:A thermo-mechanical analysis

Ali Ahmad a,⇑, Suzanne L. Sheehy b, Geoffrey T. Parks a

a Department of Engineering, University of Cambridge, Cambridge CB2 1PZ, United Kingdomb ASTeC Intense Beams Group, Rutherford Appleton Laboratory, Didcot OX11 0QX, United Kingdom

a r t i c l e i n f o a b s t r a c t

Article history:Received 28 December 2011Received in revised form 18 March 2012Accepted 19 March 2012Available online 21 April 2012

Keywords:Accelerator Driven Subcritical ReactorAccelerator reliabilityCladding thermal fatigue damage

0306-4549/$ - see front matter � 2012 Elsevier Ltd. Ahttp://dx.doi.org/10.1016/j.anucene.2012.03.021

⇑ Corresponding author. Tel.: +44 1223 748245; faxE-mail address: aa579@cam.ac.uk (A. Ahmad).

During its lifetime in the core, the cladding of an Accelerator Driven Subcritical Reactor (ADSR) fuel pin isexpected to experience variable stresses due to frequent interruptions in the accelerator proton beam.This paper investigates the thermal fatigue damage in the cladding due to repetitive and unplanned beaminterruptions under certain operational conditions. Beam trip data was obtained for four operating highpower proton accelerators, among which the Spallation Neutron Source (SNS) superconducting acceler-ator was selected for further analysis. 9Cr–1Mo–Nb–V (T91) steel was selected as the cladding materialbecause of its proven compatibility with proposed ADSR design concepts. The neutronic, thermal andstress analyses were performed using the PTS-ADS, a code that has been specifically developed for study-ing the dynamic response to beam-induced transients in accelerator driven subcritical systems. The life-time of the fuel cladding in the core was estimated for three levels of allowed pin power and specificoperating conditions.

� 2012 Elsevier Ltd. All rights reserved.

1. Introduction

Accelerator Driven Subcritical Reactors are one of the possiblefuture fission reactor systems under consideration that target sus-tainability, enhanced safety and economic competitiveness. Inaddition, ADSRs can be used to incinerate problematic actinidewaste and long-lived radiotoxic fission products. Interest in ADSRsalso arises from the possibility of deploying thorium in them. Theuse of thorium in an ADSR was first proposed by Bowman et al.(1992). Thorium is three to four times more abundant in naturethan uranium and under certain circumstances produces fewerminor actinides than uranium-based nuclear fuel (InternationalAtomic Energy Agency, 2005).

The concept of an ADSR is based on the coupling of a particleaccelerator that delivers a beam of protons with energies of about1 GeV to initiate spallation reactions in a heavy metal target and ofa subcritical reactor fed by the spallation neutrons. The fact thatthe reactor core is inherently subcritical means that the reactorcan be shut down simply by shutting off the accelerator. Althoughthis coupling represents a major safety feature of the concept, itmakes the core dynamics susceptible to any change in the profileof the accelerator beam. Beam interruptions are a common occur-rence in all current accelerator technologies; the frequency and

ll rights reserved.

: +44 1223 332662.

duration of these interruptions, however, differ from one accelera-tor technology to another.

Following a beam trip, due to the subcritical nature of the reac-tor, the neutron flux in the core drops rapidly to a very low valueand so does the power. Consequently, temperatures across the corewill fall due to the lack of a heat source.1 Lengthy beam interrup-tions will have both economic and engineering impacts. The formeris related to unplanned shutdowns which according to Steer et al.(2011) can have a significant financial cost, while the latter is relatedto the degradation of the cladding mechanical integrity due to ther-mal fatigue. This study focusses attention on the thermo-mechanicalresponse of the fuel cladding to beam interruptions as this is thebarrier that prevents fission fragments from leaking into the coolantcircuit. As long as the cladding maintains its integrity, thermo-mechanical damage to the fuel pellets is of limited significance.

2. The accelerator system

High power proton accelerators are complex systems, consist-ing of many thousands of individual components. Existing acceler-ators of this kind are primarily based at research facilities and havenot been specifically designed or budgeted for very high reliability(Steer et al., 2012). Nevertheless, as a percentage of scheduledoperational time, mature high power proton accelerator facilities

1 As a conservative assumption, no contribution of decay heat to reactor power wasincluded in this study.

98 A. Ahmad et al. / Annals of Nuclear Energy 46 (2012) 97–105

can achieve availabilities of around 85–90% (Galambos et al.,2008). Experience dictates that it takes around 5 years of operatingto reach this level (Galambos, 2010). Accelerator reliability is theprobability that an item will perform a required function withoutfailure under stated conditions for a stated period of time (Hardy,2011). It is important to distinguish this from the availability ofan accelerator, defined as the delivered beam time as a percentageof the scheduled beam time, which also takes into account themaintainability of an item, or how quickly it can be repaired (Kece-cioglu, 1991). The reliability of an accelerator is closely related tothe occurrence of beam ‘‘trips’’, a term commonly used to describethe unscheduled or unplanned unavailability of the beam or theaccelerator system.

2.1. Causes and frequency of beam trips

The operational experience of existing facilities is usually docu-mented as part of operating procedures. It might be assumed thatinformation about the cause and frequency of trips could be usedto identify common failure points and therefore reduce the num-ber of trips in the future. For relatively new facilities this may in-deed be the case, such as for the Spallation Neutron Source(SNS), where the ion source and RF system were identified as beingprimary causes of down time during 2010 (Galambos, 2010). How-ever, every individual accelerator has different failure points, andanalysis supports the idea that, in mature facilities, no one partic-ular cause is accountable for beam down time, but rather a largenumber of causes contribute (Findlay, 2010).

The trip frequency and duration were collated in 2008(Galambos et al., 2008) for the following operating high powerproton accelerators:

� The ISIS Pulsed Neutron Source, a rapid cycling synchrotron atthe Rutherford Appleton Laboratory in the UK (0.24 MW pulsedbeam).� The separated sector cyclotron chain at the Paul Scherrer Insti-

tute (PSI) in Switzerland (1.2 MW continuous beam).� The normal conducting proton linear accelerator at Los Alamos

National Laboratory (LANSCE) (1 MW pulsed beam).� The superconducting proton linear accelerator for the SNS at

Oak Ridge National Laboratory in the USA (1.1 MW pulsedbeam).

This information is presented in Fig. 1, in which the data for ISIShas been updated to include a 12 year average up to 2010 (Findlay,2010) and the SNS data has been updated to 2010 values(Galambos, 2011). A standard deviation is shown where therelevant data has been provided.

Fig. 1. Trip frequency versus trip duration for existing high power protonaccelerators.

3. The PTS-ADS code

PTS-ADS is a Fortran77 code developed to couple the neutronkinetics of subcritical systems to a fuel pin heat transfer model.The code uses an implicit finite difference method, based onforward time-marching. At present, the code models a single chan-nel in a fast neutron spectrum reactor. The reactor kinetics aredescribed by a six-group point kinetics model with temperature-to-reactivity feedback included. The single channel heat transfermodel consists of a fuel heating model and a heat transfer modelfrom a heated wall to the coolant bulk.

The reactor physics of an ADSR is fundamentally different fromthat of critical reactors. Its subcriticality has many implications forthe neutronic behaviour of the core and thus for reactor control.While the power level of critical reactors depends on the fuel masspresent in the core and the deployment of control materials (con-trol rods, soluble boron, etc.), the power level in an ADSR dependson the margin of subcriticality and the accelerator beam current. Insubcritical reactors the total neutron flux is the summation of thesource neutrons, prompt fission neutrons and delayed neutrons.The source neutrons are produced via the spallation processthrough the interaction between the high energy protons in theaccelerator beam and the heavy metal spallation target, and there-fore their population is independent of the characteristics of themultiplying medium. In contrast, the populations of prompt anddelayed neutrons depend of the properties of the multiplying med-ium and on the intensity of the source. The neutronic kinetics canbe described by a six-group point kinetics model with a time-dependent neutron source. The use of a point kinetics model todescribe the physics of ADSRs was successfully demonstrated byEriksson et al. (2005). Detailed models and benchmarks of theneutronic and thermal aspects of the PTS-ADS code are includedin Ahmad and Parks (2012). In order to study the large variationsof stress in the cladding during beam interruptions, a thermalstress subroutine was added to the PTS-ADS code.

3.1. The PTS-ADS thermal stress model

The fuel pin cladding can be modelled as a thin hollow cylinderof inner radius rg and outer radius rc. Since the radius-to-heightratio is much less than unity, a plane axisymmetric stress modelcan be used to estimate the thermal stresses in steady-state andtransient operation. The model assumes that the axial loading atthe end of the cladding tube does not affect the calculation of thethermal stress at the fuel rod midplane, in accordance with SaintVenant’s principle (Boley and Weiner, 1960). The stress calcula-tions can be assumed independent of the end boundary conditionsbecause the radius-to-height ratio is very small.

The general stress–strain equation in an axisymmetric modelcan be written as:

r ¼ Dðe� ethÞ ð1Þ

where r, eth and e are vectors defined by:

r ¼

rz

rr

rh

s

26666664

37777775

; eth ¼

aT

aT

aT

0

26666664

37777775

; e ¼

@v=@z

@u=@r

u=r

@u=@zþ @v=@r

26666664

37777775

ð2Þ

where rz, rr and rh are the stress components in the axial, radialand azimuthal directions respectively, s is the shear stress, a isthe coefficient of thermal expansion, T is the temperature, and uand v are the displacements in the radial and axial directions. WhileD is a matrix that has the following form:

Fig. 2. Comparison of the PTS-ADS and ANSYS predicted stress distributions acrossthe cladding.

A. Ahmad et al. / Annals of Nuclear Energy 46 (2012) 97–105 99

D ¼ Eð1þ mÞð1� 2mÞ

ð1� mÞ m m 0

m ð1� mÞ m 0

m m ð1� mÞ 0

0 0 0 ð1� 2mÞ=2

26666664

37777775ð3Þ

where E is Young’s modulus and m is Poisson’s ratio.Since the problem is axisymmetric and axial displacement is

neglected, the equilibrium equation in the absence of body forcescan be written as:

@rr

@rþ ðrr � rhÞ

r¼ 0 ð4Þ

Using Eqs. (1) and (4), one can obtain the following differentialequation for the radial displacement u:

ddr

1r

dðruÞdr

� �¼ a

1þ m1� m

� �dTdr

ð5Þ

By integrating twice, the general solution of Eq. (5) is:

uðrÞ ¼ a1þ m1� m

� �1r

Z r

rg

Trdr þ Ar þ Br

ð6Þ

where A and B are integration constants. The radial stress can benow deduced by using Eqs. (1) and (6):

rrðrÞ ¼ �aEð1� mÞ

1r2

Z r

rg

Tr dr þ Eð1� mÞA�

Eð1þ mÞ

1r2 B ð7Þ

A and B can be found using the boundary conditions on theradial stress at the cladding inner and outer surfaces:

rrðrgÞ ¼ �pg ð8ÞrrðrcÞ ¼ �pe ð9Þ

where pg is the internal pressure due to the accumulation of fissiongases and pe is the external pressure acting on the cladding outersurface. In this case we have:

Eð1� mÞA�

Eð1þ mÞ

Br2

g¼ �pg ð10Þ

� aEð1� mÞ

1r2

c

Z rc

rg

Tr dr þ Eð1� mÞA�

Eð1þ mÞ

Br2

c¼ �pe ð11Þ

Using Eqs. (10) and (11):

A ¼ a

r2c � r2

g

� � Z rc

rg

Tr dr þ ð1� mÞE

pgr2g � per2

c

� �r2

c � r2g

� � ð12Þ

B ¼ 1þ m1� m

� � ar2g

r2c � r2

g

� � Z rc

rg

Tr dr þ ð1þ mÞE

r2c r2

gðpg � peÞ

r2c � r2

g

� � ð13Þ

If we define:

vðrÞ ¼r2 � r2

g

r2c � r2

g; wðrÞ ¼

r2 þ r2g

r2c � r2

gð14Þ

then, using the results in Eqs. (12) and (13), rr(r) can be written as:

rrðrÞ ¼aEð1� mÞ

1r2 vðrÞ

Z rc

rg

Tr dr �Z r

rg

Tr dr

" #� pg

þ r2c

r2

� �vðrÞðpg � peÞ ð15Þ

In a similar manner, rh(r) and rz(r) can be written as follows:

rhðrÞ ¼aEð1� mÞ

1r2 wðrÞ

Z rc

rg

Tr dr þZ r

rg

Tr dr � Tr2

" #� pg

þ r2c

r2

� �wðrÞðpg � peÞ ð16Þ

rzðrÞ ¼aEð1� mÞ

2

r2c � r2

g

� � Z rc

rg

Tr dr � T

24

35� 2pg þ

2r2c

r2c � r2

g

� ��ðpg � peÞ ð17Þ

At every time step during the simulation of a beam interruptiontransient, the PTS-ADS code computes the integrals in Eqs. (15)–(17) numerically using the extended quadrature rule (Monegato,1976):

Z rc

rg

Tr dr ¼ dcTðrcÞrc � TðrgÞrg

2þPnc�1

i¼2TðriÞri

� �ð18Þ

where nc is the number of radial cladding nodes and dc = [rc � rg]/nc.The stress components can be then calculated at each time step andconsequently the equivalent stress requsing:

req ¼1ffiffiffi2p

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiðrr � rhÞ2 þ ðrh � rzÞ2 þ ðrz � rrÞ2

qð19Þ

The comparison between the PTS-ADS stress calculations andthose of a finite element (FE) model of the cladding is shown inFig. 2. The FE model was built using the commercial code ANSYS(ANSYS, 2009). Fig. 2 shows that the results of PTS-ADS’s semi-ana-lytical stress model are in good agreement with those predicted byANSYS. The radial, axial and tangential (hoop) stresses in steady-state operation depend on the fission gas pressure within the clad-ding, the external coolant pressure and the temperature distribu-tion across the cladding. Assuming that the external and fissiongas pressures remain constant over time, the steady-state stressdistribution in the cladding will depend only on the fuel pin power.For the validation case shown in Fig. 2, no pressure loads were ap-plied to the cladding inner and outer surfaces. The radial stressesare negligible compared to other stress components and can there-fore be ignored. The hoop stress is negative at the inner claddingsurface and positive at the outer surface. This is due to the fact thatthe cladding inner surface is hotter than the average cladding

100 A. Ahmad et al. / Annals of Nuclear Energy 46 (2012) 97–105

temperature. This induces compressive stresses on the inner sur-face, while the outer surface is in tension as it is colder than theaverage cladding temperature.

4. Analysis parameters

4.1. T91 steel as a cladding material

The choice of the fuel pin cladding material depends primarlyon the reactor technology involved. While magnesium and zirco-nium alloys are favoured for thermal reactors, mainly because oftheir low neutron absorption cross-sections, stainless steel is thestandard fuel cladding material for fast reactors cooled by liquidmetals, such as lead or lead–bismuth eutectic (LBE). The issue ofneutron absorption is not as important in fast reactors as it is inthermal reactors. The main requirement of the cladding materialin a fast reactor is good mechanical properties at elevated temper-atures. For a LBE-cooled ADSR, the fuel pin cladding material mustexhibit:

� sufficient strength with limited loss of ductility and fracturetoughness;� high swelling resistance;� low creep rates;� excellent thermal properties;� high corrosion resistance.

Finding a cladding material that meets the above criteria is achallenging process that requires extensive research and testing.For a LBE-cooled ADSR, ferritic–martensitic steels (FMS) seem tobe promising candidates (Klueh et al., 2002). Among FMS there isa particular interest in the modified 9Cr–Mo (T91) steel becauseof its lower swelling rates and embrittlement under neutron irradi-ation at T > 350 �C (Van den Bosch, 2008; Gupta et al., 2006). TheMYRRHA (Multi-purpose hYbrid Research Reactor for High-techApplications) project has selected 15–15 Ti stabilized austeniticsteel as the fuel cladding material for the first MYRRHA cores butplans to use T91 steel for future fuel loadings, once qualificationis completed (MYRRHA, 2002).

4.2. The SNS superconducting linear accelerator

In an ADSR, the accelerator provides protons of sufficient energyto initiate spallation interactions in the target. The SNS facility cou-ples a 1 GeV superconducting linear proton accelerator to a liquidmercury spallation target developed at Oak Ridge National Labora-tory. The facility provides the most intense pulsed neutron beamsin the world for scientific research and industrial development.Among the accelerator facilities for which data is shown in Fig. 1,SNS was chosen for further study here because, of the four facilitiesstudied, it was able to provide the most detailed statistics on beamtrips, with data broken down into relevant time intervals, includinga number of intervals between 1 s and 1 min.

SNS is the most recently built high power accelerator and hasthe highest proton beam energy of existing facilities. The beamproduces a high number of spallation neutrons per incident proton,and is therefore comparable to that required for an industrialADSR. The superconducting linear accelerator at SNS regularly pro-vides 1.1 MW of proton beam power to the target, with a designvalue of 1.4 MW, and plans for future upgrades to increase thisto around 3 MW (Henderson, 2010). Fig. 3 shows the beam trip fre-quency per day of the SNS accelerator for its 2009 and 2010 runs.The averages of the 2009 and 2010 beam trip values were taken asinput for the thermo-mechanical analysis performed in this work.

4.3. Cladding temperature limits

The temperature is an important factor in determining the fuelpin cladding thermo-mechanical response. During its lifetime inthe reactor core, the cladding may suffer a variety of effects suchas fatigue, creep, swelling, embrittlement and irradiation damage.All these effects vary with temperature, and more importantly, theconsequences of these effects can depend significantly on the clad-ding temperature. Therefore, it is important to define an operatingtemperature range outside which the cladding is likely to fail.

4.3.1. Lower temperature limitIn liquid–metal-cooled reactors two main issues can potentially

cause serious problems at relatively low temperatures: solidifica-tion of the liquid metal coolant and irradiation embrittlement.While the former is unlikely to occur in the case under consider-ation, because of the low melting point of LBE (Tm = 123.5 �C) andthe presence of emergency core heating systems, the latter is moreserious as the embrittlement upper temperature limit is close tothe cladding temperature at nominal operation. According to thefinal report of the SPIRE project (Alamo, 2002), all martensiticsteels, including T91, show a high degree of embrittlement underneutron irradiation in the temperature range 100–325 �C due todisplacement damage. Consequently, the SPIRE report recom-mends that the cladding service temperature needs to be greaterthan 350 �C to avoid embrittlement effects.

4.3.2. Upper temperature limitIn a lead–bismuth environment, corrosion is an important issue

as it contributes significantly to the degradation of the mechanicalintegrity of the reactor structures, including the fuel cladding. Thecompatibility of various cladding materials with an LBE environ-ment under different operating conditions was tested in the TECLAproject (Ait Abderrahim, 2005). More recent work on the corrosionof T91 in an LBE environment has been undertaken by Weisen-burger et al. (2011) with a particular focus on long-term corrosionbehaviour. High operating temperatures were observed greatly toinfluence the build-up of oxide scales in LBE with a high oxygenconcentration. The estimated thickness of the oxide layer (magne-tite and spinel) measured for an oxygen concentration of 10�6 wt.%and an LBE flow velocity of 1 m/s was about 29 lm at 480 �C and45 lm at 550 �C for a period of operation of less than 1 year.According to Weisenburger et al. (2011), too thick an oxide scalehas three major effects: (1) it deteriorates the thermal conductivityof the cladding; (2) it might spall off and plug cooling channels;and (3) it induces metal recession which reduces the load bearingcapacity. One of the main findings of the TECLA project is the pres-ence of an upper temperature threshold in the range 550–650�C.However, as discussed in Weisenburger et al. (2011), we considerthis temperature range to be too broad and a bit too high. There-fore, for this study, an upper cladding temperature limit of550 �C was chosen. Consequently, the maximum thermal powera fuel pin can generate was found to be 12.8 kW. Two other powerlevels were also studied: 7.2 kW, the power of an XADS fuel pin(D’Angelo et al., 2004), and 10 kW, an intermediate power level be-tween the XADS and maximum values.

5. Results and discussion

In steady-state operation, the cladding has a constant logarith-mic temperature distribution, and therefore the thermal stress in-duced as a result of the radial temperature variation has a constantvalue. When a beam trip occurs, the fuel pin power will fall rapidlyto a very low value due to the subcritical nature of the core, andconsequently the fuel and cladding temperatures will start to

Fig. 3. SNS distribution of beam interruptions per day in 2009 and v010 (Galambos, 2011).

Fig. 4. Cladding inner surface temperature variation for different beam tripdurations at 12.8 kW pin power.

A. Ahmad et al. / Annals of Nuclear Energy 46 (2012) 97–105 101

decrease. If the trip is prolonged, the core power will fall to the le-vel of the decay heat power, which depends on the composition ofthe fuel and its burn-up. Thus, during beam interruptions the clad-ding temperature drops significantly. Frequent large temperaturevariations due to repetitive beam interruptions are expected tocontribute to the degradation of the mechanical integrity of thecladding through cyclic thermal fatigue.

The PTS-ADS code was used to calculate the temperature varia-tions in the fuel cladding during beam interruptions. The fuel pingeometry and the physical properties of the fuel, cladding andcoolant were taken from the XADS fuel pin design (D’Angeloet al., 2003; D’Angelo et al., 2004). The values and correlationsfor the thermo-physical properties of XADS materials are listed inTable 1. In sodium-cooled fast reactors the temperature differencebetween the cladding and the coolant bulk does not normally ex-ceed 10 K. However, the lower thermal conductivity of lead andLBE (the main candidate coolants for fast ADSRs) increases theclad–coolant temperature difference significantly. Therefore, anappropriate choice of correlation for the heat transfer coefficientis essential. The current version of the PTS-ADS code uses the heattransfer correlation derived by Mikityuk (Pfrang and Struwe,2007). The adopted correlation, shown in Eq. (20), is for triangularfuel bundles and represents the best fit of 658 experimental datapoints.

Nu ¼ 0:047 1� e�3:8 PD�1ð Þ

� �ðPe0:77 þ 250Þ ð20Þ

where Nu is Nusselt number, P is the pitch, D is the cladding outerdiameter and Pe is Peclet number.

Fig. 4 shows the temperature variation of the cladding innersurface during beam trips of different durations for a fuel pinpower of 12.8 kW, which corresponds to the maximum allowedpin power. Throughout the period of the transient, the inlet coolant

Table 1XADS fuel pin material properties (D’Angelo et al., 2003).

Property Units Correlation or value

Clad thermal conductivity, kc (W K�1 m�1) 15.4767 + 0.003448TClad density, qc (kg m�3) 7924Clad specific heat capacity, Cpc (J kg�1 K�1) 620Fuel thermal conductivity, kf (W K�1 m�1) [0.042 + 2.71 � 10�4T]�1 + 6.9 � 10Fuel density, qf (kg m�3) 10,354UO2 specific heat capacity, CpUO2

(J kg�1 K�1) 81.825 + 0.78695T � 1.1552 � 10�

PuO2 specific heat capacity,CpPuO2

(J kg�1 K�1) �4.9236 � 106T�2 + 240.89 + 0.325

Fuel specific heat capacity, Cpf (J kg�1 K�1) 214:65270:21

CpUO2þ 55:56

270:21CpPuO2

Coolant density, q (kg m�3) 11,112 � 1.375TCoolant specific heat capacity, Cp (J kg�1 K�1) 146.5

temperature was kept constant at 300 �C. It can be seen that inter-ruptions of duration longer than 30 s have the same thermaleffects. Consequently, for the purposes of assessing thermal fati-gue, one can treat all beam trips of duration longer than 30 s asequivalent.

Following a beam interruption, the fuel pin cladding will expe-rience a thermal shock due to the rapidly decreasing temperature.The equivalent (Von Mises) stress will then reach a peak value cor-responding to the maximum strain induced by thermal expansion.The variation in the peak equivalent stress for beam trips of differ-ent durations is shown in Fig. 5. As predicted by the thermalresponse shown in Fig. 4, interruptions of longer than 30 s resultin the same peak stress for a given pin power. Fig. 5 also confirms

�11T3

3T2 + 9.9037 � 10�7T3 � 5.1982 � 10�10T4 + 1.5241 � 10�13T5 � 1.7906 � 10�17T6

56T � 3.5398 � 10�4T2 + 1.512 � 10�7T3 � 1.9707 � 10�11T4

Fig. 5. Cladding peak equivalent stress for different beam trip durations and yieldstresses at different values of pin power.

102 A. Ahmad et al. / Annals of Nuclear Energy 46 (2012) 97–105

the agreement between the PTS-ADS estimations of the peak stressand those predicted by the FE model.

5.1. Life prediction of fuel pin cladding

To assess the impact of frequent beam interruptions on thecladding of an ADSR fuel pin, we need to calculate the thermalfatigue damage fraction associated with each beam trip of specificduration. The first step towards this is to calculate the number ofstress cycles to failure Nf for each beam trip duration separately.Nf is related to the amplitude of stress or strain variation byBasquin’s law (Basquin, 1910):

ra ¼ r0f ð2Nf Þb ð21Þ

where ra is the stress amplitude:

ra ¼rmax � rmin

2ð22Þ

r0f is the fatigue strength coefficient and b is the fatigue strengthexponent (Basquin’s exponent). Coffin (1971) and Manson (1966)proposed a more general formula which accounts for plasticcycling:

Det ¼ Dee þ Dep ¼ KeðNf ÞCe þ KpðNf ÞCp ð23Þ

where Det, Dee and Dep are the total, elastic and plastic strain rangesrespectively, Ke is the elastic coefficient, Kp the plastic coefficient, Ce

is the elastic exponent and Cp the plastic exponent. According to thework of Manson and Coffin, the Dee term dominates where stressesare lower than the yield stress. The cyclic straining in this case isgenerally associated with high cyclic fatigue. On the other hand,the Dep term is dominant where stresses are higher than the yieldstress and, in this case, the number of cycles to failure is expectedto decrease further due to plastic deformation.

Fig. 5 shows the peak equivalent stresses as a function of tripduration for different pin power levels along with lines indicatingthe yield stress of T91 steel at the corresponding steady-state oper-ating temperatures. For the 7.2 kW and 10 kW pin power cases, thepeak equivalent stresses are below the yield stress. Therefore, Bas-quin’s law, which is the reduced form of the Manson–Coffin law forelastic straining, can be used to estimate the number of cycles tofailure. In the 12.8 kW pin power case, the peak equivalent stressexceeds the yield stress for trips of duration of more than �20 s.Therefore, the number of cycles to failure for all beam interruptions

longer than 20 s in the 12.8 kW case were calculated using the plas-tic term of the Manson–Coffin law.

For the elastic calculations based on Eq. (21), r0f and b can be ob-tained using (Socie et al., 1978):

r0f ¼ ruts þ 345 ð24Þ

b ¼ �16

log10

2r0fruts

� �ð25Þ

where ruts is the ultimate tensile strength of T91 steel in MPa. Thethermo-mechanical properties of T91 steel at operating tempera-tures corresponding to fuel pin powers of 7.2, 10 and 12.8 kW arelisted in Table 2.

For the calculations using the plastic term of the Manson–Coffinlaw, r0f is again estimated using Eq. (24), then the cyclic strainhardening exponent n0 and the cyclic strength coefficient K0 canbe obtained using (Troshchenko and Khamaza, 2010):

n0 ¼ Ce

Cpð26Þ

K 0 ¼r0fðKpÞn

0 ð27Þ

The plastic strain component can be then calculated using:

ra ¼ K 0Dep

2

� �n0

ð28Þ

Finally, the number of cycles to failure, Nf, can be calculated usingEq. (23). Values of the coefficients of the elastic and plastic termsof Eq. (23) for T91 steel in air are shown in Table 3. Values forT91 steel in an air environment are used here, because the focusof this study is the impact of thermal fatigue damage on ADSR fuelpin cladding; the additional impact of environmental factors, suchas corrosion due to the LBE coolant, is the focus of ongoing work.

The effect of the mean stress was accounted for by introducing acorrection factor to the stress amplitude ra. The corrected stressamplitude rmod

a has the following form:

rmoda ¼ ra

1� ðrm=rutsÞ2ð29Þ

where rm is the mean stress:

rm ¼rmax þ rmin

2ð30Þ

Eq. (29) was taken from Lafuente et al. (2008). It is a variation of theGoodman model (Goodman, 1989) which was proposed by Wire etal. (1999).

Fig. 6 shows the variation in the number of cycles to failure as afunction of beam interruption time for the three pin power levelsconsidered. According to the above analysis, no plasticity correc-tion is required for the 7.2 and 10 kW cases. In the 12.8 kW case,the plasticity correction takes effect for trips of duration exceeding�20 s. As expected, plasticity effects reduce the numbers of cyclesto failure. However, the reduction in Nf is not dramatic as the peakequivalent stress at the maximum allowed pin power is onlyslightly higher than the yield stress of T91 steel at 550 �C, as shownin Fig. 5.

After estimating Nf at different beam trip durations separately,the second step in predicting the life expectancy of the claddingis to estimate the combined impact of beam interruptions basedon the SNS data presented in Fig. 3. The cladding of an ADSR fuelpin is expected to experience stresses of various amplitudes inthe face of beam interruptions of different durations. The thermalfatigue damage in such a case can be assessed by expressing thenumber of cycles experienced at each stress amplitude (corre-sponding to a beam interruption of given duration) as a fraction

Table 2T91 steel mechanical properties at different operating temperatures.

Temperature (�C) 440 495 550 Reference

Young’s modulus (MPa) 178,885 175,333 163,000 Ashrafi-Nik (2006)a (10�6/K) 11.96 12.14 12.33 Ashrafi-Nik (2006)Yield stress (MPa) 610 560 500 Maloy et al. (2002)Ultimate tensile strength (MPa) 650 600 525 Maloy et al. (2002)

Table 3Coefficients of the elastic and plastic terms of the Manson–Coffin fatigue relationship for T91 steel in air.

Temperature (�C) Ke Ce Kp Cp n0 K0 Reference

550 0.502 �0.09 20.52 �0.61 0.147 557 Weisenburger et al. (2008)

Fig. 6. Number of cycles to failure as a function of beam trip duration and pinpower.

2 It is important to note, however, that in synchrotron light sources the ‘availability’statistics are commonly improved by the addition of more running time at the end ofa user cycle to make up for ‘lost time’ due to a failure. This changed definition ofavailability is not to be neglected when comparing availability statistics (Lüdeke,2011).

A. Ahmad et al. / Annals of Nuclear Energy 46 (2012) 97–105 103

of the total number of cycles to failure for that stress amplitude.The accumulated cladding fatigue life can then be found by sum-ming these contributions over the distribution of beam interrup-tions experienced. When the sum reaches unity, the cladding’sfatigue life is exhausted. This method for combining the fatigue ef-fects of different stresses is known as Miner’s Rule of cumulativedamage (Miner, 1945), and the failure condition can be expressedmathematically as:

Pmi¼1

ni

Nfi¼ 1 ð31Þ

where m is the number of different beam trip durations considered,Nfi is the number of cycles to failure corresponding to ith beam tripduration, and ni is the number of trips of that duration experienced.ni depends on the total number of trips experienced and the relativedistribution of trips of different durations.

The thermal fatigue damage fraction contributions from eachbeam interruption interval based on the above analysis for a pinpower of 12.8 kW using the SNS data are shown in Fig. 7. Theoperational life expectancy of the cladding can now be predictedby dividing unity by the total damage fraction accumulated perday. The lifetime estimations for T91 steel cladding at operatingpin powers of 7.2, 10 and 12.8 kW are reported in Table 4. Twoapproaches were used to estimate the cladding lifetime: a conser-vative estimation based on the assumption that all beam tripsthat occur with a specified duration range have the duration ofthe upper bond of the range, and an average approach which

assumes that all beam trips have the duration of the midpointof the range.

Table 4 shows that the T91 steel cladding of a fuel pin operatingat 12.8 kW can be expected to fail in about 24 days according to theconservative estimate and in 33 days according to the average esti-mate. The cladding lifetime is significantly extended by moving tolower power levels. Fuel dwell times of about 5 years are envisagedfor ADSRs (Rubbia et al., 1995). Therefore, assuming acceleratorreliability similar to that of the SNS linear accelerator, these calcu-lations show that ADSR cladding mechanical integrity would notbe limited by thermal fatigue damage if the operational pin powerwas 7.2 or 10 kW. However, long beam interruptions may still beeconomically costly as a result of bringing the whole system to ahalt (Steer et al., 2011).

It is important to note that the operational life expectanciesestimated here do not take into account the impact of environmen-tal effects, such as oxide scale formation (as mentioned in Section4.3.2), cracking or liquid metal corrosion; for instance, Jianu et al.(2009) found that an LBE environment affected the creep-to-rup-ture behaviour of T91. The effect of environmental factors on theintegrity of ADSR fuel pin cladding is the subject of ongoingresearch and a planned future publication by the authors.

6. Achieving high accelerator reliability

It should be noted that not all accelerator facilities operate withthe same availability. For example, synchrotron radiation sourcesexert a lot of effort in maintaining good reliability, and routinelyachieve an availability of 98–99% with between 40 and 100 faultsper year (Hardy, 2011).2 While these machines are quite differentto most high power proton sources in both design and operation,it is clear that an effort to improve reliability can positively impacton the operational availability of an accelerator.

The necessary approach is to adopt reliability-oriented design.Three main areas of design have been identified that will contrib-ute to improved reliability for a given machine (Biarrotte, 2009).The first area is the ‘over-design’ of components, to ensure thatitems are running well within the limits of existing technology.This may include the preferential choice of technology with ademonstrated capacity for reliability. Redundancy is the secondkey focus area, particularly for elements with a history of hightrip-rates. In a linear accelerator this includes the ion source and

Fig. 7. The thermal fatigue damage fraction contributions per day for beam interruptions of various durations for T91 cladding at a pin power of 12.8 kW.

Table 4Estimates of the operational life expectancy of T91 cladding at different pin powerlevels.

Pin power (kW) Conservative estimate (days) Average estimate (days)

7.2 3,027,195 3,659,61410 7109 833212.8 24 33

104 A. Ahmad et al. / Annals of Nuclear Energy 46 (2012) 97–105

RF power supplies (Galambos, 2010), whereas in a high powercyclotron the electrostatic extraction elements are a frequent causeof down-time (Seidel, 2011). The third possible area is ‘fault-toler-ance’, or the ability for continued operation despite faults in basiccomponents.

Naturally, system complexity and the total number of compo-nents is also a critical driver in machine reliability. This is mostpertinent in systems where a single component failure can leadto a whole system failure. Reducing the overall complexity of themachine could therefore play a large role in improving the reliabil-ity of the system, thereby allowing improved system availability. Itis not currently known what the ultimate achievable level of reli-ability for a high power proton accelerator is. However, it is clearthat approaches involving reliability-oriented design together withdetailed reliability analysis will be necessary to achieve the highreliability required for future applications including ADSRs.

7. Conclusion

In this paper, a thermo-mechanical analysis of ADSR fuel clad-ding subjected to frequent beam interruptions has been conducted.Results show that the operating temperature has a significant im-pact on cladding fatigue damage and therefore its lifetime in thecore. Cladding operating near the upper temperature limit of550 �C is expected to fail due to thermal fatigue in less than amonth if the current accelerator technology is deployed. To operatean ADSR at high power levels, accelerator reliability will need toimprove significantly, particularly with respect to the beam inter-ruptions of between 10 s and 10 min. Beam trips of shorter dura-tion have a limited impact because of the low stress peaksinduced, while those of longer duration also have little impact onthe fatigue damage because of their low frequency of occurrence.However, lengthy beam trips will certainly have economic conse-quences which need to be assessed separately.

Acknowledgements

The authors thank J. Thomason (ISIS), J. Galambos (SNS) and M.Seidel (PSI) for their helpful discussions regarding beam trips inoperational accelerators.

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