1、Designation: E2207 08 (Reapproved 2013)1Standard Practice forStrain-Controlled Axial-Torsional Fatigue Testing with Thin-Walled Tubular Specimens1This standard is issued under the fixed designation E2207; the number immediately following the designation indicates the year oforiginal adoption or, in
2、the case of revision, the year of last revision. A number in parentheses indicates the year of last reapproval. Asuperscript epsilon () indicates an editorial change since the last revision or reapproval.1NOTEReferenced document E606s title was editorially updated from a Practice to a Test Method in
3、 October 2013.1. Scope1.1 The standard deals with strain-controlled, axial,torsional, and combined in- and out-of-phase axial torsionalfatigue testing with thin-walled, circular cross-section, tubularspecimens at isothermal, ambient and elevated temperatures.This standard is limited to symmetric, co
4、mpletely-reversedstrains (zero mean strains) and axial and torsional waveformswith the same frequency in combined axial-torsional fatiguetesting. This standard is also limited to characterization ofhomogeneous materials with thin-walled tubular specimensand does not cover testing of either large-sca
5、le components orstructural elements.1.2 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-bility of regulatory limi
6、tations prior to use.2. Referenced Documents2.1 ASTM Standards:2E3 Guide for Preparation of Metallographic SpecimensE4 Practices for Force Verification of Testing MachinesE6 Terminology Relating to Methods of Mechanical TestingE8 Test Methods for Tension Testing of Metallic MaterialsE9 Test Methods
7、of Compression Testing of Metallic Mate-rials at Room TemperatureE83 Practice for Verification and Classification of Exten-someter SystemsE111 Test Method for Youngs Modulus, Tangent Modulus,and Chord ModulusE112 Test Methods for Determining Average Grain SizeE143 Test Method for Shear Modulus at Ro
8、om TemperatureE209 Practice for Compression Tests of Metallic Materials atElevated Temperatures with Conventional or Rapid Heat-ing Rates and Strain RatesE467 Practice for Verification of Constant Amplitude Dy-namic Forces in an Axial Fatigue Testing SystemE606 Practice for Strain-Controlled Fatigue
9、 TestingE1012 Practice for Verification of Testing Frame and Speci-men Alignment Under Tensile and Compressive AxialForce ApplicationE1417 Practice for Liquid Penetrant TestingE1444 Practice for Magnetic Particle TestingE1823 Terminology Relating to Fatigue and Fracture Testing3. Terminology3.1 Defi
10、nitionsThe terms specific to this practice aredefined in this section. All other terms used in this practice arein accordance with Terminologies E6 and E1823.3.2 Definitions of Terms Specific to This Standard:3.2.1 axial strainrefers to engineering axial strain, , andis defined as change in length d
11、ivided by the original length(Lg/Lg).3.2.2 shear strainrefers to engineering shear strain, ,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 displacem
12、ent, Lsis perpendicular to ratherthan parallel to the gage length, Lg, that is, = Ls/Lg(see Fig.1).NOTE 1= is related to the angles of twist, and as follows: = tan , where is the angle of twist along the gage length of thecylindrical specimen. For small angles expressed in radians, tan approaches an
13、d approaches . =(d/2)/Lg, where expressed in radians is the angle of twist betweenthe planes defining the gage length of the cylindrical specimen and d is thediameter of the cylindrical specimen.NOTE 2Lsis measurable directly as displacement using speciallycalibrated torsional extensometers or as th
14、e arc length Ls=(d/2), where is measured directly with a rotary variable differential transformer.3.2.2.1 DiscussionThe shear strain varies linearly throughthe thin wall of the specimen, with the smallest and largest1This practice is under the jurisdiction of ASTM Committee E08 on Fatigue andFractur
15、e and is the direct responsibility of Subcommittee E08.05 on CyclicDeformation and Fatigue Crack Formation.Current edition approved Oct. 15, 2013. Published November 2013. Originallyapproved in 2002. Last previous edition approved in 2008 as E220708. DOI:10.1520/E2207-08R13.2For referenced ASTM stan
16、dards, 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.Copyright ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, P
17、A 19428-2959. United States1values occurring at the inner and outer diameters of thespecimen, respectively. The value of shear strain on the outersurface, inner surface, and mean diameter of the specimen shallbe reported. The shear strain determined at the outer diameterof the tubular specimen is re
18、commended for strain-controlledtorsional tests, since cracks typically initiate at the outersurfaces.3.2.3 biaxial strain amplitude ratioin an axial-torsionalfatigue test, the biaxial strain amplitude ratio, is defined asthe ratio of the shear strain amplitude (a) to the axial strainamplitude (a), t
19、hat is, a/a.3.2.4 phasing between axial and shear strains in anaxial-torsional fatigue test, phasing is defined as the phaseangle, , between the axial strain waveform and the shearstrain waveform. The two waveforms must be of the same type,for example, both must either be triangular or both must bes
20、inusoidal.3.2.4.1 in-phase axial-torsional fatigue test forcompletely-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, = 0 and the test is defined as an “in-phase”axial-torsio
21、nal 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.3.2.4.2 out-of-phase axial-torsional fatig
22、ue test forcompletely-reversed axial and shear strain waveforms, if themaximum value of the axial strain waveform leads or lags themaximum value of the shear strain waveform by a phase angle0 then the test is defined as an “out-of-phase” axial-torsional fatigue test. Unlike in the in-phase loading,
23、the shearstrain is not proportional to the axial strain at every instant inFIG. 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-Torsional TestsE2207 08 (2013)12time. An example of out-of-ph
24、ase axial-torsional fatigue testwith = 75 is shown in Fig. 2(b). Typically, for anout-of-phase axial-torsional fatigue test, the range of ( 0)is from -90 (axial waveform lagging the shear waveform) to +90 (axial waveform leading the shear waveform).NOTE 4In plasticity literature, nonproportional loa
25、ding is the genericterminology for the out-of-phase loading described in this practice.3.2.5 shear stressrefers to engineering shear stress, ,acting in the orthogonal tangential and axial directions of thegage section and is a result of the applied torsional moment,(Torque) T, to the thin-walled tub
26、ular specimen. The shearstress, like the shear strain, is always the greatest at the outerdiameter. Under elastic loading conditions, shear stress alsovaries linearly through the thin wall of the tubular specimen.However, under elasto-plastic loading conditions, shear stresstends to vary in a nonlin
27、ear fashion. Most strain-controlledaxial-torsional fatigue tests are conducted under elasto-plasticloading conditions. Therefore, assumption of a uniformlydistributed shear stress is recommended. The relationshipbetween such a shear stress applied at the mean diameter of thegage section and the tors
28、ional moment, T,is 516Tdo22 di2!do1di!(1)Where, is the shear stress, doand diare the outer andinner diameters of the tubular test specimen, respectively.However, if necessary, shear stresses in specimens not meet-ing the criteria for thin-walled tubes can also be evaluated(see Ref (1).3Under elastic
29、 loading conditions, shear stress, (d)atadiameter, d in the gage section of the tubular specimen canbe calculated as follows:d! 516Tddo42 di4!(2)In order to establish the cyclic shear stress-strain curve fora material, both the shear strain and shear stress shall bedetermined at the same location wi
30、thin 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.Since most engineering components are subjected to cycl
31、icmultiaxial forces it is necessary to characterize the deformationand fatigue behaviors 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 syste
32、ms and isessentially a biaxial type of loading. Thin-walled tubularspecimens subjected 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 becau
33、se the stressstate in the thin-walled tubular specimens is constant over theentire 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
34、 conditions.5. Empirical Relationships5.1 Axial and Shear Cyclic Stress-Strain CurvesUnderelasto-plastic loading conditions, axial and shear strains are3The boldface numbers in parentheses refer to the list of references at the end ofthis standard.FIG. 2 Schematics of Axial and Shear Strain Waveform
35、s for In- and Out-of-Phase Axial-Torsional Tests (continued)E2207 08 (2013)13composed 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 relat
36、ionships 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 Li
37、feRelationshipsThe 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 also
38、shown in 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 loa
39、ding conditions 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 b
40、e performed in a testsystem 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 Test Method E606 andPractice E1012. The test system shall pos
41、sess sufficient lateralstiffness and torsional stiffness to minimize distortions of thetest frame at the rated maximum axial force and torquecapacities, respectively.6.2 Gripping FixturesFixtures used for gripping the thin-walled tubular specimen shall be made from a material that canwithstand prolo
42、nged usage, particularly 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
43、 as those specified in Test Method E606 (forexample, specimens with threaded ends) are also acceptableprovided they meet the alignment criteria. Typically specimenswith threaded ends tend to require significantly more effortthan the smooth shank specimens to meet the alignment criteriaspecified in T
44、est Method E606. For this reason, smooth shankspecimens are preferred over the specimens with threadedends.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 a
45、nd must comply with the specifi-cations in Practices E4 and E467. The cross-talk between theaxial force and the torque shall not exceed 1 % of full scalereading, whether a single transducer or multiple transducers areused for these measurements. Specifically, application of therated axial force (alo
46、ne) shall not produce a torque outputgreater than 1% of the rated torque and application of the ratedtorque (alone) shall not produce an axial force output greaterthan 1% of the rated axial force. In other words, the cross-talkbetween the axial force and the torque shall not exceed 1%,whether a sing
47、le transducer or multiple transducers are used forthese measurements.6.4 ExtensometersAxial deformation in the gage sectionof the tubular specimen shall be measured with an extensom-eter such as, a strain-gaged extensometer, a Linear VariableDifferential Transformer (LVDT), or a non-contacting (opti
48、calor capacitance type) extensometer. Procedures for verificationand classification of extensometers are available in PracticeE83. Twist in the gage section of the tubular specimen shall bemeasured with a troptometer such as, a strain-gaged externalextensometer, internal Rotary Variable Differential
49、 Trans-former (RVDT), or a non-contacting (optical or capacitancetype) troptometer (Refs (6, 7). Strain-gaged axial-torsionalextensometers that measure both the axial deformation andtwist in the gage section of the specimen may also be usedprovided the cross-talk is less than 1 % of full scale reading(Ref (8) ). Specifically, application of the rated extensometeraxial strain (alone) shall not produce a torsional output greaterthan 1 % the rated total torsional strain and application o
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