Fracture toughness prediction for highly irradiated RPV materials: From test results to RPV integrity assessment

Journal of Nuclear Materials 432 (2013) 313–322

Contents lists available at SciVerse ScienceDirect

Journal of Nuclear Materials journal homepage: www.elsevier.com/locate/jnucmat

Fracture toughness prediction for highly irradiated RPV materials: From test results to RPV integrity assessment B. Margolin a,⇑, B. Gurovich b, V. Fomenko a, V. Shvetsova a, A. Gulenko a, D. Zhurko b, M. Korshunov b, E. Kuleshova b a b

Central Research Institute of Structural Materials ‘‘Prometey’’, Saint-Petersburg, Russia Russian Research Center ‘‘Kurchatov Institute’’, Moscow, Russia

a r t i c l e

i n f o

Article history: Received 17 March 2012 Accepted 3 September 2012 Available online 9 September 2012

a b s t r a c t New fracture toughness data are represented for highly irradiated RPV materials that were obtained by testing standard compact specimens with thickness of 12.5 mm and 25 mm and pre-cracked Charpy specimens machined from the RPV decommissioned. Two advanced engineering methods, the Master Curve and the Unified Curve, are applied for treatment of the test results. Application of the dependence of fracture toughness KJC on test temperature T predicted with the Master Curve and the Unified Curve methods on the basis of surveillance specimens testing is discussed for RPV integrity assessment when the reference KJC(T) curve is recalculated to the crack front length of the postulated flaw that is considerable larger than thickness of surveillance specimens. The prediction of the KJC(T) curve transformation caused by neutron irradiation is considered. Ó 2012 Elsevier B.V. All rights reserved.

1. Introduction Radiation embrittlement data for RPV materials are input information for assessment of RPV structure integrity that is known to be calculated by the criterion of resistance to brittle fracture. The base characteristic for such assessment is the temperature dependence of fracture toughness, KJC(T). The neutron irradiation damage effect on RPV materials is estimated using data that are obtained from surveillance programs. These surveillance programs include irradiation and testing of small-size specimens only, usually, pre-cracked Charpy specimens. In this paper abbreviation of such specimens is taken as SEB-10 (Single-edge Notched Bend). Abbreviations of standard compact specimens with thickness of 12.5 mm and 25 mm are CT-12.5 and CT-25 respectively. Currently, there are two engineering methods, namely, the Master Curve [1,2] and the Unified Curve [3], that allow the construction of KJC(T) curve from fracture toughness test results of small-size specimens. Both methods use the Weibull statistics to describe the scatter in KJC results and the effect of specimen thickness on KJC(T) curve. To describe the KJC(T) curves for embrittled material the Master Curve method uses also the lateral temperature shift concept, i.e. assumption about an invariance of the shape of the KJC(T) curve for different conditions of a material. The Unified Curve method provides a prediction of the KJC(T) curve allowing for

⇑ Corresponding author. Tel.: +7 812 710 25 38. E-mail address: [email protected] (B. Margolin). 0022-3115/$ - see front matter Ó 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.jnucmat.2012.09.005

the possibility of shift of KJC(T) curve to higher temperature range and a variation in the KJC(T) curve shape. By other words, the Unified Curve, as distinct from the Master Curve, takes into account the transformation of the shape of the KJC(T) curve as a function of the degree of embrittlement of a material. At present the Unified Curve method has been verified for more than 35 experimental data sets for ferritic steels with various degrees of embrittlement when the parameter T0 varies from 150 to 250 °C and yield stress rY – from 300 to 1000 MPa [3,4]. Western and Russian steels were considered, as well as their welds in different conditions: initial, thermally embrittled and after neutron irradiation. It was found that for materials in the initial (asreceived) condition and with small degrees of embrittlement the curves predicted with the Unified Curve and Master Curve methods coincide practically, and for materials with high degree of embrittlement the description of KJC(T) by the Unified Curve becomes more adequate than the description by the Master Curve. This circumstance is connected with a variation of the KJC(T) curve shape when degree of embrittlement increases. Nevertheless, in spite of wide verification of the Unified Curve method as well as the Master Curve method there is a lack of the verification for irradiated RPV materials. It is connected with two circumstances. First of all, the fracture toughness data were too few for largescale (no less than CT-12.5) specimens from irradiated RPV materials as most tests for irradiated steels were performed on small-size (pre-cracked Charpy) fracture toughness specimens over a limited temperature range. It should be noted that namely

314

B. Margolin et al. / Journal of Nuclear Materials 432 (2013) 313–322

pre-cracked Charpy specimens are usually tested for justification of the Master Curve shape. Secondly, previous studies [5,6] have shown that the test results of small-size specimens may, in principle, be described by any engineering method – Unified Curve or Master Curve with practically the same error. Let us consider briefly these study results. As is known the Master Curve and the Unified Curve use KJC(med)(T) as reference function where KJC(med)(T) is the median value of KJC that is KJC 6 KJC(med) with the probability Pf = 0.5. That’s why for quantitative comparison of the Master Curve and the Unified Curve the value of d

vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u L  2 u1 X exp ; d¼t  K pr JCðmedÞj  K JCðmedÞj L j¼1

ð1Þ

may be used, where L is the number of temperatures at which tests were carried out; K pr JCðmedÞj is the predicted median value of KJC calculated by the Master or Unified Curves at test temperature Tj; K exp JCðmedÞj is the median value of KJC determined by treatment of experimental data at T = Tj with the maximum likelihood method according to ASTM E 1921-02 [1]. It follows from Eq. (1) that the description of experimental data by the Master Curve or the Unified Curve methods is more adequate when the value of d is smaller. It is necessary to note that formula (1) is applicable if KJC(med) may be reliably determined for each test temperature. According to [1] for reliable determination of KJC(med) for a given temperature 6–8 specimens should be tested. In the used database for some test temperatures, the number of tested specimens is less than necessary according to [1]. That’s why the parameter r which is similar to d is introduced for quantitative comparison of the Master Curve and the Unified Curve. The parameter r is calculated as

vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u N  2 u1 X exp ; r¼t  K pr JCðmeanÞj  K JCj N j¼1

ð2Þ

where N is the total number of tested specimens, K exp JCj is experimental KJC value for jth-specimen and K pr JCðmeanÞj is the predicted mathematical expectation of KJC at test temperature for j th-specimen. Using the Weibull function for distribution of KJC at a given temperature [1] K pr JCðmeanÞj may be calculated by formula

K pr JCðmeanÞj ¼

K pr JCðmedÞj  K min ðln 2Þ1=4



C 1þ

 1 þ K min ; 4

ð3Þ

where C is gamma function. Eq. (2) may be used instead of Eq. (1) when there is no sufficient number of experimental values to calculate reliably the median value of KJC and to use Eq. (1).

300

(b) 400

0 Set 28 T0=57.1 C To= 57.1oC o - tests - tests

Pf =0.5

K IC, K JC, MPa √m

K IC, K JC, MPa √m

(a) 400

It is necessary to underline that the parameter r differs from the parameter d. If the prediction coincides with experiment completely then d = 0 but r – 0. Nevertheless both the parameter d and r reduce when the predicted results are approaching to the experimental data. So, for reliable comparison of the Master Curve and the Unified Curve the both parameters may be used for all considered sets of specimens. In papers [5–7] the experimental KJC(T) curves were compared for 2Cr–Ni–Mo–V steel in the embrittled condition (the DBTT shift is equal to 180 °C) obtained from tests of CT specimens 50 mm thick and of SEB specimens 10 mm thick. For the investigated steel the dominant mode of fracture is transcrystalline micro-cleavage fracture. Fig. 1a and b shows the curves KJC(T) and experimental data for this steel for the specimen thickness of B = 25 mm, the curves being constructed by the Master Curve and the Unified Curve methods. These curves were constructed by the multi-temperature method from the test results of CT-50 specimens recalculated for the thickness of B = 25 mm. Fig. 2 demonstrates the test results of SEB-10 specimens with 50% side grooves, the results being recalculated for the thickness of B = 25 mm taking into account that the real crack front length for SEB-10 specimens with 50% side grooves is 5 mm. The figure also demonstrates the KJC(T) curves constructed by the Master Curve and Unified Curve methods for these specimens. For quantitative comparison of the experimental and predicted results the parameters d and r are used. For the data in Fig. 1 values of the parameters d and r for the Master Curve and the Unified p p Curve are the following: dmc = 99.5 MPa m, duc = 21.1 MPa m, p p rmc = 121.6 MPa m and ruc = 48.6 MPa m. Hence dmc/duc = 4.72 p and rmc/ruc = 2.5. For the data in Fig. 2 dmc = 7.22 MPa m, p p p duc = 7.63 MPa m, rmc = 17.69 MPa m, and ruc = 17.74 MPa m and, hence, dmc/duc = 0.95, rmc/ruc = 0.99. It is seen from these results that for CT specimens the Unified Curve describes experimental data better than the Master Curve, as shape of K JC (T) for highly embrittled material changes. The test results of small-size specimens may, in principle, be described by any engineering method – the Unified Curve or the Master Curve with practically the same error. This is due to a highly limited range of correct values of fracture toughness for these specimens. It means that advantages of a method cannot be revealed from test results of small-size specimens and the real shape of KJC(T) curve (see Fig. 1) may be revealed only from the test results of full-size (no less than CT-12.5) specimens [5,6]. Thus, the main purpose of the present study is to analyze the applicability of the Unified Curve and Master Curve methods for highly irradiated RPV materials that has been achieved through

Pf =0.95

200

100

300

Set 28 Ω=199 MPa√m Ω = 199 MPa √ m o -- tests tests Pf =0.95

200 Pf =0.5

100 Pf =0.05

Pf =0.05

0 -200 -150 -100

-50

0

temperature, o C

50

100

150

0 -200 -150 -100

-50

0

temperature, o C

50

100

150

Fig. 1. Experimental results and KJC(T) curves calculated by the Master Curve (a) and Unified Curve (b) methods for 2Cr–Ni–Mo–V steel in the embrittled condition: T0 and X are determined by multi-temperature method; dots – test results of 2T-CT specimens [7] recalculated for thickness B = 25 mm; dmcduc = 4.72, rmc/ruc = 2.5.

315

B. Margolin et al. / Journal of Nuclear Materials 432 (2013) 313–322

200

T0=52°C Ω=196 MPa√m

2. The main considerations of the Master Curve and Unified Curve methods

Pf =0.95

160

The main considerations of the Master Curve and Unified Curve methods are as follows [1–3].

KJC, MPa√m

KJC(lim)

120

1. According to the Master Curve the temperature dependence of fracture toughness at Pf = 0.5 for specimens with thickness B = 25 mm for any degree of embrittlement may be described by

Pf =0.5

80

40

K JCðmedÞ ¼ 30 þ 70½0:019 expðT  T 0 Þ MPa

Pf =0.05

0 -100

-50

0

50

pffiffiffiffiffi m;

ð4Þ

where T0 is some constant for given condition of a material (named the reference temperature), T is temperature in °C. When degree of material embrittlement increases T0 increases also. According to the Unified Curve

100

T, o C Fig. 2. Experimental data and KJC(T) curves calculated with the Master Curve (solid lines) and Unified Curve (dotted lines) methods for 2Cr–Ni–Mo–V steel in the embrittled condition: T0 and X values are determined by multi-temperature method; dots – test results of SEB-10 specimens with 50% side-grooves recalculated for thickness B = 25 mm; dmcduc = 0.95, rmc/ruc = 0.99 [5,6].

   pffiffiffiffiffi T  130 MPa m; K JCðmedÞ ¼ K shelf þ X 1 þ tanh J 105

ð5Þ

C (wt%)

Si (wt%)

Mn (wt%)

Cr (wt%)

Ni (wt%)

Mo (wt%)

Cu (wt%)

V (wt%)

P (wt%)

pffiffiffiffiffi where K JC m; X is a constant for a given condition of a shelf ¼ 26 MPa material; T is temperature in °C. It is assumed that for the embrittled materials the only parameter, X, varies, the rest of the numerical parameters in Eq. (5) are fixed. When degree of material embrittlement increases X0 decreases. 2. The dependence KJC(T) at Pf#– 0.5 is calculated by equation [1,8] "

0.23

0.28

0.49

3.30

1.07

0.40

0.10

–

0.018

ð6Þ

Table 1 Chemical composition of 3Cr–Ni–Mo steel.

 experimental determination of KJC(T) values over wide temperature range by testing fracture toughness CT-25, CT-12.5 and SEB-10 specimens machined from highly irradiated RPV material;  treatment of the test results with the Unified Curve and Master Curve methods and the quantitative comparison of the predicted and experimental results. The present paper briefly reviews the Master Curve and Unified Curve methods, represents new results on fracture toughness for irradiated PWR RPV material and their treatment with the Unified Curve and Master Curve methods, and discusses an applicability of the KJC(T) curve constructed with the Unified Curves or Master Curve methods for the RPV integrity assessment.

fatigue crack

Fig. 3. Typical fracture surface for fracture toughness specimen tested at room temperature for irradiated metal (CT-1T-specimen) of Reactor 27 RPV. (Fatigue crack is on the left.)

 4 K JC  K min Pf ¼ 1  exp  ; K 0  K min

where K0 is a scale parameter depending on the test temperature and specimen thickness; Kmin is the minimum value of fracture p toughness. In accordance with [8], Kmin = 20 MPa m. 3. The dependence KJC(T) for B – 25 mm is calculated by equation [1,9]

K XJC  K min K YJC  K min

¼

 1=4 BY ; BX

ð7Þ

where K XJC and K YJC are fracture toughness values for specimens with thickness BX and BY at the same fracture probability. The parameter X as well as the parameter T0 in the Master Curve may be determined on the basis of test results at one temperature (single temperature method) or at several temperatures (multi-temperature method). Basic equations for calculation of the parameter X are represented in [3]. Requirements for the number and size of fracture toughness specimens are the same as for determination of the parameter T0 in the Master Curve [1]. 3. Test results for irradiated RPV material and their treatment with the Unified Curve and Master Curve methods In this section the experimental data obtained by testing fracture toughness CT-25, CT-12.5 and SEB-10 specimens machined from highly irradiated RPV material are treated with the Unified Curve and Master Curve methods. The predicted and experimental results are compared. The experimental investigations of fracture toughness were performed as applied to irradiated 3Cr–Ni–Mo steel with chemical composition given in Table 1. The irradiated steel was taken from the core shell metal cut off the decommissioned prototype ‘‘Reactor 27’’ RPV irradiated by neutron fluence 4.5  1023 n/m2 (E > 0.5 MeV) at temperature 270 °C. Fracture surfaces of broken fracture toughness specimens were investigated by SEM. For the investigated steel, the mixed brittle fracture mode was observed (cleavage and intergranular fracture) and the dominant mode is intercrystalline fracture with fraction near 90%. Typical SEM photograph is shown in Fig. 3.

316

B. Margolin et al. / Journal of Nuclear Materials 432 (2013) 313–322

Table 2 Test temperature and fracture toughness for irradiated 3Cr–Ni–Mo steel (Fig. 4). Specimens

Test temperature (°C)

KJc (MPa

CT-25 with 12% side grooves

90 140 150 160 170 170 180

58.0 106.8 82.0 79.7 174.5 157.4 175.1

CT-12.5 without side grooves

78 22 18 50 75 95 130 168 180 193

35.3 37.1 58.9 77.8 82.7 59.6 129.5 185.0 170.8 190.7

SEB-10 with 20% side grooves

24 50 60 81 105 125 140 140 145 145 146 156

36.8 47.6 59.0 61.9 127.9 136.4 145.2 123.1 138.1 85.1 187.2 201.9

p

m)

Experimental data on fracture toughness are presented in Table 2 and Fig. 4. Fig. 4 shows the test results for all tested specimens from this steel recalculated for the thickness of B = 25 mm and the KJC(T) curves constructed by the Master Curve and Unified Curve methods. (When recalculating the fracture toughness test results the actual crack front length was taken but not the nominal thickness of specimen, i.e. the depth of side-grooves was taken into account.) For all the cases the parameters T0 and X are determined by the multiple temperature method according to [1,3]. The test results for SEB-10 are shown in Fig. 4a with the Master Curve and in Fig. 4b with the Unified Curve. For these specimens the ratio dmc/duc  1.29, rmc/ruc = 1.27. For incorrect specimen (dark point) the value of KJC was taken to be equal to KJC = KJC(limit). The parameters T0, X, dmc, duc, dmc/duc, rmc, ruc and rmc/ruc for these specimens are given in Table 3. The test results for CT-25 and CT-12.5 specimens are shown in Fig. 4c and d. It is necessary to mention here that for two CT-12.5 specimens (the shaded points in Fig. 4c and d) the ductile tearing, Da, was a little larger (Da = 0.71 and 0.87 mm) than the limit ductile tearing (Da(limit) = 0.625 mm). That’s why we tested CT-25 specimens to expand the temperature range for testing. The combined data set for CT-25 and CT-12.5 specimens is treated by the Master Curve (Fig. 4c) and by the Unified Curve (Fig. 4c). The parameters T0, X, dmc, duc, dmc/duc, rmc, ruc and rmc/ruc were calculated with and without the points with the overestimated ductile tearing. The obtained values are given in Table 3. It is seen that the ratios dmc/duc and rmc/ruc do not practically vary: for one case the ratio dmc/duc  2.34, rmc/ruc = 1.92 for other dmc/duc  2.36, rmc/ruc = 2.01. It means that the description with the Unified Curve is more adequate than with the Master Curve. Several findings may be found when analyzing these data. In addition to the results earlier obtained in [5,6] and cited in Section 1 the test results for SEB-10 specimens have shown that small-size specimen cannot be used for experimental determina-

tion of real shape of KJC(T) curve. This is due to a highly limited range of correct values of fracture toughness for these specimens. At the same time it is interesting to note here that both the Unified Curve and Master Curve describe well the test results for SEB-10 specimens from irradiated 3Cr–Ni–Mo steel in spite of that the dominant mode is intercrystalline brittle fracture. Comparison of new experimental data obtained from CT specimens for highly irradiated RPV materials with the KJC(T) curves predicted by the Master Curve and Unified Curve methods has shown that the description with the Unified Curve is more adequate than with the Master Curve. Once more interesting result may be found from Fig. 4. The parameter T0 for highly embrittled steel that was calibrated from SEB-10 specimens (Fig. 4a) is practically the same as calibrated from CT specimens (Fig. 4c). For materials in unirradiated condition another tendency is usually observed: SEB-10 specimens, as a rule, provide T0 value being lower by 15–20° than T0 for CT specimens [5,6,10]. The obtained result seems to provide a possibility to decrease the margin on the type of tested specimens [11] when estimating structural integrity of irradiated RPV. However, this issue requires special studies. In addition to the above results, in Fig. 5 new test results [12] for CT-25 specimens from thermally aged A508 steel are treated both the Master Curve and Unified Curve methods. For quantitative estimation as well as above the ratios dmc/duc and rmc/ruc are used. For the data in Fig. 5 the ratios dmc/duc = 3.54 and rmc/ruc = 3.03. This result shows again that for highly embrittled condition the Unified Curve method provides more adequate description as this method takes into account a variation of KJC(T) curve shape.

4. Comparison of the Master Curve and Unified Curve methods Earlier the Unified Curve method has been verified for available experimental data sets for ferritic steels with various degrees of embrittlement when the parameter T0 varies from 150 to 250 °C [3,4]. The base and weld metals of Western and Russian RPV steels were considered in different conditions: as received, thermally embrittled and irradiated. Moreover, other ferritic structural steels were considered. The brittle fracture mode for these materials varies from cleavage to mixed mode (cleavage and intergranular fracture). In Table 4 the treatment of available experimental data sets and new experimental results is presented. Several examples of the predicted curves and test results are given in Fig. 6. For all the cases the parameters T0 and X are determined with the multiple temperature method. For determination of T0 the equation from [1] was used, for determination of X – from [3]. It is seen from Fig. 6 and Table 4, as the degree of embrittlement increases (T0 increases), the description of KJC(T) by the Unified Curve becomes more adequate than the prediction by the Master Curve. On the basis of Table 4 in Fig. 7 the values of the ratios dmc/duc and rmc/ruc are summarized for all the available data for materials with various T0 values. It is clearly seen from Fig. 7 that for materials with not high degree of embrittlement prediction by the Master Curve practically coincides with prediction by the Unified Curve; for high degree of embrittlement the description of KJC(T) by the Unified Curve becomes more adequate than the description by the Master Curve. Thus, new fracture toughness data obtained for irradiated RPV materials by testing CT-25 and CT-12.5 specimens confirm the conclusion drawn early in [3,4] that the Unified Curve method is most appropriate method for construction of KJC(T) curve for irradiated RPV materials.

317

B. Margolin et al. / Journal of Nuclear Materials 432 (2013) 313–322

(a)

(b) - SEB-10 specimens recalculated on В=25mm - incorrect specimen Pf=95%

200 KJC, MPa√m

250

В=25 mm T0=130.6 °С

Pf=50%

150

Pf=5%

100

150 Pf=50%

100

Pf=5%

50

50

0 -100

-50

0

50

100

150

0 -100

200

Т, °С

-50

0

50

100

150

200

Т, °С

(c)

(d)

200

150

250

В=25 mm T0=130.6 °С - СТ-1 specimens - СТ-0.5 specimens recalculated on В=25mm - exceeding the limit ductile crack growth

В=25 mm Ω=79.1 MPa√m - СТ-1 specimens - СТ-0.5 specimens recalculated on В=25mm - exceeding the limit ductile crack growth

Pf=95% Pf=50%

Pf=5%

100

200 KJC, MPa√m

250

KJC, MPa√m

В=25 mm Ω=70.1MPa√m - SEB-10 specimens recalculated on В=25mm - incorrect specimen Pf=95%

200 KJC, MPa√m

250

150

Pf=95%

Pf=50% 100 Pf=5%

50

50

0 -100

-50

0

50

100

150

0 -100

200

Т, °С

-50

0

50

100

150

200

Т, °С

Fig. 4. Test results (dots) for SEB-10 specimens (a and b), CT-0.5T and CT-1T specimens (c and d) and KJC(T) curves calculated by the Master Curve (a and c) and the Unified Curve (b and d) for irradiated 3Cr–Ni–Mo steel. (All test results are recalculated for B = 25 mm.)

Table 3 The parameters T0, X, dmc, duc, dmc/duc, rmc, ruc and rmc/ruc for irradiated 3Cr–Ni–Mo steel. Specimens

T0 (°C)

X (MPa

SEB-10 CT-25 + CT-12.5 with the shaded points CT-25 + CT-12.5 without the shaded points

130.6 130.6 128

70.1 79 79

p

m)

dmc (MPa 15.5 50.7 54.0

5. Application of KJC(T) curve predicted from small-size specimens to RPV structural integrity assessment The results represented above have shown that the Unified Curve method allows one to construct the KJC(T) curve adequately for irradiated RPV steels with any degree of embrittlement. Hereafter some issues of application of the fracture toughness temperature curve for WWER RPV integrity assessment are considered. It should be noted that for the first time, advance methodology based on statistical approach to brittle fracture was incorporated in RPV structural integrity assessment in papers [25,26] and included in Russian Standard [27] and later in European procedure VERLIFE [28]. According to [25–27] the structural integrity of WWER RPV on the brittle fracture criterion is estimated from condition

K I ðTÞdK I dT

<0

< K JC ðTÞB ¼ B ; flaw  P ¼P f

ð8Þ

f

where KI is stress intensity factor under pressurized thermal shock, Bflaw is a front length of a postulated crack and Pf is a given level of fracture probability, usually, Pf ¼ 0:05.

p

m)

duc (MPa 12.0 21.7 22.9

p

m)

p

p

dmc/duc

rmc (MPa m)

ruc (MPa m)

rmc/ruc

1.29 2.34 2.36

20.9 43.3 47.0

16.4 22.5 23.4

1.27 1.92 2.01

When analyzing the RPV integrity a postulated crack-like flaw is considered with the front length Bflaw  10 mm (according to [27] Bflaw may reach 150 mm). In this case the KJC(T) curves constructed with the Master Curve and Unified Curve methods from the test results of specimens 10 mm in thickness should be recalculated to a considerably greater front length of the postulated flaw Bflaw compared to the crack front of reference or surveillance specimens. It is evident that with such recalculation the situation demonstrated in Fig. 8 is quite possible [12]. For specimens 10 mm in thickness, curves 1 and 3 constructed by the Master Curve and Unified Curve methods practically coincide. Here T is maximum temperature when fracture toughness data from small-size specimens are valid and corrected. At the same time for the postulated flaw in the temperature range T > T the KJC(T) curve shape changes and the lateral shift condition is not satisfied. If the temperature range for RPV integrity assessment (designated hereafter as TRPV) does not coincide with the temperature range for small-size specimen testing (designated hereafter as TSST), the Master Curve method may provide non-conservative estimation of RPV strength. This example demonstrates once more the advantage of the Unified Curve method for assessment of the resistance to brittle fracture of RPV over the Master Curve method. It is apparent that the Master Curve method as a tool of describing mathematically

318

B. Margolin et al. / Journal of Nuclear Materials 432 (2013) 313–322

300 Pf=50%

250

Pf=5%

200 150 100

Pf=95% Pf=50%

200 150

Pf=5%

100 50

50 0 -50

B=25 mm Ω=164 MPa√m

Pf=95%

KJC, MPa√m

KJC, MPa√m

250

300 B=25 mm T0=66.0 0C

50

0

100

150

200

0 -50

250

0

50

o

100

150

200

250

T, oC

T, C

Fig. 5. Test results (dots) for CT-25 specimens and KJC(T) curves calculated by the Master Curve (left) and Unified Curve (right) methods for thermally aged A508 steel [12]: d – ductile fracture (out of account), dmc/duc = 3.54 , rmc/ruc = 3.03.

may be applied for cracked structural component with any given crack front length that may be considerable larger than thickness of fracture toughness specimens of the reference thickness of 25 mm. Such a possibility follows from the fact that the Unified Curve describes a possible variation of the KJC(T) curve shape. It is important to emphasize that a variation of the KJC(T) curve shape may happen both for transcrystalline and intercrystalline fracture. For example, the dominant mode of fracture for tests in Fig. 1 is transcrystalline micro-cleavage fracture and for tests in Fig. 5 – intercrystalline fracture. It is clear also that sufficiently widespread view is incorrect that an insignificant variation of the KJC(T) curve shape due to irradiation (determined from small-size specimen tests) is not important

the results of small-size specimen tests can be used, as was shown above, even for materials with sufficiently high degree of embrittlement. However its use to assess the RPV integrity should be limited. The Unified Curve method does not use the lateral shift condition and, hence, can be applied to analyze the resistance to brittle fracture of RPV without any restrictions. Nevertheless, it is necessary to note that even if the KJC(T) curve shape changes the Master Curve may describe experimental data sufficiently adequately and conservatively when TSST is not large. Then if TRPV coincides with TSST the Master Curve may be used for RPV structural integrity assessment. Thus, for RPV structural integrity assessment it is most important that the KJC(T) curve predicted with the Unified Curve method Table 4 Treatment of available and new test results by the Master Curve and the Unified Curve. Set number

Material

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34

A533B steel (in) A508 steel (in) HY130L (in) ABS DS (in) A470 steel (in) 2CrNiMoV steel (in) NVA (in) 3CrNiMoV steel (in) WF70 weld (in) HSST weld 73W (in) HSST weld 72W (in) A533 steel JRQ (in) WF-70 weld (in) A508 steel (TSE-5&6) KWO RPV A508 steel A508 steel (TSE-7) A533 steel A508 steel (TSE-5&6) NiCrMoV steel E36 WF-70 weld (irr) HSST weld 72 W (irr) HSST weld 73 W (irr) A533B steel 2.5CrMoV steel (embr) WF-70 weld (irr) 2CrNiMoV steel (embr) NP2 A533 steel JRQ (irr) Weld KS01 (irr) 2.5CrMoV steel PTS-1 (embr) Weld KS01 (irr) 3Cr-Ni-Mo steel (irr)

35

A508 steel (embr)

ry at T = 20 °C

duc p (MPa m)

dmc duc

rmc

[13,3] [13,3] [13,3] [13,3] [14,3] [15,3] [13,3] [16,3] [17,3] [18,3] [18,3] [19,3] [17,3] [20,3] [21,3] [14,3] [20,3] [14,3] [20,3] [13,3] [13,3] [17,3] [18,3] [18,3] [22,3] [3] [17,3] [7,3] [13,3] [19,3] [23,3] [24,3]

17.4 26.8 16.9 192 27.1 207 43.4 54.7 77.9 11.3 31.1 61.9 25.6 115.3 29.6 15 66 25.3 112 387 51.2 110 39 15.5 80.5 32.5 14.6 99.5 83.7 32 62.6 168

19.2 29.4 18.4 188 28.5 178 41.5 56.6 77 11.9 32 58.3 26.6 96.7 31.9 15.9 54.2 22.8 79.9 185 42.1 99.1 17.5 15.9 58.6 25.4 11.4 21.1 36.2 23.8 12.4 11.3

0.91 0.91 0.92 1.02 0.95 1.16 1.05 0.97 1.01 0.95 0.97 1.06 0.96 1.19 0.93 0.94 1.22 1.11 1.40 2.09 1.22 1.11 2.23 0.97 1.38 1.28 1.28 4.72 2.31 1.34 5.05 14.87

24.0 28.0 19.8 187.0 32.2 118.8 43.6 37.2 51.4 33.3 62.1 58.7 38.6 115.7 27.1 24.5 86.1 17.0 63.6 316.9 41.8 54.3 57.3 45.2 69.9 29.2 24.3 121.6 84.1 29.3 56.9 100.4

22.6 29.7 20.2 183.0 33.0 105.5 44.2 39.6 51.8 33.3 62.0 55.6 39.1 96.6 28.6 24.9 73.6 16.7 62.4 144.1 51.0 51.6 53.8 43.9 55.1 26.1 22.0 48.6 37.3 31.7 25.0 23.0

1.06 0.94 0.98 1.02 0.98 1.13 0.99 0.94 0.99 1.0 1.0 1.06 0.99 1.2 0.95 0.98 1.17 1.01 1.02 2.2 0.82 1.05 1.06 1.03 1.27 1.12 1.10 2.5 2.26 0.92 2.28 4.37

[20,3] Fig. 4c and d [12] Fig. 5

26.2 50.7

8 21.7

3.28 2.34

21.6 43.3

9.3 22.5

2.3 1.92

78.5

22.2

3.54

54.0

17.8

3.03

X p (MPa m)

567 650 955 270 – 565 218 550 740 513 496 480 790 605 – – 450 – 710 925 303 930 620 648 – 730 860 900 676 630 820 1037

148 140 131 91.3 86.5 82.5 72.1 67.4 63.5 61.3 60.4 59.7 55.8 52.2 49.2 48 32.7 28.5 20.1 11.3 21.2 24.9 29.3 37.2 39.9 45.6 49 57.1 69.0 86.9 137 164

7397 6441 6511 2615 2384 2196 1783 1695 1521 1472 1455 1433 1330 1242 1205 1175 880 786 723 685 113 345 333 291 259 241 211 199 161 142 73.4 65.9

950 931

251 130.6

21.5 79

66

164

(MPa

p

ruc

rmc ruc

dmc p (MPa m)

T0 (°C)

Reference

(MPa)

m)

(MPa

Remark: In the bracket the condition of a material is designated as: in – received condition, embr – thermally embrittled condition, irr – after irradiation.

p

m)

319

B. Margolin et al. / Journal of Nuclear Materials 432 (2013) 313–322

400

300

Set 10 To= -61.3oC - tests

Pf =0.5

Pf =0.95

200 Pf =0.05

100

0 -200

-150

-100

-50

0

K IC, K JC, MPa √m

K IC, K JC, MPa √m

400

300

Pf =0.05

100

-150

o

K IC, K JC, MPa √m

K IC, K JC, MPa √m

300

Pf =0.95

200

100

Pf =0.05

0 -200 -150 -100

-50

0

50

100

300

200

100

Pf =0.05

0 -200 -150 -100

150

Pf =0.05

100

100

150

Pf =0.5

100 Pf =0.05

0 -200

200

-100

0

100

200

temperature, oC 200

200 Set 31 o To= 137 C - tests

Pf =0.5 Pf =0.95

120 80 Pf =0.05

40

-100

0

100

200

o

temperature, C

K IC, K JC, MPa √m

K IC, K JC, MPa √m

50

Pf =0.95

200

temperature, oC

0 -200

0

Set 30 Ω = 142 MPa √ m - tests

K IC, K JC, MPa √m

K IC, K JC, MPa √m

Pf =0.95

100

160

-50

300

Pf =0.5

Set 30 To= 86.9 oC - tests

0

Pf =0.5

temperature, oC

300

-100

50

Pf =0.95

temperature, C

0 -200

0

Set 23 Ω = 333 MPa √ m - tests

o

200

-50

400

Pf =0.5

Set 23 o To= 29.3 C - tests

-100

temperature, oC

temperature, C 400

Pf =0.5 Pf =0.95

200

0 -200

50

Set 10 Ω = 1472 MPa √ m - tests

160

Set 31 Ω = 73.4 MPa √ m - tests Pf =0.95

120

Pf =0.5

80 Pf =0.05

40 0 -200

-100

0

100

200

temperature, oC

Fig. 6. Test results and KJC(T) curves calculated by the Master Curve (left) and the Unified Curve (right) for steels with various degree of embrittlement [3]: set 10 – HSST weld 73 W (initial condition), set 23 – HSST weld 72 W (irradiated), set 30 – A533 steel JRQ (irradiated), set 31 – KS01 weld (irradiated). (The test results are recalculated for B = 25 mm.)

for assessment of RPV integrity, so that it is possible to apply the Master Curve method (or other using the lateral temperature shift condition). Thus, it has to be concluded that at present the Unified Curve method is the most reliable approach for representing the shape

of the fracture toughness curve for RPV materials from viewpoint of RPV structural integrity assessment. For estimation and management of RPV service life it is important to know how KJC(T) curve transforms due to neutron irradiation. To use the Unified Curve for prediction of the KJC(T)

320

B. Margolin et al. / Journal of Nuclear Materials 432 (2013) 313–322

6

(b)

6

5

5

4

4

σmc /σuc

δmc /δuc

(a)

3

3

2

2

1

1

0 -200

-100

0

100

200

300

0 -200

-100

o

0

100

200

300

T0 , o C

T0 , C

Fig. 7. The ratios dmc/duc (a) and rmc/ruc (b) vs the reference temperature T0.

KJC

To find the dependence X(F) the so-called dose dependence of embrittlement of a material may be used. For WWER RPV steels the dose dependence is represented as [30]

Master 2 Curve 1

В=Вflaw

В=Bss

DT k ¼ A F 

Unified 4 Curve 3

temperature range for small-size specimens tests

T, 0C temperature range in which RPV integrity is considered



X ¼ ðX0  Xmin Þ exp C F

Fig. 8. The KI(T) curve in the postulated crack tip for pressurized thermal shock condition and the KJC(T) curves for crack front length B = 10 mm (curves 1 and 3) and the postulated crack front length B = Bflaw  10 mm (curves 2 and 4): 1 and 2 – prediction by the Master curve; 3 and 4 – prediction by the Unified Curve.

dependence on neutron fluence F, it is necessary to know the dependence X(F). The dependence X(F) may be obtained from the Unified Curve concept [29]. In [29] the following equation was deduced

  shelf 2 X  K  K 0 JC JC 105 C  ; ln ¼ 2  JC  K shelf 2X  K JC

DT K JC

ð9Þ

where DT K JC is a shift of a conditional temperature T K JC due to neutron irradiation, and this temperature T K JC corresponds to some given level of KJC designated as K JC for the fracture probability Pf = 0.5 and specimen thickness of 25 mm. Thus, T K JC is the temperature corresponding to the condition K JCðmedÞ ¼ K JC . (The K JC value pffiffiffiffiffi may be taken, for example, as K JC ¼ 100 MPa m.) In Eq. (9) X0 is a value of X for unirradiated condition of a material. Eq. (9) may be presented in the form

X ¼ ðX0  Xmin Þexp 

2 105 C  DT K JC

!

þ Xmin ;

ð11Þ

where DTk is the shift of the transition temperature (DBTT shift) which is determined from the Charpy-energy vs temperature curve at the specific energy index of 47 J; AF and m are constants, dependent on irradiation temperature, neutron spectrum and chemical composition of a material, unit of F: n/cm2, F0 = 1  1018 n/cm2. Assuming that DT k ¼ DT K JC and thermal aging is absent, Eq. (10) is rewritten in the form

KI (for thermoshock)

T*

 m F ; F0

ð10Þ

  . Taking into account that K shelf where Xmin  12 K JC  K shelf ¼ JC JC pffiffiffiffiffi pffiffiffiffiffi 26 MPa m for K JC ¼ 100 MPa m the value of Xmin is found as pffiffiffiffiffi Xmin ¼ 37 MPa m.

 m  F þ Xmin ; F0

ð12Þ

where C F ¼ 1052 C AF . Thus, the coefficients CF and m in (12) are determined if the dependence (11) is known. They may be also directly determined from fracture toughness test results of irradiated specimens. It is interesting to note here that the exponential dependence of X on neutron fluence F follows from the probabilistic model for brittle fracture [31,32] (known as the Prometey model) when analyzing the effect of various radiation defects on the critical stress for cleavage microcrack nucleation [29,31,33,34]. It was shown in [31–34] that the main physical process controlling brittle fracture of cracked specimens from highly irradiated RPV steels is cleavage microcrack nucleation, and the main parameter controlling the dependence KJC(T) is the critical stress rd for microcrack nucleation. Once more interesting consequence may be drawn from the Prometey model and Eq. (12). According to the Prometey model, even for very high degree of embrittlement the dependence KJC(med)(T) will be not constant (although this dependence may be very sloping as long as dependence rY(T) is not constant). This fact follows also from Eq. (12). Indeed, Eq. (12) shows that for very high degree of embrittlement (when F ? 1) the dependence KJC(med)(T) in some temperature interval will be not constant due to free term Xmin . It should be mentioned here that for not high degree of embrittlement (when the first term in (12) significantly larger than the second term) Eq. (12) may be written without Xmin as it was used earlier in [29].

B. Margolin et al. / Journal of Nuclear Materials 432 (2013) 313–322

It should be noted that, as a common case, Eq. (10) allows one to take into account thermal aging of a material if the DBTT shift DTk is taken in the form [30,35]

DT k ðF; tÞ ¼ DT t ðtÞ þ DT F ðFÞ;

ð13Þ

where DTt is the DBTT shift caused by thermal aging and depending on time t, DTF is the DBTT shift caused by neutron irradiation. The dependence DTF(F) is described by Eq. (11) and the dependence DTt(t) is described by equation [35]

     tT  t t  th ; DT t ðtÞ ¼ DT inf þ b exp T t tOT t OT

ð14Þ

where DT inf t , bT, tOT and tT are material constants, dependent on aging temperature. (The parameter DT inf is the DBTT shift for t t = 1). Numerical values of the coefficients in Eqs. (11) and (14) for WWER-1000 RPV are represented in [35]. The parameter X0 in Eq. (12) may be determined on the basis of fracture toughness data of specimens in the unirradiated condition. Another way is calibration of X0 from the known value of DBTT, designated as Tk0, for a material in unirradiated condition. Correlation between X0 and Tk0 may be found when taking into account that for RPV materials in unirradiated condition the KJC(T) curves predicted with the Unified Curve [3], the Master Curve [1] and Basic Curve [4,36] methods are practically coincide. Let us take the specific fracture toughness level KJC(med) = p 100 MPa m to find a desired correlation. It follows from the Unified Curve equation (Eq. (5)) that

X0 ¼

100  K shelf JC  130 ; 1 þ th T100105

ð15Þ

where T100 is a value of temperature T in Eq. (5) for which p KJC(med)(T100) = 100 MPa m. p At the same time the value of KJC(med) = 100 MPa m corresponds to the temperature T0 for the Master Curve and to the temperature equal to (Tk0 – 38 °C) for the Basic Curve [4,36]. Taking into account that the KJC(T) curves predicted with all three methods practically coincide for RPV materials in unirradiated condition the following equality takes place T100 = T0 = Tk0  38 °C. As a result, the following equation may be deduced

X0 ¼

100  K shelf p  JC  ; MPa m: T k0 168 1 þ th 105

ð16Þ

6. Conclusions 1. Fracture toughness data obtained for highly irradiated RPV steel by testing CT-25 and CT-12.5 specimens show that the Unified Curve method is more appropriate method for description of KJC(T) curve shape as compared with the Master Curve method. 2. Small-size specimens (SEB-10) cannot be used for experimental determination of real shape of KJC(T) curve. 3. If the temperature range for RPV integrity assessment does not coincides with the temperature range for small-size specimen testing, the Master Curve method may provide non-conservative estimation of RPV integrity. 4. Prediction of KJC(T) curve used for RPV integrity assessment has to be performed with account taken of variation of KJC(T) curve shape if the temperature range for RPV integrity assessment does not coincide with the temperature range for small-size specimen testing. In this case the use of the Unified Curve method may be recommended. When using the Unified Curve, equations have been proposed for prediction of the transformation of KJC(T) curve due to neutron irradiation and thermal aging.

321

Acknowledgments The part of this work has been performed within the framework of the EC-sponsored TAREG Project 2.01/03 and EC-sponsored ISTC Project 3973. References [1] ASTM E 1921-02, in: Annual Book of ASTM Standards, vol. 03.01, Philadelphia, 2002, pp. 1068–1084. [2] J.G. Merkle, K. Wallin, D.E. McCabe, Technical Basis for an ASTM Standard on Determining the Reference Temperature, T0 for Ferritic Steels in the Transition Range, NUREG/CR-5504, ORNL/TM-13631, 1999. [3] B.Z. Margolin, A.G. Gulenko, V.A. Nikolaev, L.N. Ryadkov, Int. J. Pres. Ves. Pip. 80 (2003) 817–829. [4] B.Z. Margolin, A.G. Gulenko, V.A. Nikolaev, L.N. Ryadkov, in: Proceedings of International Seminar. Transferability of Fracture Toughness Data for Integrity of Ferritic Steel Component, November 17–18, 2004, Petten, the Netherlands. EUR 21491 EN. Office for official Publications of the European Communities, Luxemburg, 2004, pp. 206–228. [5] V.A. Nikolaev, B.Z. Margolin, L.N. Ryadkov, V.N. Fomenko, Probl. Prochnosti (Probl. Strength) (2) (2009) 5–27 (in Russian). [6] B. Margolin, V. Nikolaev, V. Fomenko, L. Ryadkov, in: Proceedings of ASME 2009 PVP Conference, PVP-2009-770096. [7] B.Z. Margolin, V.A. Shvetsova, A.G. Gulenko, A.V. Ilyin, V.A. Nikolaev, V.I. Smirnov, Int. J. Pres. Ves. Pip. 79 (2002) 219–231. [8] K. Wallin, Eng. Fract. Mech. 19 (1984) 1085–1093. [9] K. Wallin, Eng. Fract. Mech. 22 (1985) 149–163. [10] D. Lidbary et al., in: Proceedings of International Seminar. Transferability of Fracture Toughness Data for Integrity of Ferritic Steel Component, November 17–18, 2004, Petten, the Netherlands. EUR 21491 EN. Office for official Publications of the European Communities, Luxemburg, 2004, pp. 38–58. [11] B. Margolin, V. Shvetsova, A. Gulenko, V. Fomenko, in: Proceedings of ASME 2009 PVP Conference, PVP-2009-77082. [12] Master Curve Approach to Monitor Fracture Toughness of Reactor Pressure Vessel in Nuclear Power Plants, IAEA-TECDOC-1631, IAEA, Vienna, 2009. [13] K. Wallin, in: Use and Applications of the Master Curve for Determining Fracture Toughness (Work Shop MASC 2002), Helsinki–Stockholm, 2002, pp. 4.1–4.17. [14] K. Wallin, Recommendations for the Application of Fracture Toughness Data for Structural Integrity Assessments. NUREG/CR-0131, ORNL/TM-12413, 1993. [15] B.Z. Margolin, G.P. Karzov, V.A. Shvetsova, E. Keim, R. Chaouadi, in: The 2002 ASME Pressure Vessels and Piping Conference, vol. 437, Vancouver, BC, Canada, August 2002, pp. 113–120. [16] B.Z. Margolin, V.A. Shvetsova, A.G. Gulenko, A.V. Ilyin, Int. J. Pres. Ves. Pip. 78 (2001) 715–729. [17] D.E. McCabe, Irradiation Effect on Engineering Materials. Heavy-section steel irradiation, Program. NUREG/CR-5591, 8(2), 2000. [18] R.K. Nanstad, D.E. McCabe, B.H. Menke, S.K. Iskander, F.M. Haggag, in: Packan N., Stoller R., Kumar A., (Eds.), Effects of Radiation on Materials: 14th Int. Symp., ASTM STP 1046, Am. Soc. for Test. and Mat., 1990, pp. 214–233. [19] J.G. Merkle, K. Wallin, D.E. McCabe, Technical Basis for an ASTM Standard on Determining the Reference Temperature, T0 for Ferritic Steels in the Transition Range. NUREG/CR-5504, ORNL/TM-13631, 1999. [20] K. Wallin, in: Use and Applications of the Master Curve for Determining Fracture Toughness (Work Shop MASC 2002), Helsinki–Stockholm, 2002, pp. 8.1–8.19. [21] E. Keim, R. Bartsch, G. Nagel, in: Use and Applications of the Master Curve for Determining Fracture Toughness (Work Shop MASC 2002), Helsinki– Stockholm, 2002. [22] S.R. Ortner, in: Use and Applications of the Master Curve for Determining Fracture Toughness (Work Shop MASC 2002), Helsinki–Stockholm, 2002, p. 19.1–19.14. [23] M.A. Sokolov, R.K. Nanstad, M.K. Miller, in: M. Grossbeck (Ed.), Effects of Radiation on Materials, ASTM STP 1447, ASTM Intern., West Conshohocken, PA, in press. [24] T. Planman, H. Keinanen, K. Wallin, R. Rintamaa, in: Irradiation Embrittlement and Mitigation. Proceed. of the IAEA Specialists Meeting in Gloucester, UK, 2001, Work. doc. IAEA TWG-LMNPP-01/2, 2002, pp. 521–535. [25] B.Z. Margolin, E.Yu. Rivkin, G.P. Karzov, V.I. Kostylev, A.G. Gulenko, in: Proc. VI Int. Conf.: Material Issues in Design, Manufacturing and Operation of Nuclear Power Plants Equipment, 19–23 June 2000, vol. 1, St-Petersburg, 2000, pp.159–77. [26] G. Karzov, B. Margolin, E. Rivkin, Int. J. Pres. Ves. Pip. 81 (2004) 651–656. [27] Procedure of Calculation on Brittle Fracture Resistance for WWER RPV in Service. MRKR CHR 2004, RD EO 0606-2005. St-Petersburg, Moscow, 2004, (Translation is published in: CRP 9: Review and Benchmark of Calculation Methods for Structural Integrity Assessment of RPVs during PTS, IAEA, Vienna, 2009) (in Russian). [28] Unified procedure for integrity and lifetime assessment of components and piping in WWER NPPs during operation ‘‘VERLIFE’’, version 2011, IAEA, Vienna, in press. [29] B.Z. Margolin, A.G. Gulenko, V.A. Nikolaev, L.N. Ryadkov, Int. J. Pres. Ves. Pip. 82 (2005) 679–686.

322

B. Margolin et al. / Journal of Nuclear Materials 432 (2013) 313–322

[30] Standards for Strength Calculation of Equipments and Pipelines of Nuclear Power Plants. PNAE G-7-002-86, Energoatomizdat, Moscow, 1989 (in Russian). [31] B.Z. Margolin, V.A. Shvetsova, A.G. Gulenko, V.I. Kostylev, Eng. Fract. Mech. 75 (2008) 3483–3498. [32] B.Z. Margolin, V.A. Shvetsova, A.G. Gulenko, V.I. Kostylev, Int. J. Pres. Ves. Pip. 84 (5) (2007) 320–336. [33] B. Margolin, A. Gulenko, V. Shvetsova, V. Nikolaev, D. Lidbury, E. Keim, in: Proceeding of 2008 ASME Pressure Vessels and Piping Conference, PVP 200861133.

[34] B.Z. Margolin, A.G. Gulenko, V.A. Shvetsova, E.V. Nesterova, Probl. Prochnosti (Probl. Strength) 5 (2010) 31–61 (in Russian). [35] B.Z. Margolin, V.A. Nikolaev, E.V. Yurchenko, Yu.A. Nikolaev, D.Yu. Erak, A.V. Nikolaeva, J. Pres. Ves. Pip. 89 (2012) 178–186. [36] B.Z. Margolin, V.A. Shvetsova, A.G. Gulenko, in: Use and Applications of the Master Curve for Determining Fracture Toughness (Work Shop MASC 2002), Helsinki–Stockholm, 2002, pp. 12.1–12.22.