ASTM E1876-99
(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.
1.5 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 – 99 An American National Standard
AMERICAN SOCIETY FOR TESTING AND MATERIALS
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Reprinted from the Annual Book of ASTM Standards. Copyright ASTM
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 2. Referenced Documents
1.1 This test method covers determination of the dynamic 2.1 ASTM Standards:
elastic properties of elastic materials at ambient temperatures. C 215 Test Method for Fundamental Transverse, Longitu-
Specimens of these materials possess specific mechanical dinal, and Torsional Frequencies of Concrete Specimens
resonant frequencies that are determined by the elastic modu- C 372 Test Method for Linear Thermal Expansion of Por-
lus, mass, and geometry of the test specimen. The dynamic celain Enamel and Glaze Frits and Fried Ceramic Whitew-
elastic properties of a material can therefore be computed if the are Products by the Dilatometer Method
geometry, mass, and mechanical resonant frequencies of a C 623 Test Method for Young’s Modulus, Shear Modulus,
suitable (rectangular or cylindrical geometry) test specimen of and Poisson’s Ratio for Glass and Glass-Ceramics by
that material can be measured. Dynamic Young’s modulus is Resonance
determined using the resonant frequency in either the flexural C 747 Test Method for Moduli of Elasticity and Fundamen-
or longitudinal mode of vibration. The dynamic shear modulus, tal Frequencies of Carbon and Graphite Materials by Sonic
or modulus of rigidity, is found using torsional resonant Resonance
vibrations. Dynamic Young’s modulus and dynamic shear C 848 Test Method for Young’s Modulus, Shear Modulus,
modulus are used to compute Poisson’s ratio. and Poisson’s Ratio for Ceramic Whitewares by Reso-
1.2 Although not specifically described herein, this test nance
method can also be performed at cryogenic and high tempera- C 1161 Test Method for Flexural Strength of Advanced
tures with suitable equipment modifications and appropriate Ceramics at Ambient Temperature
modifications to the calculations to compensate for thermal C 1198 Test Method for Dynamic Young’s Modulus, Shear
expansion. Modulus, and Poisson’s Ratio for Advanced Ceramics by
1.3 There are material specific ASTM standards that cover Sonic Resonance
the determination of resonance frequencies and elastic proper- C 1259 Test Method for Young’s Modulus, Shear Modulus
ties of specific materials by sonic resonance or by impulse and Poisson’s Ratio for Advanced Ceramics by Impulse
excitation of vibration. Test Methods C 215, C 623, C 747, Excitation of Vibration
C 848, C 1198, and C 1259 may differ from this test method in E 6 Terminology Relating to Methods of Mechanical Test-
several areas (for example; sample size, dimensional toler- ing
ances, sample preparation). The testing of these materials shall E 177 Practice for Use of the Terms Precision and Bias in
be done in compliance with these material specific standards. ASTM Test Methods
Where possible, the procedures, sample specifications and
3. Terminology
calculations are consistent with these test methods.
3.1 Definitions—The definitions of terms relating to me-
1.4 The values stated in SI units are to be regarded as the
standard. chanical testing appearing in Terminology E 6 should be
considered as applying to the terms used in this test method.
1.5 This standard does not purport to address all of the
safety concerns, if any, associated with its use. It is the 3.1.1 dynamic mechanical measurement, n—a technique in
which either the modulus or damping, or both, of a substance
responsibility of the user of this standard to establish appro-
priate safety and health practices and determine the applica- under oscillatory applied force or displacement is measured as
a function of temperature, frequency, or time, or combination
bility of regulatory limitations prior to use.
thereof.
1 2
This test method is under the jurisdiction of ASTM Committee E-28 on Annual Book of ASTM Standards, Vol 04.02.
Mechanical Testing and is the direct responsibility of Subcommittee E28.03 on Annual Book of ASTM Standards, Vol 15.02.
Elastic Properties. Annual Book of ASTM Standards, Vol 15.01.
Current edition approved April 10, 1999. Published July 1999. Last previous Annual Book of ASTM Standards, Vol 03.01.
edition E 1876-97. Annual Book of ASTM Standards, Vol 14.02.
E 1876
–2
3.1.2 elastic limit [FL ], n—the greatest stress that a nodes are located at 0.224 L from each end, where L is the
material is capable of sustaining without permanent strain length of the specimen.
remaining upon complete release of the stress. E6 3.2.8 out-of-plane flexure, n—for rectangular parallelepiped
–2
3.1.3 elastic modulus [FL ], n—the ratio of stress to strain geometries, a flexure mode in which the direction of displace-
ment is perpendicular to the major plane of the test specimen.
below the proportional limit. E6
3.1.4 Poisson’s ratio (μ) [nd], n—the absolute value of the 3.2.9 resonant frequency, n—naturally occurring frequen-
cies of a body driven into flexural, torsional, or longitudinal
ratio of transverse strain to the corresponding axial strain
resulting from uniformly distributed axial stress below the vibration that are determined by the elastic modulus, mass, and
dimensions of the body. The lowest resonant frequency in a
proportional limit of the material.
3.1.4.1 Discussion—In isotropic materials, Young’s Modu- given vibrational mode is the fundamental resonant frequency
of that mode.
lus ( E), shear modulus (G), and Poisson’s ratio (μ) are related
by the following equation: 3.2.10 slender rod or bar, n—in dynamic elastic property
testing, a specimen whose ratio of length to minimum cross-
μ 5 ~E/2G! – 1 (1)
sectional dimension is at least 5 and preferably in the range
E6
from 20 to 25.
–2
3.1.5 proportional limit [FL ], n—the greatest stress that a
3.2.11 torsional vibrations, n—the vibrations that occur
material is capable of sustaining without deviation from
when the oscillations in each cross-sectional plane of a slender
proportionality of stress to strain (Hooke’s law). E6
rod or bar are such that the plane twists around the length
–2
3.1.6 shear modulus (G) [FL ], n—the elastic modulus in
dimension axis.
shear or torsion. Also called modulus of rigidity or torsional
3.2.12 longitudinal vibrations, n—the vibrations that occur
modulus. E6
when the oscillations in a slender rod or bar are parallel to the
–2
3.1.7 Young’s modulus (E) [FL ], n—the elastic modulus in
length of the rod or bar.
tension or compression. E6
4. Summary of Test Method
3.2 Definitions of Terms Specific to This Standard:
3.2.1 antinodes, n—two or more locations that have local
4.1 This test method measures the fundamental resonant
maximum displacements, called antinodes, in an unconstrained
frequency of test specimens of suitable geometry by exciting
slender rod or bar in resonance. For the fundamental flexure
them mechanically by a singular elastic strike with an impulse
resonance, the antinodes are located at the two ends and the
tool. A transducer (for example, contact accelerometer or
center of the specimen.
non-contacting microphone) senses the resulting mechanical
3.2.2 elastic, adj—the property of a material such that an
vibrations of the specimen and transforms them into electric
application of stress within the elastic limit of that material
signals. Specimen supports, impulse locations, and signal
making up the body being stressed will cause an instantaneous
pick-up points are selected to induce and measure specific
and uniform deformation, which will be eliminated upon
modes of the transient vibrations. The signals are analyzed, and
removal of the stress, with the body returning instantly to its
the fundamental resonant frequency is isolated and measured
original size and shape without energy loss. Most elastic
by the signal analyzer, which provides a numerical reading that
materials conform to this definition well enough to make this
is (or is proportional to) either the frequency or the period of
resonance test valid.
the specimen vibration. The appropriate fundamental resonant
3.2.3 flexural vibrations, n—the vibrations that occur when
frequencies, dimensions, and mass of the specimen are used to
the oscillations in a slender rod or bar are in a plane normal to
calculate dynamic Young’s modulus, dynamic shear modulus,
the length dimension.
and Poisson’s ratio.
3.2.4 homogeneous, adj—the condition of a specimen such
5. Significance and Use
that the composition and density are uniform, so that any
5.1 This test method may be used for material development,
smaller specimen taken from the original is representative of
characterization, design data generation, and quality control
the whole. Practically, as long as the geometrical dimensions of
purposes.
the test specimen are large with respect to the size of individual
5.2 This test method is specifically appropriate for deter-
grains, crystals, components, pores, or microcracks, the body
mining the modulus of materials that are elastic, homogeneous,
can be considered homogeneous.
and isotropic (1).
3.2.5 in-plane flexure, n—for rectangular parallelepiped
5.3 This test method addresses the room temperature deter-
geometries, a flexure mode in which the direction of displace-
mination of dynamic moduli of elasticity of slender bars
ment is in the major plane of the test specimen.
(rectangular cross section) and rods (cylindrical). Flat plates
3.2.6 isotropic, adj—the condition of a specimen such that
and disks may also be measured similarly, but the required
the values of the elastic properties are the same in all directions
equations for determining the moduli are not addressed herein.
in the material. Materials are considered isotropic on a mac-
5.4 This dynamic test method has several advantages and
roscopic scale, if they are homogeneous and there is a random
differences from static loading techniques and from resonant
distribution and orientation of phases, crystallites, components,
techniques requiring continuous excitation.
pores, or microcracks.
3.2.7 nodes, n—a slender rod or bar in resonance containing
one or more locations having a constant zero displacement. For
The boldface numbers in parentheses refer to the list of references at the end of
the fundamental flexural resonance of such a rod or bar, the this standard.
E 1876
5.4.1 The test method is nondestructive in nature and can be cylinders, and disks) for which analytical equations are avail-
used for specimens prepared for other tests. The specimens are
able to relate geometry, mass, and modulus to the resonant
subjected to minute strains; hence, the moduli are measured at
vibration frequencies. This test method is not appropriate for
or near the origin of the stress-strain curve, with the minimum
determining the elastic properties of materials that cannot be
possibility of fracture.
fabricated into such geometries.
5.4.2 The impulse excitation test uses an impact tool and
6.2.1 The analytical equations assume parallel and concen-
simple supports for the test specimen. There is no requirement
tric dimensions for the regular geometries of the specimen.
for complex support systems that require elaborate setup or
Deviations from the specified tolerances for the dimensions of
alignment.
the specimens will change the resonant frequencies and intro-
5.5 This technique can be used to measure resonant frequen-
duce error into the calculations.
cies alone for the purposes of quality control and acceptance of
6.2.2 Edge treatments such as chamfers or radii are not
test specimens of both regular and complex shapes. A range of
considered in the analytical equations. Edge chamfers change
acceptable resonant frequencies is determined for a specimen
the resonant frequency of the test bars and introduce error into
with a particular geometry and mass. The technique is particu-
larly suitable for testing specimens with complex geometries the calculations of the dynamic modulus. It is recommended
(other than parallelepipeds, cylinders/rods, or disks) that would that specimens for this test method not have chamfered or
not be suitable for testing by other procedures. Any specimen
rounded edges.
with a frequency response falling outside the prescribed
6.2.3 For specimens with as-fabricated and rough or uneven
frequency range is rejected. The actual modulus of each
surfaces, variations in dimension can have a significant effect
specimen need not be determined as long as the limits of the
in the calculations. For example, in the calculation of dynamic
selected frequency range are known to include the resonant
modulus, the modulus value is inversely proportional to the
frequency that the specimen must possess if its geometry and
cube of the thickness. Uniform specimen dimensions and
mass are within specified tolerances.
precise measurements are essential for accurate results.
5.6 If a thermal treatment or an environmental exposure
6.3 This test method assumes that the specimen is vibrating
affects the elastic response of the test specimen, this test
freely, with no significant restraint or impediment. Specimen
method may be suitable for the determination of specific effects
supports should be designed and located properly in accor-
of thermal history, environment exposure, and so forth. Speci-
dance with the instructions so the specimen can vibrate freely
men descriptions should include any specific thermal treat-
in the desired mode. In using direct contact transducers, the
ments or environmental exposures that the specimens have
transducer should be positioned away from antinodes and with
received.
minimal force to avoid interference with free vibration.
6. Interferences
6.4 Proper location to the impulse point and transducer is
6.1 The relationships between resonant frequency and dy-
important in introducing and measuring the desired vibration
namic modulus presented herein are specifically applicable to
mode. The locations of the impulse point and transducer should
homogeneous, elastic, isotropic materials.
not be changed in multiple readings; changes in positio
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