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ASTM E 1921-2003

Designation:E1921–03

Standard Test Method for

Determination of Reference Temperature,T o,for Ferritic Steels in the Transition Range1

This standard is issued under the?xed designation E1921;the number immediately following the designation indicates the year of original adoption or,in the case of revision,the year of last revision.A number in parentheses indicates the year of last reapproval.A superscript epsilon(e)indicates an editorial change since the last revision or reapproval.

1.Scope

1.1This test method covers the determination of a reference temperature,T o,which characterizes the fracture toughness of ferritic steels that experience onset of cleavage cracking at elastic,or elastic-plastic K Jc instabilities,or both.The speci?c types of ferritic steels(3.

2.1)covered are those with yield strengths ranging from275to825MPa(40to120ksi)and weld metals,after stress-relief annealing,that have10%or less strength mismatch relative to that of the base metal.

1.2The specimens covered are fatigue precracked single-edge notched bend bars,SE(B),and standard or disk-shaped compact tension specimens,C(T)or DC(T).A range of specimen sizes with proportional dimensions is recommended. The dimension on which the proportionality is based is specimen thickness.

1.3Median K Jc values tend to vary with the specimen type at a given test temperature,presumably due to constraint differences among the allowable test specimens in1.

2.The degree of K Jc variability among specimen types is analytically predicted to be a function of the material?ow properties(1)2 and decreases with increasing strain hardening capacity for a given yield strength material.This K Jc dependency ultimately leads to discrepancies in calculated T o values as a function of specimen type for the same material.T o values obtained from C(T)specimens are expected to be higher than T o values obtained from SE(B)specimens.Best estimate comparisons of several materials indicate that the average difference between C(T)and SE(B)-derived T o values is approximately10°C(2). C(T)and SE(B)T o differences up to15°C have also been recorded(3).However,comparisons of individual,small datasets may not necessarily reveal this average trend.Datasets which contain both C(T)and SE(B)specimens may generate T o results which fall between the T o values calculated using solely C(T)or SE(B)specimens.It is therefore strongly recommended that the specimen type be reported along with the derived T o value in all reporting,analysis,and discussion of results.This recommended reporting is in addition to the requirements in11.1.1.

1.4Requirements are set on specimen size and the number of replicate tests that are needed to establish acceptable characterization of K Jc data populations.

1.5The statistical effects of specimen size on K Jc in the transition range are treated using weakest-link theory(4) applied to a three-parameter Weibull distribution of fracture toughness values.A limit on K Jc values,relative to the specimen size,is speci?ed to ensure high constraint conditions along the crack front at fracture.For some materials,particu-larly those with low strain hardening,this limit may not be sufficient to ensure that a single-parameter(K Jc)adequately describes the crack-front deformation state(5).

1.6Statistical methods are employed to predict the transi-tion toughness curve and speci?ed tolerance bounds for1T specimens of the material tested.The standard deviation of the data distribution is a function of Weibull slope and median K Jc. The procedure for applying this information to the establish-ment of transition temperature shift determinations and the establishment of tolerance limits is prescribed.

1.7The fracture toughness evaluation of nonuniform mate-rial is not amenable to the statistical analysis methods em-ployed in this standard.Materials must have macroscopically uniform tensile and toughness properties.For example,multi-pass weldments can create heat-affected and brittle zones with localized properties that are quite different from either the bulk material or weld.Thick section steel also often exhibits some variation in properties near the surfaces.Metallography and initial screening may be necessary to verify the applicability of these and similarly graded materials.Paticular notice should be given to the2%and98%tolerance bounds on K Jc presented in 9.3.Data falling outside these bounds may indicate nonuniform material properties.

1This test method is under the jurisdiction of ASTM Committee E08on Fatigue

and Fracture and is the direct responsibility of E08.08on Elastic-Plastic Fracture

Mechanics Technology.

Current edition approved Nov.1,2003.Published December2003.Originally

approved https://www.wendangku.net/doc/5513422075.html,st previous edition approved in2002as E1921–02.

2The boldface numbers in parentheses refer to the list of references at the end of

this standard.

1.8This standard does not purport to address all of the safety concerns,if any,associated with its use.It is the responsibility of the user of this standard to establish appro-priate safety and health practices and determine the applica-bility of regulatory limitations prior to use.

2.Referenced Documents 2.1ASTM Standards:3

E 4Practices for Force Veri?cation of Testing Machines E 8M Test Methods for Tension Testing of Metallic Mate-rials (Metric)

E 23Test Methods for Notched Bar Impact Testing of Metallic Materials

E 74Practice for Calibration of Force Measuring Instru-ments for Verifying the Force Indication of Testing Ma-chines

E 208Test Method for Conducting Drop-Weight Test to Determine Nil-Ductility Transition Temperature of Ferritic Steels

E 399Test Method for Plane-Strain Fracture Toughness of Metallic Materials

E 436Test Method for Drop-Weight Tear Tests of Ferritic Steels

E 561Practice for R-Curve Determination

E 812Test Method for Crack Strength of Slow-Bend,Pre-cracked Charpy Specimens of High-Strength Metallic Materials

E 1820Test Method for Measurement of Fracture Tough-ness

E 1823Terminology Relating to Fatigue and Fracture Test-ing 3.Terminology

3.1Terminology given in Terminology E 1823is applicable to this test method.3.2De?nitions :

3.2.1ferritic steels —are typically carbon,low-alloy,and higher alloy grades.Typical microstructures are bainite,tem-pered bainite,tempered martensite,and ferrite and pearlite.All ferritic steels have body centered cubic crystal structures that display ductile-to-cleavage transition temperature fracture toughness characteristics.See also Test Methods E 23,E 208and E 436.

N OTE 1—This de?nition is not intended to imply that all of the many possible types of ferritic steels have been veri?ed as being amenable to analysis by this test method.

3.2.2stress-intensity factor,K[FL –3/2]—the magnitude of the mathematically ideal crack-tip stress ?eld coefficient (stress ?eld singularity)for a particular mode of crack-tip region deformation in a homogeneous body.

3.2.3Discussion —In this test method,Mode I is assumed.See Terminology E 1823for further discussion.

3.2.4J-integral,J[FL –1]—a mathematical expression;a line or surface integral that encloses the crack front from one crack surface to the other;used to characterize the local stress-strain ?eld around the crack front (6).See Terminology E 1823for further discussion.

3.3De?nitions of Terms Speci?c to This Standard:

3.3.1control load,P M [F]—a calculated value of maximum load used in Test Method E 1820,Eqs.A1.1and A2.1to stipulate allowable precracking limits.

3.3.1.1Discussion —In this method,P M is not used for precracking,but is used as a minimum load above which partial unloading is started for crack growth measurement.3.3.2crack initiation —describes the onset of crack propa-gation from a preexisting macroscopic crack created in the specimen by a stipulated procedure.

3.3.3effective modulus,E e [FL –2]—an elastic modulus that can be used with experimentally determined elastic compliance to effect an exact match to theoretical (modulus-normalized)compliance for the actual initial crack size,a o .

3.3.4elastic modulus,E 8[FL –2]—a linear-elastic factor re-lating stress to strain,the value of which is dependent on the degree of constraint.For plane stress,E 8=E is used,and for plane strain,E /(1–v 2)is used,with v being Poisson’s ratio.3.3.5elastic-plastic K J [FL –3/2]—An elastic-plastic equiva-lent stress intensity factor derived from J -integral.

3.3.5.1Discussion —In this test method,K J also implies a stress intensity factor determined at the test termination point under conditions determined to be invalid by 8.9.2.

3.3.6elastic-plastic K Jc [FL –3/2]—an elastic-plastic equiva-lent stress intensity factor derived from the J -integral at the point of onset of cleavage fracture,J c .

3.3.7Eta (h )—a dimensionless parameter that relates plas-tic work done on a specimen to crack growth resistance de?ned in terms of deformation theory J -integral (7).

3.3.8failure probability,p f —the probability that a single selected specimen chosen at random from a population of specimens will fail at or before reaching the K Jc value of interest.

3.3.9initial ligament length,b o [L]—the distance from the initial crack tip,a o ,to the back face of a specimen.

3.3.10pop-in —a discontinuity in a load versus displace-ment test record (8).

3.3.10.1Discussion —A pop-in event is usually audible,and is a sudden cleavage crack initiation event followed by crack arrest.A test record will show increased displacement and drop in applied load if the test frame is stiff.Subsequently,the test record may continue on to higher loads and increased displace-ment.

3.3.11precracked charpy specimen —SE(B)specimen with W =B =10mm (0.394in.).

3.3.12reference temperature,T o [°C]—The test temperature at which the median of the K Jc distribution from 1T size specimens will equal 100MPa =m (91.0ksi =in.).

3.3.13SE(B)specimen span,S[L]—the distance between specimen supports (See Test Method E 1820Fig.3).

3.3.14specimen thickness,B[L]—the distance between the sides of specimens.

For referenced ASTM standards,visit the ASTM website,https://www.wendangku.net/doc/5513422075.html,,or contact ASTM Customer Service at service@https://www.wendangku.net/doc/5513422075.html,.For Annual Book of ASTM Standards volume information,refer to the standard’s Document Summary page on the ASTM

website.

3.3.1

4.1Discussion—In the case of side-grooved speci-mens,thickness,B N,is the distance between the roots of the side-groove notches.

3.3.15specimen size,nT—a code used to de?ne specimen dimensions,where n is expressed in multiples of1in.

3.3.15.1Discussion—In this method,specimen proportion-ality is required.For compact specimens and bend bars, specimen thickness B=n inches.

3.3.16temperature,T Q[°C]—For K Jc values that are devel-oped using specimens or test practices,or both,that do not conform to the requirements of this test method,a temperature at which K Jc(med)=100MPa=m is de?ned as T Q.T Q is not a provisional value of T o.

3.3.17Weibull?tting parameter,K0—a scale parameter located at the63.2%cumulative failure probability level(9).

Jc =K0when p f=0.632.

3.3.18Weibull slope,b—with p f and K Jc data pairs plotted in linearized Weibull coordinates obtainable by rearranging Eq. 15,b is the slope of a line that de?nes the characteristics of the typical scatter of K Jc data.

3.3.18.1Discussion—A Weibull slope of4is used exclu-sively in this method.

3.3.19yield strength,s ys[FL–2]—a value of material strength at0.2%plastic strain as determined by tensile testing.

4.Summary of Test Method

4.1This test method involves the testing of notched and fatigue precracked bend or compact specimens in a tempera-ture range where either cleavage cracking or crack pop-in develop during the loading of specimens.Crack aspect ratio, a/W,is nominally0.

5.Specimen width in compact specimens is two times the thickness.In bend bars,specimen width can be either one or two times the thickness.

4.2Load versus displacement across the notch at a speci?ed location is recorded by autographic recorder or computer data acquisition,or both.Fracture toughness is calculated at a de?ned condition of crack instability.The J-integral value at instability,J c,is calculated and converted into its equivalent in units of stress intensity factor,K Jc.Validity limits are set on the suitability of data for statistical analyses.

4.3Tests that are replicated at least six times can be used to estimate the median K Jc of the Weibull distribution for the data population(10).Extensive data scatter among replicate tests is expected.Statistical methods are used to characterize these data populations and to predict changes in data distributions with changed specimen size.

4.4The statistical relationship between specimen size and

Jc fracture toughness can be assessed using weakest-link

theory,thereby providing a relationship between the specimen size and K Jc(4).Limits are placed on the fracture toughness range over which this model can be used.

4.5For de?nition of the toughness transition curve,a master curve concept is used(11,12).The position of the curve on the temperature coordinate is established from the experimental determination of the temperature,designated T o,at which the median K Jc for1T size specimens is100MPa=m(91.0 ksi=in.).Selection of a test temperature close to that at which the median K Jc value will be100MPa=m is encouraged and a means of estimating this temperature is suggested.Small specimens such as precracked Charpys may have to be tested at temperatures below T o where K Jc(med)is well below100 MPa=m.In such cases,additional specimens may be required as stipulated in8.

4.6Tolerance bounds can be determined that de?ne the range of scatter in fracture toughness throughout the transition range.The standard deviation of the?tted distribution is a function of Weibull slope and median K Jc value,K Jc(med).

5.Signi?cance and Use

5.1Fracture toughness is expressed in terms of an elastic-plastic stress intensity factor,K Jc,that is derived from the J-integral calculated at fracture.

5.2Ferritic steels are inhomogeneous with respect to the orientation of individual grains.Also,grain boundaries have properties distinct from those of the grains.Both contain carbides or nonmetallic inclusions that can act as nucleation sites for cleavage microcracks.The random location of such nucleation sites with respect to the position of the crack front manifests itself as variability of the associated fracture tough-ness(13).This results in a distribution of fracture toughness values that is amenable to characterization using statistical methods.

5.3Distributions of K Jc data from replicate tests can be used to predict distributions of K Jc for different specimen sizes. Theoretical reasoning(9),con?rmed by experimental data, suggests that a?xed Weibull slope of4applies to all data distributions and,as a consequence,standard deviation on data scatter can be calculated.Data distribution and specimen size effects are characterized using a Weibull function that is coupled with weakest-link statistics(14).An upper limit on constraint loss and a lower limit on test temperature are de?ned between which weakest-link statistics can be used.

5.4The experimental results can be used to de?ne a master curve that describes the shape and location of median K Jc transition temperature fracture toughness for1T specimens (15).The curve is positioned on the abscissa(temperature coordinate)by an experimentally determined reference tem-perature,T o.Shifts in reference temperature are a measure of transition temperature change caused,for example,by metal-lurgical damage mechanisms.

5.5Tolerance bounds on K Jc can be calculated based on theory and generic data.For added conservatism,an offset can be added to tolerance bounds to cover the uncertainty associ-ated with estimating the reference temperature,T o,from a relatively small data set.From this it is possible to apply a margin adjustment to T o in the form of a reference temperature shift.

5.6For some materials,particularly those with low strain hardening,the value of T o may be in?uenced by specimen size due to a partial loss of crack-tip constraint(5).When this occurs,the value of T o may be lower than the value that would be obtained from a data set of K Jc values derived using larger specimens.

6.Apparatus

6.1Precision of Instrumentation—Measurements of applied loads and load-line displacements are needed to obtain work done on the specimen.Load versus load-line

displacements

may be recorded digitally on computers or autographically on x-y plotters.For computers,digital signal resolution should be 1/32,000of the displacement transducer signal range and 1/4000of the load transducer signal range.

6.2Grips for C(T)Specimens—A clevis with?at-bottom holes is recommended.See Test Method E399-90,Fig.A6.2, for a recommended design.Clevises and pins should be fabricated from steels of sufficient strength to elastically resist indentation loads(greater than40Rockwell hardness C scale (HRC)).

6.3Bend Test Fixture—A suitable bend test?xture scheme is shown in Fig.A3.2of Test Method E399-90.It allows for roller pin rotation and minimizes friction effects during the test. Fixturing and rolls should be made of high-hardness steel (HRC greater than40).

6.4Displacement Gage for Compact Specimens:

6.4.1Displacement measurements are made so that J values can be determined from area under load versus displacement test records(a measure of work done).If the test temperature selection recommendations of this practice are followed,crack growth measurement will probably prove to be unimportant. Results that fall within the limits of uncertainty of the recommended test temperature estimation scheme will prob-ably not have signi?cant slow-stable crack growth prior to instability.Nevertheless,crack growth measurements are rec-ommended to provide supplementary information,and these results may be reported.

6.4.2Unloading compliance is the primary recommendation for measuring slow-stable crack growth.See Test Method E1820.When multiple tests are performed sequentially at low test temperatures,there will be condensation and ice buildup on the grips between the loading pins and?ats of the clevis holes.Ice will interfere with the accuracy of the unloading compliance method.Alternatively,crack growth can be mea-sured by other methods such as electric potential,but care must be taken to avoid specimen heating when low test temperatures are used.

6.4.3In compact C(T)specimens,displacement measure-ments on the load line are recommended for J determinations. However,the front face position at0.25W in front of the load line can be used with interpolation to load-line displacement, as suggested in

7.1.

6.4.4The extensometer calibrator shall be resettable at each displacement interval within0.0051mm(0.0002in.).Accuracy of the clip gage at test temperature must be demonstrated to be within1%of the working range of the gage.

6.4.5All clip gages used shall have temperature compensa-tion.

6.5Displacement Gages for Bend Bars,SE(B):

6.5.1The SE(B)specimen has two displacement gage locations.A load-line displacement transducer is primarily intended for J computation,but may also be used for calcula-tions of crack size based on elastic compliance,if provision is made to subtract the extra displacement due to the elastic compliance of the?xturing.The load-line gage shall display accuracy of1%over the working range of the gage.The gages used shall not be temperature sensitive.

6.5.2Alternatively,a crack-mouth opening displacement (CMOD)gage can also be used to determine the plastic part of J.However,it is necessary to employ a plastic eta(h p)value developed speci?cally for that position(16)or to infer load-point displacement from mouth opening using an expression that relates the two displacements(17).In either case,the procedure described in9.1.4is used to calculate the plastic part of J.The CMOD position is the most accurate for the compliance method of slow-stable crack growth measurement.

6.5.3Crack growth can be measured by alternative methods such as electric potential,but care must be taken to minimize specimen heating effects in low-temperature tests(see also 6.4.2)(18).

6.6Force Measurement:

6.6.1Testing shall be performed in a machine conforming to Practices of E4-93and E8M-95.Applied force may be measured by any transducer with a noise-to-signal ratio less than1/2000of the transducer signal range.

6.6.2Calibrate force measurement instruments by way of Practice E74-91,10.2.Annual calibration using calibration equipment traceable to the National Institute of Standards and Technology is a mandatory requirement.

6.7Temperature Control—Specimen temperature shall be measured with thermocouple wires and potentiometers.It is recommended that the two thermocouple wires be attached to the specimen surface separately,either by welding,spot weld-ing,or by being affixed mechanically.Mechanical attachment schemes must be veri?ed to provide equivalent temeprature measurement accuracy.The purpose is to use the test material as a part of the thermocouple circuit(see also8.6.1).Accuracy of temperature measurement shall be within3°C of true temperature and repeatability among specimens shall be within 2°C.Precision of measurement shall be61°C or better.The temperature measuring apparatus shall be checked every six months using instruments traceable to the National Institute of Standards and Technology in order to ensure the required accuracy.

7.Specimen Con?guration,Dimensions,and Preparation 7.1Compact Specimens—Three recommended C(T)speci-men designs are shown in Fig.1.One C(T)specimen con?gu-ration is taken from Test Method E399-90;the two with cutout sections are taken from E1820.The latter two designs are modi?ed to permit load-line displacement measurement.Room is provided for attachment of razor blade tips on the load line. Care should be taken to maintain parallel alignment of the blade edges.When front face(at0.25W in front of the load line)displacement measurements are made with the Test Method E399design,the load-line displacement can be inferred by multiplying the measured values by the constant 0.73(19).The ratio of specimen height to width,2H/W is1.2, and this ratio is to be the same for all types and sizes of C(T) specimens.The initial crack size,a o,shall be0.5W60.05W. Specimen width,W,shall be2B.

7.2Disk-shaped Compact Specimens—A recommended DC(T)specimen design is shown in Fig.2.Initial crack size,

a o,shall be0.5W60.05W.Specimen width shall be2B.

7.3Single-edge Notched Bend—The recommended SE(B) specimen designs,shown in Fig.3,are made for use with

span-to-width ratio,S/W =4.The width,W,can be either 1B or 2B.The initial crack size,a o ,shall be 0.5W 60.05W.7.4Machined Notch Design —The machined notch plus fatigue crack for all specimens shall lie within the envelope shown in Fig.4.

7.5Specimen Dimension Requirements —The crack front straightness criterion de?ned in 8.9.1must be satis?ed.The specimen remaining ligament,b o ,must have sufficient size to maintain a condition of high crack-front constraint at fracture.The maximum K Jc capacity of a specimen is given by:

K Jc ~limit !5

Eb o s ys 30~12v 2!

(1)

where:

s ys =material yield strength at the test temperature.

K Jc data that exceed this requirement may be used in a data censoring procedure.Details of this procedure are described in section 10.2.2for single-temperature data and 10.4.2for multi-temperature data.

7.6Small Specimens —At high values of fracture toughness relative to specimen size and material ?ow properties,the values of K Jc that meet the requirements of Eq 1may not always provide a unique description of the crack-front stress-strain ?elds due to some loss of constraint caused by excessive plastic ?ow (5).This condition may develop in materials

with

N OTE 1—A surfaces shall be perpendicular and parallel as applicable to within 0.002W TIR.

N OTE 2—The intersection of the crack starter notch tips with the two specimen surfaces shall be equally distant from the top and bottom extremes of the disk within 0.005W TIR.

N OTE 3—Integral or attached knife edges for clip gage attachment may be used.See also Fig.6,Test Method E 399.

FIG.2Disk-shaped Compact Specimen DC(T)Standard

Proportions

N OTE 1—All surfaces shall be perpendicular and parallel within 0.001W TIR;surface ?nish 64v.N OTE 2—Crack starter notch shall be perpendicular to specimen surfaces to within 62°.

FIG.3Recommended Bend Bar Specimen

Design

low starin hardening.When this occurs,the highest K Jc values of the valid data set could possibly cause the value of T o to be lower than the value that would be obtained from testing speciemens with higher constraint.

7.7Side Grooves —Side grooves are optional.Precracking prior to side-grooving is recommended,despite the fact that crack growth on the surfaces might be slightly behind.Speci-mens may be side-grooved after precracking to decrease the curvature of the initial crack front.In fact,side-grooving may be indispensable as a means for controlling crack front straightness in bend bars of square cross section.The total side-grooved depth shall not exceed 0.25B.Side grooves with an included angle of 45°and a root radius of 0.560.2mm (0.0260.01in.)usually produce the desired results.

7.8Precracking —All specimens shall be precracked in the ?nal heat treated condition.The length of the fatigue precrack extension shall not be less than 5%of the total crack size.Precracking may include two stages—crack initiation and ?nish sharpening of the crack tip.To avoid growth retardation from a single unloading step,intermediate levels of load shedding can be added,if desired.One intermediate level usually suffices.To initiate fatigue crack growth from a machined notch,use K max /E =0.00013m 1/2(0.00083in.1/2)65%.4Stress ratio,R,shall be controlled within the following range:0.01

?nish sharpening is to be 0.000096m 1/2(0.0006in.1/2)65%and stress ratio shall be maintained in the range 0.01

8.Procedure

8.1Testing Procedure —The objective of the procedure described here is to determine the J -integral at the point of crack instability,J c .Crack growth can be measured by partial unloading compliance,or by any other method that has precision and accuracy,as de?ned below.However,the J -integral is not corrected for slow-stable crack growth in this test method.

8.2Test Preparation —Prior to each test,certain specimen dimensions should be measured,the clip gage checked,and the starting crack size estimated from the average of the optical side face measurements.5

8.2.1The dimensions B,B N ,and W shall be measured to within 0.05mm (0.002in.)accuracy or 0.5%,whichever is larger.

Elastic (Young’s)modulus,E,in units of MPa will result in K max in units of MPa =m.Elastic (Young’s)modulus,E,in units of ksi will result in K max in units of ksi =in.

When side-grooving is to be used,?rst precrack without side grooves and optically measure the fatigue crack growth on both

surfaces.

N OTE 1—Notch width need not be less than 1.6mm (1?16in.)but not exceed W/16.

N OTE 2—The intersection of the crack starter surfaces with the two specimen faces shall be equidistant from the top and bottom edges of the specimen within 0.005W.

FIG.4Envelope Crack Starter

Notches

8.2.2Because most tests conducted under this method will terminate in specimen instability,clip gages tend to be abused,thus they shall be examined for damage after each test and checked electronically before each test.Clip gages shall be calibrated at the beginning of each day of use,using an extensometer calibrator as speci?ed in 6.4.4.

8.2.3Follow Test Method E 1820,8.5for crack size mea-surement,8.3.2for testing compact specimens and 8.3.1for testing bend specimens.

8.3The required minimum number of valid K Jc tests is speci?ed according to the value of K Jc(med).See also 8.5.8.4Test Temperature Selection —It is recommended that the selected temperature be close to that at which the K Jc(med)values will be about 100MPa =m for the specimen size selected.Charpy V-notch data can be used as an aid for predicting a viable test temperature.If a Charpy transition temperature,T CVN ,is known corresponding to a 28J Charpy V-notch energy or a 41J Charpy V-notch energy,a constant C can be chosen from Table 1corresponding to the test specimen size (de?ned in 3.3.15),and used to estimate 6the test tempera-ture from (12,20).

T 5T CVN 1C

(2)

TABLE 1Constants for Test Temperature Selection Based on

Charpy Results

Specimen Size,

(nT )

Constant C (°C)28J 41J 0.4A ?32?380.5?28?341?18?242?8?143?1?74

For precracked Charpy specimens,use C =?50or ?56°C.

8.4.1This correlation is only appropriate for determining an initial test temperature.The iterative scheme described in 10.4.3may be necessary to re?ne this test temperature in order to increase T o accuracy.Testing below the temperature speci-?ed in Eq 2may be appropriate for low upper-shelf toughness materials to avoid crack growth,and for low yield strength materials to avoid specimen size invalidity (Eq 1).7

8.5Testing Below Temperature,T o —When the equivalent value of K Jc(med)for 1T specimens is greater than 83MPa =m,the required number of valid K Jc values to perform the analyses covered in Section 10is six.However,small specimens such as precracked Charpy specimens (Test Method E 812)can de-velop excessive numbers of invalid K Jc values by Eq 1when testing close to the T o temperature.In such cases it is advisable to test at temperatures below T o ,where most,if not all,K Jc data developed can be valid.The disadvantage here is that the uncertainty in T o determination increases as the lower-shelf toughness is approached.This increase in uncertainty can be countered by testing more specimens thereby increasing the K Jc(med)accuracy.Table 2establishes the number of valid K Jc test results required to evaluate T o according to this test method.If

K Jc(med)of a data set is lower than 58MPa =m,then the T o determination using that data set shall not be allowed.

TABLE 2Number of Valid K Jc Test Results Required to Evaluate

T o

(T ?T o )i range

(°C)K Jc(med)range A

(MPa =m)Number of valid K Jc required

Possible number of invalid tests by Eq 1B

50to ?14212to 8463?15to ?3583to 6671?36to ?50

65to 58

A Convert K Jc(med)equivalence using Eq.16.Round off to nearest whole digit.B

Established speci?cally for precracked Charpy https://www.wendangku.net/doc/5513422075.html,e this column for total specimen needs.

8.6Specimen Test Temperature Control and Measurement —For tests at temperatures other than ambient,any suitable means (liquid,gas vapor,or radiant heat)may be used to cool or heat the specimens,provided the region near the crack tip can be maintained at the desired temperature as de?ned in 6.7during the conduct of the test.

8.6.1The most dependable method of monitoring test tem-perature is to weld or spot weld each thermocouple wire separately to the specimen,spaced across the crack plane.The specimen provides the electrical continuity between the two thermocouple wires,and spacing should be enough not to raise any question of possible interference with crack tip deforma-tion processes.Alternative attachment methods can be me-chanical types such as drilled hole,or by a ?rm mechanical holding device so long as the attachment method is veri?ed for accuracy and these practices do not disturb the crack tip stress ?eld of the specimen during loading.

8.6.2To verify that the specimen is properly seated into the loading device and that the clip gage is properly seated,repeated preloading and unloading in the linear elastic range shall be applied.Load and unload the specimen between loads of 0.2P max and P max (where P max is the top precracking load of the ?nishing cycles)at least three times.Check the calcu-lated crack size from each unloading slope against the average precrack size de?ned in 8.2.Refer also to Test Method E 1820,Eq.A2.12for C(T)specimens and to Eq.A1.10for SE(B)specimens.Be aware that ice buildup at the loading clevis hole between tests can affect accuracy.Therefore,the loading pins and devices should be dried before each test.For working-in ?xtures,the elastic modulus to be used should be the nominally known value,E ,for the material,and for side-grooved speci-mens,the effective thickness for compliance calculations is de?ned as:

B e 5B N ~2–B N /B !

(3)

8.6.3For J calculations in Section 9,B N is used as the thickness dimension.All calculated crack sizes should be within 10%of the visual average and replicate determinations within 1%of each other.If the repeatability of determination is outside this limit,the test setup is suspect and should be thoroughly rechecked.After working-in the test ?xtures,the load shall be returned to the lowest practical value at which the ?xture alignment can be maintained.

8.7Testing for K Jc —All tests shall be conducted under displacement control.Load versus load-point displacement measurements shall be recorded.Periodic partial unloading can

6Standard deviation on this estimate has been determined to be 15°C.7

Data validation is covered in 8.9.2and Section

10.

be used to determine the extent of slow-stable crack growth if it occurs.Alternative methods of measuring crack extension, for example the potential drop method,can be used(18).If displacement measurements are made at a location other than at the load point,the ability to infer load point displacement within2%of the absolute values shall be demonstrated.In the case of the front face for compact specimens(7.1),this requirement has been sufficiently proven so that no demonstra-tion is required.For bend bars,see6.5.2.Crack size prediction from partial unloading slopes at a different location will require different compliance calibration equations than those recom-mended in8.6.2.Table2in Practice E561-92a contains equations that de?ne compliance for other locations on the compact specimen.

8.7.1Load specimens at a rate such that the time of loading taken to reach load P M lies between0.1and10min.P M is nominally40%of limit load;see Test Method E1820,Eqs. A1.1and A2.1.The crosshead speed during periodic partial unloadings may be as slow as needed to accurately estimate crack growth,but shall not be faster than the rate speci?ed for loading.

8.7.2Partial unloadings that are initiated between load levels P M and1.5P M can be used to establish an“effective”elastic modulus,E e,such that the modulus-normalized elastic compliance predicts an initial crack size within0.001W of the actual initial crack size.The resulting E e should not differ from an expected or theoretical E of the material by more than10% (see also Practice E561-92a,Section10).A minimum of two such unloadings should be made and the slopes should be repeatable within1%of the mean value.Slow-stable crack growth usually develops at loads well above1.5P M and the spacing of partial unloadings depends on judgement.As an aim,every0.01a o increment of crack growth is https://www.wendangku.net/doc/5513422075.html,e E e in place of E and B e for thickness to calculate crack growth.

8.8Test Termination—After completion of the test,opti-cally measure initial crack size and the extent of slow-stable crack growth or crack extension due to crack pop-in,or both, when applicable.

8.8.1When the failure event is full cleavage fracture, determine the initial fatigue precrack size,a o,as follows: measure the crack length at nine equally spaced points centered about the specimen centerline and extending to0.01B from the free surfaces of plane sided specimens or near the side groove roots on side grooved specimens.Average the two near-surface measurements and combine the average of these two readings with the remaining seven crack measurements.Determine the average of those eight values.Measure the extent of slow-stable crack growth if it develops applying the same procedure. The measuring instruments shall have an accuracy of0.025 mm(0.001in.).

8.9Quali?cation of Data:

8.9.1The K Jc datum shall be considered a non-test and discarded if any of the nine physical measurements of the starting crack size differ by more than5%of thickness dimension,B,or0.5mm,whichever is larger,from the average de?ned in8.8.1.

8.9.2A K Jc datum is invalid if the specimen exceeds K Jc(limit)requirement of7.5,or if a test has been discontinued at a value of K J without cleavage fracture after surpassing K Jc(limit).For tests that terminate in cleavage after more than 0.05(W?a o)or1mm(0.040in.),whichever is smaller,of slow-stable crack growth,corresponding to the longest crack length dimension measured by section8.8.1,resulting K Jc value also shall be regarded as invalid.Should both the K Jc(limit)and the maximum crack growth validity criteria be violated,the lower value of the two shall prevail for data censoring purposes.When K J or K Jc values are invalid,these data contain statistically useable information that can be applied as censored data in10.2.2or10.4.2as appropriate.

8.9.3For any test terminated with no cleavage fracture,and for which the?nal K J value does not exceed either validity limit,cited in8.9.2,the test record is judged to be a nontest,the result of which shall be discarded.

8.9.4Data sets that contain all valid K Jc values can be used without modi?cation in Section10.Data sets that contain some invalid data but that meet the requirements of8.5can be used with data censoring(10.2.2).Remedies for excessive invalid data include(1)testing at a lower test temperature,(2)testing with larger specimens,or(3)testing more specimens to satisfy the minimum data requirements.

8.9.5A discontinuity in a load-displacement record,that may be accompanied by a distinct sound like a click emanating from the test specimen,is probably a pop-in event.All pop-in crack initiation K values for cracks that advance by a cleavage-driven mechanism are to be regarded as eligible K Jc data.It is recognized that test equipment can at times introduce false pop-in indications in test records.If a questionable discontinu-ity develops,stop the loading as soon as possible and assess the compliance ratio by9.2.If the compliance change leads to a ratio calculated by9.2that is greater than the calculated ratio corresponding to more than a1%increase in crack size,the recommended practice is to assume that a pop-in event has occurred and to terminate the test,followed by heat tinting and breaking the specimen open at liquid nitrogen temperature. Measure the initial crack size and calculate K Jc,for the pop-in load,based on that crack size.Measure the post pop-in crack size visually and record it.If there is no evidence of crack extension by cleavage,then the K Jc value at the discontinuity point is not a part of the K Jc data distribution.

9.Calculations

9.1Determine the J-integral at onset of cleavage fracture as the sum of elastic and plastic components:

J c5J e1J p(4) 9.1.1For compact specimens,C(T),the elastic component of J is calculated as follows:

J e5

~12v2!K e2

E(5) where:

K e=[P/(BB N W)1/2]f(a o/W),

f~a o/W!5

~21a o/W!

~1–a o/W!3/2

@0.88614.64~a o/W!–13.32~a o/W!2

114.72~a o/W!3–5.6~a o/W!4#,(6) and a o=initial crack

size.

9.1.2For disk-shaped compact specimens,DC(T),the elas-tic component of J is calculated as follows:

J e 5~12v 2!K e

(7)

where:

K e =[P/(BB N W)1/2]f (a o /W ),

f ~a o /W !5

~21a o /W !

~1–a o /W !3/2

@0.7614.8~a o /W !–11.58~a o /W !

111.43~a o /W !3–4.08~a o /W !4#,

(8)

and a o =initial crack size.

9.1.3For SE(B)specimens of both B 3B and B 32B cross sections and span-to-width ratios of 4,the elastic component of J is calculated as follows:

J e 5

~12v 2!K e

(9)

where:

K e ={PS /[(BB N )1/2W 3/2]}f (a o /W ),

f ~a o /W !5

3~a o /W !1/2

2[112~a o /W !#

1.99–~a o /W !~1–a o /W !@

2.15–

3.93~a o /W !12.7~a o /W !2#

~1–a o /W !,

(10)

and a o =the initial crack size.

9.1.4The plastic component of J is calculated as follows:

J p 5h A p

B N b

(11)

where:

A p =A –1/2C o P 2,A =A e +A p (see Fig.5),

C o =reciprocal of the initial elastic slope,V/P (Fig.5),

and

b o =initial remaining ligament.

9.1.4.1For standard and disk-shaped compact specimens,A p is based on load-line displacement (LLD)and h =2+0.522b o /W .For bend bar specimens of both B 3B and B 32B cross sections and span-to-width ratios of 4,A p may be based on

either LLD or crack-mouth opening displacement (CMOD).Using LLD,h =1.9.Values of h for bend bars based on CMOD are discussed in 6.5.2.

9.1.5K Jc is determined for each datum from J at onset of cleavage fracture,J c .Assume plane strain for elastic modulus,E:

K Jc 5

J c

E 12v 2

(12)

9.1.6All data with K Jc in excess of the limits prescribed in 8.9.2are considered invalid,but values can be used in the censoring analysis that is described in 10.2.2or 10.4.2as appropriate.Invalid data developed as a part of a data set disquali?es that data set for analysis by 10.2.1.

9.2Pop-in Evaluation —Test records that can be used for K Jc analyses are those that show complete specimen separation due to cleavage fracture and those that show pop-in.If a load-displacement record shows a small but perceptible dis-continuity without the audible click of the typical pop-in,a mid-test decision will be needed.Following Fig.6,determine the post pop-in to initial compliance ratio,C i /C o ,and compare this to the value of the right-hand side of the following inequality which implies that a pop-in has occurred:

C i C o .F 110.01h S

W a o –1

D –1

(13)

where:

a o =nominal initial crack size (high accuracy on dimen-sion a o is not required here),and

h =parameter based on LLD de?ned in 9.1.4.1.

Eq 13involves the use,by approximation,of the plastic parameter,h ,in an otherwise elastic equation,as suggested in Test Method E 1820.When a o /W =0.5,C i /C o shall be greater than 1.02,to follow the pop-in evaluation procedure prescribed in 8.9.5.

9.3Outlier —Occasionally,an individual K Jc datum will appear to deviate greatly from the remainder of the data set.The impact and character of this datum can be evaluated as follows.First determine the 2%and 98%tolerance bounds using the equations

below:

FIG.5De?nition of the Plastic Area for J p

Calculations

K Jc ~0.02!50.415K Jc ~med !111.70MPa =m (14)

K Jc ~0.98!51.547K Jc ~med !210.94MPa =m

If the suspected datum is outside the tolerance bounds dictated by Eqs.(14)(for example,K Jc K Jc (0.98))it may be possible to reduce the in?uence of the outlier datum on K Jc(med)by testing additional specimens.Typically,a total of 12replicate specimens is sufficient.However,outliers shall not be discarded from the data utilized to calculate K Jc(med).The emergence of additional outliers may indicate that the test material is not homogenious.

10.Prediction of Size Effects and Transition Temperature 10.1Weibull Fitting of Data Sets :

10.1.1Test Replication —A data set consists of at least six valid replicate test results determined at one test temperature,or the equivalent thereof;see also 8.5for single temperature and 10.4for multi-temperature requirements.

10.1.2Determination of Scale Parameter,K o ,and median K [K Jc(med)]—The three-parameter Weibull model is used to de?ne the relationship between K Jc and the cumulative prob-ability for failure,p f .The term p f is the probability for failure at or before K Jc for an arbitrarily chosen specimen taken from a large population of specimens.Data samples of six or more specimens are used to estimate the true value of scale param-eter,K o ,for the following Weibull model:

p f 51–exp $–[~K Jc –K min !/~K o –K min !#b %

(15)

10.1.3Ferritic steels of yield strengths ranging from 275to 825MPa (40to 120ksi)will have fracture toughness cumu-

lative probability distributions of nearly the same shape,independent of specimen size and test temperature,when K min is set at 20MPa =m (18.2ksi =in.).The shape of the distribution is de?ned by the Weibull exponent,b ,which tends to be near 4.Scale parameter,K o ,is the data ?tting parameter determined when using the maximum likelihood statistical method of data ?tting (21).When K Jc and K o in Eq.15are equal,P f =0.632.

10.1.4Size Effect Predicitons —The statistical weakest-link theory is used to model specimen size effect in the transition range between lower shelf and upper shelf fracture toughness.The following Eq.16can be used to size adjust individual K Jc values,K Jc(med),or K o .K Jc serves as the example case:

K Jc ~x !5K min 1[K Jc ~o !–K min #S B o

1/4

(16)

where:

K Jc(o)=K Jc for a specimen size B o ,

B o

=gross thickness of test specimens (side grooves ignored),

B x

=gross thickness of prediction (side grooves ig-nored),and

K min

=20MPa =m (18.2ksi =in.).10.2The recommendation advanced by this standard test method is to perform K Jc data replication at a single test temperature,as near as possible to an estimated T o temperature.However,all data obtained at temperatures within the range ?50oC #(T ?T o )#50oC shall be considered in the determi-nation of T o .Therefore,if testing is performed at more than

one

FIG.6Schematic of Pop-in Magnitude

Evaluation

temperature,the multi-temperature procedure described in 10.4.2shall be used.In this case,the combination of valid specimen numbers and test temperatures shall satisfy Eq.(22) in10.4.1.Iteration in terms of testing additional specimens may be required.For single-temperature tests,use8.4or8.5for test temperature estimation assistance.The following sections 10.2.1and10.2.2can be used to calculate the scale parameter, K o,for data developed at a single test temperature and consisting of at least six valid K Jc values,or the equivalent thereof,see also8.5.Data sets containing only valid data(as de?ned in8.9.2)shall be analyzed as per10.2.1.Paragraph 10.2.2shall be applied if any invalid data(as de?ned in8.9.2) exist.

10.2.1Determination of K o with all Valid Data—If the data are generated from specimens of other than1T size,the data must?rst be converted to1T size equivalence using Eq.(16) (see section3.3.15).The following Eq.(17)shall be then

applied to determine K o:

K o5F(i51N~K Jc~i!–K min!4N G1/41K min(17)

where:

N=number of specimens tested as de?ned in8.9,and K min=20MPa=m(18.2ksi=in.).

See X1.2for an example solution.

10.2.2Determination of K o with Censored Data—Replace all invlaid K Jc values(8.9.2)with dummy K Jc values.If invalidity was due to violation of K Jc(limit),Eq.(1),the experimental K Jc value shall be replaced by K Jc(limit)for the specimen size https://www.wendangku.net/doc/5513422075.html,e the material yield strength at the test temperature.In the case of K Jc invalidity due to exceeding the 0.05(W?a o)or1-mm(0.04-in.)limitation on stable crack growth(8.9.2),the K Jc test value shall be replaced with the highest valid K Jc in the data set for any specimen size.The Weibull scale parameter,K o,shall be calculated using the following Eq.(18),in which all K Jc(i)and dummy values for specimens other than1T size are converted to1T size equiva-lence,using Eq.(16).See section3.3.15and X1.3for example

solution.

K o5F(i51N~K Jc~i!–K min!4r G1/41K min(18)

where:

r=number of valid data as de?ned in8.9,

K min=20MPa=m(18.2ksi=in.),and

N=number of data(valid and invlaid).

10.2.3K o to K Jc(med)Conversion—The scale parameter,K o calculated according to either,10.2.1or10.2.2,corresponds to a63%cumulative probability level for specimen failure by cleavage.The median K Jc of a data population corresponds to 50%cumulative probability for fracture and K Jc(med)can be determined from K o using the following:

K Jc~med!5K min1~K o2K min![1n~2!#1/4(19) where:

K min=20MPa=m(18.2ksi=in.).

10.3Establishment of a Transition Temperature Curve (Master Curve)—Transition temperature K Jc data tend to con-form to a common toughness versus temperature curve shape in the same manner as the ASME K lc and K IR lower-bound design curves(21,22).For this method,the shape of the median K Jc toughness,K Jc(med),for1T specimens(3.3.15)is described by:

K Jc~med!530170exp[0.019~T–T o!#,MPa=m,(20) where:

T=test temperature(°C),and

T o=reference temperature(°C).

10.3.1Master curve positioning involves the determination of T o using the computational steps presented below.

10.3.2Determine Reference Temperature(T o)—Use only 1T K Jc(med)values,converted by Eq.16if necessary.

T o5T–S10.019

D ln F K Jc~med!–3070G(21)

Units of K Jc(med)are in MPa=m;units of T o are in°C. 10.4Multi-temperature Option—The reference tempera-ture,T o,should be relatively independent of the test tempera-ture that has been selected.Hence,data that are distributed over a restricted temperature range,namely T o650oC,can be used to determine T o.As it is with the single test temperature option, a minimum of six valid K Jc data(8.9.2)or the equivalence,by weight factor,described in10.4.1below is required.In the case of data generated at test temperatures from14oC below T o to 50oC above T o,the minimum requirement of six valid data will be satisfactory.

10.4.1Data generated at test temperatures in the range of T o -50to T o-14°C are considered to make reduced accuracy contribution to T o determinations.As a consequence,more data development within the aforementioned temperature range is required.The following weighting system speci?es the re-quired number of data:

(

i51

r i n i$1(22)

where r i is the number of valid specimens within the i-th temperature range,(T?T o),and n i is the specimen weighting factor for the same temperature range as shown in Table3.

10.4.2All K Jc data,including valid and dummy values resulting from Eq.1violation at each test temperature,must ?rst be converted to1T equivalence using Eq.16.If the slow-stable crack growth limitation is violated as speci?ed in 8.9.2,the highest valid K Jc shall be used for censoring.The K Jc(limit)in8.9.2shall be chosen from data at any temperature as this value should be largely temperature insensitive.Also this value is specimen-size-independent and size correction of this limit shall not be performed.The K J value corresponding to J Ic also can be used for crack growth censoring if J Ic is

TABLE3Weight Factors for Multi-Temperature Analysis

(T?T o)range A

(°C)

1T K Jc(med)range A

(MPa=m)

Weight factor

n i 50to?14212to841/6

?15to?3583to661/7

?36to?5065to581/8

A Rounded off to the closest

integer.

known for the test material.The following equality shall be used to determine T o for tests made at varied temperatures (21,23):

(i 51N

d i exp [0.019~T i 2T o

11177exp [0.019~T i 2T o !#(23)

2(i 51N

~K Jc ~i !220!4exp [0.019~T i 2T o !#

$11177exp [0.019~T i 2T o !#%

550where:

N =number of specimens tested,T i =test temperature corresponding to K Jc(i),

K Jc(i)=either a valid K Jc datum or dummy value substitute

for an invalid datum (section 8.9.2).All K Jc input values,valid or dummy K Jc ,must be converted to 1T equivalence (section 3.3.15)before entry,d i

= 1.0if the datum is valid or zero if the datum is a dummy substitute value,

11=integer equivalent of 10/(ln2)1/4MPa =m,and 77=integer equivalent of 70/(ln2)1/4MPa =m.Solve Eq.23for T o temperature by iteration.

10.4.3Since the valid test temperature range is only known after T o has been determined,the following iterative scheme may be helpful for identifying proper test temperature.Choose an initial test temperatures as described within 8.4using the value of “C”appropriate for the test specimen size.Conduct 3-4valid tests at this temperature and evaluate a preliminary T o value using 10.2to determine K o .Base all subsequent test temperatures on this preliminary value of T o .See Appendix X3for an example solution.

10.4.4Certain multi-temperature data sets may result in an oscillating iteration between two (or more)distinct T o values upon satisfying the T o 650°C limit of 10.4.In these instances,the T o value reported shall be the average of the calculated values.One example is for hypothetical data with toughness values such that the initial T o estimation requires that data at one temperature be excluded.The second iteration then results in the inclusion of this same data.Subsequent T o iterations will then oscillate between the original ?rst and second estimations.This phenomenon is more likely for sparse data sets when test results exist near the T o 650°C limit.More testing near the average T o will likely resolve this problem.

10.5K Jc values that are developed using specimens or test practices or both,that do not conform to the requirements of this method can be used to establish the temperature of 100MPa =m fracture toughness.Such temperatures shall be re-ferred to as T Q .Currently existing experimental evidence indicates that data populations developed without the con-trolled constraint conditions required by the present standard method are apt to have Weibull slopes that are other than 4and,as such,the use of the equations provided here and the use of the master curve toughness trend to determine T Q is not technically justi?able.Hence,values of T Q are of use for unique circumstances only and are not to be regarded as provisional values of T o .

10.6Uses for Master Curve —The master curve can be used to de?ne a transition temperature shift related to metallurgical damage mechanisms.Fixed values of Weibull slope and median K Jc de?ne the standard deviation;hence the represen-

tation of data scatter.This information can be used to calculate tolerance bounds on toughness,for the specimen reference size chosen.The data scatter characteristics modeled here can also be of use in probabilistic fracture mechanics analysis,bearing in mind that the master curve pertains to a 1T size specimen.The master curve determined by this procedure pertains to cleavage fracture behavior of ferritic steels.Extensive ductile tearing beyond the validity limit set in 8.9.2,may precede cleavage as the upper-shelf range of temperature is approached.Such data can be characterized by separate methods (see Test Method E 1820).

11.Report

11.1Report the following information:

11.1.1Specimen type,specimen thickness,B ,net thickness,B N ,specimen width,W ,

11.1.2Specimen initial crack size,

11.1.3Visually measured slow-stable crack growth to fail-ure,if evident,

11.1.4Crack plane orientation according to Terminology E 1823,

11.1.5Test temperature,

11.1.6Number of valid specimens and total number of specimens tested at each temperature,

11.1.7Crack pop-in and compliance ratio,C i /C o ,11.1.8Material yield strength and tensile strength,

11.1.9The location of displacement measurement used to obtain the plastic component of J (load-line or crack-mouth),11.1.10A list of individual K Jc values and the median K Jc(med)(MPa =m)obtained from that list,

11.1.11Reference temperature on master curve,T o (°C),11.1.12Fatigue precracking condition in terms of K max for the last 0.64mm (0.025in.)of precrack growth,and

11.1.13Difference between maximum and minimum crack length measurement expressed as a percentage of the initial crack size.

11.2The report may contain the following supplementary information:

11.2.1Specimen identi?cation codes,

11.2.2Measured pop-in crack extensions,and 11.2.3Load-displacement records.

12.Precision and Bias

12.1Precision —The variability of material toughness in the transition range is an accepted fact and the modeling of the data scatter is an integral feature of this test procedure.It has been observed that when K min of 20MPa =m is used as a determin-istic parameter in the three-parameter Weibull statistical model,K Jc data distributions will tend to display a Weibull slope of approximately 4.Small sample sizes,such as required by 8.5,are prone at times to show slopes that vary randomly above and below 4,but such behavior does not necessarily indicate a lack-of-precision problem.This variability becomes small only with extremely large sets of specimens (11).Despite slope variations with sample sizes,the median K Jc will be within 20%of the true median of the full data population and it is this value that is used to establish the reference temperature,T o .The number of specimens required by this standard is increased for tests performed at temperatures below T o .Tests that

use

more than the minimum number of six specimens have increased precision of K Jc(med)determination.This is required at test temperatures approaching lower shelf where more precision is needed to maintain an equal uncertainty level in the T o determination.If reference temperatures,T o,are calculated from K Jc(med)values determined at several test temperatures, some scatter can be expected.The standard deviation of this scatter is de?ned by Eq X4.1in Appendix X4.Eq X4.3solved using the sample size required for validity and applied with a standard normal deviate for85%con?dence suggests that T o values determined at different temperatures can be expected to be within a scatter band of20°C(15,22).

12.2Bias—As discussed in1.3,there is an expected bias among T o values as a function of the standard specimen type.The bias size is expected to increase inversely to the strain hardening ability of the test material at a given yield strength. On average,T o values obtained from C(T)specimens are higher than T o values obtained from SE(B)specimens.Best estimate comparison indicates that the average difference between C(T)and SE(B)-derived T o values is approximately 10°C(2).C(T)and SE(B)T o differences up to15°C have also been recorded(3).However,comparisons of individual,small datasets may not necessarily reveal this average trend.Datasets which contain both C(T)and SE(B)specimens may generate T o results which fall between the T o values calculated using solely C(T)or SE(B)specimens.

APPENDIXES

(Nonmandatory Information)

X1.WEIBULL FITTING OF DATA

X1.1Description of the Weibull Model:

X1.1.1The three-parameter Weibull model is used to?t the

relationship between K Jc and the cumulative probability for

failure,p f.The term p f is the probability for failure at or before

K Jc for an arbitrarily chosen specimen from the population of

specimens.This can be calculated from the following:

p f51–exp$–[~K Jc–K min!/~K o–K min!#b%(X1.1)

X1.1.2Ferritic steels of yield strengths ranging from275to

825MPa(40to120ksi)will have fracture toughness distri-

butions of nearly the same shape when K min is set at20

MPa=m(18.2ksi=in.).This shape is de?ned by the Weibull

exponent,b,which is constant at4.Scale parameter,K o,is a

data-?tting parameter.The procedure is described in X1.2.

X1.2Determination of Scale Parameter,K o,and Median

K Jc—The following example illustrates the use of10.2.1.The

data came from tests that used4T compact specimens of A533

grade B steel tested at-75°C.All data are valid and the chosen

equivalent specimen size for analysis will be1T.

Rank (i)

K Jc(4T)

(MPa=m)

K Jc(1T)

Equivalent

(MPa=m)

159.175.3 268.388.3 377.9101.9 497.9130.2 5100.9134.4 6112.4150.7

K o~1T!5F(i51N~K Jc~i!–20!4N G1/4120(X1.2)

N56

K o~1T!5123.4MPa=m

X1.2.1Median K Jc is obtained as follows:

K Jc~med!5201~K o~1T!–20!~0.9124!MPa=m(X1.3)

5114.4MPa=m

X1.2.2

T o5T2S10.019

D ln F K Jc~med!23070G(X1.4)

5285°C

X1.3Data Censoring Using the Maximum Likelihood Method:

X1.3.1Censoring When K Jc(limit)is Violated—The follow-ing example uses10.2.2where all tests have been made at one test temperature.The example data set is arti?cially generated for a material that has a T o reference temperature of0°C.Two specimen sizes are1/2T and1T with six specimens of each size.Invalid K Jc values and their dummy replacement K Jc(limit) values will be within parentheses.

X1.3.2The data distribution is developed with the follow-ing assumptions:

Material yield strength=482MPa or70ksi

T o temperature=0°C

Test temperature=38°C

1/2T and1T specimens;all a/W=0.5

X1.3.3K Jc(limit)values in MPa=m from Eq.1.

0.5T1T

Specimen size206291

1T equivalent176291

X1.3.4Simulated Data Set:

Raw Data

(K Jc,MPa=m)

Size Adjusted

(K Jc(1T),MPa=m) 1/2T1T1/2T A1T

138.8119.9119.9119.9

171.8147.6147.6147.6

195.2167.3167.3167.3

(216.2)185.0(176)185.0

(238.5)203.7(176)203.7

(268.3)228.8(176)228.8

A K

Jc(1T)

=(K Jc(0.5T)

?20)(1/2/1)1/4+20MPa=m

K o ~1T !5[(i 51

~K Jc ~i !220!4r #1/4

120(X1.5)

where:N =12,r =9,

K o(1T)

=188MPa =m,K Jc(med)

=174MPa =m,and T o =0°C.

X1.3.5Censoring When D a p #0.05(W ?a p ),not to Exceed 1mm Limit is Violated —The following example uses 10.2.2where all tests have been made at a single test temperature of 38°C.Assume that the test material has properties as de?ned in X1.3.2and toughness data as de?ned in X1.3.4.However,for this example assume that the steel has a low upper shelf.The crack growth limit (see 8.9.2)is 0.64mm and 1mm for 0.5T and 1T specimen respectively.The K J value after 0.64mm of slow-stable growth is only 197MPa =m and after 1mm of slow-stable growth is only 202MPa =m.Therefore,the crack growth limit controls all censoring.The K j ?R curve is speci-men size independent so that both 0.5T and 1T specimens will have censored data.In this case the dummy replacement value as per 10.2.2is the highest ranked valid K Jc value.

Raw Data

1T Size Adjusted Data 0.5T

0.5T A

D a p ,

mm K Jc ,Mpa =m D a p ,mm K Jc ,Mpa =m K Jc ,Mpa =m 0.00138.80.00119.9119.9119.90.25171.80.15147.6147.6147.60.50195.20.20167.3167.3167.30.67(216.2)0.55185.0(167.3)1850.70(238.5) 1.10(203.7)(167.3)(185)0.71

(268.3)

1.15

(228.8)

(167.3)

(185)

K Jc(1T)=K Jc(0.5T)?20)·(0.5/1)1/4+20Mpa =m

K o ~1T !5F

(i 51

~K Jc ~i !220!4

r G

1/4

120(X1.6)

where:

N =12,r =7,

K o(1T)=186MPa =m,K Jc(med)=171MPa =m,and T o

=1°C.

X2.MASTER CURVE FIT TO DATA

X2.1Select Test Temperature (see 8.4):X2.1.1Six 1?2T compact specimens,X2.1.2A 533grade B base metal,and X2.1.3Test temperature,T =–75°C.

X2.2In this data set,there are no censored data.

Rank (i )K Jc(1/2T)(MPa =m)K Jc(1T)Equivalent (MPa =m)191.480.02103.189.93120.3104.34133.5115.45144.4124.66

164.0

141.1

X2.3Determine K o using Eq X1.2:K o(1T)=115.8MPa =m,and

K Jc(med)=[ln(2)]1/4(K o –20)+20=107.4MPa =m.X2.4Position Master Curve :

T o 5T –~0.019!–1ln [~K Jc ~med !–30!/70](X2.1)

5–75–ln @~108.5–30!/70]/0.0195–80°C.

X2.5Master Curve :

K Jc ~med !530170exp[0.019~T 180!#

(X2.2)

X2.5.1See Fig.

X2.1.

X3.EXAMPLE MULTITEMPERATURE T o DETERMINATION

X3.1Material:A533Grade B plate Quenched and tempered

900°C WQ;and 440°C (5h)temper X3.2Mechanical Properties:Yield strength:641MPa (93ksi)Tensile strength:870MPa (117.5ksi)Charpy V:

28-J temperature =?5°C (23°F)41-J temperature =16°C (61°F)NDT:41°C (106°F)X3.3K Jc Limit Values:Specimen Types:

1/2T C(T)with a o /W =0.51T SE(B)with a o /W =0.5

Test Temperature

(°C)

Yield Strength (MPa)K Jc(limit)(MPa =m)1/2T 1T ?10651239338?5649238337064823833723

641

237

335

X3.4Slow-stable Crack Growth Limits:

K Jc ~1mm !5263MPa =m for 1T SE ~B !specimen;K Jc ~0.64mm !5255MPa =m for 1/2T C ~T !specimen

X3.5Estimation Procedure #1from Charpy Curve:

T o ~est !5T 28J 1C 525°218°5223°C

T o ~est !5T 41J 1C 516°224°528°C

Conduct four 1T SE(B)tests at ?20°C.

X3.6T o Estimation Procedure #2from Results of First Four Tests:

First four tests at ?20°C:

K Jc ,MPa =m

135.1108.9177.1141.7

Calculate preliminary T o(est)#2from data to determine allow-able test temperature range:

K Jc ~med !5137MPa =m ;T 0~est !#25242°C

Estimated temperature range or usable data:

5T 0~est !#2650°C 5292°C ,T i ,18°C

Now conduct additional testing within this range for T o determination.

X3.7Calculation of T o (Eq.23):

Use data between ?92°C and 8°C based on T o(est)#2

T o 5248°C

The valid test temeprature range is ?98°C to 2°C.Original claculations were performed with data in this regime.

There-fore,no iteration is required.

N OTE 1—Toughness data are converted to 1T equivalence.

FIG.X2.1Master Curve for 1T Specimens Based on

1/2T Data Tabulated in Step X2.2

X3.8Quali?ed Data Summation:

(T ?T o )range

(°C)Number of valid tests,r i

Weight factor,n i

r i ·n i 50to ?14431/67.2?15to ?3551/70.7?36to ?50

1/8

Validity check:

S r i n i 57.9.1.0

TABLE X3.1Data Tabulation

Test temperature,

(°C)Specimen K Jc

(MPa =m)

d j

Type Size Raw data 1T equivalent ?130

C(T)

1/2T

59.553.2185.174.7155.349.7156.450.61?80C(T)1/2T

51.346.3187.977.11113.498.51?65SE(B)1T 73.973.91126.8126.81?55

C(T)

1/2T

167.7144.2188.577.61115.2100.0181.471.61121.9105.71145.0125.11104.290.8164.457.3196.884.61114.599.51107.493.5181.071.3170.062.01131.8114.0169.561.6167.559.91?30C(T)1/2T

102.389.21194.0166.31170.4146.51129.5112.11118.2102.61147.9127.51178.8153.5195.983.81?20SE(B)1T

135.1135.11108.9108.91177.1177.11141.7141.71174.4174.4184.884.81132.1132.11?10C(T)1/2T

211.4180.91179.9154.51171.8147.61153.0131.81236.9(204)0156.81351?5C(T)1/2T

121.5105.31194.2166.51110.496.01197.0168.81134.7116.51264.4(203)00C(T)1/2T

277.8(198.9)0218.9187.21107.793.71269.3(203)0327.1(203)023C(T)1/2T

325A (202)0328A (202)0227

194

R-curve (no cleavage

instability).

X4.CALCULATION OF TOLERANCE BOUNDS

X4.1The standard deviation of the ?tted Weibull distribu-tion is a mathematical function of Weibull slope,K Jc(med),and K min ,and because two of these are constant values,the standard deviation is easily determined.Speci?cally,with slope b of 4and K min =20MPa =m,standard deviation is de?ned by the following (24):

s 50.28K Jc ~med ![1–20/K Jc ~med !#

(X4.1)

X4.1.1Tolerance Bounds —Both upper and lower tolerance bounds can be calculated using the following equation:

K Jc ~0.xx !5201F ln S

120.xx

D G

1/4

$11177exp [0.019~T 2T o !#%

(X4.2)

where temperature “T”is the independent variable of the equation;xx represents the selected cumulative probability level;for example,for 2%tolerance bound,0.xx =0.02.As an example,the 5and 95%bounds on the Appendix X2master curve are:

K Jc ~0.05!525.2136.6exp [0.019~T 180!#(X4.3)

K Jc ~0.95!534.51101.3exp [0.019~T 180!#

X4.1.2The potential error due to ?nite sample size can be considered,in terms of T o ,by calculating a margin adjustment,as described in X4.2.

X4.2Margin Adjustment —The margin adjustment is an upward temperature shift of the tolerance bound curve,Eq X4.3.Margin is added to cover the uncertainty in T o that is associated with the use of only a few specimens to establish T o .The standard deviation on the estimate on T o is given by:

s 5b /=r ~°C !,

(X4.4)

where:

r =total number of specimens used to establish the value of

T o .

X4.2.1When K Jc(med)is equal to or greater than 83MPa =m,b =18°C (25).If the 1T equivalent K Jc(med)is below 83MPa =m,values of b must be increased according to the following schedule:

K Jc(med)

1T equivalent A

(MPa =m)b (°C)83to 6618.865to 58

20.1

Round off K Jc(med)to nearest whole number.

X4.2.2To estimate the uncertainty in T o ,a standard two-tail normal deviate,Z ,should be taken from statistical handbook tabulations.The selection of the con?dence limit for T o adjustment is a matter for engineering judgment.The following example calculation is for 85%con?dence (two-tail)adjust-ment to Eq X4.3for the six specimens used to determine T o .

D T o 5s~Z 85!5

~1.44!510°C (X4.5)

T o ~margin !5T o 1D T o 5–80°110°5–70°C

Then the margin-adjusted 5%tolerance bound of Eq X4.3is revised to:

K Jc ~05!525.2136.6exp [0.019~T 170!#

(X4.6)

Eq X4.6is plotted in Fig.X4.2as the dashed line

(L.B.).

FIG.X4.1Master Curve With Upper and Lower 95%Tolerance

Bounds

REFERENCES

(1)Gao,X,and Dodds,R.H.,“Constraint Effects on the Ductile-to-Cleavage Transition Temperature of Ferritic Steels:A Weibull Stress Model,”International Journal of Fracture ,102,2000,pp.43-69.(2)Wallin,K.,Planman,T.,Valo,M.,and Rintamaa,R.,“Applicability of Miniature Size Bend Specimens to Determine the Master Curve Reference Temperature T o ,”Engineering Fracture Mechanics ,V ol 68,2001,pp.1265-1296.

(3)Joyce,J. A.,and Tregoning,R.L.,“Investigation of Specimen Geometry Effects and Material Inhomogeneity Effects in A533B Steel,”ECF 14—Fracture Mechanics Beyond 2000,Proceedings of the 14th European Conference on Fracture ,Krakow,September 2002,to be published.

(4)Anderson,T.L.,Steinstra,D.,and Dodds,R.H.,“A Theoretical Framework for Addressing Fracture in the Ductile-Brittle Transition Region,”Fracture Mechanics ,24th V olume,ASTM STP 1207,ASTM,1994,pp.185-214.

(5)Ruggeri, C.,Dodds,R.H.,and Wallin,K.,“Constraint Effects on Reference Temperature,T o ,for Ferritic Steels in the Transition Region,”Engineering Farcture Mechanics ,60(1),1998,pp.19-36.(6)Paris,P.C.,“Fracture Mechanics in the Elastic-Plastic Regime,”Flaw Growth in Fracture,ASTM STP 631,ASTM,August 1976,pp.3-27.(7)Turner, C. E.,“The Eta Factor,”Post Yield Fracture Mechanics ,Second Ed.,Elsevier Applied Science Publishers,London and New York,1984,pp.451-459.

(8)McCabe,D.E.,Evaluation of Crack Pop-ins and the Determination of their Relevance to Design Considerations ,NUREG/CR-5952(ORNL/TM-12247),February 1993.

(9)Wallin,K.,“The Scatter in K lc Results,”Engineering Fracture Me-chanics ,19(6)(1984),pp.1085-1093.

(10)McCabe,D.E.,Zerbst,U.,and Heerens,J.,“Development of Test

Practice Requirements for a Standard Method of Fracture Toughness Testing in the Transition Range,”GKSS Report 93/E/81,GKSS Forschungszentrum,Geesthacht,GmBH,Germany,1993.

(11)Steinstra,D.I.A.,“Stochastic Micromechanical Modeling of Cleav-age Fracture in the Ductile-Brittle Transition Region,”MM6013-90-11,Ph.D.Thesis,Texas A &M University,College Station,TX,August 1990.

(12)Wallin,K.,“A Simple Theoretical Charpy V-K lc Correlation for

Irradiation Embrittlement,”ASME Pressure Vessels and Piping Con-ference,Innovative Approaches to Irradiation Damage and Fracture Analysis ,PVP-V ol 170,American Society of Mechanical Engineers,New York,July 1989.

(13)Heerens,J.,Read, D.T.,Cornec, A.,and Schwalbe,K.-H.,

“Interpretation of Fracture Toughness in the Ductile-to-Brittle Tran-sition Region by Fractographical Observations,”Defect Assessment in Components -Fundamentals and Applications ,J.G.Blauel and K.H.Schwalbe,eds.,ESIS/EGF9,Mechanical Engineering Publica-tions,London,1991,pp.659-78.

(14)Landes,J.D.,and McCabe,D.E.,“Effect of Section Size on

Transition Temperature Behavior of Structural Steels,”Fracture Mechanics:Fifteenth Symposium,ASTM STP 833,ASTM,1984,pp.378-392.

(15)Wallin,K.,“Recommendations for the Application of Fracture

Toughness Data for Structural Integrity Assessments,”Proceedings of the Joint IAEA/CSNI Specialists Meeting on Fracture Mechanics Veri?cation by Large-Scale Testing ,NUREG/CP-0131(ORNL/TM-12413),October 1993,pp.465-494.

(16)Kirk,M.T.,and Dodds,R.H.,“J and CTOD Estimation Equations

for Shallow Cracks in Single Edge Notch Bond Specimens,”Journal of Testing and Evaluation,JTEVA ,V ol 21,No.4,July 1993,pp.228-238.

(17)Scibetta,M.,“3-D Finite Element Simulation of the PCCv Specimen

Statically Loaded in Three-Point Bending,”(report R-3440)report BLG-860,SCK*CEN Mol,Belgium,March 2000.

(18)Schwalbe,K.H.,Hellmann, D.,Heerens,J.,Knaack,J.,and

Mueller-Roos,J.,“Measurement of Stable Crack Growth Including Detection of Initiation of Growth Using Potential Drop and Partial Unloading Methods,”Elastic-Plastic Fracture Test Methods,Users Experience,ASTM STP 856,ASTM,1983,pp.338-62

(19)Landes,J. D.,“J Calculation from Front Face Displacement

Measurements of a Compact Specimen,”International Journal of Fracture ,V ol 16,1980,pp.R183-86.

(20)Sokolov,M.A.,and Nanstad,R.K.,“Comparison of Irradiation-Induced Shifts of K Jc and Charpy Impact Toughness for Reactor Pressure Vessel Steels,”in Effects of Radiation on Materials:18th International Symposium,ASTM STP 1325,R.K.Nanstad,M.L.Hamilton,F.A.Garner,and A.S.Kumar,Eds.,American Society for Testing and Materials,West Conshohocken,PA,1999,pp.

167-190.

FIG.X4.2Master Curve Showing the Difference Between 5%Tolerance Bound and Lower Bound That Includes 85%

Con?dence Margin on T

(21)Wallin,K.,“Validity of Small Specimen Fracture Toughness Esti-

mates Neglecting Constraint Corrections,”in Constraint Effects in Fracture:Theory and Applications,ASTM STP1244,M.Kirk and A.

Bakker,eds.,ASTM,1994,pp.519-537.

(22)ASME Boiler and Pressure Vessel Code.An American National

Standard,Sect.XI,“Rules for Inservice Inspection of Nuclear Power Plant Components,”Article A-4000,American Society of Mechanical Engineers,New York,1993.

(23)Merkle,J.G.,Wallin,K.,and McCabe,D.E.,Technical Basis for an

ASTM Standard on Determining the Reference Temperature,T

for Ferritic Steels in the Transition Range,NUREG/CR-5504(ORNL/ TM-13631),November1998.

(24)Johnson,L.G.,The Statistical Treatment of Fatigue Experiments,

Elsevier,NY,1957.

(25)Wallin,K.,Master Curve Analysis of Ductile to Brittle Transition

Region Fracture Toughness Round Robin Data(The Euro Fracture Toughness Curve),VTT Technical Document367.58P,Espoo,Fin-land,1998.

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美国在线学校排名标准

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