1、Designation: E 2207 02Standard Practice forStrain-Controlled Axial-Torsional Fatigue Testing with Thin-Walled Tubular Specimens1This standard is issued under the fixed designation E 2207; the number immediately following the designation indicates the year oforiginal adoption or, in the case of revis
2、ion, the year of last revision. A number in parentheses indicates the year of last reapproval. Asuperscript epsilon (e) indicates an editorial change since the last revision or reapproval.1. Scope1.1 The standard deals with strain-controlled, axial, tor-sional, and combined in- and out-of-phase axia
3、l torsionalfatigue testing with thin-walled, circular cross-section, tubularspecimens at isothermal, ambient and elevated temperatures.This standard is limited to symmetric, completely-reversedstrains (zero mean strains) and axial and torsional waveformswith the same frequency in combined axial-tors
4、ional fatiguetesting. This standard is also limited to thin-walled tubularspecimens (machined from homogeneous materials) and doesnot cover testing of either large-scale components or structuralelements.1.2 This standard does not purport to address all of thesafety concerns, if any, associated with
5、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:E 3 Practice for Preparation of Metallographic Specimens2E 4 Practices
6、 for Force Verification of Testing Machines2E 6 Terminology Relating to Methods of Mechanical Test-ing2E 8 Test Methods for Tension Testing of Metallic Materials2E 9 Test Methods of Compression Testing of Metallic Ma-terials at Room Temperature2E 83 Practice for Verification and Classification of Ex
7、ten-someters2E 111 Test Method for Youngs Modulus, Tangent Modulus,and Chord Modulus2E 112 Test Methods for Determining Average Grain Size2E 143 Test Method for Shear Modulus at Room Tempera-ture2E 209 Practice for Compression Tests of Metallic Materialsat Elevated Temperatures with Conventional or
8、RapidHeating Rates or Strain Rates2E 467 Practice for Verification of Constant Amplitude Dy-namic Forces in an Axial Fatigue Testing System2E 606 Practice for Strain-Controlled Fatigue Testing2E 1012 Practice for Verification of Specimen Alignmentunder Tensile Loading2E 1417 Practice for Liquid Pene
9、trant Examination3E 1444 Practice for Magnetic Particle Examination3E 1823 Terminology Relating to Fatigue and Fracture Test-ing23. Terminology3.1 Definitions:3.1.1 axial strainrefers to engineering axial strain, e, andis defined as change in length divided by the original length(DLg/Lg).3.1.2 shear
10、 strainrefers to engineering shear strain, g,resulting from the application of a torsional moment to acylindrical specimen. Such a torsional shear strain is simpleshear and is defined similar to axial strain with the exceptionthat the shearing displacement, DLsis perpendicular to ratherthan parallel
11、 to the gage length, Lg, that is, g = DLs/Lg(see Fig.1).NOTE 1g= is related to the angles of twist, u and C as follows:g = tan C, where C is the angle of twist along the gage length of thecylindrical specimen. For small angles tan C approaches C and gapproaches C.g =(d/2)u/Lg, where u expressed in r
12、adians is the angle of twist betweenthe planes defining the gage length of the cylindrical specimen and d is thediameter of the cylindrical specimen.NOTE 2DLsis measurable directly as displacement using speciallycalibrated torsional extensometers or as the arc length DLs=(d/2)u, whereu is measured d
13、irectly with a rotary variable differential transformer.3.1.2.1 DiscussionThe shear strain varies linearly throughthe thin wall of the specimen, with the smallest and largestvalues occurring at the inner and outer diameters of thespecimen, respectively. The value of shear strain on the outersurface,
14、 inner surface, and mean diameter of the specimen shallbe reported. The shear strain determined at the outer diameterof the tubular specimen is recommended for strain-controlledtorsional tests, since cracks typically initiate at the outersurfaces.3.1.3 biaxial strain amplitude ratioin an axial-torsi
15、onalfatigue test, the biaxial strain amplitude ratio, l is defined as1This practice is under the jurisdiction of ASTM Committee E08 on Fatigue andFracture and is the direct responsibility of Subcommittee E08.05 on CyclicDeformation and Fatigue Crack Formation.Current edition approved May 10, 2002. P
16、ublished August 2002.2Annual Book of ASTM Standards, Vol 03.01.3Annual Book of ASTM Standards, Vol 03.03.1Copyright ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959, United States.the ratio of the shear strain amplitude (ga) to the axial strainamplitude (ea),
17、that is, ga/ea.3.1.4 phasing between axial and shear strainsin an axial-torsional fatigue test, phasing is defined as the phase angle, f,between the axial strain waveform and the shear strain wave-form. The two waveforms must be of the same type, forexample, both must either be triangular or both mu
18、st besinusoidal.3.1.4.1 in-phase axial-torsional fatigue testforcompletely-reversed axial and shear strain waveforms, if themaximum value of the axial strain waveform occurs at thesame time as that of the shear strain waveform, then the phaseangle, f = 0 and the test is defined as an “in-phase”axial
19、-torsional fatigue test (Fig. 2(a). At every instant in time,the shear strain is proportional to the axial strain.NOTE 3Proportional loading is the commonly used terminology inplasticity literature for the in-phase axial-torsional loading described inthis practice.3.1.4.2 out-of-phase axial-torsiona
20、l fatigue testforcompletely-reversed axial and shear strain waveforms, if themaximum value of the axial strain waveform leads or lags theFIG. 1 Twisted Gage Section of a Cylindrical Specimen Due to a Torsional MomentFIG. 2 Schematics of Axial and Shear Strain Waveforms for In- and Out-of-Phase Axial
21、-Torsional TestsE 22072maximum value of the shear strain waveform by a phase anglef 0 then the test is defined as an “out-of-phase” axial-torsional fatigue test. Unlike in the in-phase loading, the shearstrain is not proportional to the axial strain at every instant intime. An example of out-of-phas
22、e axial-torsional fatigue testwith f = 75 is shown in Fig. 2(b). Typically, for anout-of-phase axial-torsional fatigue test, the range of f ( 0)is from -90 (axial waveform lagging the shear waveform) to +90 (axial waveform leading the shear waveform).NOTE 4In plasticity literature, nonproportional l
23、oading is the genericterminology for the out-of-phase loading described in this practice.3.1.5 shear stressrefers to engineering shear stress, t,acting in the orthogonal tangential and axial directions of thegage section and is a result of the applied torsional moment, T,to the thin-walled tubular s
24、pecimen. The shear stress, like theshear strain, is always the largest at the outer diameter. Underelastic loading conditions, shear stress also varies linearlythrough the thin wall of the tubular specimen. However, underelasto-plastic loading conditions, shear stress tends to vary in anonlinear fas
25、hion. Most strain-controlled axial-torsional fa-tigue tests are conducted under elasto-plastic loading condi-tions. Therefore, assumption of a uniformly distributed shearstress is recommended. The relationship between such a shearstress applied at the mean diameter of the gage section and thetorsion
26、al moment, T,ist516Tpdo22 di2!do1 di!(1)where t is the shear stress, doand diare the outer and innerdiameters of the tubular test specimen, respectively. However,if necessary, shear stresses in specimens not meeting thecriteria for thin-walled tubes can also be evaluated (see Ref(1).4Under elastic l
27、oading conditions, shear stress, t(d)atadiameter, d in the gage section of the tubular specimen can becalculated as follows:td! 516Tdpdo42 di4!(2)In order to establish the cyclic shear stress-strain curve for amaterial, both the shear strain and shear stress shall bedetermined at the same location w
28、ithin the thin wall of thetubular test specimen.4. Significance and Use4.1 Multiaxial forces often tend to introduce deformationand damage mechanisms that are unique and quite differentfrom those induced under a simple uniaxial loading condition.4The boldface numbers in parentheses refer to the list
29、 of references at the end ofthis standard.FIG. 2 Schematics of Axial and Shear Strain Waveforms for In- and Out-of-Phase Axial-Torsional Tests (continued)E 22073Since most engineering components are subjected to cyclicmultiaxial forces it is necessary to characterize the deformationand fatigue behav
30、iors of materials in this mode. Such acharacterization enables reliable prediction of the fatigue livesof many engineering components. Axial-torsional loading isone of several possible types of multiaxial force systems and isessentially a biaxial type of loading. Thin-walled tubularspecimens subject
31、ed to axial-torsional loading can be used toexplore behavior of materials in two of the four quadrants inprincipal stress or strain spaces. Axial-torsional loading is moreconvenient than in-plane biaxial loading because the stressstate in the thin-walled tubular specimens is constant over theentire
32、test section and is well-known. This practice is useful forgenerating fatigue life and cyclic deformation data on homo-geneous materials under axial, torsional, and combined in- andout-of-phase axial-torsional loading conditions.5. Empirical Relationships5.1 Axial and Shear Cyclic Stress-Strain Curv
33、esUnderelasto-plastic loading conditions, axial and shear strains arecomposed of both elastic and plastic components. The math-ematical functions commonly used to characterize the cyclicaxial and shear stress-strain curves are shown in Appendix X1.Note that constants in these empirical relationships
34、 are depen-dent on the phasing between the axial and shear strainwaveforms.NOTE 5For combined axial-torsional loading conditions, analysis andinterpretation of cyclic deformation behavior can be performed by usingthe techniques described in Ref (2).5.2 Axial and Shear Strain Range-Fatigue LifeRelati
35、onshipsThe total axial and shear strain ranges can beseparated into their elastic and plastic parts by using therespective stress ranges and elastic moduli. The fatigue liferelationships to characterize cyclic lives under axial (notorsion) and torsional (no axial loading) conditions are alsoshown in
36、 Appendix X1. These axial and torsional fatigue liferelationships can be used either separately or together toestimate fatigue life under combined axial-torsional loadingconditions.NOTE 6Details on some fatigue life estimation procedures undercombined in- and out-of-phase axial-torsional loading con
37、ditions aregiven in Refs (3-5). Currently, no single life prediction method has beenshown to be either effective or superior to other methods for estimating thefatigue lives of materials under combined axial-torsional loading condi-tions.6. Test Apparatus6.1 Testing MachineAll tests should be perfor
38、med in atest system with tension-compression and clockwise-counterclockwise torsional loading capability. The test system (testframe and associated fixtures) must shall be in compliance withthe bending strain criteria specified in Practices E 606 andE 1012. The test system shall possess sufficient l
39、ateral stiffnessand torsional stiffness to minimize distortions of the test frameat the rated maximum axial force and torque capacities,respectively.6.2 Gripping FixturesFixtures used for gripping the thin-walled tubular specimen shall be made from a material that canwithstand prolonged usage, parti
40、cularly at high temperatures.The design of the fixtures largely depends upon the design ofthe specimen. Typically, a combination of hydraulicallyclamped collet fixtures and smooth shank specimens providegood alignment and high lateral stiffness. However, other typesof fixtures, such as those specifi
41、ed in Practice E 606 (forexample, specimens with threaded ends) are also acceptableprovided they meet the alignment criteria. Typically specimenswith threaded ends tend to require more effort than the smoothshank specimens to meet the alignment criteria specified inPractice E 606. For this reason, s
42、mooth shank specimens arepreferred over the specimens with threaded ends.6.3 Force and Torque TransducersAxial force and torquemust be measured with either separate transducers or acombined transducer. The transducer(s) must be placed inseries with the force train and must comply with the specifi-ca
43、tions in Practices E 4 and E 467. The cross-talk between theaxial force and the torque shall not exceed 1 %, whether asingle transducer or multiple transducers are used for thesemeasurements.6.4 ExtensometersAxial deformation in the gage sectionof the tubular specimen shall be measured with an exten
44、som-eter such as, a strain-gaged extensometer, a Linear VariableDifferential Transformer (LVDT), or a non-contacting (opticalor capacitance type) extensometer. Twist in the gage section ofthe tubular specimen shall be measured with an extensometersuch as, a strain-gaged external extensometer, intern
45、al RotaryVariable Differential Transformer (RVDT), or a non-contacting(optical or capacitance type) extensometer (Refs (6, 7).Strain-gaged axial-torsional extensometers that measure boththe axial deformation and twist in the gage section of thespecimen may also be used provided the cross-talk is les
46、s than1 % (Ref (8). Specifically, application of the rated extensom-eter axial strain (alone) shall not produce a torsional outputgreater than 1 % of the rated total torsional strain and applica-tion of the rated extensometer torsional strain (alone) shall notproduce an axial output greater than 1 %
47、 of the rated total axialstrain. In other words, the cross-talk between the axial dis-placement and the torsional twist shall not exceed 1 %, whethera single transducer or multiple transducers are used for thesemeasurements.6.5 Transducer CalibrationAll the transducers shall becalibrated in accordan
48、ce with the recommendations of therespective manufacturers. Calibration of each transducer shallbe traceable to the National Institute of Standards and Tech-nology (NIST).6.6 Data Acquisition SystemDigital acquisition of cyclictest data is recommended or analog X-Y and strip chartrecorders shall be
49、employed to document axial and torsionalhysteresis loops and variation of axial force/strain and torque/shear strain with time.7. Thin-Walled Tubular Test Specimens7.1 Test Specimen DesignThe specimens wall thicknessshall be large enough to avoid instabilities during cyclicloading without violating the thin-walled tube criterion, that is,a mean diameter to wall thickness ratio of 10:1 or greater. Forpolycrystalline materials, at least 10 grains should be presentthrough the thickness of the wall to preserve isotropy. In orderto determine the grain
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