Analysis of irradiation creep and the structural integrity of fusion in-vessel components

Fusion Engineering and Design 48 (2000) 527 – 537 www.elsevier.com/locate/fusengdes

Analysis of irradiation creep and the structural integrity of fusion in-vessel components Panayiotis J. Karditsas * UKAEA 1 Fusion, Culham Science Centre, Abingdon, Oxfordshire OX14 3DB, UK

Abstract This paper presents a brief review of the irradiation creep mechanism, analyses of the effect on the performance and behaviour of fusion in-vessel components, and discusses procedures for the estimation of in-service time (or lifetime) of components under combined creep–fatigue. The irradiation creep models and proposed theories are examined and analysed to produce a creep law relevant to fusion conditions. The necessary material data, constitutive equations and other parameters needed for estimation of in-service time from the combination of creep and fatigue damage are identified. Wherever possible, design curves are proposed for stress and strain. Time dependent non-linear elastoplastic example calculations are performed, for a typical first wall structure under power plant loading conditions, assuming austenitic and martensitic steel as structural materials, including material irradiation creep. The results of calculations for the stress and strain history of the first wall are used together with the proposed cumulative damage expressions derived in this study to estimate the in-service time, including the effects of stress relaxation due to creep, reduction of ductility (or fracture strain) and helium-to-displacement-damage ratio. The calculations give a displacement damage of  70 dpa for the 316 austenitic steel and 110 – 130 dpa for the martensitic steel. Provided there are no power transients, for a design strain of 0.5%, the in-service time is estimated to be  3 years for the 316 steel case (at 2.2 MW/m2 wall load) and the high wall loading martensitic steel (5.0 MW/m2 case), and  5.3 years for the martensitic steel at lower wall load (2.2 MW/m2 case). The difficulty in defending these results lies in the uncertainty arising from the limited database and experience of the material properties, especially the creep constitutive law, when exposed to fusion environments. © 2000 Elsevier Science S.A. All rights reserved. Keywords: Irradiation creep; Fusion in-vessel components; Fatigue

1. Introduction

* Tel.: +44-1235-464277; fax: +44-1235-463435. E-mail address: [email protected] (P.J. Karditsas). 1 UKAEA/Euratom Fusion Association.

This study presents the irradiation creep mechanism and its effects on the performance and behaviour of a typical first wall section. Example calculations are given for typical power plant first wall relevant conditions, and a section of a first wall is used for calculations to produce the stress and strain histories of the component.

0920-3796/00/$ - see front matter © 2000 Elsevier Science S.A. All rights reserved. PII: S 0 9 2 0 - 3 7 9 6 ( 0 0 ) 0 0 1 7 1 - X

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In general, there are two parameters that are important and control the behaviour of material under irradiation conditions: the displacement damage rate and the production rate of transmutant helium. The ratio of helium production rate to damage rate plays a significant role in the microstructural behaviour of the materials under irradiation. In a typical fast fission neutron spectrum, this ratio is around 0.35 appm/dpa but for fusion spectra is expected to be in the range 1–20 appm/dpa across the first wall and blanket of the machine, with the highest values observed in the first wall. This fact has a direct impact on the material ductility. The irradiation creep models and proposed theories are examined and analysed to produce a creep law relevant to fusion conditions. Procedures are set up to examine the behaviour of structures including irradiation creep. The necessary material data, constitutive equations and other parameters needed for a complete and accurate calculation of in-vessel component behaviour, and estimation of in-service time from the combination of creep and fatigue damage, are identified. Wherever possible, design curves are proposed for stress and strain, including the effects of irradiation creep and helium-to-displacement-damage ratio, pending the necessary experimental measurements to obtain relevant data for the proposed materials in a fusion environment. Time dependent non-linear elastoplastic analyses are performed, for a typical first wall structure, assuming austenitic and martensitic steel as structural materials, using temperature dependent properties and including material irradiation creep. The analysis assumes water cooling to limit first wall temperatures below 350 – 400°C, thus resulting in negligible creep enhancement due to swelling. The effects of stress relaxation due to creep, reduction of ductility (or fracture strain) and helium-to-displacement-damage ratio, on component performance are also included. The results of calculations for the stress and strain history of the first wall are used together with the proposed cumulative damage expressions derived in this study to estimate the component in-service time.

2. Irradiation creep Irradiation creep has been extensively studied by the fission industry for various types of materials used in fission power plants, but data and experience gathered over the years refers mainly to the class 316 austenitic stainless steels and lately to ferritic-martensitic stainless steels and vanadium alloys. The focus of much of the experimental work has been the study of the microstructural evolution in the materials and the nucleation and growth of voids leading to swelling [1–13]. The majority of these experiments and the data gathered for the austenitic stainless steels are from fast fission reactors; there are no data that are fusion specific although some attempts have been made to simulate the fusion environment [14,15], and then draw conclusions about the material behaviour. The ratio of helium production rate to damage rate R= GHe/Gdpa is an important parameter for materials under irradiation. Other important parameters are the local stress and the neutron spectrum. The damage and helium production response functions are used in conjunction with the neutron spectrum to produce the damage rate Gdpa, in dpa per second (dpa/s) and helium production rate GHe, in atom parts per million per second (appm/s), for the material. Irradiation creep strain oc can in general be expressed in terms of the dose D, temperature T and the local stress s in the structure [16], as follows: doc = B(D,T)s n (1) dD with B the instantaneous creep coefficient which is a function of the dose and temperature and n an exponent which from experimental evidence [1,2,4–6,14,15], assumes a value around n:1. The instantaneous creep coefficient B is assumed to comprise the zero damage rate (and swelling rate) creep compliance B0 which has been shown to be a constant for a particular set of alloys, and a swelling part which is temperature- and dose-dependent [4,5,13,15]. The swelling-enhanced creep coefficient C0 is shown to be relatively constant over a wide range of steels and temperatures. The expression for B is as follows:

P.J. Karditsas / Fusion Engineering and Design 48 (2000) 527–537

B(D,T)= B0 +C0

dSv(D,T) dD

(2)

with Sv(D, T) the material swelling and dSv/dD the swelling rate. This form of the creep coefficient was necessary in order to explain the enhancement of creep at the onset of swelling in the material. Using Eqs. (1) and (2) the irradiation creep strain can be expressed as follows: oc = [B0D + C0Sv(D, T)s

(3)

The dose D can be expressed in terms of the damage rate Gdpa (dpa/s) as follows: D =Gdpat

(4)

with t (s) the time. For negligible swelling and/ or swelling rate the irradiation creep strain law and instantaneous creep coefficient are given by the following expressions: (5)

oc = (B0Gdpa)st

(6)

!

B(D, T)=B0

C

Experimental evidence and observations of the microstructure in stainless steels allowed for the establishment of an accepted sequence of events and the formation of a model: in a neutron flux, tiny cavities (assumed to be helium bubbles) found on dislocations and precipitate sites are formed first, and then grow slowly. Cavity density increases with helium concentration and above a critical size there is a transition, and a fraction of the bubble population converts to voids which subsequently grow without the need for any additional helium. In general the critical size increases with increasing temperature and decreasing displacement damage rate and a population of small cavities can persist up to high doses with little change in size and density. Void swelling in steels is characterised by: 1. an incubation period with significant microstructural and microchemical evolution. This period is postulated to be the time required for the helium bubbles to grow sufficiently to undergo the transition to voids.

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2. a steady-state swelling period characterised by rapid void growth coupled with a tendency for saturation of a number of micro-processes. The observed high steady-state swelling rates suggest that structural lifetimes win be governed by the incubation period which is sensitive to the micro-processes and the environmental and material variables. Theoretical and semi-empirical analysis and data suggest that the material ductility in a fusion neutron spectrum would be a function of several variables: of = function{D, T, s, (He/dpa)}

(7)

A semi-empirical model, based on microstructural behaviour, is proposed in [5–12,15,17], including an expression that links ductility to the creep law constants, stress and helium to displacement damage ratio. The proposed model assumes that stress activates the growth of a fraction of grain boundary bubbles which contain helium in excess of a critical number; therefore when the bubble cavity density exceeds normal values, embrittlement occurs. The resulting expression for fracture strain (ductility) of is as follows [17]: I B(D,T) of = (8) s R with the constant for austenitic steels I: 1500 MPa − 3/2 dpa − 1/2, when data from fission spectra and measurements are used. Presently there is no comparable formulation for martensitic steels or other alloys. In general, these models show that high stress and low helium environments, as in fission, are less sensitive to helium ernbrittlement than low stress and high helium, as in fusion environments. More experimental data and analysis of the microstructural behaviour of candidate materials are needed in order to characterise behaviour in a fusion environment. For creep, the material ductility and appropriate strain limits, under fusion neutron spectrum irradiation conditions, are yet to be determined.

2.1. Design cur6es and component in-ser6ice time (lifetime) The accurate prediction of lifetime and pre-

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vention of component failure is usually based on well-defined procedures and requires the use of well established design curves for the structural material. The existing design codes [18 – 20] cover component operation at low and elevated temperatures, and guard against creep-fatigue effects at high temperatures and against time independent failure modes at low temperatures. They do not directly address irradiation effects unless the dose is less than 1 dpa during the life of the component. Until the necessary experimental measurements are conducted to obtain relevant data for the proposed materials to be used in the construction of in-vessel components, the expressions developed here for creep strain (Eqs. 3, 6) and the expression for ductility (Eq. (8)), can be used as a guide to produce relevant design curves and failure criteria needed for the design of components. Setting the creep strain oc equal to the fracture/design strain of in Eq. (3), results in an expression for the stress-to-failure or stress to reach the design strain, dependent on the creep coefficient B and damage rate Gdpa, as follows: s=

of B0D +C0Sv

(9)

Similarly, using Eq. (8) for the creep strain in Eq. (3), an expression is derived for the stress-tofailure/design strain variation with time, including the effect of helium to damage ratio R and the creep coefficient B, as follows: s=



n

B (B D

R 0 +C0Sv) 1

1/2

(10)

This model provides the basis for estimating the stress-to-failure/design strain curves for the material including effects of helium production and damage rate and considering the specific form of the creep law. It can equally be applied to other than austenitic stainless steel structural materials used in fusion environments, provided the creep coefficient and calibration constant are taken from appropriate data. Serni-empirical expressions and data for the creep coefficients for the austenitic 316 and martensitic stainless steels can be found in [1,21– 24]. The data are based on fast reactor measure-

ments and experiments in the US Fast Flux Test Facility (FFIT). For the austenitic steel, calculations show that for a wall load of 2.2 MW/m2, temperatures up to 350°C and doses to  40 dpa, swelling and swelling rate effects are within  10% of the no swelling values. The effects are increasingly pronounced as the temperature exceeds 450°C or the dose exceeds 40 dpa. The values of the creep parameters are as follows: B0 = 1.0× 10 − 6, Gdpa = 7.08× 10 − 7, R =16.6 for [T5 400°C, D5 40 dpa]

(11)

Using these values in Eq. (6), the irradiation creep strain constitutive equation for austenitic 316 stainless steel, is as follows: oc = 7.08× 10 − 13st for [T5 400°C, D5 40 dpa] (12) with the stress s in MPa and the time t in s. The coefficient C= 7.08× 10 − 13 (MPa s) − 1. This damage rate results in 22.3 dpa/year for this material. Using Eq. (12), and assuming fracture/design strains of 1% and 0.5%, the stress–time design curve can be obtained, and is shown in Fig. 1. Also, shown are the stress–time curves based on a stress dependent fracture/design strain (Eq. (8)), and the ASME design code limit for stress-to-rupture (thermal-creep related, the flat part of the curve). The results indicate that the ductility based design curve is quite restrictive as compared to the curves derived assuming a constant upper limit for the fracture/design strain. Fig. 2 shows the variation of the fracture/design strain with stress, together with the material bilinear law stress–strain diagram at 350°C. Combination of the curves indicates a fracture/design strain of  0.0028 at a stress level of 130 MPa. For the martensitic steel, calculations show that for a wall load of 2.2 MW/m2, temperatures up to 450°C and doses to  50 dpa, swelling and swelling rate effects are negligible, but swelling

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rapidly increases as the dose exceeds 50 dpa. The values of the various creep parameters are as follows: B0 =5× 10 − 7, Gdpa =6.6 ×10 − 7 for [T 5 450°C, D 550 dpa]

(13)

Using these values in Eq. (6), the irradiation creep strain constitutive equation for martensitic stainless steel, is as follows: oc = 3.30× 10 − 13st for T 5 450°C, D 550 dpa (14) with the stress s in MPa and the time t in s. The

Fig. 3. Martensitic steel (9%Cr) proposed stress to failure/design strain curves including the effects of irradiation creep.

Fig. 1. Austenitic 316 steel proposed stress to failure/design strain curves including the effects of irradiation creep.

coefficient C= 3.30×10 − 13 (MPa s) − 1. This damage rate results in 20.8 dpa/year for this material. Again, assuming fracture/design strains of 1 and 0.5%, the stress–time design curve can be obtained, and is shown in Fig. 3. A general statement that can be made about the proposed design curves is that the irradiation creep limit is more restrictive than the thermal creep for the material or component exposed to the fusion environment.

2.2. Combined creep–fatigue Under irradiation and time varying loading conditions the effects of fatigue and creep damage must be superimposed. For cumulative loading conditions the following summation rule used in the design codes [25] must be satisfied for no failure: dt n + % 5w events tr all eventsNf

Á Ã Í Ã Ä

all

D creep

Fig. 2. Semi-empirical theory for the variation of austenitic steel (316) ductility with stress for temperatures less than 350°C.

(15)

Á Ã Í Ã Ä

%

D=

D fatigue

with dt the time and n the number of cycles spend at a given stress level, D the total damage, tr the time to reach the design strain or component to fail at a given stress level and Nf the number of cycles to failure at a given stress level. The theoretical value of the constant is w =1, but experimental data suggest lower values. Data specific to fusion

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operating environments are needed to determine the range of the constant w to be used with Eq. (15). The creep damage term Dcreep can be written in integral form when time dependent stress analysis is performed, where a continuous curve (function) is obtained for the stress and strain distribution in the component. Modern finite element analysis computer codes allow the use of creep constitutive equations in the calculation of the stress and strain distribution in the component. Such a capability allows the analyst to avoid the use of the complicated procedures in presently existing design codes to account for the observed stress relaxation and enhanced strain effects. The procedure for calculating the creep damage ratio requires the value of time to failure tr at the applied stress level from the stress-to-failure /design strain design curve. Therefore, the creep cumulative damage Dcreep is given by the following expression: Dcreep =

&

dt tr

(16)

The design curves developed in Section 2.1 can be used to determine the cumulative damage due to creep in the summation rule (Eqs. (15) and (16)), provided the stress variation with time in the component is known. If the stress and frac-

Fig. 4. Schematic of the water-cooled first wall used for thermal – structural calculations.

ture/design strain are assumed to remain constant in time (i.e. no stress relaxation or fracture strain dependence on stress), and the creep enhancement due to swelling is negligible (i.e. B: B0), the following expression is developed for the creep cumulative damage: Dcreep =





B0Gdpa s0tdesign of

(17)

which can be used to evaluate the in-service time tdesign of the component, setting Dcreep = 1. Similar expressions can be derived if instead of Eq. (9), where the fracture/design strain is assumed to be a constant, Eq. (10) is utilised, with the fracture/design strain assumed to vary with stress.

3. Results and discussion Thermal and structural analysis is performed on a typical first wall section for power plant relevant conditions, to determine the behaviour when irradiation creep is included in the finite element structural analysis. The time dependent non-linear analysis, using temperature dependent material properties, was performed with the finite element analysis (FEA) code COSMOS/M [25]. This type of analysis is computationally more complex, since it requires knowledge of the stress–strain and hardening/softening behaviour of the material as well as of the creep law. It does not though require application of any correction factors or fixes (as in presently existing codes). The time histories for stress and strain can be directly entered into the design curves to determine component failure and in-service time. Modem finite element codes have the capability to perform such analysis with the difficulty lying in obtaining the proper material data and constitutive laws to be used for the calculations. A schematic of the geometry, with loading conditions and dimensions, implemented in the thermal and structural calculations is shown in Fig. 4. The full power conditions for the heating loads are given in Table 1. Plane strain conditions are assumed with no bending in the out of plane direction. Section AA movement (translation or rotation) is restricted, and section BB is a symme-

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Table 1 Damage rates, cooling channel thermal hydraulic data and heating loads

Wall load (MW/m2) Surface heat flux (MW/m2) Coolant pressure (MPa) Coolant temperature (C) Heat transfer coefficient (W/m2 K) Flow velocity (m/s) Surface heat flux (MW/m2) Volumetric heat flux (MW/m3) Damage rate (dpa/s) Displacement damage (dpa/year) Creep coefficient C (s−1 MPa−1) Time to reach 50 dpa (h)

2.2 0.4 15.0 300.0 32 540.0 5.0 0.4 – – – – –

316 stainless steel

Martensitic steel

– – – – – – – 31.8 7.08×10−7 22.3 7.08×10−13 19 617

– – – – – – – 28.0 6.60×10−7 20.8 3.3×10−13 21 043

Table 2 Thermal and structural properties of 9%Cr martensitic steel Temperature (°C) 20 100 200 300 400 500 600

a (106) m/m K

E (GPa)

r (kg/m3)

C (J/kg K)

k (W/m K)

S0.2% (MPa)

10.4 11.1 11.9 12.4 13.0 13.6 13.8

206.0 201.0 194.0 188.0 181.5 175.0 151.0

7730 7710 7680 7650 7610 7580 7540

448.85 484.11 523.04 526.69 609.96 671.75 754.96

25.9 27.0 28.1 28.8 29.2 29.0 28.5

551.08 516.23 499.05 489.73 465.32 402.86 279.38

Table 3 Thermal and structural properties of 316 stainless steel Temperature (°C) 20 100 200 300 400 500 600

a (106) m/m K

E (GPa)

r (kg/m3)

C (J/kg K)

k (W/m K)

S0.2% (MPa)

16.2 16.6 17.1 17.5 17.8 18.1 18.4

192.0 186.0 178.0 170.0 161.0 153.0 145.0

7900

469.3 485.2 505.1 530.0 544.9 564.8 584.6

14.6 15.7 17.1 18.6 20.0 21.4 23.3

206.8 178.7 144.2 127.1 116.3 108.5 102.6

try plane. The zero thermal stress temperature is taken to be the coolant temperature and is Tref = 300°C. The unirradiated thermal and structural properties of the 9%Cr – martensitic and the 316LN-austenitic stainless steels [20,26] used in the calculations are given in Tables 2 and 3. The thermal analysis shows the maximum temperature occurring in the area between the cooling

channels and facing the plasma (at the edge of section CC). The temperatures attained by the 316 stainless steel vary between  319°C and a maximum temperature of  461°C. The corresponding temperature variation for the martensitic steel is 317–412°C for the 2.2 MW/m2 wall loading and 325–440°C for the 5.0 MW/m2 wall loading. The results of the time dependent calculations,

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for both materials examined in this study, for the stress and strain (average values across section CC) are shown in Figs. 5 – 9. The variation of stress and strain with time is shown in Figs. 5 and 6, and demonstrates the stress relaxation and strain enhancement due to creep of the component. The stress and strain in the component would have remained unchanged if no creep was accounted for, at the level of the initial values. Instead, the stress relaxes and the strain increases. A summary of values for the two materials is as follows:

Time (h)

5000 12 000 20 000

316 Austenitic steel

9% Cr martensitic steel

2.2 MW/m2

2.2 MW/m2

5.0 MW/m2

Stress (MPa)

Stress (MPa)

Strain (%)

Stress (MPa)

120 50 30

0.095 0.14 0.16

50 24 24

Strain (%) 0.29 0.36 0.40

60 24 24

Fig. 6. The average strain across section CC variation with time.

Strain (%) 0.12 0.20 0.25

Fig. 7. The stress – strain diagram and the ductility limit curve for the 316 stainless steel.

Fig. 5. The average stress across section CC variation with time.

The results show that stress relaxation is a function of the wall loading, and is accelerated, i.e. it takes the stress less time to relax, as the wall loading increases. For example, for the martensitic steel at 2.2 NW/m2 the stress relaxes after  20 000 h whereas at 5.0 NW/m2 it relaxes after only 12 000 h. From the structural point of view, the major concern of creep induced stress relaxation is operation of the structural materials close to the ductility limit, which is reduced due to embrittle

P.J. Karditsas / Fusion Engineering and Design 48 (2000) 527–537

Fig. 8. The stress–strain diagram for the 9%Cr– martensitic stainless steel.

ment (the helium production and displacement damage effects). This can be demonstrated by the stress–strain diagram for the component, as shown in Figs. 7 and 8 for the various loading conditions analysed in this study. Fig. 7 shows the stress – strain diagram for the 316 austenitic steel and the comparison with the design stress – strain curve at the ductility limit (from Eq. (8)). The results show that for this particular example the structure exceeds the limit early on during operation (1000 h).

Fig. 9. The cumulative creep damage variation with time and loading conditions.

535

This behaviour though is typical of structures that creep under irradiation. Creep damage is accumulating faster at the beginning of operation of the machine but as the stress relaxes with time the operation moves further and further away from the ductility limit. The problem with the structure at this ‘relaxed’ stress state is its reduced ability to accommodate any further load fluctuations. For example, powering down after 12 000 h, will result in the structure wanting to resume its original shape, thus introducing a complete stress reversal, i.e. in the stress–strain diagram (Fig. 7) this will represent movement in the vertical direction towards the high stress values, thus resulting in crossing the limit and leading to structural failure. A power transient (over or under power) will tend to have a similar effect. The structure, according to the calculations in this paper, can only allow a load fluctuation that does not produce a stress greater than 90 MPa. Fig. 8 shows the stress–strain diagram for the martensitic steel. There are no data available presently for the stress at the ductility limit for this material. The results for the creep cumulative damage variation with time are shown in Fig. 9. They demonstrate that the accumulation of creep damage in the structure is fast at the beginning of operation but eventually reaches a steady value. This behaviour can be explained by examination of the stress variation with time and the stress– fracture/design strain curves, At the beginning of power plant operation the stress is high and the time to failure is low, resulting in large values of the damage ratio (dt/tr). As time goes on the stress relaxes and tr values progressively increase, resulting in decreasing values of the damage ratio (dt/tr) and minimal contributions to the sum (or accumulation of damage). The rate of damage accumulation, for times beyond  20 000 h, is expected to rapidly accelerate when the creep enhancement due to swelling becomes significant. Assuming there are no power transients the cumulative damage ratio D= 1.0, and there is no fatigue contribution to the damage ratio; an estimation of in-service time for the first wall, with a design strain of 0.5% gives the following results:

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In-service time Constant stress (Eq. (17)) Years

dpa

With stress relaxation Years

dpa

316 Austenitic steel (2.2 MW/m2)

1.57

35

3.17

71

Martensitic steel (2.2 MW/m2) Martensitic steel (5.0 MW/m2)

2.35

49

5.28

107

0.82

39

2.87

133

4. Conclusions In general the problems associated with irradiation creep which will generate difficulties in the design and licensing process of future power plants are related to the lack of understanding of the irradiation creep mechanism and its effects on material properties and structure behaviour. The material properties desired are the creep constitutive equation and the stress – strain diagram for the material, including the variations of fracture strain (ductility limit) with stress and helium to damage ratio, i.e. a diagram similar to the one shown in Fig. 2 for the 316 austenitic steel. The results indicate that the major concern of creep induced stress relaxation is operation of the structural material close to the ductility limit, which is reduced due to embrittlement (the helium production and displacement damage effects). The estimated in-service times suggest a displacement damage of 70 dpa for the 316 austenitic steel and  110 – 130 dpa for the martensitic steel. Provided there are no loading fluctuations, for a design strain of 0.5%, the in-service time is estimated to be  3 years for the 316 steel (2.2 MW/m2) case and for the

high wall loading martensitic steel case (5.0 MW/m2), and  5.3 years for the lower wall load martensitic steel case (2.2 MW/m2). The difficulty in defending these results lies in the uncertainty arising from the limited database and experience of the material properties, especially the creep constitutive law, when exposed to fusion environments. Stress relaxation is a function of the wall loading, and is accelerated as the wall loading increases. Calculations show that for the martensitic steel at 2.2 MW/m2 the stress relaxes after  20 000 h, whereas at 5.0 MW/m2 it relaxes after only 12 000 h. The 316 austenitic steel relaxes after  10 000–12 000 h. In conclusion, for successful in-vessel component design, the structural material properties under irradiation conditions must be known and the microstructural behaviour of the material must be established. The in-service time of the component is governed and limited by the combined creep–fatigue cumulative damage.

Acknowledgements This work was jointly funded by the UK Department of Trade and Industry and Euratom.

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