Journal of Nuclear Materials 464 (2015) 281–293

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Journal of Nuclear Materials

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Warm PreStress effect on highly irradiated reactor pressure vessel steel

http://dx.doi.org/10.1016/j.jnucmat.2015.04.0460022-3115/� 2015 Elsevier B.V. All rights reserved.

⇑ Corresponding author.E-mail address: benoit.tanguy@cea.fr (B. Tanguy).

J. Hure a, C. Vaille a, P. Wident b, D. Moinereau c, C. Landron c, S. Chapuliot d, C. Benhamou d, B. Tanguy a,⇑a CEA Saclay, Service d’Etudes des Matériaux Irradiés, 91191 Gif-sur-Yvette, Franceb CEA Saclay, Service de Recherche en Métallurgie Appliquée, 91191 Gif-sur-Yvette, Francec EDF R&D, Site des Renardières, 77818 Moret-sur-Loing, Franced AREVA NP, 92084 Paris La Défense, France

a r t i c l e i n f o

Article history:Received 13 January 2015Accepted 22 April 2015Available online 1 May 2015

a b s t r a c t

This study investigates the Warm Prestress (WPS) effect on 16MND5 (A508 Cl3) RPV steel, irradiated upto a fluence of 13 � 1023 n:m�2 (E > 1 MeV) at a temperature of 288 �C, corresponding to more than60 years of operations in a French Pressurized Water Reactor (PWR). Mechanical properties, includingtensile tests with different strain rates and tension–compression tests on notched specimens, have beencharacterized at unirradiated and irradiated states and used to calibrate constitutive equations todescribe the mechanical behavior as a function of temperature and fluence. Irradiation embrittlementhas been determined based on Charpy V-notch impact tests and isothermal quasi-static toughness tests.Assessment of WPS effect has been done through various types of thermomechanical loadings performedon CT(0.5 T) specimens. All tests have confirmed the non-failure during the thermo-mechanical tran-sients. Experimental data obtained in this study have been compared to both engineering-based modelsand to a local approach (Beremin) model for cleavage fracture. It is shown that both types of modelinggive good predictions for the effective toughness after warm prestressing.

� 2015 Elsevier B.V. All rights reserved.

1. Introduction

Reactor pressure vessels (RPV) steels used in nuclear powerplant (NPP) show a ductile–brittle transition (DBT), i.e. a largeincrease of the fracture toughness with temperature associatedwith a change of fracture mechanism. Neutron irradiation inducesan increase of the transition temperature related to microstruc-tural changes [1] which can be addressed either by CharpyV-notch impact tests as in surveillance programs [2] either directlybased on isothermal quasi-static toughness tests. Fracture tough-ness lower bound curve and its shift with irradiation are then usedto ensure the structural integrity of the RPV in nominal and hypo-thetical accidental situations. Practical rules assessment requiresthat the stress intensity factor at a postulated or detected defectshould be below the reference deterministic fracture toughnesscurve in any situation. In the case of a Loss Of Coolant Accident(LOCA), as shown for example in [3] where the stress intensity fac-tor varies as the temperature decreases, these practical rules maybe over-pessimistic as they do not account for load history effectson fracture toughness of RPV steel, as the so-called Warm PreStress(WPS) effect.

The WPS effect describes the fact that, when a crack is loaded ata temperature TWPS to a stress intensity factor KWPS, no brittle frac-ture will occur if the stress intensity factor decreases or is held con-stant between TWPS and Tf 6 TWPS (Fig. 1), even if the isothermalfracture toughness of the virgin material (i.e without prior loading)is exceeded, and the apparent enhancement of the fracture tough-ness of the material if the crack is reloaded at Tf (see [4,5] forreviews). The WPS effect may thus become relevant in the contextof prolongation of nuclear power plant lifetime. The physicalexplanations of this effect are mainly related to the evolution ofyield strength with temperature and crack tip blunting occurringduring the loading at a temperature where the material shows aductile behavior [6], that cannot be captured through aone-parameter criterion (either elastic KIc or elasto-plastic energyrelease rate Jc), thus explaining the possibility of crossing fracturetoughness curves for a thermomechanical loading.

A large number of experimental studies have evidenced theWPS effect for ferritic steels (see for example [7]), mostly on unir-radiated materials. More recently, studies have shown the rele-vance of WPS effect on complex geometries [8,9] and biaxialloading conditions [10], which have been shown to better mimicthe mechanical state encountered by a subcladding defect inRPV. The possibility of a positive stress intensity factor variationas the temperature decreases has also been assessed [11,12].Engineering deterministic [13] and statistical [7] models have been

LCFLTF

LCTF

TWPSf

WPS

K

Kf

r

Loading

TemperatureT Tr

Toughness

KLCIKF

Fig. 1. Thermo-mechanical loadings used in this study to assess the warm prestresseffect. LCF, LTF, LCTF and LICKF refer to Load–Cool–Fracture, Load–Transient–Fracture, Load–Cool–Transient–Fracture, and Load–Cool–Increase K-fracture,respectively.

Table 2Irradiation conditions: the indicated fast neutron (E > 1 MeV) fluence corresponds tothe fluence obtained in the maximum flux plane of the irradiated device. In thefollowing, fluence corresponding to specimens tested is indicated.

Fluence (E > 1 MeV)(n:m�2)

Flux (E > 1 MeV)ðn:m�2 s�1Þ

Iron damage(mdpa)

Temperature(�C)

13:9 � 1023 4:77 � 1016 200 288 (+5–7)

Table 3Conventional tensile properties for the irradiated material. / corresponds to thefluence (E > 1 MeV), Tirr and Ttest to the irradiation and test temperature, respectively,Rp;0:2 to the yield stress at 0.2% plastic strain, Rm to the tensile strength, Ag to theconventional plastic strain at striction and Z ¼ ½S0 � Sf �=S0 to the striction parameter.Rel corresponds to the value of Piobert–Lüders plateau, if any.

/ (E > 1 MeV)

ð1023 n:m�2ÞTirr

ð�CÞTtest

ð�CÞRp;0:2

(MPa)ReL

(MPa)Rm

(MPa)Ag

(%)Z(%)

13.2 288 �75 735 734 822 10.8 5510.9 283 �75 699 728 816 9.5 5610.9 283 �50 693 699 791 9.4 6211.4 283 �50 698 707 796 10.7 6010.9 283 �25 672 677 768 8.2 6211.4 283 0 661 663 750 9.4 5411.4 283 0 657 657 746 10.3 6110.9 283 15 644 644 731 9.2 5913.6 287 15 657 654 738 7.3 6110.9 283 50 632 630 714 9.1 6011.4 283 50 634 634 719 6.9 5911.4 283 100 608 608 692 8.2 6213.2 288 99 610 608 690 7.7 5713.6 287 300 569 – 687 7.7 52

282 J. Hure et al. / Journal of Nuclear Materials 464 (2015) 281–293

developed to quantify the effective toughness after warm prestress-ing. Overall, these K-based models give predictions in good agree-ment with experimental data. Thermomechanical loadings such asones performed to show the WPS effect are also being used toassess the capability of fracture criterion [14]. Local Approach toFracture (LAF) models [15,16] have been shown to give satisfactorypredictions for the WPS effect [17–20].

Few studies have assessed the WPS effect for irradiated RPVsteels [21] so that experimental data are still scarce, especially atfluence levels higher than those corresponding to 40 years of oper-ation. For a potential use of the WPS effect for structural integrityassessment of French RPVs, additional experimental results at highfluence have been identified as a key work so that a dedicatedexperimental program has been developed at CEA in collaborationwith EDF and AREVA-NP. Therefore, in this study, the WPS effect isinvestigated on French pressurized water vessels 16MND5 (closeto A508 Cl3) steel, irradiated up to a fluence of 13 � 1023 n:m�2

(E > 1 MeV), which typically corresponds to more than 60 yearsof operation in French PWR. The objectives are twofold: first toassess experimentally the WPS effect on highly irradiated RPV steelsubmitted to thermomechanical loadings relevant for LOCA situa-tions, secondly to provide a complete characterization and model-ing of the mechanical and fracture behavior in temperature for thislevel of fluence.

The paper is organized as follows. In the first part, after thedescription of the material investigated and the irradiation condi-tions, the evolution of tensile and fracture properties with irradia-tion are reviewed. The thermomechanical tests performed on bothunirradiated and irradiated materials are then presented and dis-cussed in Section 3. Prediction of effective fracture toughness afterthermomechanical transients is then presented in Section 4. Twoengineering models proposed in the literature are firstly used.Then Local Approach to Fracture methodology is applied. To thatpurpose, a constitutive law able to reproduce experimental datasuch as tensile tests and tension–compression tests on axisymmet-ric notched specimens with temperature and fluence isfirstly described. Finally, cleavage fracture Beremin model iscalibrated and used to predict the effective toughness afterwarm-prestressing for both unirradiated and irradiated state.

Table 1Chemical composition of 16MND5 steel (wt.%).

C S P Mn Si Ni

0.15 0.006 0.013 1.31 0.22 0.70

2. Material and mechanical properties assessment

2.1. Material description and irradiation conditions

The studied material is a 16MND5 steel (closed to A508 Cl3steel) that originates from a forged nozzle shell of a pressurizedwater reactor of 220 mm thickness. Table 1 gives its chemicalcomposition.

The material was heat treated (two austenitizing treatmentsfollowed by water quenching and tempering and a final stressrelief treatment). The microstructure is essentially a temperedbainite with a room temperature yield strength Rp;0:2 ¼ 500 MPaand an ultimate tensile strength, Rm ¼ 620 MPa. Flat Tensile,Axisymmetric Notched Tensile (NT, with minimal diameterd ¼ 3:5 mm and notch radius r ¼ 1:4 mm), Charpy V-notch(CVN), 0.5 T thick compact tension (CT) specimens were machinedfrom a layer located at 3/4 thickness of the shell in the T–L orien-tation and irradiated in the Material Testing Reactor (MTR) OSIRIS(CEA Saclay). All CT specimens have been precracked in fatigue atroom temperature up tu a ratio a0=W ¼ 0:55 prior to irradiation.Table 2 gives the principal characteristics of the irradiation. Asthere is a flux gradient along the irradiation rig, thefluence obtained for the specimens varies between 13.9 and8:8 � 1023 n:m�2 at the highest and lowest flux planes, respectively.

Accelerating irradiation results from the flux achieved in MTRwhich is, in the case of Osiris reactor, approximatively forty timeshigher that the one seen by RPV in French PWR. Representativity of

Cr Mo V Cu Co Al

0.19 0.52 0.009 0.07 0.02 0.022

400

500

600

700

800

900

1000

−150 −100 −50 0 50 100 150 200 250 300

Rp,0

.2,R

m(M

Pa)

T (◦C)

Rp,0.2(Unirradiated)Rm(Unirradiated)

Rp,0.2(φ = 13.1023 n.m−2)Rm(φ = 13.1023 n.m−2)

Rp,0.2(φ = 11.1023 n.m−2)Rm(φ = 11.1023 n.m−2)

(a)

500

600

700

800

900

1000

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16

−75◦C

−25◦C

20◦C

100◦C

φ = 10.1023n.m−2

σ(M

Pa)

p

5.10−4s−1 ↔ 5.10−3s−1

5.10−5s−1 ↔ 5.10−4s−1

(b)

Fig. 2. (a) Yield stress at 0.2% plastic strain, Rp;0:2, and tensile strength, Rm , as a function of temperature and level of irradiation /. Solid and dashed lines corresponds toadjustment of the experimental data. (b) True stress – cumulated plastic strain curves for tensile tests on irradiated material with strain rate variations.

Table 4Results of Charpy V-notch impact tests for irradiated material. / corresponds to thefluence (E > 1 MeV), Tirr and Ttest to the irradiation and test temperature, respectively.Charpy V-notch fracture energy, lateral expansion and crystallinity have beenmeasured according to [25].

/ ðE > 1 MeVÞð1023 n:m�2Þ

Tirr

ð�CÞTtest

ð�CÞCVN fractureenergy (J)

Lateralexpansion(mm)

Crystallinity(%)

8.8 290 �50 8.8 0.03 10010.4 281 25 50.7 0.74 8210.1 281 25 39.9 0.64 8411.1 283 50 63.5 0.92 8411.4 283 50 49.3 0.67 8510.1 283 50 32.9 0.51 85

9.2 290 75 101.0 1.48 379.2 290 75 130.6 2.17 268.8 290 150 139.0 2.13 0

J. Hure et al. / Journal of Nuclear Materials 464 (2015) 281–293 283

data obtained in accelerated conditions has been validated as far asthe flux level is not too high: for low-copper Mn–Mo–Ni steels(<0.1 wt.% Cu) such as the one used in this study, it has been shownthat for flux up to 1 � 1016 n:m�2 s�1 (E > 1 MeV), there is no clearevidence of flux effects on the irradiation-induced microstructure[22]. For higher flux, formation of unstable matric defects has been

0

50

100

150

200

−200 −100 0 100 200 300

CV

NE

nerg

y (J

)

T (◦C)

Unirradiatedφ = 10.1023n.m−2

(a)

Fig. 3. (a) Charpy V-notch fracture energy as a function of temperature for unirradiated anlines to 95% confidence bounds. (b) Isothermal quasi-static toughness as a function of temto tolerance bounds (2%, 5%, 50%, 95%, 98%) of the Master Curve approach [27] with T0

reported, but with no significant consequence on index tempera-ture shifts ductile–brittle transition temperature that may be hardto detect up to dose rates of 1 � 1017 n:m�2 s�1 (E > 1 MeV) [23].Estimated upper bound fluence after 40 years of operation inFrench 900 MWe NPP is 6:5 � 1023 n:m�2, an upper bound fluenceof 9:75 � 1023 n:m�2 can be extrapolated for 60 years of operation.Maximal fluence in this study obtained thus corresponds to morethat 60 years of operation in French 900 MWe PWR.

2.2. Tensile properties

Tensile tests were performed on flat tensile specimens with aSection 4 � 3 mm2 and a 12 mm gauge length, at a mean strain rate_� ¼ 5 � 10�4 s�1, in accordance with [24] on both unirradiated andirradiated materials. For irradiated specimens, fluence levels inthe range [10.9–13.6]�1023 n:m�2 were obtained (see Table 3) sothat the specimens were separated in two fluence levels (11 and13 � 1023 n:m�2) for testing. Conventional properties, yield stressat 0.2% plastic strain Rp;0:2 and tensile strength Rm as a function oftemperature for unirradiated specimens and the two levels of irra-diation (see above) are shown in Fig. 2a. A classical saturation ofthe tensile properties is observed above 100 �C. It is noted thatRmð100 �CÞ < Rmð300 �CÞ for both unirradiated and irradiated state

0

50

100

150

200

250

−150 −100 −50 0 50 100

K12

.5m

mJc

(MPa.

√ m)

T (◦C)

Unirradiatedφ = 13.1023n.m−2

(b)

d irradiated material. Solid lines correspond to a fit of the experimental data, dottedperature for unirradiated and irradiated material. Solid and dashed lines correspond¼ �93 �C and T0 ¼ 33 �C for unirradiated and irradiated material, respectively.

Table 5Isothermal quasi-static toughness test results (0.5 T CT specimens) for the irradiatedmaterial. / corresponds to the fluence (E > 1 MeV), Tirr and Ttest to the irradiation andtest temperature, respectively. K f

elas is given as an indication of load at fracture,K12:5 mm

Jc to the elastoplastic stress intensity factor without length correction on K. a0 isthe initial crack length, measured according to [27].

/(E > 1 MeV)

ð1023 n:m�2ÞTirr

ð�CÞa0

ðmmÞTtest

ð�CÞK f

elas

ðMPaffiffiffiffiffimpÞ

K12:5 mmJc

ðMPaffiffiffiffiffimpÞ

12.8 288 13.92 �5 40 4113.4 286 13.95 �5 50 5212.0 286 13.90 �5 55 5712.1 289 13.90 �5 61 6312.7 291 13.82 �5 70 7412.1 286 13.90 �5 73 7812.5 289 13.94 10 63 6612.0 289 13.91 10 90 10612.2 289 13.90 10 97 12512.7 289 13.85 30 69 7313.3 286 13.86 30 91 10713.3 289 13.83 30 93 11513.9 286 13.87 45 51 5212.6 291 13.83 45 91 10712.8 289 13.84 45 97 12813.5 286 14.86 45 100 13013.2 291 13.90 45 100 13912.9 289 13.98 45 104 216

284 J. Hure et al. / Journal of Nuclear Materials 464 (2015) 281–293

which probably reflects the occurrence of strain ageing at temper-atures closed to 300 �C. Piobert–Lüders instability well-known forcarbon steels has been observed at both unirradiated and irradi-ated states. Fig. 2a shows a significant hardening due to the irradi-ation with DRp;0:2ð300 �CÞ ¼ 127 MPa. Conventional tensileproperties as well as ReL the stress corresponding to the Lüders pla-teau and Z the striction parameter are given in Table 3 for irradi-ated material. Supplementary tensile tests were performed withvarying strain rates during the test in order to determine the vis-cous behavior of the 16MND5 steel (see Section 4.2.1). These testswere performed in the temperature range ½�75 �C : þ100 �C� withstrain rate variation approximately every 2.5% strain. As shownin Fig. 2b where the true stress–strain curves are shown for theirradiated material, two types of strain rate variation were per-formed: 5 � 10�4 to 5 � 10�3 s�1 and 5 � 10�5 to 5 � 10�4 s�1. It isshown in Fig. 2b that for temperatures ranging from �75 �C toþ20 �C an increase in the strain rate corresponds to a markedstress jump, the effect being lower at þ100 �C.

0

50

100

150

200

250

−160 −140 −120 −100 −80 −60 −40 −20 0

K12

.5m

mJc

(MPa.

√ m)

T (◦C)

Iso.LCF − 60

(a)

Fig. 4. Load–Cool–Fracture (LCF) tests performed on 0.5 T CT specimens at unirradiatedtoughness tests as well as to margin-adjusted 2% tolerance bound of the Master Curve,

2.3. Fracture properties

Impact energies have been measured on standard CharpyV-Notch (CVN) specimens, according to [25]. For irradiated speci-mens, fluence levels range from 8.8 to 10:4 � 1023 n:m�2.Specimens with the lowest fluence have been tested at lower andupper shelf temperatures where a 10% fluence variation isexpected to be not significant. For the other specimens a mean flu-ence value of 10 � 1023 n:m�2 has been considered. Results aregiven in Table 4 for irradiated material and compared to dataobtained on unirradiated material in Fig. 3a. Assuming an asymp-totic normal distribution for CVN energy, 95% confidence boundsof T56J index have been determined for unirradiated and irradiatedmaterials to be ½�51 �C : �29 �C� and ½23 �C : 61 �C�, respectively.The irradiation-induced shift DT56J is thus equal to þ84þ28

�32�C, for

a mean fluence of 10 � 1023 n:m�2.Prediction of the mean embrittlement of base metal as a func-

tion of the chemical composition of the material and fluence isstandardized in RSE-M code [26] and is given by:

DTT ¼ DT56J ¼ 15:4½1þ 35:7 maxðP� 0:008;0Þ

þ 6:6 maxðCu� 0:08;0Þ þ 5:8Ni2Cu� /

1019

� �0:59

ð1Þ

Based on Eq. (1), a mean embrittlement value DTT ¼ 82:5 �C isobtained for the steel considered with is in very good agreementwith the value DT56J ¼ þ84þ28

�32�C obtained from the Charpy tests

performed in this study.Isothermal toughness tests on 0.5 T Compact Tension speci-

mens have been performed in accordance to [27], with across-head speed of 0:15 mm mn�1. Tests were performed in therange [�150 : �80 �C] and [�5 : þ45 �C] at the unirradiated and

irradiated state, respectively. Elastic Kfelas

� �and elasto-plastic

K12:5 mmJc

� �stress intensity factor values obtained on irradiated

material are given in Table 5. The Master Curve methodology hasbeen applied to determine the reference temperature T0. T0 isequal to �93 �C for the unirradiated material (where data at�150 �C have not been taken into account [27]) and to þ33 �C forthe irradiated material (for a mean fluence of 13 � 1023 n:m�2).Toughness values are reported on Fig. 3b with the tolerancebounds 2%, 5%, 50%, 95%, 98% of the Master curve determined fora thickness 0.5 T. Overall the experimental datapoints are well

0

50

100

150

200

250

−160 −140 −120 −100 −80 −60 −40 −20 0

K12

.5m

mJc

(MPa .

√ m)

T (◦C)

Iso.LCF − 80

(b)

state. Thermomechanical loading paths are superposed to the results of isothermalwith T0 þ DT0 ¼ �84 �C.

0

50

100

150

200

250

−160 −140 −120 −100 −80 −60 −40 −20 0

K12

.5m

mJc

(MPa.

√ m)

T (◦C)

Iso.LTF − 60

(a)

0

50

100

150

200

250

−160 −140 −120 −100 −80 −60 −40 −20 0

K12

.5m

mJc

(MPa .

√ m)

T (◦C)

Iso.LTF − 80

(b)

Fig. 5. Load–Transient–Fracture (LTF) tests performed on 0.5 T CT specimens at unirradiated state. Thermomechanical loading paths are superposed to the results ofisothermal toughness tests as well as to margin-adjusted 2% tolerance bound of the Master Curve, with T0 þ DT0 ¼ �84 �C. A dotted line is used for the decreasing load part ofthe path, as the elasto-plastic stress intensity factor is not defined for non-proportional loading.

0

50

100

150

200

−20 0 20 40 60 80 100 120

K12

.5m

mJc

(MPa.

√ m)

T (◦C)

Iso.LCF − 60

(a)

0

50

100

150

200

−20 0 20 40 60 80 100 120

K12

.5m

mJc

(MPa.

√ m)

T (◦C)

Iso.LCF − 70

(b)

Fig. 6. Load–Cool–Fracture (LCF) tests performed on 0.5 T CT specimens at irradiated state. Thermomechanical loading paths are superposed to the results of isothermaltoughness tests as well as to margin-adjusted 2% tolerance bound of the Master Curve, with T0 þ DT0 ¼ 42 �C.

J. Hure et al. / Journal of Nuclear Materials 464 (2015) 281–293 285

described by the Master Curve. The irradiation-induced shift in ref-erence temperature T0 is thus 126 �C for a mean fluence of13 � 1023 n:m�2. In following graphs describing thermomechanicalloadings performed to assess the WPS effect, margin-adjusted 2%tolerance bound will be used, using the 95% upper confidencebound T0 ¼ �93þ 1:96½b=

ffiffiffiffiNp� ¼ �84 �C for the unirradiated mate-

rial (with b the standard deviation and N the number of specimenstested), and T0 ¼ þ33þ 1:96½b=

ffiffiffiffiNp� ¼ þ42 �C for the irradiated

material [27].From the measured DT56Jð/ ¼ 10 � 1023 n:m�2Þ ¼ þ84 �C and the

dependence in fluence of Eq. (1), it is possible to estimate DT56J forthe level of fluence relevant for 0.5 T CT specimens, leading to

DTestimated56J ð/ ¼ 13 � 1023 n:m�2Þ ¼ þ98 �C.

3. Warm PreStress assessment

Warm PreStress assessment has been carried out using 0.5 TCompact Tension specimens. A dedicated software has beendeveloped to perform paths where the load applied to thespecimen is monitored by the temperature of the specimen. Thesame software has been used for both tests on unirradiated andirradiated materials.

3.1. Unirradiated state

Eighteen 0.5 T Compact Tension specimens have been tested atthe unirradiated state with thermomechanical loadings, as shownon Figs. 4 and 5. Two pre-stress loadingKWPS

J ¼ 60 and 80 MPaffiffiffiffiffimp

relevant for LOCA situations (consid-

ered by EDF) have been used. The prestress temperature, TWPS,has been set to �25 �C and the reloading temperature to �150 �Cwhere a significant number (6) of isothermal fracture toughnesstests have been obtained. Thermomechanical loading paths havebeen chosen so as to cross isothermal toughness tolerance boundscurves (see Fig. 3b) for constant load while cooling. The tempera-ture rate was set to �1:5 �C mn�1. 9 LCF (Load–Cooling–Fracture)(Fig. 4) and 9 LTF (Load–Transient–Fracture) (Fig. 5) cycles wereperformed. The elasto-plastic stress intensity factor at fracture,

K fJ after WPS was computed following [27] with the load vs. crack

mouth opening displacement curve, using the elastic slope ofprestressing. Finite elements simulations have confirmed that suchmethodology gives accurate KJ values.

All 18 specimens got past the transient thermomechanical load-ing paths, and failed by brittle fracture at the reloading tempera-

ture after significant reloading, i.e. K fJ > KWPS

J . No clear difference

0

50

100

150

200

−20 0 20 40 60 80 100 120

K12

.5m

mJc

(MPa.

√ m)

T (◦C)

Iso.LCTF − 70

(a)

0

50

100

150

200

−20 0 20 40 60 80 100 120

K12

.5m

mJc

(MPa.

√ m)

T (◦C)

Iso.LCTF − 80a

(b)

0

50

100

150

200

−20 0 20 40 60 80 100 120

K12

.5m

mJc

(MPa.

√ m)

T (◦C)

Iso.LCTF − 80b

(c)

0

50

100

150

200

−20 0 20 40 60 80 100 120

K12

.5m

mJc

(MPa.

√ m)

T (◦C)

Iso.LCTF − 80c

(d)

Fig. 7. Load–Cool–Transient–Fracture (LCTF) tests performed on 0.5 T CT specimens at irradiated state. Thermomechanical loading paths are superposed to the results ofisothermal toughness tests as well as to margin-adjusted 2% tolerance bound of the Master Curve, with T0 þ DT0 ¼ 42 �C. A dotted line is used for the decreasing load part ofthe path, as the elasto-plastic stress intensity factor is not defined for non-proportional loading.

0

50

100

150

200

−20 0 20 40 60 80 100 120

K12

.5m

mJc

(MPa.

√ m)

T (◦C)

Iso.LCIKF − 80a

(a)

0

50

100

150

200

−20 0 20 40 60 80 100 120

K12

.5m

mJc

(MPa.

√ m)

T (◦C)

Iso.LCIKF − 80b

(b)

Fig. 8. Load-Cool-Increase K Fracture (LCIKF) tests performed on 0.5 T CT specimens at irradiated state. Thermomechanical loading paths are superposed to the results ofisothermal toughness tests as well as to margin-adjusted 2% tolerance bound of the Master Curve, with T0 þ DT0 ¼ 42 �C. The slopes jDK=DTj are equal to (a) 0:02 MPa

ffiffiffiffiffimp

and (b) 0:04 MPaffiffiffiffiffimp

.

286 J. Hure et al. / Journal of Nuclear Materials 464 (2015) 281–293

between the two types of loadings (LCF – LTF) was observed for asame level of preloading.

This is probably due to the relative small slope used for LTFcycles. These tests confirmed the Warm-PreStress effect for thematerial used in this study at the unirradiated state, and will beused as a reference case for the modeling presented inSection 4.2.1.

3.2. Irradiated state

Twenty-four 0.5 T CT specimens have been tested for irradiatedmaterial following thermomechanical loadings, as shown inFigs. 6–8. LCF (Load–Cooling–Fracture) (Fig. 6), LCTF (Load–Cooling Transient Fracture) (Fig. 7) and LCIKF (Load CoolingIncreasing-K Fracture) (Fig. 8) cycles were performed with

Table 6Warm-PreStress tests results for the irradiated material. / corresponds to the fluence (E > 1 MeV), Tirr and Ttest to the irradiation and test temperature, respectively.TWPS ; Tr ; Tf ;KWPS ;Kr and Kf are defined in Fig. 1. KJ corresponds to the elastoplastic stress intensity factor, without length correction. a0 is the initial crack length, measuredaccording to [27] and Kr to the unloading load as defined in [7].

Cycle / (E > 1 MeV)

ð1023 n:m�2ÞTirr

ð�CÞa0

ðmmÞTWPS

ð�CÞK12:5mm

J;WPS

ðMPaffiffiffiffiffimpÞ

Tr ð�CÞ Kr

ðMPaffiffiffiffiffimpÞ

Tf

ð�CÞK12:5mm

J;f

ðMPaffiffiffiffiffimpÞ

K12:5mmJ;f =K12:5mm

J;WPS

13.3 289 13.90 100 65 – – �5 74 1.1413.2 292 13.87 100 65 – – �5 101 1.55

LCF-60 13.8 286 13.94 100 65 – – �5 78 1.2013.7 286 13.90 100 64 – – �5 74 1.1614.2 286 13.91 100 64 – – �5 73 1.1413.5 284 13.90 100 72 – – 10 79 1.10

LCF-70 14.1 284 13.87 100 73 – – 10 78 1.0713.6 284 13.94 100 74 – – 10 80 1.08

LCTF-70 13.7 284 13.87 100 73 5 43 �5 99 1.3613.6 286 13.93 100 74 5 43 �5 81 1.09

LCTF-80a 13.2 292 13.84 100 82 30 40 �5 100 1.2213.7 292 13.85 100 84 30 40 �5 115 1.3712.5 286 13.87 100 83 5 22 �5 108 1.30

LCTF-80b 13.7 282 13.91 100 84 5 22 �5 95 1.1313.6 282 13.90 100 84 5 20 �5 99 1.1812.0 287 13.53 100 82 30 20 10 89 1.09

LCTF-80c 13.6 282 13.87 100 83 30 27 10 113 1.3614.2 282 13.92 100 83 30 20 10 113 1.3611.2 284 13.85 100 83 100 85 �5 114 1.37

LCIKF-80a 11.0 284 13.88 100 82 100 84 �5 100 1.2211.1 284 13.90 100 83 100 85 �5 95 1.1410.0 286 13.85 100 85 100 87 �5 106 1.25

9.7 286 13.82 100 84 100 84 �5 123 1.46LCIKF-80b 9.7 286 13.82 100 89 100 93 �5 96 1.08

9.6 286 13.87 100 85 100 89 �5 114 1.34

J. Hure et al. / Journal of Nuclear Materials 464 (2015) 281–293 287

KWPSJ ¼ 60 (LCF cycles), 70 (LCF and LCTF) and 80 MPa

ffiffiffiffiffimp

(LCTFand LCIKF). For LCTF cycles, different slopes DK=DT were testedduring cooling. As shown in Fig. 7, K values at the end of coolinghave been chosen either at the minimum of isothermal fracturetoughness values (Fig. 7a and b) either well below the MasterCurve 2% isoprobability (Fig. 7c and d). For all cycles, TWPS; Tf andKWPS have been chosen to be relevant in LOCA situations.

All 24 specimens got past the transient thermomechanical load-ing paths, and failed by brittle fracture at the reloading tempera-

ture after reloading, i.e. K fJ > KWPS

J . Figs. 6, 7 confirm for LCF andLCTF cyles for the fluence level corresponding to more than60 years of operation the first principle of WPS effect, i.e. no crackpropagation if the load is held constant of decreased at the temper-ature decreases.

Data relative to all the tests are given in Table 6. For all of thetests performed in this campaign, a reloading at a level higherthan KWPS was observed to trigger brittle fracture. The ratioK12:5mm

J;f =K12:5mmJ;WPS varies between 1.07 and 1.55 and between 1.09

and 1.37 for LCF and LCTF cycles, respectively so that no clear effectof cycle types was evidenced.

A first evaluation of the margin regarding the first WPS princi-ple, i.e. no brittle fracture during cooling if constant or decreasingK, was carried out performing tests with an increasing load whiledecreasing the temperature as firstly described in [11] and furtherstudied in [12,28] for unirradiated 16MND5 steel. As few speci-mens at the irradiated state were available, the slopes jDK=DTjhave been determined based on F.E. simulations (seeSection 4.2.1) so that the fracture process zone, defined by the sizeof the plastic zone where plasticity is activated (i.e. with anincreasing plastic strain during loading) has to decrease whilecrossing the isothermal fracture toughness bounds. This criteriawas shown to be conservative for WPS cycles with increasing Kduring cooling for unirradiated materials [28].

Slopes jDK=DTj of 0.02 (5 tests) and 0.04 (2 tests) MPaffiffiffiffiffimp �C�1

were tested in this study. A K12:5mmJ;WPS value of 80 MPa

ffiffiffiffiffimp

was chosento perform these tests. Results of the 7 tests are given in Fig. 8 whereit is shown that all the specimens survived to the transients and thata reloading was necessary to trigger cleavage fracture. Although thenumber of LCIKF tests performed in this study is not statisticallysignificant, these results confirm that a positive slope jDK=DTj canbe applied to the irradiated material after it has been submitted toa Warm-prestress. Moreover it is confirmed that the criterionproposed in [28] for unirradiated material is conservative as nospecimen failed during this campaign and can be applied forirradiated materials which show a weak variation of yield stress inthe temperature range where the cooling phase undergoes.

As a summary of the experimental part of this study, a 16MND5RPV steel has been irradiated up to a fluence corresponding tomore than 60 years of operation in French PWR and mechanicallycharacterized. Several types of WPS cycles have been performedincluding cycles where the load increases during the coolingtransient.

Measured hardening and embrittlement are in accordance withprevious studies [29] which confirms that increasing the flux bytwenty (4:8 � 1016 in this study against 8 � 1017 n.m�2 s�1 in [29])has no marked effect on mechanical properties. All tests confirmedthe WPS effect on the irradiated material, i.e. no fracture if the loadis held constant or decreases while the temperature decreases.Additional tests on irradiated material have confirmed that aftera Warm-prestress a reloading is possible during the transient. Amaximum slope of 0.04 MPa

ffiffiffiffiffimp �C�1 has been applied in this

study. Fractographic investigations by SEM (not presented here)on few specimens at the irradiated state have shown that the mainmode of fracture at the initiation site is transgranular cleavagealthough few intergranular facets can be observed in the vicinityof the triggering site.

40

50

60

70

80

90

100

110

120

LCF− 60

LCF− 80

LTF− 60

LTF− 80

K12

.5m

mJ,f

(MPa.

√ m)

ACEWallin 5% − 95%

(a)

40

60

80

100

120

140

LCF− 60

LCF− 70

LCTF

− 70

LCTF

− 80a

LCTF

− 80b

LCTF

− 80c

LCIK

F− 80

a

LCIK

F− 80

b

K12

.5m

mJ,f

(MPa.

√ m)

ACEWallin 5% − 95%

(b)

Fig. 9. Comparisons of toughness after WPS to the predictions of Wallin’s and ACE models, for (a) unirradiated and (b) irradiated material.

288 J. Hure et al. / Journal of Nuclear Materials 464 (2015) 281–293

4. Prediction of effective fracture toughness after WPS

4.1. Engineering models

Various engineering models have been proposed in the litera-ture to predict the effective toughness after warm-prestressing(see e.g. [30,7,31,32]). These models are known as simplified orengineering models as for most of them, they describe, either in adeterministic or statistic manner, only partially the origins of theWPS effect. Based on the Master Curve approach, Wallin’s model[7], derived from the statistical analysis of data published in the lit-erature, has been used recently in several studies. Predictive for-mula for LCF and LUCF (Load–Unload–Cool–Fracture) tests wereproposed in [7], however the later is not fully relevant to describeLTF/LCTF cycles performed in this study, so that only LCF is consid-ered in the following. For LCF cycles, the effective fracture tough-ness after warm-prestressing, Kf , is given by:

Kf ¼max KIcðTÞ; 0:15KIc þmin KWPS; Kr þffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiKIcðTÞðKWPS � KrÞ

q� �h i;

ð2Þ

where KIc is the isothermal toughness at the reloading temperature,and KWPS is the prestress stress intensity factor, Kr is the minimalstress intensity factor during the transient which is equal to KWPS

in case of LCF cycle.Recently another WPS criterion was proposed in the frame of

the efforts towards WPS implementation in French RSE-M code.By construction, the ACE [33] criterion aims to provide a conserva-tive deterministic lower bound for loading conditions relevant topressurized thermal shock and calibrated over a large WPS data-base with differents types of cycles and different specimen geome-tries. Following ACE criterion, the effective fracture toughness afterwarm-prestressing is given by:

Kf ¼max KIcðTÞ; min Kr þKWPS

2;KWPS

� �� �ð3Þ

where Kr is the minimal stress intensity factor during the transient.Comparisons of experimental fracture toughness values after

WPS loading for the 18 tests at the unirradiated state and 24 testsat the irradiated state are shown in Fig. 9a and b, respectively.Although Eq. (2) is not strictly appropriate to describe effectivefracture toughness for LTF, LCTF and LCIKF cycles, 5% and 95% prob-ability bounds are also shown for these cycles on Fig. 9. Overall, Eq.

(2) gives mean predictions in agreement with experimental data.For LCF cycles at the unirradiated state, the 5% probability boundgiven by Wallin criterion (Eq. (2)) is also conservative. Howeverfor irradiated state, it is shown in Fig. 9b that for LCF-70 cycle,the 5% probability bound is slightly higher than all the experimen-tal fracture toughness values obtained, which indicate that the 5%probability bound given by Eq. (2) cannot be taken as a conserva-tive lower bound. This result is confirmed for other cycle types per-formed in this study. On the other side, comparisons reported inFig. 9 shown that for all the WPS tests performed in this study,the ACE criterion predicts an effective fracture toughness whichis lower that the minimum experimental values thus confirmingthe expected conservatism of ACE criterion.

4.2. Local approach to fracture model

In this section, Local Approach to Fracture (LAF) is applied toevaluate its capacity to predict the effective fracture toughness asa function of KWPS level and type of WPS cycles. LAF methodology isbased on accurate description of the stress–strain fields in the pro-cess zone of fracture combined with the use of a physically-basedfracture criterion. Firstly, a constitutive law is proposed and cali-brated in order to reproduce the mechanical behavior of16MND5 steel as a function of temperature and fluence.Considering WPS application, a particular attention is paid on thebehavior at large deformations and on kinematic hardening deter-mination based on tension–compression tests. Secondly, the cleav-age fracture model and its calibration are presented. Finally,fracture toughness predictions after warm-prestressing obtainedfrom F.E simulations are presented and discussed.

4.2.1. Constitutive law and finite elements simulationsFollowing the results reported in [11] for unirradiated RPV

material, an elasto-viscoplastic constitutive law with both isotro-pic and kinematic hardening was assumed to describe the mechan-ical behavior of the material used in this study. Stress tensor r isrelated to the elastic strain tensor �el with Hooke’s law:

r ¼ Emð1þ mÞð1� 2mÞ tr�el

h i1þ E

1þ m�el ð4Þ

where E and m are the Young’s modulus and Poisson’s ratio, respec-tively. The yield surface is given by the following formula:

Table 7Unirradiated material. Parameters of the constitutive law identified in the temper-ature range ½�150 : 300� �C.

E (GPa) 200m 0.3R0 (MPa) 430þ 10 exp½�0:019 T ð�CÞ�Rl (MPa) 461þ 28 exp½�0:016 T ð�CÞ�Q1 (MPa) 0:45R0

b1 12C1 (MPa) 4R0

D1 25k1 ðMPa sn1 Þ max½80� 0:5 T ð�CÞ;0�n1 7k2 ðMPa sn2 Þ 0.185n2 1.15

J. Hure et al. / Journal of Nuclear Materials 464 (2015) 281–293 289

Fðr;X; pÞ ¼ r� X� �

eq� R0 � Q 1½1� expð�b1pÞ� with

_X ¼ C1 _�p � D1X _p ð5Þ

where r� X� �

eq¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi½3=2� s� X

� �: s� X� �r

is the Von Mises equiv-

alent stress, with s the deviatoric stress tensor, and

_p ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi½2=3� _�p : _�p

� �rthe cumulated plastic strain rate, with _�p the

plastic strain tensor. R0 is the initial yield stress, Q1; b1;C1 and D1

material parameters which are given in Table 7. Plastic flow is sup-posed to obey the normality rule:

_�p ¼ _p@F@r

with1_p¼ F

k1

�n1

þ Fk2

�n2

ð6Þ

with the brackets are defined as < : >¼maxð:;0Þ. fk1; n1g andfk2;n2g are viscous parameters. The two terms in the expressionof the equivalent plastic strain rate _p (Eq. (6)) are inferred fromthe model proposed in [34,35]. Each term is representative of adeformation mechanism: (1) Peierls friction, (2) phonon drag.Large deformations are accounted for by using the logarithmicstrain framework developed by Miehe et al. [36]. Eqs. (4)–(6) aresolved by an implicit method with the open-source MFront codegenerator [37]. Numerical simulations have been performed usingthe code generated by MFront with Cast3M finite element software[38], with quadratic full integration elements. Mesh convergencehas been performed for all results reported in this study. 3DCompact Tension specimens mesh includes a fine meshing of thecrack tip with a crack tip radius taken as 5 lm.

Fig. 10. Stress variations associated with strain rate variations, as a function oftemperature, for unirradiated (open black symbols) and irradiated (filled redsymbols) material (/ ¼ 10 � 1023 n:m�2). Solid and dashed lines correspond to theviscous stress given by Eq. (6) with identified parameters (Table 7). (For interpre-tation of the references to colour in this figure legend, the reader is referred to theweb version of this article.)

Fig. 11. Dimensionless tensile curves for unirradiated material. Rescaling stress bya flow stress R0ðTÞ shows the existence of a master curve for the hardening behaviorof the material in the temperature range ½�150 : 300� �C.

4.2.2. Identification of the constitutive law11 parameters fE; m;R0;Q 1; b1; C1;D1; k1; n1; k2;n2g need to be

identified for both unirradiated and irradiated materials, each ofthem potentially depending on temperature. According to previousstudies [35,39], Young’s modulus E and Poisson’s ration m wereassumed to be independent of temperature and irradiation, andequal to 200 GPa and 0.3, respectively. Viscous parametersfk1; n1g and fk2;n2g aim at reproducing strain rate effects for bothlow and high strain rate, respectively. In this study, all experimentscorrespond to low strain rates regime, thus the values of fk2;n2gare assumed to be identical for unirradiated and irradiated mate-rial to those adjusted in another study on a similar unirradiatedmaterial [35]. Identification of fk1; n1g parameters was based onsupplementary tensile tests performed with varying strain ratesduring the test (see Section 2.2). Fig. 10 resumes the values ofstress jumps associated with a change of strain rate, as a functionof temperature for both unirradiated and irradiated materials. At awhole, considering the mean values of the stress jumps, the vis-cous behavior of the material appears to be weakly affected bythe irradiation, for a fluence of 10:3 � 1023 n:m�2 (E > 1 MeV) so thatthe parameters fk1;n1g will be considered independent of theirradiation in this study. For unirradiated material, whatever thetemperature, the mean value of the stress jump is higher for astrain rate variation from 5 � 10�4 to 5 � 10�3 s�1 than from5 � 10�5 to 5 � 10�4 s�1 whereas this difference is less marked atthe irradiated state. From Fig. 10, it is inferred that for tempera-tures at þ100 �C and above, the viscosity becomes negligible.

Rescaling all stress–strain curves by a flow stress R0 for unirra-diated material (Fig. 11) suggests the existence of a master curvefor the hardening behavior of the material, i.e. the evolution ofhardening parameters with temperature can be writtenQ 1ðTÞ ¼ q1 R0ðTÞ and C1ðTÞ ¼ c1 R0ðTÞ, where q1 and c1 are constantparameters.

Fig. 11 also shows for low temperature tests at low strain astress plateau resulting from Piobert–Lüders instability whereinhomogeneous deformations appear along the gage length of ten-sile specimens. The real stress–strain curve is thus unknown overthe range of macroscopic plastic strain where this instabilityoccurs. However, the real true stress is close to the value of thestress plateau, as for example shown in [40]. It has been chosen

200

400

600

800

1000 ε̇ = 5.10−4 s−1

Unirradiated

1200

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14

σ(M

Pa)

p

−150◦C−125◦C−75◦C−25◦C

20◦C300◦C

Simulation

(a)

−2000

−1500

−1000

−500

0

500

1000

1500

−0.2 −0.15 −0.1 −0.05 0 0.05 0.1

ε̇ = 5.10−4 s−1

Unirradiated

F/S

0(M

Pa)

Δd/d0

10%20%40% 30%

20%

−145◦C−100◦C

20◦CSimulation

(b)

Fig. 12. Comparisons of experimental data and simulations on unirradiated material, for tensile tests on flat specimens (true stress r vs. cumulated plastic strain p) (a) andtension–compression on axisymmetric notched specimens (mean stress F=S0 vs. mean radial strain Dd=d0, where d0 is the initial minimal diameter of the notch, andS0 ¼ pðd0=2Þ2).

400

500

600

700

800

900

1000

0 0.01 0.02 0.03 0.04

ε̇ = 5.10−4 s−1

φ = 11 − 13.1023 n.m−2

0.05 0.06 0.07 0.08 0.09 0.1

σ(M

Pa)

p

−75◦C−25◦C

20◦C300◦C

Simulation

(a)

−1500

−1000

−500

0

500

1000

1500

−0.12 −0.1

ε̇ = 5.10−4 s−1

φ = 10.1023 n.m−2

−0.08 −0.06 −0.04 −0.02 0 0.02

F/S

0(M

Pa)

Δd/d0

10%15%20%

20◦CSimulation

(b)

Fig. 13. Comparisons of experimental data and simulations on irradiated material, for tensile tests on flat specimens (true stress r vs. cumulated plastic strain p) (a) andtension–compression on axisymmetric notched specimens (mean stress F=S0 vs. mean radial strain Dd=d0, where d0 is the initial minimal diameter of the notch, andS0 ¼ pðd0=2Þ2). For a given temperature, closed and open symbols correspond to different level of fluence (see Table 3).

290 J. Hure et al. / Journal of Nuclear Materials 464 (2015) 281–293

to model the observed behavior, so that the yield surface is modi-fied as:

Fðr;X; pÞ ¼ r� X� �

eq�maxðR0 þ Q 1½1� expð�b1pÞ�;RlÞ ð7Þ

where Rl is the value of the stress plateau, derived from the engi-neering stress–strain curves.

Mechanical behavior at large deformations and kinematic hard-ening have been determined from tension–compression tests onaxisymmetric notched tensile specimens (minimal diameter/0 ¼ 3:5 mm and notch radius rn ¼ 1:4 mm). For both unirradiatedand irradiated materials, tension–compression tests were per-formed for different values of cumulated plastic strainp ¼ 2 lnðd0=dÞ obtained before compression, where the diameterd is measured with diametral extensometer. For the unirradiatedmaterial, tension–compression tests were performed at�150 �C;�100 �C and room temperature (RT) whereas tests wereperformed at RT for irradiated material. A compression-tensiontest was also performed at RT for unirradiated materials.

For the unirradiated material, the set of parameters determinedto reproduce the tests in the temperature range ½�150 �C : þ300 �C�is given in Table 7. A good agreement between modeling and

experimental stress–strain curves is obtained including for theLüders plateau as shown on Fig. 12a. The model is shown onFig. 12b to reproduce with a very good accuracy the behavior atlarge deformation, up to 40%.

Effect of irradiation on the tensile behavior is considered fol-lowing the work proposed in [41,42] where irradiation is consid-ered as (i) an increase of the yield stress, (ii) a decrease of thestrain hardening rate. Two terms were introduced, Dri

Y and Dpi,the increase of yield stress and an equivalent plastic strain incre-ment due to irradiation, respectively. A two parameters strategyis thus considered here, where the increase of the yield stressand decrease of the hardening capacities are considered separately,such as:

Rirr0 ¼ aR0 Q irr

1 ¼ Q 1 expð�b1DpÞ Cirr1 ¼ C1 expð�D1DpÞ ð8Þ

where a and Dp are two constant parameters which depends of thelevel of irradiation. The stress plateau Rl is derived considering

Rirrl ¼ aRl. Numerical simulations have been performed to adjust

these two parameters so as to reproduce tensile curves and ten-sion–compression tests on irradiated material (Fig. 13). Most ofthe data used for the identification corresponds to fluence of

0

5

10

15

20

Unirradiated

0 0.2 0.4 0.6 0.8 1 1.2 1.4

F(k

N)

CMOD (mm)

−80◦CSimulation

(a)

0

0.2

0.4

0.6

0.8

1σu = 2875MPa, m = 16

Unirradiated

1.2

0 20 40 60 80 100 120

Pf

Kelasf (MPa.

√m)

−150◦C−125◦C−100◦C

Simulation

(b)

Fig. 14. (a) Comparison of Force F vs. Crack Mouth Opening Displacement (CMOD) experimental data and simulation for unirradiated material. (b) Cumulative fractureprobability as a function of stress intensity factor for unirradiated material: comparison of experimental evaluation (with Pf ¼ ½i� 0:5�=N, where i corresponds to the ithspecimen tested and N the total number of specimens tested) to predictions from Beremin model.

J. Hure et al. / Journal of Nuclear Materials 464 (2015) 281–293 291

½10� 11� � 1023 n:m�2. However, comparison in Fig. 13 shows thatthe constitutive law reproduce also accurately tensile curves for afluence of 13 � 1023 n:m�2, relevant for 0.5 CT specimens.1 Valuesa ¼ 1:35 and Dp ¼ 0:012 have been identified in the temperaturerange ½�75 : 300� �C.

It is noted that considering a pure pre-strain effect for theeffect of irradiation on macroscopic tensile properties as proposedin [43] would lead with the value Dp determined to a hardeningof a¼1þ½ðQ1=R0Þð1�expð�b1DpÞÞ�þ½ðC1=D1R0Þð1�expð�D1DpÞÞ�¼1:1, which greatly underestimates the observed hardening.

4.2.3. Cleavage fracture modelLocal Approach to Fracture Beremin model [15] is used to pre-

dict cleavage fracture probability after WPS transient. Bereminmodel is based on the weakest link assumption among apower-law distribution of pre-existing flaws.

The model uses the following definition of a local effectivestress for brittle failure rIp:

rIp ¼rI if _p > 0; p > pc

0 otherwise

�ð9Þ

where rI is the maximum principal stress of r. The condition_p > 0 expresses the fact than failure can only occur when plasticdeformation occurs. pc is the critical strain over which cleavagecan occur. This brittle failure model can be applied as apost-processor of calculations including ductile tearing or WPSdecreasing loadings. Considering that each material point is sub-jected to a load history, rðtÞ; pðtÞ (t = time) the probability of sur-vival of each point at time t is determined by the maximum loadlevel in the time interval ½0; t�. An effective failure stress ~rIp is thendefined as:

~rIpðtÞ ¼ maxt02½0;t�

rIpðt0Þ ð10Þ

The failure probability, Pf , is obtained by computing the Weibullstress, rw:

rw ¼Z

V

~rmIp

dVV0

� �1=m

Pf ¼ 1� exp � rw

ru

� �m� �ð11Þ

1 As a consequence of the small exponent of fluence on the evolution of mechanicalproperties (Eq. (1)).

where the volume integral is taken over the whole volume of thespecimen. V0 is a reference volume which can be arbitrarily fixedtaken as 100 lm3 in this study. m is the Weibull modulus whichdescribes the scatter of the distribution, ru is a scaling parameterwhich can be interpreted as a measure of the mean cleavagestrength of a reference volume V0. Model parameters (ru;m; pc)must be adjusted. pc ¼ 0 has been chosen in this study.

Considering the thermomechanical history encountered in WPScycles, an adaptation of the original model to account for thetemperature dependence of the model parameters proposed in[39] will be used in this study. The rupture probability of a volumeelement is then no longer represented by rIp but by x ¼ ðrIp=ruÞm

where both ru and m may be temperature dependent. The loadhistory integrating stress variations but also temperature changesis represented by:

~xðtÞ ¼ maxt02½0;t�

xðt0Þ ð12Þ

Finally the failure probability is given by:

PRðtÞ ¼ 1� expð�XðtÞÞ with XðtÞ ¼Z

V

~xðtÞdVV0

: ð13Þ

4.2.4. Calibration of cleavage model parametersThe parameters ru and m of the model for brittle fracture have

been identified based on finite element simulation of 0.5CT speci-mens. As shown in Fig. 14a, the proposed constitutive law is ablewith the identified parameters to reproduce very accuratelyforce-opening curve for 0.5 T CT specimens. For the unirradiatedstate, values of ru ¼ 2875 MPa and m ¼ 16 have been determinedon the temperature range ½�150 : �100 �C� and are shown to beable to reproduce experimental toughness probability of fracturein the lower shelf of the DBT, in the temperature range[�150 �C : �100 �C] (Fig. 14b). The identified parameters are fullyconsistent with the ones obtained in [39] (ru ¼ 2925 MPa andm ¼ 17:8) for the same range of temperatures.

The same procedure is applied on the irradiated material. mvalue is kept constant as it is related to the statistical distributionof flaws in the material, and it is supposed that irradiation does notmodified the microdefects involved in cleavage fracture. Asmicrostructural changes induced by irradiation might howeverchange fracture toughness at the microscale, ru is re-identifiedon irradiated material, imposing a minimum value consistent withthe identification on unirradiated material rirr

u P 2875 MPa.

40

50

60

70

80

90

100

110

120

LCF− 60

LCF− 80

LTF− 60

LTF− 80

K12

.5m

mJ,f

(MPa.

√ m)

Beremin 5% − 95%Unirradiated

(a)

40

60

80

100

120

140

LCF− 60

LCF− 70

LCTF

− 70

LCTF

− 80a

LCTF

− 80b

LCTF

− 80c

LCIK

F− 80

a

LCIK

F− 80

b

K12

.5m

mJ,f

(MPa.

√ m)

Beremin 5% − 95%φ = 10 − 14.1023n.m−2

(b)

Fig. 16. Comparisons of fracture toughness after WPS to the predictions of Beremin model fracture probabilities for (a) unirradiated and (b) irradiated material. On this graph,tests where reloading were performed at þ10 �C are colored in gray.

0

5

10

15

20

0 0.2

φ = 13.1023 n.m−2

0.4 0.6 0.8 1

F(k

N)

CMOD (mm)

45◦CSimulation

(a)

0

0.2

0.4

0.6

0.8

1

1.2

0 20

φ = 12 − 14.1023 n.m−2σu = 2905 + 6.5T (T ∈ [−5 : 45]◦C), m = 16

40 60 80 100 120

Pf

Kelasf (MPa.

√m)

−5◦C45◦C

Simulation

(b)

Fig. 15. (a) Comparison of Force F vs. Crack Mouth Opening Displacement (CMOD) experimental data and simulation for irradiated material. (b) Cumulative fractureprobability as a function of stress intensity factor for irradiated material: comparison of experimental evaluation (with Pf ¼ ½i� 0:5�=N, where i corresponds to the ithspecimen tested and N the total number of specimens tested) to prediction from Beremin model.

292 J. Hure et al. / Journal of Nuclear Materials 464 (2015) 281–293

As for the unirradiated material, the experimentalforce-opening curve of 0.5 T CT specimen is very well reproducedwith the identified constitutive law as shown on Fig. 15a wherethe simulation at þ45 �C is reported. A this temperature, a slightoverestimation of the load for large opening is observed. Fig. 15b

shows the fracture probabilities as a function of the level of Kelasf .

For T ¼ �5 �C, the model (thick lines) underestimates the fractureprobabilities with ru ¼ 2875 MPa determined at the unirradiatedstate. A better agreement with experimental data will be obtainedusing a lower ru value. A decrease of ru value would be the resultof a decrease of the mean strength of the RVE (representative vol-ume element) due to irradiation which can be reasonably inferred.However without further microstructural investigations a mini-mum value ru consistent with the value obtained at the unirradi-ated state was kept, keeping in mind a possible overestimation ofresults when applying to WPS experiments. Contrary to the caseof unirradiated material where ru has been determined in therange [�150 �C : �100 �C],a ru value independent of thetemperature is not able to reproduce fracture probability inthe range of temperature considered ([�5 �C : þ45 �C]). A valueof ru ¼ 3200 MPa for T ¼ þ45 �C has been identified. Betweenthese two temperatures, the evolution of ru is supposed to be

linear. A similar evolution of ru with temperature is also observedon unirradiated material typically above �80 �C [39] and may berelated to changes of micro-toughness properties (due to plasticstrain, crack arrest see e.g [16] . . .).

4.2.5. Predictions of fracture toughness after warmpressingAll WPS cycles performed in this study have been simulated

with finite elements on 3D 0.5 T CT specimens using the identifiedconstitutive law. Beremin model post-processing of the simula-tions with the identified parameters (Section 4.2.3) leads to theprediction of fracture toughness probabilities. Fig. 16 shows thecomparison between the experimental elastoplastic fracturetoughness values K12:5mm

J;f and the 5% and 95% probability predic-tions obtained from the Beremin model for the different WPScycles for both unirradiated and irradiated materials.

For the unirradiated material (Fig. 16a), Beremin model givespredictions in good agreement with experimental results: 5% frac-ture probabilities model is a lower bound whatever the WPS cycleconsidered, but one test LTF-80 and more than 50% of experimentalresults lie between 5% and 95% fracture probabilities of the model.For the irradiated material (Fig. 16b), model predicts also correctlythe fracture toughness after prestressing. Again the 5% fracture

J. Hure et al. / Journal of Nuclear Materials 464 (2015) 281–293 293

probabilities model is a lower bound whatever the WPS cycle consid-ered and the model globally gives conservatives estimates. Also themodel is able to capture the large scatter observed experimentallyfor the effective toughness after prestressing for the irradiatedconditions.

As a summary of the modeling part, an elasto-viscoplastic con-stitutive law including isotropic and kinematic hardening has beenidentified for a 16MND5 steel. This law reproduces accuratelyexperimental results for tensile tests and large deformations ten-sion–compression tests, both with temperature and irradiation. ABeremin model for cleavage fracture taking into account thermo-mechanical transients has been parametrized on isothermal frac-ture toughness tests at both unirradiated and irradiated state. Ithas been shown that satisfactory predictions of the effective tough-ness after WPS for all the cycles considered in this study can beobtained for both unirradiated and irradiated material.

5. Discussion and conclusions

A508 Cl.3 RPV steel has been irradiated up to a maximal fluenceof 13:9 � 1023 n:m�2 (E > 1 MeV) at a flux of 4:8 � 1016 n:m�2 s�1 andtemperature of 288 �C under mixed spectrum representative ofPWRs in the MTR Osiris. An hardening of 127 MPa has beenobserved at 300 �C for a fluence of 13:2 � 1023 n:m�2.Embrittlement has been quantified through both the evaluationof the shift of the T56J index with Charpy V-Notch tests and refer-ence temperature T0 of the Master Curve approach with toughnesstests on 0.5 T CT specimens, leading to DT56Jð10:2 � 1023 n:m�2Þ ¼þ84 �C and DT0ð12:8 � 1023 n:m�2Þ ¼ þ126 �C. The shift of T56J

index is in good agreement with irradiation-induced embrittle-ment formula given in RSE-M code which predicts a shift of82.5 �C although the present fluence is much larger than the actualupper bound of Eq. (1) for fluence (i.e. 11:5 � 1023 n.m2 (E > 1 MeV)).All thermomechanical loadings performed on the irradiated mate-rial have confirmed the Warm-PreStress effect, i.e. no fracture ifthe load is held constant or decreased while temperaturedecreases. Two engineering models proposed in the literature(Wallin and ACE models) have been shown to give predictions ingood agreement with experimental data. A constitutive law havebeen proposed to model the behavior of the unirradiated andirradiated material. This law is able to reproduce very accuratelytensile curves and tension–compression tests on the whole rangeof temperature ½�150 �C : 300 �C� up to strain of 40%. Finally,Local Approach to cleavage Fracture has been applied to assessthe cleavage fracture after warm-prestressing. Beremin modeladapted for thermomechanical transients has been applied to bothunirradiated and irradiated material. After calibration of theparameters of the model on isothermal toughness tests, it has beenshown that the model is able to predict quite accurately the effec-tive toughness after warm-prestressing.

Acknowledgments

We thank Ph. Coffre, J. Pegaitaz, L. Ziolek, K. Jaakou for themechanical tests, C. Mallet for fractographic observations, and G.Perez for developing the software used to perform WPS tests.This study has been realized in the frame of a collaborative projectbetween CEA, EDF and AREVA NP.

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