Application and comparative study of the master curve methodology for fracture toughness characterization of 20MnMoNi55 steel

e m f 2 ad ndia olog pe el u tes r th arat 1. Introduction For safe design and operation of reactor of pressurized water reactors (PWRs), it is m systematic fracture toughness database and . The v ered an on (DB ue to in dis bility of cleavage fracture in terms of KJC at each temperature over the DBT region [8]. As a result, it is possible to determine median values and appropriate bounds for fracture toughness measure- ments in the transition region. It is observed from experimental re- sults that temperature dependence curve of median fracture toughness in DBT regimes takes a common shape for all ferritic steels differed only by their location in the temperature axis. As experimental data and for brittle fracture with initial ductile stretch, JC is determined from experimental J–R data using ASTM method. T0 is determined using both single and multi-temperature evaluation method on 1T-CT and 1/2T-CT specimens and values are compared. In case of single temperature evaluation, T0 is deter- mined at three different test temperatures for 1/2T-CT and two different test temperatures for 1T-CT specimens. While evaluating T0 using multi-temperature evaluation method, different range and combination of test temperature are used. The effect of a/W ratio ⇑ Corresponding author. Fax: +91 33 2414 6890. Materials and Design 39 (2012) 309–317 Contents lists available at an els E-mail addresses: [email protected], [email protected] (P. Sahoo). toughness–temperature curves along temperature axis. In ASME code for boilers and pressure vessels, KIC curve provides fracture toughness characterization for static crack initiation and KIR curve gives the same for dynamic crack initiation which are based upon the results from Charpy V-notch and drop weight nil ductility tran- sition temperature tests. But in many cases, the transition temper- ature obtained by above methods is overly conservative relative to the actual toughness [1–3]. The cleavage fracture in ferritic steel is of statistical nature and cleavage fracture toughness measurement of steels in the lower shelf and DBT region reveals significant scat- ter [4–6]. The ASTM standard test method E1921-02 [7] prescribes a three parameter Weibull distribution for the cumulative proba- tive of this work to study how the value of T0 differs depending on method or the other specimen parameters. This method also en- ables the use of small number of specimens for quantitative frac- ture toughness estimation, thus reducing testing cost and enabling surveillance size specimens to be used for a direct mea- surement of fracture toughness. The master curve method is also used to construct a bounding curve on the fracture toughness [9,10]. In this paper, the master curve reference temperature (T0) is estimated for 20MnMoNi55 ferritic steel for the complete description of the fracture toughness in DBT region using 1T-CT and 1/2T-CT specimen. For completely unstable brittle fracture, JC (J value at the onset of cleavage fracture) is measured directly from information in integrity assessment ness for RPV materials is very scatt dent in ductile to brittle transiti ductility and fracture toughness d RPV materials is also reflected 0261-3069/$ - see front matter � 2012 Elsevier Ltd. A http://dx.doi.org/10.1016/j.matdes.2012.02.050 pressure vessels (RPVs) andatory to develop a methods to apply this alue of fracture tough- d temperature depen- T) zone. The loss of neutron irradiation in placement of fracture minimum fracture toughness in DBT region is suggested to be a fixed value, hence the median fracture toughness in DBT regime is described with only one parameter, the reference temperature (T0). This T0 is defined as the temperature at which median fracture toughness for 1T (one inch thick) specimen equals 100 MPa p m. In this method, T0 the only fracture toughness characterizing param- eter can be evaluated using different methods like single tempera- ture and multi-temperature and also using specimens having different size, shape, crack depth and loading type. The main objec- Technical Report Application and comparative study of th for fracture toughness characterization o S. Bhowmik a, P. Sahoo a,⇑, S.K. Acharyya a, J. Chattop aDepartment of Mechanical Engineering, Jadavpur University, Kolkata 700 032, India bReactor Safety Division, Bhabha Atomic Research Centre, Trombay, Mumbai 400 085, I a r t i c l e i n f o Article history: Received 5 January 2012 Accepted 24 February 2012 Available online 7 March 2012 a b s t r a c t The master curve method master curve reference tem material 20MnMoNi55 ste perature range, number of The correction proposed fo and 1/2T-CT specimen sep 95% bound. Materials journal homepage: www. ll rights reserved. aster curve methodology 0MnMoNi55 steel hyay b, S. Dhar a y proposed by Kim Wallin (ASTM E1921-02) has been used to evaluate rature (T0) from full compact tension (CT) and 1/2T-CT specimens for the sing single temperature and multi-temperature method. The effect of tem- t temperatures and initial crack length on the value of T0 are also studied. ickness adjustment has been verified. Master curves are drawn using full ely and compared with best fit characteristic curve and found to be within � 2012 Elsevier Ltd. All rights reserved. SciVerse ScienceDirect d Design evier .com/locate /matdes and 2. Master curve analysis The transition fracture toughness curve definition for ferritic steels, as specified in ASTM E1921-97 [11] was originally derived in 1991 from data measured on various quenched and tempered structural steel. After the statistical size correction of these data, on the evaluated reference temperature is also studied. The correc- tion suggested for thickness adjustment is verified for the 20MnMoNi55 material. Master curve suggested by Wallin is devel- oped using 1T-CT and 1/2T-CT specimen separately and compared with best fitted characterizing curve. Nomenclature a physical half crack size, mm B gross thickness of specimens, mm B0 thickness of the tested specimen, mm B1T thickness of 1T (one inch thick) compact tension specimen, mm Bx thickness variable x that represents the specimen thickness of prediction, mm b0 initial remaining ligament length in specimens, mm E Young’s modulus, MPa J a path independent integral, J-integral, kJ/m2 JC J value at the onset of cleavage fracture JIC critical J-integral value for mode I loading, kJ/m2 KIC plane strain stress intensity factor determined as per the requirements of E399 KIR dynamic crack initiation toughness KJC stress intensity factor determined by conversion from JIC, MPa m1/2 KJC(limit) the maximum value of KJC data where KJC can be consid- ered valid, MPa m1/2 KJC(x) the predicted KJC value for a specimen of size Bx MPa m1/2 310 S. Bhowmik et al. /Materials which had been measured with different size specimens, the curve shape was determined from the maximum likelihood fit to data. Wallin [12] showed that the brittle fracture probability (Pf) for a gi- ven temperature in the transition region can be described by a three parameter Weibull model in the form: Pf ¼ 1� exp � KJC � KminK0 � Kmin � �4" # ð1Þ where Pf is the probability of fracture at KJC for an arbitrary chosen specimen from a specimen set, KJC is the cleavage fracture tough- ness in MPa p m, K0 is a scale parameter dependent on the test tem- perature and specimen thickness located at 63.2% cumulative failure probability level, and Kmin is the minimum possible fracture toughness. Wallin and International Atomic Energy Agency [13] have suggested that Kmin should be assumed to be equal to 20 MPa p m for all the ferritic RPV material. The temperature depen- dence of the median fracture toughness in the transition region is given by the following equation [14,15]: KJCðmedianÞ ¼ 30þ 70exp½0:019ðT � T0Þ� ð2Þ where T0 is master curve reference temperature in �C. At T = T0, the median fracture toughness is 100 MPa p m. Once T0 is known for a given material, the fracture toughness distribution can be obtained as a function of temperature using Eqs. (1) and (2). The measured KJC values should be checked to verify whether they fulfill the de- fined validity criterion. A KJC datum is invalid if the specimen size requirement is exceeded. The KJC limit is calculated according to the ASTM E1921-02 [7] standard as given below, KJCðlimitÞ ¼ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Eb0rys Mð1� m2Þ s ð3Þ where E is the modulus of elasticity of the material GPa, b0 is the initial specimen ligament length (W–a0) in mm, M is the constraint value which is equal 30 as per ASTM E1921-02 [7], m is the Poisson’s ratio (equal to 0.33) and rys is the material yield strength at the test temperature. In addition to size requirement there is the maximum ductile crack growth limit of 0.05 (W–a0) or 1 mm, whichever is smaller. KJC values beyond the validity criteria will be censored. KJC(0.xx) lower and upper tolerance bound for estimated fracture toughness, MPa m1/2 KJC(median) the median of a KJC data distribution for which Pf = 0.5, MPa m1/2 K0 a KJC value that represents the 63 percentile level of a KJC data distribution, MPa m1/2 Kmin a deterministic constant of the Weibull distribution, 20 MPa m1/2 M ASTM material constant, 30 Pf probability of failure for a specimen, chosen at random from an infinite population of specimens, to fail at or be- fore the KJC of interest T0 master curve reference temperature, �C W specimen width, mm di censoring parameter either one or zero: (1) used for valid KJC entries and (0) for dummy value entries t Poisson’s ratio ry flow stress, MPa rys yield strength, MPa rus ultimate strength, MPa Design 39 (2012) 309–317 The value of T0 is calculated after inclusion of all valid values according to the single or multi-temperature methods. For the sin- gle temperature method, multiple tests are done at the chosen test temperature. However, multi-temperature method is more effec- tive way than the single temperature method. The critical fracture toughness (KJC) is determined from the JC value obtained from experiment using following equation: KJC ¼ ffiffiffiffiffiffiffiffiffiffiffiffiffiffi JC � E 1� m2 r ð4Þ Now both upper and lower tolerance bounds can be calculated using the following equation [10]: KJCð0:xxÞ ¼ 20þ ln 11� 0:xx � �� �1 4 f11þ 77 exp½0:019ðT � T0Þ�g ð5Þ where 0.xx represents the cumulative probability level. The statistical weakest link theory is used to consider the effect of specimen size on the probability of failure in the transition re- gion. Now the measured KJC values are adjusted to a specimen size of 1T-CT specimen using the following equation [16]: KJCð1TÞ ¼ Kmin þ ½KJCðXÞ � Kmin� b0B1T � �1 4 ð6Þ where b0 is the thickness of the tested specimen (side grooves are not considered), B1T is the thickness of 1T-CT specimen, KJC(1T) is the fracture toughness of equivalent 1T-CT specimen, KJC(X) is the fracture toughness of the tested specimen. The KJC values below 50 MPa p m are not size adjusted. Replicate fracture toughness tests at a constant temperature are performed to determine T0. The ASTM standard [7] recommends minimum six tests and these data are used to determine K0 at the test temperature. tion of the scale parameter K0, is performed according to the fol- In case of multi-temperature evaluation the reference tempera- 4. Results and discussion 4.1. Tensile test results Tensile tests are performed on round bar specimen with diam- eter of 6.5 mm and gauge length of 30 mm according to ASTM E8/ E8M-09 [17] standard at different temperatures in the range be- tween 22 �C and �140 �C. The variation of yield strength and ulti- mate tensile strength of 20MnMoNi55 steel with temperature are shown in Fig. 1. With the decrease of test temperature both yield and ultimate tensile strength increase as expected. The relation between yield and ultimate strength with temperature are given in the following equation: Yield strength;rys ¼ 0:0112T2 � 0:0431T þ 494:01 ð11Þ Ultimate Strength;rus ¼ 0:0058T2 � 0:6817T þ 644:81 ð12Þ here T is in �C and strengths are in MPa. 4.2. J-integral test results J-integral test is performed according to ASTM E399-09e2 stan- dard [18] on 1T-CT and 1/2T-CT specimens at different tempera- tures in the range between 22 �C to �140 �C and a/W ratio. All the experimental result using 1T-CT and 1/2T-CT specimen at dif- ferent temperature and different crack length are shown in Figs. 2a and b. S. Bhowmik et al. /Materials and Design 39 (2012) 309–317 311 ture T0 is directly determined. The value of T0 is evaluated by an iterative solution of the following equation: XN i¼1 di exp½0:019ðTi � T0Þ� 11þ 77 exp½0:019ðTi � T0Þ� � XN i¼1 ðKJCðiÞ � KminÞ4 exp½0:019ðTi � T0Þ� f11þ 77 exp½0:019ðTi � T0Þ�g5 ¼ 0 ð10Þ here Ti is the test temperature corresponding to KJC(i) and di is the censoring parameter. di ¼ 1; if theKJCðiÞdatum is valid: ¼ 0; if theKJCðiÞdatum is not valid and censored: Margins are usually added to cover the uncertainty in T0 that is associated with the use of only a few specimens to establish this reference temperature. 3. Material details The material investigated for determining the master curve ref- erence temperature is 20MnMoNi55 steel used for pressure vessel applications. The chemical composition of the material is given in Table 1. Table 1 Chemical composition of 20MnMoNi55 steel. lowing equation: K0 ¼ XN i¼1 ðKJCðiÞ � KminÞ4 N " #1 4 þ Kmin ð7Þ The fracture toughness for a median (50%) cumulative probability of fracture is estimated according to the following equation: KJCðmedianÞ ¼ Kmin þ ðK0 � KminÞðln 2Þ 1 4 ð8Þ here KJC(i) is the individual KJC(1T) value and N is the number of KJC values. The term N is replaced by the number of valid KJC values in the calculation. Now the KJC(median) value determined at the test temperature is used to calculate T0 by using the following equation: T0 ¼ T � 10:019 � � ln KJCðmedianÞ � 30 70 � � ð9Þ 2.2. Multi-temperature evaluation method 2.1. Single temperature evaluation method For single temperature evaluation, the determination of T0 with KJC values is distributed over a restricted temperature range, namely, T0 = ±50 �C. For single temperature evaluation, the estima- Name of element C Si Mn P Percentage composition (in weight) 0.20 0.24 1.38 0.01 Fig. 1. Values of yield and ultimate strength at different temperatures. The fracture toughness values for only those specimens which have undergone brittle failure have been considered for master curve. S Al Ni Mo Cr Nb 1 0.005 0.068 0.52 0.30 0.06 0.032 and 312 S. Bhowmik et al. /Materials 4.3. T0 estimation at temperature �80 �C Six tests are done at �80 �C for 1T-CT and 1/2T-CT specimen each to determine the reference temperature T0 by single temper- ature method. At �80 �C, measured fracture toughness values vary from 108 to 267 MPa p m for 1T-CT and from 166 to 256 MPa p m for 1/2T-CT specimen respectively. From Eq. (7), K0 is obtained as 236 MPa p m for 1T-CT and 218 MPa p m for 1/2T-CT specimens respectively. The values of KJC(median) and T0 obtained from Eqs. (8) and (9) are 218 MPa p m and �132 �C for 1T-CT and 201 MPa p m and �127 �C for 1/2T-CT specimen respectively. The dif- ference between test temperature and reference temperature is greater than ±50 �C for 1T-CT specimen. Hence the result is invalid. On the other hand, the difference between test temperature and Fig. 2a. Experimental fracture toughness values of 1T-CT and 1/2T-CT specimens at different test temperatures. Fig. 2b. Experimental fracture toughness values of 1T-CT and 1/2T-CT specimens at different a/W ratios (without censoring). Design 39 (2012) 309–317 reference temperature is less than ±50 �C for 1/2T-CT specimen. Hence the result is valid. The master curve at test temperature of �80 �C is shown in Fig. 3a. Now the reference temperature T0 is determined by combining both 1T-CT and 1/2T-CT values. The value of T0 is obtained as �130 �C. The difference between test temperature and reference temperature is 50 �C. Hence the result is valid. The master curve combining both the specimens at �80 �C is shown in Fig. 3b. 4.4. T0 estimation at temperature �100 �C At �100 �C six tests have been carried out using 1/2T-CT spec- imen where the values of fracture toughness vary from 86 to 199 MPa p m. The values of K0 and T0 are obtained as 153 MPa p m and �125 �C respectively. The difference between test temperature Fig. 3a. Master curves at �80 �C test temperature for 1/2T-CT specimen. Fig. 3b. Master curves at �80 �C test temperature for 1T-CT and 1/2T-CT. 4.5. T0 estimation at temperature �110 �C From fracture toughness test it is found that material exhibits a very high scatter of fracture toughness in the transition region. At �110 �C, nine tests are done using 1T-CT specimen and six tests are done using 1/2T-CT specimen. The values of experimental fracture toughness vary from 17.8 to 162 MPa p m for 1T-CT and 85–166 MPa p m for 1/2T-CT specimen respectively. The character- istic feature of these data reveals that both the upper bound and and Design 39 (2012) 309–317 313 S. Bhowmik et al. /Materials and reference temperature is less than ±50 �C for 1/2T-CT specimen. Hence the result is valid. The master curve at test temperature �100 �C is shown in Fig. 4a. Now the reference temperature T0 is determined by combining both 1T-CT and 1/2T-CT results. The value of T0 = �123 �C. The dif- ference between test temperature and reference temperature is less than ±50 �C. Hence the result is valid. The master curve com- bining all the fracture toughness values at �100 �C is shown in Fig. 4b. But from the figure it is apparent that most of the experi- mental results are below the median fracture toughness curve obtained. lower bound of fracture toughness increase with temperature as expected. The value of K0, KJC(median) and T0 for 1T-CT specimen are 142.0 MPa p m, 132.0 MPa p m and �130 �C respectively. The master curve at test temperature �110 �C for 1T-CT specimen is shown in Fig. 5a. Similarly the value of K0, KJC(median) and T0 for 1/2T-CT specimen are 143.0 MPa p m, 133.0 MPa p m and �130 �C respectively after the adjust for size of specimen. The master curve at test tempera- ture �110 �C for 1/2T-CT specimen is shown in Fig. 5b. Now the reference temperature T0 is determined by combining both 1T-CT and 1/2T-CT specimen values. The value of T0 = �130 �C. The difference between test temperature and refer- ence temperature is less than ±50 �C. Hence the result is valid. and temperature dependence of the fracture toughness in the Fig. 4a. Master curves at �100 �C test temperature for 1/2T-CT specimen. Fig. 4b. Master curves at �100 �C test temperature for 1T-CT and 1/2T-CT combination. DBT region is expected to be best reflected in the master curve developed combining all the 1T-CT and 1/2T-CT specimens and The master curve combining all the fracture toughness values at �110 �C is shown in Fig. 5c. 4.6. T0 estimation using multi-temperature evaluation In case of multi temperature evaluation different temperature sequences have been considered. The value of T0 is �129 �C for 1T-CT specimen. The corresponding master curve is shown in Fig. 6a. The result is very close to reference temperature �123 �C obtained for the same material earlier by Merkle et al. [19]. Similarly the value of T0 using multi-temperature method is �126 �C for 1/2T-CT specimen. The corresponding master curve is shown in Fig. 6b. The multi-temperature method for evaluating the T0 is more effective way than the single temperature evaluation. The scatter Fig. 5a. Master curves at �110 �C test temperature using 1T-CT specimen. and 314 S. Bhowmik et al. /Materials using multi-temperature method. Hence the corresponding master curve and T0 are taken to be reference values for comparison of other results. After combining all the values of 1T-CT and 1/2T-CT specimens the reference temperature T0 is obtained as �129 �C. First, all the T0 values and corresponding master curve de- rived from 1/2T-CT specimens using single temperature evaluation are compared with the best characterizing curve and shown in Fig. 7a. Then all the T0 values derived from combining 1T-CT and 1/2T-CT specimen results using single and multi-temperature eval- uation is compared with the best characterizing curve and shown in Fig. 7b. A number of master curves are obtained for the same material using different methods and specimens. All the values of fracture toughness are presented in Fig. 7c for comparison with the master Fig. 5b. Master curves at �110 �C test temperature using 1/2T-CT specimen. Fig. 5c. Master curve at �110 �C test temperature using 1T-CT and 1/2T-CT combined. Design 39 (2012) 309–317 curve obtained using 1T-CT and 1/2T-CT specimens combined and using multi-temperature method. 4.7. Effect of test temperature combination on reference temperature The value of T0 is estimated using 1T-CT and 1/2T-CT specimen by multi-temperature evaluation for different combination of test temperature and the results are listed in Table 2. When the data of two test temperature is used for evaluating T0, the value of T0 varies from �128 �C to �133 �C for 1T-CT specimen and from �124 �C to �129 �C for 1/2T-CT specimen. When the data of three test temperatures are used the value of T0 varies between �127 �C to �131 �C for 1T-CT specimen and�124 �C to �128 �C for Fig. 6a. Master curves from multi-temperature evaluations using 1T-CT specimen. Fig. 6b. Master curves from multi-temperature evaluations using 1/2T-CT specimen. and S. Bhowmik et al. /Materials 1/2T-CT specimen. Also the range is �126 �C to �130 �C for 1T-CT and �123 �C to �126 �C for 1/2T-CT when data of four test temper- ature is used. In case of 1T-CT specimen in all the cases except one when �80 �C test temperature test data is evaluated the T0 ob- tained fail to satisfy ±50�C condition which is not observed to be happened in case of 1/2T-CT specimen. This indicates that as the number of test temperature increases, the value of T0 is more con- sistent. Therefore at least three different temperature tests should be performed to estimate the reference temperature when multi- temperature method is used. 4.8. Independence of reference temperature from test temperature The standard deviation for T0 has been calculated according to the formula given in the ASTM E1921-97 standard [11]. Fig. 7a. Master curve from single temperature evaluation for 1/2T-CT specimen. Fig. 7b. Master curve from single and multi-temperature evaluation for 1T-CT and 1/2T-CT specimen. Design 39 (2012) 309–317 315 rðT0Þ ¼ bffiffiffi r p ð13Þ where b is a function parameter for 1T-CT median fracture tough- ness and r is the number of valid. In this work b is taken 18 �C as all the median fracture toughness values are greater than 83 MPa p m. The T0 value obtained at different test temperature by different sized specimen are compared with the T0 obtained by mul- ti-temperature method considering the all the data. The following expression is used for deriving an engineering estimate of equiva- lent 1T-CT median fracture toughness for a multi-temperature data set, Fig. 7c. Comparison in master curve for all the values. Table 2 Values of T0 at different test temperature combination. Number of test temperature Combination of test temperature Value of T0 for 1T-CT (�C) Value of T0 for 1/2T-CT (�C) 2 �80 and �140 �131 �124 2 �80 and �100 �133 �125 2 �80 and �120 �131 �125 2 �80 and �130 �131 �125 2 �100 and �110 �129 �127 2 �80 and �110 �131 �128 2 �110 and �140 �128 �128 2 �110 and �120 �128 �129 2 �110 and �130 �128 �129 3 �80, �100, and �140 �131 �124 3 �80, �130, and �140 �130 �124 3 �80, �100, and �130 �131 �125 3 �80, �100, and �120 �131 �125 3 �100, �110, and �120 �128 �127 3 �110, �120, and �130 �127 �128 4 �80, �120, �130, and �140 �130 �123 4 �80, �100, �110, and �120 �130 �126 4 �100, �110, �120, and �130 �127 �126 4 �110, �120, �130, and �140 �126 �126 4 �80, �100, �110, and �130 �130 �126 5 �80, �110, �120, �130, and �140 �129 �121 5 �100, �110, �120, �130, and �140 �126 �125 5 �80, �100, �110, �120, and �130 �129 �126 6 �80, �100, �110, �120, �130, and �140 �129 �126 KeqJCðmedÞ1T ¼ 1 N XN i¼1 ½30þ 70 expð0:019ðTi � T0ðMTÞÞÞ� ð14Þ where Ti is the temperature of the individual test and N is the total number of tests performed. The results of standard deviation are shown in Fig. 8 where the T0 values for the individual data sets are within ±r error bands. Lucon et al. [20] found that the T0 values for 22NiCrMo37 steel for the individual data set are within ±2r error bands. Also the standard deviation calculated considering 1/2T-CT specimen T0 and 1T-CT and 1/2T-CT specimen combined T0. It is found that the value is 4.6 and 6.6 respectively and closer to the value men- tioned in IAEA report [13]. 4.9. Effect of temperature range on reference temperature Here Pearson’s product-moment correlation coefficient is used to measure the dependence of T0 for both the cases of 1T-CT and 1/2T-CT specimen with test temperature range. The values of cor- relation coefficient for both 1T-CT and 1/2T-CT are shown in Table 3. From these analysis is has been found that as the temperature values of T0 are evaluated for a/W of 0.45, 0.50, and 0.55. The result is plotted in Fig. 9. From the figure it is observed that as the value 5. Conclusion Reference temperature (T0) is evaluated for the material 20MnMoNi55 steel using single temperature and multi- temperature method and effect of temperature range, number of test temperatures and initial crack length on the value of T0 are studied. The correction proposed for thickness adjustment has been verified. From the results following observations are obtained. i. With the decrease of test temperature both yield and ulti- mate strength increases. ii. The fracture toughness values are very scattered at any tem- perature in DBT regime and brittle fracture is observed beyond and from �80 �C. iii. Master curve reference temperature obtained by combining all the 1T-CT and 1/2T-CT fracture toughness values and using multi-temperature method are considered as best characterizing curve for this material. The value of reference Fig. 9. T0 vs. a/W for different CT specimen. 316 S. Bhowmik et al. /Materials and of a/W increases the value of T0 also increases. Hence a dependence of T0 on a/W ratio is found from the results. range increases the value of T0 from consistent for both the specimen. 4.10. Effect of a/W for fixed thickness on reference temperature T0 In IAEA report [13], it was observed that for different type spec- imen the value of T0 decreases with decreasing crack depth for the different RPV steel. Here specimens from both 1T-CT and 1/2T-CT having same a/W ratio are taken together in a sample to evalu- ateT0. KJC values for 1/2T-CT are adjusted with size correction. Thus Fig. 8. Standard deviation of reference temperature calculated by considering different factors. Table 3 Coefficient correlation measurement. Difference in test temperature range T0 for 1T-CT (�C) T0 for 1/2T-CT (�C) Pearson correlation for 1T-CT Pearson correlation for 1/2T-CT 60 �129 �126 0.0083 0.498201895 50 �129 �126 40 �130 �126 30 �131 �127 20 �133 �125 40 �126 �125 30 �127 �126 20 �128 �127 10 �129 �127 30 �126 �126 20 �127 �128 10 �128 �129 Design 39 (2012) 309–317 temperature is very close to available results for the same material. All master curve and reference temperature values obtained by different methods, specimen size and a/W ratios are compared with this curve. It is observed that all the curves falls within the 70% and 30% bound of the best char- acterizing curve. iv. The variation in reference temperature for 1T-CT and 1/2T-CT specimens for different methods is within ±5 �C. Also the T0 are evaluated using multi-temperature evalua- tion method for 1T-CT and 1/2T-CT specimens separately, it is observed that reference temperature variation is within ±3 �C. Hence the correction suggested for thickness adjust- ment is found to effective for this material. v. When the different combinations of test temperatures are used to evaluate T0, it is observed that the value of reference temperature is more consistent as the number of test tem- perature considered increases. The correlation coefficient of T0 with temperature range is measured using Pearson’s product-moment correlation coefficient and it shows that T0 is linearly dependent on range of test temperature. Also the effect of a/W variation on the reference temperature is noticeable. More experiment is required to study the effect of a/W on reference temperature in details. vi. The reference temperature is independent of specimen size References [1] Rosinski ST, Server WL. Application of the master curve in the ASME code. Int J Press Ves Pip 2000;77:591–8. [2] Serrano M, Perosanz FJ, Lepeña J. 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For negligible variation in reference temperature derived from different methods and differently sized specimen one can derive the reference temperature by single temperature evaluation method and 1/2T-CT speci- mens to reduce time, material utilization and cost also. Acknowledgements Authors acknowledge the support of Board of Research in Nuclear Science (BRNS), DAE, Government of India for providing experimental infrastructure and also the support of Department of Science and Technology, Government of India through PURSE program. Fract Mech 2002;69:451–81. [13] IAEA-TECDOC-1631. Master curve approach to monitor fracture toughness of reactor pressure vessels in nuclear power plants; 2009. p. 65. [14] Viehrig H-W, Boehmert J, Dzugan J. Some issues by using the master curve concept. Nucl Eng Des 2002;212:115–24. [15] Wallin K. Structural integrity assessment aspects of the master curve methodology. Eng Fract Mech 2010;77:285–92. [16] Hohe J, Hebel J, Friedmann V, Siegele D. 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Application and comparative study of the master curve methodology for fracture toughness characterization of 20MnMoNi55 steel 1 Introduction 2 Master curve analysis 2.1 Single temperature evaluation method 2.2 Multi-temperature evaluation method 3 Material details 4 Results and discussion 4.1 Tensile test results 4.2 J-integral test results 4.3 T0 estimation at temperature −80°C 4.4 T0 estimation at temperature −100°C 4.5 T0 estimation at temperature −110°C 4.6 T0 estimation using multi-temperature evaluation 4.7 Effect of test temperature combination on reference temperature 4.8 Independence of reference temperature from test temperature 4.9 Effect of temperature range on reference temperature 4.10 Effect of a/W for fixed thickness on reference temperature T0 5 Conclusion Acknowledgements References