ASTM E1876-01(2006)
(Test Method)Standard Test Method for Dynamic Young's Modulus, Shear Modulus, and Poisson's Ratio by Impulse Excitation of Vibration
Standard Test Method for Dynamic Young's Modulus, Shear Modulus, and Poisson's Ratio by Impulse Excitation of Vibration
SCOPE
1.1 This test method covers determination of the dynamic elastic properties of elastic materials at ambient temperatures. Specimens of these materials possess specific mechanical resonant frequencies that are determined by the elastic modulus, mass, and geometry of the test specimen. The dynamic elastic properties of a material can therefore be computed if the geometry, mass, and mechanical resonant frequencies of a suitable (rectangular or cylindrical geometry) test specimen of that material can be measured. Dynamic Young's modulus is determined using the resonant frequency in either the flexural or longitudinal mode of vibration. The dynamic shear modulus, or modulus of rigidity, is found using torsional resonant vibrations. Dynamic Young's modulus and dynamic shear modulus are used to compute Poisson's ratio.
1.2 Although not specifically described herein, this test method can also be performed at cryogenic and high temperatures with suitable equipment modifications and appropriate modifications to the calculations to compensate for thermal expansion.
1.3 There are material specific ASTM standards that cover the determination of resonance frequencies and elastic properties of specific materials by sonic resonance or by impulse excitation of vibration. Test Methods C 215, C 623, C 747, C 848, C 1198, and C 1259 may differ from this test method in several areas (for example; sample size, dimensional tolerances, sample preparation). The testing of these materials shall be done in compliance with these material specific standards. Where possible, the procedures, sample specifications and calculations are consistent with these test methods.
1.4 The values stated in SI units are to be regarded as the standard.
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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Designation: E 1876 – 01 (Reapproved 2006)
Standard Test Method for
Dynamic Young’s Modulus, Shear Modulus, and Poisson’s
Ratio by Impulse Excitation of Vibration
This standard is issued under the fixed designation E 1876; 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 1.5 This standard does not purport to address all of the
safety concerns, if any, associated with its use. It is the
1.1 This test method covers determination of the dynamic
responsibility of the user of this standard to establish appro-
elastic properties of elastic materials at ambient temperatures.
priate safety and health practices and determine the applica-
Specimens of these materials possess specific mechanical
bility of regulatory limitations prior to use.
resonant frequencies that are determined by the elastic modu-
lus, mass, and geometry of the test specimen. The dynamic
2. Referenced Documents
elastic properties of a material can therefore be computed if the
2.1 ASTM Standards:
geometry, mass, and mechanical resonant frequencies of a
C 215 Test Method for Fundamental Transverse, Longitu-
suitable (rectangular or cylindrical geometry) test specimen of
dinal, and Torsional Resonant Frequencies of Concrete
that material can be measured. Dynamic Young’s modulus is
Specimens
determined using the resonant frequency in either the flexural
C 372 Test Method for Linear Thermal Expansion of Por-
orlongitudinalmodeofvibration.Thedynamicshearmodulus,
celain Enamel and Glaze Frits and Fired Ceramic Whitew-
or modulus of rigidity, is found using torsional resonant
are Products by the Dilatometer Method
vibrations. Dynamic Young’s modulus and dynamic shear
C 623 Test Method for Young’s Modulus, Shear Modulus,
modulus are used to compute Poisson’s ratio.
and Poisson’s Ratio for Glass and Glass-Ceramics by
1.2 Although not specifically described herein, this test
Resonance
method can also be performed at cryogenic and high tempera-
C 747 Test Method for Moduli of Elasticity and Fundamen-
tures with suitable equipment modifications and appropriate
tal Frequencies of Carbon and Graphite Materials by Sonic
modifications to the calculations to compensate for thermal
Resonance
expansion.
C 848 Test Method for Young’s Modulus, Shear Modulus,
1.3 There are material specific ASTM standards that cover
and Poisson’s Ratio For Ceramic Whitewares by Reso-
the determination of resonance frequencies and elastic proper-
nance
ties of specific materials by sonic resonance or by impulse
C 1161 Test Method for Flexural Strength of Advanced
excitation of vibration. Test Methods C 215, C 623, C 747,
Ceramics at Ambient Temperature
C 848, C 1198, and C 1259 may differ from this test method in
C 1198 Test Method for Dynamic Young’s Modulus, Shear
several areas (for example; sample size, dimensional toler-
Modulus, and Poisson’s Ratio for Advanced Ceramics by
ances, sample preparation). The testing of these materials shall
Sonic Resonance
be done in compliance with these material specific standards.
C 1259 Test Method for Dynamic Young’s Modulus, Shear
Where possible, the procedures, sample specifications and
Modulus, and Poisson’s Ratio for Advanced Ceramics by
calculations are consistent with these test methods.
Impulse Excitation of Vibration
1.4 The values stated in SI units are to be regarded as the
E6 Terminology Relating to Methods of Mechanical Test-
standard.
ing
This test method is under the jurisdiction of ASTM Committee E28 on
Mechanical Testing and is the direct responsibility of Subcommittee E28.04 on For referenced ASTM standards, visit the ASTM website, www.astm.org, or
Uniaxial Testing. contact ASTM Customer Service at service@astm.org. For Annual Book of ASTM
Current edition approved Sept. 1, 2006. Published September 2006. Originally Standards volume information, refer to the standard’s Document Summary page on
approved in 1997. Last previous edition approved in 2001 as E 1876 – 01. the ASTM website.
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959, United States.
E 1876 – 01 (2006)
E 177 Practice for Use of the Terms Precision and Bias in 3.2.5 in-plane flexure, n—for rectangular parallelepiped
ASTM Test Methods geometries, a flexure mode in which the direction of displace-
ment is in the major plane of the test specimen.
3. Terminology
3.2.6 isotropic, adj—the condition of a specimen such that
thevaluesoftheelasticpropertiesarethesameinalldirections
3.1 Definitions—The definitions of terms relating to me-
in the material. Materials are considered isotropic on a mac-
chanical testing appearing in Terminology E 6 should be
roscopic scale, if they are homogeneous and there is a random
considered as applying to the terms used in this test method.
distributionandorientationofphases,crystallites,components,
3.1.1 dynamic mechanical measurement, n—a technique in
pores, or microcracks.
which either the modulus or damping, or both, of a substance
under oscillatory applied force or displacement is measured as
3.2.7 longitudinal vibrations, n—the vibrations that occur
a function of temperature, frequency, or time, or combination when the oscillations in a slender rod or bar are parallel to the
thereof.
length of the rod or bar.
–2
3.1.2 elastic limit [FL ], n—the greatest stress that a
3.2.8 nodes, n—aslenderrodorbarinresonancecontaining
material is capable of sustaining without permanent strain
oneormorelocationshavingaconstantzerodisplacement.For
remaining upon complete release of the stress. E6
the fundamental flexural resonance of such a rod or bar, the
–2
3.1.3 elastic modulus [FL ], n—the ratio of stress to strain
nodes are located at 0.224 L from each end, where L is the
below the proportional limit. E6
length of the specimen.
3.1.4 Poisson’s ratio (µ) [nd], n—the absolute value of the
3.2.9 out-of-plane flexure, n—for rectangular parallelepiped
ratio of transverse strain to the corresponding axial strain
geometries, a flexure mode in which the direction of displace-
resulting from uniformly distributed axial stress below the
ment is perpendicular to the major plane of the test specimen.
proportional limit of the material.
3.2.10 resonant frequency, n—naturally occurring frequen-
3.1.4.1 Discussion—In isotropic materials, Young’s Modu-
cies of a body driven into flexural, torsional, or longitudinal
lus ( E), shear modulus (G), and Poisson’s ratio (µ) are related
vibration that are determined by the elastic modulus, mass, and
by the following equation:
dimensions of the body. The lowest resonant frequency in a
µ 5 ~E/2G!– 1 (1)
given vibrational mode is the fundamental resonant frequency
E6
of that mode.
–2
3.1.5 proportional limit [FL ], n—the greatest stress that a 3.2.11 slender rod or bar, n—in dynamic elastic property
material is capable of sustaining without deviation from testing, a specimen whose ratio of length to minimum cross-
proportionality of stress to strain (Hooke’s law). E6 sectional dimension is at least 5 and preferably in the range
–2
3.1.6 shear modulus (G) [FL ], n—the elastic modulus in from 20 to 25.
shear or torsion. Also called modulus of rigidity or torsional
3.2.12 torsional vibrations, n—the vibrations that occur
modulus. E6
when the oscillations in each cross-sectional plane of a slender
–2
3.1.7 Young’s modulus (E)[FL ], n—theelasticmodulusin
rod or bar are such that the plane twists around the length
tension or compression. E6
dimension axis.
3.2 Definitions of Terms Specific to This Standard:
3.2.1 antinodes, n—two or more locations that have local
4. Summary of Test Method
maximum displacements, called antinodes, in an unconstrained
4.1 This test method measures the fundamental resonant
slender rod or bar in resonance. For the fundamental flexure
frequency of test specimens of suitable geometry by exciting
resonance, the antinodes are located at the two ends and the
them mechanically by a singular elastic strike with an impulse
center of the specimen.
tool. A transducer (for example, contact accelerometer or
3.2.2 elastic, adj—the property of a material such that an
non-contacting microphone) senses the resulting mechanical
application of stress within the elastic limit of that material
vibrations of the specimen and transforms them into electric
making up the body being stressed will cause an instantaneous
signals. Specimen supports, impulse locations, and signal
and uniform deformation, which will be eliminated upon
pick-up points are selected to induce and measure specific
removal of the stress, with the body returning instantly to its
modesofthetransientvibrations.Thesignalsareanalyzed,and
original size and shape without energy loss. Most elastic
the fundamental resonant frequency is isolated and measured
materials conform to this definition well enough to make this
by the signal analyzer, which provides a numerical reading that
resonance test valid.
is (or is proportional to) either the frequency or the period of
3.2.3 flexural vibrations, n—the vibrations that occur when
the specimen vibration. The appropriate fundamental resonant
the oscillations in a slender rod or bar are in a plane normal to
frequencies, dimensions, and mass of the specimen are used to
the length dimension.
calculate dynamic Young’s modulus, dynamic shear modulus,
3.2.4 homogeneous, adj—the condition of a specimen such
and Poisson’s ratio.
that the composition and density are uniform, so that any
smaller specimen taken from the original is representative of
5. Significance and Use
thewhole.Practically,aslongasthegeometricaldimensionsof
thetestspecimenarelargewithrespecttothesizeofindividual 5.1 This test method may be used for material development,
grains, crystals, components, pores, or microcracks, the body characterization, design data generation, and quality control
can be considered homogeneous. purposes.
E 1876 – 01 (2006)
5.2 This test method is specifically appropriate for deter- 6.1.2 The procedure involves measuring transient elastic
miningthemodulusofmaterialsthatareelastic,homogeneous, vibrations. Materials with very high damping capacity may be
and isotropic (1). difficult to measure with this technique if the vibration damps
5.3 This test method addresses the room temperature deter- out before the frequency counter can measure the signal
mination of dynamic moduli of elasticity of slender bars (commonly within three to five cycles).
(rectangular cross section) and rods (cylindrical). Flat plates
6.1.3 If specific surface treatments (coatings, machining,
and disks may also be measured similarly, but the required
grinding, etching, and so forth) change the elastic properties of
equations for determining the moduli are not addressed herein.
the near-surface material, there will be accentuated effects on
5.4 This dynamic test method has several advantages and
the properties measured by this flexural method, as compared
differences from static loading techniques and from resonant
to static/bulk measurements by tensile or compression testing.
techniques requiring continuous excitation.
6.1.4 This test method is not satisfactory for specimens that
5.4.1 The test method is nondestructive in nature and can be
have major discontinuities, such as large cracks (internal or
used for specimens prepared for other tests. The specimens are
surface) or voids.
subjected to minute strains; hence, the moduli are measured at
6.2 This test method for determining moduli is limited to
or near the origin of the stress-strain curve, with the minimum
specimens with regular geometries (rectangular parallelepiped,
possibility of fracture.
cylinders, and disks) for which analytical equations are avail-
5.4.2 The impulse excitation test uses an impact tool and
able to relate geometry, mass, and modulus to the resonant
simple supports for the test specimen. There is no requirement
vibration frequencies. This test method is not appropriate for
for complex support systems that require elaborate setup or
determining the elastic properties of materials that cannot be
alignment.
fabricated into such geometries.
5.5 Thistechniquecanbeusedtomeasureresonantfrequen-
6.2.1 The analytical equations assume parallel and concen-
cies alone for the purposes of quality control and acceptance of
tric dimensions for the regular geometries of the specimen.
test specimens of both regular and complex shapes.Arange of
Deviations from the specified tolerances for the dimensions of
acceptable resonant frequencies is determined for a specimen
the specimens will change the resonant frequencies and intro-
with a particular geometry and mass. The technique is particu-
duce error into the calculations.
larly suitable for testing specimens with complex geometries
6.2.2 Edge treatments such as chamfers or radii are not
(otherthanparallelepipeds,cylinders/rods,ordisks)thatwould
considered in the analytical equations. Edge chamfers change
not be suitable for testing by other procedures. Any specimen
the resonant frequency of the test bars and introduce error into
with a frequency response falling outside the prescribed
the calculations of the dynamic modulus. It is recommended
frequency range is rejected. The actual modulus of each
that specimens for this test method not have chamfered or
specimen need not be determined as long as the limits of the
rounded edges.
selected frequency range are known to include the resonant
6.2.3 For specimens with as-fabricated and rough or uneven
frequency that the specimen must possess if its geometry and
surfaces, variations in dimension can have a significant effect
mass are within specified tolerances.
in the calculations. For example, in the calculation of dynamic
5.6 If a thermal treatment or an environmental exposure
modulus, the modulus value is inversely proportional to the
affects the elastic response of the test specimen, this test
cube of the thickness. Uniform specimen dimensions and
methodmaybesuitableforthedeterminationofspecificeffects
precise measurements are essential for accurate results.
of thermal history, environment exposure, and so forth. Speci-
6.3 This test method assumes that the specimen is vibrating
men descriptions should include any specific thermal treat-
freely, with no significant restraint or impediment. Specimen
ments or environmental exposures that the specimens have
supports should be designed and located properly in accor-
received.
dance with the instructions so the specimen can vibrate freely
in the desired mode. In using direct contact transducers, the
6. Interf
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