Development of the efficiency diagram rule for ratcheting of 9Cr steels

Ph. Matherona*, G. Aielloa, A. Martinb a CEA-Saclay, DEN/DM2S/SEMT/LISN, 91191 Gif sur Yvette, France b AREVA NP, Mechanical Engineering Department, PEELS-F, 10 rue Juliette Récamier, 69456 Lyon Cedex, France Abstract 9Cr steels are being considered as structural material for fourth generation and fusion reactors because of their good mechanical properties, in particular the low thermal expansion coefficient and high thermal conductivity. With respect to more common austenitic-type steels, they present however a particular behaviour in strain hardening, characterized by low ductility and softening under cyclic loads. In fact, experimental results have already shown that design rules to prevent ratcheting damage in present-day nuclear C&S, developed mainly for austenitic steels, are not conservative for this material. This paper presents a specific rule to limit ratcheting of 9Cr steel based on the efficiency diagram method used in the French code RCC-MRx. For this purpose, tension-torsion ratcheting tests have been performed in CEA to characterize the behaviour of the material. The points corresponding to the experimental results have then been represented in the space of the significant variables SR=∆Q/P and V=P/Peff in order to determine, as a lower envelope of the most penalising tests, a new efficiency diagram for 9%Cr steels. The differences between the new diagram and the one given in the code for austenitic steels are discussed. The adaptation of the efficiency diagram criterion to 9%Cr steels implies also the definition of appropriate limits for Peff. Particular attention has been given to the peculiar cyclic behaviour of the material. By considering the reduced cyclic stress-strain curve, these limits have been proposed by relating the margins given by the new rule to a value of the yield strength (Sy) that takes into account the softening of the material. Keywords P91, 9Cr steel, ratcheting, efficiency diagram.

1. INTRODUCTION Modified 9Cr-1Mo steels are being considered as structural material for several components in fourth generation and fusion power plants [1,2] because they present good thermo-physical properties, excellent stability under neutron irradiation and good creep strength up to 550°C. However, with respect to austenitic steels, they present a very limited strain-hardening capability and soften under cyclic loads. Qualification of the material comprises therefore the verification of design rules contained in present-day Codes&Standards, in particular for type S (cyclic) damage modes like ratcheting and fatigue. In this paper, the efficiency diagram rule to prevent ratcheting, used in the RCC-MRx code [3], is investigated. In fact, results of tension torsion ratcheting tests performed on 9Cr specimens, have already shown that, in its present form, the efficiency diagram does not form a lower envelope representative of the worst results [4]. On the basis of the obtained results, a modification of the rule is proposed in order to take into account the specific behaviour of 9%Cr steels. This implies the definition of a new efficiency diagram, specific to 9Cr steels, but also the definition of appropriate limits for the corresponding effective primary stress (Peff).

2. RULES TO PREVENT RATCHETING IN RCC-MRX Ratcheting is by definition the accumulation of plastic deformation in structures subjected to cyclic stressing above the elastic limit with a non-zero primary stress. When a structure is subjected to cyclic loading, it may show signs of permanent deformation at the end of the first cycle. During subsequent cycles the following cases may arise:

• Plastic adaptation (elastic shakedown): the structure is said to be plastically adapted if, after a few cycles, its behaviour becomes elastic at every point in the structure.

• Plastic accommodation (plastic shakedown): the structure undergoes plastic accommodation if, after a

few cycles, its behaviour, while remaining elastoplastic, is the same at each cycle. Plastic accommodation excludes the possibility of progressive deformation.

• Progressive deformation:, there is progressive deformation or ratcheting if an increase of deformation

appears at each cycle under the effect of cyclic loads. The limitation of the progressive deformation allows preventing macroscopic geometrical effects, such as the filling of gaps, which could lead to additional loads not taken into account in the design. More importantly, the additional plastic deformation due to ratcheting could impact the assessment of damage modes like fatigue and creep, where the significant parameter is the total strain of the material. The rules used in RCC-MRx to prevent ratcheting are briefly recalled and further explained in the following sections.

THE «3SM» RULE By definition, the limit for which a material experiences no permanent deformation is the elastic limit. Since the elastic limit is extremely difficult to quantify in a practical way, the engineering yield strength Sy is usually assumed as corresponding to the elastic limit. It can then be shown that, for an elastic-perfectly-plastic material, the theoretical limit for which a structure cannot experience progressive deformation is when the sum of the

primary stress )( bL PPP += and of the variation of the secondary stress ( Q∆ ) is less than two times the yield strength [5]:

ybL SQPPMax 2)( ≤∆++

The 2Sy limit is therefore conservative for any material presenting strain hardening. Since for austenitic stainless steels like 316L(N), the primary allowable stress Sm (at temperatures up to 150°C) is defined as Sm=(2/3)Sy, the above rule can also be expressed as the well-known 3Sm rule:

)2(3)( ymbL SSQPPMax =≤∆++ (austenitic steels, T<150°C)

Note that for T>150°C, Sm is defined as 0.9Sy and the 3Sm limit is less conservative than the 2Sy limit, which is justified by the high strain hardening capability of these steels and their cyclic hardening behaviour. For austenitic steels, this rule insures shakedown after a few cycles.

For 9%Cr steels like P91, however, Sm is defined from the ultimate strength (Su) as Sm=(Su/3) at Room

Temperature (RT) or Sm=(Su/2,7) for T>150°C. As a consequence, the calculated value QPPMax bL ∆++ )(

becomes significantly less than the theoretical 2Sy limit: at RT, for example, yum SSS 3.13 ≅= . The 3Sm criterion

for 9%Cr steels is therefore very conservative although this conservativism is not based on a quantitative estimation of the effects of cycling softening but derives only from the different definition of Sm.

THE EFFICIENCY DIAGRAM RULE The efficiency diagram criterion used in RCC-MRx has been developed in order to allow a limited amount of the cumulative strain to take place without compromising the lifetime of the material [6]. By allowing a limited amount of plastic deformation to occur, this method is in principle less conservative than the 3Sm rule. The basis of the efficiency diagram is empirical and it shall therefore be validated whenever a new material is used, especially if the strain hardening behaviour changes substantially. The efficiency diagram limits the cumulated strain by defining an allowable stress that can be calculated starting from the results of elastic analysis. For the application of the efficiency diagram rule, the effective primary stress (Peff) is defined as the primary stress that, when acting alone, would give the same strain on the monotonic stress-strain curve as the cumulative strain due to the superposed cyclic primary and secondary load. Using the efficiency diagram, the limitation of ratcheting consists then in defining an allowable value for the effective primary stress Peff. This value corresponds to a maximum allowable cumulative strain as determined on the monotonic tension curve. In RCC-MRx, two limits (P1 and P2) on Peff are defined, corresponding to the primary membrane stress alone and the sum of the primary membrane and bending stress:

mm S

V

PMaxP 3.1

)(

11 <= m

bL SV

PPMaxP 5.13.1

)(

22 ×≤+=

Where V1 and V2 are the efficiency indexes corresponding to the secondary ratios:

)(1

mPMax

QSR

∆= )(

2

bL PPMax

QSR

+∆=

According to the code, for austenitic steels, setting the limit of P1 to 1.3Sm means that, in the most unfavourable cases, a membrane strain of 1% is accepted and setting the limit of P2 to 1.3 x 1.5 Sm means that, in the most unfavourable cases, a membrane plus bending strain of 1.7% is accepted. In fact, the complete expression of the rule as given in RCC-MRx is more general, taking also into account the cases of loadings with secondary membrane stresses and with or without overstress of short duration. Also, when creep is significant, the additional creep strain must be taken into account in the calculation, but the calculation of the ratcheting strain component always relies on Peff.

For the construction of the efficiency diagram, the results of experimental tests are represented on the space of the two variables:

-) effP

PV = (efficiency index)

-) P

QSR

∆= (secondary ratio),

where:

-) P is the the equivalent primary (constant) stress acting on the specimens

-) Q∆ is the equivalent elastic secondary stress range applied on the specimens. Using this representation for ratcheting tests, Peff increases with the cumulative strain, the calculated value of the efficiency index (V) decreases and the representative point moves downward in the space of the efficiency diagram (Figure 1).The evolution of the cyclic behaviour (more or less favourable) is implicitly taken into account in the determination of Peff because it is the final experimental accumulated deformation obtained from different tests that is used. The efficiency diagram is then constructed as the lower envelope curve representing the «worst» results in order to obtain a conservative estimation of Peff using SR = ∆Q/P.

The efficiency diagram presently given in the RCC-MRx code has in fact been constructed and validated starting from a considerable number of results of experimental test (tension-torsion, internal pressure-axial deformation, etc.), at different temperatures and with or without hold times (creep), but performed mainly on austenitic stainless steels (Figure 2).

Figure 1: Construction of the representative points starting from experimental results.

Figure 2: Experimental base used to construct the efficiency diagram presently in the RCC-MRx code.

COMPARISON OF THE 3SM, 2SY, AND EFFICIENCY DIAGRAM RULE FOR 316L(N) STEEL. A direct comparison of the conservatism of the different rules used to prevent ratcheting can be made by representing the allowable operating domains, bounded by the conditions

mm SP < and mbm SPP 5.1<+ ,

respectively in the space of the dimensionless ratios [(mm SP / ),(

mSQ /∆ )] and [ )5.1/( mbm SPP + ,(mSQ 5.1/∆ )], i.e.

scaling the primary and secondary applied loads to the allowable primary stress. All comparisons in the following are based on equivalent stresses according to the Von Mises criterion. The comparison between the 3 criteria in Figure 3 and Figure 4 shows that:

-) at 20°C, the value of 3Sm and 2Sy coincide and there is no difference between the two limits;

-) at 500°C, the theoretical 2Sy limit is always the most conservative;

-) at 550°C, for primary membrane stresses and Pm=Sm, the efficiency diagram rule is as conservative as the theoretical 2Sy limit;

-) for primary membrane stresses and low values of the ratio (mm SP / ), i.e. for low primary membrane

stresses, the efficiency diagram rule is considerably less conservative than 3Sm limit. In this region of low primary stresses, the efficiency diagram rule takes into account the fact that progressive deformation is actually difficult to produce;

-) for primary membrane stresses and values of the ratio (mm SP / ) higher than ~0.7, i.e. when the primary

membrane stress part of the load is high, the efficiency diagram rule is more conservative than the 3Sm rule, but the two criteria are very close with differences lower than 30%;

-) when the primary load has also a bending component, the efficiency diagram rule is always the less conservative of the criteria;

316L(N) – T=20°C

Figure 3: Comparison between the 3Sm, 2Sy criteria and efficiency diagram rule for 316L(N) at 20°C.

316L(N) – T=550°C

Figure 4: Comparison between the 3Sm, 2Sy criteria and efficiency diagram rule for 316L(N) at 550°C.

Using the minimum stress-strain laws for 316L(N) given in appendix A3.1S of RCC-MRx, it can also be verified that limiting P1 to 1.3Sm would limit the total membrane deformation to less than 0.15% at 20°C and to less than 0.89% at 550°C in the most unfavourable of cases (Figure 5).

ymm SSQPMax 23)( =≤∆+

mm S

V

PMaxP 3.1

)(

11 <=

ymbL SSQPPMax 23)( =≤∆++

mbL S

V

PPMaxP 5.13.1

)(

22 ×≤+=

mm SQPMax 3)( ≤∆+

mm S

V

PMaxP 3.1

)(

11 <=

ym SQPMax 2)( ≤∆+

mbL SQPPMax 3)( ≤∆++

mbL S

V

PPMaxP 5.13.1

)(

22 ×≤+=

ybL SQPPMax 2)( ≤∆++

Figure 5: Comparison between the maximum allowed primary membrane strain for 316L(N) at 20° and 550°C.

In fact the conservatism of the efficiency diagram rule depends on the limits for Peff as shown in Figure 6. As the limit on Peff increases, the maximum allowed total deformation, as determined on the monotonic stress-strain curve, increases but the relation is not linear: the distance between the iso-curves reflects the strain hardening and cyclic hardening (in case of 316-L(N)) capability of the material.

Figure 6: Comparison between different limits of Peff – 316L(N) at 550°C.

3. DEVELOPMENT OF A MODIFIED EFFICIENCY DIAGRAM FOR P91 STEEL

Tension-torsion tests on P91 steel specimens at 450°C and 550°C have been performed and are reported in [4]. The results of these tests have been used to verify the validity of the efficiency diagram given in the code by positioning their representative points on the diagram as explained in § 2.2.

Older tests had been made in the 1990's at room temperature with a simpler test bench, because the transducers didn't need to support high temperature and the primary stress was obtained with a dead weight as described in [6] for such tests. The 9Cr steel is not exactly the same as for the recent study at high temperature [5], but the results of these tests can be used for a comparison.

On Figure 7, it can be seen that the main part of the points representative of the tests are located under the efficiency diagram of RCC-MRx. Therefore, this diagram, in its present form, does not represent a lower envelope

0

50

100

150

200

250

300

350

0 0,2 0,4 0,6 0,8 1 1,2 1,4 1,6

σ(M

Pa

)

ε (%)

Minimum stress strain curve - 20°C.

0

20

40

60

80

100

120

140

160

180

200

0 0,2 0,4 0,6 0,8 1 1,2 1,4 1,6

σ(M

Pa

)

ε (%)

Minimum stress strain curve - 550°C

2Sy

Peff=1,23Sm - ε= 0.5%

Peff=1,32Sm - ε= 1%

Peff=1,64Sm - ε= 2% Peff=2,27Sm - ε= 4%

meff SP 3.1=meff SP 3.1=

for tests done with 9%Cr steel. Its use for the design would lead to cumulative strains lower than those observed experimentally.

On the basis of these experimental results, a new efficiency diagram is proposed for P91 and other 9%Cr steel which represents the “worst case” envelope of the obtained results. The equations describing the new diagram have been determined as:

72,0

2

2

98,04

)1(

15.11.1445.0

145.0

SRVSR

SR

SRVSR

VSR

=>

+×−=≤<

=≤

The new diagram is shown in Figure 7 and compared with the one used for austenitic steels.

Figure 7: Representation of the tests and of the new efficiency diagram developed for P91 and 9%Cr steels.

DISCUSSION The differences between austenitic and 9%Cr steels with respect to ratcheting behaviour can be highlighted using the same representation used in Figure 6 for 316L(N). In Figure 8 it can be seen that the Peff iso-curves are «flatter» and also more closer to each other than those of 316L(N), especially for the higher values of Peff.

The difference between the tension behaviour of 9%Cr steel, with its lower hardening in comparison with austenitic steels, is one factor explaining the difference between the curves shown in Figure 8 and those in Figure 6. The difference in cyclic behaviours, because of the cyclic softening of 9%Cr, is another explanation: the cyclic strain hardening of 316LN steel is conducive to slow ratcheting and stabilisation of the cumulative strain during cycling.

Figure 8: Comparison between different limits of Peff – P91 at 550°C.

In order to limit ratcheting, the efficiency diagram criterion defines limits on the effective primary stress Peff that implicitly correspond to strain limitations. These limits are expressed as multiples of the maximum allowable primary stress Sm : k·Sm and the corresponding allowed deformation can be determined on the monotonic stress-strain curves. However, since the stress-strain relation depends on the material, the same values of k lead to different cumulative strains depending on the material. These differences affect not only the slope of the codified efficiency diagram, but also the limits associated with the criterion.

For the same “class” of materials, and for cumulative strains that are considerably lower than the uniform elongation of the material, this difference is usually negligible. This allows using the same efficiency diagram and the same limitations for all austenitic-type steels contained in RCC-MRx. The adaptation of the efficiency diagram criterion to 9%Cr steels implies therefore not only the development of a new efficiency diagram but also the definition of appropriate limits for Peff.

4. APPLICATION OF CRITERION: LIMITS ON Peff FOR 9%Cr STEEL

For 316L(N), the limits on Peff correspond to a maximum cumulative strain of 1% for membrane stresses and 1.7% for membrane plus bending stresses. This is no longer true in case of 9%Cr steels: in particular, with the limit on Peff equal to 1.3Sm, the cumulative strain does not correspond to 1%, but about 0.1% instead (Figure 8). The material still has an elastic behaviour. Under these conditions, there is no ratcheting phenomenon and therefore no question about limitation of ratcheting. So, while the current efficiency diagram is not conservative for 9%Cr steels, using the same limits on Peff as for austenitic steels appears to be too restrictive.

In an attempt to define an appropriate limit for Peff for 9Cr steels, the proposed approach is to relate the conservatism given efficiency diagram rule to that of the 2Sy rule which, as discussed before, is a theoretical limit to avoid progressive deformation in perfectly plastic materials and a conservative limit for strain hardening materials. Using the 2Sy value for P91 is however not satisfactory because of its softening behaviour. As a matter of fact, this would lead to values of the “worst cases” cumulative deformation higher than 1.3% (Figure 8) which seems excessive considering that the uniform elongation of the material at 550°C is close to 2%. Moreover, the limit would fall in a region where the criterion is very sensible to the variations of Peff. The cyclic softening of the material shall therefore be considered when defining the limits to apply to 9%Cr steels.

ACCOUNTING FOR THE CYCLIC SOFTENING OF THE MATERIAL Figure 9 shows the results of two tension-torsion ratcheting tests performed on P91 at 550°C for total loadings P+∆Q close to the theoretical 2Sy limit. One can see that because of the continuous softening of the material there is no stabilization of ratcheting: in fact even at this level of loading, P91 tests show the accumulation of progressive deformation. The «theoretical» 2Sy limit needs therefore to be reassessed taking into account the cyclic softening. The limits on the efficiency diagram rule can then be determined on the basis of the «softened» 2Sy rule.

Peff=1,3Sm - ε= 0,10 %

Peff=1,7Sm - ε= 0,13%

Peff=1,9Sm - ε= 0,18%

Peff=2,0Sm - ε= 0,31%

Peff=2,1Sm - ε= 0,77%

Peff=2,15Sm - ε= 1,32%

Figure 9: Results of tension-torsion ratcheting tests softening and progressive deformation at loadings ~2Sy

In order to take into account the cyclic softening of the material, it is here proposed to measure the value of the yield strength on the (reduced) cyclic stress-strain curve, instead of the monotonic one. Note that the cyclic-stress strain curve does not correspond to the physical behaviour of the «softened» material but is rather constructed as a set of points obtained from strain controlled fatigue tests by taking the value of the half-life stress variation for a given strain variation. As such, its points do not correspond to any codified property (Sy or Su) of the material, but nonetheless they give an estimation of the expected degree of softening at a given level of deformation. Moreover, since fatigue criteria impose a margin with a reduction by a factor (at least) equal to 20 on the experimentally measured fatigue life of the material, the level of softening estimated on the cyclic curve is probably too pessimistic, but in any case conservative.

Figure 10 shows the construction used to determine the «softened» value of the yield strength on the cyclic stress-strain curve of the material as given in RCC-MRx. All values are taken at 550°C, since high temperature is detrimental to ratcheting and this is the highest temperature at which experimental results are available. Note however that since the efficiency diagram uses dimensionless variables the final results are independent of temperature. It shall be checked that the final result is actually conservative also at other temperatures. The cyclic curve in the figure has been corrected, to be compared with the monotonic (uniaxial) curve, taking into account that the one given in the code is expressed in terms of the Von Mises equivalents for stress and strain. On the other hand, the curve represents the average behaviour of the material, while limits shall rather be defined with respect to the minimum properties. In order to obtain an equivalent minimum value, it is here proposed to scale the softened Sy value by the same ratio between the minimum and average yield strengths:

avgy

yavgsofty

softy S

SSS

minmin )()( =

Figure 10: Determination of a «softened» Sy limit on the reduced cyclic stress-strain curve (numerical values at T=550°C).

LIMITS ON PEFF FOR 9%CR STEELS

Assuming the min)(2 softyS value as the redefined limit for which there is no progressive deformation, the limit on

Peff can then be determined by imposing the same conservatism of the two rules when Pm=Sm, i.e. in the most penalising condition for the occurrence of progressive deformation (§2.3). Since in this case:

min)(2 softym SQP <∆+

then, for Pm=Sm, we have:

min)(2 softym SQS =∆+

which corresponds to a value of the secondary ratio SR:

31.21)(2 min

1 =−=∆=m

softy

m S

S

S

QSR

Using the equations of the efficiency diagram for 9%Cr steel proposed in §3, this would correspond to an efficiency index:

54.0)31.21(

31.215.11.1 2

2

1 =+

×−=V

and therefore, since Pm=Sm, a limit on Peff calculated for membrane stress alone equal to:

mmm S

V

S

V

PP ×=== 85,1

111

The limit on P1 is then:

mSP ×≤ 85,11 Figure 11 show the procedure used for determining the limit of Peff for membrane stress.

MPaS avgsofty 271)( =

MPaS avgy 329)( =

Figure 11: Determination of the limit on Peff for primary membrane stress.

The same procedure can be used to determine the limit on P2 when taking also into account primary membrane plus bending stresses. The maximum allowable primary stress to consider would be in this case 1.5Sm. This gives:

75.0;21.115.1

)(22

min

2 ==−= VS

SSR

m

softy

And then:

mm S

V

SP ×== 2

5.1

22

The limit on P2 is then:

mSP ×≤ 22 As shown Figure 12 in the assumed limits give, in the most unfavourable cases, a membrane strain of 0.15% and a membrane+bending strain of 0.31%. Note that this limit on P2 is probably extremely severe. However, considering the peculiar ratcheting behaviour of P91 steel, and considering that for values of Peff close to 2Sm the efficiency diagram rule is very sensitive to the imposed limit (Figure 8), this conservatism seems justified.

Figure 12: Total cumulated deformations for P91 steel at 550°C using the modified efficiency diagram rule.

At temperature lower than 550°C, the maximal allowed cumulative strain depending on the temperature and corresponding to the two limits (1.85Sm and 2Sm) can be calculated with the same procedure using the stress-strain curves of the material given in the RCC-MRx. Values of the uniform elongation corresponding to the maximum load at each temperature have been determined from results of monotonic tension tests taken from CEA database. This permits to determine the margin obtained with the two criteria by comparing the maximum cumulative strain to the minimum uniform elongation of the material at different temperatures. The calculated margins given in the table are always greater than 90 % as regards the values relative to membrane stress alone, and greater than 78 % for the values relative to membrane and bending stress.

T (°C) (εu)min εtot

1,85 Sm Margin

εtot

2Sm Margin

20 8,356 0,19 98% 0,28 97%

50 7,99 0,20 97% 0,35 96%

100 7,38 0,25 97% 0,54 93%

150 6,77 0,29 96% 0,72 89%

200 6,16 0,31 95% 0,81 87%

250 5,55 0,31 94% 0,78 86%

300 4,94 0,30 94% 0,68 86%

350 4,33 0,29 93% 0,64 85%

400 3,72 0,26 93% 0,50 87%

450 3,11 0,25 92% 0,43 86%

500 2,5 0,20 92% 0,36 86%

550 1,89 0,15 92% 0,31 84%

600 1,28 0,12 91% 0,29 78% Table 1: Margins defined by the proposed efficiency diagram rules with respect to the minimum elongation of the material at different temperatures.

5. CONCLUSIONS The objective of this work was to propose a specific rule to limit progressive deformation in 9%Cr steels starting from the efficiency diagram rule contained in the French nuclear C&S RCC-MRx.Previous experimental results had shown that the use of efficiency diagram in its present form, originally developed for austenitic steel, would lead to estimated values of the cumulative deformation that were lower than the experimentally measured ones.

meff SP 85.1=

meff SP 2=

Moreover, the limits defined for Peff were not suitable for this material, since they were based on the value of the allowable primary stress (Sm) defined for austenitic steels. The origin and the rationale of the efficiency diagram rule are recalled in the first part of the paper. Then, starting from the results of tension-torsion ratcheting tests, a new efficiency diagram is proposed for 9%Cr steels constructed as the lower envelope of the most penalising results. The differences between the new diagram and the one given in the code are discussed. The adaptation of the efficiency diagram criterion to 9%Cr steels implies however not only the development of a new efficiency diagram but also the definition of appropriate limits for Peff. Particular attention has been be given to the peculiar cyclic softening behaviour of the material. By considering the reduced cyclic stress-strain curve, these limits have been proposed by relating the margins given by the new rule to those of a Sy value that takes into account the softening of the material. Finally, to assess the conservatism of the proposed rules at different temperatures, the values of the maximum allowed cumulative deformation are compared to the uniform elongation of the material. The calculated margins are always greater than 90 % as regards the values relative to membrane stress alone, and greater than 78% for the values relative to membrane and bending stress. Note that the proposed criteria will have to be further developed and validated taking into account the effects of creep and verifying that the limits defined for the progressive deformation do not impact fatigue life calculations. More experimental tests under different loading combinations, as well as tests with hold times could be used alongside the results presented in this article to search for modifications or changes to the proposed efficiency diagram rule for 9%Cr steel. Acknowledgments The authors wish to acknowledge the support from the MATTER project under the umbrella of EERA Joint Program Nuclear Materials (Project no: 269706 – FP7-Fission-2010).

REFERENCES [1] R.L. Klueh, A.T. Nelson, Ferritic/martensitic steels for next-generation reactors, Journal of Nuclear Materials, Volume 371, Issues 1–3, 15 September 2007, Pages 37-52

[2] F. Gauché, J. Roualt, French SFR R&D program and design activities for SFR prototype ASTRID, Energy Procedia, Volume 7, 2011 Pages 314-316

[3] RCC-MRx, « Règles de Conception et de construction des matériels Mécaniques des installations nucléaires» (Design and construction rules for Mechanical equipment in nuclear facilities), published by AFCEN, 2013 edition.

[4] P. Matheron, G. Aiello, C. Caes, P. Lamagnere, A. Martin, M. Sauzay. Tension – torsion ratcheting tests on 9Cr steel at high temperature, Nuclear Engineering and Design, vol 284, 2015, pages 207–214

[5] P. Lamagnère, Y. Lejeail, C. Pétesch, T. Lebarbé, P. Matheron, S. Taheri, A. Martin. Design rules for ratcheting damage in AFCEN RCC-MRx 2012 Code, PVP2014-28324.

[6] G. Clément, J. Lebey, R. Roche. A design rule for thermal ratcheting, 5th International Conference on Pressure Vessel Technology - Vol. 1- Design and Analysis - San Francisco ,1984.