1、Designation: E2207 15Standard 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 the case of revisio
2、n, 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.1. Scope1.1 The standard deals with strain-controlled, axial,torsional, and combined in- and out-of-phase axial tor
3、sionalfatigue 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-torsional
4、 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, associated w
5、ith 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 Practices
6、for Force Verification of Testing MachinesE6 Terminology Relating to Methods of Mechanical TestingE8/E8M Test Methods for Tension Testing of Metallic Ma-terialsE9 Test Methods of Compression Testing of Metallic Mate-rials at Room TemperatureE83 Practice for Verification and Classification of Exten-s
7、ometer SystemsE111 Test Method for Youngs Modulus, Tangent Modulus,and Chord ModulusE112 Test Methods for Determining Average Grain SizeE143 Test Method for Shear Modulus at Room TemperatureE209 Practice for Compression Tests of Metallic Materials atElevated Temperatures with Conventional or Rapid H
8、eat-ing Rates and Strain RatesE467 Practice for Verification of Constant Amplitude Dy-namic Forces in an Axial Fatigue Testing SystemE606/E606M Test Method for Strain-Controlled FatigueTestingE1012 Practice for Verification of Testing Frame and Speci-men Alignment Under Tensile and Compressive Axial
9、Force ApplicationE1417/E1417M Practice for Liquid Penetrant TestingE1444/E1444M Practice for Magnetic Particle TestingE1823 Terminology Relating to Fatigue and Fracture TestingE2624 Practice for Torque Calibration of Testing Machinesand Devices3. Terminology3.1 DefinitionsThe terms specific to this
10、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 divided by the original length(Lg/L
11、g).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 displacement, Lsis perpendicular to rathert
12、han parallel to the gage length, Lg, that is, = Ls/Lg(see Fig.1).3.2.2.1 Discussion= is related to the angles of twist, and as follows: = tan , where is the angle of twist along the gagelength of the cylindrical specimen. For small angles ex-pressed in radians, tan approaches and approaches . =(d/2)
13、/Lg, where expressed in radians is the angle oftwist between the planes defining the gage length of thecylindrical specimen and d is the diameter of the cylindricalspecimen.1This practice is under the jurisdiction of ASTM Committee E08 on Fatigue andFracture and is the direct responsibility of Subco
14、mmittee E08.05 on CyclicDeformation and Fatigue Crack Formation.Current edition approved May 1, 2015. Published July 2015. Originally approvedin 2002. Last previous edition approved in 2013 as E220708(2013)1. DOI:10.1520/E2207-15.2For referenced ASTM standards, visit the ASTM website, www.astm.org,
15、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, PA 19428-2959. United States13.2.2.2 Discussio
16、nLsis measurable directly as displace-ment using specially calibrated torsional extensometers or asthe arc length Ls=(d/2), where is measured directly witha rotary variable differential transformer.3.2.2.3 DiscussionThe shear strain varies linearly throughthe thin wall of the specimen, with the smal
17、lest and largestvalues 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 recommended fo
18、r 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), that is, a/a.
19、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 besinusoidal.3.
20、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-torsional fatigue
21、test (Fig. 2(a). At every instant in time,the shear strain is proportional to the axial strain.NOTE 1Proportional 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 test forc
22、ompletely-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, the shearstr
23、ain 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 152time. An example of out-of-phase axial-torsional
24、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 2In plasticity literature, nonproportional loading is the generict
25、erminology 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 tubular specimen. The s
26、hearstress, 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 nonlinear fashion. Most st
27、rain-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 torsional moment, T,is 5
28、16Tdo22 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 loading conditions,
29、 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 within the thin wall o
30、f 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 cyclicmultiaxial forces
31、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 systems and isessentially
32、 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 because the stressstate i
33、n 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 conditions.5. Empir
34、ical 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 Waveforms for In- and Out-of
35、-Phase Axial-Torsional Tests (continued)E2207 153composed 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-dent on t
36、he phasing between the axial and shear strainwaveforms.NOTE 3For 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 LifeRelationshipsThe total axi
37、al 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 Appendix X1. These
38、axial and torsional fatigue liferelationships can be used either separately or together toestimate fatigue life under combined axial-torsional loadingconditions.NOTE 4Details on some fatigue life estimation procedures undercombined in- and out-of-phase axial-torsional loading conditions aregiven in
39、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 performed in a testsystem
40、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/E606M and Practice E1012. The test system shall possesssufficient latera
41、l stiffness and torsional stiffness to minimizedistortions of the test frame at the rated maximum axial forceand 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, particula
42、rly 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 specified i
43、n Test Method E606/E606M (for example, specimens with threaded ends) are alsoacceptable provided they meet the alignment criteria. Typicallyspecimens with threaded ends tend to require significantlymore effort than the smooth shank specimens to meet thealignment criteria specified in Test Method E60
44、6/E606M. Forthis reason, smooth shank specimens are preferred over thespecimens 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
45、comply with the specifi-cations in Practices E4, E467 and E2624. The cross-talkbetween the axial force and the torque shall not exceed 1 % offull scale reading, whether a single transducer or multipletransducers are used for these measurements. Specifically,application of the rated axial force (alon
46、e) shall not produce atorque output greater than 1% of the rated torque and applica-tion of the rated torque (alone) shall not produce an axial forceoutput greater than 1% of the rated axial force. In other words,the cross-talk between the axial force and the torque shall notexceed 1%, whether a sin
47、gle transducer or multiple transducersare used for these 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 (opt
48、icalor 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 Differentia
49、l 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 of t
