1、Designation: E 2207 08Standard 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 characterization ofhomogeneous materials with thin-walled tubular specimensand does not cover testing of either large-scale components orstructural elements.1.2 This standard does not purport to address all of thesafety concerns, if any, associa
5、ted 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:2E3 Guide for Preparation of Metallographic SpecimensE4 Pract
6、ices for Force Verification of Testing MachinesE6 Terminology Relating to Methods of Mechanical Test-ingE8 Test Methods for Tension Testing of Metallic MaterialsE9 Test Methods of Compression Testing of Metallic Ma-terials at Room TemperatureE83 Practice for Verification and Classification of Exten-
7、someter SystemsE 111 Test Method forYoungs Modulus, Tangent Modulus,and Chord ModulusE112 Test Methods for Determining Average Grain SizeE 143 Test Method for Shear Modulus at Room Tempera-tureE 209 Practice for Compression Tests of Metallic Materialsat Elevated Temperatures with Conventional or Rap
8、idHeating Rates and Strain RatesE 467 Practice for Verification of Constant Amplitude Dy-namic Forces in an Axial Fatigue Testing SystemE 606 Practice for Strain-Controlled Fatigue TestingE 1012 Practice for Verification of Test Frame and Speci-men Alignment Under Tensile and Compressive AxialForce
9、ApplicationE 1417 Practice for Liquid Penetrant TestingE 1444 Practice for Magnetic Particle TestingE 1823 Terminology Relating to Fatigue and Fracture Test-ing3. Terminology3.1 DefinitionsThe terms specific to this practice aredefined in this section. All other terms used in this practice arein acc
10、ordance with Terminologies E6and E 1823.3.2 Definitions of Terms Specific to This Standard:3.2.1 axial strainrefers to engineering axial strain, e, andis defined as change in length divided by the original length(DLg/Lg).3.2.2 shear strainrefers to engineering shear strain, g,resulting from the appl
11、ication 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 to the gage length, Lg, that is, g = DLs/Lg(see Fig.1).NOTE 1g= is
12、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 expressed in radians, tan Capproaches C and g approaches C.g =(d/2)u/Lg, where u expressed in radians is the angle of twist betweenthe planes
13、 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 directly with a rotary variable differential tr
14、ansformer.3.2.2.1 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 outer1This practice is under the jurisdiction of ASTM Commi
15、ttee E08 on Fatigue andFracture and is the direct responsibility of Subcommittee E08.05 on CyclicDeformation and Fatigue Crack Formation.Current edition approved Jan. 1, 2008. Published February 2008. Originallyapproved in 2002. Last previous edition approved in 2002 as E 220702.2For referenced ASTM
16、 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.1Copyright ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohoc
17、ken, PA 19428-2959, United States.surface, 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.3.2.3 biaxi
18、al strain amplitude ratioin an axial-torsionalfatigue test, the biaxial strain amplitude ratio, l is defined asthe ratio of the shear strain amplitude (ga) to the axial strainamplitude (ea), that is, ga/ea.3.2.4 phasing between axial and shear strainsin an axial-torsional fatigue test, phasing is de
19、fined 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 must besinusoidal.3.2.4.1 in-phase axial-torsional fatigue testforcompletely-reversed axial and shear strain wa
20、veforms, 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-torsional fatigue test (Fig. 2(a). At every instant in time,the shear strain is proportional to the axial st
21、rain.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 fatigue testforcompletely-reversed axial and shear strain waveforms, if themaximum value of the axial strai
22、n waveform leads or lags themaximum value of the shear strain waveform by a phase angleffi0 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-o
23、f-phase 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 (fi 0)is from -90 (axial waveform lagging the shear waveform) to +90 (axial waveform leading the shear waveform).NOTE 4In plasticity literature, nonpropor
24、tional loading is the genericterminology for the out-of-phase loading described in this practice.FIG. 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 TestsE22070823.2.5 shear stre
25、ssrefers 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,(Torque) T, to the thin-walled tubular specimen. The shearstress, like the shear strain, is always the greatest at the outerdiameter. Un
26、der 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 nonlinear fashion. Most strain-controlledaxial-torsional fatigue tests are conducted under elasto-plasticloa
27、ding 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 torsional moment, T,ist516Tpdo22 di2!do1 di!(1)Where, t is the shear stress, doand diare the outer and inn
28、erdiameters 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).3Under elastic loading conditions, shear stress, t(d)atadiameter, d in the gage section of the tubular specimen ca
29、n 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 within the thin wall of thetubular test specimen.4. Significance and Use4.1 Multiaxial forces often
30、 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 cyclicmultiaxial forces it is necessary to characterize the deformationand fatigue behaviors of mater
31、ials 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 subjected to axial-t
32、orsional 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 test section a
33、nd 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 CurvesUnderelasto-
34、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 are depen-den
35、t on the phasing between the axial and shear strainwaveforms.3The boldface numbers in parentheses refer to the list 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)E2207083NOTE 5For combined axia
36、l-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 LifeRelationshipsThe total axial and shear strain ranges can beseparated into their elastic and plastic part
37、s 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 Appendix X1. These axial and torsional fatigue liferelationships can be used either separately or
38、 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 conditions aregiven in Refs (3-5). Currently, no single life prediction method has beenshown to be ei
39、ther 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 performed in atest system with tension-compression and clockwise-counterclockwise torsional loading capa
40、bility. 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 lateral stiffnessand torsional stiffness to minimize distortions of the test frameat the rated maxi
41、mum 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, particularly at high temperatures.The design of the fixtures largely depends upon the design ofthe spec
42、imen. Typically, a combination of hydraulicallyclamped collet fixtures and smooth shank specimens providegood alignment and high lateral stiffness. However, other typesof fixtures, such as those specified in Practice E 606 (forexample, specimens with threaded ends) are also acceptableprovided they m
43、eet the alignment criteria. Typically specimenswith threaded ends tend to require significantly more effortthan the smooth shank specimens to meet the alignment criteriaspecified in Practice E 606. For this reason, smooth shankspecimens are preferred over the specimens with threadedends.6.3 Force an
44、d 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-cations in Practices E4and E 467. The cross-talk between theaxial force and the torque
45、shall not exceed 1 % of full scalereading, whether a single transducer or multiple transducers areused for these measurements. Specifically, application of therated axial force (alone) shall not produce a torque outputgreater than 1% of the rated torque and application of the ratedtorque (alone) sha
46、ll 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 single transducer or multiple transducers are used forthese measurements.6.4 ExtensometersAxial deformation in the gage sec
47、tionof 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 (opticalor capacitance type) extensometer. Procedures for verificationand classification of extensometers are available in P
48、racticeE83. Twist in the gage section of the tubular specimen shall bemeasured with a troptometer such as, a strain-gaged externalextensometer, internal Rotary Variable Differential Trans-former (RVDT), or a non-contacting (optical or capacitancetype) troptometer (Refs (6, 7). Strain-gaged axial-tor
49、sionalextensometers 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 of therated extensometer torsional strain (alone) shall not produce anaxial output greater than 1 % of the rated total axial strain. Inother words, the cross-talk between the axial dis
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