1、Designation: E561 102Standard Test Method forK-R Curve Determination1This standard is issued under the fixed designation E561; 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 indic
2、ates the year of last reapproval. Asuperscript epsilon () indicates an editorial change since the last revision or reapproval.1NOTE3.2.2 was editorially updated in December 2011.2NOTE3.2.2 was editorially updated in March 2013.1. Scope*1.1 This test method covers the determination of theresistance t
3、o fracture of metallic materials under Mode Iloading at static rates using either of the following notched 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
4、) in terms of KRplotted against crack extensionin the specimen as a crack is driven under an increasing 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 predo
5、minantly elasticto the effective crack extension value of interest.1.3 Specimens of standard proportions 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 cov
6、ered in thismethod.1.5 The test is applicable to conditions where a materialexhibits slow, stable crack 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 thestand
7、ard. The values given in parentheses are for informationonly.1.7 This standard does not purport to address 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-
8、bility of regulatory limitations prior to use.2. Referenced Documents2.1 ASTM Standards:2E4 Practices for Force Verification of Testing MachinesE399 Test Method for Linear-Elastic Plane-Strain FractureToughness KIcof Metallic MaterialsE1823 Terminology Relating to Fatigue and Fracture Testing2.2 Oth
9、er Document:AISC Steel Construction Manual33. Terminology3.1 DefinitionsTerminology E1823 is applicable 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 ach
10、ieved during the test. Kappis an engineer-ing estimate of toughness that can be used to calculate residualstrength. Kappdepends on the material, specimen size, andspecimen thickness and as such is not a material property.3.2.2 effective modulus, EeffFL-2an elastic modulus thatallows a theoretical (m
11、odulus normalized) compliance tomatch an experimentally measured compliance for an actualinitial crack size ao.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 siz
12、e, and specimen thickness and as such is not amaterial property.3.2.3.1 DiscussionSee the discussion of plane-strain frac-ture toughness in Terminology E1823.4. Summary of Test Method4.1 During slow-stable fracturing, the developing crackextension resistance KRis equal to the applied stress intensit
13、y1This test method is under the jurisdiction of ASTM Committee E08 on Fatigueand Fracture and is the direct responsibility of Subcommittee E08.07 on FractureMechanics.Current edition approved Nov. 1, 2010. Published November 2010. Originallyapproved in 1974. Last previous edition approved in 2008 as
14、 E561 081. DOI:10.1520/E0561-10E02.2For referenced ASTM standards, visit the ASTM website, www.astm.org, orcontact ASTM Customer Service at serviceastm.org. For Annual Book of ASTMStandards volume information, refer to the standards Document Summary page onthe ASTM website.3Available from American I
15、nstitute of Steel Construction (AISC), One E.Wacker Dr., Suite 3100, Chicago, IL 60601-2001.*A Summary of Changes section appears at the end of this standardCopyright ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States1factor K. The crack is driven
16、 forward 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 cra
17、ck starter is a low-stress-level fatigue crack.4.3 The method covers two techniques for determination ofeffective crack size: (1) direct measurement of the physicalcrack size which is then adjusted for the developing plasticzone size, and (2) compliance measurement techniques thatyield the effective
18、 crack size directly. Methods of measuringcrack extension 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
19、. Significance and Use5.1 The K-R curve characterizes the 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
20、a crack is driven stably underincreasing applied stress 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 ext
21、ent, testing machinecharacteristics.5.2 For an untested 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
22、 as being independent of original crack sizeaoand the specimen 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 ae(2).5.2.1 To predict crack behavior and instability in aco
23、mponent, a family of crack driving curves is generated bycalculating K as a function of crack size for the componentusing a series of force, displacement, or combined loadingconditions. The K-R curve may be superimposed on the familyof crack driving curves as shown in Fig. 1, with the origin ofthe K
24、-R curve coinciding with the assumed original crack sizeao. The intersection of the crack driving curves with the K-Rcurve shows the expected effective stable crack extension foreach loading condition. The crack driving curve that developstangency with the K-R curve defines the critical loadingcondi
25、tion that will cause the onset of unstable fracture 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 crac
26、kinstability under that loading condition.5.3 If the 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 t
27、oughness level is reached (3, 4, 5). Whena specimen 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 cra
28、ck extension.NOTE 2With force control, K usually increases 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
29、verified forceapplication range of the testing machine 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
30、grips can be usedon specimens less than 305 mm (12 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 a
31、long the entire widthof the specimen end shall be used 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 al
32、igned to minimize theintroduction of bending strain into the specimen. Pin or gimbal4The boldface numbers in parentheses refer to the list of references at the end ofthis standard.FIG. 1 Schematic Representation of K-R curve and Applied KCurves to Predict Instability; Kc, P3, ac, Corresponding to an
33、Original Crack Size, aoE561 1022connections 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
34、Fixtures for Compact Tension (C(T)SpecimensThe grips and fixtures described in Test MethodE399 are recommended for K-R curve testing where C(T)-typespecimens are loaded in tension.6.4 Buckling ConstraintsBuckling may develop in unsup-ported specimens depending upon the specimen thickness,material to
35、ughness, crack size, and specimen size (6). Bucklingseriously 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 regio
36、nswhen conditions for buckling are anticipated. A procedure 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 incr
37、eases as W/B and 2a/W ratios increase and as theforce 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
38、 crack plane and sheet wrinkling along thespecimen width. 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 recommende
39、d (6). Friction between the specimen and thebuckling 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
40、clamping force to prevent buckling while allowingfree 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.
41、2 For C(T) specimens, the portion of the specimen armsand 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
42、for crack size observations. Friction between bucklingFIG. 2 Middle-Cracked Tension (M(T) Panel Test SetupE561 1023restraints 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 k
43、eep lubricants out of thecrack. Sheet TFE-fluorocarbon or heavy oils or both can beused. The initial clamping forces 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 Dis
44、placement GagesDisplacement gages are used toaccurately measure the crack-mouth opening displacement(CMOD) across the crack at a specified location and span. Forsmall C(T) specimens, the gage recommended in Test MethodE399 may have a sufficient linear working range to be used.However, testing specim
45、ens with W greater than 127 mm (5in.) may require gages 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
46、used in the calibration. Detail drawings of the gage 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.How
47、ever, other types of gages used over different span lengthsare equally acceptable provided the precision and accuracyrequirements are retained. For example, the conventional clipgage of Test Method E399 may be used with screw attachedknife edges spanning the crack at a chosen span 2Y. In M(T)tests,
48、the proper compliance calibration curve must be usedbecause 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
49、measurement point, not the gage length of the clipgage 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 E399. 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 Equipmen
