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  Estimation of ASTM E-1921 reference temperature from Charpy tests:Charpy energy-fracture toughness correlation method P.R. Sreenivasan Metallurgy and Materials Group, Indira Gandhi Centre for Atomic Research, Kalpakkam 603102, India a r t i c l e i n f o  Article history: Received 21 December 2006Received in revised form 12 August 2008Accepted 20 August 2008Available online 28 August 2008 Keywords: Reference temperatureCharpy correlationMaster curve (MC)Mean-4 procedure (M4P)Reactor pressure vessel steel (RPV) a b s t r a c t In this paper, some of the older and newer Charpy-fracture toughness correlations havebeen examined and new correlations have been developed for predicting the ASTM E-1921 standard reference temperature,  T  0 . The results have been applied to some selectednew steels and compared with measured  T  0 , where available. It is found that the predictedreference temperature from the new procedure gives reliable and acceptably conservativeengineering estimate of   T  0 . Predicted values of reference temperatures under dynamic con-ditions from these  T  0  using Wallin’s strain rate shift equation agree well with measureddynamic values for a few steels giving added support to the new procedure.   2008 Elsevier Ltd. All rights reserved. 1. Introduction Nuclear reactor pressure vessel (RPV) steels are degraded by various causes during plant operation. Various embrittle-ment phenomena like thermal ageing embrittlement, neutron irradiation embrittlement etc. contribute to the degradationin toughness of ferritic steels – the latter, neutron irradiation embrittlement, is one of the severest and leads to increase inductile brittle transition temperature (DBTT), increase in strength and reduction in fracture toughness. High fracture tough-ness and low DBTT values are needed to avoid fracture not only during service (for example, start-up and cool-down or acci-dent situations like Pressurised Thermal Shock – PTS) but also prior to start-up in the case of some ferritic RPV componentslike steam generator subjected to proof-testing. To ensure structural integrity and assure continued or extended life of theplant, precise fracture-safe analysis is done using fracture mechanics principles-usually, Linear Elastic Fracture Mechanics,LEFM. LEFM analysis requires exact evaluation of material fracture toughness,  K  IC , which shows large scatter in the transitionregion and requires very large specimens to obtain valid linear elastic fracture toughness values [1,2]. Due to nuclear reactorspace limitations and specimen radiation problems during testing, small test specimens are preferred for irradiation-embrit-tlement and surveillance studies.Because of advances in fracture mechanics technology, elastic–plastic fracture mechanics based  J  -integral techniques en-able determination of fracture toughness values with much smaller specimens. Moreover, the inherent scatter in the tough-ness in the lower-shelf and transition region has been recognized, and toughness values in the transition region have beenshown to follow the weakest link statistics and Weibull distribution [6,7]. Based on this, a new Master Curve (MC) approachhas been proposed indexed to a reference temperature,  T  0 , defined as the temperature at which the median fracture tough-ness for 1 in. specimens is 100 MPa p  m; this can be determined using small specimens through a  J  -integral and  K   JC  approach[8]. Since the new MC is statistically based and depends on direct measurement of fracture toughness, some of the over con-servatism of the earlier RTNDT based approach [3–5] can be avoided and also there are theoretically and empirically based 0013-7944/$ - see front matter    2008 Elsevier Ltd. All rights reserved.doi:10.1016/j.engfracmech.2008.08.007 E-mail address:  sreeprs@yahoo.co.inEngineering Fracture Mechanics 75 (2008) 5229–5245 Contents lists available at ScienceDirect Engineering Fracture Mechanics journal homepage: www.elsevier.com/locate/engfracmech  Nomenclature a 0  initial crack or notch depth (or length) = 2 mm for a CVN specimen B  specimen thickness, usually length along the crack front (=10 mm for a CVN specimen)BRS Barsom–Rolfe shift T  28J  Charpy transition temperature at which Charpy energy = 28 J T  41J  Charpy transition temperature at which Charpy energy = 41 J C  V  energy absorbed by a CVN specimen during an impact testCVN Charpy V-notchDBTT (ductile brittle transition temperature) temperature corresponding to a fixed C V , lateral expansion or fractureappearance; for example,  T  28J  is a DBTT  J  i  or  J  d  initiation  J  -integral values under quasi-static or dynamic loading conditions, respectively E   Young’s modulus K  IC  valid linear elastic fracture toughness as per ASTM E-399 standard K  Id  valid linear elastic fracture toughness under dynamic loading (say, during impact test) K   JC  valid (quasi-static) elastic–plastic fracture toughness obtained from  J   integral as per ASTM E-1820 standard K   Jd  K   JC  equivalent obtained under dynamic (say, impact) loading conditionsLEFM Linear Elastic Fracture MechanicsMaster curve (MC) a standard reference fracture toughness curve for ferritic steels indexed to reference temperature,  T  0 ,as per ASTM E-1921 standardM4P mean 4 procedure n  work-hardening index  p  ratio of   P  m / P  gy  or  r maxd / r yd  in instrumented CVN test-subscript ‘ d ’ indicates dynamic loading P  fd  mean of   P  m  and  P  gy  during instrumented CVN impact test P  gy  general yield load P  dygy  RT  P  gy  at room temperature under impact test P  m  maximum load in the CVN test load-time tracePTS pressurised thermal shock P  IGC1  parameter-IGC1 defined as: ( r f  / r ys-RT ) * T  41J P  IGC2  parameter-IGC2 defined as: ( r ys-T41 / r ys-RT ) * T  41J R  correlation coefficient of regression R 2 coefficient of determination of a regressionRPV reactor pressure vessel T  0  reference temperature determined as per ASTM E 1921 standard T  dy0  reference temperature under dynamic loading conditionsRLB Robert’s lower-bound correlationRNB Rolfe, Novak and Barsom correlationRT NDT  a reference temperature determined from a combination of CVN impact And ASTM E-208 drop-weight testsSC Sailors and Corten correlationMSP Modified-Schindler-ProcedureSEE standard error of estimate T  Q-28  T  0  predicted by an empirical correlation of   T  28J  with  T  0 T  Q-28CON  T  0  predicted by a conservative empirical correlation of   T  28J  with  T  0 T  Q-41  T  0  predicted by an empirical correlation of   T  41J  with  T  0 T  K100-BRKd  temperature corresponding to a  K  d  = 100 MPa p  m from an empirical  C  V  K  d  (dynamic fracture toughness) cor-relation in BRS procedure T  K100-BRS  temperature corresponding to a  K   = 100 MPa p  m based on BRS procedure T  Q-IGC1  T  0  predicted from  P  IGC1  correlation with  T  0 T  Q-IGC2  T  0  predicted from  P  IGC2  correlation with  T  0 T  K100-RLB  temperature corresponding to a  K   = 100 MPa p  m based on RLB procedure T  K100-RN  temperature corresponding to a  K   = 100 MPa p  m based on RNB procedure T  K100-SC  temperature corresponding to a  K   = 100 MPa p  m based on SC procedure T  dyK75  Sch  temperature corresponding to a dynamic toughness of   K   Jd  = 75 MPa p  m based on MSP procedure T  Q-MSP  T  0  predicted from  T  dyK75  Sch  T  0  correlation derived from MSP T  Q-M4  T  0  predicted by the M4P (mean of   T  Q-28 ,  T  Q-41 ,  T  Q-IGC1  and  T  Q-IGC2 ) T  4kN  Temperature at which the arrest-load in an instrumented CVN impact test is 4 kN W   width of the test specimen (=10 mm for a CVN specimen) r f   microcleavage fracture stress r fd  flow stress corresponding to  P  fd  from the impact test 7 r maxd  dynamic yield stress at maximum load,  P  max , of instrumented Charpy V notch (CVN) test 5230  P.R. Sreenivasan/Engineering Fracture Mechanics 75 (2008) 5229–5245  procedures to incorporate the thickness effects on fracture toughness. In 1999, the Master Curve method was adopted by  ASME  Code Committee as Code Case N-629 for Section XI applications and Code Case N-631 for Section III applications[1]. Hence, nowadays, ferritic RPV materials are increasingly being characterized by the  T  0  and the associated MC approach.However, actual fracture toughness determination requires use of precracked specimens and is sophisticated and expen-sive compared to the easily conducted simple Charpy (CVN) specimen impact test. Moreover, in irradiation embrittlementand surveillance studies, as RPV materials have been evaluated mainly by Charpy test, there are abundant Charpy test datafor old RPVs [1]. Hence a methodology for accurate or conservative estimation of   T  0  from CVN test results would be usefulfrom the point of view of cost and simplicity of testing; in addition, it will enable evaluation of CVN data of ageing RPVs forthe purpose of life extension. Though correlations have been proposed to predict the  T  0  from Charpy transition temperature T  28J  or instrumented impact test parameters like  T  4kN , nonecan be taken as a universal correlation [9–12]. In this paper, someof the older and newer Charpy-fracture toughness correlationshave been reviewed and correlationsdeveloped for predicting T  0 . The results have been applied to some selected new steels and compared with measured  T  0 , where available. In this con-text, it would be instructive for the reader to refer to papers by Pineau [71], Chaouadi [72] and Norris et al. [73], which detail difficulties involved in generating fracture toughness correlations over the whole transition range and also discuss microm-echanics and computer based modelling. Hence, for engineering applications assured conservative correlations, even thoughempirical, are desirable. 2. Methodology for development of correlations  2.1. Direct charpy energy ( C  V  ) temperature – T  0  correlations One of the simplest and direct correlations is that between the temperature for 28 J  C  V  energy,  T  28J , and  T  0  [12] as given byEq. (1) (all temperatures in Eqs. (1)–(4) are   C): T  0  ¼  T  28J   18  ð r  ¼  15   C Þ ð 1 Þ Subsequently, the above has been revised by many authors,including the present one [13,14]. One of the latestmodificationsof Eq. (1) is as given by Eq. (2) [13]: T  0  ¼  T  28J   19  ð r  ¼  22   C Þ ð 2 Þ with T  0  1 r  ¼  T  28J  þ 3  ð 2a Þ Eq.(2a)isrecommendedasaconservativeestimate.Basedontheauthor’searlierwork[14],the T  28J correlationobtainedwas: T  0  ¼  1 : 09 T  28J   11 : 2  ð r  ¼  18   C Þ ð 3 Þ with conservative estimate given by T  0  ¼  1 : 18 T  28J  þ 12 : 52  ð 3a Þ Similarly, based on  T  41J , the following correlations have been given [13]: T  0  ¼  T  41J   26  ð r  ¼  25   C Þ ð 4 Þ with conservative estimate given by T  0  1 r  ¼  T  41J   1  ð 4a Þ For some steels with known  T  0 ,  T  28J  and  T  41J , the estimates from Eqs. (1), (2), (3), and (4a) are shown in Fig. 1 in compar- ison with measured  T  0  (for obvious reasons Eqs. (1) and (2) are treated the same as Eq. (1)). It is obvious that Eqs. (3a) and (4a) give the most conservative estimates over the range of temperatures involved, the former being closer to the 1:1 linemost of the time (i.e., showing more accuracy and lower residuals), except in two or three cases. Hence for comparison with T  28J  or  T  41J  based correlation from literature, only Eq. (3a) will be used in further discussions. For conformity with the ter-minology in ASTM E-1921 [8] as explained later, the conservative  T  0  from Eq. (3a) is referred as  T  Q-28CON , CON indicating con-servative. In fact, Eq. (3a) was obtained by the author [14] using the semi-empirical relationship between static initiation J and dynamic Charpy energy data provided by Norris et al. in [73] based on experimental and computer based modelling.Another tendency that becomes obvious in Fig. 1 is the existence of a non-linear correlation between measured and pre-dicted values; instead of a linear, a quadratic, exponential or rational function would have been better. This aspect is pursuedin the new  T  28J  or  T  41J  based correlations developed in this paper. r ys  quasi-static yield stress, dependent on temperature r yd  dynamic yield stress r yd-RT  dynamic yield stress at broom temperature r ys-RT  quasi-static yield stress at room temperature r ys-T41  quasi-static yield stress at  T  41  temperature P.R. Sreenivasan/Engineering Fracture Mechanics 75 (2008) 5229–5245  5231   2.2. Older CVN energy (C  V  ) – K  IC   correlations and T  0  estimates The basic philosophy in this method is to generate fracture toughness data using well-known  C  V – K  IC  correlations and ob-tain the temperature corresponding to a fracture toughness of 100 MPa p  m called  T  K100-X , with X referring to the particularcorrelation used (as explained later).  T  K100-X  is correlated to actual  T  0  by a correlative procedure to yield the estimated ref-erence temperature,  T  Q-X , where  X   has the same implication as described in the first sentence. Perhaps, Kim and co-workers[1] were the first ones to use this procedure followed by the present author and co-workers [5,15]. However, the procedure given here is more simplified than that used by Kim and co-workers. Several empirical correlations have been proposed be-tween  K  IC  and Charpy (CVN) energy,  C  V , for different regions of the Charpy transition curve [9–12,16–21]. The  C  V –K IC  corre-lations examined in this paper are the following pertaining to the Charpy transition region:Rolfe, Novak and Barsom (RNB correlation) [20,19] given by Eq. (5), K  IC  ¼ ð E  : 1000 : ð 2 : 28 Þ  10  4   C  1 : 5V  Þ 0 : 5 ð YS range  ¼  270  1700 MPa; C  V  range  ¼  4  82 J Þ ð 5 Þ where K IC  is in MPa p  m,  E   is the Young’s modulus in GPa and  C  V  is the Charpy energy in J.Sailors and Corten (SC correlation) [17] given by Eq. (6), K  IC  ¼  14 : 63 C  0 : 5V  ð YS range  ¼  410  480 MPa;  C  V  range  ¼  7  68 J Þ ð 6 Þ Robert’s lower-bound correlation (RLB correlation) [9] given by Eq. (7), K  IC  ¼  8 : 47 C  0 : 63V  ð 7 Þ and Barsom and Rolfe’s  K  d – K  c  (dynamic to static fracture toughness) temperature shift (Barsom–Rolfe Shift – BRS) procedure[19] given by Eqs. (7a) and (7b), K  d  ¼ ð 0 : 64 EC  V Þ 0 : 5 ð YS range  ¼  250  345 MPa;  C  V  range  ¼  2 : 7  61 J;  E   in MPa Þ ð 7a Þ T  shifted  ¼  T  CVN   ð 119  0 : 12 r ys  RT Þ ð 7b Þ ( T  shifted  = temperature after shift;  T  CVN  = CVN test temperature at which  K  d  is given by Eq. (7a);  K  d  at  T  CVN  =  K  IC  at  T  shifted ; r ys-RT  = room temperature yield stress).Each of the above equations gives a  K  IC – T   curve corresponding to the  C  V – T   (Charpy transition) curve; in addition, appli-cation of Eq. (7a) alone gives a  K  d – T   curve. From each of the fracture toughness-temperature curve obtained from the abovecorrelations, a temperature corresponding to a fracture toughness of 100 MPa p  m can be obtained (that is, a reference tem-perature estimate). The  T  0  values based on fracture toughness data obtained using Eqs. (5)–(7), (7a) will be referred as T  K100-RNB ,  T  K100-SC ,  T  K100-RLB ,  T  K100-BRS , and  T  K100-BRKd  (from  K  d – T   data using Eq. (7a) alone), respectively. The direct choiceof the temperature corresponding to 100 MPa p  m fracture toughness obtained from the  C  V – K  IC  correlations as the estimatedreference temperature – instead of application of the ASTM E-1921 size correction procedure to the fracture toughness data Fig. 1.  Comparision of measured T 0  with those predicted from Eqs. 1, 2, 2a, 3, 3a, 4 (see text).5232  P.R. Sreenivasan/Engineering Fracture Mechanics 75 (2008) 5229–5245
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