ASTM E1875-00

NOTICE: This standard has either been superseded and replaced by a new version or discontinued.
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Designation: E 1875 – 00 An American National Standard
Standard Test Method for
Dynamic Young’s Modulus, Shear Modulus, and Poisson’s
Ratio by Sonic Resonance
This standard is issued under the fixed designation E 1875; 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 mass are within specified tolerances.
1.5 There are material specific ASTM standards that cover
1.1 This test method covers the determination of the dy-
the determination of resonance frequencies and elastic proper-
namic elastic properties of elastic materials. Specimens of
ties of specific materials by sonic resonance or by impulse
these materials possess specific mechanical resonant frequen-
excitation of vibration. Test Methods C 215, C 623, C 747,
cies that are determined by the elastic modulus, mass, and
C 848, C 1198, and C 1259 may differ from this test method in
geometry of the test specimen. Therefore, the dynamic elastic
several areas (for example; sample size, dimensional toler-
properties of a material can be computed if the geometry, mass,
ances, sample preparation). The testing of these materials shall
and mechanical resonant frequencies of a suitable test speci-
be done in compliance with these material specific standards.
men of that material can be measured. Dynamic Young’s
Where possible, the procedures, sample specifications, and
modulus is determined using the resonant frequency in the
calculations are consistent with these test methods.
flexural mode of vibration. The dynamic shear modulus, or
1.6 The values stated in SI units are regarded as the
modulus of rigidity, is found using torsional resonant vibra-
standard.
tions. Dynamic Young’s modulus and dynamic shear modulus
1.7 This standard does not purport to address all of the
are used to compute Poisson’s ratio.
safety concerns, if any, associated with its use. It is the
1.2 This test method is specifically appropriate for materials
responsibility of the user of this standard to establish appro-
that are elastic, homogeneous, and isotropic (1). Materials of
priate safety and health practices and determine the applica-
a composite character (particulate, whisker, or fiber reinforced)
bility of regulatory limitations prior to use.
may be tested by this test method with the understanding that
the character (volume fraction, size, morphology, distribution,
2. Referenced Documents
orientation, elastic properties, and interfacial bonding) of the
2.1 ASTM Standards:
reinforcement in the test specimen will have a direct effect on
C 215 Test Method for Fundamental Transverse, Longitu-
the elastic properties. These reinforcement effects must be
dinal and Torsional Frequencies of Concrete Specimens
considered in interpreting the test results for composites. This
C 623 Test Method for Young’s Modulus, Shear Modulus,
test method is not satisfactory for specimens that have cracks
and Poisson’s Ratio for Glass and Glass-Ceramics by
or voids that are major discontinuities in the specimen. Neither
Resonance
is the test method satisfactory when these materials cannot be
C 747 Test Method for Moduli of Elasticity and Fundamen-
fabricated in a uniform rectangular or circular cross section.
tal Frequencies of Carbon and Graphite Materials by Sonic
1.3 A high-temperature furnace and cryogenic cabinet are
Resonance
described for measuring the dynamic elastic moduli as a
C 848 Test Method for Dynamic Young’s Modulus, Shear
function of temperature from –195 to 1200°C.
Modulus, and Poisson’s Ratio for Ceramic Whitewares by
1.4 Modification of this test method for use in quality
Resonance
control is possible. A range of acceptable resonant frequencies
C 1198 Test Method for Dynamic Young’s Cynamic Modu-
is determined for a specimen with a particular geometry and
lus, Shear Modulus and Poisson’s Ratio for Advanced
mass. Any specimen with a frequency response falling outside
Ceramics by Sonic Resonance
this frequency range is rejected. The actual modulus of each
C 1259 Test Method for Dynamic Young’s Modulus, Shear
specimen need not be determined as long as the limits of the
Modulus and Poisson’s Ratio for Advanced Ceramics by
selected frequency range are known to include the resonant
Impulse Excitation of Vibration
frequency that the specimen must possess if its geometry and
E 6 Terminology Relating to Methods of Mechanical Test-
ing
This test method is under the jurisdiction of ASTM Committee E28 on
Mechanical Testing and is the direct responsibility of Subcommittee E28.03 on
Elastic Properties.
Current edition approved Oct. 10, 2000. Published January 2001. Annual Book of ASTM Standards, Vol 15.02.
Originally published as E1875-97. Last previous edition E1875–97. Annual Book of ASTM Standards, Vol 15.01.
2 5
Annual Book of ASTM Standards, Vol 04.02. Annual Book of ASTM Standards, Vol 03.01.
Copyright © ASTM, 100 Barr Harbor Drive, West Conshohocken, PA 19428-2959, United States.
E 1875
E 177 Practice for Use of the Terms Precision and Bias in 3.2.5 isotropic, adj—the condition of a specimen such that
ASTM Test Methods the values of the elastic properties are the same in all directions
in the material. Materials are considered isotropic on a mac-
3. Terminology
roscopic scale, if they are homogeneous and there is a random
3.1 Definitions:
distribution and orientation of phases, crystallites, and compo-
3.1.1 dynamic mechanical measurement, n— a technique in
nents.
which either the modulus or damping, or both, of a substance
3.2.6 nodes, n—slender rod or bar in resonance contains one
under oscillatory applied force or displacement is measured as
or more locations having a constant zero displacement, called
a function of temperature, frequency, or time, or a combination
nodes. For the fundamental flexural resonance, the nodes are
thereof.
located at 0.224 L from each end, where L is the length of the
–2
3.1.2 elastic limit [FL ], n—the greatest stress that a
specimen.
material is capable of sustaining without permanent strain
3.2.7 resonance, n—slender rod or bar driven into one of the
remaining upon complete release of the stress. (E 6
modes of vibration described in 3.2.3 or 3.2.9 is said to be in
–2
3.1.3 elastic modulus [FL ], n—the ratio of stress to strain
resonance when the imposed frequency is such that the
below the proportional limit. (E 6)
resultant displacements for a given amount of driving force are
3.1.4 Poisson’s ratio (μ) [nd], n—the absolute value of the
at a maximum. The resonant frequencies are natural vibration
ratio of transverse strain to the corresponding axial strain
frequencies that are determined by the elastic modulus, mass,
resulting from uniformly distributed axial stress below the
and dimensions of the test specimen.
proportional limit of the material.
3.2.8 slender rod or bar, n—in dynamic elastic property
3.1.4.1 Discussion—In isotropic materials Young’s modu-
testing, a specimen whose ratio of length to minimum cross-
lus ( E), shear modulus (G), and Poisson’s ratio (μ) are related
sectional dimension is at least five and preferably in the range
by the following equation:
from 20 to 25.
3.2.9 torsional vibrations, n—when the oscillations in each
μ 5 ~E/2G! –1 (1)
cross-sectional plane of a slender rod or bar are such that the
(E 6)
plane twists around the length dimension axis, the vibrations
–2
3.1.5 proportional limit [FL ], n—the greatest stress that a
are said to be in the torsional mode.
material is capable of sustaining without deviation from
proportionality of stress to strain (Hooke’s law). (E 6)
4. Summary of Test Method
–2
3.1.6 shear modulus (G) [FL ], n—the elastic modulus in
4.1 This test method measures the resonant frequencies of
shear or torsion. Also called modulus of rigidity or torsional
test specimens of suitable geometry by exciting them at
modulus.
continuously variable frequencies. Mechanical excitation of
–2
3.1.7 Young’s modulus (E) [FL ], n—the elastic modulus in
the bars is provided through the use of a transducer that
tension or compression. (E 6)
transforms a cyclic electrical signal into a cyclic mechanical
3.2 Definitions of Terms Specific to This Standard:
force on the specimen. A second transducer senses the resulting
3.2.1 anti-nodes, n—an unconstrained slender rod or bar in
mechanical vibrations of the specimen and transforms them
resonance contains two or more locations that have local
into an electrical signal. The amplitude and frequency of the
maximum displacements, called anti-nodes. For the fundamen-
signal are measured by an oscilloscope or other means to detect
tal flexure resonance, the anti-nodes are located at the two ends
resonance. The resonant frequencies, dimensions, and mass of
and the center of the specimen.
the specimen are used to calculate dynamic Young’s modulus
3.2.2 elastic, adj—the property of a material such that an
and dynamic shear modulus.
application of stress within the elastic limit of that material
making up the body being stressed will cause an instantaneous
5. Significance and Use
and uniform deformation, that will be eliminated upon removal
5.1 This test method has advantages in certain respects over
of the stress, with the body returning instantly to its original
the use of static loading systems for measuring moduli.
size and shape without energy loss. Most elastic materials
5.1.1 This test method is nondestructive in nature. Only
conform to this definition well enough to make this resonance
minute stresses are applied to the specimen, thus minimizing
test valid.
the possibility of fracture.
3.2.3 flexural vibrations, n—when the oscillations in a
5.1.2 The period of time during which measurement stress
slender rod or bar are in a vertical plane normal to the length
is applied and removed is of the order of hundreds of
dimension, the vibrations are said to be in the flexural mode.
microseconds. With this test method it is feasible to perform
3.2.4 homogeneous, adj—the condition of a specimen such
measurements at high temperatures, where delayed elastic and
that the composition and density are uniform, such that any
creep effects would invalidate modulus measurements calcu-
smaller specimen taken from the original is representative of
lated from static loading.
the whole. Practically, as long as the geometrical dimensions of
5.2 This test method is suitable for detecting whether a
the test specimen are large with respect to the size of individual
material meets specifications, if cognizance is given to one
grains, crystals, or components, the body can be considered
important fact in materials are often sensitive to thermal
homogeneous.
history. Therefore, the thermal history of a test specimen must
be considered in comparing experimental values of moduli to
Annual Book of ASTM Standards, Vol 14.02. reference or standard values. Specimen descriptions should
E 1875
include any specific thermal treatments that the specimens have shall serve as a prescope amplifier.
received. 6.6 Cathode-Ray Oscilloscope, any model suitable for gen-
eral laboratory work.
6. Apparatus
6.7 Frequency Counter, preferably digital, shall be able to
6.1 The test apparatus is shown in Fig. 1. It consists of a
measure frequencies to within 61 Hz.
variable-frequency audio oscillator, used to generate a sinusoi-
6.8 Furnace—If data at an elevated temperature are desired,
dal voltage, and a power amplifier and suitable transducer to
a furnace shall be used that is capable of controlled heating and
convert the electrical signal to a mechanical driving vibration.
cooling. It shall have a specimen zone large enough for the
A frequency meter (preferably digital) monitors the audio
specimen to be uniform in temperature within 65°C along its
oscillator output to provide an accurate frequency determina-
length through the range of temperatures encountered in
tion. A suitable suspension-coupling system supports the test
testing. It is recommended that an independent thermocouple
specimen. Another transducer acts to detect mechanical vibra-
be placed in close proximity to (within 5 min), but not
tion in the specimen and to convert it into an electrical signal
touching, the center of the specimen to accurately measure
that is passed through an amplifier and displayed on an
temperature during heating and cooling.
indicating meter. The meter may be a voltmeter, microamme-
6.9 Cryogenic Chamber—For data at cryogenic tempera-
ter, or oscilloscope. An oscilloscope is recommended because
tures, any chamber shall suffice that shall be capable of
it enables the operator to positively identify resonances,
controlled heating/cooling, frost-free and uniform in tempera-
including higher order harmonics, by Lissajous figure analysis.
ture within 65°C over the length of the specimen at any
If a Lissajous figure is desired, the output of the oscillator is
selected temperature. A suitable cryogenic chamber is shown in
also coupled to the horizontal plates of the oscilloscope. If
Fig. 2 (2). It is recommended that an independent thermo-
temperature-dependent data are desired, a suitable furnace or
couple be placed in close proximity to (within 5 mm), but not
cryogenic chamber is used. Details of the equipment are as
touching, the center of the specimen to accurately measure
follows:
temperature during heating and cooling.
6.2 Audio Oscillator, having a continuously variable fre-
6.10 Specimen Suspension—Any method of specimen sus-
quency output from about 100 Hz to at least 30 kHz. Frequency
pension shall be used that is adequate for the temperatures
drift shall not exceed 1 Hz/min for any given setting.
encountered in testing and that allows the specimen to vibrate
6.3 Audio Amplifier, having a power output sufficient to
without significant restriction. Thread suspension is the system
ensure that the type of transducer used can excite any specimen
of choice for cryogenic and high-temperature testing. (See Fig.
the mass of which falls within a specified range.
1 and Fig. 3.) Common cotton thread, silica-glass fiber thread,
6.4 Transducers— Two are required; one used as a driver
oxidation-resistant nickel (or platinum) alloy wire, or platinum
may be a speaker of the tweeter type or a magnetic cutting head
wire may be used. If metal wire suspension is used in the
or other similar device depending on the type of coupling
furnace, coupling characteristics will be improved if, outside
chosen for use between the transducer and the specimen. The
the temperature zone, the wire is coupled to cotton thread, and
other transducer, used
...