Only three tokamaks have operated with beryllium as the limiter or first-wall material. The first experi­ments were performed by UNITOR,45 which were then followed by ISX-B.46 Both tokamaks investi­gated the effects of small beryllium limiters on plasma behavior (UNITOR had side limiters at two toroidal locations and ISX-B had one top limiter) in support of the more ambitious beryllium experiment in JET (see below). The motivation to use beryllium came from the problem of controlling the plasma density and impurities when graphite was used.

Both UNITOR and ISX-B showed that once beryllium is evaporated from the limiter and coated over a large segment ofthe first wall, oxygen gettering leads to significant reduction of impurities. When the heat load on the beryllium limiter was increased to the point of evaporating beryllium, the oxygen concentration was decreased dramatically. Although the concentration of beryllium in the plasma was increased, its contribution to Zeff (the ion effective charge of the plasma Zeff provides a measure for impurity concentration) was more than compensated by the reduction of oxygen, carbon, and metal impu — rities.45 The plasma Zeff was observed to be reduced from 2.4 to near unity with beryllium. It must be noted that there was a negative aspect associated with beryl­lium operation during the ISX-B campaign. The reduction in plasma impurities was not observed until the limiter surface was partially melted causing beryllium to be evaporated and coated on the first wall. Once melting did occur, the droplets made subsequent evaporation more likely but hard to con­trol. The consequent strong reduction in plasma impurities associated with gettering then made dis­charge reproducibility hard to obtain. However, if a much larger plasma contact area is already covered with Be, one does not need to rely on limiter melting to obtain the beneficial effect ofberyllium. This effect could be achieved by using large area beryllium lim­iter, or coating the inside wall with beryllium which was the approach taken by JET when it introduced beryllium in 1989.

Large tokamak devices such as JET had found it very difficult to control the plasma density with graphite walls as the discharge pulse length got longer. Motivated by the frequent occurrence of a phenomenon that plagued the earlier campaigns — the so-called carbon blooms due to the overheating of poorly designed divertor tiles and the subsequent influx of carbon impurities in the plasma due to evaporation — JET decided to use beryllium as a plasma-facing material.

Thin evaporated beryllium layers on the graphite walls were used initially (~ 100 A average thickness per deposition) on the plasma-facing surface of the device. Subsequently, beryllium tiles were installed on the toroidal belt limiter.

The main experimental results with beryllium can be summarized as follows:

1. The concentration of carbon and oxygen in the plasma were 4-7% and 0.5-2%, respectively, when graphite was used as belt limiter. With a beryllium belt limiter, the carbon content was reduced to 0.5% and oxygen became negligible, because of oxygen gettering by beryllium. During ohmically heated discharges, the concentration of beryllium remained negligible even though beryllium was the dominant impurity.

2. While the value of Zeff was ^3 using the graphite limiter and auxiliary heating power of 10 MW, Zeff was ~1.5 even with additional heating powers of up to 30 MW with a beryllium limiter.

3. The fuel density control was greatly improved with the beryllium limiter and beryllium evapo­rated wall. Gas puffing to maintain a given plasma density was typically 10 times larger when using beryllium than graphite.

Following the beryllium limiter experience, diver­tor beryllium targets were installed in JET for two configurations. An extensive set of experiments with toroidally continuous X-point divertor plates was car­ried out inJET in the period 1990-1996 to characterize beryllium from the point of view of its thermomecha­nical performance, as well as its compatibility with

47-50

various plasma operation regimes.

In the JET Mk I experiments, melting of the beryllium tiles was reached by increasing (in a pro­gressive way) the power flux to a restricted area of the divertor target in fuelled, medium density ELMy H-mode discharges (Pinp ~ 12 MW). Large beryllium influxes were observed when the divertor target tem­perature reached 1300 °C. In these conditions, it became difficult to run low-density ELMy H-mode discharges (Pinp ~ 12 MW) without fast strike point movement (to achieve lower average power load) and the discharges either had very poor performance or were disrupted. However, no substantial plasma performance degradation was observed for medium density H-modes with fixed strike point position, or if fast strike point movement was applied in low — density H-modes, despite the large scale distortion of the target surface caused by the melt layer displace­ment and splashing due to the previous ^25 high power discharges48,51 (see Figure 2 52). This demon­strated that it was possible to use the damaged Be divertor target as the main power handling PFC if the

average power load was decreased, either by increas­ing plasma density and radiative losses, or by strike point sweeping. The damage did not prohibit subsequent plasma operation inJET, but would seri­ously limit the lifetime of Be PFCs in long-pulse ITER-like devices.

The latest results of the operation of JET with beryllium have been reviewed recently by Loarte eta/.10

Beryllium is a low-density metal that is used in a number of industries, including the nuclear, automo­tive, aerospace, defense, medical, and electronics

industries, for various applications because it is exceptionally strong, is light in weight compared with other metals, has high heat-absorbing capability, and has dimensional stability in a wide range of temperatures.

Beryllium has been considered for many years as a primary candidate for protection of PFCs in toka — maks because it offers distinct advantages when com­pared with alternative materials such as carbon and tungsten. It has a low atomic number and is an excel­lent oxygen getter. The interaction of beryllium with tritium is also significantly weaker than that of carbon, leading to potentially reduced tritium inven­tory. Beryllium does not form stable hydrides above 300 °C, so there should be very little trapping expected in codeposited layers formed at such tem­peratures in the divertor after sputtering, although work is still underway to clarify this problem. How­ever, beryllium has a relatively high physical sputter­ing rate and a relatively low melting temperature and as such is more susceptible to melting damage that may occur in a tokamak during thermal transients. In addition, because of its toxicity, special precautions are needed for working with beryllium, either for manufacturing or research investigation purposes.

Beryllium has been used with success in various tokamaks in the past mainly because of its ability to getter oxygen and to improve plasma performance. In particular, its successful deployment in JET that started in 1989 and is continuing today with the installation of a completely new beryllium wall is the main rationale for the selection of beryllium as a plasma-facing material for the first wall of ITER, on the basis of a combination of plasma compatibility and design considerations.

This paper reviewed the properties of beryllium that are of primary relevance for plasma protection applications in magnetic fusion devices (i. e., PWIs, thermal and mechanical properties for power handling, fabricability and ease of joining, chemical reactivity, etc.) together with the available knowledge on performance and operation in existing fusion machines.

Special attention was given to beryllium’s erosion and deposition, formation of mixed materials, and its hydrogen retention and release characteristics. These phenomena have a profound impact on component design, machine operation, and safety. Extensive data on the behavior of Be with plasmas have been col­lected from existing tokamaks and simulators during the last two decades and this has enabled great strides to be made in our understanding of the PWI pro­cesses involved. However, there are many issues for which there are still uncertainties and we will only learn from operating the next two major experiments that foresee the use of large amounts of Be (JET and ITER). Much work remains to be done in this area and more machine operational time and diagnostics dedicated to PWIs are required. Initiatives on these fronts, together with modeling of the results, are essential to advance the understanding of PWIs. This includes (1) the possible surface damage (melt­ing) during transients such as ELMs and disruptions and its implications for operations and (2) the prob­lem of beryllium mixing with other armor materials and in particular the issue of codeposition of tritium with Be, which is eroded from the first wall and deposited at the divertor targets. Such material may also be locally redeposited into shadowed areas ofthe shaped ITER first wall. Both issues are part of
ongoing research, the initial results of which are being taken into account in the ITER design so that the influence of these two factors on ITER operation and mission are minimized. For example, ITER will very likely employ, ELM control systems based on pellets and RMP coils, disruption mitigation systems, and increased temperature baking of the divertor to release Tfrom Be-codeposits. Dust generation is still a process which requires more attention. Conversion from gross or net erosion to dust and the assessment of dust on hot surfaces need to be investigated.

At the time of writing this paper, the ITER first wall and shielding blanket is undergoing a major rede­sign effort to overcome some ofthe main shortcomings that were identified in the context of a recent design review scrutinizing the internal components.

Complex and interrelated materials, manu­facturing, and design issues were briefly reviewed in this paper together with the progress of the manufacturing technologies being used and tested to demonstrate the durability of the joints. A critical feature of the ITER first-wall design is the beryllium to copper alloy bond. The joints must withstand the thermal, mechanical, and neutron loads and the cyclic mode of operation, and operate under vacuum, while providing an acceptable design for lifetime performance and reliability. The availability of reli­able joining technologies has a large impact on the design of the PFCs and on the overall cost of these components.

The status of the available techniques presently considered to join the Be armor to the heat sink material of Cu alloys for the fabrication of Be-clad actively cooled components for the ITER first wall was discussed. During earlier ITER design phases, the feasibility of manufacturing reliable Be-CuCrZr joints was demonstrated. The results of the perfor­mance and durability heat flux tests conducted in the framework of the further ITER first-wall qualifica­tion program were described. This program has been launched and is in progress in the ITER parties in order to qualify the design and manufacturing routes. The integrity of this bond must be assured for reliable ITER performance whatever process is used to fabri­cate joints. The original procurement sharing that assigned the fabrication of first-wall panels up to six parties was seen as a risk and the number of parties supplying these critical components has now been reduced to three, Europe, the Russian Federation, and China.

The selection of specific grades of specific beryl­lium for the ITER first wall was described. The effects of neutron irradiation on the degradation of the properties of beryllium itself and on the joints were also analyzed. Some of the changes are impor­tant while others are not significant for the ITER conditions. Change of thermal conductivity and swelling are not important because of the low fluence. The bulk tritium retention in neutron irradiated Be is expected to be significantly less than tritium reten­tion in the codeposited layers. The most critical consequence of neutron irradiation under ITER con­ditions is embrittlement. This is typical of all grades of beryllium. The structural integrity of neutron irradiated brittle Be is a key issue. Embrittlement of neutron-irradiated Be could lead to increased ther­mal erosion and crack formation, which is also observed to occur for unirradiated beryllium under severe transient heat loads. These cracks could serve as thermal fatigue crack initiation sites and accelerate this type of damage. While this effect has not been extensively studied because of the difficulty of simu­lating disruptions in the laboratory, it may not be a critical issue as thermal fatigue cracks form after a few hundred cycles in most materials and they grow only to depths where the thermal stress level is above the yield stress.

On the basis of the information available from exist­ing fusion machines, we discussed the problems that are still at issue in the design and operation of ITER. This includes, in particular, the problem of erosion/ damage and the problem of up-take and control of tritium in the beryllium-based codeposited films. Finally, on the basis of these results some tentative and speculative consideration of the limited prospects that beryllium has in future reactors was offered.

The worldwide fusion energy research over the last four decades has developed a tremendous amount of knowledge on plasma physics and related technolo­gies. From this point of view, collecting the latest information from a wide range of studies is important in order to help the fusion community to recognize the critical issues and the status. That has been the intent of this chapter. (See also Chapter 4.17, Tungsten as a Plasma-Facing Material and Chapter 4.18, Carbon as a Fusion Plasma-Facing Material).

Acknowledgments

The views expressed in this publication are the sole responsibility of the authors and do not necessarily reflect the views of Fusion for Energy. Neither Fusion for Energy nor any person acting on behalf of Fusion for Energy is responsible for the use which might be made of the information in this publication.

The authors from the ITER Organization wish to acknowledge that this paper was prepared as an account of work by or for the ITER Organization. The Members of the Organization are the People’s Repub­lic of China, the European Atomic Energy Commu­nity, Republic of India, Japan, Republic of Korea, the Russian Federation, and the United States. The views and opinions expressed herein do not necessarily reflect those of the Members or any agency thereof. Dissemination of the information in this paper is governed by the applicable terms of the ITER Joint Implementation Agreement.

As with the DC electrical properties, it soon became apparent, even before ITER CDA, that data for radi­ation effects on the AC/RF dielectric properties (dielectric loss and permittivity) of suitable insulating materials for fusion applications were almost nonex­istent. Such materials will be needed for both H&CD and diagnostic applications, where they will be required to maintain their dielectric properties from kHz to GHz under a radiation field in high vacuum. Initial work concentrated on the characterization of candidate materials (Al2O3, MgAl2O4, BeO, AlN, and Si3N4), and also PIE of neutron — and proton- irradiated materials.109-114 In general, changes in permittivity were observed to be small (<5%) and considered to be acceptable for fusion applications. However, results for dielectric loss (loss tangent mea­surements) showed orders of magnitude variation for similar materials («10~5-10~2 for different forms of alumina at 100 MHz) even before irradiation. To address this problem, a standard material (MACOR) was distributed and measured by the main laboratories involved (EU, JA, US) to check the dif­ferent measuring systems used. However, the results showed good agreement,115 and the large variation in reported loss tangent values was later shown to be real, in part because of the effect of the different impurity contents of the materials.116,117 This may be clearly seen in Figure 8, where loss tangent data for different aluminas over a wide frequency range are given, showing marked absorption band struc­tures due to polarizable defects (impurities).116

During the early postirradiation loss tangent measurements, there was an indication of recovery, suggesting that loss during irradiation could be signif­icantly higher.65,109-111 This implied that the already difficult measurements should be made in situ during irradiation. In a simple way, dielectric loss can be considered as being due to two contributions:

Loss a (DC conductivity)/Frequency + Polarization term

Clearly, both terms can be modified by the radiation. RIC and RIED will increase the DC conductivity and give rise to dose rate (flux) and dose (fluence) effects, although the contribution will decrease with frequency. The polarization term depends on the defects in the material, which exist as, or can form, dipoles through charge transfer processes due to ionization (impurities, vacancies), and produces the absorption band structure observed in the loss as a function of frequency (Figure 8). This term also gives rise to both flux and fluence effects. Furthermore, defects which are modified by radiation-induced charge transfer processes, for example, levels in the band gap occupied by electrons from the conduction band, are unstable and decay after irradiation. This process is responsible for the slow decrease in electrical conductivity observed at the end of RIC experiments, and will similarly cause a slow decrease in the polari­zation term. Hence, the initial observations ofrecovery in dielectric loss are to be expected, and the effort required to make measurements during irradiation fully justified.

Following the earlier measurements made during X-ray and proton irradiation,65,109,118 work concen­trated on the needs for ICRH at about 100 MHz with the first measurements being made during pulsed neutron irradiation (Figure 9).119,120 These pulsed neutron experiments with ionizing dose rates >104Gys-1 found increases in loss of only about a factor 4. Such a small increase is not compatible with the PIE results, which indicated that the order of

Time (s)

magnitude increases during irradiation. This discrep­ancy may be related to the pulsed nature of the irradiation; although the peak dose rate was high, the integrated dose is only about 500 Gy per pulse, far too low for RIC to reach saturation.59-63 However,

recent results indicate that for low dose (fluence), that is, at the beginning of operation, the influence of the DC conductivity term (RIC) is small for frequencies above about 1 MHz even for dose rates > 1 kGy s~ . Furthermore, in these pulsed experiments, the dpa per

pulse («10-7 dpa) is too small to affect either the DC conductivity (RIC) or the polarizable defects, even though this term at these dose rates becomes important even down to 100 kHz.

Candidate RF heating systems for ITER (IC, ion cyclotron; LH, lower hybrid; EC, electron cyclotron) operating at about 100 MHz, 5 GHz, and 200 GHz will require insulators (feedthroughs, stand­offs, windows) to operate with large electric fields in a radiation field. In general, the in situ experiments employed low-voltage RF, and the question then arises as to whether RIED could possibly affect the dielectric loss.120 At a time of intense RIED activity, two quite different theoretical models were presented in an attempt to explain why the application of a relatively small electric field during irradiation can substantially modify the damage production pro­cess and lead to volume electrical degradation.98,100 The earlier model was based on charge buildup and breakdown, that is, a DC mechanism, but failed to explain many of the results observed during RIED experiments.100 The later model however ex­plained the role of the ionization taking into account the production of highly unstable F+-centers,1 2 the electric field threshold, as well as g-alumina and colloid production, but more importantly predicted that RIED could occur for applied fields at frequen­cies >100 GHz.98 This was in agreement with early observations of RIED from DC to >100 MHz, and indications for RIED at frequencies above 1 GHz.69 Dielectric loss measurements at 15 GHz, made during electron irradiation at 2kGys-1, and postirradiation from 1 kHz to 15 GHz, for sapphire, alumina, BeO, and MgAl2O4, show very varied results.123,124 Sap­phire, the purest alumina grade, and BeO showed no prompt increase in loss, nor with a dose up to 50 MGy. However, the 999 and 997 alumina grades showed significant prompt and dose-dependent increases in loss, consistent with a modification in the polarization term. Furthermore, these in situ mea­surements show postirradiation recovery similar to the early reports for proton — and neutron-irradiated materials.65,109-111 In addition, sapphire samples, which had been preirradiated to 7 MGy, 10-6dpa at 450 °C with a DC electric field (210 kVm-1) to pro­duce RIED showed a significant increase in the loss (2 x increase), and also in the prompt dielectric loss («5x increase). Similar increases have only been observed for sapphire neutron irradiated, with­out an electric field applied, to >10-3dpa.9 In this context, one should also mention recent work concerned with RF ion sources for NBI systems, where in situ measurements of dielectric loss during and following electron irradiation of alumina (Dera — nox 999) to 110 MGy with a 1 MHz RF voltage (0.8 MV m-1) applied indicate a permanent increase in loss for irradiation at 240 °C, but not at 120 °C, as expected from previous RIED studies.125

While various alumina and BeO grades were available with adequate initial properties (dielectric loss, thermal conductivity, and mechanical strength) before irradiation for NBI, IC, and even LH applica­tions, and with potential to withstand the expected ITER radiation levels, this was not the case for ECRH windows. Sapphire or high-purity alumina, the initial ECRH window reference materials with low dielectric loss in the MHz to GHz range,116,126-128 exhibit increasing loss with increasing frequency reaching >10-4 (loss tangent) by 100 GHz. Hence, to transmit the megawatts of RF power that will be required,9 these materials would have to be employed at cryogenic temperatures, and furthermore with a very low neutron tolerance level, <1020nm-2.12 However, in recent years, considerable progress has been made with CVD diamond, a material with the required combination of low dielectric loss, high ther­mal conductivity, and mechanical strength.19,25,129-134

In this context, initial work began to examine both high-purity silicon and diamond homopolar crystal­line materials which as a result of their decreasing loss with increasing frequency offered the possibility for operation at frequencies above 150 GHz with loss tangents <10- , at room temperature.129 These two materials required development in completely oppo­site directions.

The initial high-resistivity silicon had very low loss but extreme radiation sensitivity. Because of its perfection, electrons excited into the conduction band by purely ionizing radiation had very long life­times (no defect recombination sites) leading to high dielectric loss through the high electrical conductiv­ity. In contrast, the CVD diamond, initially almost black in color, had high loss because of the numerous defects in the material giving rise to polarization losses, but was almost insensitive to ionizing radia­tion because of the extremely short lifetime of the conduction band electrons. Although the radiation sensitivity of silicon could be notably reduced by electron irradiation and also by Au doping because of the introduction of recombination defects, the main limitation for silicon comes from its small

1.1 eV band gap. This allows electrons to be readily thermally excited into the conduction band at tem­peratures only slightly above room temperature,

which rapidly increases the dielectric loss.135-138 In the case of CVD diamond, the progress has been remarkable, available samples going from black and irregular in shape to almost transparent 2 mm thick 100 mm diameter disks, with room temperature loss «1 x 10~5 at 145 GHz, comparable with sapphire at 77 K, and furthermore increasing only to about 5 x 10~5 by 450 °C.130,132 Loss measurements during electron and X-ray irradiation at 18 and 40 GHz, respectively of the developed CVD diamond, show almost negligible contributions of conductivity (RIC) and polarizable defects, and successful high-power transmission tests have now been carried out.13 ,

As may be seen in Figure 10, PIE loss tangent mea­surements of neutron-irradiated ‘window grade’ CVD diamond indicate that even by 1022 n m~2 (10~3 dpa), the room temperature loss only increases to 5 x 10- at 145 GHz (6 x 10-5 at 190 GHz).134

During the intense activity to find suitable mate­rials for the high-power IC, LH, and EC heating applications, work was also being carried out on materials for diagnostic systems. In particular, KU1 quartz glass provided by the Russian Federation within the ITER-EDA task sharing agreement was shown to be highly radiation resistant with respect to its optical properties for use in both diagnostic and remote handling applications, and became the main reference material not only for optical windows, but also fibers.26,139,140 In view of this, the material was also examined for possible use in DC and RF appli­cations. Both RIC and RIED, together with dielectric
loss and permittivity, have been determined for as-received, as well as electron and neutron irra­diated material. A large number of different experi­mental setups were employed to obtain the dielectric spectrum of KU1 over a very wide frequency range (10 mHz to 145 GHz), and where possible, values were obtained during electron irradiation. In addition, data have been obtained for samples neutron irra­diated to 10~4dpa. The results indicate that for low radiation doses the electrical and dielectric properties are only slightly degraded, and in particu­lar the use of KU 1 for electron cyclotron emission (ECE) windows and low-loss DC applications is feasible.134,141

4.14.1 Introduction

4.14.1.1 Historical Review of Fracture Toughness Determination for Ferritic Steels

Fracture mechanics is an engineering discipline which concerns the behavior of crack-like defects in struc­tures or components and their effect on integrity. Initially conceived by Griffith during World War I, early applications were limited to the study of frac­ture of highly brittle materials (e. g., glass).1 Interest in the discipline languished until World War II, when ^25% of the all-welded US Liberty ships experi­enced brittle fracture, exposing the urgent need to understand failure in ferritic structural steels and weldments. The earliest development in fracture mechanics of metals was focused on linear-elastic theory for understanding the fracture behavior of primarily high-strength steels and aluminum alloys. Application to brittle cleavage fracture in structures

made of welded ferritic steels of low-moderate strength evolved later.

One of the basic quantities of fracture mechanics is the stress-intensity factor, K, which is used to describe the loading condition of a cracked structure as a function of crack depth, a, and the applied stress, a. In the simplest case, a wide plate containing a central crack (2a), the loading condition can be expressed using the stress-intensity factor in the form:

K = af%a [1]

Increasing the stress eventually results in a situation where the crack starts to propagate. Depending on the material and loading condition, this can occur by a ductile, cleavage, intergranular, or some mixed­mode mechanism. Once the crack starts to propagate, the critical stress intensity (i. e., the fracture tough­ness) of the material has been exceeded. The fracture toughness is thus a material property, but it may be strongly affected by many environmental factors like temperature and air humidity. Using fatigue pre­cracked test specimens, the fracture toughness of a material can be determined experimentally. This frac­ture toughness quantity can be used to evaluate the integrity of real structures with real or postulated flaws. The fracture mechanism can be different depending on the material, and for ferritic steels, different fracture modes are possible at different tem­peratures due to the ductile-brittle transition. There­fore, different approaches for the characterization of fracture mechanics are needed.

The fracture toughness in body-centered cubic (bcc) ferritic steels exhibits a temperature depen­dence characterized by: (1) a low toughness cleavage initiation shelf at low temperatures; (2) an increasing transitional rise in toughness (going from cleavage to a mixture of cleavage and ductile-tearing fracture) with increasing temperature defined arbitrarily as a ductile-brittle transition temperature; and (3) an upper shelf characterized by fully ductile initiation fracture (Figure 1). The lower shelf and the region around the ductile-brittle transition temperature can be characterized using linear-elastic fracture mechanics (LEFM). LEFM considers material defects (flaws and cracks) and the effects of those defects on brittle cleavage crack behavior. LEFM is based on elastic stress analysis of the stress-strain field in the vicinity of the crack tip and a singularity called the stress-intensity factor, K. The linear-elastic theory was soon followed by elastic-plastic fracture mechanics (EPFM), which involved a different type of singular­ity parameter called the У-integral. Determination of

Temperature

Figure 1 Schematic description of the fracture toughness transition region and parameters used to characterize fracture toughness in the lower shelf, over the transition region, and in and near the upper shelf where ductile cracking gradually becomes the predominant fracture mode.

material У-integral fracture resistance (J-R) curves expanded the scope of application to also include stable crack growth characterized by ductile tearing. Regardless of which theory is being used, it is neces­sary to know the material resistance to fracture, that is, the fracture toughness of the material being eval­uated. Standardized test methods for determining material fracture toughness properties have been developed. In LEFM, fracture toughness is charac­terized by the parameter KIc; in EPFM, the initiation toughness parameter yc (often converted to an approximate equivalent K value termed Kjc) is used to characterize the onset of unstable crack growth under significant crack-tip plastic deformation con­ditions. (The statistical size effect and the elastic — plastic parameter Kjc are associated with the Master Curve methodology discussed in Section 4.14.1.3.3. The linear-elastic parameter KIc is not presently recommended to characterize the transition region, as shown in Figure 1, due to the inherently large scatter of data in this region.) The J-R curve deter­mination and parameters for the onset of stable crack growth are described in separate standards or sec­tions of standards (not discussed here in detail).2

Historically, LEFM concepts for determining the fracture toughness of ferritic, bcc steels have been used, often together with conventional Charpy V-notch impact tests, to characterize the lower shelf and the transition fracture toughness region. There have been few alternatives to the LEFM meth­odology when combined with Charpy V-notch tran­sition temperature results, as this is the current
methodology applied for irradiated reactor pressure vessel (RPV) integrity following the ASME Boiler and Pressure Vessel Code. The LEFM approach itself is simple, because only the load record and specimen dimensions are needed for KIc determination, that is, due to the qualification requirements, the test tends to be invalid if there is any significant plastic area under the load versus displacement record. This restriction imposes a major disadvantage in that the amount of test material needed is often large, even if only one large specimen is tested. In this respect, the J-integral EPFM concepts using the parameter JIc are more applicable, as they make possible testing with smaller specimens due to less severe size requirements.

Although current KIc and crack opening displace­ment (COD) testing standards better correspond to the latest fracture mechanics understanding (e. g., size restrictions relative to test specimen ligament and thickness dimensions), these standards generally are no longer recommended for characterizing the tran­sition behavior of ferritic steels; they are more appli­cable to cases where the fracture mode is known to be ductile or possibly quasicleavage, and the material shows predominantly elastic behavior. The reason is that these older standards do not account for the statistical nature of the brittle fracture process in ferritic steels. More recently, a statistical assessment methodology, called the Master Curve procedure, has been developed as an improved method for char­acterizing the material fracture toughness (both LEFM and EPFM) of ferritic bcc materials, and for characterizing the temperature dependence of the transition temperature fracture toughness curve. It is the purpose of this chapter to provide a summary review of the Master Curve methodology.

The following summary review of the Master Curve fracture toughness approach provides the basis and general framework for the methodology, but it also focuses on some key technical details that are often misunderstood. The reader should consult several of the references for greater detail regarding the various considerations needed in applying the Master Curve methodology for structural integrity assessments. In this chapter, the discussion is first devoted to LEFM involving the standard methods for experimentally determining the value of KIc; then, the more advanced approach based on EPFM and the approximate equiv­alent Kjc is reviewed. Finally, the Master Curve proce­dure is discussed in depth and is the primary focus of this chapter.

Reimann eta/94’96,110 obtained typical load displace­ment data for the ceramic pebble beds introduced above. The typical setup used is given in Figure 19.1 The pebble beds, contained in cylindrical cavities, are compressed by a piston and the pressure (equal to the uniaxial stress s) and the bed deformation (strain e) are measured, and the modulus E of the pebble bed is derived. These uniaxial compression tests (UCTs) should not be performed with bed height H to diameter D ratios larger than 1 so as to avoid a significant influence of friction effects at the cylindrical wall.

Figure 20110 shows a typical result in terms of stress and strain. Key features of the pebble-bed deformation under monotonous isothermal mechan­ical loading are as follows:

• Nonlinear elasticity: the pebble-bed stiffens with higher degrees of deformation.

• Irreversible deformation is observed after initial unloading due to pebble relocation and plastic deformation at pebble-pebble and pebble-wall contacts (which disappears after multiple loading­unloading cycles).

• Thermal creep at constant load with further irreversible deformation.

• Further stiffening observed at loading and unload­ing cycles.

• In addition, friction forces may provide some hysteresis at any loading-unloading cycle.

The permeation of hydrogen and its isotopes through many of the transition metals is lower than that dis­played by iron and the ferritic steels; the notable excep­tions include groups 4 and 5 as well as palladium. Figure 21 shows the permeability of several metals; the diffusivity and the solubility are listed in Table 1 for these metals. In general, the activation energy asso­ciated with permeability (AHs + Ed) is larger for the materials with lower permeability and the permeability tends to converge at elevated temperatures.

We do not attempt to comprehensively review the data for nonferrous metals. However, gas permeation studies are considered the standard for transport prop­erties, particularly studies that report permeability, diffusivity, and solubility. Permeation of tritium through metals and alloys was reviewed by Steward.101

4.16.3.3.5.1 Molybdenum

Several reviews ofthe literature on hydrogen transport in molybdenum have noted variability ofthe transport
parameters.101,106,118 The reported permeability values are relatively consistent between the majority of studies, while the diffusivity and solubility values range over several orders of magnitude. The results of Tanabe et a/.106 are proposed here as they appear to represent nearly upper bounds of both diffusivity and solubility, without overestimating permeability. The study of Tanabe and coworkers also has the advantage that permeability and diffusivity were measured over a wide range of temperature and pressure, confirming the appropriate pressure depen­dencies of permeability and diffusivity for diffusion — limited transport.

4.16.3.3.5.2 Silver

The available data for hydrogen permeation through silver are limited. The diffusivity of hydrogen is reported by Katsuta and McLellan.107 McLellan also reports the solubility ofGroup IB metals from satura­tion experiments.108 Although these saturation experi­ments do not appear to provide reasonable values for other Group IB metals and are not consistent with other reported solubility measurements,217 Stew­ard, nevertheless, suggests estimating the permeability of hydrogen using these reported relationships.108

4.16.3.3.5.3 Platinum

There are relatively few gas permeation studies of platinum. Ebisuzaki et a/.109 report the permeability, diffusivity, and solubility of both hydrogen and

deuterium through single crystals of high-purity plat­inum. The permeability of hydrogen in platinum is similar to that in copper.

4.16.3.3.5.4 Gold

Caskey and Derrick110 report the permeability of deuterium through gold; Begeal103 reports a similar relationship. Diffusivity measurements, however, differ depending on the conditions of the measure­ment and the microstructural state of the gold.110,21 Cold-worked gold tends to give a higher activation for diffusion, suggesting that trapping is active to relatively high temperatures. Caskey and Derrick110 speculate that trapping is related to vacancies.

The diffusivity shown in Table 1 is from Eichenauer and Liebscher,11 while the solubility is estimated from this diffusivity and the permeability reported by Caskey and Derrick.110

Perfect containment ofthe high-density plasma needed for power production, where perfection means no interaction of the high-energy plasma and its sur­roundings, is not a practical reality. Whether through normal operation, or in off-normal incidents such as plasma ‘disruptions,’ plasma-material interaction (PMI) will occur in fusion devices. Components

in line of sight with the plasma, and therefore impacted by the hot gasses and particles, are referred to as plasma-facing components (PFCs) or materials (PFMs). The reactions between the fusion plasma and the PFMs are quite severe and typically cause melting or sublimation, component mechanical fail­ure due to high thermal stress, and excessive surface erosion. The plasma ion flux and associated heat loading to the PFMs can be highly nonuniform and quite dependent on the tokamak design.

The hot plasma gasses are made up of unburned hydrogen fuel, fusion byproducts such as helium, plasma electrons, and impurities, which include ele­ments previously removed from PFCs. As can be seen in eqn [1], the types of particles that may strike the PFMs are dependent on the fusion fuel. For the D+T fuel system, the plasma will contain not only the

D+T fuel, but also high-energy alpha particles (3.5 MeV He) and neutrons (14.1 MeV). The parti­tioning of the reaction energy between helium and the neutron is both an advantage and a disadvantage for the D+T fuel system. Because the energetic helium nucleus quickly collides with the surrounding gasses, most of its energy remains in the plasma and helps to sustain the high plasma temperature. Con­versely, the neutron has very little chance of collision in the low-density plasma and loses its energy outside of the plasma, usually over meters of path length inside the structure of the reactor. Because less than 30% of the D+T reaction energy remains in the plasma, only this fraction is eventually dumped on the PFCs, thus reducing the heat load handling requirement and material erosion. However, as discussed in Section 4.18.3, the material damage associated with the 14.1 MeV neutron collisions is significant and perhaps offsets the advantages of reduced D+T heat loading.

A characteristic classifying the fusion device type is the manner in which the plasma edge is defined and the plasma power handled. The classic approach is to define the plasma edge by placing a sacrificial com­ponent in contact with the plasma. This component, which intercepts the plasma edge particle flux, is known as a bumper or bumper limiter, and extends circumferentially around the torus. A second approach to defining the plasma edge is magnetically capturing and diverting the edge plasma onto a divertor plate well removed from the central plasma. Once the plasma gasses strike the surfaces and are thus cooled, they are pumped away. Unless mitigated, the energy
deposited locally on the ‘divertor’ can be excessive. Many techniques, such as magnetic sweeping to spread the load and puffing of gas to ‘soften’ the ion impact, have been used to reduce the particle flux and energy. Regardless of whether the limiter or divertor design is employed, the majority of the par­ticle and heat flux is intercepted by these components (Table 1). However, a significant flux also impacts the balance of the torus lining, generally referred to as the first wall. A convenient comparison for the heat load­ings given in Table 1 is that the maximum output from a conventional propane torch is approximately 10MWm~ , or about the maximum seen in current fusion devices.

The physical properties of beryllium are summarized in Table 2, which is taken from ITER MPH.128 These properties have been used for design and performance assessments. In addition to its low atomic number, beryllium has several excellent ther­mal properties that make it well-suited for heat removal components. The thermal conductivity is comparable with that of graphite or CFC at low and high temperatures but, in contrast to C-based mate­rials, is not significantly degraded as a result of neutron-irradiation. The specific heat of beryllium exceeds that of C-based materials typically by a factor of 2 over the temperature range of interest for operation. However, Be has poor refractory

properties, such as low melting temperature and high vapor pressure. The high heat capacity and good thermal conductivity of Be can be used to maintain low surface temperatures in PFCs during normal operation, but its low melting temperature and high vapor pressure cause great design difficul­ties from the standpoint of survivability from off — normal events such as vertical displacement event (VDE), ELMs, disruptions, and runaway electron impact (see Section 4.19.6.2).

For the beryllium hexagonal close packed crystal structure, the main physical properties, such as the coefficient of thermal expansion, elastic modulus etc. have some anisotropy. However, for the polycrystal­line grades these properties could be, in the first approximation, considered as isotropic. Some anisot­ropy is also typical for the highly deformed grades. The physical properties (thermal conductivity, spe­cific heat, elastic modulus, etc.) in first approximation are the same for beryllium grades with similar BeO and other impurity content and they are produced by the same fabrication method.

Copper alloys are subjected to severe thermal cycles in high heat flux applications in fusion systems, and so, fatigue as well as creep-fatigue performance is a primary concern. Figure 6 shows the fatigue perfor­mance of OFHC Cu, PH CuCrZr and CuNiBe, and DS CuAl25.53 All three copper alloys show signifi­cantly better fatigue performance than OFHC cop­per. Among the three alloys, CuNiBe has the best

fatigue response. The temperature dependence of fatigue behavior is stronger in CuAl25 and CuNiBe than in CuCrZr at temperatures between 25 and 350°C. Heat treatments have an insignificant effect on fatigue life in CuCrZr.54

The fatigue life of copper and copper alloys can be significantly reduced when a hold time is applied at peak tensile and/or compressive strains during fatigue cycling. The hold time effect is evident even at room temperature and with a hold time as short as a few seconds.53,55,56 As shown in Figure 7, the fatigue life of OFHC copper is reduced significantly by the introduction of a hold time of 10 s at both tensile and compressive peak strains. The reduction in fatigue life is more severe in the high-cycle, long­life regime than in the low-cycle, short-life fatigue regime. A similar effect of the hold time was observed in copper alloys. The hold time effect appears to be more severe in CuAl25 than in CuCrZr. The effect of hold time is stronger in overaged CuCrZr (e. g., HT2 in Figure 7) than in prime-aged CuCrZr. Stress relaxation was observed during the hold periods even at room temperature where thermally activated creep processes are not expected. The reduction in fatigue life is apparently due to a change in the crack initiation mode from transgranular with no hold period to intergranular with a hold period.56,57 The fatigue life reduction under creep-fatigue load­ing could be more severe at high temperatures, particularly in PH copper alloys. Their softening behavior at elevated temperature due to overaging

100 000

and recrystallization could have significant impact on the fatigue life with a very long hold time.

Few studies have been performed to characterize the fatigue propagation rates of copper alloys. The fatigue crack growth rate of CuAl25 was found to be higher than that of CuCrZr at a lower stress intensity range, AK, at room temperature.58 Crack growth rates of CuCrZr and CuAl25 alloys increase with increas-

49,59

ing temperature.

4.14.3.1 Transferability of Test Data

The statistical size adjustment enables one to extend the fracture toughness estimation to specimens and structures with different crack front lengths. A longer crack front means that a larger volume of material is exposed to tensile stress ahead of the crack tip, which increases the probability that a crack exceed­ing the critical size will exist in this volume leading, according to the weakest link theory, to brittle frac­ture. This size effect is addressed in a conservative way by the size adjustment formula (eqn [15]). Generally, the size adjustment is made for all test specimens so that a single reference thickness (nor­mally 1 in.) is used for the Master Curve. As described earlier, when approaching the lower shelf, the size effect diminishes to zero for both EPFM Kjc data and LEFM KIc data; note that KIc data are often characterized as being size independent, but as pre­viously described in the transition region, a size cor­rection appears to be applicable. An example is presented in Figure 20, which shows LEFM fracture toughness values (including both KIc and Kq) from a

T (°C) T (°C)

large dataset measured in the heavy-section steel technology (HSST) program with different size spe­cimens ranging from 25.4 up to 152 mm (6 in.) thick­ness.23 The data from different specimen sizes follow the same Master Curve prediction after the size adjustment as shown in the second plot in Figure 20.

Another example of applying the size adjustment is presented in Figure 21, showing LEFM Kic data measured by MPA (Materialpriifungsanstalt Universitat Stuttgart, Germany) with different size
specimens, including two very large ones (B = 500 mm).24 A distinct size effect is visible in the uncor­rected data (Figure 21, plot on the left), but not in the data size adjusted to the 25.4 mm specimen thickness (plot on the right in Figure 21).

The above transferability principle also applies for a structure when the size adjustment is made for a real or postulated crack front length, if the material and load conditions remain constant over the whole crack length. If they do not, their variation has to

Master Curve K0, corresponding to the reference temperature (Tref) along the crack front and has the form for 63.2% failure probability of:

K0T[ef = 31 + 77 exp{0.019(Tref — T>)} [34]

K0 F is the local K0 value, based on local temperature and constraint and can be expressed in the form:

K0 F = K0T, т„[… = 31 + 77

Tst

0deep 10 MPa °С-1

Equation [35] is directly applicable with the ASME Code Case N-629 fracture toughness reference curve,26 since it is written in terms of the standard deep specimen T0.11(ASME Code Case N-629 and N-631 allow the determination of RTt0 when T0 is measured, see Section 4.14.4.2) Equations [33]—[35] give the effective crack driving force, normalized to represent a standard Master Curve 25.4 mm crack front (B0) and the minimum temperature along the crack front.

It should be noted that the area of applicability of the constraint correction based on the Tstress has not yet been fully established.19 The Tm:ess actually is a LEFM concept that does not work when excessive plasticity is present. In this case, a more advanced concept should be used, such as the Q-parameter or a local approach.27 The Х/геж equation (eqn [26] as applied in eqn [35]) works well for the negative values of Tstress, but the effect saturates at higher values. However, in actual components, the Х/геж is generally negative. The new Tstress equation [27] is expected to be valid up to the Tstress value of 300 MPa.2

The fracture toughness can be expressed either with the 5% lower bound Master Curve, which can be expressed in the form:

K5% ,Trf = 25.2 + 36.6 exp{°.°19( Tref — T0 deep) }

[36]

or by using the fracture toughness reference curve from ASME Code Case N-629 or N-631.26,28 Details on these Code Cases are presented in Section

4.14.4.2. The following expressions are derived:

Kic-ASME. Tref = 36.5 + 11.4

exp{0.036(Tref — T) deep) } [37]

or

Kic-ASME, Tref = 36.5 + 3.083

exp{0.036(Tref — RTt0 + 56 °C)}

The curves are compared in Figure 23. Note that the fracture toughness curve is not directly com­pared to the crack driving force estimated from stress analysis. Instead, the fracture toughness is compared to an effective driving force, which accounts for the local stress and constraint state and temperature along the crack front, as well as the crack front length. In this way, it is possible to combine the classical fracture mechanics and Master Curve analyses, and to present the comparison in a conventional format. One should remember, how­ever, that postulated flaws often contain unrealisti­cally long crack fronts. An assumed quarter thickness elliptical surface flaw (а/t = 1/4; c/ a = 3), as used in the ASME Code for pressure-temperature operating curves for RPVs, may be used from a conservative deterministic driving force perspective (as was the intention), but from a statistical size adjustment point of view, this assumption is too conservative. If such postulated flaws are analyzed using KIeff, an additional size adjustment to the Master Curve is recommended. Note that s for a 200-mm thick RPV would correspond to an a of 50 mm, 2 c of 300 mm, and an s of about 400 mm. A more realistic maxi­mum crack front length (s) is 150 mm or less. This value of s is also consistent with much of the original KIc data for the ASME Code KIc curve and therefore justifiable in terms of the functional equivalence principle. The form of KIeff for an excessively large postulated flaw (s > 150 mm) becomes11: