J. Plasma Fusion Res. SERIES, Vol. 11 (2015)

Thermo-mechanical analysis of tungsten and its alloys monoblock divertor
under heat load conditions relevant to a fusion reactor
Makoto FUKUDAa, Shuhei NOGAMIa, Akira HASEGAWAa, Kiyohiro YABUUCHIa, Koichiro
EZATOb, Satoshi SUZUKIb, Hitoshi TAMURAc, and Takeo MUROGAc
Department of Quantum Science and Energy Engineering, Tohoku University, Sendai, JapanaJapan Atomic Energy Agency, Ibaraki, Japanbc

National Institute for Fusion Science, Gifu, Japan(Received: 22 September 2014 / Accepted: 19 January 2015)

To evaluate the applicability of tungsten alloys as the plasma-facing materials in a fusion reactor,
thermo-mechanical analysis of monoblocks of pure W and its alloys under heat load was carried out in this work.
Potassium (K) and rhenium (Re) doped W (namely K-doped W-3%Re) showed the highest recrystallization
resistance because of its high temperature where the recrystallization starts, although its thermal conductivity was
lower than those of pure W and K-doped W. Thermal stress in the monoblock under the heat load was relatively
high at the top surface and in the neighborhood of the interface between W and OFHC-Cu. The distribution ofthermal stress was similar in pure W, K-doped W, and K-doped W-3%Re.
Keywords: Pure W, K-doped W, K-doped W-3%Re, thermo-mechanical analysis, finite element analysis, divertor

1. Introduction

between the thermal properties and the improvedproperties, such as mechanical properties and resistance torecrystallization and irradiation. In this case, the decreaseof the thermal conductivity by 3% Re in K-doped W-3%Re
should be considered at below ~800 °C.
The objective of this work is to investigate the effectsof the trade-off relationship between the decrease inthermal conductivity and the improvements in otherproperties, such as recrystallization and irradiation
resistance and mechanical properties in pure W, K-doped
W, and K-doped W-3%Re.

Tungsten (W) is attractive as a plasma-facing material(PFM) for use in divertors and blankets in fusion reactors
because of its high melting point, high thermal conductivity,and high sputtering resistance. On the other hand,
improvement of its material properties, such as mechanicalproperties and irradiation resistance, is desired to increase
the reliability of W as the PFM of a divertor. W is
subjected to a high heat load and high energy of neutron
irradiation during the operation of a fusion reactor. It has
been reported that crack formation and recrystallization
can occur in a W monoblock due to the cyclic heat load
relevant to ITER [1]. Crack formation may decrease theheat transfer ability and cause contamination of the plasma.
Recrystallization decreases the mechanical properties of W
significantly [2, 3]. In addition, changes in material
properties due to neutron irradiation might become an issue
for the application of W as a PFM in DEMO because of its
long-term operation. The neutron irradiation induces theirradiation defect clusters, such as voids, dislocation loops,
and irradiation-induced precipitates. As a result,degradation of the mechanical and thermal properties may
occur [4-11].
Based on these backgrounds, we fabricated the W
alloys (i.e. potassium (K)-doped W and K-doped W-3%
rhenium (Re) alloy) to increase their mechanical properties
and resistances to recrystallization and irradiation. The
details of the material design are described in the literature[12]. The point to be considered to evaluate theapplicability of the W alloys as PFMs is the trade-off

2. Finite element analysis

11.5

28

16.5

This work calculates the temperature and stressvalues and their distributions in a W monoblock used for
an ITER divertor made of pure W, K-doped W, andK-doped W-3%Re during the heat load condition relevant
to a fusion reactor. A three-dimensional thermo-mechanicalanalysis was conducted for the W monoblock by the finiteelement analysis (FEA). Figure 1 shows the dimensions ofCuCrZrOFHC-CuWYX

27.8ZY12Fig. 1 Dimensions of the FE-model (1/4 of monoblock).

author’s e-mail: fukuda@jupiter.qse.tohoku.ac.jp

99©2015 by The Japan Society of Plasma
Science and Nuclear Fusion Research

M. Fukuda et al., Thermo-Mechanical Analysis of Tungsten and its Alloys Monoblock Divertor under Heat Load Conditions Relevant to a Fusion Reactor

Pure W

K-doped W

K-doped W-3%Re
R& Fig. 2 Temperature distribution in 1/4 model of W monoblock after a heat load of 20 MW/m2 for 10 s.

(A)

201500

15A1000

10500

50010Time, s2030(B)500

Pure W
K-doped WK-doped W-3%ReHeat load

400

Point B

252015300
10B

200

5100
00010Fig. 3 Temperature change during heat load at selected points.

the FE-model, and the 1/4 model of the monoblock (bluedotted line). The thermo-mechanical analysis wasconducted using ANSYS ver. 15.0. The materials used in
the analysis were pure W and its alloys (K-doped W andK-doped W-3%Re), CuCrZr, and OFHC-Cu. CuCrZr andOFHC-Cu are the coolant channel material and the buffermaterial between W and CuCrZr, respectively. The
assigned temperature-dependent thermal and mechanicalproperties of W were based on experimental results andliterature [13, 14]. The material properties of CuCrZr andOFHC-Cu were based on the literature [15]. In thisanalysis, W materials were defined as elastic solids. TheOFHC-Cu and CuCrZr were defined as perfectelastro-plastic solids. As a heat load condition, a heat fluxof 5 - 20 MW/m2 with a dwell time of 10 s was applied atHeat load, MW/m2

Point A

Heat load, MW/m2Temperature, oC

2000

600

25Pure W
K-doped W
K-doped W-3%Re
Heat load

Temperature, oC

2500

Time, s20300

the top surface of the W block. The cooling watertemperature was 25 °C, and its pressure was 2 MPa. The
axial symmetry surface of the X and Y axes were fixed.

3. Results and discussions

Figure 2 shows the temperature distributions in pureW, K-doped W, and K-doped W-3%Re after a heat load of20 MW/m2 for 10 s. Temperature change profiles at theselected points were plotted as shown in Fig. 3. The edgeof the top surface showed a higher temperature than otherparts because of its greater distance from the coolingchannel. This trend was the same for all W materials. Themaximum temperature on the top surface during the heatload changed depending on the W materials, and K-doped
W-3%Re showed a ~200 °C higher maximum temperature100M. Fukuda et al., Thermo-Mechanical Analysis of Tungsten and its Alloys Monoblock Divertor under Heat Load Conditions Relevant to a Fusion Reactor

Pure W

K-doped W

K-doped W-3%ReFig. 4 The area above the temperature where the recrystallization starts in W monoblocks after a heat load of 20 MW/m2 for 10 s.
2500

Recrystallized depth from top surface, mm

A

2000
Temperature, oC

10Point A

1500

1000

Pure W500

K-doped W
K-doped W-3%Re

005

1015Heat load, MW/m2

208642025

Pure W
K-doped W
K-doped W-3%Re051015Heat load, MW/m220Fig. 5 Relationship between the heat load and the top surface
temperature in a W monoblock.

Fig. 6 Relationship between the heat load and the recrystallized
depth in a W monoblock.

than pure W and K-doped W. This was caused by the lower
thermal conductivity of K-doped W-3%Re than the others
due to the 3% Re addition. K-doped W showed almost thesame temperature and distribution as did pure W, and theeffect of the K dope was not clearly observed.
Figure 4 shows the area above the temperature where
the recrystallization starts in W materials after a 20
MW/m2 heat load for 10 s. The temperature where therecrystallization starts of pure W, K-doped W, and K-doped
W-3%Re were experimentally obtained by grain structure
observation and the Vickers hardness measurement [13].
The temperatures where the recrystallization starts of pureW, K-doped W, and K-doped W-3%Re were ~1100, ~1300,
and ~1800 °C in our previous works, respectively. For pureW, the depth of the area above the temperature where therecrystallization starts was ~8 mm from the top surface.

The area above the temperature where the recrystallization
starts in K-doped W and K-doped W-3%Re was smaller
than that of pure W, and its depth were 6 and 3 mm fromthe top surface for K-doped W and K-doped W-3%Re,respectively. Although the thermal conductivity of
K-doped W-3%Re is lower than those of pure W andK-doped W, the effect of the increase in recrystallization
resistance was clearly observed in the heat load conditionof this work. K-doped W also demonstrated theeffectiveness of the K dope on the recrystallization
behavior of pure W during heat load.
Figure 5 shows the relationship between the heatload and the maximum temperature on the top surface. Themaximum temperature linearly increased with increasingheat load. The threshold heat load of the recrystallization
was estimated as ~10, ~12, and 15 MW/m2 for pure W,101

M. Fukuda et al., Thermo-Mechanical Analysis of Tungsten and its Alloys Monoblock Divertor under Heat Load Conditions Relevant to a Fusion Reactor

EquivalentYZ

X direction

ZX

YY
ZX

ZX

YX

 03D 03DY direction

YZX

Z direction

ZX

YYZ

03DXZYX
03DFig. 7 Stress distribution in a pure W monoblock after a heat load of 20 MW/m2 for 10 s.

resistivity to deformation and crack formation during acyclic heat load. The thermo-mechanical analysis of pureW, K-doped W, and K-doped W-3%Re monoblocks
considering plastic deformation and hardening is a futurework.

K-doped W, and K-doped W-3%Re, respectively. The heatload dependence of the recrystallization depth is shown in
Fig. 6. The recrystallization depth increased linearly withincreasing heat load.
Figure 7 shows the stress distribution in the pure W
monoblock after a 20 MW/m2 heat load for 10 s. Highstress was observed at the top surface and the interface
between W and OFHC-Cu. Tensile stress at the top surface
and compression stress in the vicinity of the OFHC-Cu in
the center of the monoblock were observed in theX-direction. The high tensile stress in the vicinity of theOFHC-Cu layer and compression stress at the side surface
in the monoblock were observed in the Y-direction. In theZ-direction, the high tensile stress was observed in thevicinity of the OFHC-Cu layer; however, the magnitude ofthe stress was lower than that in the X-direction. Although
the magnitude of the stress depends on the W materials, thestress distribution was not changed between pure W,
K-doped W, and K-doped W-3%Re. Because the K-doped
W and K-doped W-3%Re shows higher strength than does
pure W, it is expect that these W materials will show higher

4. Summary

The thermo-mechanical analysis of pure W, K-doped
W, and K-doped W-3%Re monoblocks under a heat load ofup to 20 MW/m2 was performed in this work. The resultsof this work are summarized as follows:
x K-doped W-3%Re showed the highest surface
temperature, as compared to pure W and K-doped W
under the same heat load condition because of its lower
thermal conductivity due to 3% Re addition.
x K-doped W and pure W showed almost the same
temperature distribution during heat load, and the effectof the K dope was not clearly observed because thethermal conductivity of K-doped W is almost the same asthat of pure W.

102M. Fukuda et al., Thermo-Mechanical Analysis of Tungsten and its Alloys Monoblock Divertor under Heat Load Conditions Relevant to a Fusion Reactor

x The recrystallization threshold heat load andrecrystallization depth were estimated. K-doped
W-3%Re showed the highest resistance torecrystallization due to the increased the temperature
where the recrystallization starts resulting from Re
addition and K dope.
x Higher stress was observed at the top surface and thevicinity of the OFHC-Cu layer in each direction. The
stress distributions of pure W, K-doped W, and K-doped
W during the heat load were almost the same.

Acknowledgement

This work was supported by Grant-in-Aid for JSPS
Fellows (26-3841) and NIFS collaboration research
program (NIFS14KERF024).

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