Copper-beryllium (<1wt% Be) binary alloys pro­vide a good combination of strength and conductivity. The precipitation of Cu-Be binary alloys occurs in both continuous and discontinuous modes. Continu­ous precipitation creates uniformly distributed fine particles in the copper matrix, as a result of the following precipitation process19:

a0 (supersaturated) ! GP zones! y" ! g! y(CuBe)

The sequence and morphology of precipitation depends mainly on aging temperature. The first phase to nucleate from a supersaturated Cu-Be solid solution is coherent Cu-rich GP zones. Follow­ing the GP zones formation is the precipitation of so-called transition phases, y00and y0. The equilibrium phase, y, forms after the transition phases, and its appearance indicates overaging of the alloy. Discon­tinuous precipitation in Cu-Be binary alloys leads to nonuniform precipitation of long, lamellar precipi­tates, resulting in cell structure at grain boundaries, which increases the tendency to intergranular frac­ture in the alloy.

High-conductivity Cu-Be alloys generally con­tain a third element. The addition of a small amount of nickel to Cu-Be binary alloys further increases the strength of the alloys without degrading elec­trical and thermal conductivities. The addition of nickel increases the precipitate solvus temperatures of Cu-Be binary alloys.2 A higher solute super­saturation condition can be reached in the solution treatment which provides a larger driving force for precipitation during the aging treatment. The strength of ternary Cu-Ni-Be alloys, therefore, is significantly increased from enhanced precipitation hardening. The electrical and thermal conductivities of Cu-Ni-Be alloys are also increased because of the depletion of the alloying elements from the solid solution during aging, resulting in high strength and high conductivity. CuNiBe exhibits very high strength with respect to other PH copper alloys. The drawback ofthis alloy is its very low ductility and low fracture toughness after low-dose irradiation.

4.20.2.2.1 CuNiSi

CuNiSi is another PH copper alloy that has been considered for fusion applications. CuNiSi has a nominal composition of 2.5% Ni and 0.6% Si. When heat treated properly, CuNiSi can have a much higher yield strength and higher electrical resistivity than CuCrZr. It has been extensively used for the Joint European Torus (JET) compo­nents, for example, the divertor cryopump, the water-cooled baffles, and the Lower Current Hybrid

Drive cryopump.21

There are two methods of determining the value of T0: the single-temperature method, which is used when the tests have been conducted at a single tem­perature; and the multitemperature method, used if testing is performed at more than one temperature. In the first case, the analysis is simpler and can be performed in analytical form, but the results do not provide further insight on temperature dependence or the lower shelf behavior. The multitemperature analysis can be performed only iteratively, but it gives more comparative information on temperature dependence, scatter, and the lower shelf behavior. As for their effects on T0, both methods give statisti­cally equal confidence levels ifthe numbers ofthe valid test data are equal and the measurements have been made close enough to the final T0 (see Figure 7). Ifsufficient specimens are available, the multitempera­ture method is generally preferred since there is less risk in exceeding the limits of T0 ± 50 °C (discussed next) and the maximum KJc from eqn [14].

4.14.2.1.2 Data qualification

Data qualification is described in detail in ASTM E 1921 and is not repeated in detail here. In addition to actions associated with the test procedure and equipment, there are measures which have to be undertaken after each test or test series to ensure that only valid data will be included in the final T0 analysis. The optimum test temperature range for the T0 determination is generally selected iteratively by taking into account the already measured data. For example, three or four tests may be conducted at a selected temperature and then a preliminary T0 is determined from the data; subsequent test tempera­tures are then based on that preliminary T0.

As discussed previously, the Master Curve cleav­age fracture model is accurate only in the transition area, where stress state and cleavage crack initiation are the main controlling factors for the fracture event. The data used for T0 determination should therefore be populated in the mid-transition area rather than near the lower or upper shelf. The shape of the transition curve causes the uncertainty of the T0 determination to increase when data measured near the lower shelf are used. There can be an optimum range within the ASTM E1921 validity range of T0 ± 50 °C (Figure 9) depending upon test speci­men size. The resultant data outside of the validity range are excluded from the analysis but still can be compared to the Master Curve determined for the

valid temperature range data. The closer the test temperature is to T0, the fewer the number of test specimens that are needed. However, when testing small specimens, the maximum KJc limit is closer to the 100 MPa Vm level at T0, and the test temperature generally has to be moved to temperatures below T0 with more specimens than the minimum number needed for a valid analysis.

DEM is used to study the interparticle force distri­bution and translate the microscopic information into macroscopic information such as stress-strain re­sponse. This method is important for estimating the overall properties of pebble beds, such as yield strength and crush probability. The use of DEM for
fusion reactor blanket analyses was started at the Uni­versity of California, Los Angeles (UCLA)124,131,205 and has been continued by KIT.91,119,132,133

A standard experiment, used by both groups, to validate DEM is UCTs; see corresponding section above. Figure 31 from An et al.205 shows three cycles of a pebble bed with an initial packing factor of 60.3%. With increasing cycle number, the pebble bed becomes stiffer. The strong dependence of the stress-strain curves on the packing factor was also stated by Gan and Kamlah.119

DEM analyses were also compared with the SCA — TOLA experiments.124 Some features were well described (see Figure 32), but thermal creep was not satisfactorily predicted.

With increasing load on the pebble bed, the number of contacts between pebbles, Nc, increases, as shown in Figure 33.91 An important quantity to assess the frac­tion of crushed pebbles during blanket operation is the

Although the present DEM codes have proven to be very helpful for the understanding of the interaction between pebbles, there is still consider­able development work required until quantitative results for small thermally loaded pebble-bed geo­metries can be expected. The method will certainly not be applicable for large components in the near future because of computational costs, but the improved understanding of the micromechanism will be beneficial for the improvement of the con­tinuum codes.

In the current design of the ITER divertor32-34 for the start-up phase, tungsten has been selected as armor for the divertor dome and the upper part of the divertor vertical targets. In addition, due to exces­sive co-deposition of tritium in CFC raising regu­latory concerns related to tritium inventory limits, a full tungsten divertor will be installed before the D-T phase of operation.32

The PFC design for ITER consists of bulk W bonded to an actively pressurized water-cooled Cu alloy heat sink. Here W has no primary structural function. However, due to the operating conditions listed in Table 1, the PFMs face large mechanical loads particularly at the interface to the heat sink material during cyclic steady state heat loads (see Section 4.17.4.2) and at the plasma-loaded surface during transient thermal events (see Section 4.17.4.1). Furthermore, the material response to these loads is influenced by the material damage or degradation due to neutron irradiation (see Table 1, Sections

4.17.4.3.3 and 4.17.4.3.4).

Along with thermally induced loads, the interac­tion of the PFM with the plasma, that is, the hydro­gen isotopes D and T as well as the fusion product He, is of importance (see Section 4.17.4.4) because they have an influence on material erosion and near­surface material degradation.

The further development of the ITER design led to four conceptual designs for the DEMO divertor.25,35 These designs include either water (inlet 140 °C/outlet 170 °C) or, due to the higher achievable efficiency, more probably He-cooling (inlet 540 °C/outlet 700 °C). In all cases bulk W is foreseen as the armor material that will have to face peak steady state heat loads of 15 MW m-2 in case of the water-cooled design and 10MWm-2 for the He-cooled designs. In contrast to ITER, off-normal events such as disruptions have to be avoided completely and transient thermal events during nor­mal operation, for example, ELMs, have to be miti­gated below the damage threshold of the material (see Section 4.17.4.1). This may be particularly important considering the expected neutron damage that will amount up to 40-60 dpa during the planned operation of the fusion reactor35 leading to a signifi­cant amount of transmutation products.36 However, the main limiting factor is expected to be the materi­al’s erosion leading to a maximum lifetime of 2 years for the divertor armor.35

In comparison to tokamaks, calculations for a device such as ARIES-CS predict steady state heat loads between 5 and 18MWm-2.30,37 Similar to DEMO, a He-cooled W divertor is anticipated with a maximum heat removal capability of 10 MW m~2. The design limits for neutron irradiation at the shield of ARIES-CS are up to 200 dpa at 40 fpy (full power years).38 The component lifetime limits are similarly dictated by the material’s expected erosion.

Finally, tungsten or more specifically tungsten coatings find their application also in the dry wall concept for inertial fusion devices, for example, the National Ignition Facility (NIF). In future, inertial confinement devices, thermal loads will occur only in the form of transient thermal loads (P = 0.1 MJ m~2, t = 1-3 ms, f= 5-15 Hz, Tbase > 500 °C).31 These are similar to those expected during ELMs and almost identical to those occurring in an X-ray anode39 and, therefore, affect a thin surface layer only.

4.18.3.1 Graphite Irradiation Damage

Gross physical property changes can occur in the graphite PFMs through two generic routes: (1) near­surface damage caused by interaction with plasma ions and, to a lesser extent, electrons, and, (2) bulk dis­placements caused by neutrons emanating from the plasma or back scattered by the surrounding struc­ture. Of the tokamaks, only TFTR had significant D+T fusion reactions and, therefore, experienced a
significant flux of fusion neutrons (see eqn [1]). Even so, the dose from that TFTR was not high enough for the structural materials to experience appreciable neutron effects. However, machines such as the ITER will see a significant neutron dose from both D+D and D+T reactions.

As energetic particles travel through matter, they can interact with their surroundings, losing energy (per unit path length) in three ways: elastic collisions, electron excitations, and nuclear inter­actions. The interaction of primary interest from the materials property evolution point of view results from the particle elastic collisions with the graphite crystal. This has also been discussed in Chapter 4.10, Radiation Effects in Graphite (Section 4.10.4). If an ion or a neutron can provide sufficient energy to overcome an atom’s binding energy (Ed carbon«20-30 eV), the carbon can be displaced from its original lattice position. If the energy transferred to the displaced atom is sufficient to displace further atoms, a series of displacement events or a ‘cascade’ occurs. In the simplest interpre­tation, the Kinchin-Pease5 model is used to calculate the total number of atoms displaced. For example, if a carbon atom were ejected by the plasma and

reimpacted onto the carbon tile with a kinetic energy (Ecarbon) of 1 keV, the estimated number of atoms displaced (n) would be estimated as follows:

n = — ar—£^ = ^20 atoms [5]

The interaction of high-energy neutrons with matter is very similar to that of high-energy ions. The pri­mary difference between the two is the amount of energy transferred in a single collision and the dis­tance over which the interactions take place. An ion, which has a relatively large coulombic interaction radius, loses its energy over a short path length (typi­cally less than a micron). In contrast, the compara­tively small uncharged 14.1 MeV fusion neutrons undergo only simple elastic or ‘billiard ball’ collisions with a mean free path between collisions of ~10 cm. So, on average, a fusion neutron will have an elastic collision with a carbon atom once in 10 cm of graph­ite. The amount of energy transferred to the carbon in this first collision (—c) is calculated by simple elastic theory as: 4mcmn

(«c + mn)2

4 x 12 x 1 (12 + 1)2

where mc and mn are the carbon and neutron mass (in amu), respectively, —o is the neutron energy, and a is the angle between the neutron path before and after the collision. For a totally back scattered neu­tron (the maximum imparted energy), the energy transferred to the displaced carbon is ^4.7 MeV. Again, from eqn [5], the number of displaced carbon atoms in this 14.1 MeV neutron collision event is nearly 100 000. The vast majority of these atoms do not stay ‘displaced,’ but condense back into the gra­phitic structure within a few picoseconds. To assess the effects such collision events will have on a mate­rial, a convention has been adopted to compare irra­diation doses. The displacement per atom (dpa) gives the average number of times an atom has been knocked from its original lattice position. The dpa is an integrated average quantity, and takes into account the atomic density, the interaction cross-section, and the neutron energy spectrum. For the next-genera­tion fusion reactors such as ITER, peak end of life values for PFMs due to neutrons will be on the order of tenths of a dpa, while power fusion reactors could potentially be subjected to greater than 10 dpayear-1.

4.18.3.2 Surface Effects

While fast neutrons will produce relatively uniform atomic displacements, ions will produce very high near-surface damage. This damage can be on the level of hundreds of dpa, even for the experimental machines in use today and certainly for machines such as ITER and beyond. However, the damage is typically limited to much less than a micron in depth. The effect of this high damage level will be the reduction of a well-graphitized structure into a struc­ture that appears amorphous. However, these near­surface regions are subjected to erosion either by physical sputtering (caused by elastic collisions), or by chemical interactions. Both these effects are addressed in Section 4.18.4. A second surface radia­tion damage issue, that is, the ability of the thin damaged surface layer to retain and transport hydro­gen, is discussed in Section 4.18.5.

4.19.5.1.1.1 Background information

The main problem of bonding Be to Cu alloys is that Be reacts with almost all possible metals (except Al, Si, Ag, and Ge) and forms brittle intermetallic phases.157-159 Such bond joints have poor mechanical integrity. More robust joints use metal interlayers to act as either diffusion barriers and/or strain accom­modating compliant layers to avoid the formation of deleterious phases and to assist in the accommoda­tion of thermal cycling-induced strains.160

R&D has been performed over a number of years to develop the design and manufacturing techniques required to meet the demanding design require­ments. Significant experience has been gained with these manufacturing techniques and the associated inspection techniques. It must be noted that in the 1990s the best joining technology developed for manufacturing the Be/Cu actively cooled compo­nents was brazing with Ag-base alloys (e. g., InCuSil with ~41.75% Ag) which was successfully used in JET. However, the use of Ag base brazing alloy was not allowed in ITER mainly because of the transmu­tation by neutron irradiation to Cd (~5 wt% Cd will be produced in Ag-Cu eutectic alloy at 1 MW am~ ) whose presence would (1) reduce the melting tem­perature of the braze; (2) lead to the formation of highly radioactive isotopes; and (3) affect the pump­ing system in case of Cd release to the vacuum chamber and codeposition in the cryopumps panels.

During the early stage of the ITER first-wall design development, dispersion-strengthened copper (DS-Cu) alloys (e. g., Glidcop Al25) were considered as the first option because (1) the stresses were within the design allowable, and (2) they had better thermal stability under the manufacturing route, which required a first wall to be integrated with a 4 t shield. The main developments for fabrication of joints between Be and DS-Cu alloys are reported in ITER MAR129 and Lorenzetto et al.161 However, as a result of a design change that took place from an integrated first-wall panel to a separated first-wall panel design, a precipitation-hardened copper-chromium-zirconium alloy (CuCrZr), was subsequently chosen. This was because the fracture toughness of DS-Cu is very low above 200 °C even for unirradiated material. Fracture toughness of the unirradiated and irradiated CuCrZr alloy decreases with increasing temperature, but it remains at a rela­tively high level in the ITER working temperature range and it is significantly higher than fracture tough­ness of DS-Cu. The use of separable first-wall panels makes it possible to perform heat treatments with fast cooling rates, which are mandatory to adequately retain the mechanical properties of precipitation — hardened materials.

Thus, extensive studies were then performed during the last 10 years to develop reliable silver free Be/CuCrZr alloy joining techniques and to modify the joining conditions to minimize the mechanical strength loss of the CuCrZr alloy. Dif­ferent methods have been considered and investi­gated. Some of these were eliminated because of bad results (e. g., explosive bonding, inertial welding, joint rolling, and some types of brazing). Two meth­ods gave good results and were kept for further investigations: HIPping and brazing. Good results were achieved with the HIP joining technique by lowering the HIP temperature as close as possible to the CuCrZr alloy ageing temperature (about 480 °C) and with the brazing technique in the development of a fast brazing method to minimize the holding time at high temperature. The latter was achieved by induction brazing in Europe and by fast heating and cooling using an e-beam test facility in the Russian Federation.

Copper and copper alloys can be joined by a variety of techniques, including mechanical coupling, weld­ing, brazing, and diffusion bonding. A comprehensive overview of joining techniques for copper and copper alloys can be found in the reference.118 The welding techniques commonly used for copper and copper alloys include arc welding, resistance welding, oxy — fuel welding, and electron beam welding. Welding is generally not recommended for joining high-strength copper alloys. PH copper alloys lose their mechanical strength because of the dissolution of precipitates

(b)

(d)

Figure 20 Examples of cleared channels formed in the OFHC-Cu irradiated (to 0.3 dpa) and tested at 323 K to different strain levels: (a) before yield, (b) before yield, (c) 1.5%, and (d) 14.5%. Note that at 14.5% strain level the grain is subdivided by numerous channels formed on different slip planes. All images shown in this figure were taken in the STEM bright field mode. Reproduced from Edwards, D. J.; Singh, B. N.; Bilde-Sorensen, J. B. J. Nucl. Mater. 2005, 342, 164.

during the welding process. The welded component must be resolution annealed and aged to recover some of the initial strength in the joint. Recrystallization in the melt layer degrades the mechanical property of the weldment. DS copper alloys cannot be welded by conventional welding processes because ofthe loss of oxide particles and recrystallization in the weld zone.

Brazing is the most common method for joining copper alloys. All conventional brazing techniques can be used to join copper and copper alloys, includ­ing furnace brazing, torch brazing, induction brazing, resistance brazing, and dip brazing. A wide range of filler metals are available, and the most common brazing filler metals are Cu-Zn, Cu—P, Cu-Ag-P, and Ag — and Au-based alloys.118 Ag — and Au-based filler metals are unacceptable in fusion reactor envir­onments because of concerns of high radioactivity from neutron-induced transmutation.1

Copper alloys are typically brazed at tempera­tures between 600 and 950 °C with hold times at the brazing temperature ranging from 10 s (torch, resistance, or induction brazing) to 10 min (furnace
brazing).2 The brazing process can significantly soften PH copper alloys as a result of the adverse precipita­tion process. To reduce the softening effect, a fast induction brazing technique has been developed to minimize the holding time at high temperature to retain sufficient mechanical properties.120 Alterna­tively, the brazed component can be aged following furnace brazing to restore part of its initial strength. Complete recovery of high strength after furnace brazing by heat treatment in PH alloys is rather diffi­cult in practice as the component must be heated to a temperature greater than typical brazing tempera­tures and rapidly quenched to create a supersatura­tion of solute prior to aging. Oxide DS copper has been successfully joined using torch, furnace, resis­tance, and induction brazing.2 Softening is not a seri­ous concern for the base metal of DS copper alloys because of their high recrystallization temperature. The brazed copper joints show good fatigue proper­ties and relatively low ductility.2

Diffusion bonding is a viable technique to produce joints with high mechanical strength for DS copper alloys, but cannot be used to produce high-strength
joints in PH alloys because of significant softening of the base metal during high-temperature exposure. The DS CuAl15 and CuAl25 alloys can be joined by diffusion bonding with acceptable bond strengths under the diffusion bonding conditions similar to the normal HIPing conditions.121

Techniques for joining copper alloys to beryllium or austenitic stainless steels have been developed for the ITER plasma-facing components. A review of the joining technology was given by Odegard and Kalin.1 9 Recent work has focused on small — and medium-scale mock-ups and full-scale prototypes of the ITER first wall panels.122 The first wall panels of the ITER blanket are composed of a composite Cu alloy/316L(N) SS water-cooled heat sink structure with Be tile clad. A number of joining techniques have been explored for joining copper alloys to aus­tenitic stainless steel, 316L(N), including diffusion bonding, brazing, roll bonding, explosive bonding, friction welding, and HIP.123 HIP joining is by far the most desirable technique. For the PH CuCrZr alloy, the heat treatment must be integrated with the bonding cycle, and a high cooling rate (>^50 °C min j is required to obtain good mechanical proper­ties of CuCrZr after subsequent aging treatments. Two alternative processes are recommended12 : the HIP cycle (1040 ° C and 140 MPa for 2 h) followed by quenching in the HIP vessel, or a normal HIP cycle with a subsequent heat treatment in a furnace with fast cooling. Gervash et al}[7] studied alternative SS/Cu alloy joining methods, for example, casting, fast brazing, and explosion bonding. Cast SS/CuCrZr joint may be suitable for some ITER applications.

Brazing and diffusion bonding have been consid­ered for joining the beryllium armor to a copper alloy heat sink. The Be/DS copper alloy joints can be made by high-temperature HIPing and furnace brazing.126 Results from shear tests on small-scale specimens and from high heat flux tests of the first wall mock-ups showed good performance of joints brazed with STEMET 1108 alloy at ^780 °C for less than 5 min.122 The Be/Cu-Al25 solid HIPing (e. g., 730 °C and 140 MPa for 1 h) showed good performance from shear tests, high heat flux tests, and neutron irradiation.122

The development of joining techniques for PH CuCrCr alloy must consider the loss of mechanical strength because of overaging at high temperatures. The HIPing temperature must be reduced to be as close as possible to the aging temperature. The best results obtained so far is for HIPing at 580 °C and 140 MPa for 2h.126 A fast induction brazing tech­nique has also been developed to minimize the holding time at high temperature. Diffusion bonding of Be/CuCrZr joints gives much better high heat flux performance than brazing, and has been selected as the reference method for the European Union ITER components.120 A low-temperature Be/Cu alloy bond­ing process has also been developed that is compatible with both DS and PH copper alloys.124,127 In the United States, several different joint assemblies for diffusion bonding a beryllium armor tile to a copper alloy heat sink have been evaluated.12 To prevent formation ofintermetallic compounds and promoting a good diffusion bond between the two substrates, aluminum or an aluminum-beryllium composite (AlBeMet-150) has been used as the interfacial mate­rial. Explosive bonding was used to bond a layer of Al or AlBeMet-150 to the copper substrate that was subsequently HIP diffusion bonded to an Al-coated beryllium tile. A thin Ti diffusion barrier (0.25 mm) was used as a diffusion barrier between the copper and aluminum to prevent the formation of Cu-Al intermetallic phases. The Be/Cu alloy joints showed good strength and failure resistance.

4.20.3 Summary

High heat flux applications for fusion energy systems require high-strength, high-conductivity materials. Selection of materials for high heat flux applica­tions must consider thermal conductivity, strength and tensile ductility, fracture toughness, fatigue and creep-fatigue, and radiation resistance. Pure copper has excellent conductivity but poor strength. PH and DS copper alloys have superior strength and suffi­cient conductivity, and are prime candidates for high heat flux applications in fusion reactors. These two classes of alloys have their own advantages and dis­advantages with regard to fabrication, joining, and in­service performance.

PH copper alloys, such as CuCrZr, are heat — treatable alloys. Their properties are strongly depen­dent on the thermomechanical treatments. They possess high strength and high conductivity in the prime-aged condition, and good fracture toughness and fatigue properties in both nonirradiated and irradiated conditions. However, this class of alloys is susceptible to softening at high temperatures because of precipitate overaging and recrystallization. Their properties can be significantly degraded during large component fabrication because of their inability to achieve rapid quenching rates. DS copper alloys such as GlidCop Al25 have excellent thermal stability, and retain high strength up to temperatures near the melting point. The main disadvantages of this class of alloys are their relatively low fracture toughness and difficulty to join.

The effect of neutron irradiation in copper alloys depends largely on the irradiation temperature. At irradiation temperatures below ^300 °C, radiation hardening occurs along with loss of strain hardening capability and complete loss of uniform elongation. Radiation hardening saturates at about ~0.1 dpa in this temperature regime. At higher temperatures, radiation-induced softening can occur. Void swelling takes place between 180 and 500 °C, and the peak swelling temperature is ^300-325 °C for neutron irradiation at damage rates near 10-7 dpas-1. PH and DS copper alloys are more resistant to void swelling than pure copper. Irradiation slightly reduces the fracture toughness of copper alloys, and the effect is stronger in CuAl25 than in CuCrZr. Irradiation has no significant effect on fatigue and creep-fatigue perfor­mance. Transmutation products can significantly change the physical properties and swelling behavior in copper alloys.

Significant R&D efforts have been made to select and characterize copper alloys for high heat flux applications. The ITER Material Property Handbook provides a comprehensive database for pure copper, CuCrZr, and CuAl25. For the ITER first wall and divertor applications, CuCrZr has been selected as the prime candidate. Current focus is on fabrication, joining, and testing of large-scale components.

The Master Curve transition temperature T0 for quasistatic loading conditions is statistically precise and measurable following testing standards such as ASTM E1921. Extension of this same type of approach to dynamic loading (KId and Kjd) and crack arrest (KIa) situations seems logical, and empir­ical studies with a large variety of structural steels have confirmed a similar relationship. In both cases, the material property (KJd and KIa) can generally be

described with the same temperature dependence as the quasistatic initiation fracture toughness, but with an increased value of T0. The correlations between T0 and other related toughness parameters are discussed next.

4.14.5.1 Crack Arrest Reference Temperature TKia

For an integrity assessment of real structures, it is often necessary to have information not only on the initiation fracture toughness but also on the crack arrest toughness, KIa. A definition of the reference curve for crack arrest toughness is given in the ASME Code, Appendix A of Section XI. The para­meters describing crack initiation, including the Master Curve T0 and the related parameter RTT0, cannot be used to directly describe the crack arrest toughness.

Associated with the development of the Master Curve concept, studies have concluded that it is possible to develop correlations describing the rela­tionship between the crack initiation and arrest toughness.43 These studies have focused on clarify­ing which elements of the Master Curve approach should be modified for assessing crack arrest; and finding possible correlations between initiation and arrest parameters. Due to different mechanisms and differences in factors controlling fracture initiation and arrest events (e. g., the local properties are crucial for crack initiation, but not so critical for crack arrest), the weakest link theory applied in the Master Curve approach is not directly suitable for crack arrest.

The analyses of nine well-defined crack arrest datasets, consisting of various pressure vessel base and weld metals (including those used to construct the ASME reference curve), confirm that43:

• No statistical size adjustment should be made to crack arrest data.

• The scatter seems to be material independent, but lower than the scatter for crack initiation.

• KIa data follow the same Master Curve tempera­ture dependence as Kjc.

Crack arrest data can thus, in general, be described following the same Master Curve approach, using the reference temperature TKIa to characterize the tem­perature corresponding to the crack arrest toughness at a level of 100 MPa Vm, consistent with the crack initiation transition temperature T0.

To clarify if a reasonable correlation exists between T0 and TKla, a total of 54 datasets, for
which both crack initiation and arrest data were available, have been analyzed with the Master Curve concept.43 The result shows an exponentially decreasing trend for TKla — T0 as a function of T0, but the standard deviation of this correlation is high. Taking into account the observed scatter, a rough estimate for the maximum TKIa can be obtained from the value of T0 at a confidence level of 85% from:

TkIs = T0 + AT + 19 °C [40]

where AT is obtained from the quasistatic T0 as follows:

Tq + 273 sys

136.3 °C + 683.3MPa where sys is the material yield strength. Equation [41] is recommended only for steels where the nickel content is less than 1%.

The crack arrest toughness (TKla) can also be assessed from instrumented Charpy V-notch data using the correlation developed between TKIa and the temperature corresponding to the crack arrest force of 4 kN. The method has been used for assessing the crack arrest toughness of irradiated RPV steels from the existing Charpy V-notch data. This correla­tion and its application are described in Wallin.43

Hydrogen and its isotopes behave similarly in many regards. Gaseous protium, deuterium, and tritium are all diatomic gases that dissociate, especially on metal surfaces, and dissolve into the metal lattice in their atomic form (in some materials, such as polymers and some ceramics, the molecules may retain their diatomic character during penetration ofthe material). The isotope atoms readily recombine on the free surfaces, resulting in permeation ofthe gaseous hydro­gen isotopes through metals that support a gradient in hydrogen concentration from one side to the other. In order to understand this process, it is necessary to characterize the source of the hydrogen isotope as well as its transport within the materials.

For the purposes of the presentation in this sec­tion, we focus on tritium and its transport through materials. Much of the discussion is equally valid for the deuterium and protium as well (and subsequent sections normalize data to protium). In this section, we provide background on the diffusivity and solu­bility of tritium in metals and relate these thermody­namic parameters to the permeability. In addition, we discuss the role of trapping of hydrogen isotopes on transport of these isotopes, as well as kinetically limited transport phenomena such as recombination.

4.16.2.1 Equation of State of Gases

In the case of gaseous exposure, the ideal gas equation of state characterizes the thermodynamic state of the gas:

V0 = RT/p [1]

where V® is the molar volume of the ideal gas, T is the temperature of the system in Kelvin, p is the partial pressure of the gaseous species of interest, and R is the universal gas constant equal to 8.31447 J mol-1 K-1. The ideal gas equation of state provides a good estimate for most gases, particularly at low pressures (near ambient) and elevated temperatures (greater than room temperature). In the context of materials exposed to hydrogen isotopes in fusion technologies, the assumption of ideal gas behavior is a reasonable estimate for gaseous hydrogen and its isotopes. More details about the equation of state for real gaseous hydrogen and its isotopes can be found in San Marchi et a/.1

Disruptions still occur frequently in operating tokamaks, and therefore they are also expected for ITER with an anticipated occurrence in <10% of the ITER pulses (3000 pulses per expected compo­nent lifetime). During a disruption in which the plasma undergoes a partial or full thermal quench, most of the plasma thermal energy will be dumped on the divertor plates.166 Taking into account the resultant loading conditions (see Section 4.17.2), significant material loss from the tungsten plasma­facing surface should occur by melting and evapora­tion particularly in the dome area.167,168 In simulating these events, the amount of melting, the melt motion and subsequent roughening of the surface, the mate­rial erosion by droplet emission, the resolidification behavior, and finally, the crack formation occurring in the loaded area or at the boundary between melted and unmelted zone are the most important para­meters to be determined.

The underlying mechanisms for the above — mentioned material degradation are well described (see Figure 5).169 Thermal loading of tungsten and metals, in general, at ‘moderate’ energy densities (up to a few MJ m~ ) will result in a homogeneous, localized melting of the sample surface. When higher energy densities are applied, surface evaporation occurs; the momentum transfer due to evaporating atoms from the surface generates an effective pressure on the melt layer, which finally results in the formation of a melting ridge. Increasing the incident energy density even fur­ther, the material’s response is characterized by intense

I Incident beam

Л

Cracking Homogeneous

roughening melting

Increasing energy density

Figure 5 Performance of tungsten and metals in general under transient thermal loads.

boiling and convection of the melt layer resulting in droplet formation and ejection.170-172 Open pores in the recrystallized material have a strong impact on the thermophysical properties.

The melting threshold and subsequently the amount of melt formation depend on the material’s thermal conductivity, which is lower for porous materials such as plasma-sprayed tungsten, and for tungsten alloys. In particular, it has to be taken into account that dispersoids such as La2O3 (Tm = 2578 K) have a lower melting temperature than tungsten. This may result in early melting and increased evaporation causing the formation of a porous and depleted sur­face layer, which becomes even more important when applying loads below the melting threshold (see below and Section 4.17.4.1.2). On the other hand, the melting threshold is correlated with the base temperature of the PFM. When the base temperature increases, the melting threshold energy decreases and the amount of melt formation, the obtained cra­ter depth, and the evaporation losses for the same applied loading conditions increase significantly.169

As it cools, the material resolidifies in a recrystallized state providing a columnar grain structure typical of PVD or CVD coatings. With further cooling, depending on the base temperature of the material/component (see ‘Base Temperature’ in Section 4.17.4.1.3), brittle crack formation will not take place above a certain threshold temperature. However, with fast cooling after loading below this temperature, the material will undergo severe cracking with crack lengths that can reach the order of millimeters.169

When the qualification of different W grades and alloys108,141,147 is done in combination with thermal fatigue loading,90 materials with high thermal con­ductivity in combination with superior mechanical properties, that is, with high ductility, performed best with regard to melt material loss and crack formation. This comprises low-alloyed W materials with increased ductility such as W-Re or W-Ta, or fine-grained pure W or W alloys.

Disruption simulation experiments on bulk tungsten and tungsten coatings have also been described in the literature. These were performed not only to investigate the melting behavior but also for the purpose of characterizing the cracking behavior.26’42’60’101’122’130’131’162’165’173-176 Although

these experiments are more related to those on the characterization of ELM conditions (see Section 4.17.4.1.2) and were often performed only at RT) the results indicate that the use of highly ductile SC materials is preferred.90’177 Alternately in case of cheaper polycrystalline materials it is necessary for the material to have the proper microstructure orientation as described above’ that is’ the grain ori­entation perpendicular to the loaded surface. The reason for this is that crack formation occurs mainly along the grain boundaries and follows the orienta­tion ofthe deformed microstructure. The crack depth is in general related to the applied loading conditions and therefore the pulse length which determines the heat penetration depth and the temperature and stress gradient induced during loading. The temper­ature gradient also determines the recrystallization zone which is generated below the loaded area as a function of temperature (< Tm) and time.

However the quantification of the applied condi­tions and by this a comparison of the materials response is often not straight forward as each testing facility has its own characteristics. Most ofthe time the cited incident power density for example in Hirooka etal.’114 Linke etal.,178 and Makhankov etal.9 does not correspond to the absorbed power density. For exam­ple’ with an electron beam at 10keV’ Pabs ~ 0.62 Pinc179 — with the ratio slightly decreasing at higher acceleration voltages. In a plasma accelerator Pabs depends on incident angle and for a perpendicular impact might only reach 0.1 Pinc.1 0 For a rough esti­mate of the temperature impact, the given conditions can be compared to the heat flux parameter introduced above. For a base temperature of RT’ this amounts to a melting threshold of ^60 MW m~2 s~1/2 for pure and fully dense tungsten. Due to the fact that this parame — ter163 is also directly proportional to the thermal con­ductivity 1 the specific heat cf, and the density p: 2 jn1cPp a decrease in thermophysical properties consequently reduces the heat flux parameter and the melting threshold.

As all performed investigations indicated that melting will cause increased material degradation
and the continuous erosion of the PFM’ it will signif­icantly limit the lifetime of the PFCs. Therefore’ the safe and economic operation of a future fusion reac­tor requires that scenarios causing melt formation have to be limited to a minimum.