ASTM E2207-02
(Practice)Standard Practice for Strain-Controlled Axial-Torsional Fatigue Testing with Thin-Walled Tubular Specimens
Standard Practice for Strain-Controlled Axial-Torsional Fatigue Testing with Thin-Walled Tubular Specimens
SIGNIFICANCE AND USE
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 thin-walled tubular specimens (machined from homogeneous materials) 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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Standards Content (Sample)
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Designation:E2207–02
Standard Practice for
Strain-Controlled Axial-Torsional Fatigue Testing with Thin-
Walled Tubular Specimens
This standard is issued under the fixed designation E 2207; 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 (e) indicates an editorial change since the last revision or reapproval.
1. Scope E 467 Practice for Verification of Constant Amplitude Dy-
namic Forces in an Axial Fatigue Testing System
1.1 The standard deals with strain-controlled, axial, tor-
E 606 Practice for Strain-Controlled Fatigue Testing
sional, and combined in- and out-of-phase axial torsional
E 1012 Practice for Verification of Specimen Alignment
fatigue testing with thin-walled, circular cross-section, tubular
under Tensile Loading
specimens at isothermal, ambient and elevated temperatures.
E 1417 Practice for Liquid Penetrant Examination
This standard is limited to symmetric, completely-reversed
E 1444 Practice for Magnetic Particle Examination
strains (zero mean strains) and axial and torsional waveforms
E 1823 Terminology Relating to Fatigue and Fracture Test-
with the same frequency in combined axial-torsional fatigue
ing
testing. This standard is also limited to thin-walled tubular
specimens (machined from homogeneous materials) and does
3. Terminology
not cover testing of either large-scale components or structural
3.1 Definitions:
elements.
3.1.1 axial strain—refers to engineering axial strain, e, and
1.2 This standard does not purport to address all of the
is defined as change in length divided by the original length
safety concerns, if any, associated with its use. It is the
(DL /L ).
g g
responsibility of the user of this standard to establish appro-
3.1.2 shear strain—refers to engineering shear strain, g,
priate safety and health practices and determine the applica-
resulting from the application of a torsional moment to a
bility of regulatory limitations prior to use.
cylindrical specimen. Such a torsional shear strain is simple
2. Referenced Documents shear and is defined similar to axial strain with the exception
that the shearing displacement, DL is perpendicular to rather
s
2.1 ASTM Standards:
thanparalleltothegagelength, L ,thatis, g= DL/L (seeFig.
g s g
E 3 Practice for Preparation of Metallographic Specimens
1).
E 4 Practices for Force Verification of Testing Machines
E 6 Terminology Relating to Methods of Mechanical Test-
NOTE 1—g= is related to the angles of twist, u and C as follows:
ing
g = tan C, where C is the angle of twist along the gage length of the
cylindrical specimen. For small angles tan C approaches C and g
E 8 TestMethodsforTensionTestingofMetallicMaterials
approaches C.
E 9 Test Methods of Compression Testing of Metallic Ma-
2 g=(d/2)u/L ,where uexpressedinradiansistheangleoftwistbetween
g
terials at Room Temperature
theplanesdefiningthegagelengthofthecylindricalspecimenand disthe
E 83 Practice for Verification and Classification of Exten-
diameter of the cylindrical specimen.
someters
NOTE 2—DL is measurable directly as displacement using specially
s
E 111 TestMethodforYoung’sModulus,TangentModulus,
calibrated torsional extensometers or as the arc length DL =(d/2)u, where
s
and Chord Modulus u is measured directly with a rotary variable differential transformer.
E 112 Test Methods for Determining Average Grain Size
3.1.2.1 Discussion—Theshearstrainvarieslinearlythrough
E 143 Test Method for Shear Modulus at Room Tempera-
the thin wall of the specimen, with the smallest and largest
ture
values occurring at the inner and outer diameters of the
E 209 Practice for Compression Tests of Metallic Materials
specimen, respectively. The value of shear strain on the outer
at Elevated Temperatures with Conventional or Rapid
surface,innersurface,andmeandiameterofthespecimenshall
Heating Rates or Strain Rates
be reported. The shear strain determined at the outer diameter
of the tubular specimen is recommended for strain-controlled
torsional tests, since cracks typically initiate at the outer
This practice is under the jurisdiction ofASTM Committee E08 on Fatigue and
surfaces.
Fracture and is the direct responsibility of Subcommittee E08.05 on Cyclic
Deformation and Fatigue Crack Formation.
Current edition approved May 10, 2002. Published August 2002.
2 3
Annual Book of ASTM Standards, Vol 03.01. Annual Book of ASTM Standards, Vol 03.03.
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959, United States.
E2207
FIG. 1 Twisted Gage Section of a Cylindrical Specimen Due to a Torsional Moment
3.1.3 biaxial strain amplitude ratio—in an axial-torsional maximum value of the axial strain waveform occurs at the
fatigue test, the biaxial strain amplitude ratio, l is defined as same time as that of the shear strain waveform, then the phase
the ratio of the shear strain amplitude (g ) to the axial strain angle, f = 0° and the test is defined as an “in-phase”
a
amplitude (e ), that is, g /e . axial-torsional fatigue test (Fig. 2(a)).At every instant in time,
a a a
3.1.4 phasing between axial and shear strains—in an axial-
the shear strain is proportional to the axial strain.
torsional fatigue test, phasing is defined as the phase angle, f,
NOTE 3—Proportional loading is the commonly used terminology in
between the axial strain waveform and the shear strain wave-
plasticity literature for the in-phase axial-torsional loading described in
form. The two waveforms must be of the same type, for
this practice.
example, both must either be triangular or both must be
sinusoidal. 3.1.4.2 out-of-phase axial-torsional fatigue test—for
3.1.4.1 in-phase axial-torsional fatigue test—for completely-reversed axial and shear strain waveforms, if the
completely-reversed axial and shear strain waveforms, if the maximum value of the axial strain waveform leads or lags the
FIG. 2 Schematics of Axial and Shear Strain Waveforms for In- and Out-of-Phase Axial-Torsional Tests
E2207
16T
maximum value of the shear strain waveform by a phase angle
t5 (1)
2 2
ffi 0° then the test is defined as an “out-of-phase” axial- ~p~d 2 d !~d 1 d !!
o i o i
torsional fatigue test. Unlike in the in-phase loading, the shear
where t is the shear stress, d and d are the outer and inner
o i
strain is not proportional to the axial strain at every instant in
diameters of the tubular test specimen, respectively. However,
time. An example of out-of-phase axial-torsional fatigue test
if necessary, shear stresses in specimens not meeting the
with f = 75° is shown in Fig. 2(b). Typically, for an
criteria for thin-walled tubes can also be evaluated (see Ref
out-of-phase axial-torsional fatigue test, the range of f (fi 0°) 4
(1)).
is from -90° (axial waveform lagging the shear waveform) to +
Under elastic loading conditions, shear stress, t(d)ata
90° (axial waveform leading the shear waveform).
diameter, d in the gage section of the tubular specimen can be
calculated as follows:
NOTE 4—In plasticity literature, nonproportional loading is the generic
terminology for the out-of-phase loading described in this practice.
16Td
t~d! 5 (2)
4 4
3.1.5 shear stress—refers to engineering shear stress, t, p d 2 d
~ ~ !!
o i
acting in the orthogonal tangential and axial directions of the
In order to establish the cyclic shear stress-strain curve for a
gage section and is a result of the applied torsional moment, T,
material, both the shear strain and shear stress shall be
to the thin-walled tubular specimen. The shear stress, like the
determined at the same location within the thin wall of the
shear strain, is always the largest at the outer diameter. Under
tubular test specimen.
elastic loading conditions, shear stress also varies linearly
through the thin wall of the tubular specimen. However, under
4. Significance and Use
elasto-plastic loading conditions, shear stress tends to vary in a
4.1 Multiaxial forces often tend to introduce deformation
nonlinear fashion. Most strain-controlled axial-torsional fa-
and damage mechanisms that are unique and quite different
tigue tests are conducted under elasto-plastic loading condi-
from those induced under a simple uniaxial loading condition.
tions. Therefore, assumption of a uniformly distributed shear
stress is recommended. The relationship between such a shear
stress applied at the mean diameter of the gage section and the 4
The boldface numbers in parentheses refer to the list of references at the end of
torsional moment, T,is this standard.
FIG. 2 Schematics of Axial and Shear Strain Waveforms for In- and Out-of-Phase Axial-Torsional Tests (continued)
E2207
Since most engineering components are subjected to cyclic The design of the fixtures largely depends upon the design of
multiaxialforcesitisnecessarytocharacterizethedeformation the specimen. Typically, a combination of hydraulically
and fatigue behaviors of materials in this mode. Such a clamped collet fixtures and smooth shank specimens provide
characterization enables reliable prediction of the fatigue lives good alignment and high lateral stiffness. However, other types
of many engineering components. Axial-torsional loading is of fixtures, such as those specified in Practice E 606 (for
one of several possible types of multiaxial force systems and is example, specimens with threaded ends) are also acceptable
essentially a biaxial type of loading. Thin-walled tubular provided they meet the alignment criteria.Typically specimens
specimens subjected to axial-torsional loading can be used to with threaded ends tend to require more effort than the smooth
explore behavior of materials in two of the four quadrants in shank specimens to meet the alignment criteria specified in
principalstressorstrainspaces.Axial-torsionalloadingismore Practice E 606. For this reason, smooth shank specimens are
convenient than in-plane biaxial loading because the stress preferred over the specimens with threaded ends.
state in the thin-walled tubular specimens is constant over the 6.3 Force and Torque Transducers—Axial force and torque
entiretestsectionandiswell-known.Thispracticeisusefulfor must be measured with either separate transducers or a
generating fatigue life and cyclic deformation data on homo- combined transducer. The transducer(s) must be placed in
geneous materials under axial, torsional, and combined in- and series with the force train and must comply with the specifi-
out-of-phase axial-torsional loading conditions. cations in Practices E 4 and E 467. The cross-talk between the
axial force and the torque shall not exceed 1 %, whether a
5. Empirical Relationships
single transducer or multiple transducers are used for these
5.1 Axial and Shear Cyclic Stress-Strain Curves—Under
measurements.
elasto-plastic loading conditions, axial and shear strains are
6.4 Extensometers—Axial deformation in the gage section
composed of both elastic and plastic components. The math-
of the tubular specimen shall be measured with an extensom-
ematical functions commonly used to characterize the cyclic
eter such as, a strain-gaged extensometer, a Linear Variable
axial and shear stress-strain curves are shown inAppendix X1.
Differential Transformer (LVDT), or a non-contacting (optical
Note that constants in these empirical relationships are depen-
or capacitance type) extensometer. Twist in the gage section of
dent on the phasing between the axial and shear strain
the tubular specimen shall be measured with an extensometer
waveforms.
such as, a strain-gaged external extensometer, internal Rotary
Variable DifferentialTransformer (RVDT), or a non-contacting
NOTE 5—For combined axial-torsional loading conditions, analysis and
(optical or capacitance type) extensometer (Refs (6, 7)).
interpretation of cyclic deformation behavior can be performed by using
the techniques described in Ref (2).
Strain-gaged axial-torsional extensometers that measure both
the axial deformation and twist in the gage section of the
5.2 Axial and Shear Strain Range-Fatigue Life
specimen may also be used provided the cross-talk is less than
Relationships—The total axial and shear strain ranges can be
1 % (Ref (8)). Specifically, application of the rated extensom-
separated into their elastic and plastic parts by using the
eter axial strain (alone) shall not produce a torsional output
respective stress ranges and elastic moduli. The fatigue life
greater than 1 % of the rated total torsional strain and applica-
relationships to characterize cyclic lives under axial (no
tion of the rated extensometer torsional strain (alone) shall not
torsion) and torsional (no axial loading) conditions are also
produce an axial output greater than 1 % of the rated total axial
shown in Appendix X1. These axial and torsional fatigue life
strain. In other words, the cross-talk between the axial dis-
relationships can be used either separately or together to
placementandthetorsionaltwistshallnotexceed1 %,whether
estimate fatigue life under combined axial-torsional loading
a single transducer or multiple transducers are used for these
conditions.
measurements.
NOTE 6—Details on some fatigue life estimation procedures under
6.5 Transducer Calibration—All the transducers shall be
combined in- and out-of-phase axial-torsional loading conditions are
calibrated in accordance with the recommendations of the
given in Refs (3-5). Currently, no single life prediction method has been
respective manufacturers. Calibration of each transducer shall
showntobeeithereffectiveorsuperiortoothermethodsforestimatingthe
be traceable to the National Institute of Standards and Tech-
fatigue lives of materials under combined axial-torsional loading condi-
tions. nology (NIST).
6.6 Data Acquisition System—Digital acquisition of cyclic
6. Test Apparatus
test data is recommended or analog X-Y and strip chart
6.1 Testing Machine—All tests should be performed in a
recorders shall be employed to document axial and torsional
test system with tension-compression and clockwise-counter
hysteresis loops and variation of axial force/strain and torque/
clockwise torsional loading capability. The test system (test
shear strain with time.
frameandassociatedfixtures)mustshallbeincompliancewith
7. Thin-Walled Tubular Test Specimens
the bending strain criteria specified in Practices E 606 and
E 1012. The test system shall possess sufficient lateral stiffness 7.1 Test Specimen Design—The specimen’s wall thickness
and torsional stiffness to minimize distortions of the test frame shall be large enough to avoid instabilities
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