Journal of Nuclear Materials 367–370 (2007) 1337–1343

www.elsevier.com/locate/jnucmat

Proposed damage evolution model for large-scale finiteelement modeling of the dual coolant US-ITER TBM

S. Sharafat a,*, J. El-Awady a, S. Liu a, E. Diegele b, N.M. Ghoniem a

a University of California Los Angeles, Los Angeles, CA 90095-1597, USAb Forschungszentrum Karlsruhe, Weberstr. 5, 76133 Karlsruhe, Germany

Abstract

Large-scale finite element modeling (FEM) of the US Dual Coolant Lead Lithium ITER Test Blanket Module includ-ing damage evolution is under development. A comprehensive rate-theory based radiation damage creep deformation codewas integrated with the ABACUS FEM code. The advantage of this approach is that time-dependent in-reactor deforma-tions and radiation damage can now be directly coupled with ‘material properties’ of FEM analyses. The coupled FEM–Creep damage model successfully simulated the simultaneous microstructure and stress evolution in small tensile test-barstructures. Applying the integrated Creep/FEM code to large structures is still computationally prohibitive. Instead, forthermo-structural analysis of the DCLL TBM structure the integrated FEM–creep damage model was used to develop truestress–strain behavior of F82H ferritic steel. Based on this integrated damage evolution-FEM approach it is proposed touse large-scale FEM analysis to identify and isolate critical stress areas for follow up analysis using detailed and fully inte-grated creep–FEM approach.� 2007 Elsevier B.V. All rights reserved.

1. Introduction

The US Dual Coolant Lead Lithium (DCLL)ITER Test Blanket Module (TBM) structure willbe subject to complex cyclic thermo-mechanicalloading [1]. Reliable performance prediction of theDCLL structure requires large-scale, 3-dimensionalfinite element analysis coupled with deformationdamage models.

Within the framework of the VISTA (VirtualInternational Structural Test Assembly) project,finite element modeling of thermo-mechanical per-

0022-3115/$ - see front matter � 2007 Elsevier B.V. All rights reserved

doi:10.1016/j.jnucmat.2007.03.252

* Corresponding author.

formance of the DCLL TBM is being developedincluding rate-dependent plasticity damage func-tions. This approach would differ from the majorityof lifetime assessments, which are based on isother-mal lifetime data and the use of predictive designrules. The VISTA project aims to incorporate dam-age evolution models as a function of irradiationand operational time into FEM analysis of theDCLL TBM.

A dislocation-based creep damage model wasdeveloped to simulate property degradation as aresult of aging and neutron irradiation. This dam-age model describes rate-dependent plasticity andthermal and irradiation creep of F82H. The damagemodel was directly coupled with the finite element

.

1338 S. Sharafat et al. / Journal of Nuclear Materials 367–370 (2007) 1337–1343

code ABACUS and typical tension bar geometrieswere analyzed. Furthermore, true stress–straincurves of F82H at various temperatures 450 �C weredeveloped.

Because of computational resource limitations, adetailed finite element analysis of the thermo-mechanical behavior of the helium cooled TBMwas performed without the inclusion of the damagemodels. Instead, the true stress–strain behavior aspredicted by the dislocation-based creep modelwas used. While this effort is a first step to includedislocation-based damage functions in large-scaleFEM analysis, it does not fully integrate damageaccumulation with FEM simulations. However,based on the successful example of using the fullyintegrated creep model with FEM for small test-bar samples, we propose a ‘global-to-local zooming’method for the large-scale FEM analysis of theDCLL TBM structure. First, a large-scale FEManalysis would be performed to identify criticalareas within the structure, to be followed by verydetailed and fully coupled damage model–FEMsimulation. Thus, incrementally changing materialproperties as a function of radiation dose and agingcan be directly coupled with the FEM analysis ofcritical areas within any structure.

The TBM model, which was analyzed using thecreep-model derived stress–strain curve includedthe First Wall, internal support panels, and theback-plate. The model also contains the coolantchannels within each structure along with filletsand rounds between joined members of the TBM.Off-normal operation was analyzed by simulatinga high pressure helium coolant leak into the DCLLTBM. It is shown that based on high-temperatureITER Structural Design Criteria [8] all primary plussecondary stress limits were satisfied.

2. Rate-dependent damage and deformation model

Extending the theory of rate processes, Ghoniem,Matthews and Amodeo (GMA) [2] were able to for-mulate a comprehensive theory of radiation-induceddefect and dislocation microstructure evolution.Their dislocation-based creep model was initiallydeveloped to predict high-temperature deformationunder arbitrary time-dependent stress and tempera-ture histories for engineering materials. Their com-prehensive dislocation creep model is based onearlier developments in creep theory [2]. The inclu-sion of sub-grain microstructure evolution is a keyaspect of this model, as recognized earlier by Holt

[3]. This dislocation-based constitutive model iscomposed of six rate equations to predict the behav-ior of six engineering parameters, namely the creepstrain, the mobile, static and boundary dislocationdensity, the average sub-grain radius, and theapplied stress. The overall model can be summa-rized in the following equations [2]:

Creep strain – Orowan equation:

dep

dt¼ bqmvg: ð1Þ

Mobile dislocation density:

oqm

ot¼ vg q3=2

m þbRsb

h2� qm

2Rsb

� 8q3=2m

vcm

vg

� ��

� dqmðqm þ qsÞ�: ð2Þ

Static dislocation density:

oqs

ot¼ vg

qm

2Rsb

� 8qs

hq3=2

m

vcs

vg

� �� dqmqs

� �: ð3Þ

Boundary dislocation density:

oqb

ot¼ 8ð1� 2fÞqs

vc

h� qb

Rsb

� �M sbðps � 2pr2

pNpcsbÞ:

ð4ÞAverage sub-grain radius:

dRsb

dt¼ M sbðps � 2pr2

pN pcsbÞ

� lgvKcRsb ðqm þ qsÞ1=2 � Kc

2Rsb

� �XDs

kT: ð5Þ

A constitutive relation has been added to calculatestress as a function of the total strain:

drdt¼ E

detot

dt� bqmvg

� �; ð6Þ

where ep is the creep or plastic strain, b is the Bur-ger’s vector, qm, qs, and qb are mobile, static, andboundary dislocations density; vg is the glide velo-city, b is a density factor, Rsb is the sub-grain radius,vcm is the mobile core glide velocity, h is the disloca-tion spacing within the sub-grains, vcs is the staticcore glide velocity, ps pressure of sub-grain growth,rp is the mean precipitate radius, f is the fraction ofdislocations that become part of the cell boundary,Np is the precipitates volume concentration, csb

grain boundary energy per unit area, Msb is coremobility, l is the shear modulus, gv is the transfercoefficient of vacancies from dislocations; Kc is aconstant with a value around 10 [4], X is the atomic

Fracture Strength is estimated

stre

ss (M

Pa)

Fig. 2. Application of the GMA dislocation-based creep modelto F82H at 450 �C (true: damage model; exp: compiled fromreference [6], Eng (FEA): 3-dimensional small specimen modelusing ANSYS FEM code (strain (mm/mm)).

S. Sharafat et al. / Journal of Nuclear Materials 367–370 (2007) 1337–1343 1339

volume, Ds is the lattice self-diffusion coefficient(Ds ¼ DvCv

e); k is Boltzman’s constant, and T istemperature.

The model is a compromise between the intensecalculations of single crystal plasticity and thesimplicity of the Orowan–Baily phenomenologicalapproach. If polycrystals were to be individuallymodelled with crystal plasticity, the volume thatcan be handled with today’s computers would beon the order of hundreds of cubic microns. How-ever, the GMA creep model captures the main hard-ening and recovery mechanisms in an average sense,and has a dependence on the sub-grain size. In otherwords, grain boundary sliding contributions areignored, with focus being directed on dislocationmechanisms, starting at the sub-grain level. It hasthe added attractive feature of being within therate-theory framework, and can hence incorporatepoint defect and microstructure evolution equa-tions, as well as equations for irradiation creepand swelling.

3. Implementation of damage evolution into FEM

The ABACUS FEM framework provides flexibi-lity by enabling to couple sophisticated materialswith the FEM analysis models in an integrated fash-ion. The GMA creep damage model was incorpo-rated by simultaneously solving the previous set ofequations with the evolution of the triaxial stress

7.11 e-02 1.01 e+01

1.17 e+03 7.85 e+02 3.98 e+02

1.56 e+03 9.48 e-01 6.08 e-01 1.55 e-01

1.29e+00

4.72 e+09

4.69 e+103.11 e+109.98 e+10

6.27 e+10

Von Mises Stress

PlasticStrain

MobileDislocation

SDislo

Fig. 1. Results of simultaneous stress and microstructure evolution usinABACUS FEM code (stress: MPa; strain (%); dislocation densities (cm

state. Sample results of this integrated approach tomodel standard tensile test-bars are shown inFig. 1 for F82H steel. The figure shows the spatialdistribution of Von-Mises stress, mobile, static andboundary dislocation densities, as well as the totalplastic strain and the average sub-boundary radius.To our knowledge, this achievement is the first inthe literature.

1.00 e-032.03 e+09

1.09 e+098.64 e+095.34 e+09

1.42 e+09

1.00 e+09

1.00 e+09 1.00 e+09 1.00 e+09

1.00 e+09 1.00 e-031.00 e-031.00 e-03

1.00 e-03

BoundaryDislocation

taticcation

Sub-grainDisl. Radius

g the fully integrated GMA dislocation-based creep model and the/cm�3); radius (mm)).

FW Helium makes 5 Passes: Pass 1: In 360oC Out 372oC Pass 2: In 372oC Out 384oC Pass 3: In 384oC Out 396oC Pass 4: In 396oC Out 408oC

Pass 5: In 408oC Out 420oC

Heat Transfer Coefficient:FW (plasma side only)

hcoef = 6979 W/m2-KFW side rib roughened all other surfaces assumedsmooth walls

hcoef = 3586 W/m2-K

FW-Tout = 420oCHeat Loads:Plasma on FW

q’’ = 0.5 MW/m2

Volumetric Heating: q’’’=15 exp (-10x) MW/m3

Leakage from PbLi into walls: 10% of heat ~ 0.05

FW

RIB StructureHelium flow: Single Pass Tin = 420oC Tout = 440oC

5 Pass Heliumflow

FW-Tin = 360oC

→→→→→

Fig. 3. Solid model of a 5-pass FW-coolant flow section of the DCLL TBM showing heat loads and heat transfer coefficients used forthermal analysis FEM.

Fig. 4. Temperature contours of the DCLL TBM 5-pass FW-coolant sector.

1340 S. Sharafat et al. / Journal of Nuclear Materials 367–370 (2007) 1337–1343

Table 1Summary of DCLL-5 channel section temperatures and stresses

Location Temperature(�C)

Memb. Pm

(MPa)Primary stress intensity (MPa) Secondary stress

intensity, Q (MPa)Primary + secondary stressintensity (MPa)

PL + Pb/Kt

Sm

(MPa)St (MPa)10000 h

Average Peak Bending(PL + Pb)

Memb. + Bending(PL + Pb)

FW 523 559 45 70 115 190 305 107 132 135Support

structure471 477 25 45 70 157 227 65 143 179

Back plate 520 557 22 38 60 187 247 56 135 140Primary plus secondary stress limits

Location Averagea temperature (�C) Yield stress (MPa) X = (PL + Pb/Kt)/Sy Y = DQ/Sy Y = (DP + DQ)/Sy

FW 523 387 0.17 0.49 0.79Poloidal Inner support structure 471 421 0.10 0.37 0.54Back plate 520 392 0.09 0.48 0.63

Pm general primary membrane stress intensityPL local primary membrane intensityPb primary bending stress intensityQ secondary stress intensityK bending shape factorSupport structure internal poloidal support structure.

a Average temperature for one plasma-on and plasma-off cycle.

S.

Sh

ara

fat

eta

l./

Jo

urn

al

of

Nu

clear

Ma

terials

36

7–

37

0(

20

07

)1

33

7–

134

31341

1342 S. Sharafat et al. / Journal of Nuclear Materials 367–370 (2007) 1337–1343

Simulations of typical TBM structures using cou-pled GMA and FEM requires significantly morecomputing resources than used to modeling a smalltensile test-bar. The present work is limited to usingthe GMA model-derived true stress–strain behaviorof F82H. Fig. 2 shows the GMA based stress–strainof F82H at 450 �C. The Young’s modulus, ultimatestrength, and elasto-plastic tangent as predicted bythe GMA–FEM model match quite well with theexperimental values [5].

4. Finite element modeling of the TBM

Thermal and thermo-elastic stress analyses of theUS ITER Dual Coolant Lead Lithium (DCLL) TestBlanket Module (TBM) were carried out using thefinite element program ANSYS. The structuralmaterial for the DCLL is the ferritic–martensiticreduced activation F82H steel [7]. A 3-dimensionalCAD model of a 5-channel section of the DCLLITER-TBM was developed for the analysis(Fig. 3). The section is located near the top of theTBM, where the highest FW temperatures areexpected. Heat conduction in the poloidal directionwas considered by applying symmetry conditions,representing adjacent coolant channels above andbelow the section. Steady-state temperature distri-butions were calculated. The maximum tempera-tures are 559 �C and 557 �C at the FW and theBack Plate, respectively, or about 17 �C higher thanthe design limit of 550 �C (Fig. 4).

The corresponding stress analyses were con-ducted using 8-node brick elements. The averageprimary membrane stress was taken as the averageacross the plasma-facing side of the FW, and theprimary bending stress was taken as �2/3 of thepeak stress based on the ITER structural design cri-teria definition [8]. Results show that all the primaryplus secondary stress limits are satisfied within the5-channel section of the TBM. The high-tempera-ture ITER Structural Design Criteria provides con-servative but simple rules to prevent progressivedeformation (cyclic creep-ratcheting) on the basisof elastic analysis by using either the 3Sm or theBree-diagram rule. These rules were applied andare summarized in Table 1. Results show thatthe maximum high-temperature time-independent((PL + Pb/K) < Sm)) and time-dependent ((PL +Pb/Kt) < St)) design rules for, both primary mem-brane and membrane plus bending stresses aresatisfied.

Structural analysis of the entire DCLL TBMrevealed that the maximum Von-Mises stress occursnot at the FW but at the sharp interface cornersbetween the internal support structure and the sideof the FW. A preliminary steady-state structuralanalysis was performed and results show that withminor design modification, the DCLL design canwithstand the loss of coolant accident conditionwithout exceeding the ultimate design limit ofF82H. Details are reported in Ref. [9].

5. Proposed coupling of damage function with

large-scaled FEM

Until implementation of the GMA creep modelwith large-scale FEM analysis is computationallyfeasible, we propose a ‘global-to-local’ FEMapproach. A large-scale FEM analysis would beperformed without damage functions to establish‘global’ stress states in the TBM and to identify crit-ical areas. These critical or ‘local’ areas are then iso-lated for modelling using the fully integrated GMAcreep model–FEM approach. The structures sur-rounding the localized section are replaced withappropriate boundary conditions to reflect the stressstate of the entire structure.

Although, our creep model captures the mainhardening and recovery mechanisms, it is still phe-nomenological in nature. Efforts are ongoing toresolve this aspect completely and to develop amaterials damage model, which includes (1) triaxialstress states, (2) rate-independent and rate-depen-dent plasticity, (3) creep-fatigue deformation, (4)void-induced and grain boundary cavitation-induced damage at large strains, and (5) irradiationcreep and swelling via additional rate equations forpoint defects and voids. Simultaneously, softwaredevelopment is ongoing to improve the GMA/ABACUS implementation for future large-scaleFEM analysis.

6. Conclusions

A comprehensive rate-theory based radiationdamage creep deformation code was incorporatedwith the ABACUS FEM code in an integrated fash-ion. The advantage of this approach is that in-reac-tor deformations and radiation damage can now bedirectly coupled with ‘material properties’ in FEManalyses. The coupled FEM–creep damage modelwas used to successfully simulate the simultaneous

S. Sharafat et al. / Journal of Nuclear Materials 367–370 (2007) 1337–1343 1343

microstructure and stress evolution in typical smalltensile test-bar structures.

Applying the integrated GMA creep–FEM codeto large structures is still computationally prohibi-tive. Instead, for the thermo-structural analysis ofthe DCLL TBM structure a true stress-curve ofF82H ferritic steel developed by the GMA creep–FEM model was used. A 5-channel section of theUS-ITER DCLL TBM was analyzed. High-temper-ature ITER Structural Design Criteria [8] to preventprogressive deformation (cyclic creep-ratcheting)were applied. All primary plus secondary stress lim-its were satisfied.

Because the direct implementation of the GMAcreep in a large-scale FEM analysis is still computa-tionally prohibitive, a ‘global-to-local zooming’approach is proposed. It is suggested that first alarge-scale damage-free FEM analysis be performedto determine the stress state of critical areas, whichis then followed by local and detailed fully coupledGMA creep–FEM analysis.

Acknowledgement

The present work was supported by the USDepartment of Energy (DOE), Office of Fusion

Energy Sciences (OFES) through grant DE-FG02-03ER54708 with UCLA.

References

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[3] D. Holt, J. Appl. Phys. 41 (1970) 3197.[4] J.H. Gittus, Philos. Mag. 39 (1979) 829.[5] J. K. Chiu, Dislocation-based finite element modeling of

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[6] Y. Kohno, A. Kohyama, M.L. Hamilton, T. Hirose, Y.Katoh, F.A. Garner, J. Nucl. Mater. 283–287 (2000) 1014.

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