1、Designation: E 561 05e1Standard 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 in
2、dicates the year of last reapproval. Asuperscript epsilon (e) indicates an editorial change since the last revision or reapproval.e1NOTEEquation 6 was editorially corrected in February 2007.1. Scope*1.1 This test method covers the determination of theresistance to fracture of metallic materials unde
3、r Mode Iloading at static rates using any of the following notched andprecracked specimens: the middle-cracked tension M(T) speci-men, the compact tension C(T) specimen, or the crack-line-wedge-loaded C(W) specimen. A K-R curve is a continuousrecord of toughness development (resistance to crack exte
4、n-sion) in terms of KRplotted against crack extension in thespecimen 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
5、 predominantly 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 three of the many possible specimen types thatcould be used to develop K-R curves
6、 are covered 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
7、thestandard. 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
8、applica-bility of regulatory limitations prior to use.2. Referenced Documents2.1 ASTM Standards:2E4 Practices for Force Verification of Testing MachinesE 399 Test Method for Linear-Elastic Plane-Strain FractureToughness of Metallic MaterialsE 1823 Terminology Relating to Fatigue and Fracture Test-in
9、g2.2 Other Documents:AISC Steel Construction Manual33. Terminology3.1 DefinitionsTerminology E 1823 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
10、 force achieved 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, Eeff(FL-2)the value of Youngsmodulus that pr
11、oduces an accurate correspondence between theexperimentally measured compliance at the original crack sizeand 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 the
12、maximum force point in the test. Kcdepends on the material,specimen size, 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 E 1823.1This test method is under the jurisdiction of ASTM Committee E08 on F
13、atigueand Fracture and is the direct responsibility of Subcommittee E08.07 on Linear-Elastic Fracture.Current edition approved June 1, 2005. Published September 2005. Originallyapproved in 1974. Last previous edition approved in 1998 as E 561 98.2For referenced ASTM standards, visit the ASTM website
14、, 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 Institute of Steel Construction (AISC), One E.Wacker Dr., Suite 3100, Chicago, IL 60601-20
15、01.1*A Summary of Changes section appears at the end of this standard.Copyright ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959, United States.4. Summary of Test Method4.1 During slow-stable fracturing, the developing crackextension resistance KRis equal to t
16、he applied stress intensityfactor K. The crack is driven 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
17、 for the material under thosetest conditions.4.2 The crack 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) c
18、ompliance measurement techniques thatyield the effective 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 spe
19、cimen is predominantly elastic areprovided.5. 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 provi
20、des a record ofthe toughness development as 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,
21、size,method of loading, and, to a lesser extent, 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
22、making this estimate, K-Rcurves are regarded 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 Dae(2).5.2.1 To
23、predict crack behavior and instability in a compo-nent, a family of crack driving curves is generated by calcu-lating K as a function of crack size for the component using aseries of force or displacement loading conditions. The K-Rcurve may be superimposed on the family of crack drivingcurves as sh
24、own in Fig. 1, with the origin of the K-R curvecoinciding with the assumed original crack 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 c
25、urve defines the critical loadingcondition that will cause the onset of unstable fracture.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 loadin
26、g 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 toughness level is reached (3,
27、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 crack extension.NOTE 2With force
28、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 verified forceapplication rang
29、e 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 grips can be usedon specimens
30、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 along the entire widthof the sp
31、ecimen 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 aligned to minimize the4The bold
32、face 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 anOriginal Crack Size, aoE56105e12introduction of bending strain into the specimen. Pin or gimb
33、alconnections 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 Fixtures for Compact Tension (
34、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.6.4 Fixtures for Crack-Line-Wedge-Loaded (C(W) Speci-mens:6.4.1 Crack-line-wedge-loaded specimens are loaded usinga low-taper-angle wedge with a poli
35、shed finish and split-pinarrangement as shown in Fig. 3. Sketches of a segmentedsplit-pin system which has proved effective for maintaining theFIG. 2 Middle-Cracked Tension (M(T) Panel Test SetupFIG. 3 Crack-Line-Loaded Specimen with Displacement-Controlled Wedge LoadingE56105e13load line independen
36、t of rotation of the specimen arms areprovided in Fig. 4. It has been found convenient to use a wedgewhose included angle is 3. With proper lubrication and systemalignment, a mechanical advantage of five can be expected.Thus, a loading machine producing15 the maximum expectedtest force will be adequ
37、ate. The wedge must be long enough todevelop the maximum expected crack-opening displacement.The maximum required stroke can be calculated from themaximum expected displacement v, using the EB (Dv/DP)values found in Table 1, the maximum expected K level in thetest, and the wedge angle.6.4.2 The wedg
38、e-load blocks which drive the load sectorsare constrained on top (not shown) and bottom to restrictmotion to a plane parallel to the plane of the specimen. Thisallows the force to be applied or released conveniently withoutdriving the load blocks and sectors out of the hole in thespecimen. The wedge
39、-load blocks are designed so that linecontact exists between the wedge-load block and the loadsector at a point that falls on the load line of the specimen. Thisenables the load sectors to rotate as the wedge is driven and theoriginal load line is maintained. Any air- or oil hardening toolsteel will
40、 be suitable for making the wedge and wedge-loadblocks.Amaraging 300-grade steel should be used for the loadsectors. The diameter of the sectors shall be slightly smaller(nominally 0.79 mm (0.03 in.) than the diameter of the drilledhole in the specimen.6.5 Buckling ConstraintsBuckling may develop in
41、 unsup-ported specimens depending upon the sheet thickness, materialtoughness, crack size, and specimen size (6). Buckling seri-ously affects the validity of a K analysis and is particularlytroublesome when using compliance techniques to determinecrack size (7). It is therefore required that bucklin
42、g constraintsbe affixed to the M(T), C(T), and C(W) specimens in criticalregions when conditions for buckling are anticipated. A proce-dure for the detection of buckling is described in 9.8.3.6.5.1 For an M(T) specimen in tension, the regions aboveand below the notch are in transverse compression wh
43、ich cancause the specimen to buckle out of plane. The propensity forbuckling increases 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
44、of thespecimen. The guides shall be so designed to prevent sheetkinking about the 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 addit
45、ionalpressure adjustment capability near the center of the specimenare recommended (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-fluor
46、ocarbonNOTEProperly dimension section line A-A to show direction.FIG. 4 Detail of Special Wedge and Split-Pin Setup Designed to Prevent Load-Line ShiftE56105e14sheet) on the contact surfaces of the constraints and by usingjust enough clamping force to prevent buckling while allowingfree movement of
47、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).6.5.2 For C(T) and C(W) specimens, the portion of thespecimen arms and
48、 back edge which are in compression shouldbe restrained from buckling. For sheet specimens, it is conve-nient to use a base plate and cover plate with ports cut atappropriate locations for attaching clip gages and for crack sizeobservations. Friction between buckling restraints and speci-men faces i
49、s detrimental and should be minimized as much aspossible.6.5.3 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 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.6.6 Displacement GagesDisplacement gages are used toaccurately measure the crack-mouth opening displacement(CMOD) across
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