1、Designation: E 561 08Standard Test Method forK-R Curve Determination1This standard is issued under the fixed designation E 561; the number immediately following the designation indicates the year oforiginal adoption or, in the case of revision, the year of last revision. A number in parentheses indi
2、cates the year of last reapproval. Asuperscript epsilon () indicates an editorial change since the last revision or reapproval.1. Scope*1.1 This test method covers the determination of theresistance to fracture of metallic materials under Mode Iloading at static rates using either of the following n
3、otched andprecracked specimens: the middle-cracked tension M(T) speci-men or the compact tension C(T) specimen. A K-R curve is acontinuous record of toughness development (resistance tocrack extension) in terms of KRplotted against crack extensionin the specimen as a crack is driven under an increas
4、ing stressintensity factor, K.1.2 Materials that can be tested for K-R curve developmentare not limited by strength, thickness, or toughness, so long asspecimens are of sufficient size to remain predominantly elasticto the effective crack extension value of interest.1.3 Specimens of standard proport
5、ions are required, but sizeis variable, to be adjusted for yield strength and toughness ofthe materials.1.4 Only two of the many possible specimen types thatcould be used to develop K-R curves are covered in thismethod.1.5 The test is applicable to conditions where a materialexhibits slow, stable cr
6、ack extension under increasing crackdriving force, which may exist in relatively tough materialsunder plane stress crack tip conditions.1.6 The values stated in SI units are to be regarded as thestandard. The values given in parentheses are for informationonly.1.7 This standard does not purport to a
7、ddress all of thesafety concerns, if any, associated with its use. It is theresponsibility 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 Documents2.1 ASTM Standards:2E4 Practice
8、s for Force Verification of Testing MachinesE 399 Test Method for Linear-Elastic Plane-Strain FractureToughness KIcof Metallic MaterialsE 1823 Terminology Relating to Fatigue and Fracture Test-ing2.2 Other Document:AISC Steel Construction Manual33. Terminology3.1 DefinitionsTerminology E 1823 is app
9、licable to thismethod.3.2 Definitions of Terms Specific to This Standard:3.2.1 apparent plane-stress fracture toughness, KappThevalue of K calculated using the original crack size and themaximum force achieved during the test. Kappis an engineer-ing estimate of toughness that can be used to calculat
10、e residualstrength. Kappdepends on the material, specimen size, andspecimen thickness and as such is not a material property.3.2.2 effective modulus, Eeff(FL-2)the value of Youngsmodulus that produces an accurate correspondence between theexperimentally measured compliance at the original crack size
11、and the analytically developed compliance calculated for thesame crack size.3.2.3 plane-stress fracture toughness, KcThe value of KRat instability in a force-controlled test corresponding to themaximum force point in the test. Kcdepends on the material,specimen size, and specimen thickness and as su
12、ch is not amaterial property.3.2.3.1 DiscussionSee the discussion of plane-strain frac-ture toughness in Terminology E 1823.4. Summary of Test Method4.1 During slow-stable fracturing, the developing crackextension resistance KRis equal to the applied stress intensityfactor K. The crack is driven for
13、ward by continuously orincrementally increasing force or displacement. Measurementsare made periodically for determination of the effective cracksize and for calculation of K values, which are individual datapoints that define the K-R curve for the material under thosetest conditions.4.2 The crack s
14、tarter is a low-stress-level fatigue crack.4.3 The method covers two techniques for determination ofeffective crack size: (1) direct measurement of the physical1This test method is under the jurisdiction of ASTM Committee E08 on Fatigueand Fracture and is the direct responsibility of Subcommittee E0
15、8.07 on FractureMechanics.Current edition approved Nov. 1, 2008. Published February 2009. Originallyapproved in 1974. Last previous edition approved in 2005 as E 561 051.2For referenced ASTM standards, visit the ASTM website, www.astm.org, orcontact ASTM Customer Service at serviceastm.org. For Annu
16、al Book of ASTMStandards volume information, refer to the standards Document Summary page onthe ASTM website.3Available from American Institute of Steel Construction (AISC), One E.Wacker Dr., Suite 3100, Chicago, IL 60601-2001.1*A Summary of Changes section appears at the end of this standard.Copyri
17、ght ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959, United States.crack size which is then adjusted for the developing plasticzone size, and (2) compliance measurement techniques thatyield the effective crack size directly. Methods of measuringcrack extensio
18、n and of making plastic-zone corrections to thephysical crack size are prescribed. Expressions for the calcu-lation of crack-extension force KRare given. Criteria fordetermining if the specimen conditions are predominantlyelastic are provided.5. Significance and Use5.1 The K-R curve characterizes th
19、e resistance to fracture ofmaterials during slow, stable crack extension and results fromthe growth of the plastic zone ahead of the crack as it extendsfrom a fatigue precrack or sharp notch. It provides a record ofthe toughness development as a crack is driven stably underincreasing applied stress
20、intensity factor K. For a givenmaterial, K-R curves are dependent upon specimen thickness,temperature, and strain rate. The amount of valid K-R datagenerated in the test depends on the specimen type, size,method of loading, and, to a lesser extent, testing machinecharacteristics.5.2 For an untested
21、geometry, the K-R curve can be matchedwith the crack driving (applied K) curves to estimate the degreeof stable crack extension and the conditions necessary to causeunstable crack propagation (1).4In making this estimate, K-Rcurves are regarded as being independent of original crack sizeaoand the sp
22、ecimen configuration in which they are developed.For a given material, material thickness, and test temperature,K-R curves appear to be a function of only the effective crackextension Dae(2).5.2.1 To predict crack behavior and instability in a compo-nent, a family of crack driving curves is generate
23、d by calcu-lating K as a function of crack size for the component using aseries of force, displacement, or combined loading conditions.The K-R curve may be superimposed on the family of crackdriving curves as shown in Fig. 1, with the origin of the K-Rcurve coinciding with the assumed original crack
24、 size ao. Theintersection of the crack driving curves with the K-R curveshows the expected effective stable crack extension for eachloading condition. The crack driving curve that developstangency with the K-R curve defines the critical loadingcondition that will cause the onset of unstable fracture
25、 underthe loading conditions used to develop the crack drivingcurves.5.2.2 Conversely, the K-R curve can be shifted left or rightin Fig. 1 to bring it into tangency with a crack driving curve todetermine the original crack size that would cause crackinstability under that loading condition.5.3 If th
26、e K-gradient (slope of the crack driving curve) ofthe specimen chosen to develop the K-R curve has negativecharacteristics (see Note 1), as in a displacement-controlledtest condition, it may be possible to drive the crack until amaximum or plateau toughness level is reached (3, 4, 5). Whena specimen
27、 with positive K-gradient characteristics (see Note2) is used, the extent of the K-R curve which can be developedis terminated when the crack becomes unstable.NOTE 1Fixed displacement in crack-line-loaded specimens results ina decrease of K with crack extension.NOTE 2With force control, K usually in
28、creases with crack extension,and instability will occur at maximum force.6. Apparatus6.1 Testing MachineMachines used for K-R curve testingshall conform to the requirements of Practices E4. The forcesused in determining KRvalues shall be within the verified forceapplication range of the testing mach
29、ine as defined in PracticesE4.6.2 Grips and Fixtures for Middle-Cracked Tension (M(T)SpecimensIn middle-cracked tension specimens, the gripfixtures are designed to develop uniform stress distribution inthe central region of the specimen. Single pin grips can be usedon specimens less than 305 mm (12
30、in.) wide if the specimenis long enough to ensure uniform stress distribution in the crackplane (see 8.5.3.) For specimens wider than 305 mm (12 in.),multiple-bolt grips such as those shown in Fig. 2 or wedgegrips that apply a uniform displacement along the entire widthof the specimen end shall be u
31、sed if the stress intensity factorand compliance equations in Section 11 are to be used. Othergripping arrangements can be used if the appropriate stressintensity factor and compliance relationships are verified andused. Grips should be carefully aligned to minimize theintroduction of bending strain
32、 into the specimen. Pin or gimbalconnections can be located between the grips and testingmachine to aid the symmetry of loading. If extra-heavy-gauge,high-toughness materials are to be tested, the suitability of thegrip arrangement may be checked using the AISC SteelConstruction Manual.6.3 Grips and
33、 Fixtures for Compact Tension (C(T)SpecimensThe grips and fixtures described in Test MethodE 399 are recommended for K-R curve testing where C(T)-typespecimens are loaded in tension.4The boldface numbers in parentheses refer to the list of references at the end ofthis standard.FIG. 1 Schematic Repre
34、sentation of K-R curve and Applied KCurves to Predict Instability; Kc, P3, ac, Corresponding to anOriginal Crack Size, aoE5610826.4 Buckling ConstraintsBuckling may develop in unsup-ported specimens depending upon the specimen thickness,material toughness, crack size, and specimen size (6). Buckling
35、seriously affects the validity of a K analysis and is particularlytroublesome when using compliance techniques to determinecrack size (7). It is therefore required that buckling constraintsbe affixed to the M(T) and C(T) specimens in critical regionswhen conditions for buckling are anticipated. A pr
36、ocedure forthe detection of buckling is described in 9.8.3.6.4.1 For an M(T) specimen in tension, the regions aboveand below the notch are in transverse compression which cancause the specimen to buckle out of plane. The propensity forbuckling increases as W/B and 2a/W ratios increase and as theforc
37、e increases. Unless it can be shown by measurement oranalysis that buckling will not occur during a test, bucklingconstraints shall be attached to the central portion of thespecimen. The guides shall be so designed to prevent sheetkinking about the crack plane and sheet wrinkling along thespecimen w
38、idth. Buckling constraints should provide a highstiffness constraint against out-of-plane sheet displacementswhile minimizing friction. Buckling constraints with additionalpressure adjustment capability near the center of the specimenare recommended (6). Friction between the specimen and thebuckling
39、 constraints shall not interfere with the in-plane stressdistribution in the specimen. Friction can be minimized byusing a low-friction coating (such as thin TFE-fluorocarbonsheet) on the contact surfaces of the constraints and by usingjust enough clamping force to prevent buckling while allowingfre
40、e movement of the guides along the length of the specimen.A suspension system to prevent the buckling constraint fromsliding down the specimen is recommended. Several bucklingconstraint configurations for M(T) specimens are shown in (7)and (8).6.4.2 For C(T) specimens, the portion of the specimen ar
41、msand back edge which are in compression may need to berestrained from buckling in thinner specimens of high tough-ness alloys. It is convenient to use a base plate and cover platewith ports cut at appropriate locations for attaching clip gagesand for crack size observations. Friction between buckli
42、ngrestraints and specimen faces is detrimental and should beminimized as much as possible.6.4.3 Lubrication shall be provided between the face platesand specimen. Care shall be taken to keep lubricants out of thecrack. Sheet TFE-fluorocarbon or heavy oils or both can beused. The initial clamping for
43、ces between opposing platesshould be high enough to prevent buckling but not high enoughto change the stress distribution in the region of the crack tip atany time during the test.6.5 Displacement GagesDisplacement gages are used toaccurately measure the crack-mouth opening displacementFIG. 2 Middle
44、-Cracked Tension (M(T) Panel Test SetupE561083(CMOD) across the crack at a specified location and span. Forsmall C(T) specimens, the gage recommended in Test MethodE 399 may have a sufficient linear working range to be used.However, testing specimens with W greater than 127 mm (5in.) may require gag
45、es with a larger working range, such as thegage shown in Fig. 3.6.5.1 A recommended gage for use in M(T) specimens isshown in Fig. 4 (13). This gage is inserted into a machined holehaving a circular knife edge. The diameter di, is the gage span2Y used in the calibration. Detail drawings of the gage
46、aregiven in Fig. 5. Radius of the attachment tip should be less thanthe radius of the circular knife edge in the specimen.6.5.2 The gage recommended in 6.5.1 is preferred becauseof its excellent linearity characteristics and ease of attachment.However, other types of gages used over different span l
47、engthsare equally acceptable provided the precision and accuracyrequirements are retained. For example, the conventional clipgage of Test Method E 399 may be used with screw attachedknife edges spanning the crack at a chosen span 2Y. In M(T)tests, the proper compliance calibration curve must be used
48、because compliance is a function of Y/W. When using thecompliance calibration curve given in Eq 5, the proper 2Yvalue to use with screw-on knife edges is the average distancebetween attachment points across the notch. This is the actualdeformation measurement point, not the gage length of the clipga
49、ge itself.6.5.3 The use of point contacts eliminates error in thereadings from the hinge-type rotation of C(T) specimens. Theprecision of all types of gages shall be verified in accordancewith the procedure in Test Method E 399. In addition, absoluteaccuracy within 2 % of reading over the working range of thegage is required for use with compliance measurements. Datafor compliance measurements must be taken within the verifiedrange of the gage. The gages shall be verified periodically.6.6 Optical EquipmentIf the material being tested issufficiently thin so that the
