1、Designation: E 1921 08a1Standard Test Method forDetermination of Reference Temperature, To, for FerriticSteels in the Transition Range1This standard is issued under the fixed designation E 1921; the number immediately following the designation indicates the year oforiginal adoption or, in the case o
2、f revision, the year of last revision. A number in parentheses indicates the year of last reapproval. Asuperscript epsilon () indicates an editorial change since the last revision or reapproval.1NOTEEditorial changes were made throughout in October 2008.1. Scope1.1 This test method covers the determ
3、ination of a referencetemperature, To, which characterizes the fracture toughness offerritic steels that experience onset of cleavage cracking atelastic, or elastic-plastic KJcinstabilities, or both. The specifictypes of ferritic steels (3.2.1) covered are those with yieldstrengths ranging from 275
4、to 825 MPa (40 to 120 ksi) andweld metals, after stress-relief annealing, that have 10 % orless strength mismatch relative to that of the base metal.1.2 The specimens covered are fatigue precracked single-edge notched bend bars, SE(B), and standard or disk-shapedcompact tension specimens, C(T) or DC
5、(T). A range ofspecimen sizes with proportional dimensions is recommended.The dimension on which the proportionality is based isspecimen thickness.1.3 Median KJcvalues tend to vary with the specimen typeat a given test temperature, presumably due to constraintdifferences among the allowable test spe
6、cimens in 1.2. Thedegree of KJcvariability among specimen types is analyticallypredicted to be a function of the material flow properties (1)2and decreases with increasing strain hardening capacity for agiven yield strength material. This KJcdependency ultimatelyleads to discrepancies in calculated
7、Tovalues as a function ofspecimen type for the same material. Tovalues obtained fromC(T) specimens are expected to be higher than Tovaluesobtained from SE(B) specimens. Best estimate comparisons ofseveral materials indicate that the average difference betweenC(T) and SE(B)-derived Tovalues is approx
8、imately 10C (2).C(T) and SE(B) Todifferences up to 15C have also beenrecorded (3). However, comparisons of individual, smalldatasets may not necessarily reveal this average trend. Datasetswhich contain both C(T) and SE(B) specimens may generateToresults which fall between the Tovalues calculated usi
9、ngsolely C(T) or SE(B) specimens. It is therefore stronglyrecommended that the specimen type be reported along withthe derived Tovalue in all reporting, analysis, and discussion ofresults. This recommended reporting is in addition to therequirements in 11.1.1.1.4 Requirements are set on specimen siz
10、e and the numberof replicate tests that are needed to establish acceptablecharacterization of KJcdata populations.1.5 Tois dependent on loading rate. Tois evaluated for aquasi-static loading rate range with 0.1KJc(0.98) it may be possible to reduce the influence of theoutlier datum on KJc(med)by tes
11、ting additional specimens.Typically, a total of 12 replicate specimens is sufficient.However, outliers shall not be discarded from the data utilizedto calculate KJc(med). The emergence of additional outliers mayindicate that the test material is not homogeneous.10. Prediction of Size Effects and Tra
12、nsition Temperature10.1 Weibull Fitting of Data Sets:10.1.1 Test Replication A data set consists of at least sixvalid replicate test results determined at one test temperature,or the equivalent thereof; see also 8.5 for single temperatureand 10.4 for multi-temperature requirements.10.1.2 Determinati
13、on of Scale Parameter, Ko, and median KKJc(med)The three-parameter Weibull model is used todefine the relationship between KJcand the cumulative prob-ability for failure, pf. The term pfis the probability for failureat or before KJcfor an arbitrarily chosen specimen taken froma large population of s
14、pecimens. Data samples of six or morespecimens are used to estimate the true value of scale param-eter, Ko, for the following Weibull model:pf5 1 exp $ KJc Kmin!/Ko Kmin!#b% (15)10.1.3 Ferritic steels with yield strengths ranging from 275to 825 MPa (40 to 120 ksi) will have fracture toughnesscumulat
15、ive probability distributions of nearly the same shape,independent of specimen size and test temperature, when Kminis set at 20 MPa=m (18.2 ksi=in.). The shape of thedistribution is defined by the Weibull exponent, b, which tendsto be near 4. Scale parameter, Ko, is the data fitting parameterdetermi
16、ned when using the maximum likelihood statisticalmethod of data fitting (22). When KJcand Koin Eq. 15 areequal, pf= 0.632.10.1.4 Size Effect PredictionsThe statistical weakest-linktheory is used to model specimen size effects in the transitionrange between lower shelf and upper shelf fracture toughn
17、ess.The following Eq. 16 can be used to size adjust individual KJcvalues, KJc(med),orKo. KJcserves as the example case:KJcx!5 Kmin1 KJco! Kmin#SBoBxD1/4(16)where:KJc(o)= KJcfor a specimen size Bo,Bo= gross thickness of test specimens (side groovesignored),Bx= gross thickness of prediction (side groo
18、ves ig-nored), andKmin= 20 MPa=m (18.2 ksi =in.).10.2 If KJcdata replication is performed at a single testtemperature, tests should be conducted as near as possible to anestimated Totemperature. However, all data obtained at tem-peratures within the range 50C # (TTo) # 50C shall beconsidered in the
19、determination of To. Therefore, if testing isperformed at more than one temperature, the multi-temperatureprocedure described in 10.4.2 shall be used. In this case, thecombination of valid specimen numbers and test temperaturesshall satisfy Eq. 22 in 10.4.1. Iteration in terms of testingadditional s
20、pecimens may be required. For single-temperaturetests, use 8.4 or 8.5 for test temperature estimation assistance.The following sections 10.2.1 and 10.2.2 can be used tocalculate the scale parameter, Ko, for data developed at a singletest temperature and consisting of at least six valid KJcvalues,or
21、the equivalent thereof, see also 8.5. Data sets containingonly valid data (as defined in 8.9.2) shall be analyzed as per10.2.1. Paragraph 10.2.2 shall be applied if any invalid data (asdefined in 8.9.2) exist.10.2.1 Determination of Kowith all Valid DataIf the dataare generated from specimens of oth
22、er than 1T size, the datamust first be converted to 1Tsize equivalence using Eq. 16 (seesection 3.3.20). The following Eq. 17 shall be then applied todetermine Ko:Ko5F(i 5 1NKJci! Kmin!4NG1/41 Kmin(17)where:N = number of specimens tested as defined in 8.9, andKmin= 20 MPa=m (18.2 ksi=in.).See X1.2 f
23、or an example solution.10.2.2 Determination of Kowith Censored DataReplaceall invalid KJcvalues (8.9.2) with dummy KJcvalues. Ifinvalidity was due to violation of KJc(limit), Eq. 1, the experi-mental KJcvalue shall be replaced by KJc(limit)for the specimensize used. Use the material yield strength a
24、t the test tempera-ture. In the case of KJcinvalidity due to exceeding the0.05(Wao) or 1-mm (0.04-in.) limitation on stable crackgrowth (8.9.2), the KJctest value shall be replaced with thehighest valid KJcin the data set for any specimen size. TheWeibull scale parameter, Ko, shall be calculated usi
25、ng thefollowing Eq. 18, in which all KJc(i)and dummy values forspecimens other than 1T size are converted to 1T size equiva-lence (3.3.20), using Eq. 16. See section X1.3 for an examplesolution.Ko5F(i 5 1NKJci! Kmin!4rG1/41 Kmin(18)where:r = number of valid data as defined in 8.9,Kmin= 20 MPa=m (18.
26、2 ksi=in.), andN = number of data (valid and invalid).E 1921 08a11310.2.3 Koto KJc(med)ConversionThe scale parameter, Kocalculated according to either, 10.2.1 or 10.2.2, corresponds toa 63 % cumulative probability level for specimen failure bycleavage. The median KJcof a data population corresponds
27、to50 % cumulative probability for fracture and KJc(med)can bedetermined from Kousing the following:KJcmed!5 Kmin1 Ko2 Kmin! 1n2!#1/4(19)where:Kmin= 20 MPa=m (18.2 ksi=in.).10.3 Establishment of a Transition Temperature Curve(Master Curve)Transition temperature KJcdata tend to con-form to a common to
28、ughness versus temperature curve shapein the same manner as the ASME Klcand KIRlower-bounddesign curves (23, 24). For this method, the shape of themedian KJctoughness, KJc(med), for 1T specimens (3.3.20)isdescribed by:KJcmed!5 30 1 70 exp 0.019T To!#, MPa=m, (20)where:T = test temperature (C), andTo
29、= reference temperature (C).10.3.1 Master curve positioning involves the determinationof Tousing the computational steps presented below.10.3.2 Determine Provisional Reference Temperature(ToQ)Use only 1T KJc(med)values, converted by Eq. 16 ifnecessary.ToQ5 T S10.019D ln FKJcmed!3070G (21)Units of KJ
30、c(med)are in MPa=m; units of ToQare in C.To=ToQif all validity requirements specified in this standardare satisfied as outlined in 10.5.10.4 Multi-temperature OptionThe reference tempera-ture, To, should be relatively independent of the test tempera-ture that has been selected. Hence, data that are
31、distributed overa restricted temperature range, namely To6 50C, can be usedto determine To.As it is with the single test temperature option,a minimum of six valid KJcdata (8.9.2) or the equivalence, byweight factor, described in 10.4.1 below is required. In the caseof data generated at test temperat
32、ures from 14C below Toto50C above To, the minimum requirement of six valid data willbe satisfactory.10.4.1 Data generated at test temperatures in the range of To-50toTo- 14C are considered to make reduced accuracycontribution to Todeterminations.As a consequence, more datadevelopment within the afor
33、ementioned temperature range isrequired. The following weighting system specifies the re-quired number of data:(i 5 13rini$1 (22)where riis the number of valid specimens within the i-thtemperature range, (TTo), and niis the specimen weightingfactor for the same temperature range as shown in Table 4.
34、10.4.2 All KJcdata, including valid and dummy valuesresulting from Eq. 1 violation at each test temperature, mustfirst be converted to 1T equivalence using Eq. 16. If theslow-stable crack growth limitation is violated as specified in8.9.2, the highest valid KJcshall be used for censoring. TheKJc(lim
35、it)in 8.9.2 shall be chosen from data at any temperatureas this value should be largely temperature insensitive. Alsothis value is specimen-size-independent and size correction ofthis limit shall not be performed. The KJvalue correspondingto JIcalso can be used for crack growth censoring if JIciskno
36、wn for the test material. The following equality shall beused to determine the provisional ToQfor tests conducted atmultiple temperatures (22, 24):(i 5 1Ndiexp 0.019 Ti2 ToQ!#11 1 77 exp 0.019 Ti2 ToQ!#(23)2(i 5 1NKJci!2 20!4exp 0.019 Ti2 ToQ!#$11 1 77 exp 0.019 Ti2 ToQ!#%55 0where:N = number of spe
37、cimens tested,Ti= test temperature corresponding to KJc(i),KJc(i)= either a valid KJcdatum or dummy value substitutefor an invalid datum (8.9.2). All KJcinput values,valid or dummy KJc, must be converted to 1Tequivalence (3.3.20) before entry,di= 1.0 if the datum is valid or zero if the datum is adu
38、mmy substitute value,11 = integer equivalent of 10/(ln2)1/4MPa=m, and77 = integer equivalent of 70/(ln2)1/4MPa=m.Solve Eq. 23 for ToQtemperature by iteration.10.4.3 Since the valid test temperature range is only knownafter Tohas been determined, the following iterative schememay be helpful for ident
39、ifying proper test temperature. Choosean initial test temperature as described in 8.4 using the value of“C” appropriate for the test specimen size. Conduct 3-4 validtests at this temperature and evaluate an estimated Tovalue(To(est) value using 10.2 to determine Ko. Base all subsequenttest temperatu
40、res on To(est). See Appendix X3 for an examplecalculation.10.4.4 Certain multi-temperature data sets may result in anoscillating iteration between two (or more) distinct Tovaluesupon satisfying the To6 50C limit of 10.4. In these instances,the Tovalue reported shall be the average of the calculatedv
41、alues. One example is for hypothetical data with toughnessvalues such that the initial Toestimation requires that data atone temperature be excluded. The second iteration then resultsin the inclusion of this same data. Subsequent Toiterations willthen oscillate between the original first and second
42、estimations.This phenomenon is more likely for sparse data sets when testresults exist near the To6 50C limit. More testing near theaverage Towill likely resolve this problem.10.5 Validation of ToQas To To=ToQif all of thefollowing requirements are met:TABLE 4 Weight Factors for Multi-Temperature An
43、alysis(T To) rangeA(C)1T KJc(med)rangeA(MPa=m)Weight factorni50 to 14 212 to 84 1/615 to 35 83 to 66 1/736 to 50 65 to 58 1/8ARounded off to the closest integer.E 1921 08a11410.5.1 The apparatus requirements of Section 6 are met orexceeded,10.5.2 The specimen configuration and dimensions meet thereq
44、uirements of Section 7,10.5.3 The specimen precracking was completed within therequirements of 7.8,10.5.4 The specimens were tested within the requirementsof Section 8, including qualification of the data according to8.9, and10.5.5 The number of specimens tested within the allowabletemperature range
45、 ToQ6 50C, meets the requirement of Table2 for single temperature testing. For multi-temperature analy-sis, the equivalent requirement is set by Eq. 22 and thecorresponding Table 4.10.6 Uses for Master CurveThe master curve can be usedto define a transition temperature shift related to metallurgical
46、damage mechanisms. Fixed values of Weibull slope andmedian KJcdefine the standard deviation; hence the represen-tation of data scatter. This information can be used to calculatetolerance bounds on toughness, for the specimen reference sizechosen. The data scatter characteristics modeled here can als
47、obe of use in probabilistic fracture mechanics analysis, bearingin mind that the master curve pertains to a 1T size specimen.The master curve determined by this procedure pertains tocleavage fracture behavior of ferritic steels. Extensive ductiletearing beyond the validity limit set in 8.9.2, may pr
48、ecedecleavage as the upper-shelf range of temperature is approached.Such data can be characterized by separate methods (see TestMethod E 1820).11. Report11.1 Report the following information for each specimen:11.1.1 Specimen type, specimen thickness, B, net thickness,BN, specimen width, W,11.1.2 Spe
49、cimen initial crack size, ao,11.1.3 Visually measured slow-stable crack growth prior toonset of cleavage, if present,11.1.4 Crack plane orientation according to TerminologyE 1823,11.1.5 Test temperature or test temperatures as applicable,11.1.6 Number of valid specimens (r) and total number ofspecimens (N) tested at each temperature,11.1.7 Crack pop-in and compliance ratio, Ci/Co, if appli-cable,11.1.8 Material yield strength and tensile strength, at the testtemperatures,11.1.9 The location of displa
