Introduction to fusion power plant materials

Richard Kemp

The JET torus.
JET torus


  1. First-wall materials in fusion power plants
    1. Introduction
    2. The first-wall environment
      1. Activation of irradiated materials
      2. Displacement damage
    3. Candidate first-wall structural materials
      1. Vanadium alloys
      2. Ferritic/martensitic steels
      3. Oxide dispersion strengthened alloys
      4. SiCf /SiC composites

  2. Irradiation hardening
    1. Hardening mechanisms
    2. Previous models
    3. Neural network model of irradiation hardening
      1. Predictions: Into the fusion regime
      2. Conclusions
    4. The need for more data

  3. Irradiation embrittlement
    1. Mechanisms of irradiation embrittlement
    2. Previous models
    3. Neural network models of Charpy fracture properties
      1. Predictions: Into the fusion regime
      2. The need for more data (redux)

  4. Voids and bubbles in irradiated materials
    1. The origin of cavities
    2. Creating swelling-resistant steels

  5. The International Fusion Materials Irradiation Facility
  6. Further information
  7. References
  8. Acknowledgements

First-wall materials in fusion power plants


At a time when global energy demands are steadily growing, the need for energy sources that do not rely on fossil fuels is becoming increasingly obvious. Alternative sources of energy are required, to mitigate the effects of global warming in the short term, and to sustainably and cleanly continue to provide energy in the long term. Fusion power, generated by the combining of atomic nuclei at extremely high temperatures, has the potential to contribute greatly towards these demands (Lako et al., 1998). Presuming it is commercially and technically feasible, it is a CO2 free and virtually inexhaustible energy source. There are, however, formidable engineering challenges still to be overcome in the design of such a power plant. Among these is the need to identify materials which will remain structurally reliable under exposure to the ferocious radiation emitted by the reaction plasma. The performance of these materials will, to a large extent, determine the commercial success (or failure) of a fusion power plant, by affecting the plant reliability, refuelling and replacement downtime, and waste production; the thermal efficiency of the plant is also determined by the maximum allowable temperature in the first-wall structure. The problems faced by such a material are outlined below.

The current international “fast track to fusion” programme calls for a reactor to test control systems and plant engineering (the to-be-built International Thermonuclear Experimental Reactor, ITER) to run concurrently with a fusion-spectrum material irradiation facility (the International Fusion Materials Irradiation Facility, IFMIF, still to be agreed) (Konishi, 2004). These will be followed, around the 2040s according to current plans, by power-generating fusion plants - the set of present designs of the first (demonstration model) of which are collectively referrred to as DEMO (Bloom et al., 2004).

Steady advances in the science and technology of fusion energy - both in materials issues and plasma control - have increased the possibility of demonstrating practical fusion power generation within the next fifty years. However, if these advances are consolidated, the prospect for fusion to markedly contribute to stabilisation and control of global CO2 emissions may be missed.

The first-wall environment

In ITER and future commercial magnetic confinement fusion power plants (such as the DEMO designs), the source of energy is the reaction between hot deuterium (symbol D) and tritium (symbol T) nuclei in a plasma chamber. To overcome the replusion between atomic nuclei, the plasma is accelerated to energies equivalent to a temperature of around 100 million degrees Celsius. The reaction is

$\displaystyle \mathrm{D+T\rightarrow \alpha+n+17.6 \textrm{ }MeV}$

The products of this reaction are alpha particles - helium ions, which are contained by the magnetic field - and neutrons - which are not. These neutrons, which have a characteristic energy peak around 14 MeV (with the remainder of the reaction energy given to the α particle), are absorbed in the surrounding material structure of the plant, transferring the heat of the reaction to an external cooling circuit and, ultimately, into electricity.

Figure 1.1: Left: Schematic diagram of a tokamak fusion reactor. 1: central solenoid; 2: shield/blanket; 3: active coil; 4: plasma chamber; 5: vacuum vessel shield; 6: plasma exhaust; 7: cryostat; 8: poloidal field coils; 9: toroidal field coils; 10: first wall; 11: divertor plates. Right: Schematic diagram of a first-wall/blanket segment around the plasma chamber of a tokomak reactor (Smith et al., 1994).
Image reactor_1 Image reactor_wall_2

This relentless bombardment of the first wall causes a number of problems for the material designer. Firstly, the temperature of the material is raised (the design operating temperature for a commercial reactor, based on the DEMO design, is in the region of 500 - 550°C (Toschi et al., 2001)); secondly, as neutrons are not deflected by electrical fields, they can impact the atomic nuclei of the material, causing activation - that is, the material becomes radioactive, resulting in production of in situ helium (highly insoluble in steels, and a cause of embrittlement and void formation), and must be treated as radioactive waste once removed from service; and thirdly, atoms are knocked out of position throughout the material as the neutrons decelerate. The last of these forms of damage severely disrupts the structure of the material, generating excess concentrations of vacancies and self-interstitials and increasing the dislocation density. These changes have strong effects on the mechanical properties of the material, and also on the diffusion rates of alloying species. It is calculated that, in the five-year design lifetime of a typical first-wall component, the material will experience displacement damage of up to 200 atomic lattice displacements per atom1.1 (dpa) and will contain transmutation helium gas at levels of up to 2000 atomic parts per million (appm) (Ehrlich et al., 2000). There have been attempts to incorporate radiation effects into the structural design criteria for ITER, based on results from fission reactors and other current experimental data (Majumdar and Smith, 1998). Table 1.1 summarises the operating conditions for ITER and a DEMO-like reactor, and Table 1.2 summarises the functions and requirements of the blanket structure.

Many of these effects have been observed in accelerated-particle experiments and in fission reactor materials. However, there is currently no suitable source of fusion-spectrum neutrons to carry out the experiments required to test and validate predictions which have been extrapolated from the current low-flux, low-neutron-energy database. It is hoped that construction of IFMIF (see section 5, below), as well as experiments carried out in the to-be-constructed ITER, can remedy this lack (Barabash, 2004).

Table 1.1: Operating conditions for the first-wall components of ITER and a DEMO-like reactor. As ITER will be an experimental reactor, the projected number of cycles will be very much higher than any commercial power plant reactor (Bolt et al., 2002). PFM = Plasma facing material, SS = stainless steel, RAFM = reduced activation ferritic/martensitic steel, dpa = displacements per atom, appm = atomic parts per million. MW yr = megawatt years - 1 MW yr ≈31.5 TJ.
  ITER DEMO-like reactor
Component replacements None 5 year cycle
Average neutron fluence (MW yr m-2) 0.3 10
Displacement damage (dpa) 3 (SS) 120 (RAFM)
Helium production (appm) 30 1200
Normal operation    
Number of cycles 30000 <1000
Peak particle flux (1023 m-2 s-1) 0.01 0.02
Surface heat flux (MW m-2) <0.5 <1
PFM operating temperature (°C) Be: 200 - 300 W: 550 - 700

Table 1.2: Functions and requirements of a fusion power-plant blanket structure. Tritium breeding occurs through the use of coatings such as lithium, which produce tritium under neutron bombardment (Smith et al., 1994).
Primary functions of the blanket
- Convert energy into sensible heat
- Breed tritium for the fuel cycle
Primary requirements of the blanket
- Adequate tritium production
- Acceptable tritium recovery
- Efficient heat recovery
- Acceptable reliability and operating lifetime
- Ease of assembly, maintenance, and repair
- Acceptable post-irradiation environmental impact
- Acceptable economics

Activation of irradiated materials

As neutrons are uncharged particles, there are no significant repulsive forces between them and an atomic nucleus. Therefore, the chances of an atomic nucleus being directly hit by a neutron under irradiation can be high. On impact, the neutron may be absorbed by the nucleus, creating an unstable, radioactive atom. The energy of the impact can also knock other particles out of the nucleus with similar effect. The process of an initially stable material becoming radioctive in this manner is termed activation, and is an issue for any material that will be used in high-energy irradiation environments.

The half-lives of resultant radionuclides can be thousands of years - once the useful life of the material is over, it must be handled as radioactive waste. The design code for fusion power plant structural steels calls for them to satisfy (at least) US Department of Energy Class C waste conditions - that is, the radioactivity should decay to an acceptable maximum level within 100 to 500 years (Abe et al., 1994). The class of steels known as reduced activation ferritic/martensitic (RAFM) steels generally meets this criterion, as solvent Fe meets the class C limit. However, some typical steel alloying elements such as Mo, Nb, Ni, and N must be significantly reduced in concentration in these alloys as they form long-lived radionuclides. In general, the total concentrations for such undesirable elements, C, must be such that

$\displaystyle C=\sum_{i}\frac{c_{i}}{c_{i,max}}\leq1$

in which ci and ci,max are, respectively, the concentration of an alloying element and its maximum permitted concentration. These are tight constraints, at the limits of both detection and readily obtainable purity for some elements. Niobium, for example, has a cmax of <3 weight parts per million (wppm) (Butterworth and Giancarli, 1988).

Table 1.3: Limits for various impurity elements for shallow land burial and hands-on materials recycling, assuming 100 yr (or 300 yr) cooling time after a 20 MW yr m-2 exposure. The lower limit is for the first wall alone; the higher limit is for the blanket average. Concentrations are in wt% (units given) or wppm (no units given) (Klueh et al., 2000).
Element Waste disposal limit Recycle limit Recycle limit (300 yr)
Ni 15 - 38% 87 - 470 1.6 - 4.3%
Mo 31 - 37 3.6 - 20 4.1 - 23
Ag 1.2 - 2.7 0.012 - 0.026 0.017 - 0.036
Co 19% - no limit 2.3 - 14 0.53 - 18%
Nb 2.4 - 3.5 0.055 - 0.08 0.055 - 0.08
Al 660 - 3900 13 - 79 13 - 79
Cu 73% - no limit 160 - no limit 20% - no limit

Principal alloying elements in RAFM steels are Cr, W, V and Ta, which have no (or very high) cmax (Table 1.3). The activation of these elements, and hence the material as a whole, can be calculated using activation cross-section and decay codes such as the European Activation System (EASY) code (Forrest, 2001). In general, the properties of these steels are similar to those of their commercial counterparts for appropriate alloying-element substitutions and heat treatments (Bloom, 1998). However, as the data available for these steels are more limited in scope than for commercial steels, less work has been done to find optimum compositions and heat treatments for particular applications. A neural network-based approach to modelling these alloys is described in Kemp et al. (2006).

Displacement damage

A neutron slows down within a first wall material through impacts with atoms in the material. These impacts produce a collision cascade as the atoms recoil, passing their energy onto other atoms, which recoil in turn. This results in a central core of the cascade which has a high density of vacancies, surrounded by a cloud of self-interstitial atoms (SIAs) (Figure 1.2). The majority of these point defects rapidly annihilate with one another, but many remain to migrate into the bulk or form extended structures such as interstitial loops or clusters.

Such cascades and the immediate structures formed have been modelled through molecular dynamics (MD) (Bacon et al. (2000); Caturla et al. (2000) and Figure 1.4) and observed experimentally in metals such as tungsten and platinum using a field ion microscope (FIM) (Seidman et al. (1981); Wei et al. (1981) and Figure 1.3).

The result of this constant production of point defects is a range of microstructural evolution effects, which affect the macroscopic properties of the material. The formation of additional dislocation loops, raising the dislocation density, causes hardening of the material. In the presence of transmutation helium, vacancy clusters can be stabilised long enough to grow into voids, causing the material to swell by up to tens of percent, as well as adversely affecting the material properties (Mansur, 1987,1994). The increased vacancy concentrations also allow heightened rates of diffusion of alloying species, which can result in the composition of the alloy being drastically altered without triggering phase transformation, especially in the vicinity of microstructural sinks such as grain boundaries, cavities, and precipitates. This is termed radiation-induced segregation (RIS), and in cases where it eventually results in a phase change or precipitation, radiation-induced precipitation (RIP).

Figure 1.2: Schematic representation of the defect arrangement in a displacement cluster showing the vacancy-rich core (the denuded zone, DZ) and the interstitial shell containing mono-, di-, tri-, etc., SIAs up to small loops. Vacancies are represented as the hollow squares, interstitials as black circles. The possible effects of thermal defect mobilities are intracascade recombination reactions (R), clustering reactions (C), and glide of small interstitial loops (G). EI and EV denote escaping interstitials and vacancies (Ullmaier and Trinkaus, 1996).
Image cascade
Figure 1.3: A visualisation of an FIM observed vacancy structure of a cascade in tungsten created by a single 30 keV Kr+ projectile ion. The rods connecting vacancies represent the first-nearest-neighbour distance and hence indicate clustering (Wei et al., 1981).
Image Cascade_cluster
Figure 1.4: Distribution of vacancies (small dots) and interstitials (large dots) for cascades in Cu, caused by a 20 keV Cu ion (left) and in Fe, caused by a 20 keV Fe ion (right) after 10 ps of an MD simulation (Caturla et al., 2000).
Image MD_Cu_Fe

Candidate first-wall structural materials

Several materials that are being considered as candidate first-wall materials are reviewed below. For near-future applications, 8-12 wt% Cr martensitic alloys show the most promise and are the main subject of the research presented in this work. In the longer term, it seems likely that silicon carbide fibre/silicon carbide matrix (SiCf /SiC) composites may be adopted if they live up to early promises.

The major issues for these materials, as well as their resistance to radiation damage, are: ease and economy of manufacture; joining of the material during the building of complex structures while preserving the radiation and structural properties of the material; and compatability with other materials in the blanket, such as tritium-breeding materials.

Vanadium alloys

Vanadium alloys are attractive candidate first wall materials. They have low activation characteristics and promise desirable high-temperature strength, good resistance to radiation damage, and useable fabrication properties. The majority of development work for fusion applications has been carried out on the V-Cr-Ti system, with the principal reference composition 4 wt% Cr-4 wt% Ti. Thermal creep data suggest, though, that this alloy will be limited to a maximum operating temperature of around 700°C. Altering the Cr content can improve the high-temperature properties, but makes the alloy markedly more susceptible to embrittlement caused by radiation damage. Moreover, little experimental work has been carried out to higher damage levels (data exist extending up to 4 dpa), and the irradiation creep database is very sparse. There is also a lack of data on the irradiation characteristics of weld metals (Bloom et al., 2004; Chen et al., 2004; Kurtz et al., 2004).

There is increasing experimental and modelling work on alternative-composition and multiphase-microstructure vanadium alloys, which may demonstrate sufficient future performance to meet the structural design criteria for components of a commercial fusion power system.

Ferritic/martensitic steels

The current leading candidate first-wall structural material for near-future fusion systems is reduced activation ferritic/martensitic (RAFM) steels. These are generally 8-12 wt%Cr steels, in which the usual commercial alloying elements have been replaced with low-activation equivalents as described in Section 1.2.1. Ferritic steels are preferred to the stainless/FCC steels often used in fission reactors due to the markedly lower swelling observed in the ferritic steels under irradiation (Garner et al., 2000). The development and experimental database of these materials are also considerably more advanced than competing first-wall materials.

RAFM steels exhibit hardening and embrittlement under irradiation. Increasing quantities of data exist and significant progress is being made on modelling these changes in properties. One major additional limitation is high-temperature creep resistance, which limits the use of these steels to around 550°C or below.

The production of RAFM steels with low impurity levels has been demonstrated (although not sufficiently low to reduce post-irradiation activity to hands-on levels), and various welding methods have been demonstrated to produce satisfactory (at least mechanically) welds. However, the performance of weld metals under irradiation still needs to be properly evaluated, although careful engineering design could protect joints from the most severe radiation damage (van der Schaaf et al., 2000).

Current key unresolved issues related to RAFM steels include incomplete understanding of radiation effects on fracture properties; details of the role of helium in swelling, and also its effect on fracture properties; and potential adverse effects on plasma control arising from the ferromagnetism of the steel.

It is currently planned to incorporate a test blanket module using the RAFM 8 wt%-Cr steel F82H into ITER - an important milestone in the engineering of a commercially viable power plant (Shiba et al., 2004) - and the 9 wt%-Cr Eurofer has been suggested for the DEMO blanket (Boccaccini et al., 2004). Future developments include dispersing fine ceramic oxide particles throughout a RAFM matrix, leading to improved high-temperature properties and described in more detail below (Jitsukawa et al., 2004).

Oxide dispersion strengthened alloys

Oxide dispersion strengthened (ODS) alloys for use in fusion applications generally consist of an ultrafine (∼2 nm diameter) dispersion of Ti-, Y-, and O-enriched particles in a Fe-Cr ferritic or martensitic matrix. This microstructure is generally produced through mechanical alloying. They offer the benefits of RAFM steels, and additionally, increased creep resistance and potentially greater high-temperature strength (and hence, higher operating temperatures), and higher resistance to swelling due to a high density of microstructural traps for helium. The mechanical properties of ODS alloys are very sensitive to microstructure, and it might be inferred that the large lattice misfit of Ti and Y atoms would cause them to diffuse slowly in an iron lattice. However, the high concentration of vacancies in the lattice produced by radiation may allow significantly faster diffusion of these species and so, instability of the microstructure at high damage levels. The microstructure also makes joining of ODS steels difficult whilst preserving the benefits of the dispersed particles. Current experimental results, though - up to displacement damage levels of 6 dpa - are very promising (Alamo et al., 2004; Cho et al., 2004; Miller et al., 2004).

SiCf /SiC composites

Silicion carbide fibre reinforced-silicon carbide matrix ceramics have been shown to have an exceptional blend of qualities that makes them potentially suitable as a first-wall fusion material. These include high corrosion resistance, low activation characteristics, limited void swelling, and the retention of strength and fracture properties to temperatures in excess of 1000°C. However, there are some fundamental issues which have to be overcome: high production of transmutation gas; radiation effects on mechanical properties; and engineering issues such as joining and hermeticity (which may require the use of coatings).

Despite these issues, there exist several blanket designs which have been studied to exploit the potential of SiCf /SiC composites, and there is some confidence that a reliable first-wall material may eventually be obtained (Bloom et al., 2004; Riccardi et al., 2004).

Irradiation hardening

Hardening mechanisms

Under irradiation, cascades produce point defects that form dislocation loops. These can coalesce with the existing dislocation network, resulting in an overall increase in dislocation density, causing the material to harden in a similar fashion to work-hardening. In addition, voids and precipitates may form, further impeding dislocation movement (Chaouadi and Gérard, 2005; Scattergood and Bacon, 1982) (Figure 2.1).

Figure 2.1: Transmission electron micrograph of a 300 series stainless steel irradiated at 500°C to a dose of 10 dpa. Dislocation loops and voids are clearly visible (Mansur, 1994).
Image microstruct

This behaviour can be generally described by dispersed barrier hardening (Bement, 1970; Hirth and Lothe, 1982). In this model the hardening effect, Δσy, of a distribution of obstacles is given by

$\displaystyle \Delta\sigma_{y,\mathrm{obstacles}}=\frac{\alpha M \mu b}{(Nd)^{-\frac{1}{2}}}$

in which M is the Taylor factor - a parameter which describes the amount of slip required to accommodate a strain, μ is the shear modulus of the material, b is the Burgers vector and α is an additional parameter which controls the strength of the effect. Bement has provided theoretical limits on the magnitude of this parameter for different obstacles. (Nd) is the mean discrete-obstacle spacing with N being the number density of obstacles per unit volume and d their diameter (Corti et al., 1974; Martin, 1980; Taylor, 1938).

For close-spaced obstacles of similar strengths, a geometric mean can then be used to calculate their superposed effects (Bement, 1970).

$\displaystyle \Delta\sigma_{y,\mathrm{total}}^{2}=\Delta\sigma_{y,\mathrm{loops}}^{2}+\Delta\sigma_{y,\mathrm{bubbles}}^{2}+\dots$

A number of models exist for tracking microstructural evolution under irradiation, based on rate theory (Bullough and Quigley, 1981), Fokker-Planck equations (Semenov and Woo, 2003), master equations (Semenov and Woo, 1999), or combinations of these (Ghoniem, 1991). While these models are phenomenologically successful - that is, they generally reproduce the microstructures seen in irradiated materials - they frequently rely on assumed values for vital parameters such as void number density. The calculated microstructures then vary markedly depending on the values chosen for these parameters. Although the parameters can sometimes be deduced for a particular material (by varying them until calculated microstructures closely resemble real ones), they do not generalise well to other materials, and so estimates of changes in yield stress from microstructural models are usually regarded as qualitative. There is currently no comprehensive model that can predict the hardening expected as a function of all the relevant inputs, although attempts have been made to marry dispersed barrier hardening theories to such microstructural models (Stoller (1992), for example).

Nevertheless, these models can lead to reliable qualitative relationships between radiation damage levels and changes in material properties. It can be shown, for example, that at elevated temperatures the microstructural changes can achieve a steady state - they saturate - as the rate at which defects are annealed becomes equal to the rate at which they are created (Makin and Minter, 1960). It can therefore be anticipated that the yield stress will also eventually saturate under irradiation at temperatures greater than 500 K (Murakami et al., 2000). Furthermore, in many cases little radiation hardening is observed at temperatures above 650 K. These observations suggest that a certain amount of radiation damage - excluding voids and stable precipitates - could potentially be annealed in situ in a manner similar to that used in fission reactors (Cottrell, 1981).

Similarly, it is expected that changes in yield stress do not depend linearly on the extent of radiation damage, but on functions of it such as $ \sqrt{Kt}$, where K is the damage rate and t the irradiation time (Brailsford, 1979).

A further problem arises from the addition of elements such as Ni and B, which can be used to investigate the effects of helium on mechanical properties (in combination with displacement damage) (Klueh and Vitek, 1987; Mansur and Farrell, 1997). Helium is not produced in significant quantities in a RAFM steel under fast neutron bombardment in currently available facilities, but is produced by a two-step reaction of 58Ni with thermal neutrons. Adding Ni at concentrations of about 2 wt%2.1 allows helium to be produced under fast neutron irradiation at roughly the same helium:damage ratios that would be seen in the original, unmodified alloys in a tokamak-type fusion reactor first wall. However, their presence may have additional direct effects on irradiation hardening which must be deconvoluted from the effects of any helium produced.

Previous models

Diverse models exist for predicting radiation hardening in steels. These include purely curve-fitting with general saturation functions (Makin and Minter (1960); Yamamoto et al. (2003), for example) and fits using power-law functions (e.g. $ \Delta\sigma_{y}=h(\mathrm{dpa})^{n}$, Byun and Farrell (2004)), which make assumptions about functional relationships. As the fitting parameters vary according to material and irradiation conditions, this approach is only weakly predictive. Simple dispersed barrier models do not predict hardening saturation and more complex versions have fitting parameters which cannot be generalised (Pokor et al. (2004), for example). Some interesting work is being carried out on deformation mode mapping, which helps to explain the form of irradiation hardening curves, but these maps require experimental data across a wide range of temperatures and damage levels to build, and are not simply transferrable to different materials (Farrell et al., 2004).

As it stands, there are no previous models which flexibly estimate a range of observed behaviour and are quantitative. Bayesian neural network models are both flexible and quantitative, and also provide a measure of the modelling uncertainty, allowing calculations from far outside the knowledge base to be identified and approached with caution.

Neural network model of irradiation hardening

The construction and details of the Bayesian artificial neural network (ANN) used here is described in Kemp et al. (2006). Previous complicated materials problems where it has been successfully applied include the modelling and optimisation of the Charpy energy and strength of steel weld metals, the yield and ultimate tensile strength of nickel-base superalloys, the behaviour of high-temperature, creep-resistant steels, and properties of polymeric and inorganic compounds and ceramics. A review of these applications is given in Bhadeshia (1999). However, this modelling method has not previously been applied to the mechanical properties of neutron-irradiated steels, although non-Bayesian ANNs have recently been applied (with limited success) to the aging of reactor pressure vessels (Wang and Rao, 2002).

Predictions: Into the fusion regime

Figure 2.2 shows the neural network predictions of σy and corresponding uncertainty estimates over a range of temperatures (300-900 K) and damage levels (0-200 dpa). The regions well outside the training database have uncertainties that are comparable to or larger than σy itself. These uncertainties provide an indication that predictions in these areas should be regarded sceptically, and that experiments in these areas would provide valuable information.

In particular, at the relevant temperatures (750-900 K), data are required for damage levels greater than 100 dpa to reduce the uncertainties for fusion-relevant predictions for these materials. Additionally, of course, fusion-spectrum irradiation experiments are required to validate this model for such irradiation energies. Further validation would come from experiments carried out on the optimised composition below, to compare the performance of this material with the performance of current candidate materials.

Figure: 2.2 Hardening predictions (and modelling uncertainties) for Eurofer97 ((a) and (b)) and F82H ((c) and (d)), as a function of temperature (Tirr=Ttest) and damage level.
(a)Image fig_12a (b)Image fig_12b
(c)Image fig_12c (d)Image fig_12d


Ideally, and certainly in the long run, mechanical property predictions will be based on hierarchical models of microstructural evolution linked to structure property relations in a way that will incorporate the effects of all important variables and their interactions, as well as incorporating all known physics and underlying mechanisms. In the meantime, however, less rigourous techniques are required to produce meaningful quantitative predictions for engineering purposes.

Direct non-linear regression fits to the data using simple phenomenological, but physically motivated models are useful. For example, the fits by Yamamoto et al. (2003) provide a good representation of the existing database. However, such models often contain assumptions that are sometimes hidden or unrecognised. In Yamamoto's case, high-dose saturation is assumed and extrapolated from low-dose trends even in the absence of high-dose data.

While uncertainties in such extrapolations can be estimated, the effects of the various assumptions are not easy to quantify in a useful way. In principle, the neural network approach avoids the need for any assumptions about the form of the fitting equation, and provides error estimates of extrapolations. However, this approach has the corollary disadvantage that it frequently does not allow easy ways to include known physics.

It is clear, however, that the flexibility and power of the neural network modelling approach can be fruitfully applied to the analysis of irradiation damage in steels. It provides a means of making wide-ranging quantitative predictions and provides a warning of when those predictions may not be trustworthy.

For the near future, the use of complementary approaches will be needed, and perhaps their most important contribution will be to highlight the most significant gaps in out knowledge to help guide future experiments.

The model and data presented on this page and instructions for its use can be found through the Materials Algorithm Project (MAP) website.

Of course, when designing a steel there are other concerns than simply the value of one material property. As well as solutions not necessarily taking account of potential metallurgical pitfalls (such as the stabilisation of unwanted phases), the weakness in this optimisation method, as it currently stands, is that it does not permit model inputs to be optimised for multiple targets. That is, a steel can be identified for a given yield stress at a given temperature, but not one that is perhaps less good at a particular temperature but generally better across a range of temperatures. Additionally, it would be advantageous to optimise for a range of material parameters - combining this Δσy model with an embrittlement model, for example. However, it is clear that this modelling method has a lot to contribute towards the engineering of a future fusion power plant.

The need for more data

One of the primary conclusions from this work is that the current database is insufficient to provide the desired refinement of the model that would markedly reduce the uncertainty in predictions of irradiated yield stresses. The construction of an improved database would be helped by future experiments providing sufficient detail of potentially important variables, such as dose rate, irradiation energy spectrum, duration of irradiation, and so forth, and by providing estimates of error in key variables such as irradiation temperature.

Ongoing work includes the addition of heat-treatment information to the database and the retraining of the model to include this data. Further work includes an extension of the genetic algorithm code to include multiple selection criteria, so that this optimisation method can be applied to complex problems where the materials properties across a range of input conditions are of interest.

Irradiation embrittlement

In a real structure, such as a fusion reactor, it must be assumed that sub-critical cracks are present and therefore defect-tolerant structural materials must be used. Embrittlement of structural materials, as a result of exposure to a corrosive environment, the presence of hydrogen, irradiation, etc. is therefore a major concern. This embrittlement is detected in Charpy V-notch tests as an increase in the ductile-to-brittle transition temperature (DBTT) and a decrease in the upper shelf energy (USE) (Figure 3.1) and, in tensile specimens, as a reduction in fracture strain.

At temperatures above the DBTT, failure occurs by ductile tearing and microvoid coalescence in the vicinity of the growing crack tip. Below the DBTT, fast fracture occurs due to unstable propagation of a crack by locally brittle cleavage. In some cases, intergranular fracture can also occur, but is rare in Charpy tests on RAFM steels (Odette et al., 2003).

Figure 3.1: Charpy curves for half-size specimens of 12Cr-1MoVW steel before and after irradiation to 10 and 17 dpa at 365°C in the Fast Flux Test Facility (FFTF) (Klueh and Harris, 2001, p. 140).
Image use_demo

When this effect occurs in response to radiation exposure, it is referred to as irradiation embrittlement. At temperatures below ∼400°C, the dominant mechanism is generally thought to be hardening embrittlement, described below. The persistence of embrittlement to higher temperatures than those at which hardening occurs demonstrates the presence of additional mechanisms (non-hardening embrittlement).

It should be noted that although Charpy impact data are a useful tool for exploring the effects of radiation on fracture behaviour, and serve as a method for rating the relative resistances of different steels to irradiation damage, they cannot be used directly for engineering design purposes as they do not measure the fracture toughness of a material, KIc. Currently, there are very limited fracture toughness data available for RAFM steels. The Charpy test is easier to conduct and the specimens are simpler to miniaturise for use in irradiation experiments - a particular concern for IFMIF, with its limited irradiation volume (Spätig et al., 2005). This miniaturisation is not without its drawbacks, however, as the values obtained for USE and DBTT during such a test cannot easily be compared for different sizes of specimen (Abe and Kayano, 1996). The fusion materials community has generally settled on specimens that are one third the size of the usual Charpy specimens (i.e. they have a cross-section of 3.3 mm by 3.3 mm), but there is, as yet, no definitive agreed standard (Kurishita et al., 2004; Möslang, 2005), and concern has been expressed that sub-size specimens might underestimate the potential of martensitic steels to experience severe irradiation embrittlement (Yamamoto et al., 2003).

Mechanisms of irradiation embrittlement

Hardening embrittlement of a material under irradiation is related to irradiation hardening. Hardening causes an increase in the flow stress of a material. If it is assumed that the fracture stress is only weakly affected by radiation and that the intersection of the fracture stress curve and the flow stress curve defines the ductile-to-brittle transition temperature, a shift in flow stress results in a corresponding shift in DBTT, as shown in Figure 3.2.

Figure 3.2: Schematic diagram illustrating how irradiation hardening results in a change in the ductile-to-brittle transition temperature.
Image flow_vs_fracture

Figure 3.2 also illustrates how the oft-quoted relation ΔDBTT=aΔσy applies, as in this construction the shift in DBTT is directly related to that in the yield stress. However, the parameter a varies widely (from ∼0.33 to ∼0.7) from material to material and is also dependent on irradiation conditions (Yamamoto et al., 2003). As hardening saturates, so does embrittlement (Murakami et al., 2000).

Irradiation damage also has an effect on the strain-hardening exponent, n. A change in n affects the volume of material which can deform ahead of a growing crack tip. To some extent, if the radiation-induced Δn is negative, this can counteract the adverse hardening effect, resulting in a lower ΔDBTT. These effects have been modelled using finite element (FE) approaches and are reasonably well understood. However, irradiation can also result in localisation of flow. Localisation of deformation in slip bands is not well understood, but appears only to play a secondary role in cleavage fracture (Odette et al., 2003).

On a microstructural scale, cleavage occurs by the propagation of microcracks starting in brittle particles (such as carbides) that are exposed to high stresses near the tip of a blunting crack. Much of the time, these microcracks arrest on reaching the tougher ferritic matrix surrounding the particle. Under critical conditions, however, the microcrack can continue into the matrix and combine with other microcracks, allowing the crack to undergo fast, unstable growth (Ritchie et al., 1973).

Microstructural changes in a steel that increase the probability of microcracking, and hence cleavage fracture, include precipitation (e.g. Laves phase) or coarsening of brittle particles (e.g. carbides); segregation of impurity elements known to have an embrittling effect (e.g. P) to grain boundaries and dissolved hydrogen. Non-hardening embrittlement can occur under thermal aging in the absence of irradiation, but irradiation displacement damage can dramatically enhance it. For example, radiation-enhanced diffusion can accelerate segregation of impurities or precipitation of brittle phases.

In addition, the formation of small, high-pressure bubbles of He formed in the material under irradiation is postulated to affect fracture properties. In the worst case, these bubbles accumulate at grain boundaries and cause intergranular fracture and unacceptably large DBTT shifts. However, there is a shortage of experimental data on both helium embrittlement effects in combination with irradiation, and non-hardening irradiation embrittlement generally (Odette et al., 2003).

Previous models

One of the most common treatments of embrittlement is the master curve (MC) approach, which assumes that there is a universal temperature-toughness curve shape (or small family of shapes) characterising cleavage fracture, that can be indexed by a reference temperature (T0) and toughness. Embrittlement can then be regarded as a shifting of this curve with respect to temperature (ΔT0). For irradiation specimens, this shift has been measured and modelled, but the master curve does not represent the data well, with a high degree of scatter (Odette et al., 2004). In addition, T0 and ΔT0 must be experimentally determined for a material - the method does not allow straightforward prediction of the properties of new materials.

This high degree of scatter with respect to empirical models is also noted by Yamamoto et al. (2003). The scatter could be due to experimental noise, or to uncontrolled factors in the models for calculating ΔT0. A description of such a model, based on irradiation hardening, is given by Odette et al. (2002).

Rieth et al. (1998), by contrast, attempted to link embrittlement directly to helium content by correlating boron content to the shift in DBTT during irradiation. This work, although promising, is still in its early stages.

A comprehensive review of irradiation embrittlement mechanisms and multiscale modelling approaches can be found in Odette et al. (2003).

Neural network models of Charpy fracture properties

These models use the Bayesian neural network structure described in Kemp et al. (2006).

Predictions: Into the fusion regime

Figure 3.3 (Eurofer97) and Figure 3.4 (F82H) show the neural network predictions of ΔDBTT and corresponding uncertainty estimates over a range of temperatures (300-900 K) and damage levels (0-200 dpa).

Figure 3.5 (Eurofer97) and Figure 3.6 (F82H) show the neural network predictions of ΔUSE and corresponding uncertainty estimates over the same range of temperatures and damage levels.

Figure 3.3: Model predictions (and modelling uncertainties) for ΔDBTT for Eurofer97 as a function of irradiation temperature and damage level. The contour scales are in Kelvin.
Image eur_fus_pred Image eur_fus_uncert

Figure 3.4: Model predictions (and modelling uncertainties) for ΔDBTT for F82H as a function of irradiation temperature and damage level. The contour scales are in Kelvin.
Image f82h_fus_pred Image f82h_fus_uncert

Figure 3.5: Model predictions (and modelling uncertainties) for ΔUSE for Eurofer97 as a function of irradiation temperature and damage level. The contour scales are in joules.
Image eur_fus_pred Image eur_fus_uncert

Figure 3.6: Model predictions (and modelling uncertainties) for ΔUSE for F82H as a function of irradiation temperature and damage level. The contour scales are in joules.
Image f82h_fus_pred Image f82h_fus_uncerts

The regions well outside the training database have uncertainties of the same order of magnitude, or greater than, the values of the predictions. These uncertainties provide an indication that predictions in these areas should be regarded sceptically, and that experiments in these regions would provide valuable information.

However, for both materials, the models predict a maximum ΔDBTT of around 200 K at irradiation temperatures of 700-800 K, the design operating temperatures of RAFM steels. The prediction of saturation and/or recovery during irradiation at these temperatures is promising, as it offers the possibility of identifying alloy compositions which have a reduced peak ΔDBTT.

The need for more data (redux)

Although it has been stated before, it bears repeating that the available data are sparse and noise levels in the dataset are high. It is important that experimental data are reported as fully as possible. In particular, the conclusion is unavoidable that the extent of radiation damage cannot be characterised by a single parameter. The dpa number, regardless of how well it is computed, is a measure of the number of defects remaining shortly after a cascade has cooled down to ambient temperature, but only a fraction of these contribute to the final macroscopic property changes observed. The effects depend not only on the material, the recoil energy, and the temperature, but also on the property change being considered (hardening, swelling, irradiation creep, embrittlement etc.). Nevertheless, the dpa number remains a useful first tool for correlating results obtained by different particles, energies, and fluxes (Ullmaier and Carsughi, 1995).

Voids and bubbles in irradiated materials

The formation of cavities4.1 in irradiated materials is a long-standing problem. Cavities grow by accumulation of vacancies - created in radiation cascades - and can grow to be hundreds of nanometres across. This results in macroscopic swelling of the material, up to tens of percent (Figure 4.1). The consequences for plant components can be severe. For structural components of a power plant, dimensional changes of less than 1% are tolerable, but still undesirable.

Figure 4.1: Photograph of 20% cold-worked 316 stainless steel rods before (left) and after (right) irradiation at 533°C to a fluence of 1.5×1023 neutrons m-2 in the EBR-11 reactor (Mansur, 1994).
Image swelling

The origin of cavities

It has long been known that the cavities formed under irradiation are not purely helium-supported, at least once they are readily visible. Cawthorne and Fulton (1967) demonstrated that there were too few helium atoms produced by the (n,α) reactions in a fast reactor to fill all the cavities observed to equilibrium pressure. However, although it is possible for voids to form through classical nucleation mechanisms of vacancy accumulation, driven by the supersaturation of vacancies in the material, this cannot account for the numbers of voids observed in irradiated metals (Stoller and Odette, 1987).

It is now generally accepted that cavities are formed when gas bubbles nucleate and slowly grow by accumulation of vacancies and more helium atoms until they become large enough to act independently as microstructural sinks and undergo further growth by vacancy accumulation alone.

During irradiation, any dissolved helium will always be at a huge supersaturation. Under such conditions, the critical radius for nucleation is extremely small (bubbles that would be in equilibrium with anything approaching the supersaturation conditions would be less than one atom across), meaning that the nucleation barrier is very small. In such circumstances, all available nucleation sites would be activated rapidly, leading to site saturation. This justifies a common assumption made in helium bubble studies, that the process simply involves the growth of a fixed number density of bubbles defined by the availability of helium and nucleation sites.

However, it is also true that the number density of nucleation sites will change under irradiation, and this should be incorporated into future models for swelling.

Heterogeneous nucleation sites such as grain boundaries have a lower effective surface energy than homogeneous sites for bubble formation, due to the grain boundary surface already present. However, because the critical bubble size is so small, there is no particular energetic advantage for helium bubble nucleation at such sites, although it may be easier for a bubble to grow on the grain boundary due to an increased helium flux along the boundary (pipe diffusion, Christian (2002, p. 413)). It would be expected that a bubble-depleted zone close to the boundary would emerge, due to reduced vacancy super-saturation.

Creating swelling-resistant steels

Swelling can be restricted in a number of ways:

  1. by decreasing the quantity of helium produced in a material, through avoidance of alloying elements such as boron or nickel, or through shielding to absorb or decrease the energy of incident neutrons and reduce the chance of transmutation
  2. by increasing the microstructural sink density, to reduce the rate at which helium reaches bubbles and to delay the onset of spontaneous nucleation
  3. by increasing the number of potential nucleation sites in a material, to disperse the available helium among more bubbles and therefore decrease the number of helium atoms per bubble.

The first of these requires careful control of impurities during alloy production - a requirement of satisfactory low-activation steels anyway - or unwarranted modification of first-wall design. The second can be accomplished through heat treatments or deformation, or simultaneously with the third through alloying with elements which result in a very fine precipitate dispersion during irradiation. Such a dispersion can also be introduced during steel manufacture by mechanical alloying. This microstructure has the added benefit that helium is held at these precipitates and kept away from grain boundaries, where the formation of cavities can cause high-temperature embrittlement (Schroeder et al., 1985).

Through combinations of these approaches, austenitic Fe-Cr-Ni base alloys, which otherwise exhibit very high swelling, can have swelling delayed to more than 100 dpa and several thousand appm helium (Mansur et al., 1986). It is therefore expected that such modifications would apply equally to ferritic alloys and other candidate fusion reactor materials.

The International Fusion Materials Irradiation Facility

One major outstanding issue in the modelling of irradiation effects, as mentioned above, is the extrapolation of models from the lower-energy and fission-relevant regime - where there is a goodly range of data - to the high-dose, high-energy fusion-relevent regime, where past experience suggests that there is a good chance of encountering surprises not predicted by existing theories. Experiments in ITER will provide much valuable information, but will be limited in terms of maximum damage and helium levels achieved (up to 5 dpa and 70 appm respectively), as well as suffering from operational constraints such as variable irradiation temperatures (Barabash, 2004). IFMIF, if and when built, will provide suitable experimental facilities for testing the predictions of mechanistic models on candidate power plant materials by simulating a stable, sustained fusion irradiation spectrum (Möslang et al., 1998). The design for IFMIF consists of two 40 MeV deuteron linear accelerators, focused on a molten lithium target, producing high-energy neutrons (Jameson et al., 2004). IFMIF is intended to carry out materials experiments concurrently with the operation of ITER, providing a high-quality database to assist the engineering of a commercial fusion power reactor.

However, the available experimental volume in the high-flux region in IFMIF is ∼0.5 litres, and the highest-damage (≥150 dpa) experiments will last 5 years or more, meaning that experiments must be carefully chosen to make best use of this space. Considerable progress has been made in developing sub-size experimental specimens for this purpose, and the reliability of small specimens for evaluating the properties of RAFM steels has been established (Möslang, 2005). This is, however, a mixed blessing as in some cases (for example, Charpy ductile to brittle transition temperature measurements) the specimen size has a significant effect on experimental results and hence these results cannot easily be compared with existing full-size data.

The choice of candidate experimental materials and irradiation regimes must be carefully optimised to maximise the useful information gained from IFMIF experiments.

Further information

Fusion research at UKAEA Culham - Home of the JET experimental reactor
IFMIF - The International Fusion Materials Irradiation Facility
ITER - The International Thermonuclear Experimental Reactor
Neural-Network Analysis of Irradiation Hardening in Low-Activation Steels - Journal of Nuclear Materials 348 (2006) 311-328
Design of new Fe-9CrWV reduced-activation martensitic steels for creep properties at 650°C
Practical Mechanically Alloyed ODS Iron-base and Nickel-base Alloys
Materials Algorithm Project (MAP) website


F Abe and H Kayano.
Effect of specimen size on ductile to brittle transition behaviour of martensitic 9Cr steels after various heat treatments.
Journal of Nuclear Materials, 232: 44 - 51, 1996.

F Abe, Noda Tetsuji, Araki Hiroshi, and Okada Masatoshi.
Development of reduced-activation martensitic 9Cr steels for fusion reactor.
Journal of Nuclear Science And Technology, 4 (31): 279 - 292, 1994.

A Alamo, V Lambard, X Averty, and M H Mathon.
Assessment of ODS-14%Cr ferritic alloy for high temperature applications.
Journal of Nuclear Materials, 329 - 333: 333 - 337, 2004.

D J Bacon, F Gao, and Yu N Osetsky.
The primary damage state in fcc, bcc and hcp metals as seen in molecular dynamics simulations.
Journal of Nuclear Materials, 276: 1 - 12, 2000.

V Barabash.
Role and contribution of ITER in research of materials and reactor components.
Journal of Nuclear Materials, 329 - 333: 156 - 160, 2004.

A L Bement.
Fundamental materials problems in nuclear reactors.
In 2nd International Conference on the Strength of Metals and Alloys, volume 2, pages 693 - 728, 1970.

H K D H Bhadeshia.
Neural networks in materials science.
ISIJ International, 39 (10): 966 - 979, 1999.

E E Bloom.
The challenge of developing structural materials for fusion power systems.
Journal of Nuclear Materials, 258 - 263: 7 - 17, 1998.

E E Bloom, S J Zinkle, and F W Wiffen.
Materials to deliver the promise of fusion power - progress and challenges.
Journal of Nuclear Materials, 329 - 333: 12 - 19, 2004.

L V Boccaccini, L Giancarli, G Janeschitz, S Hermsmeyer, Y Poitevin, A Cardella, and E Diegele.
Materials and design of the European DEMO blankets.
Journal of Nuclear Materials, 329 - 333: 148 - 155, 2004.

H Bolt, V Barabash, G Federici, J Linke, A Loarte, J Roth, and K Sato.
Plasma facing and high heat flux materials - needs for ITER and beyond.
Journal of Nuclear Materials, 307 - 311: 43 - 52, 2002.

A D Brailsford.
Vacancy dislocation loop microstructure formed during heavy-particle bombardment.
Journal of Nuclear Materials, 84: 245 - 268, 1979.

R Bullough and T M Quigley.
Dislocation sink strengths for the rate theory of irradiation damage.
Journal of Nuclear Materials, 103 - 104: 1397 - 1402, 1981.

G J Butterworth and L Giancarli.
Some radiological limitations on the compositions of low-activation materials for power reactors.
Journal of Nuclear Materials, 155 - 157: 575 - 580, 1988.

T S Byun and K Farrell.
Irradiation hardening behavior of polycrystalline metals after low temperature irradiation.
Journal of Nuclear Materials, 326: 86 - 96, 2004.

M J Caturla, N Soneda, E Alonso, B D Wirth, T Díaz de la Rubia, and J M Perlado.
Comparative study of radiation damage accumulation in Cu and Fe.
Journal of Nuclear Materials, 276: 13 - 21, 2000.

C Cawthorne and E J Fulton.
Voids in irradiated stainless steel.
Nature, 216: 575 - 576, 1967.

R Chaouadi and R Gérard.
Copper precipitate hardening of irradiated RPV materials and implications on the superposition law and re-irradiation kinetics.
Journal of Nuclear Materials, 345: 65 - 74, 2005.

J M Chen, T Muroga, S Y Qiu, T Nagasaka, W G Huang, M J Tu, Y Chen, Y Xu, and Z Y Xu.
The development of advanced vanadium alloys for fusion applications.
Journal of Nuclear Materials, 329 - 333: 401 - 405, 2004.

H S Cho, A Kimura, S Ukai, and M Fujiwara.
Corrosion properties of oxide dispersion strengthened steels in super-critical water environment.
Journal of Nuclear Materials, 329 - 333: 387 - 391, 2004.

J W Christian.
The theory of transformations in metals and alloys: Part I.
Pergamon, 3 edition, 2002.

C W Corti, P Cotterill, and G A Fitzpatrick.
The evaluation of the interparticle spacing in dispersion alloys.
International Metallurgical Reviews, 19: 77, 1974.

A Cottrell.
Annealing a nuclear reactor: an adventure in solid-state engineering.
Journal of Nuclear Materials, 100: 64 - 66, 1981.

K Ehrlich, E E Bloom, and T Kondo.
International strategy for fusion materials development.
Journal of Nuclear Materials, 283 - 287: 79 - 88, 2000.

K Farrell, T S Byun, and N Hashimoto.
Deformation mode maps for tensile deformation of neutron-irradiated structural alloys.
Journal of Nuclear Materials, 335: 471 - 486, 2004.

R A Forrest.
The European Activation System: EASY-2001 overview.
Technical report, UKAEA, 2001.

F A Garner, M B Toloczko, and B H Sencer.
Comparison of swelling and irradiation creep behaviour of FCC-austenitic and BCC-ferritic/martensitic alloys at high neutron exposure.
Journal of Nuclear Materials, 276: 123 - 142, 2000.

N M Ghoniem.
Theory of microstructure evolution under fusion neutron irradiation.
Journal of Nuclear Materials, 179 - 181: 99 - 104, 1991.

John Price Hirth and Jens Lothe.
Theory Of Dislocations.
John Wiley & Sons, 2 edition, 1982.

R A Jameson, R Ferdinand, H Klien, J Rathke, J Sredniawski, and M Sugimoto.
IFMIF accelerator facility.
Journal of Nuclear Materials, 329 - 333: 193 - 197, 2004.

S Jitsukawa, A Kimura, A Kohyama, R L Klueh, A A Tavassoli, B van der Schaaf, G R Odette, J W Rensman, M Victoria, and C Petersen.
Recent results of the reduced activation ferritic/martensitic steel development.
Journal of Nuclear Materials, 329 - 333: 39 - 46, 2004.

R Kemp, G A Cottrell, H K D H Bhadeshia, G R Odette, T Yamamoto, and H Kishimoto.
Neural-network analysis of irradiation hardening in low-activation steels.
Journal of Nuclear Materials, 348: 311 - 328, 2006.

R L Klueh and D R Harris.
High-Cr ferritic and martensitic steels for nuclear applications.
ASTM, 2001.

R L Klueh and J M Vitek.
Postirradiation tensile behavior of nickel-doped ferritic steels.
Journal of Nuclear Materials, 150: 272 - 280, 1987.

R L Klueh, E T Cheng, M L Grossbeck, and E E Bloom.
Impurity effects on reduced-activation ferritic steels developed for fusion applications.
Journal of Nuclear Materials, 280: 353 - 359, 2000.

S Konishi.
Discussion on fast track and impact on materials R&D strategy - fusion material issues for the energy systems in future.
Journal of Nuclear Materials, 329 - 333: 161 - 165, 2004.

H Kurishita, T Yamamoto, M Harui, H Suwarno, T Yoshitake, Y Yano, M Yamazaki, and H Matsui.
Specimen size effects on ductile-brittle transition temperature in Charpy impact testing.
Journal of Nuclear Materials, 329 - 333: 1107 - 1112, 2004.

R J Kurtz, K Abe, V M Chernov, D T Hoelzer, H Matsui, T Muroga, and G R Odette.
Recent progress on development of vanadium alloys for fusion.
Journal of Nuclear Materials, 329 - 333: 47 - 55, 2004.

P Lako, J R Ybema, and A J Seebregts.
The long term potential of fusion power in Western Europe.
Technical Report ECN-C-98-071, ECN Petten, December 1998.

S Majumdar and P Smith.
Treatment of irradiation effects in structural design criteria for fusion reactors.
Fusion Engineering and Design, 41: 25 - 30, 1998.

M J Makin and F J Minter.
Irradiation hardening in copper and nickel.
Acta Metallurgica, 8: 691 - 699, 1960.

L K Mansur.
Mechanisms and kinetics of radiation effects in metals and alloys.
In G R Freeman, editor, Kinetics of Nonhomogeneous Processes, pages 377 - 463. John Wiley & Sons, 1987.

L K Mansur.
Theory and experimental background on dimensional changes in irradiated alloys.
Journal of Nuclear Materials, 216: 97 - 123, 1994.

L K Mansur and K Farrell.
Mechanisms of radiation-induced degradation of reactor vessel materials.
Journal of Nuclear Materials, 244: 212 - 218, 1997.

L K Mansur, E H Lee, P J Maziasz, and A P Rowcliffe.
Control of helium effects in irradiated materials based on theory and experiment.
Journal of Nuclear Materials, 141 - 143: 633 - 646, 1986.

J W Martin.
Micromechanisms in particle-hardened alloys.
Cambridge Solid State Science Series. Cambridge University Press, Cambridge, 1 edition, 1980.

M K Miller, D T Hoelzer, E A Kenik, and K F Russell.
Nanometer scale precipitation in ferritic MA/ODS alloy MA957.
Journal of Nuclear Materials, 329 - 333: 338 - 341, 2004.

A Möslang.
Development of IFMIF test matrix.
Technical report, Institut für Materialforschung, 2005.

A Möslang, C Antonnucci, E Daum, J R Haines, I Jitsukawa, K Noda, and S Zinkle.
Overview of the IFMIF test facility.
Journal of Nuclear Materials, 258 - 263: 427 - 432, 1998.

S Murakami, A Miyazaki, and M Mizuno.
Modeling of irradiation embrittlement of reactor pressure vessel steels.
Journal of Engineering Materials and Technology, 122 (1): 60 - 66, 2000.

G R Odette, H J Rathbun, J W Rensman, and F P van den Broek.
On the transition toughness of two RA martensitic steels in the irradiation hardening regime: a mechanism-based evaluation.
Journal of Nuclear Materials, 307 - 311: 1011 - 1015, 2002.

G R Odette, T Yamamoto, H J Rathbun, M Y He, M L Hribernik, and J W Rensman.
Cleavage fracture and irradiation embrittlement of fusion reactor alloys: mechanisms, multiscale models, toughness measurements and implications to structural integrity assessment.
Journal of Nuclear Materials, 323: 313 - 340, 2003.

G R Odette, T Yamamoto, H Kishimoto, M Sokolov, P Spätig, W J Yang, J W Rensman, and G E Lucas.
A master curve analysis of F82H using statistical and constraint loss size adjustments of small specimen data.
Journal of Nuclear Materials, 329 - 333: 1243 - 1247, 2004.

C Pokor, Y Brechet, P Dubuisson, J P Massoud, and A Barbu.
Irradiation damage in 304 and 316 stainless steels: experimental investigation and modeling. Part I: Evolution of the microstructure.
Journal of Nuclear Materials, 326: 19- 29, 2004.

B Riccardi, L Giancarli, A Hasegawa, Y Katoh, A Kohyama, R H Jones, and L L Snead.
Issues and advances in SiCf /SiC composites development for fusion reactors.
Journal of Nuclear Materials, 329 - 333: 56 - 65, 2004.

M Rieth, B Dafferner, and H D Röhrig.
Embrittlement behaviour of different international low activation alloys after neutron irradiation.
Journal of Nuclear Materials, 258 - 263: 1147 - 1152, 1998.

R O Ritchie, J F Knott, and J R Rice.
On the relationship between critical tensile stress and fracture toughness in mild steel.
Journal of the Mechanics and Physics of Solids, 21 (6): 395 - 410, 1973.

R O Scattergood and D J Bacon.
The strengthening effect of voids.
Acta Metallurgica, 30: 1665 - 1677, 1982.

H Schroeder, W Kesternich, and H Ullmaier.
Helium effects on the creep and fatigue resistance of austenitic stainless steels at high temperatures.
Nuclear Engineering and Design/Fusion, 2: 65 - 95, 1985.

D N Seidman, M I Current, D Pramanik, and C Y Wei.
Direct observation of the primary state of radiation damage of ion-irradiated tungsten and platinum.
Nuclear instruments and methods, 182 - 183: 477 - 481, 1981.

A A Semenov and C H Woo.
Applicability of the conventional master equation for the description of microstructure evolution under cascade-producing irradiation.
Applied Physics A, 69 (4): 445 - 451, 1999.

A A Semenov and C H Woo.
Classical nucleation theory of microstructure development under cascade-damage irradiation.
Journal of Nuclear Materials, 323 (2 - 3): 192 - 204, 2003.

K Shiba, M Enoeda, and S Jitsukawa.
Reduced activation martensitic steels as a structural material for ITER test blanket.
Journal of Nuclear Materials, 329 - 333: 243 - 247, 2004.

D L Smith, R F Mattas, and M C Billone.
Fusion reactor materials.
In B R T Frost, editor, Materials science and technology, a comprehensive treatment, Volume 10B, Nuclear materials part II, volume 10B, pages 243 - 340. Wiley-VCH, 1994.

P Spätig, E N Campitelli, R Bonadé, and N Baluc.
Assessment of plastic flow and fracture properties with small specimen test techniques for IFMIF-designed specimens.
Nuclear Fusion, 45: 635 - 641, 2005.

R E Stoller.
Modeling the influence of irradiation temperature and displacement rate on radiation-induced hardening in ferritic steels.
Technical Report NUREG/CR-5859 and ORNL/TM-12073, Oak Ridge National Laboratory, July 1992.

R E Stoller and G R Odette.
A comparison of the relative importance of helium and vacancy accumulation in void nucleation.
In 13th International Symposium on Radiation-Induced Changes in Microstructure, ASTM-STP 955, pages 358 - 370, 1987.

G I Taylor.
Plastic strain in metals.
Journal of the Institute of Metals, 62: 307 - 324, 1938.

R Toschi, P Barabaschi, D Campbell, F Elio, D Maisonnier, and D Ward.
How far is a fusion power reactor from an experimental reactor?
Fusion Engineering and Design, 56 - 57: 163 - 172, 2001.

H Ullmaier and F Carsughi.
Radiation damage problems in high power spallation neutron sources.
Nuclear Instruments and Methods in Physics Research B, 101: 406 - 421, 1995.

H Ullmaier and H Trinkaus.
Radiation damage in metallic structural materials.
In Physical Processes of the Interaction of Fusion Plasmas with Solids. Academic Press, Inc., 1996.

B van der Schaaf, D S Gelles, S Jitsukawa, A Kimura, R L Klueh, A Möslang, and G R Odette.
Progress and critical issues of reduced activation ferritic/martensitic steel development.
Journal of Nuclear Materials, 283 - 287: 52 - 59, 2000.

J A Wang and N S Rao.
A new technique for the prediction of non-linear behaviour.
Journal of Nuclear Materials, 301: 193 - 202, 2002.

C Y Wei, M I Current, and D N Seidman.
Direct observation of the primary state of damage of ion-irradiated tungsten I: Three-dimensional spatial distribution of vacancies.
Philosophical magazine A, 44 (2): 459 - 491, 1981.

T Yamamoto, G R Odette, H Kishimoto, and J W Rensman.
Compilation and preliminary analysis of a irradiation hardening and embrittlement database for 8Cr martensitic steels.
Technical Report DOE/ER-0313/35, ORNL, 2003.


The creation of this document was supported by the Higher Education Funding Council for England, via the U.K. Centre for Materials Education, and by the EPSRC and EURATOM/UKAEA.

May 11th 2006


... atom1.1
That is, each atom will, on average, be displaced from its lattice position 200 times during service. Details of how this figure is calculated can be found in Mansur (1987), starting on page 399.

... 2 wt%2.1
Precisely because nickel produces helium under neutron irradiation, the concentration of Ni is kept as low as possible in candidate fusion steels. Boron occurs as an impurity in RAFM steels (or is also deliberately added to investigate helium effects) and its concentration must be controlled.

... cavities4.1
In this section, I have tried to consistently use cavity to denote any hollow inclusion in a material, bubble to denote a cavity which is primarily stabilised by internal gas pressure, and void to denote a cavity which is not gas-stabilised ( $ P\ll\frac{2\gamma}{r}$). Only radiation-induced cavities are of interest here.

Superalloys Titanium Bainite Martensite Widmanstätten ferrite
Cast iron Welding Allotriomorphic ferrite Movies Slides
Neural Networks Creep Mechanicallly Alloyed Theses

PT Group Home Materials Algorithms Any Valid CSS!