- Email: [email protected]
Fracture mechanical analysis of a tungsten monoblock-type plasma-facing component without macroscopic interlayer for high-heat-flux divertor target
Fusion Engineering and Design xxx (xxxx) xxx–xxx
Contents lists available at ScienceDirect
Fusion Engineering and Design journal homepage: www.elsevier.com/locate/fusengdes
Fracture mechanical analysis of a tungsten monoblock-type plasma-facing component without macroscopic interlayer for high-heat-flux divertor target ⁎
Muyuan Lia, , Franklin Gallayb, Marianne Richoub, Jeong-Ha Youa, a b
⁎
Max Planck Institute for Plasma Physics, Boltzmann Str. 2, 85748 Garching, Germany CEA, IRFM, F-13108 Saint-Paul-Lez-Durance, France
A R T I C L E I N F O
A B S T R A C T
Keywords: Divertor Plasma-facing component High-heat-flux component Tungsten monoblock Fracture Structural failure
In the framework of the European DEMO divertor project, several novel design concepts of the plasma-facing components of vertical targets are being developed. One of those concepts is the tungsten monoblock design (similar to the ITER divertor) but with a very thin interlayer (roughly 25 mm thick only) at the armor/tube bond interface instead of a thick (1 mm) copper interlayer as has been the case in the conventional tungsten monoblock design developed for ITER divertor. The thin interlayer serves as bonding agent, but not as structural constituent. The reasoning for this novel design concept to omit the thick soft copper interlayer, which has been used as stress-relaxing buffer between the stiff armor block and tube, is to prevent plastic fatigue damage under cyclic high heat flux loads and irradiation embrittlement which the soft copper interlayer is predicted to undergo. On the other hand, the desirable stress relaxation effect on a global scale is abandoned. In this study, such trade-off effects are computationally investigated in a comparative assessment of structural impact, which the presence (or absence) of the thick copper interlayer is expected to bring forth, in terms of the fracture and fatigue behaviour of the armour block and cooling tube in two representative cases of tungsten monoblock plasma facing component design, namely, with and without a thick copper interlayer. Quantitative results of cyclic plastic strain history and crack tip fracture energy are presented for the armour surface, bond interface and tube of the respective plasma facing component models. The positive and negative implications of these impacts on the structural integrity are discussed.
1. Introduction Divertor is one of the major in-vessel components in a fusion power reactor. Being responsible for power exhaust and plasma particle removal, divertor shall be subjected to significant thermal loads by surface heat flux as well as volumetric nuclear heating. Particularly, the plasma-facing components (PFCs) of the vertical targets will be exposed to severe high heat flux (HHF) loads reaching about 20 MW/m2 or higher locally at the strike point in the next generation fusion reactors such as ITER and DEMO [1,2]. For both ITER and DEMO, the divertor PFCs will be fully armoured with tungsten (W) [1,2]. The standard design of a ITER divertor target PFC is based on a joint structure consisting of W monoblocks as armour, copper alloy (CuCrZr) tube as water-cooled heat sink and a rather thick (typically 1 mm) copper (Cu) interlayer between the armour and the tube (see Fig. 1) [1]. Such an ‘ITER-like’ PFC design concept was also adopted for the European DEMO divertor target as a baseline design model while several other novel design variants are being developed in parallel in the framework of the EUROfusion Work Package “Divertor” ⁎
[2,3]. One of those novel PFC design concepts is the W monoblock design with a very thin interlayer (roughly 20 μm thick) at the bond interface as illustrated in Fig. 2. The characteristic feature of this design concept proposed by a group at French Alternative Energies and Atomic Energy Commission (CEA) is that there is no macroscopic constituent between the armour and tube, which is in contrast to the ITER divertor PFC where a thick Cu interlayer is integrated. The thin interlayer serves actually as metallurgical bonding agent at the bond interface, but no more as structural entity. In order to improve adhesion and reduce thermal strain mismatch, the interlayer was compositionally graded on microscopic scale starting from full W layer on the armour side and ending up in full Cu on the tube side. Recently, Richou et al. demonstrated that real PFC mock-ups of this design concept could be successfully manufactured by means of Physical Vapour Deposition (PVD) coating of graded W/Cu interlayer and Hot Isostatic Pressing (HIP) joining process [3]. The mock-ups exhibited a sound joining quality and quite robust HHF fatigue performance at least up to 300 load cycles at 20 MW/m2 (screening test up to 25 MW/m2 without visible damage)
Corresponding authors. E-mail addresses: [email protected] (M. Li), [email protected] (J.-H. You).
http://dx.doi.org/10.1016/j.fusengdes.2017.09.002 Received 20 February 2017; Received in revised form 14 July 2017; Accepted 1 September 2017 0920-3796/ © 2017 Elsevier B.V. All rights reserved.
Please cite this article as: Li, M., Fusion Engineering and Design (2017), http://dx.doi.org/10.1016/j.fusengdes.2017.09.002
Fusion Engineering and Design xxx (xxxx) xxx–xxx
M. Li et al.
2. FEM model, materials & boundary conditions In this work, the FEM model (see Fig. 1) was built according to the novel divertor target with a very thin graded interlayer proposed by a group at CEA. The ITER-like baseline design with an interlayer of 1 mm in the EUROfusion Work Package “Divertor” was set as a reference case for comparison. The single W monoblock has a dimension of 23 × 22 × 4 mm3, and the monoblock in ITER-like baseline design has a dimension of 25 × 23 × 4 mm3 [8]. The cooling tube has a thickness of 1 mm (baseline design: 1.5 mm) and an inner diameter of 12 mm (baseline design: 12 mm). The thin interlayer of 25 μm is not included in the FEM model, which yields a conservative result, as the stress induced by the thermal mismatch will be higher than the reality. The armor thickness (the shortest distance from the armor surface to the interlayer) is 5 mm (baseline design: 5 mm). Commercial finite element analysis code ABAQUS was employed. The material data of W and CuCrZr were listed in Table 1 and obtained from ITER SDC-IC [9] and ITER material properties handbook [10]. The typical thermal history of a target mock-up from the fabrication to HHF tests was considered for modelling: fabrication (cooled from stress-free temperature to room temperature), stand-by (pre-heated to coolant temperature uniformly) and HHF load cycles (cyclic heating and cooling) as illustrated in Fig. 3. During the fabrication, an ageing process at 480 °C follows the HIP joining at 950 °C for hardening treatment of CuCrZr. In this study, the actual thermal history of the fabrication process was simplified into a single uniform cooling step from an effective stress-free temperature to the ambient temperature. For the sake of direct comparability between the two PFC design cases, the same effective stress-free temperature (580 °C) was assumed for both design concepts. This temperature corresponds to the joining temperature of the HRP (Hot Radial Pressing) process employed for manufacturing the ITER-like divertor PFC mock-ups [11]. The applied HHF loads were 10 MW/m2 and 20 MW/m2. The duration of a heat pulse was 10 s and the time interval between subsequent pulses is 20 s. A DEMO relevant cooling condition was assumed in this simulation (coolant temperature: 150 °C; pressure: 5 MPa; speed: 16 m/s) [2]. The heat transfer coefficient was calculated using Sieder/Tate [12] and CEA/Thom [13] correlations (considering swirl tape). The nodal degrees of freedom on the end cut section of the tube were constrained to produce a uniform displacement in the axial direction. Further details about the simulations can be found in [14].
Fig. 1. Materials and mesh of the quarter model of the monoblock divertor target. (reference nodes for studying of low cycle fatigue of W armor and CuCrZr tube are shown).
[4]. Actually, this fairly positive HHF test result is quite remarkable and even surprising when considering the fact that it has been a widely accepted practice in the PFC engineering to employ a thick Cu interlayer in order to mitigate thermal stresses with the help of the softness and ductility of annealed Cu. Now, the recent HHF test result indicates that to incorporate a thick Cu interlayer may not necessarily be an indispensable requirement for achieving reliable HHF performance. Moreover, there are two material issues supporting the idea to omit thick Cu interlayer as in the present design concept: 1) Under cyclic HHF loads (15–20 MW/m2), a thick Cu interlayer tends to undergo pronounced plastic fatigue leading to a premature low cycle fatigue failure of a PFC [5]. This failure feature was also experimentally observed where ductile strain damage was revealed in form of growth and coalescence of voids [6]. With increasing dpa dose, plastic fatigue behaviour of Cu will be affected by the equilibrium between irradiation hardening and thermal recovery. 2) A previous neutron irradiation test indicated that the uniform elongation of irradiated pure Cu diminished drastically even at elevated temperatures (350–400 °C) due to helium embrittlement resulting from transmutation [7]. The originally expected effect of stress relaxation via ductile yield of soft Cu will gradually disappear. These two empirical findings put the effectiveness of the thick Cu interlayer into question. As mentioned above, the promising HHF test result of the PFC mock-ups having no thick Cu layer puts the indispensability of the thick Cu interlayer into question. From this background arose the motivation to interpret the HHF performance and to understand the structure mechanical benefits of the underlying design concept to omit a thick Cu interlayer. In this paper, a rigorous numerical study is reported on the structural effect caused by the absence of a thick Cu interlayer in terms of armour cracking and plastic fatigue of tube. To this end, fracture mechanical and cyclic-plastic simulations based on finite element method (FEM) were carried out.
3. Results and discussion 3.1. Temperature distribution Fig. 4 shows the temperature distribution of the divertor target mockup without interlayer. The maximum temperature of W monoblock at 10 MW/m2 (805 °C) is well below the recrystallization temperature of W. At 20 MW/m2 the maximum temperature at the edge of the W monoblock is 1610 °C, while at the mid line of the top surface along the axial direction the maximum temperature is 1391 °C. The Fig. 2. Manufacturing of the mockups with a thin graded interlayer. 1, Coating graded interlayer in W tile; 2, CuCrZr tubes machining; 3, Hot Isostatic Pressing for assembling W tiles to the CuCrZr tubes.
2
Fusion Engineering and Design xxx (xxxx) xxx–xxx
M. Li et al.
Table 1 Properties of the considered materials at selected temperatures [9,10]. Tungstena(recrystallizedb) 20 °C Young’s modulus (GPa) 398 Yield stress (MPa) 1360 (380) Thermal conductivity (W/mK) 173 Coefficient of thermal expansion (10−6/K) 4.5 Kinematic hardening parameters entering the model for CuCrZr
CuCrZrc
400 °C
1200 °C
2000 °C
20 °C
350 °C
393 947 (363) 140 4.6
356 346 (224) 105 5.0
285 −(70) 99 5.4 C(MPa) γ
128 348 318 16.7 48399 599
116 296 347 18.0 7849 512
a
Rolled and stress-relieved state. The ultimate tensile strength of recrystallized tungsten is used as yield stress assuming a pre-hardened state. Heat treatment A (solution annealing + cold work + ageing) in ITER SDC-IC, and the yield stresses and kinematic hardening parameters are calibrated from cyclic stress-strain curves. b c
et al. [16] shows that the hardness of tungsten is dependent on the annealing temperature, where a sharp decrease of hardness of W was found if the annealing temperature increased from 1300 °C to 1500 °C. Considering the hardness is usually proportional to the yield stress, and to capture the mechanical benefit resulting from a lower temperature in the W divertor target design with a thin graded layer, a “less recrystallized W” with modified yield stress should be applied in the calculation. Hence, average of the yield stresses of recrystallized W used for ITER-like baseline design and stress relieved W was applied as a rough estimation of the yield stress in the “less recrystallized” W layer for the novel concept. 3.2. Stress distribution
Fig. 3. Schematic illustration of the thermal history considered for modelling.
Figs. 5 and 6 show the distributions of the hoop and radial stress component on the front view of the divertor targets without and with a Cu interlayer at 20 MW/m2. The plots indicate the stress fields during the stationary HHF loading and cooling (down to coolant temperature) at the 5th loading cycle. Significant tensile hoop stress occurs during HHF loading in the upper part of the W block near the interlayer or the tube, respectively, in both design cases. After cooling, tensile stress occurs in the top surface layer of the W block in both design cases, but higher stress occurs when there is no Cu interlayer. This effect is owing to the higher yield stress of tungsten due to lower surface temperature as mentioned in Section 3.1. In the case of radial stress component, higher tensile stress occurs during cooling in the W block near the bond interface around the tube without Cu interlayer. On the contrary, the presence of the thick Cu interlayer considerably reduced the radial stress component during cooling. During the HHF loading the radial stress component was mostly relaxed in both design cases. The circumferential concentration of tensile radial stress may provide a sufficiently high driving force for interfacial debonding between the armor block and the tube. The stress concentration of the radial component occurs mostly near the free surface edge only whereas the concentration of hoop stress is present in the bulk as well through the axial direction. Fig. 7 shows the axial stress distribution at 20 MW/m2 in the target PFCs without and with a Cu interlayer. Since the W block was not fully constrained in the axial direction but allowed to move in that direction, there is nearly no axial stress developing in the W block. However, the CuCrZr tube experiences a significant axial stress. The asymmetry in the stress distribution (tensile in the upper part, compressive in the lower part) indicates a possible bending deformation of the tube. For a precise prediction of the bending effect on the tube stress, however, full 3D modelling of the whole mock-up geometry is needed, which shall be a topic of future study.
Fig. 4. Temperature distribution at 10 MW/m2 and 20 MW/m2 of the novel concept. Black colour shows the area where the temperature is higher than the recrystallization temperature of W.
temperature at the top surface of W armor is more than 100 °C (50 °C at 10 MW/m2) lower than that (1723 °C at the edge, 1515 °C at the mid line) of ITER-like concept at 20 MW/m2. At high temperature (> recrystallization temperature of W: 1300 °C), W will experience the recrystallization process causing softening. To capture the mechanical behaviour more accurately, a recrystallized W layer should be defined assigning the material properties (yield stress) of the recrystallized W. As the plastic strain is accumulated only in the central part of the W surface layer [15], the depth of recrystallized W layer is defined as the distance from the mid line at the top surface to the vertical position where the local maximum temperature is above recrystallization temperature of W. The recrystallized depth is therefore defined as 0.5 mm. A recent study by X.-X Zhang
3.3. LCF failure of W and CuCrZr Assessment of low cycle fatigue (LCF) lifetime is of great importance in the divertor target design. LCF failure of W might lead to the 3
Fusion Engineering and Design xxx (xxxx) xxx–xxx
M. Li et al.
Fig. 5. Hoop stress distribution for divertor targets without and with Cu interlayer at 20 MW/m2 in the 5th HHF cycle.
only during the manufacturing process for both concepts. Therefore the plastic strain is the same for both 10 MW/m2 and 20 MW/m2. The similar amount of the plastic deformation indicates with or without Cu interlayer does not have a significant impact on the plastic deformation at the inner wall of CuCrZr tube.
initiation of deep cracking in W monoblock, while LCF failure should be strictly avoided in the CuCrZr heat sink, which is considered as the structural component. The reference nodes selected for studying of LCF of W armor and CuCrZr tube are shown in Fig. 1. The simulation shows that W behaves purely elastically at 10 MW/m2, which is the same as the ITER-like baseline design and no damage is expected in W monoblock at 10 MW/ m2. Fig. 8 shows the accumulated equivalent plastic strain with respect to the number of cycles at the reference of W armor at 20 MW/m2. Nearly no increase of accumulated equivalent plastic strain is found after the 1st HHF load cycle for the novel concept both with and without assuming the recrystallized layer, while a cyclic increase for the ITER-like baseline design is observed. As a result, no LCF failure in W armor is expected during the HHF loadings at 10 or 20 MW/m2 for the concept with a thin graded interlayer. For the ITER-like baseline design, a conservative LCF lifetime of ca. 500 cycles at 20 MW/m2 was predicted [14]. Fig. 9 shows accumulated equivalent plastic strains with respect to the number of cycles at the reference node of CuCrZr tube at 10 MW/m2 and 20 MW/m2. Plastic deformation at the reference node is generated
3.4. Brittle cracking in W monoblock 3.4.1. Deep cracking Although no LCF failure is expected to initiate the deep crack in the W monoblock at the HHF testing of up to 20 MW/m2 for the concept with a thin graded interlayer, crack initiation might be induced by the complex loading condition in the real operation (e.g. repetitive Edge Localised Mode (ELM) loading [17,18]). If a macrocrack (e.g. 0.5 mm) is created, the tensile residual stress generated by the plastic deformation during the HHF loading at 20 MW/m2 might be able to open the crack further (Fig. 10). In this part a radial crack extending through the axial thickness of the W monoblock is assumed, see Fig. 10. J-integral is calculated for this crack at both free surface and plane of symmetry to assess the possibility of brittle cracking propagation after the divertor target is Fig. 6. Radial stress distribution for divertor targets without and with a Cu interlayer at 20 MW/m2 in the 5th HHF cycle.
4
Fusion Engineering and Design xxx (xxxx) xxx–xxx
M. Li et al.
Fig. 7. Axial stress distribution for divertor targets without and with a Cu interlayer at 20 MW/m2 in the 5th HHF cycle.
Fig. 10. Crack inserted for the J-integral calculation. Fig. 8. Accumulated equivalent plastic strain with respect to the number of cycles at the reference node of W armor at 20 MW/m2 for both divertor target designs. No recrystallized W means the data of stress relieved W is applied for the whole W monoblock. The markers in the picture are only used for selected data point for a better illustration.
Fig. 11. J-integral for the deep crack with respect to different crack lengths for both divertor target designs.
cooled down from the HHF load of 20 MW/m2. J-integral is a fracture mechanics parameter, and if it is larger than its critical value, crack will propagate. Fig. 11 shows J-integral for the crack with respect to different crack lengths at 20 MW/m2. The values of J-integrals are slightly smaller for
Fig. 9. Accumulated equivalent plastic strain with respect to the number of cycles at the reference node of CuCrZr tube at 10 MW/m2 and 20 MW/m2 for both divertor target designs. The markers in the picture are only used for selected data point for a better illustration. As HHF loading does not lead to any plastic deformation at the reference node, the solid lines of the same color with or without marker have identical data points.
5
Fusion Engineering and Design xxx (xxxx) xxx–xxx
M. Li et al.
Fig. 13. J-integral for the crack (crack width: 0.125 mm) inserted 0.25 mm above the tube extending in hoop direction after the different stages of thermal excursions for both divertor target designs. Cool to RT: manufacturing process in which the mockup is assumed to be cooled to room temperature from the stress-free temperature. PreHeat: the whole mockup is heated uniformly to the coolant temperature. Loading: HHF load is applied on the component. Cool down: the mockup is cooled to coolant temperature.
Fig. 12. Crack inserted 0.25 mm above the tube for calculation of J-integral. The crack width (w) varies from 0.125 mm to 0.5 mm in this work.
the concept with a thin graded interlayer than ITER-like baseline design. Compared to the critical value of J-integral of W (0.25 mJ/mm2 transferred using fracture toughness value taken from [19]), the brittle cracking propagation will stop at a depth of between 1 mm and 1.5 mm for both concepts. A slight increase of J-integral was observed for ITERlike case, as the recrystallized layer was 1 mm, and within the recrystallized layer the stress was not significantly decreased. In case of a constant stress field, the value of J-integral is proportional to the crack length.
in case of an existed crack. Although the value of J-integral at the cooled stages after HHF loads of 10 MW/m2 or 20 MW/m2 is not larger than the critical value, due to the cyclic operation, this amount of driving force might induce fatigue failure. The situation at 20 MW/m2 could be more critical as the difference of the driving force between stages of loading and cooling down is larger than that at 10 MW/m2. Further experimental fatigue tests for the graded material are required for the lifetime estimation. For ITER-like case, the value of J-integral is close to zero through all stages of the thermal excursion for both 10 MW/m2 and 20 MW/m2 indicating that the soft Cu interlayer relaxed most of stress concentration due to thermal mismatch (see Fig. 6). As shown in Fig. 13, the largest value of J-integral occurs at the stage where the mockup was cooled from the stress-free temperature, i.e. during the manufacturing process. A more detailed study at this stage concerning different extending directions was conducted. Fig. 14 shows J-integral for the pre-crack inserted 0.25 mm above the tube for both the concept with a thin graded interlayer and ITER-like concept. The pre-crack was assumed before the manufacturing and J-integral was calculated when the divertor target was cooled from stress-free temperature, when the driving force for crack opening achieved its maximum during the whole thermal excursion. The J-integrals for the
3.4.2. Debonding between W and CuCrZr heat sink The previous study shows that due to the residual stress, the joining with a Cu interlayer of 0.1 mm was not successful [20], and the W and Cu alloy were bonded only with a Cu interlayer of over 0.3 mm. For the novel concept, the joining was successful with a thin graded interlayer of 25 μm [3], which indicates that the bonding strength should be higher than the bonding strength with pure Cu interlayer. In this work, the “debonding risk” is estimated by calculating Jintegral for a crack inserted in the W monoblock above the interlayer, see Fig. 12. There are two reasons for choosing the cracks in the W part. One is that the facture location by debonding tests often occurred in the W part [20]. The other is that, it is difficult to calculate the debonding strength at the interface due to numerical difficulties as the material on one side (W) behaves pure elastically while the material on the other side (Cu) suffers from plenty of plastic deformation. As a result, a crack is defined in the W monoblock 0.25 mm above the tube extending both in hoop and axial directions. This location is chosen for the simplicity and the validity of the J-integral calculation. At the same time, it is within the stress concentration region between the W armor and CuCrZr tube. The crack depth is fixed as 0.5 mm and crack width varies from 0.125 mm to 0.5 mm (angle of approximately 1° to 4° with respect to the tube axis for symmetric model). It is assumed that the driving force for opening such a crack is similar or proportional to the debonding driving force. The calculated J-integral can be compared with the critical value of J-integral of W for a rough estimation of the debonding possibility. Inserted cracks are assumed not to have impact on the temperature distribution. Fig. 13 shows the J-integral for crack extending in hoop direction after different stages of the thermal excursion. For the target without Cu interlayer, the largest value comes from the stage where the mockup was cooled from the stress-free temperature during the manufacturing. The value of J-integral at this stage is larger than the critical value of W indicating a risk of cracking in the W monoblock during manufacturing
Fig. 14. J-integral for the pre-crack inserted 0.25 mm above the tube extending in both hoop and axial directions after cool down from the stress-free temperature for both divertor target designs.
6
Fusion Engineering and Design xxx (xxxx) xxx–xxx
M. Li et al.
the hoop direction than in the axial direction. Already at the small crack length of 100 μm the crack tip stress intensity began to exceed the toughness of tungsten if there is no thick interlayer. This was not the case in the conventional PFC where the stress intensity factor remained below the toughness. 6. It is noted that the conclusions of this study were derived for the same armour thickness (5 mm) in both PFC models.
cracks, which grow towards axial direction, are mainly below the critical value of W, while the J-integrals for the cracks, which propagate towards hoop direction, are all above the critical value. Cracks defined here are therefore preferred to grow in the hoop direction than in the axial direction. It should be noted that a macroscopic crack was assumed in the calculation. In the reality, a crack of this size appears rarely before the bonding process, as the visual, microstructural and ultrasonic examinations were performed for the delivered W tiles. Moreover, the cooling during the manufacturing occurs monotonously in a controlled manner, the risk is further reduced. Nevertheless, compared to the concept with a thin graded interlayer, the values of Jintegral of ITER-like concept are much smaller, and it is larger than critical value only where there is a long crack (e.g. 0.5 mm) existed. The risk of debonding with a thin graded layer seems to be higher than the ITER-like design according to the simulation results. It should be noted that the crack studied here is smaller than the threshold of detection in non-destructive examinations [21,22]. These small cracks studied in this part are used to qualitatively estimate the required bonding strength and the risk of initiation of debonding. These cracks do not necessarily lead to unacceptable bonding defects which violates the acceptance criteria (e.g. 50° debonding between W and Cu interlayer for ITER W monoblock divertor target at 10 MW/m2 [21]), as the debonding growth rate is not clear.
Acknowledgments This work has been carried out within the framework of the EUROfusion Consortium and has received funding from the Euratom research and training program 2014–2018 under grant agreement No 633053. The views and opinions expressed herein do not necessarily reflect those of the European Commission. References [1] T. Hirai, F. Escourbiac, V. Barabash, A. Durocher, A. Fedosov, L. Ferrand, T. Jokinen, V. Komarov, M. Merola, S. Carpentier-Chouchana, N. Arkhipov, V. Kuznetcov, A. Volodin, S. Suzuki, K. Ezato, Y. Seki, B. Riccardi, M. Bednarek, P. Gavila, Status of technology R & D for the ITER tungsten divertor monoblock, J. Nucl. Mater. 463 (2015) 1248–1251. [2] J.H. You, et al., Conceptual design studies for the European DEMO divertor: rationale and first results, Fusion Eng. Des. 109-111 (2016) 1598–1603. [3] M. Richou, F. Gallay, I. Chu, M. Li, P. Magaud, M. Missirlian, S. Rocella, E. Visca, J. You, Status on the W monoblock type high heat flux target with graded interlayer for application to DEMO divertor, Fusion Eng. Des. (2017) (in Press). [4] M. Richou, F. Gallay, B. Boswirth, I. Chu, M. Lenci, Th. Loewenhoff, G.A. Quet, H. Greuner, G. Kermouche, E. Meillot, G. Pintsuk, E. Visca, J.H. You, Realization of high heat flux tungsten monoblock type target with graded interlayer for application to DEMO divertor, Phys. Scr. (2017) (Submitted). [5] M. Li, E. Werner, J.-H. You, Low cycle fatigue behavior of ITER-like divertor target under DEMO-relevant operation conditions, Fusion Eng. Des. 90 (2015) 88–96. [6] G. Pintsuk, M. Bednarek, P. Gavila, S. Gerzoskovitz, J. Linke, P. Lorenzetto, B. Riccardi, F. Escourbia, Characterization of ITER tungsten qualification mock-ups exposed to high cyclic thermal loads, Fusion Eng. Des. 98–99 (2015) 1384–1388. [7] S.A. Fabritsievand, A.S. Pokrovsky, Neutron irradiation induced high temperature embrittlement of pure copper, Plasma Devices Oper. 5 (2) (1997) 133–141. [8] F. Crescenzi, C. Bachmann, M. Richou, S. Roccella, E. Visca, J.-H. You, Design study of ITER-like divertor target for DEMO, Fusion Eng. Des. 98–99 (2015) 1263–1266. [9] ITER Structural Design Criteria for In-vessel Components (SDC-IC), Appendix A: Materials Design Limit Data, ITER, 2012. [10] ITER Document No.G74M 16, ITER Material Properties Handbook, (2005). [11] E. Visca, E. Cacciotti, A. Komarov, S. Libera, N. Litunovsky, A. Makhankov, A. Mancini, M. Merola, A. Pizzuto, B. Riccardi, S. Roccella, Manufacturing, testing and post-test examination of ITER divertor vertical target W small scale mock-ups, Fusion Eng. Des. 86 (2011) 1591–1594. [12] E.N. Sieder, G.E. Tate, Heat transfer and pressure drop of liquids in tubes, Indust. Eng. Chem. 28 (1936) 1429–1435. [13] J. Thom, W. Walker, T. Fallon, G. Reising, Boiling in sub-cooled water during flow up heated tubes or annuli, Proc. Inst. Mech. Eng. (London) 180 (Pt 3C) (1966) 226–246. [14] M. Li, J.-H. You, Structural impact of armor monoblock dimensions on the failure behavior of ITER-type divertor target components: size matters, Fusion Eng. Des. 113 (2016) 162–170. [15] M. Li, J.-H. You, Interpretation of the deep cracking phenomenon of tungsten monoblock targets observed in high-heat-flux fatigue tests at 20 MW/m², Fusion Eng. Des. 101 (2015) 1–8. [16] X.-X. Zhang, Q.-Z. Yan, C.-T. Yang, T.-N. Wang, M. Xia, C.-C. Ge, Recrystallization temperature of tungsten with different deformation degrees 567, Rare Met. 35 (2016) 566–570. [17] G. Pintsuk, A. Prokhodtseva, I. Uytdenhouwen, Thermal shock characterization of tungsten deformed in two orthogonal directions, J. Nucl. Mater. 481–486 (2011) 417. [18] M. Li, J.-H. You, Cracking behavior of tungsten armor under ELM-like thermal shockloads II: A revised prediction for crack appearance map, Nucl. Mater. Energy 9 (2016) 598–603. [19] B. Gludovatz, S. Wurster, A. Hoffmann, R. Pippan, Fracture toughness of polycrystalline tungsten alloys, Int. J. Refract. Metals Hard Mater. 28 (2010) 674–678. [20] S. Saito, K. Fukaya, S. Ishiyama, K. Sato, Mechanical properties of HIP bonded W and Cu-alloys joint for plasma facing components, J. Nucl. Mater. 307–311 (2002) 1542–1546. [21] F. Escourbiac, M. Richou, R. Guigon, S. Constans, A. Durocher, M. Merola, J. Schlosser, B. Riccardi, A. Grosman, Definition of acceptance criteria for the ITER divertor plasma-facing components through systematic experimental analysis, Phys. Scr. T138 (2009) 014002. [22] S. Roccella, E. Cacciotti, F. Escourbiac, A. Pizzuto, B. Riccardi, A. Tatì, P. Varonee, E. Visca, Development of an ultrasonic test method for the non-destructive examination of ITER divertor components, Fusion Eng. Des. 84 (2009) 1639–1644.
4. Summary and conclusions The thick Cu interlayer which has been used as stress-relaxing soft buffer between the stiff armor block and tube in an ITER-type W monoblock PFC is predicted to undergo severe plastic fatigue damage under cyclic HHF loads. Furthermore, the pure Cu interlayer is anticipated to be heavily embrittled under neutron irradiation due to transmuted helium. Thus, the presence (or absence) of the thick Cu interlayer is expected to bring forth trade-off effects on the structural integrity of a W monoblock PFC. In this study, such trade-off effects were computationally investigated in a comparative assessment of fracture and fatigue behaviour of the armour block and cooling tube in two representative cases, namely, with and without a thick Cu interlayer. The prominent structure-mechanical effects caused by the presence (or absence) of the thick Cu interlayer are summarized in the following: 1. Omitting a thick (1 mm) Cu interlayer from the conventional (ITERlike) W monoblock PFC led to a temperature decrease on the W armor surface by more than 100 °C under HHF load of 20 MW/m2 for the same armour thickness. 2. This temperature decrease was big enough (for 5 mm armor thickness) to suppress the plastic yield of tungsten so that cumulative plastic straining in the armour surface layer is prevented. No plastic fatigue is expected in this case. On the contrary, the armour of a conventional W monoblock PFC with a thick interlayer of Cu often suffers from surface cracking at 20 MW/m2 which is initiated by fatigue damage for the same armour thickness. 3. Once a crack is initiated on the armour surface by any cause, no difference was found in the crack driving force between the two cases (with and without thick Cu interlayer). In both cases, the crack was predicted to grow in a brittle manner up to the vertical depth of about 1.5 mm at 20 MW/m2. 4. The absence (or presence) of a thick Cu interlayer had nearly no impact on the deformation behaviour of the CuCrZr tube. After initial plastic yield during manufacturing stage, the tube existed in a fully elastic shakedown state during the cyclic HHF loading. No plastic failure is foreseen here. 5. On the other hand, for an interfacial crack locating between armour and the tube, the PFC without thick Cu interlayer exhibited much higher crack tip loads than the conventional PFC. The driving force of the interfacial crack causing debonding was more significant in 7
Contents lists available at ScienceDirect
Fusion Engineering and Design journal homepage: www.elsevier.com/locate/fusengdes
Fracture mechanical analysis of a tungsten monoblock-type plasma-facing component without macroscopic interlayer for high-heat-flux divertor target ⁎
Muyuan Lia, , Franklin Gallayb, Marianne Richoub, Jeong-Ha Youa, a b
⁎
Max Planck Institute for Plasma Physics, Boltzmann Str. 2, 85748 Garching, Germany CEA, IRFM, F-13108 Saint-Paul-Lez-Durance, France
A R T I C L E I N F O
A B S T R A C T
Keywords: Divertor Plasma-facing component High-heat-flux component Tungsten monoblock Fracture Structural failure
In the framework of the European DEMO divertor project, several novel design concepts of the plasma-facing components of vertical targets are being developed. One of those concepts is the tungsten monoblock design (similar to the ITER divertor) but with a very thin interlayer (roughly 25 mm thick only) at the armor/tube bond interface instead of a thick (1 mm) copper interlayer as has been the case in the conventional tungsten monoblock design developed for ITER divertor. The thin interlayer serves as bonding agent, but not as structural constituent. The reasoning for this novel design concept to omit the thick soft copper interlayer, which has been used as stress-relaxing buffer between the stiff armor block and tube, is to prevent plastic fatigue damage under cyclic high heat flux loads and irradiation embrittlement which the soft copper interlayer is predicted to undergo. On the other hand, the desirable stress relaxation effect on a global scale is abandoned. In this study, such trade-off effects are computationally investigated in a comparative assessment of structural impact, which the presence (or absence) of the thick copper interlayer is expected to bring forth, in terms of the fracture and fatigue behaviour of the armour block and cooling tube in two representative cases of tungsten monoblock plasma facing component design, namely, with and without a thick copper interlayer. Quantitative results of cyclic plastic strain history and crack tip fracture energy are presented for the armour surface, bond interface and tube of the respective plasma facing component models. The positive and negative implications of these impacts on the structural integrity are discussed.
1. Introduction Divertor is one of the major in-vessel components in a fusion power reactor. Being responsible for power exhaust and plasma particle removal, divertor shall be subjected to significant thermal loads by surface heat flux as well as volumetric nuclear heating. Particularly, the plasma-facing components (PFCs) of the vertical targets will be exposed to severe high heat flux (HHF) loads reaching about 20 MW/m2 or higher locally at the strike point in the next generation fusion reactors such as ITER and DEMO [1,2]. For both ITER and DEMO, the divertor PFCs will be fully armoured with tungsten (W) [1,2]. The standard design of a ITER divertor target PFC is based on a joint structure consisting of W monoblocks as armour, copper alloy (CuCrZr) tube as water-cooled heat sink and a rather thick (typically 1 mm) copper (Cu) interlayer between the armour and the tube (see Fig. 1) [1]. Such an ‘ITER-like’ PFC design concept was also adopted for the European DEMO divertor target as a baseline design model while several other novel design variants are being developed in parallel in the framework of the EUROfusion Work Package “Divertor” ⁎
[2,3]. One of those novel PFC design concepts is the W monoblock design with a very thin interlayer (roughly 20 μm thick) at the bond interface as illustrated in Fig. 2. The characteristic feature of this design concept proposed by a group at French Alternative Energies and Atomic Energy Commission (CEA) is that there is no macroscopic constituent between the armour and tube, which is in contrast to the ITER divertor PFC where a thick Cu interlayer is integrated. The thin interlayer serves actually as metallurgical bonding agent at the bond interface, but no more as structural entity. In order to improve adhesion and reduce thermal strain mismatch, the interlayer was compositionally graded on microscopic scale starting from full W layer on the armour side and ending up in full Cu on the tube side. Recently, Richou et al. demonstrated that real PFC mock-ups of this design concept could be successfully manufactured by means of Physical Vapour Deposition (PVD) coating of graded W/Cu interlayer and Hot Isostatic Pressing (HIP) joining process [3]. The mock-ups exhibited a sound joining quality and quite robust HHF fatigue performance at least up to 300 load cycles at 20 MW/m2 (screening test up to 25 MW/m2 without visible damage)
Corresponding authors. E-mail addresses: [email protected] (M. Li), [email protected] (J.-H. You).
http://dx.doi.org/10.1016/j.fusengdes.2017.09.002 Received 20 February 2017; Received in revised form 14 July 2017; Accepted 1 September 2017 0920-3796/ © 2017 Elsevier B.V. All rights reserved.
Please cite this article as: Li, M., Fusion Engineering and Design (2017), http://dx.doi.org/10.1016/j.fusengdes.2017.09.002
Fusion Engineering and Design xxx (xxxx) xxx–xxx
M. Li et al.
2. FEM model, materials & boundary conditions In this work, the FEM model (see Fig. 1) was built according to the novel divertor target with a very thin graded interlayer proposed by a group at CEA. The ITER-like baseline design with an interlayer of 1 mm in the EUROfusion Work Package “Divertor” was set as a reference case for comparison. The single W monoblock has a dimension of 23 × 22 × 4 mm3, and the monoblock in ITER-like baseline design has a dimension of 25 × 23 × 4 mm3 [8]. The cooling tube has a thickness of 1 mm (baseline design: 1.5 mm) and an inner diameter of 12 mm (baseline design: 12 mm). The thin interlayer of 25 μm is not included in the FEM model, which yields a conservative result, as the stress induced by the thermal mismatch will be higher than the reality. The armor thickness (the shortest distance from the armor surface to the interlayer) is 5 mm (baseline design: 5 mm). Commercial finite element analysis code ABAQUS was employed. The material data of W and CuCrZr were listed in Table 1 and obtained from ITER SDC-IC [9] and ITER material properties handbook [10]. The typical thermal history of a target mock-up from the fabrication to HHF tests was considered for modelling: fabrication (cooled from stress-free temperature to room temperature), stand-by (pre-heated to coolant temperature uniformly) and HHF load cycles (cyclic heating and cooling) as illustrated in Fig. 3. During the fabrication, an ageing process at 480 °C follows the HIP joining at 950 °C for hardening treatment of CuCrZr. In this study, the actual thermal history of the fabrication process was simplified into a single uniform cooling step from an effective stress-free temperature to the ambient temperature. For the sake of direct comparability between the two PFC design cases, the same effective stress-free temperature (580 °C) was assumed for both design concepts. This temperature corresponds to the joining temperature of the HRP (Hot Radial Pressing) process employed for manufacturing the ITER-like divertor PFC mock-ups [11]. The applied HHF loads were 10 MW/m2 and 20 MW/m2. The duration of a heat pulse was 10 s and the time interval between subsequent pulses is 20 s. A DEMO relevant cooling condition was assumed in this simulation (coolant temperature: 150 °C; pressure: 5 MPa; speed: 16 m/s) [2]. The heat transfer coefficient was calculated using Sieder/Tate [12] and CEA/Thom [13] correlations (considering swirl tape). The nodal degrees of freedom on the end cut section of the tube were constrained to produce a uniform displacement in the axial direction. Further details about the simulations can be found in [14].
Fig. 1. Materials and mesh of the quarter model of the monoblock divertor target. (reference nodes for studying of low cycle fatigue of W armor and CuCrZr tube are shown).
[4]. Actually, this fairly positive HHF test result is quite remarkable and even surprising when considering the fact that it has been a widely accepted practice in the PFC engineering to employ a thick Cu interlayer in order to mitigate thermal stresses with the help of the softness and ductility of annealed Cu. Now, the recent HHF test result indicates that to incorporate a thick Cu interlayer may not necessarily be an indispensable requirement for achieving reliable HHF performance. Moreover, there are two material issues supporting the idea to omit thick Cu interlayer as in the present design concept: 1) Under cyclic HHF loads (15–20 MW/m2), a thick Cu interlayer tends to undergo pronounced plastic fatigue leading to a premature low cycle fatigue failure of a PFC [5]. This failure feature was also experimentally observed where ductile strain damage was revealed in form of growth and coalescence of voids [6]. With increasing dpa dose, plastic fatigue behaviour of Cu will be affected by the equilibrium between irradiation hardening and thermal recovery. 2) A previous neutron irradiation test indicated that the uniform elongation of irradiated pure Cu diminished drastically even at elevated temperatures (350–400 °C) due to helium embrittlement resulting from transmutation [7]. The originally expected effect of stress relaxation via ductile yield of soft Cu will gradually disappear. These two empirical findings put the effectiveness of the thick Cu interlayer into question. As mentioned above, the promising HHF test result of the PFC mock-ups having no thick Cu layer puts the indispensability of the thick Cu interlayer into question. From this background arose the motivation to interpret the HHF performance and to understand the structure mechanical benefits of the underlying design concept to omit a thick Cu interlayer. In this paper, a rigorous numerical study is reported on the structural effect caused by the absence of a thick Cu interlayer in terms of armour cracking and plastic fatigue of tube. To this end, fracture mechanical and cyclic-plastic simulations based on finite element method (FEM) were carried out.
3. Results and discussion 3.1. Temperature distribution Fig. 4 shows the temperature distribution of the divertor target mockup without interlayer. The maximum temperature of W monoblock at 10 MW/m2 (805 °C) is well below the recrystallization temperature of W. At 20 MW/m2 the maximum temperature at the edge of the W monoblock is 1610 °C, while at the mid line of the top surface along the axial direction the maximum temperature is 1391 °C. The Fig. 2. Manufacturing of the mockups with a thin graded interlayer. 1, Coating graded interlayer in W tile; 2, CuCrZr tubes machining; 3, Hot Isostatic Pressing for assembling W tiles to the CuCrZr tubes.
2
Fusion Engineering and Design xxx (xxxx) xxx–xxx
M. Li et al.
Table 1 Properties of the considered materials at selected temperatures [9,10]. Tungstena(recrystallizedb) 20 °C Young’s modulus (GPa) 398 Yield stress (MPa) 1360 (380) Thermal conductivity (W/mK) 173 Coefficient of thermal expansion (10−6/K) 4.5 Kinematic hardening parameters entering the model for CuCrZr
CuCrZrc
400 °C
1200 °C
2000 °C
20 °C
350 °C
393 947 (363) 140 4.6
356 346 (224) 105 5.0
285 −(70) 99 5.4 C(MPa) γ
128 348 318 16.7 48399 599
116 296 347 18.0 7849 512
a
Rolled and stress-relieved state. The ultimate tensile strength of recrystallized tungsten is used as yield stress assuming a pre-hardened state. Heat treatment A (solution annealing + cold work + ageing) in ITER SDC-IC, and the yield stresses and kinematic hardening parameters are calibrated from cyclic stress-strain curves. b c
et al. [16] shows that the hardness of tungsten is dependent on the annealing temperature, where a sharp decrease of hardness of W was found if the annealing temperature increased from 1300 °C to 1500 °C. Considering the hardness is usually proportional to the yield stress, and to capture the mechanical benefit resulting from a lower temperature in the W divertor target design with a thin graded layer, a “less recrystallized W” with modified yield stress should be applied in the calculation. Hence, average of the yield stresses of recrystallized W used for ITER-like baseline design and stress relieved W was applied as a rough estimation of the yield stress in the “less recrystallized” W layer for the novel concept. 3.2. Stress distribution
Fig. 3. Schematic illustration of the thermal history considered for modelling.
Figs. 5 and 6 show the distributions of the hoop and radial stress component on the front view of the divertor targets without and with a Cu interlayer at 20 MW/m2. The plots indicate the stress fields during the stationary HHF loading and cooling (down to coolant temperature) at the 5th loading cycle. Significant tensile hoop stress occurs during HHF loading in the upper part of the W block near the interlayer or the tube, respectively, in both design cases. After cooling, tensile stress occurs in the top surface layer of the W block in both design cases, but higher stress occurs when there is no Cu interlayer. This effect is owing to the higher yield stress of tungsten due to lower surface temperature as mentioned in Section 3.1. In the case of radial stress component, higher tensile stress occurs during cooling in the W block near the bond interface around the tube without Cu interlayer. On the contrary, the presence of the thick Cu interlayer considerably reduced the radial stress component during cooling. During the HHF loading the radial stress component was mostly relaxed in both design cases. The circumferential concentration of tensile radial stress may provide a sufficiently high driving force for interfacial debonding between the armor block and the tube. The stress concentration of the radial component occurs mostly near the free surface edge only whereas the concentration of hoop stress is present in the bulk as well through the axial direction. Fig. 7 shows the axial stress distribution at 20 MW/m2 in the target PFCs without and with a Cu interlayer. Since the W block was not fully constrained in the axial direction but allowed to move in that direction, there is nearly no axial stress developing in the W block. However, the CuCrZr tube experiences a significant axial stress. The asymmetry in the stress distribution (tensile in the upper part, compressive in the lower part) indicates a possible bending deformation of the tube. For a precise prediction of the bending effect on the tube stress, however, full 3D modelling of the whole mock-up geometry is needed, which shall be a topic of future study.
Fig. 4. Temperature distribution at 10 MW/m2 and 20 MW/m2 of the novel concept. Black colour shows the area where the temperature is higher than the recrystallization temperature of W.
temperature at the top surface of W armor is more than 100 °C (50 °C at 10 MW/m2) lower than that (1723 °C at the edge, 1515 °C at the mid line) of ITER-like concept at 20 MW/m2. At high temperature (> recrystallization temperature of W: 1300 °C), W will experience the recrystallization process causing softening. To capture the mechanical behaviour more accurately, a recrystallized W layer should be defined assigning the material properties (yield stress) of the recrystallized W. As the plastic strain is accumulated only in the central part of the W surface layer [15], the depth of recrystallized W layer is defined as the distance from the mid line at the top surface to the vertical position where the local maximum temperature is above recrystallization temperature of W. The recrystallized depth is therefore defined as 0.5 mm. A recent study by X.-X Zhang
3.3. LCF failure of W and CuCrZr Assessment of low cycle fatigue (LCF) lifetime is of great importance in the divertor target design. LCF failure of W might lead to the 3
Fusion Engineering and Design xxx (xxxx) xxx–xxx
M. Li et al.
Fig. 5. Hoop stress distribution for divertor targets without and with Cu interlayer at 20 MW/m2 in the 5th HHF cycle.
only during the manufacturing process for both concepts. Therefore the plastic strain is the same for both 10 MW/m2 and 20 MW/m2. The similar amount of the plastic deformation indicates with or without Cu interlayer does not have a significant impact on the plastic deformation at the inner wall of CuCrZr tube.
initiation of deep cracking in W monoblock, while LCF failure should be strictly avoided in the CuCrZr heat sink, which is considered as the structural component. The reference nodes selected for studying of LCF of W armor and CuCrZr tube are shown in Fig. 1. The simulation shows that W behaves purely elastically at 10 MW/m2, which is the same as the ITER-like baseline design and no damage is expected in W monoblock at 10 MW/ m2. Fig. 8 shows the accumulated equivalent plastic strain with respect to the number of cycles at the reference of W armor at 20 MW/m2. Nearly no increase of accumulated equivalent plastic strain is found after the 1st HHF load cycle for the novel concept both with and without assuming the recrystallized layer, while a cyclic increase for the ITER-like baseline design is observed. As a result, no LCF failure in W armor is expected during the HHF loadings at 10 or 20 MW/m2 for the concept with a thin graded interlayer. For the ITER-like baseline design, a conservative LCF lifetime of ca. 500 cycles at 20 MW/m2 was predicted [14]. Fig. 9 shows accumulated equivalent plastic strains with respect to the number of cycles at the reference node of CuCrZr tube at 10 MW/m2 and 20 MW/m2. Plastic deformation at the reference node is generated
3.4. Brittle cracking in W monoblock 3.4.1. Deep cracking Although no LCF failure is expected to initiate the deep crack in the W monoblock at the HHF testing of up to 20 MW/m2 for the concept with a thin graded interlayer, crack initiation might be induced by the complex loading condition in the real operation (e.g. repetitive Edge Localised Mode (ELM) loading [17,18]). If a macrocrack (e.g. 0.5 mm) is created, the tensile residual stress generated by the plastic deformation during the HHF loading at 20 MW/m2 might be able to open the crack further (Fig. 10). In this part a radial crack extending through the axial thickness of the W monoblock is assumed, see Fig. 10. J-integral is calculated for this crack at both free surface and plane of symmetry to assess the possibility of brittle cracking propagation after the divertor target is Fig. 6. Radial stress distribution for divertor targets without and with a Cu interlayer at 20 MW/m2 in the 5th HHF cycle.
4
Fusion Engineering and Design xxx (xxxx) xxx–xxx
M. Li et al.
Fig. 7. Axial stress distribution for divertor targets without and with a Cu interlayer at 20 MW/m2 in the 5th HHF cycle.
Fig. 10. Crack inserted for the J-integral calculation. Fig. 8. Accumulated equivalent plastic strain with respect to the number of cycles at the reference node of W armor at 20 MW/m2 for both divertor target designs. No recrystallized W means the data of stress relieved W is applied for the whole W monoblock. The markers in the picture are only used for selected data point for a better illustration.
Fig. 11. J-integral for the deep crack with respect to different crack lengths for both divertor target designs.
cooled down from the HHF load of 20 MW/m2. J-integral is a fracture mechanics parameter, and if it is larger than its critical value, crack will propagate. Fig. 11 shows J-integral for the crack with respect to different crack lengths at 20 MW/m2. The values of J-integrals are slightly smaller for
Fig. 9. Accumulated equivalent plastic strain with respect to the number of cycles at the reference node of CuCrZr tube at 10 MW/m2 and 20 MW/m2 for both divertor target designs. The markers in the picture are only used for selected data point for a better illustration. As HHF loading does not lead to any plastic deformation at the reference node, the solid lines of the same color with or without marker have identical data points.
5
Fusion Engineering and Design xxx (xxxx) xxx–xxx
M. Li et al.
Fig. 13. J-integral for the crack (crack width: 0.125 mm) inserted 0.25 mm above the tube extending in hoop direction after the different stages of thermal excursions for both divertor target designs. Cool to RT: manufacturing process in which the mockup is assumed to be cooled to room temperature from the stress-free temperature. PreHeat: the whole mockup is heated uniformly to the coolant temperature. Loading: HHF load is applied on the component. Cool down: the mockup is cooled to coolant temperature.
Fig. 12. Crack inserted 0.25 mm above the tube for calculation of J-integral. The crack width (w) varies from 0.125 mm to 0.5 mm in this work.
the concept with a thin graded interlayer than ITER-like baseline design. Compared to the critical value of J-integral of W (0.25 mJ/mm2 transferred using fracture toughness value taken from [19]), the brittle cracking propagation will stop at a depth of between 1 mm and 1.5 mm for both concepts. A slight increase of J-integral was observed for ITERlike case, as the recrystallized layer was 1 mm, and within the recrystallized layer the stress was not significantly decreased. In case of a constant stress field, the value of J-integral is proportional to the crack length.
in case of an existed crack. Although the value of J-integral at the cooled stages after HHF loads of 10 MW/m2 or 20 MW/m2 is not larger than the critical value, due to the cyclic operation, this amount of driving force might induce fatigue failure. The situation at 20 MW/m2 could be more critical as the difference of the driving force between stages of loading and cooling down is larger than that at 10 MW/m2. Further experimental fatigue tests for the graded material are required for the lifetime estimation. For ITER-like case, the value of J-integral is close to zero through all stages of the thermal excursion for both 10 MW/m2 and 20 MW/m2 indicating that the soft Cu interlayer relaxed most of stress concentration due to thermal mismatch (see Fig. 6). As shown in Fig. 13, the largest value of J-integral occurs at the stage where the mockup was cooled from the stress-free temperature, i.e. during the manufacturing process. A more detailed study at this stage concerning different extending directions was conducted. Fig. 14 shows J-integral for the pre-crack inserted 0.25 mm above the tube for both the concept with a thin graded interlayer and ITER-like concept. The pre-crack was assumed before the manufacturing and J-integral was calculated when the divertor target was cooled from stress-free temperature, when the driving force for crack opening achieved its maximum during the whole thermal excursion. The J-integrals for the
3.4.2. Debonding between W and CuCrZr heat sink The previous study shows that due to the residual stress, the joining with a Cu interlayer of 0.1 mm was not successful [20], and the W and Cu alloy were bonded only with a Cu interlayer of over 0.3 mm. For the novel concept, the joining was successful with a thin graded interlayer of 25 μm [3], which indicates that the bonding strength should be higher than the bonding strength with pure Cu interlayer. In this work, the “debonding risk” is estimated by calculating Jintegral for a crack inserted in the W monoblock above the interlayer, see Fig. 12. There are two reasons for choosing the cracks in the W part. One is that the facture location by debonding tests often occurred in the W part [20]. The other is that, it is difficult to calculate the debonding strength at the interface due to numerical difficulties as the material on one side (W) behaves pure elastically while the material on the other side (Cu) suffers from plenty of plastic deformation. As a result, a crack is defined in the W monoblock 0.25 mm above the tube extending both in hoop and axial directions. This location is chosen for the simplicity and the validity of the J-integral calculation. At the same time, it is within the stress concentration region between the W armor and CuCrZr tube. The crack depth is fixed as 0.5 mm and crack width varies from 0.125 mm to 0.5 mm (angle of approximately 1° to 4° with respect to the tube axis for symmetric model). It is assumed that the driving force for opening such a crack is similar or proportional to the debonding driving force. The calculated J-integral can be compared with the critical value of J-integral of W for a rough estimation of the debonding possibility. Inserted cracks are assumed not to have impact on the temperature distribution. Fig. 13 shows the J-integral for crack extending in hoop direction after different stages of the thermal excursion. For the target without Cu interlayer, the largest value comes from the stage where the mockup was cooled from the stress-free temperature during the manufacturing. The value of J-integral at this stage is larger than the critical value of W indicating a risk of cracking in the W monoblock during manufacturing
Fig. 14. J-integral for the pre-crack inserted 0.25 mm above the tube extending in both hoop and axial directions after cool down from the stress-free temperature for both divertor target designs.
6
Fusion Engineering and Design xxx (xxxx) xxx–xxx
M. Li et al.
the hoop direction than in the axial direction. Already at the small crack length of 100 μm the crack tip stress intensity began to exceed the toughness of tungsten if there is no thick interlayer. This was not the case in the conventional PFC where the stress intensity factor remained below the toughness. 6. It is noted that the conclusions of this study were derived for the same armour thickness (5 mm) in both PFC models.
cracks, which grow towards axial direction, are mainly below the critical value of W, while the J-integrals for the cracks, which propagate towards hoop direction, are all above the critical value. Cracks defined here are therefore preferred to grow in the hoop direction than in the axial direction. It should be noted that a macroscopic crack was assumed in the calculation. In the reality, a crack of this size appears rarely before the bonding process, as the visual, microstructural and ultrasonic examinations were performed for the delivered W tiles. Moreover, the cooling during the manufacturing occurs monotonously in a controlled manner, the risk is further reduced. Nevertheless, compared to the concept with a thin graded interlayer, the values of Jintegral of ITER-like concept are much smaller, and it is larger than critical value only where there is a long crack (e.g. 0.5 mm) existed. The risk of debonding with a thin graded layer seems to be higher than the ITER-like design according to the simulation results. It should be noted that the crack studied here is smaller than the threshold of detection in non-destructive examinations [21,22]. These small cracks studied in this part are used to qualitatively estimate the required bonding strength and the risk of initiation of debonding. These cracks do not necessarily lead to unacceptable bonding defects which violates the acceptance criteria (e.g. 50° debonding between W and Cu interlayer for ITER W monoblock divertor target at 10 MW/m2 [21]), as the debonding growth rate is not clear.
Acknowledgments This work has been carried out within the framework of the EUROfusion Consortium and has received funding from the Euratom research and training program 2014–2018 under grant agreement No 633053. The views and opinions expressed herein do not necessarily reflect those of the European Commission. References [1] T. Hirai, F. Escourbiac, V. Barabash, A. Durocher, A. Fedosov, L. Ferrand, T. Jokinen, V. Komarov, M. Merola, S. Carpentier-Chouchana, N. Arkhipov, V. Kuznetcov, A. Volodin, S. Suzuki, K. Ezato, Y. Seki, B. Riccardi, M. Bednarek, P. Gavila, Status of technology R & D for the ITER tungsten divertor monoblock, J. Nucl. Mater. 463 (2015) 1248–1251. [2] J.H. You, et al., Conceptual design studies for the European DEMO divertor: rationale and first results, Fusion Eng. Des. 109-111 (2016) 1598–1603. [3] M. Richou, F. Gallay, I. Chu, M. Li, P. Magaud, M. Missirlian, S. Rocella, E. Visca, J. You, Status on the W monoblock type high heat flux target with graded interlayer for application to DEMO divertor, Fusion Eng. Des. (2017) (in Press). [4] M. Richou, F. Gallay, B. Boswirth, I. Chu, M. Lenci, Th. Loewenhoff, G.A. Quet, H. Greuner, G. Kermouche, E. Meillot, G. Pintsuk, E. Visca, J.H. You, Realization of high heat flux tungsten monoblock type target with graded interlayer for application to DEMO divertor, Phys. Scr. (2017) (Submitted). [5] M. Li, E. Werner, J.-H. You, Low cycle fatigue behavior of ITER-like divertor target under DEMO-relevant operation conditions, Fusion Eng. Des. 90 (2015) 88–96. [6] G. Pintsuk, M. Bednarek, P. Gavila, S. Gerzoskovitz, J. Linke, P. Lorenzetto, B. Riccardi, F. Escourbia, Characterization of ITER tungsten qualification mock-ups exposed to high cyclic thermal loads, Fusion Eng. Des. 98–99 (2015) 1384–1388. [7] S.A. Fabritsievand, A.S. Pokrovsky, Neutron irradiation induced high temperature embrittlement of pure copper, Plasma Devices Oper. 5 (2) (1997) 133–141. [8] F. Crescenzi, C. Bachmann, M. Richou, S. Roccella, E. Visca, J.-H. You, Design study of ITER-like divertor target for DEMO, Fusion Eng. Des. 98–99 (2015) 1263–1266. [9] ITER Structural Design Criteria for In-vessel Components (SDC-IC), Appendix A: Materials Design Limit Data, ITER, 2012. [10] ITER Document No.G74M 16, ITER Material Properties Handbook, (2005). [11] E. Visca, E. Cacciotti, A. Komarov, S. Libera, N. Litunovsky, A. Makhankov, A. Mancini, M. Merola, A. Pizzuto, B. Riccardi, S. Roccella, Manufacturing, testing and post-test examination of ITER divertor vertical target W small scale mock-ups, Fusion Eng. Des. 86 (2011) 1591–1594. [12] E.N. Sieder, G.E. Tate, Heat transfer and pressure drop of liquids in tubes, Indust. Eng. Chem. 28 (1936) 1429–1435. [13] J. Thom, W. Walker, T. Fallon, G. Reising, Boiling in sub-cooled water during flow up heated tubes or annuli, Proc. Inst. Mech. Eng. (London) 180 (Pt 3C) (1966) 226–246. [14] M. Li, J.-H. You, Structural impact of armor monoblock dimensions on the failure behavior of ITER-type divertor target components: size matters, Fusion Eng. Des. 113 (2016) 162–170. [15] M. Li, J.-H. You, Interpretation of the deep cracking phenomenon of tungsten monoblock targets observed in high-heat-flux fatigue tests at 20 MW/m², Fusion Eng. Des. 101 (2015) 1–8. [16] X.-X. Zhang, Q.-Z. Yan, C.-T. Yang, T.-N. Wang, M. Xia, C.-C. Ge, Recrystallization temperature of tungsten with different deformation degrees 567, Rare Met. 35 (2016) 566–570. [17] G. Pintsuk, A. Prokhodtseva, I. Uytdenhouwen, Thermal shock characterization of tungsten deformed in two orthogonal directions, J. Nucl. Mater. 481–486 (2011) 417. [18] M. Li, J.-H. You, Cracking behavior of tungsten armor under ELM-like thermal shockloads II: A revised prediction for crack appearance map, Nucl. Mater. Energy 9 (2016) 598–603. [19] B. Gludovatz, S. Wurster, A. Hoffmann, R. Pippan, Fracture toughness of polycrystalline tungsten alloys, Int. J. Refract. Metals Hard Mater. 28 (2010) 674–678. [20] S. Saito, K. Fukaya, S. Ishiyama, K. Sato, Mechanical properties of HIP bonded W and Cu-alloys joint for plasma facing components, J. Nucl. Mater. 307–311 (2002) 1542–1546. [21] F. Escourbiac, M. Richou, R. Guigon, S. Constans, A. Durocher, M. Merola, J. Schlosser, B. Riccardi, A. Grosman, Definition of acceptance criteria for the ITER divertor plasma-facing components through systematic experimental analysis, Phys. Scr. T138 (2009) 014002. [22] S. Roccella, E. Cacciotti, F. Escourbiac, A. Pizzuto, B. Riccardi, A. Tatì, P. Varonee, E. Visca, Development of an ultrasonic test method for the non-destructive examination of ITER divertor components, Fusion Eng. Des. 84 (2009) 1639–1644.
4. Summary and conclusions The thick Cu interlayer which has been used as stress-relaxing soft buffer between the stiff armor block and tube in an ITER-type W monoblock PFC is predicted to undergo severe plastic fatigue damage under cyclic HHF loads. Furthermore, the pure Cu interlayer is anticipated to be heavily embrittled under neutron irradiation due to transmuted helium. Thus, the presence (or absence) of the thick Cu interlayer is expected to bring forth trade-off effects on the structural integrity of a W monoblock PFC. In this study, such trade-off effects were computationally investigated in a comparative assessment of fracture and fatigue behaviour of the armour block and cooling tube in two representative cases, namely, with and without a thick Cu interlayer. The prominent structure-mechanical effects caused by the presence (or absence) of the thick Cu interlayer are summarized in the following: 1. Omitting a thick (1 mm) Cu interlayer from the conventional (ITERlike) W monoblock PFC led to a temperature decrease on the W armor surface by more than 100 °C under HHF load of 20 MW/m2 for the same armour thickness. 2. This temperature decrease was big enough (for 5 mm armor thickness) to suppress the plastic yield of tungsten so that cumulative plastic straining in the armour surface layer is prevented. No plastic fatigue is expected in this case. On the contrary, the armour of a conventional W monoblock PFC with a thick interlayer of Cu often suffers from surface cracking at 20 MW/m2 which is initiated by fatigue damage for the same armour thickness. 3. Once a crack is initiated on the armour surface by any cause, no difference was found in the crack driving force between the two cases (with and without thick Cu interlayer). In both cases, the crack was predicted to grow in a brittle manner up to the vertical depth of about 1.5 mm at 20 MW/m2. 4. The absence (or presence) of a thick Cu interlayer had nearly no impact on the deformation behaviour of the CuCrZr tube. After initial plastic yield during manufacturing stage, the tube existed in a fully elastic shakedown state during the cyclic HHF loading. No plastic failure is foreseen here. 5. On the other hand, for an interfacial crack locating between armour and the tube, the PFC without thick Cu interlayer exhibited much higher crack tip loads than the conventional PFC. The driving force of the interfacial crack causing debonding was more significant in 7