cleavage fracture stress model for fractoughness estimation

Materials Performance andCharacterization

P. R. Sreenivasan1

DOI: 10.1520/MPC20130079

Estimation of ASTM E1921Master Curve of FerriticSteels FromInstrumented ImpactTest of CVN SpecimensWithout Precracking

VOL. 3 / NO. 1 / 2014

http://http://www.astm.org/Standards/E1921






P. R. Sreenivasan1

Estimation of ASTM E1921 MasterCurve of Ferritic Steels FromInstrumented Impact Test of CVNSpecimens Without Precracking

Reference

Sreenivasan, P. R., “Estimation of ASTM E1921 Master Curve of Ferritic Steels From

Instrumented Impact Test of CVN Specimens Without Precracking,” Materials Performance

and Characterization, Vol. 3, No. 1, 2014, pp. 285–308, doi:10.1520/MPC20130079. ISSN

2165-3992

ABSTRACT

A semi-empirical cleavage fracture stress (CFS) model, mainly depending on

the CFS, rf, has been derived for estimating the ASTM E1921 reference

temperature (T0) and demonstrated for ferritic steels with yield strength in the

range 400–750 MPa. This requires only instrumented impact test of CVN

specimens without precracking and static yield stress data. The T0 estimate

based on the CFS model, TQcfs, lies within a 620�C band, being conservative

for most of the steels, but less conservative than TQIGC based on the IGC-

procedure (see Nomenclature for definition). Applicability and acceptability of

the present calibration curves for highly irradiated steels need further

examination.

Keywords

Charpy V-notch, instrumented impact test, reference temperature, fracture toughness,

cleavage fracture stress

Manuscript received October 21,

2013; accepted for publication May

14, 2014; published online June 23,

2014.

1

Metallurgy and Materials Group,

Indira Gandhi Centre for Atomic

Resaearch, Kalpakkam,

Tamilnadu-603 102, India,

e-mail: [email protected]

Copyright VC 2014 by ASTM International, 100 Barr Harbor Drive, P.O. Box C700, West Conshohocken, PA 19428-2959 285

Materials Performance and Characterization

doi:10.1520/MPC20130079 / Vol. 3 / No. 1 / 2014 / available online at www.astm.org



http://www.astm.org/Standards/E1921

Nomenclature

CFS ¼Cleavage fracture stress, rf

CV ¼Energy absorbed by a CVN specimen during animpact test

CVN ¼Charpy V-notchDBTT ¼Ductile-Brittle Transition Temperature. Temperature

corresponding to a fixed CV, lateral expansion, or frac-ture appearance; for example, T28J is a DBTT

d ¼displacement experienced by the CVN specimen dur-ing IIT

IGC-procedureðor IGCAR procedureÞ

¼ a multi-stage correlation procedure to estimate TQIGC,where TQIGC is the estimate of T0 obtained using theIGCAR procedure detailed in Ref. [6]. TQIGC valuesare conservative to the extent of 20�C–30�C.

IIT ¼ instrumented impact testKIC ¼ valid linear elastic fracture toughness as per ASTM

E399 standardKJC ¼ valid linear elastic-plastic fracture toughness as per the

ASTM E1921 standard [5]LTD ¼Load Temperature Diagram; a plot of various loads

from the P-d traces of several CVN specimens testedin the DBTT range plotted as a function of test tem-perature, with the same loads (say, PGY, PF, etc.) joinedby average smooth curves, if possible.

MC ¼ a standard reference fracture toughness curve for fer-ritic steels indexed to reference temperature, T0, as perASTM E1921 standard [5]

P ¼ a general symbol for specimen load; here, experiencedby the CVN specimen during IIT

PA ¼brittle fracture arrest load on the P–d trace of a CVNIIT test record

PF ¼brittle fracture load on the P–d trace of a CVN IIT testrecord

PGY or Pgy ¼ general yield load on the P–d trace of a CVN IIT testrecord

Pmax or PM ¼maximum load on the P-d trace of a CVN IIT testrecord

T0 ¼ reference temperature determined as per ASTM E1921standard

TD ¼ the brittleness transition temperature, end of the grosselastic region in the load-temperature diagram ofinstrumented impact or slow-bend tests and representsalmost end of 100 % cleavage fracture withPF¼ Pmax¼ PGY

TQ ¼Estimated T0 by a non-standard methodTQIGC ¼T0 estimated by the IGCAR-procedure

SREENIVASAN ON CVN SPECIMENS WITHOUT PRECRACKING 286






Introduction

Charpy V-notch (CVN) impact test is very attractive because of its low-cost, sim-

plicity, wide familiarity, and availability [1]. Instrumented impact test (IIT), while

maintaining these advantages—in addition to the conventional Charpy energy

(CV), lateral expansion (LE), and % shear fracture (PSF)—provides additional

load (P)–time (t) or displacement (d) data of the CVN specimen during

deformation and fracture (time can be converted to displacement). Figure 1 shows

the various load parameters obtainable: general yield load-PGY (or Pgy, used inter-

changeably; see nomenclature), initiation load-Pinit (determined by compliance

change or key-curve technique or by acoustic emission or similar sophisticated

instrumentation), maximum load-PM or Pmax, brittle-fracture load-PF and arrest

load-PA, and the corresponding times/displacements— say, for example, dF, the

displacement to PF. The various load parameters plotted against test temperature

(T) provides the load-temperature diagram (LTD) characterizing various regions

of fracture [1,2]; see, for example, Fig. 2 [3]. A typical ferritic steel tested in the

ductile-brittle transition temperature (DBTT) region shows characteristic P–d

traces: at the lower-shelf, the fracture is purely linear-elastic with sudden brittle

TQcfs ¼T0 estimated by the CFS model-TQcfs is the most con-servative of the four, namely, TQcfs1, TQcfs2, TQcfs3, andTQcfs4

TQcfs1 ¼TQcfs obtained from rf/rys (as a function of temperature)and rf/rys*1 ratio

TQcfs2 ¼TQcfs obtained from rf/rys (as a function of temperature)and rf/rys*2 ratio

TQcfs3 ¼TQcfs obtained from rf/ryd (as a function of tempera-ture) and rf/ryd*1 ratio

TQcfs4¼TQcfs obtained from rf/ryd (as a function of temperature)and rf/ryd*2 ratio

TQBT ¼T0 predicted from the empirical correlation of TD withT0

T28J ¼Charpy transition temperature at which Charpyenergy¼ 28 J

T41J ¼Charpy transition temperature at which Charpyenergy¼ 41 J

rf ¼ cleavage fracture stress (CFS) determined from thePF¼ Pmax¼ PGY loads at the temperature TD

rys ¼quasi-static yield stress, dependent on temperatureryd ¼dynamic yield stress, dependent on temperature

ryd-RT ¼dynamic yield stress at room temperaturerys-RT ¼quasi-static yield stress at room temperaturerys*1 ¼rys at (T41J�24)�Crys*2 ¼rys at (T41J�50)�Cryd*1 ¼ryd at (T41J�24)�Crys*2 ¼ryd at (T41J�50)�C



failure occurring at the maximum load, PM (¼PF) corresponding to 100 % cleav-

age, while, at higher temperatures, as the test progresses to the upper shelf, PGYprecedes cleavage fracture. Then PM and PF separate, with substantial ductile

crack extension preceding PF and, at some temperature interval, brittle fracture

started at PF arrests at PA. Ultimately, at the upper shelf, the traces do not show

any brittle fracture: no PF and PA. From the various load parameters, the % shear

fracture (PSF) can be obtained as a function of temperature as also the brittleness

transition temperature (TD), the temperature at which PM (¼PF)¼ PGY [2] and at

higher temperatures, brittle fracture occurs after general yielding. These features

are delineated clearly in Fig. 2. From the PM (¼PF)¼ PGY load at TD, the micro-

cleavage fracture stress, rf, can be calculated. Moreover, from the PGY load values

at various temperatures, the dynamic yield stress, ryd, as a function of tempera-

ture is obtained [1,4]. These data are very important for the present paper, as will

be shown later.

FIG. 1

Characteristic loads marked on

an IIT load-time (t) trace and

energy partitioning related to

fracture surface of a CVN

specimen.

FIG. 2

Load temperature (P–T)

diagram for the 9Cr–1Mo BM

from instrumented CVN impact

tests at V0¼5.12 ms�1.



For obtaining design relevant dynamic fracture toughness (KId), however, test-

ing of fatigue precracked CVN (PCVN) specimens is necessary. This is costly and

time consuming [4]. Moreover, testing of PCVN specimens introduces problems

in data reduction due to superimposed oscillations. To overcome these difficulties,

testing at reduced velocity [3] (say, at� 1ms�1 instead of at the usual impact test

velocity of �5ms�1, with resultant loss of strain rate) or the use of complicated

dynamic analysis methods have been suggested [1]. Nowadays, reactor pressure

vessel (RPV) steels are increasingly being characterized in terms of the reference

temperature T0 and master curve (MC) as per the ASTM E1921 standard [5]. The

present author had previously proposed a multi-stage correlation procedure to esti-

mate TQIGC, where TQIGC is the estimate of T0 obtained using the procedure (IGCAR

procedure) detailed in Ref. [6]. TQIGC values are conservative to the extent of

20�C–30�C. The present paper examines in a new empirical perspective the relation

of rf to fracture toughness and, thereby, tries to derive a methodology to estimate

fracture toughness and master curve from the load-temperature data and Charpy

energy obtained from instrumented impact test (IIT) of CVN specimens without

precracking.

First, the semi-theoretical-empirical basis of the present approach will be

delineated in the light of previous literature. Then the method to obtain the new em-

pirical methodology will be given. The new methodology will be applied to the cali-

bration steels as also to many steels presented in Ref. [6] and others. The results will

be compared with actual T0 or estimated TQ (as a convention, non-standard, i.e., not

following the ASTM E1921 standard for master curve determination, estimates of T0

are designated TQ [6]). In addition to being fast and less costly (as no precracking is

required), the new method, being a single assessment method (compared to the

multi-stage method in Ref. [6]), will simplify the evaluation and hence will be less

error-prone. Moreover, it will enhance the utility and purpose of the IIT of blunt-

notched CVN specimens of ferritic steels. Particularly relevant is the fact that the

new procedure will help obtain more valuable and design relevant master curve

from IIT of irradiation surveillance specimens.

Theoretical-Empirical Basis and Methodology

LITERATURE REVIEW

Based on the concept of brittle cleavage fracture occurring ahead of a crack on the

attainment of a critical cleavage fracture stress (rf) over a critical distance (X0) of

Ritchie et al. [7] and using the stress analysis of Hutchinson [8], Curry [9] related

the cleavage fracture toughness, KIC to rf and rys in the following way:

KIC ¼ b�ðNþ1Þ

2 � X120r

Nþ12

f

rN�12

ys

(1)

where:

b¼ a material dependent constant (mainly a function of Ramberg–Osgood

work-hardening exponent, N, and can be evaluated based on expressions given in

Ref. [8]),





X0¼ the critical distance (depending on the microstructure, it has been related

to 2–3 ferrite grain diameters in ferrite–pearlite steels, or packet or bainite size in

martensitic or bainitic steels or no microstructural feature in certain steels), and

rf¼ independent of temperature and strain rate, and in most cases, even of irra-

diation conditions.

The accurate determination of X0 for various steels is a problem. Later, Hahn

et al. [10] and Kotilianen [11] empirically put KIC to rf and rys relation as:

rf

rys¼ a � KIC

rys

� �c

(2)

where a and c are constants for a particular steel and also depend on the tempera-

ture range of fit. Thus, the above equations have not found universal application;

although Eq 1 is theoretically more satisfying.

Recently, in the mesoscopic (given as mezzo-scopic in the referred paper) analy-

sis of fracture toughness of steels, Miyata and Tagawa [12] simplified the statistical

local fracture criterion approach to fracture toughness analysis of steels by both an

analogous and an empirical approach. Using a two-parameter Weibull stress distri-

bution for predicting fracture probability, they derived the expression relating KIC to

Weibull Stress, rW. Then, using analogy, they replaced the Weibull stress with the

cleavage fracture stress, rc—the fracture stress defined in deterministic terms (the

cleavage fracture stress, rc, is defined as the local maximum principal stress at the

cleavage fracture initiation in round bar tensile specimens with 1mm radius circum-

ferential notch) [12]. Finally, based on both fracture toughness tests and rc tests on a

large number of carbon and low-alloy steels (YS range: 250–1100MPa), they found

the following empirical relation:

KCðMPaffiffiffiffimpÞ ¼ 2:85� 10�3

BðmmÞ14

rCðMPaÞ rC

rys

� �g

(3)

where g is fit constant for a steel (g is represented as a in Ref. [12]).

Since it needs a large number of specimens to obtain the statistical Weibull

parameters compared to the determination of rc, Eq 3 is a simplification. In

Ref. [12], the exponent g was given as a function of T150 temperature. Here, T150 is

the temperature corresponding to a fracture toughness of 150MPaHm. The g-T150plot in Ref. [12] shows high scatter and wide dispersion. Hence, even Eq 3 is not

amenable to practical application. This paper, while retaining the simplicity of the

above methods (rf/rys and rf/ryd ratio or fracture to yield stress ratio method), tries

to overcome their limitations by an empirical procedure.

The features of the above theoretical, semi-empirical, or empirical formula-

tions can be summarized as follows. Basically, at the point of brittle fracture initia-

tion, the local crack tip tensile stress reaches a critical value, namely, the

microscopic cleavage fracture stress, rf or rC (the cleavage fracture stress can be

determined from either notch-tensile tests—many authors denote this as rC—or

three-point bend or instrumented impact tests of Charpy V-notch (CVN) speci-

mens, mostly denoted by rf; based on consideration of differences in sampled and

stressed volume for the two types of specimens, rf; especially determined from



instrumented impact tests, is slightly larger than rC from notch-tensile tests [13])

at a critical distance, usually the distance to the weakest link. In fact, a two- or

three-parameter distribution of Weibull stress distribution is the basis of the mas-

ter curve based on the ASTM E1921 standard [5]. The mesoscopic analysis of

fracture toughness as described in the previous section implies that fracture tough-

ness variation with temperature can be expressed as a function of critical fracture

stress to yield stress ratio.

PRESENT METHODOLOGY

Based on the above considerations, the variation of the ratios, rf/rys or rf/ryd, (ryd,

is the dynamic yield stress determined from instrumented Charpy V-notch speci-

men tests at various temperatures) are related to the relevant static MC fracture

toughness data; i.e., for the same temperature range, at various temperatures, the

ratio, rf/rys or rf/ryd, are evaluated along with the corresponding static MC KJC.

Then the resulting, rf/rys or rf/ryd, values are plotted against the corresponding

static MC KJC and a smooth curve of the following form fitted:

KJC ¼ 20þ a � expðbyÞ(4)

where y ¼ rf=rys or rf=ryd.

Equation 4 is justified because it is general practice to express variation of KJC

with temperature by an equation similar to Eq 4 with rf/ryd replaced by T. Equiva-

lently, T can be replaced by the corresponding rf/ryd (or rf/rys), which depends

only on variation of ryd or rys with temperature as rf is independent of temperature.

The basic methodology adopted in this paper is to fit Eq 4 based on rf/rys and

rf/ryd ratios to the MC data of the 21 calibration steels (with known IIT and T0data as described later) and determine a and b for each steel. For each steel, the 1 in.

MC-KJC data are fitted to Eq 4 in the range of T0 6 50�C, as ASTM E1921 [5] MC is

valid in that range. The MC equation is given by:

KJC ¼ 30þ 70 � expð0:019 � ðT � T0ÞÞ(5)

where T0 is the ASTM E1921 standard reference temperature for the material. Then

an average a (aav) is determined and a second fitting done to Eq 6a or Eq 6b:

KJC ¼ 20þ aavs: exp Brf

rys

� �(6a)

KJC ¼ 20þ aavd: exp Brf

ryd

� �(6b)

where aavs and aavd (corresponding to y¼ rf/rys and rf/ryd, respectively, in Eq 4)

are treated as constants. Then the constant B for various calibration steels based

on aavs is correlated to rf/rys*1 and rf/rys*2 and B for various calibration steels

based on aavd is correlated to rf/ryd*1 and rf/ryd*2, where rys*1 is the rys at

(T41J – 24)�C and rys*2 is the rys at (T41J – 50)�C, ryd*1 is the ryd at

(T41J – 24)�C and ryd*2 is the ryd at (T41J – 50)�C for each steel. rf/rys*1, rf/rys*2,

rf/ryd*1 and rf/ryd*2 are more definitive material identifiers than the simple ratio

of rf/rys-RT, as rys*1, rys*2, ryd*1 and ryd*2 lie on the steeply rising portion of the






T versus rys or T versus ryd curve. Then, there will be four B calibration curves

generated: B1 based on rf/rys*1, B2 based on rf/rys*2, B3 based on rf/ryd*1 and B4based on rf/ryd*2; application of B1 and B2 in Eq 6a generates two sets of MC

KIC values and application of B3 and B4 in Eq 6b generates another two sets of

MC KIC values. Thus, the present methodology ties the constant B indirectly to

the Charpy transition curve (T versus CV)—DBTT-curve.

APPLICATION OF THE NEWMETHODOLOGY FOR ESTIMATING TQ

For a material with known IIT data but with no T0, T0 can be calculated by the

following procedure:

1. Plot the load-temperature diagram (LTD) as in Fig. 2 and determine TD

2. Determine ryd at TD, using Eq 7 and rf using Eq 8The dynamic yield stress of an impact three-point bend (TPB) specimen isgiven by:

ryd ¼ 2:99PGYW

BðW � aÞ2(7)

where W¼B¼ 10mm and a¼ 2mm for a standard (full-size) CVN specimen,and PGY is in N.The micro-cleavage fracture stress, rf is given by [14]:

rf ¼ 2:52ryd(8)

where ryd is the value at TD.Many people have used different values for the multiplication factor (plasticstress concentration factor) on the RHS of Eq 8, which has values 2.18 or2.52, depending on the selected yield criterion, Tresca or von Mises, respec-tively [15]. Some earlier studies even used a value of 2.57 [1,13]. WhileChaouadi and Fabry [15] use an average value of 2.35, in this paper, the fac-tor has been taken as 2.52 and all values of reported rf have been correctedaccordingly. As such, many rf values given here will differ from those givenin the source references.

3. Plot the T versus CV curve and determine (T41J – 24)�C and (T41J – 50)�Ctemperatures. In case of excessive scatter, use a lower bound (LB) curve deter-mined by a fit to the lowest data at various temperatures.

4. Plot the T versus rys and T versus ryd (PGY at various temperatures isconverted to ryd using Eq 7) and obtain rys*1, rys*2, ryd*1 and ryd*2 and thecorresponding rf/rys*1, rf/rys*2, rf/ryd*1 and rf/ryd*2 values.

5. Plot the rf/rys and rf/ryd versus temperature curves.6. By plugging-in the rf/rys*1, rf/rys*2, rf/ryd*1 and rf/ryd*2 values in the B1 ver-

sus rf/rys*1, B2 versus rf/rys*2, B3 versus rf/ryd*1 and B4 versus rf/ryd*2 cali-bration equations generated earlier, determine the B1, B2, B3, and B4 valuescorresponding to the rf/rys*1, rf/rys*2, rf/ryd*1, and rf/ryd*2 values for the par-ticular steel.

7. For each B, for selected values from the rf/rys or rf/ryd curve, calculate KJC

using Eq 6a or Eq 6b (using a spread-sheet program, this can be easilydone for a column of rf/ryd values corresponding to various temperatures).Since calibration was done using MC data of calibration steels, the



generated KJC data are treated as MC curve data. Then select the KJC data inthe 80–120MPaHm and the corresponding temperatures and apply to themulti-temperature equation due to Wallin to obtain the corresponding TQestimate.

0 ¼Xi¼ni¼1

di expf0:019ðTi � T0Þ½31� Kmin þ 77 expf0:019ðTi � T0Þg�

�Xni¼1

ðKJCi � KminÞ4 expf0:019ðTi � T0Þg½31� Kmin þ 77 expf0:019ðTi � T0Þg�5

(9)

where:Kronecker di¼ 1 for valid data and 0 for non-cleavage or censored data (in thepresent case, take di¼ 1 always),Kmin¼ 20MPaHm, andTi¼ the test temperature (temperature corresponding to a particular KJC valuewith the corresponding rf/rys or rf/ryd ratio).

8. Because the new methodology is mainly based on rf, the micro-cleavage stress,T0 estimate, TQ, based on the new methodology will be designated TQcfs, toimply the cleavage fracture stress (CFS) method. Since there will be four esti-mates of TQcfs values corresponding to the four values, B1, B2, B3, and B4, theywill be designated as TQcfs1, TQcfs2, TQcfs3, and TQcfs4, respectively. The crite-rion for selection of the final estimate, TQcfs, will be given later.

Calculated values of TQcfs for the calibration steels and also for other steels will

be compared with actual T0 or other estimates like TQIGC (where T0 is not available).

Material Data

The 21 steels listed in Tables 1 and 2 along with source references (listed in brackets

appropriately) were used for generating the calibration curves as described in the

previous section. All the steels, except the five Said steels, have rf values determined

from either IIT or 4-point bend tests (only for the Lambert steels). All the rf values

have been adjusted as described after Eq 8. The static yield stress data and its varia-

tion with temperature for the 21 calibration steels are experimentally determined.

For the five Said steels, rf values have been determined in the following

two independent ways. Based on Chaouadi’s data, Sreenivasan [6] gave the following

fit:

TQBT ¼ 1:5TD þ 40(10)

where TQBT is the estimate of T0 obtained from TD, with BT representing

brittleness-transition (as TD is called the brittleness-transition temperature). Thus,

putting the actual T0 in Eq 10, an estimate of TD can be obtained. The TD values

listed in Table 2 for the five Said steels were so determined; hence the exact agree-

ment between actual T0 and TQBT (see, Table 2). As mentioned in Ref. [6], although

Eq 10 has a tendency to accuracy, due to various reasons, including the robustness

of the TD measurement from experimental data (especially for steels exhibiting high

scatter), the estimated TQBT can be highly non-conservative as is demonstrated by

the values for the two steels, 16 MND5 and HT9, listed in Table 2. After estimating



the TD, the dynamic yield stress at TD is determined and, then, applying Eq 8, the

corresponding rf value is determined.

It must be mentioned that for the five Said steels and also for the four Lambert

steels in Tables 1 and 2, as IIT data are not available, dynamic yield stress variation

with temperature has been determined using Eq 11 [23].

ryd ¼ rys-RT þ666 500

ðT þ 273Þ � logð2� 1010 � tÞ � 190(11)

where:

rys-RT¼ the room-temperature static yield stress,

T¼ the test temperature in �C, and

t¼ the time in ms (usually 0.1ms is the time to general yielding in IIT). As

such, t can be taken as 0.1 for obtaining the ryd corresponding to standard impact

tests at a strain rate of �103 [1]. Additionally, a scaling can be applied, if the actual

ryd at room or other temperature is known. If, for example, the actual ryd at RT

exceeds that from Eq 11, the absolute difference (of the RT values) can be added to

TABLE 1

(Micro) CFS and other strength properties of calibration steels.

Steel rys-RT (MPa) rf (MPa) T41J (�C) rys*1 (MPa) rys*2 (MPa) ryd*1 (MPa) ryd*2 (MPa)

JAERI Steels [16]

JRQ 488 1873 �25 542 569 718 746

Steel-A 469 2089 �42 536 568 757 813

Steel-B 462 2089 �61 560 607 802 852

SCK–CEN (Report R-4122) Steels [17]

T91 544 2262 �66 620 683 968 1082

E97 557 2488 �72 648 719 934 1037

EM10 495 2310 �96 650 748 937 1024

F82H 562 2293 �65 633 697 888 1005

Lambert-Perlade Steels [18]

BM 433 2065 �84 542 598 832 933

CGHAZ-100s 586 2211 �16 626 645 775 817

ICCGHAZ-100s 534 1755 3 529 537 713 751

CGHAZ-500s 481 1483 29 470 477 648 680

SAID Steels [19]

Steel-1 591 2148 �86 703 766 792 849

Steel-2 493 1856 �60.5 588 633 775 836

Steel-3 266 1280 8.5 315 339 516 547

Steel-4 339 1297 �61.5 411 454 481 543

Steel-5 387 1651 �40 505 556 664 713

Other Steels

DuplxSS [20] 450 2290 �83 676 732 904 944

HT9 [21] 604 2381 �18.5 651 672 802 844

JSPS [15] 461 1701 36 475 479 568 609

20MnMoNi55 [15] 430 2129 �70 496 549 793 892

16MND5 [22] 491 2331 �88 612 675 856 945



those computed using Eq 11 at various temperatures to yield the scaled ryd values. If

the actual ryd at RT is less than that from Eq 11, the absolute difference (of the RT

values) must be subtracted from those computed using Eq 11 at various tempera-

tures to yield the scaled ryd values. If the RT ryd (ryd-RT) is not known, a good way

to estimate ryd-RT is to apply the empirical relation—Eq 12—to obtain the RT

dynamic general yield load (Pdygy-RT, as will be obtained from instrumented Charpy

V-notch tests) from the easily available RT static yield stress (rys-RT). The empirical

equation for estimating Pgy-RT due to Mathy and Greday [24] is as follows:

Pdygy-RTðNÞ ¼ 6300þ 14:8rys-RT(12)

where rys-RT is in MPa and ryd-RT is estimated from the Pdygy-RT using Eq 7. Combin-

ing Eqs 7 and 12 and applying the full-size standard Charpy specimen dimensions

results in the following direct relation:

ryd-RT ¼ 294:33þ 0:691rys-RT(13)

TABLE 2

TQcfs estimates for the calibration steels compared with other TQ estimates

SteelT0 (�C)

(ASTM E1921)TD

(�C)TQ-BT(�C)

TQ-IGC(�C)

TQcfs1

(�C)TQcfs2(�C)

TQcfs3(�C)

TQcfs4

(�C)TQcfs(�C)

JAERI Steels

JRQ �65 �60 �50.0 �47.2 �70 �64 �70 �59 �59Steel-A �76 �80 �80.0 �60.1 �83 �78 �85 �87 �78Steel-B �97 �85 �87.5 �84.3 �96 �101 �106 �106 �96

SCK-CEN (Report R-4122) Steels

T91 �118 �110 �125 �87.4 �100 �109 �106 �116 �100E97 �115 �110 �125 �101.8 �103 �113 �110 �116 �103EM10 �138 �115 �132.5 �101.7 �125 �140 �144 �142 �125F82H �118 �95 �102.5 �95.8 �98 �108 �101 �108 �98

Lambert-Perlade Steels

BM �132 – – �103 �116 �124 �123 �128 �116CGHAZ-100s �45 – – �45 �81 �52 �65 �66 �52ICCGHAZ-100s �12 – – �30 �56 �27 �50 �37 �27CGHAZ-500s �6 – – 18 �23 �5 �29 �19 �5

SAID Steels

Steel-1 �119 �106 �119 �101 �114 �108 �85 �86 �85Steel-2 �103 �95.3 �103 �73 �95 �94 �110 �105 �94Steel-3 �48.5 �59 �48.5 �38 �31 �33 �48 �34 �31Steel-4 �83 �82 �83 �92 �92 �92 �96 �105 �92Steel-5 �78 �78.7 �78 �77 �73 �78 �90 �82 �73

Other Steels

DuplxSS �120 �90 �95 �90.3 �120 �126 �150 �133 �120HT9 �34.8 �112 �128 �33 �71 �50 �64 �58 �50JSPS 5 �40 �20 18 �55 13 �3 �8 13

20MnMoNi55 �126 �105 �117.5 �82 �122 �125 �106 �114 �10616MND5 �95a �133 �160 �94 �120 �128 �126 �133 �120

aValues vary from �85 to �102�C; the mid-value is reported in the table.




Equation 12 is based on the results of low and medium strength steels (mainly of the

ferrite-pearlite type) and, hence, its applicability (as also of Eq 13) to higher strength

steels and to irradiated steels is to be done with caution. However, it can be used,

provided the results are consistent with each other as will be shown when discussing

the results.

Similarly, for estimation of the rys as a function of temperature, the following

equation due to Server [25] can be used:

T� ¼ T95

� �� þ 32(14a)

rys ¼ 6:895 73:62� 0:0603T� þ ð1:32� 10�4Þ T�ð Þ2�ð1:16� 10�7ÞðT�Þ3� �

(14b)

where T is in �C and rys is in MPa. Equation 14a actually converts �C to �F for use

in Eq 14b. The above equation can also be scaled using known values at one or two

temperatures as discussed after Eq 11 in the case of ryd estimation. As far as possible,

test results are preferred.

One method of estimating rf for the Said steels in Tables 1 and 2 was described

above. The other method is based on the experimental tensile fracture stress results

presented in Said et al. [19]. The fracture stress of a smooth tensile test specimen at

zero-ductility temperature (designated Tsp in Ref. [19]) is related to rf. For the ratio

rf/rf-tension (rf-tension is the fracture stress in a smooth specimen tensile test where

tensile and yield stress coincide at Tsp and is designated Skop in Ref. [19]), Saario

et al. [26] give a value of 1.66 while Said and Talas [27] give a value of 1.71. Taking

the value as 1.71, rf can be computed using the rf-tension values given in Ref. [19].

The results are reported in Table 3 for the five Said steels listed in Table 1. They show

excellent agreement within experimental error with those determined from ryd at

TD (also listed in Table 3) and, hence, a mean value is taken as the rf value for the

steels in Table 3 and the same has been reported in Table 2. Thus, the agreement

between rf values from two independent methods lends confidence to our estimates.

Another point to be mentioned about the Said steels (Tables 1 and 2) is that they

range from low-strength ferrite-pearlite to medium to intermediate strength

quenched and tempered steels, too. The Lambert steels in Tables 1 and 2 pertain to

base metal (BM) and weld heat affected zones including coarse grained heat affected

zone (CGHAZ) material in two cooling conditions and one intercritical CGHAZ

material (ICCGHAZ) in one cooling condition simulated in a Gleeble type test

machine. The other steels are mostly of the reactor pressure vessel (RPV) type

ASTM A533B or similar steels or the 9Cr1Mo type and reduced activation marten-

sitic (RAFM) steels and a Q&T 12Cr martensitic steel, HT9.

The steels used for prediction based on the present CFS model, apart from the

calibration steels in Tables 1 and 2, are listed in Table 4 with source references. The

IGCAR steels consist of a quenched and tempered 9Cr-1Mo martensitic steel

(91BM-IGC) [3], a normalized C-Mn steel A48P2 steel (A48P2-IGC) [28], a service-

exposed 2.25Cr-1Mo steel (21IGC) [2], a post-weld heat treated 9Cr-1Mo weld

(91Wld-IGC) [29], a quenched and tempered ASTM A403 stainless steel (12Cr

martensitic SS) (403SS-IGC) [30] and a normalized and tempered ASTM A203D

3.5 %Ni steel (A203D-IGC) [31]. The ASTM STP 870 steels are old RPV steels of



http://www.astm.org/Standards/A533


http://www.astm.org/Standards/A203D

types similar to ASTM A302B or A212B and their welds and some old A533B steels

also. The ASTM STP 1046 steels are modern RPV steels of the types ASTM A533B

or A508 and their welds tested at BARC, India under an IAEA program. Among the

other steels, HSST-02 is an ASTM A533, Grade B, Class 1 steel well-characterised

under the Heavy Section Steel Technology (HSST) program in both unirradiated

and irradiated (I) conditions [34,35] while the 403SS-DQT steel is an ASTM ASTM

403 SS (12Cr martensitic SS) [36,37] subjected to double quench and tempering heat

treatment to improve toughness. All the Table 4 steels have IIT data available, but

the static yield stress variation with temperature has been estimated mostly using the

relations discussed before.

Results and Discussion

CALIBRATION CURVES ANDTQcfs ESTIMATIONS FOR THE

CALIBRATION STEELS

The values of T41J, rys*1, rys*2, ryd*1, and ryd*2 for the calibration steels are listed in

Table 1 along with rf. As discussed in the Present Methodology, the a and b values

determined based on free fit of rf/rys and rf/ryd in Eq 4 are given in Table 5. as and

bs are values obtained from the fit to the static ratio rf/rys and ad and bd are values

obtained from the fit to the dynamic ratio rf/ryd, respectively. Table 5 also gives the

average values of a and b for both the static and dynamic cases, i.e., aavs and bavs,

aavd and bavd, respectively. Then, keeping the a values as constants at aavs (0.366)

and aavd (1.858), respectively, a second fit was done as described in the

Present Methodology section. The resulting b values (designated B) are shown in

Figs. 3–6; Figs. 3 and 4 display the B values based on fit to Eq 6a against rf/rys*1 and

rf/rys*2, respectively (Figs. 3 and 4 have the same B values as ordinates but abscissae

are different), while Figs. 5 and 6 display the B values based on fit to Eq 6b against

rf/ryd*1 and rf/ryd*2, respectively (Figs. 5 and 6 have the same B values as ordinates

but abscissae are different). The B values based on best fit to the data in Figs. 3–6 are

designated B1, B2, B3, and B4, respectively.

It was found that a cubic fit gives the best fit in all cases. The resulting equations

or calibration curves are given below.

B1 ¼ � 11:0557þ 11:8355rf

rys�1� 3:5165

rf

rys�1

� �2

þ 0:3344rf

rys�1

� �3

(15a)

TABLE 3

Cleavage fracture stress for the five Said steels [19] of Table 1 by two independent methods.

SteelTD fromT0 (�C)

ryd atTD (MPa)

rf from rydat TD (MPa)

TSP

(�C)Skop(MPa)

rf fromSkop¼ 1.71 Skop (MPa)

Meanrf (MPa)

Steel-1 �106 892 2248 �219 1198 2049 2148

Steel-2 �95.3 798 2011 �199 995 1702 1856

Steel-3 �59 572 1441 �180 654 1118 1280

Steel-4 �82 474 1194 �201 819 1401 1297

Steel-5 �78.6 690 1739 �197 914 1563 1651



http://www.astm.org/Standards/A302B

http://www.astm.org/Standards/A212B

http://www.astm.org/Standards/A53B3


with correlation coefficient R¼ 0.9153 and validity range for (rf/rys*1)¼ 3.05 to 4.3.

MC KJC data from B1 is given by:

KJC ¼ 20þ 0:366 � exp B1rf

rys

� �(15b)

B2 ¼ � 25:8537þ 25:7755rf

rys�2� 7:8807

rf

rys�2

� �2

þ 0:7858rf

rys�2

� �3

(16a)

with correlation coefficient R¼ 0.8525 and validity range for (rf/rys*2)¼ 2.8 to 3.89.

MC KJC data from B2 is given by:

TABLE 4

(Micro) CFS and other strength properties of test steels.

Steel rys-RT (MPa) rf (MPa) T41J (�C) rf/rys*1 (MPa) rf/rys*2 (MPa) rf/ryd*1 (MPa) rf/ryd*2 (MPa)

IGCAR Steels [6]

91BM-IGC [3] 512 2425 �79 3.9113 3.6631 2.558 2.1032

A48P2-IGC [28] 556 2019 �76.6 2.7695a 2.5428a 2.4682 2.141

21IGC [2] 280 1613 �20.5 4.7949a 4.3128a 2.5767 2.3209

91Wld-IGC [29] 560 2140 8.5 3.5762 3.435 2.5659 2.4318

403SS-IGC [30] 656 2143 34.5 3.2226 3.1376 2.7369 2.6424

A203D-IGC [31] 390 1367 �57.5 2.7672a 2.5744a 2.0252a 1.8374a

ASTM STP 870 Steels [6,32]

M–Y–Wld 453 1907 �36 3.5922 3.4133 2.4799 2.3241

M–Y–Wld–I 703 1926 182 2.9051 2.8877 2.7086 2.6316

M–Y–TL–P 436 1735 �29 3.4909 3.3111 2.4506 2.295

M–Y–TL–P–I 558 1723 77 3.1442 3.0823 2.6549 2.5451

EPRI–EP–24–Wld 350 1890 �29.5 4.621a 4.3349a 2.9905 2.8125

EPRI–EP–24–Wld–I 541 1943 72.5 3.673 3.5783 2.9938a 2.9a

EPRI–EP–23–Wld 367 1824 �11 4.4706a 4.2125a 2.9372 2.7511

EPRI–EP–23–Wld–I 552 1911 72 3.5323 3.4432 2.922 2.8103

A302BRCM–P 432 1695 �12 3.5759 3.3968 2.5148 2.3673

A302BRCM–P–I 599 1801 58 3.0269 2.9573 2.5729 2.4841

ASTM STP 1046 Steels [33]

AP 440 1778 �3.5 3.7669 3.5992 2.6498 2.3519

AP-I 504 1884 28 3.6092 3.575 2.6761 2.3788

FH 467 2343 �88 3.9378 3.6898 2.6355 2.277

FH-I 559 2143 �78 3.1842 3.0141 2.3971 2.1957

GW 478 1895 �60 3.3246 3.1426 2.3927 2.8931a

GW-I 568 1949 �34 3.0887 2.953 2.351 2.1801

JH 459 2190 �80.5 3.7955 3.561 2.6165 2.3224

JH-I 595 2285 �63 3.3116 3.1561 2.5474 2.3777

Other Steels

HSST Plate02 [34,35] 489 1801 6 3.5876 3.4971 2.6761 2.4272

HSST Plate02–I [34] 580 2054 34 3.4932 3.395 2.5934 2.4136

403SS–DQT [36,37] 615 2550 �25 3.8231 3.701 2.9651 2.6927

aThe bold underlined values indicate values outside the permitted range.



KJC ¼ 20þ 0:366 � exp B2rf

rys

� �(16b)

B3 ¼ 2:1566þ 1:1167rf

ryd�1� 0:8441

rf

ryd�1

� �2

þ 0:1263rf

ryd�1

� �3

(17a)

with correlation coefficient R¼ 0.8695 and validity range for (rf/ryd*1)¼ 2.28 to

2.995. MC KJC data from B3 is given by:

TABLE 5

aavs and aavd estimates for the calibration steels.

Steel/Statistics as bs ad bd

JAERI Steels

JRQ 4.11� 10�3 2.9453 4.4571 9.55� 10�4

Steel-A 9.00� 10�3 2.3494 2.4095 0.1092

Steel-B 0.1556 1.7351 2.7429 0.077

SCK–CEN (Report R-4122) Steels

T91 0.8643 1.3824 1.9 1.8084

E97 0.9783 1.2427 1.3052 1.6686

EM10 1.29� 10�68 34.2963 0.922 1.9038

F82H 1.1233 1.3223 3.1518 1.4515

Lambert-Perlade Steels

BM 1.1427 1.2325 2.0854 1.6468

CGHAZ-100s 3.10� 10�5 4.513 7.93� 10�3 3.2716

ICCGHAZ-100s 3.00� 10�21 15.5422 2.47� 10�3 4.1667

CGHAZ-500s 1.46� 10�15 12.2952 3.44� 10�3 4.4864

SAID Steels

Steel-1 0.2736 1.9249 2.3646 0.3507

Steel-2 0.1775 2.0533 2.5768 0.2379

Steel-3 0.4476 1.4149 2.9937 0.0844

Steel-4 0.2687 1.8056 1.5252 1.2825

Steel-5 0.8321 1.4731 2.6979 0.129

Other Steels

DuplxSS 3.47� 10�5 3.9743 4.22� 10�3 3.9731

HT9 8.46� 10�27 18.0926 3.1917 5.51� 10�3

JSPS 0.9407 1.1781 0.1183 2.252

20MnMoNi55 0.1134 1.5854 2.3438 1.5211

16MND5 0.1134 1.5854 2.2129 0.115

STATISTICS

Mean aavs 5 0.3659 bavs¼ 5.4297 aavd 5 1.8579 bavd¼ 1.4544

Median 0.1775 1.8056 2.2129 1.4515

SD 0.423 8.2441 1.2755 1.4717

Standard Error 0.0923 1.799 0.2783 0.3212

95 % Conf 0.1925 3.7527 0.5806 0.6699

99 % Conf 0.2626 5.1192 0.792 0.9139



FIG. 3

B values obtained from fit to

Eq 6a—KJC¼20þ aavsexp

(B*rf/rys) with aavs¼0.366

plotted against rf/rys*1 for each

steel in Table 1.

FIG. 4


Eq 6a—KJC¼20þ aavsexp

(B*rf/rys) with aavs¼0.366

plotted against rf/rys*2 for each

steel in Table 1.

FIG. 5


Eq 6b—KJC¼20þ aavdexp

(B*rf/ryd) with aavd¼ 1.858

plotted against rf/ryd*1 for each

steel in Table 1.



KJC ¼ 20þ 1:858 � exp B3rf

ryd

� �(17b)

B4 ¼ 33:7517� 37:5066rf

ryd�2þ 14:713

rf

ryd�2

� �2

� 1:9472rf

ryd�2

� �3

(18a)

with correlation coefficient R¼ 0.8334 and validity range for (rf/ryd*2)¼ 2.09 to

2.82. MC KJC data from B4 is given by:

KJC ¼ 20þ 1:858 � exp B4rf

ryd

� �(18b)

Estmates of T0, based on MC KJC data from Eqs 15b, 16b, 17b, and 18b are desig-

nated TQcfs1, TQcfs2, TQcfs3, and TQcfs4, respectively. Following the procedures

described above, the estimated TQcfs values for the calibration steels are tabulated in

Table 2 along with actual T0 and other estimates like TQIGC and TQBT. The four TQcfs

values show excellent agreement with each other within the error that can be

expected for this. The criterion for choosing the estimate based on the present CFS

model, namely, TQcfs, is the most conservative of the four: TQcfs1, TQcfs2, TQcfs3, and

TQcfs4. The TQcfs values so determined are given in the last column of Table 2.

Figure 7 compares the T0 of calibration steels with the TQcfs estimates tabulated

in Table 2. TQcfs estimates are conservative for most of the calibration steels. This

becomes more apparent in Fig. 8, which plots the residuals (i.e., (T0 – TQcfs) values)

for the 21 calibration steels; only for two steels, the values lie outside the 620�C

band, one being conservative (Steel 1) and the other being non-conservative

(16MND5 steel). For the 16MND5 steel, there is large scatter in the basic T0 data

(see footnote to Table 2) and other estimate TQBT also shows this tendency for non-

conservatism. It must be noted that for the Steel 1 (also, for all the Said Steels in

Tables 1 and 2), as discussed before, the dynamic yield stress has been estimated

using Eqs 11 to 13. There may be some error in this leading to large over conserva-

tism as TQcfs for the Steel 1 is determined by TQcfs3, the value based on ryd and ryd*1.

FIG. 6

B values obtained from Eq 6b—

KJC¼20þ aavdexp

(B*rf/ryd) with aavd¼ 1.858

plotted against rf/ryd*2 for each

steel in Table 1.



Otherwise, based on the results for all other steels, the premise for choosing the

value of TQcfs, namely, the most conservative of the four estimates TQcfs1, TQcfs2,

TQcfs3, and TQcfs4, seems to be sound. Figure 9 compares the TQcfs estimates for the

calibration steels with their TQIGC estimates. TQcfs is less conservative than TQIGC

and, hence, closer to the actual T0. This is to be expected from Fig. 8, which shows

620�C error band for TQcfs whereas TQIGC is mostly conservative to the extent of

20�C–30�C (see the Introduction).

TQcfs ESTIMATIONS FOR THE TEST STEELS

For all the IGCAR steels in Table 6, except for the A48P2-IGC, static yield stress esti-

mates have been made by scaling yield stress data given in literature for similar

steels, instead of Eq 14. For example, for 9Cr-1Mo steels, the data given by Chaouadi

FIG. 7

ASTM E1921 reference

temperature (T0) of calibration

steels compared with TQcfs

estimated using the CFS model.

FIG. 8

Residuals for the calibration

steels based on TQcfs estimated

using the CFS model.



in Ref. [17] has been used with suitable scaling. This makes the static yield stress

estimates closer to actual values. Estimates of TQcfs obtained for the test steels are

tabulated in Table 6 while the strength properties are given in Table 4. In Table 6, the

ratios rf/rys*1, rf/rys*2, rf/ryd*1, and rf/ryd*2 have been given and the values that fall

outside the range specified by Eqs 15a–18a have been highlighted in bold fonts with

underlining. Comparison of highlighted values in Table 4 with the corresponding

TQcfsx (where x stands for 1, 2, 3, or 4, as the case may be) in Table 6 indicates that

when the rf/rys*x or rf/ryd*x value falls outside the specified range, the correspond-

ing TQcfsx prediction is unacceptably large or small and such values have not been

considered for evaluation. In such cases, the largest of the valid values has been

reported as TQcfs in the last column of Table 6. Such behavior occurs mostly for steels

with low-strength, say, rys-RT< 400MPa. For the low-strength IGCAR steel,

A203D-IGC, none of the TQcfsx values are acceptable (vide Tables 4 and 6). Hence,

the present CFS model based on the calibration curves derived in this paper seems

to be applicable to steels with rys-RT in the range of 400–700–750MPa. The require-

ment for strict concurrence of the rf/rys*x or rf/ryd*x values to the validity range

arises from the fact that the calibration curves are cubic equations which will behave

wildly outside their range of fit. For the GW steel, though rf/ryd*2 has been shown

outside the validity range in Table 4, the corresponding prediction in Table 6,

namely, TQcfs4 does not show much difference from other values. This may be due

the fact that rf/ryd*2 value for the GW steel exceeds the upper limit only marginally

and hence does not have any effect on B4 value.

For the HSST-02 plate, Ref. [35] gives a T0 of �28�C which excellently com-

pares with the TQcfs value of �18�C reported in Table 6. For the M–Y Wld, Ref. [38]

gives a T0 of �106�C in the unirradiated condition and a T0 of 106�C in the

irradiated condition (fluence: 6.11� 1011 n cm�2; E> 1 MeV) which also compare

excellently with the TQcfs value of �76�C and 118�C (fluence: 1.3� 1011 n cm�2;

E> 1 MeV) reported in Table 6 for the two conditions, respectively. However, TQIGC

values are very conservative. Finally, Fig. 9 also shows the TQIGC values for the

FIG. 9

TQIGC compared with TQcfs for

the calibration and test steels.



Table 6 test steels plotted against the respective TQcfs values which are in excellent

accord with the trend shown by the calibration steels displayed in the same figure

and discussed in the previous section. Figure 9 also suggests the conclusion that

TQIGC values for steels with high reference temperature (like the highly irradiated

steels) have a tendency to be much more conservative than the corresponding TQcfsvalues as compared to steels having lower reference tempaeratures (i. e., steels near

the left axis of Fig. 9). The implication is that, in such cases, TQcfs values may even

be unacceptably non-conservative. However, the data for HSST-02 and M–Y Wld

do not warrant such a conclusion. Nevertheless, the present data are not sufficient to

draw a definite conclusion. This aspect needs further verification.

TABLE 6

TQcfs estimates for the test steels compared with other TQ estimates.

Steel TQIGC (�C) TD (�C) TQ-BT (�C) TQcfs1 (�C) TQcfs2 (�C) TQcfs3 (�C) TQcfs4 (�C) TQcfs (�C)

IGCAR Steels

91BM-IGC �86.6 �105 �118 �112 �110 �122 �157 �110A48P2-IGC �104.8 �69 �64 277a 232a �91 �69 �6921IGC �56.6 �49 �33.5 2322a 2640a �60 �63 �6091Wld-IGC �26.9 �34 �11 �36 �26 �32 �25 �25403SS-IGC 22.3 �39 �18.5 �20 �8 �9 �4 �4A203D-IGC �70 �86 �89 257a 215a 296a 2142a ––

ASTM STP 870 Steels

M-Y–Wld �52.5 �73 �69.5 �81 �76 �86 �78 �76M–Y–Wld–I 150 71 146.5 113 113 100 118 118

M–Y–TL–P �52.4 �53 �39.5 �69 �65 �73 �65 �65M–Y–TL–P–I 77.8 10 55.0 28 38 23 33 38

EPRI–EP–24–Wld �66 �109 �123.5 2145a �211a �56 �56 �56EPRI–EP–24–Wld–I 70.8 �49 �33.5 39 20 �52a 233a 39

EPRI–EP–23–Wld �39.6 �93 �99.5 298a 2138a �53 �58 �53EPRI–EP–23–Wld–I 72 �39.5 �19.3 �5 34 9 24 34

A302BRCM–P �37.3 �34 �11.0 �57 �51 �61 �53 �51A302BRCM–P–I 67 17 65.5 6.4 34 �16 2.4 34

ASTM STP 1046 Steels

AP �33 �33.3 �9 �46 �33 �35 �42 �33AP–I 24 �4 34 �32 6 �2 �6 6

FH �95 �120 �140 �127 �125 �120 �132 �120FH-I �89 �82.9 �84 �119 �115 �124 �123 �115GW �91 �64.9 �57 �86 �84 �89 285a �84GW-I �58 �32 �8 �46 �40 �63 �60 �40JH �92 �112.8 �129 �119 �117 �117 �123 �117JH-I �64 �91.8 �97 �111 �106 �115 �108 �106

Other Steels

HSST-02 �25 �33.5 �10.3 �36 �18 �31 �36 �18HSST-02-I 37 �2 37 �27 �5 �11 �8 �5403SS-DQT �32.3 �69 �63.5 �45 �33 �46 �60 �33

aValues highlighted and underlined are invalid.



Conclusions

Thus, a semi-empirical formulation of the CFS (cleavage fracture stress) model,

based on the microscopic cleavage fracture stress, rf, for estimating the ASTM

E1921 reference temperature of ferritic steels from instrumented impact test (IIT) of

unprecracked CVN specimens has been established. The relevant calibration equa-

tions necessary for applying the model have been derived and demonstrated for

steels with room temperature yield strength in the range 400–750MPa, including

irradiated steels. However, applicability and acceptability of the present calibration

curves for highly irradiated steels need further examination. The estimate of T0,

based on the present CFS model, TQcfs, lies within a 620�C band, being conservative

for most of the steels, but less conservative than TQIGC based on the IGC-procedure.

Moreover, the CFS model is a single step assessment procedure as compared to the

multi-stage IGCAR-procedure and, hence, less error-prone due to calculation

errors. However, the parameters must strictly meet the validity conditions for the

calibration equations. CFS model enhances the validity and utility of the CVN IIT

by enabling estimation of design-relevant master curve from unprecracked CVN

specimens. Although some researchers have called an approach based on the CFS

mesoscopic (i.e., lying between microscopic and macroscopic scales), at least in

steels, rf operates over microstructural distances. As such, the CFS model or

approach should be the preferred Nomenclature.

ACKNOWLEDGMENTS

The writer acknowledges with thanks the excellent support and encouragement

received from Director, MMG and Director, IGCAR, Kalpakkam, India.

References

[1] Sreenivasan, P. R., “Instrumented Impact Testing—Accuracy, Reliability, and

Predictability of Data,” Trans. Indian Inst. Metals, Vol. 49, No. 5, 1996, pp.

677–696.

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cleavage fracture stress model for fractoughness estimation

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