Standard Practice for Strain-Controlled Axial-Torsional Fatigue Testing with Thin-Walled Tubular Specimens

SIGNIFICANCE AND USE
4.1 Multiaxial forces often tend to introduce deformation and damage mechanisms that are unique and quite different from those induced under a simple uniaxial loading condition. Since most engineering components are subjected to cyclic multiaxial forces it is necessary to characterize the deformation and fatigue behaviors of materials in this mode. Such a characterization enables reliable prediction of the fatigue lives of many engineering components. Axial-torsional loading is one of several possible types of multiaxial force systems and is essentially a biaxial type of loading. Thin-walled tubular specimens subjected to axial-torsional loading can be used to explore behavior of materials in two of the four quadrants in principal stress or strain spaces. Axial-torsional loading is more convenient than in-plane biaxial loading because the stress state in the thin-walled tubular specimens is constant over the entire test section and is well-known. This practice is useful for generating fatigue life and cyclic deformation data on homogeneous materials under axial, torsional, and combined in- and out-of-phase axial-torsional loading conditions.
SCOPE
1.1 The standard deals with strain-controlled, axial, torsional, and combined in- and out-of-phase axial torsional fatigue testing with thin-walled, circular cross-section, tubular specimens at isothermal, ambient and elevated temperatures. This standard is limited to symmetric, completely-reversed strains (zero mean strains) and axial and torsional waveforms with the same frequency in combined axial-torsional fatigue testing. This standard is also limited to characterization of homogeneous materials with thin-walled tubular specimens and does not cover testing of either large-scale components or structural elements.  
1.2 This standard does not purport to address all of the safety concerns, if any, associated with its use. It is the responsibility of the user of this standard to establish appropriate safety and health practices and determine the applicability of regulatory limitations prior to use.

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Publication Date
31-Dec-2007
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ASTM E2207-08(2013)e1 - Standard Practice for Strain-Controlled Axial-Torsional Fatigue Testing with Thin-Walled Tubular Specimens
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NOTICE: This standard has either been superseded and replaced by a new version or withdrawn.
Contact ASTM International (www.astm.org) for the latest information
´1
Designation: E2207 − 08(Reapproved 2013)
Standard Practice for
Strain-Controlled Axial-Torsional Fatigue Testing with Thin-
Walled Tubular Specimens
This standard is issued under the fixed designation E2207; the number immediately following the designation indicates the year of
original adoption or, in the case of revision, the year of last revision. A number in parentheses indicates the year of last reapproval. A
superscript epsilon (´) indicates an editorial change since the last revision or reapproval.
ε NOTE—Referenced document E606’s title was editorially updated from a Practice to a Test Method in October 2013.
1. Scope E143 Test Method for Shear Modulus at Room Temperature
E209 PracticeforCompressionTestsofMetallicMaterialsat
1.1 The standard deals with strain-controlled, axial,
Elevated Temperatures with Conventional or Rapid Heat-
torsional, and combined in- and out-of-phase axial torsional
ing Rates and Strain Rates
fatigue testing with thin-walled, circular cross-section, tubular
E467 Practice for Verification of Constant Amplitude Dy-
specimens at isothermal, ambient and elevated temperatures.
namic Forces in an Axial Fatigue Testing System
This standard is limited to symmetric, completely-reversed
E606 Test Method for Strain-Controlled Fatigue Testing
strains (zero mean strains) and axial and torsional waveforms
E1012 Practice for Verification of Testing Frame and Speci-
with the same frequency in combined axial-torsional fatigue
men Alignment Under Tensile and Compressive Axial
testing. This standard is also limited to characterization of
Force Application
homogeneous materials with thin-walled tubular specimens
E1417 Practice for Liquid Penetrant Testing
and does not cover testing of either large-scale components or
E1444 Practice for Magnetic Particle Testing
structural elements.
E1823 TerminologyRelatingtoFatigueandFractureTesting
1.2 This standard does not purport to address all of the
safety concerns, if any, associated with its use. It is the
3. Terminology
responsibility of the user of this standard to establish appro-
3.1 Definitions—The terms specific to this practice are
priate safety and health practices and determine the applica-
defined in this section.All other terms used in this practice are
bility of regulatory limitations prior to use.
in accordance with Terminologies E6 and E1823.
2. Referenced Documents
3.2 Definitions of Terms Specific to This Standard:
3.2.1 axial strain—refers to engineering axial strain, ε, and
2.1 ASTM Standards:
E3 Guide for Preparation of Metallographic Specimens is defined as change in length divided by the original length
(∆L /L ).
E4 Practices for Force Verification of Testing Machines
g g
E6 Terminology Relating to Methods of Mechanical Testing
3.2.2 shear strain—refers to engineering shear strain, γ,
E8 Test Methods for Tension Testing of Metallic Materials
resulting from the application of a torsional moment to a
E9 Test Methods of Compression Testing of Metallic Mate-
cylindrical specimen. Such a torsional shear strain is simple
rials at Room Temperature
shear and is defined similar to axial strain with the exception
E83 Practice for Verification and Classification of Exten-
that the shearing displacement, ∆L is perpendicular to rather
s
someter Systems
thanparalleltothegagelength, L ,thatis,γ=∆L/L (seeFig.
g s g
E111 Test Method for Young’s Modulus, Tangent Modulus,
1).
and Chord Modulus
NOTE 1—γ= is related to the angles of twist, θ and Ψ as follows:
E112 Test Methods for Determining Average Grain Size
γ = tan Ψ, where Ψ is the angle of twist along the gage length of the
cylindrical specimen. For small angles expressed in radians, tan Ψ
approaches Ψ and γ approaches Ψ.
This practice is under the jurisdiction ofASTM Committee E08 on Fatigue and
γ=(d/2)θ/L ,whereθexpressedinradiansistheangleoftwistbetween
g
Fracture and is the direct responsibility of Subcommittee E08.05 on Cyclic
theplanesdefiningthegagelengthofthecylindricalspecimenand disthe
Deformation and Fatigue Crack Formation.
diameter of the cylindrical specimen.
Current edition approved Oct. 15, 2013. Published November 2013. Originally
NOTE 2—∆L is measurable directly as displacement using specially
approved in 2002. Last previous edition approved in 2008 as E2207–08. DOI: s
calibrated torsional extensometers or as the arc length∆L =(d/2)θ, where
10.1520/E2207-08R13.
s
θ is measured directly with a rotary variable differential transformer.
For referenced ASTM standards, visit the ASTM website, www.astm.org, or
contact ASTM Customer Service at service@astm.org. For Annual Book of ASTM
3.2.2.1 Discussion—The shear strain varies linearly through
Standards volume information, refer to the standard’s Document Summary page on
the ASTM website. the thin wall of the specimen, with the smallest and largest
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States
´1
E2207 − 08 (2013)
FIG. 1 Twisted Gage Section of a Cylindrical Specimen Due to a Torsional Moment
values occurring at the inner and outer diameters of the same time as that of the shear strain waveform, then the phase
specimen, respectively. The value of shear strain on the outer angle, φ = 0° and the test is defined as an “in-phase”
surface,innersurface,andmeandiameterofthespecimenshall axial-torsional fatigue test (Fig. 2(a)).At every instant in time,
be reported. The shear strain determined at the outer diameter the shear strain is proportional to the axial strain.
of the tubular specimen is recommended for strain-controlled
NOTE 3—Proportional loading is the commonly used terminology in
torsional tests, since cracks typically initiate at the outer
plasticity literature for the in-phase axial-torsional loading described in
surfaces.
this practice.
3.2.3 biaxial strain amplitude ratio—in an axial-torsional
3.2.4.2 out-of-phase axial-torsional fatigue test— for
fatigue test, the biaxial strain amplitude ratio, λ is defined as completely-reversed axial and shear strain waveforms, if the
the ratio of the shear strain amplitude (γ ) to the axial strain
maximum value of the axial strain waveform leads or lags the
a
amplitude (ε ), that is, γ /ε .
maximum value of the shear strain waveform by a phase angle
a a a
φ≠ 0° then the test is defined as an “out-of-phase” axial-
3.2.4 phasing between axial and shear strains— in an
torsional fatigue test. Unlike in the in-phase loading, the shear
axial-torsional fatigue test, phasing is defined as the phase
strain is not proportional to the axial strain at every instant in
angle, φ, between the axial strain waveform and the shear
time. An example of out-of-phase axial-torsional fatigue test
strainwaveform.Thetwowaveformsmustbeofthesametype,
with φ = 75° is shown in Fig. 2(b). Typically, for an
for example, both must either be triangular or both must be
out-of-phase axial-torsional fatigue test, the range of φ (≠ 0°)
sinusoidal.
is from -90° (axial waveform lagging the shear waveform) to +
3.2.4.1 in-phase axial-torsional fatigue test— for
90° (axial waveform leading the shear waveform).
completely-reversed axial and shear strain waveforms, if the
maximum value of the axial strain waveform occurs at the NOTE 4—In plasticity literature, nonproportional loading is the generic
FIG. 2 Schematics of Axial and Shear Strain Waveforms for In- and Out-of-Phase Axial-Torsional Tests
´1
E2207 − 08 (2013)
FIG. 2 Schematics of Axial and Shear Strain Waveforms for In- and Out-of-Phase Axial-Torsional Tests (continued)
terminology for the out-of-phase loading described in this practice.
determined at the same location within the thin wall of the
tubular test specimen.
3.2.5 shear stress—refers to engineering shear stress, τ,
acting in the orthogonal tangential and axial directions of the
4. Significance and Use
gage section and is a result of the applied torsional moment,
4.1 Multiaxial forces often tend to introduce deformation
(Torque) T, to the thin-walled tubular specimen. The shear
and damage mechanisms that are unique and quite different
stress, like the shear strain, is always the greatest at the outer
from those induced under a simple uniaxial loading condition.
diameter. Under elastic loading conditions, shear stress also
Since most engineering components are subjected to cyclic
varies linearly through the thin wall of the tubular specimen.
multiaxialforcesitisnecessarytocharacterizethedeformation
However, under elasto-plastic loading conditions, shear stress
tends to vary in a nonlinear fashion. Most strain-controlled and fatigue behaviors of materials in this mode. Such a
characterization enables reliable prediction of the fatigue lives
axial-torsional fatigue tests are conducted under elasto-plastic
loading conditions. Therefore, assumption of a uniformly of many engineering components. Axial-torsional loading is
one of several possible types of multiaxial force systems and is
distributed shear stress is recommended. The relationship
between such a shear stress applied at the mean diameter of the essentially a biaxial type of loading. Thin-walled tubular
specimens subjected to axial-torsional loading can be used to
gage section and the torsional moment, T,is
explore behavior of materials in two of the four quadrants in
16T
τ 5 (1) principalstressorstrainspaces.Axial-torsionalloadingismore
2 2
~π~d 2 d !~d 1d !!
o i o i
convenient than in-plane biaxial loading because the stress
Where, τ is the shear stress, d and d are the outer and
state in the thin-walled tubular specimens is constant over the
o i
inner diameters of the tubular test specimen, respectively.
entiretestsectionandiswell-known.Thispracticeisusefulfor
However, if necessary, shear stresses in specimens not meet-
generating fatigue life and cyclic deformation data on homo-
ing the criteria for thin-walled tubes can also be evaluated
geneous materials under axial, torsional, and combined in- and
(see Ref (1)).
out-of-phase axial-torsional loading conditions.
Under elastic loading conditions, shear stress, τ(d)ata
5. Empirical Relationships
diameter, d in the gage section of the tubular specimen can
be calculated as follows:
5.1 Axial and Shear Cyclic Stress-Strain Curves—Under
elasto-plastic loading conditions, axial and shear strains are
16Td
τ~d! 5 (2)
4 4 composed of both elastic and plastic components. The math-
~π~d 2 d !!
o i
ematical functions commonly used to characterize the cyclic
In order to establish the cyclic shear stress-strain curve for
axial and shear stress-strain curves are shown in Appendix X1.
a material, both the shear strain and shear stress shall be
Note that constants in these empirical relationships are depen-
dent on the phasing between the axial and shear strain
waveforms.
The boldface numbers in parentheses refer to the list of references at the end of
this standard. NOTE 5—For combined axial-torsional loading conditions, analysis and
´1
E2207 − 08 (2013)
interpretation of cyclic deformation behavior can be performed by using
6.4 Extensometers—Axial deformation in the gage section
the techniques described in Ref (2).
of the tubular specimen shall be measured with an extensom-
5.2 Axial and Shear Strain Range-Fatigue Life eter such as, a strain-gaged extensometer, a Linear Variable
Relationships—The total axial and shear strain ranges can be Differential Transformer (LVDT), or a non-contacting (optical
separated into their elastic and plastic parts by using the or capacitance type) extensometer. Procedures for verification
respective stress ranges and elastic moduli. The fatigue life and classification of extensometers are available in Practice
relationships to characterize cyclic lives under axial (no E83. Twist in the gage section of the tubular specimen shall be
torsion) and torsional (no axial loading) conditions are also measured with a troptometer such as, a strain-gaged external
shown in Appendix X1. These axial and torsional fatigue life extensometer, internal Rotary Variable Differential Trans-
relationships can be used either separately or together to former (RVDT), or a non-contacting (optical or capacitance
estimate fatigue life under combined axial-torsional loading type) troptometer (Refs (6, 7)). Strain-gaged axial-torsional
conditions. extensometers that measure both the axial deformation and
NOTE 6—Details on some fatigue life estimation procedures under
twist in the gage section of the specimen may also be used
combined in- and out-of-phase axial-torsional loading conditions are
provided the cross-talk is less than 1 % of full scale reading
given in Refs (3-5). Currently, no single life prediction method has been
(Ref (8) ). Specifically, application of the rated extensometer
showntobeeithereffectiveorsuperiortoothermethodsforestimatingthe
axial strain (alone) shall not produce a torsional output greater
fatigue lives of materials under combined axial-torsional loading condi-
tions. than 1 % the rated total torsional strain and application of the
rated extensometer torsional strain (alone) shall not produce an
6. Test Apparatus
axial output greater than 1 % of the rated total axial strain. In
other words, the cross-talk between the axial displacement and
6.1 Testing Machine—Alltestsshouldbeperformedinatest
the torsional twist shall not exceed 1 %, whether a single
system with tension-compression and clockwise-counter
transducer or multiple transducers are used for these measure-
clockwise torsional loading capability. The test system (test
ments.
frameandassociatedfixtures)mustshallbeincompliancewith
the bending strain criteria specified in Test Method E606 and
6.5 Transducer Calibration—All the transducers shall be
Practice E1012. The test system shall possess sufficient lateral
calibrated in accordance with the recommendations of the
stiffness and torsional stiffness to minimize distortions of the
respective manufacturers. Calibration of each transducer shall
test frame at the rated maximum axial force and torque
be traceable to the National Institute of Standards and Tech-
capacities, respectively.
nology (NIST).
6.2 Gripping Fixtures—Fixtures used for gripping the thin-
6.6 Data Acquisition System—Digital acquisition of cyclic
walledtubularspecimenshallbemadefromamaterialthatcan
test data is recommended or analog X-Y and strip chart
withstand prolonged usage, particularly at high temperatures.
recorders shall be employed to document axial and torsional
The design of the fixtures largely depends upon the design of
hysteresis loops and variation of axial force/strain and torque/
the specimen. Typically, a combination of hydraulically
shear strain with time.
clamped collet fixtures and smooth shank specimens pro
...

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