E-Journal of Advanced Maintenance Vol.7-2 (2015) 166-171
Japan Society of Maintenology

Fracture Toughness Curves of Japanese Reactor Pressure Vessel Steels
considering Neutron Irradiation Embrittlement
Kentaro YOSHIMOTO 1,*, Takatoshi HIROTA 2 and Hiroyuki SAKAMOTO 2
1
2

Mitsubishi Heavy Industries, Ltd. 1-1 Arai-cho Shinhama 2-chome Takasago, 676-8686, Japan
Mitsubishi Heavy Industries, Ltd.1-1 Wadasaki-cho 1-chome, Hyogoku, Kobe, 652-8585, Japan

ABSTRACTIn Japanese nuclear power plants, surveillance tests are conducted according to the Japan Electric Association
Code JEAC4201 in order to monitor the degree of embrittlement of reactor pressure vessel (RPV) material due
to neutron irradiation. Through the surveillance tests for Pressurized Water Reactor (PWR) plants, a large
number of fracture toughness data have been accumulated for Japanese RPV irradiated materials. New fracture
toughness curves have been developed adopting the Master Curve (MC) concept and these curves have beencorrelated with the Charpy V-notch 30 ft-lb transition temperature, Tr30 for evaluation against Pressurized
Thermal Shock (PTS) events. The developed curves are also intended to represent the 5% tolerance lower boundof fracture toughness trend incorporating fracture toughness variation depending on the product form, which
consists of plates, forgings and weld metals. In this study, the reliability of the curves is evaluated for predicted
Tr30 values in consideration of application to PTS evaluation for Japanese PWR plants and it was demonstrated
that the developed lower bound curve has reliability comparable to that for the measured Tr30 by adding amargin of 3 ºC to the predicted Tr30.
KEYWORDS

ARTICLE INFORMATION

Fracture Toughness, Master Curve, Reactor Pressure Vessel

Article history:
Received 21 November 2014
Accepted 22 June 2015

1. Introduction
Reactor pressure vessel (RPV) material is subjected to neutron irradiation embrittlement during
plant operation. In order to monitor the degree of embrittlement, surveillance tests have been
conducted for Japanese nuclear power plants based on the Japan Electric Association CodeJEAC4201[1]. The surveillance tests have resulted in the accumulation of a large number of fracture
toughness data for irradiated RPV materials of Japanese Pressurized Water Reactor (PWR) plants.
Considering such a situation, new fracture toughness curves have been developed for evaluation
against pressurized thermal shock (PTS) events. A major feature of the curves is that they adopt the
Master Curve (MC) concept utilizing the Charpy V-notch 30 ft-lb transition temperature, Tr30, as anindexing parameter instead of reference temperature To. The MC is a universal fracture toughnesstransition curve widely used to express the scatter and temperature dependence of fracture toughness
quantitatively for ferritic materials. The median curve of MC is expressed by the following equation.

K Jc ( med )  30  70 exp 0.019(T  To )
KJc(med)TTo[MPa√m](1): Median value of one inch-thickness (1T) equivalent fracture toughness: Temperature, in ºC: Reference temperature defined as a transition temperature at which themedian value of 1T-equivalent KJc is 100 MPa√m, in ºC

The newly developed curves are also intended to represent the 5% tolerance lower bound of thefracture toughness trend incorporating fracture toughness variation depending on the product form,*

Corresponding author, E-mail: kentarou_yoshimoto@mhi.co.jp

ISSN-1883-9894/10 © 2010 – JSM and the authors. All rights reserved.

166

K. Yoshimoto, et al./ Fracture toughness Curves of Japanese Reactor
Pressure Vessel Steels considering Neutron Irradiation Embrittlement

which consists of plates, forgings and weld metals.
In this study, the reliability of the curves is evaluated for predicted Tr30 values in consideration of
application to PTS evaluation for Japanese PWR plants.

2.

Procedure

UnirradiatedIrradiated500

Rolled plates (RP)

400
300
200
100
0
-300

-200

-100

0

100

200

600
500

UnirradiatedIrradiated400

Forgings (FS)Fracture toughness KJc (MPa√m)

600

Fracture toughness KJc (MPa√m)

Fracture toughness KJc (MPa√m)

2.1. Fracture toughness database
Fracture toughness data used to develop the curves are those obtained from surveillance tests for
RPV beltline region materials of 24 Japanese PWR plants. The materials include rolled plates(SA533B Cl.1 steel, RP), forgings (JIS SFVQ1A steel, which is equivalent to SA508 Cl.3 steel, FS)
and weld metals (WM). Figure 1 shows the temperature dependence of the fracture toughness data.
Data scatter seems to be large due to different fluence and material heat for each datum. The data for
irradiated materials tend to lie in the higher temperature region compared with those for unirradiatedmaterials because of neutron irradiation embrittlement.

300
200
100

600

UnirradiatedIrradiated

500
400

Weld metals (WM)

300
200
100
0

0
-300

-200

-100

T (ºC)

0

100

200

-300

T (ºC)(a) Rolled plates(b) Forgings
Fig. 1

-200

-100

0

100

200

T (ºC)(c) Weld metals

Fracture toughness data used for this study

2.2. Approach
2.2.1. Data screening and adjustment
Fracture toughness curves were developed based on the MC concept. As the first step of thisstudy, screening and adjustment of data were performed as described below;
 All the data obtained by 1/2TCT (compact tension specimen of one half inch thickness)
specimens are adjusted to the 1T equivalent values by Eq. (2) specified in ASTM E1921 [2].
Adjustment was not made for the data obtained by 1X-WOL (wedge opening loading specimenof one inch thickness) specimens because the data are just 1T values.
1/ 4

B 
K Jc ( x )  K min  K Jc ( 0)  K min   0  Bx 

KJc(x)
KJc(0)
Kmin
B0
Bx




(2)

: KJc for a specimen thickness Bx, in MPa√m: KJc for a specimen thickness B0, in MPa√m: 20 MPa√m,: gross thickness of tested specimen (side grooves are not considered), in mm: gross thickness of adjusted data (side grooves are not considered),
Bx =25.4mm in this study

The data in the lower shelf temperature region corresponding to T-To lower than -50 ºC, andthose exceeding KJc(limit) specified in ASTM E1921 are excluded.

K Jc(limit) b0
σys

Eb0 ys

30 1  2

[MPa√m]: Initial ligament, i.e. initial uncracked part of specimen width, in m
: 0.2% offset yield strength, in MPa
167

(3)

K. Yoshimoto, et al./ Fracture toughness Curves of Japanese Reactor
Pressure Vessel Steels considering Neutron Irradiation EmbrittlementEν: Elastic modulus (=206,000 MPa)
: Poisson’s ratio (=0.3)

2.2.2. Determination of indexing parameterIn the next step, an appropriate parameter for indexing fracture toughness data was examined. 1T
equivalent fracture toughness data, KJc(1T) were indexed by T-Tx, where Tx is one of the following
candidates, which could correlate fracture toughness data and are obtained generally in thesurveillance program.
 Reference temperature, RTNDT, in ºC
 Charpy V-notch 30ft-lb transition temperature, Tr30, in ºC
 Charpy V-notch 50ft-lb transition temperature, Tr50, in ºC
 Fracture appearance transition temperature corresponding to 50% shear fracture, Trs, in ºC
 Charpy V-notch 35mils lateral expansion transition temperature, Tr35M, in ºC
After that, the 1T-equivalent fracture toughness data indexed by each parameter were fitted to Eq. (4).

K Jc ( med )  30  70 exp 0.019(T  (Tx  Tt ))
ΔTt[MPa√m](4): Constant, which is corresponding to the difference between TO and Tx, in ºC

The constant ΔTt was determined so that the logarithm of the likelihood function expressed by Eq (5)becomes maximum value.
b 1  K Jc (i )  K min b  b K Jc (i )  K min    
F K Jc (i )    n exp  
K  K min 
K 0  K min  K 0  K min   
i 1

 0

b
: Weibull scale parameter (b=4)
K0: Weibull fitting parameter, in MPa√m
KJc(i): 1T-equivalent KJc datum, in MPa√mn(5)Finally, the temperature difference Δ(med) between KJc(i) data and KJc(med) curve were calculated by thefollowing equation.

 1
 K Jc (i )  30 Δ( med )  T  Tx  Tt   n70 0.019 


[ºC]

(6)

T-RTNDT
T-Tr30
T-Tr50
T-Trs
T-Tr35M

Material : RP

40
30
20
10
0

Material : FS
40
30

2
Irradiated(a) Rolled plates
Fig. 2

T-RTNDT
T-Tr30
T-Tr50
T-Trs
T-Tr35M

20
10
0

1
Unirradiated

50

50

1
Unirradiated2
Irradiated(b) Forgings

Standard deviation of Δ(med) ， σΔ (ºC)

50Standard deviation of Δ(med) ， σΔ (ºC)

Standard deviation of Δ(med) ， σΔ (ºC)

The standard deviation σΔ of Δ(med) was also calculated statistically. Figure 2 illustrates comparisons of
σΔ for each material data set. Although σΔ for Trs is the smallest among all indexing parameters, Tr30
was chosen because σΔ is relatively smaller for RP, WM and the shift of Tr30 due to neutron irradiation
is currently used for the irradiation embrittlement prediction in the integrity assessment of RPV [1].
T-RTNDT
T-Tr30
T-Tr50
T-Trs
T-Tr35M

Material : WM
40
30
20
10
0

1
Unirradiated2
Irradiated(c) Weld metals

Standard deviation of temperature difference Δ(med) between KJc and KJc(med) curve

168

K. Yoshimoto, et al./ Fracture toughness Curves of Japanese Reactor
Pressure Vessel Steels considering Neutron Irradiation Embrittlement

2.2.3. Definition of lower bound curves
The new fracture toughness curve was developed for each product form. The 1T-equivalent
fracture toughness data for irradiated materials with 5×1019 n/cm2 or more of neutron fluence were
employed for development of the curves because such data for irradiated materials with higher
fluence are more important for integrity assessment of irradiated RPV after 60 years of operation. The
5% tolerance bound was selected as the lower bound of fracture toughness considering the followings:
 ASME Sec.XI reference fracture toughness KIc curve is used for P-T limit determination, flaw
evaluation and design for operating conditions A and B, whose probabilities of occurrence arehigher than those of PTS events.
 5% tolerance lower bound MC has been adopted as fracture toughness lower bound in ASME
Code Case N-830 entitled “Direct Use of Master Fracture Toughness Curve for
Pressure-Retaining Materials of Class 1 Vessels”. It was also demonstrated that it has equivalentreliability to the conventional ASME Sec.XI KIc curve [4].
As a result, the lower bound curve is expressed by Eq. (7). The constant ΔTt in Eq. (7) was
calculated again so that the logarithm of likelihood function of Eq. (5) becomes maximum value.

K Jc (0.05)  25.2  36.6 exp 0.019(T  (Tr 30  Tt ))

[MPa√m](7)

KJc(0.05) : 5% tolerance lower bound of 1T-equivalent KJc

3.

Results

3.1 Evaluation of ΔTt [3]Figure 3 shows the temperature dependence of fracture toughness data indexed by the measured
Tr30 along with the developed fracture toughness curves. The ΔTt values in Eq. (7) are -15, 8, 14 ºC for
RP, FS and WM, respectively. The result implies that the difference between Tr30 and To depends on
the product form. As seen in Fig. 3, the fracture toughness data with 5×1019n/cm2 or more neutron
fluence seem to locate in the higher temperature region obviously for FS.

300

200

500
UnirradiatedIrradiatedKJc(med) KJc(0.05)

Irradiated (Fluence:≧5E19 n/cm^2)

Rolled plates (RP)
ΔTt = -15 ºC

100

0
-300

400

UnirradiatedIrradiatedIrradiated (Fluence:≧5E19 n/cm^2)

300

Forgings (FS)500
UnirradiatedKJc(med) KJc(0.05)

ΔTt = 8 ºC
200
100

-100

0

T－Tr30 (ºC)(a) Rolled plates
Fig. 3100

200

KJc(med) KJc(0.05)

Irradiated400

Irradiated (Fluence:≧5E19 n/cm^2)

Weld metals (WM)

300

ΔTt = 14 ºC
200
100
0

0
-200

1T equivalent KJc (MPa√m)

400

1T equivalent KJc (MPa√m)

1T eqivalent KJc (MPa√m)

500

-300

-200

-100

0

T－Tr30 (ºC)(b) Forgings

100

200

-300

-200

-100

0

100

200

T－Tr30 (ºC)(c) Weld metals

Temperature dependence of fracture toughness data indexed by measured Tr30 [3]3.2 Reliability of the lower bound curves
The reliability of the lower bound fracture toughness curve was evaluated on the data for
irradiated materials by the following two methods.
 Percentage of data enveloped (PDE) by the lower bound curve, which is defined by the ratio of
number of data enveloped by the curve to the number of all the data Failure probability (FP) assessment method by Wallin to re-evaluate the safety level of ASME
KIc reference curve [4] (see Fig. 4)
Table 1 summarizes the results of PDE and FP for each data set, respectively. For all the productforms, the PDE is higher than 95% and the FP is lower than 5%.

169

Sample datum
for evaluation

Cumulative failure probability Pf

1T equivalent fracture toughness K Jc(1T)

K. Yoshimoto, et al./ Fracture toughness Curves of Japanese Reactor
Pressure Vessel Steels considering Neutron Irradiation Embrittlement
Normal distribution

KJc(0.05) lower
bound curve

Δ(i) =T.0.05(i) T(i)T(i) Tr30
Temperature T-Tr30 (ºC)

Failure probability forlower bound curve
1.0

Normal distribution
Lower tail data

00

T0.05(i) Tr30

Temperature difference Δ (ºC)

Fig. 4

Outline of failure probability assessment method proposed by Wallin [4]Table 1

Reliability of the 5% tolerance lower bound curves (Tr30；measured value)

5% tolerance
lower bound curve

Data evaluated*1

Material

ΔTt (ºC)

Number of data

Rolled Plates (RP)Forgings (FS)Weld Metals (WM)

-15
8
14

230
259
117

Number of dataenveloped by curve
221
255
116

Percentage of dataenveloped by curve(PDE) (%)

Failureprobability*2(FP) (%)

96.1
98.5
99.1

4.8
1.4
1.0

Note) *1: Data for irradiated materials, *2: Evaluated by Wallin’s method [4]3.3 Applicability of the lower bound curves for predicted Tr30
3.3.1. Determination of predicted Tr30
In application of the curves to PTS evaluation of actual plants, the predicted Tr30 value isrequired to determine fracture toughness of RPV at the end of the plant operation period. Therefore,
the reliability of the curves was examined for the predicted Tr30 value. The predicted value can becalculated by Eq. (8).
Predicted Tr30 = Initial Tr30 + ΔRTNDT + Mc

[ºC]

(8)

ΔRTNDT means RTNDT shift due to neutron irradiation, which is equal to Tr30 shift and it is calculated
according to the irradiation embrittlement prediction method of JEAC4201 [1]. Mc is the correction
factor defined in JEAC4201 and determined in consideration of the difference between the measured
and the calculated ΔRTNDT. Once predicted Tr30 is obtained from Eq. (8), a margin of 3 ºC is added tothe predicted Tr30 considering the error of ΔRTNDT prediction and fracture toughness variation in thetemperature axis. The derivation and adequacy of 3 ºC as a margin will be described in detail in
another paper.
3.3.2. Applicability of the lower bound curves
Figure 5 shows the temperature dependence of fracture toughness data indexed by T-Tr30 alongwith the developed lower bound curve for predicted Tr30 with a margin of 3 ºC. The curve seems toenvelope almost all the data for irradiated materials. In addition, the data of the material with higher
copper content, i.e. Cu ≥ 0.1%, for which irradiation embrittlement is larger, can be evaluated by the
curves conservatively.
500

Irradiated (Cu≧0.1%)

Rolled plates (RP)300

Tr30： predicted + margin (3ºC)
200

ΔTt = -15 ˚C100

Irradiated

0
-300

-200

-100

T－Tr300(ºC)(a) Rolled plates

100

200

IrradiatedKJc(0.05)

400

1T eqivalent KJc (MPa√m)

400

KJc(0.05)

1T eqivalent KJc (MPa√m)

1T eqivalent KJc (MPa√m)

500

500
IrradiatedForgings (FS)300

Tr30： predicted + margin (3ºC)
200

ΔTt = 8 ˚C

100

0
-300

KJc(0.05)

Irradiated (Cu≧0.1%)

400

Weld metals (WM)300

Tr30： predicted + margin (3ºC)
200

ΔTt = 14 ˚C
100
0

-200

-100

0

T－Tr30 (ºC)(b) Forgings

100

200

-300

-200

-100

T－Tr30

0

100

200

(ºC)

(c) Weld metals

Fig. 5 Temperature dependence of fracture toughness data indexed by predicted Tr30 with margin of 3 ºC

170

K. Yoshimoto, et al./ Fracture toughness Curves of Japanese Reactor
Pressure Vessel Steels considering Neutron Irradiation Embrittlement

The reliability of the lower bound curve was examined again for the data for irradiated material in thesame manner as for the measured Tr30. Table 2 summarizes the PDE and FP of the curve evaluated by
Wallin’s method [4]. By adding the margin of 3 ºC to the predicted Tr30, the lower bound fracture
toughness curve has reliability comparable to the measured Tr30 as shown in Table 1.
Table 2

Reliability of the 5% tolerance lower bound curves (Tr30；predicted value with margin of 3 ºC)

5% tolerance
lower bound curve

Data evaluated*1

Material

ΔTt (ºC)

Number of data

Rolled Plates (RP)Forgings (FS)Weld Metals (WM)

-15
8
14

230
259
117

Number of dataenveloped by curve
223
257
116

Percentage of dataenveloped by curve(PDE) (%)

Failureprobability*2(FP) (%)

97.0
99.2
99.1

4.0
0.9
0.9

Note) *1: Data for irradiated materials, *2: Evaluated by Wallin’s method [4]4.

Conclusion

Fracture toughness curves for Japanese RPV materials depending on the product form that
employ the Master Curve concept have been developed. The results are summarized as follows;
1) Tr30 were chosen as an appropriate indexing parameter for the fracture toughness curves
developed in this study.
2) The 5% tolerance lower bound curve was developed using fracture toughness data for irradiatedmaterial with 5×1019 n/cm2 or more neutron fluence for each product form based on the Master
Curve concept. The developed curves are expressed by the following equation.

K Jc (0.05)  25.2  36.6 exp 0.019(T  (Tr 30  Tt ))

[MPa√m]Tt : -15 ºC for rolled plates, 8 ºC for forgings and 14 ºC for weld metals

3) It was demonstrated that the newly developed curves based on the 5% tolerance lower boundcurve indexed by Tr30 can envelope more than 95% of the data evaluated for the measured Tr30
4) For predicted Tr30, the lower bound curve has reliability comparable to the measured Tr30 byadding a margin of 3 ºC to predicted Tr30.

Acknowledgement
This study was conducted as a co-operative research program "Development of structural
integrity evaluation technique for neutron irradiation embrittlement of reactor vessel, Step2" of The
Kansai Electric Power Co., Inc., Hokkaido Electric Power Co., Inc., Shikoku Electric Power Co., Inc.,
Kyushu Electric Power Co., Inc., The Japan Atomic Power Company and Mitsubishi Heavy Industries,
Ltd. The authors would like to express their thanks to the members of Fracture Toughness Committeeof Japan Electric Association for their fruitful discussions.

References[1] JEAC4201-2007(2013 addenda): “Method of Surveillance Tests for Structural Materials of
Nuclear Reactors.”[2] ASTM E1921-12: “Standard Test Method for Determination of Reference Temperature, To, forFerritic Steels in the Transition Range,” (2012).
[3] K. Yoshimoto, T. Hirota and H. Sakamoto: “Development of fracture toughness curves forJapanese reactor pressure vessel steels,” JSME Annual Meeting 2014, in Japanese (2014).
[4] K. Wallin: “Statistical re-evaluation of ASME KIc and KIR fracture toughness reference curves,”
Nuclear Engineering and Design, 193(1999), 317-326.

171