ASTM E1875-20a
(Test Method)Standard Test Method for Dynamic Young's Modulus, Shear Modulus, and Poisson's Ratio by Sonic Resonance
Standard Test Method for Dynamic Young's Modulus, Shear Modulus, and Poisson's Ratio by Sonic Resonance
SIGNIFICANCE AND USE
5.1 This test method has advantages in certain respects over the use of static loading systems for measuring moduli.
5.1.1 This test method is nondestructive in nature. Only minute stresses are applied to the specimen, thus minimizing the possibility of fracture.
5.1.2 The period of time during which measurement stress is applied and removed is of the order of hundreds of microseconds. With this test method it is feasible to perform measurements at elevated temperatures, where delayed elastic and creep effects would invalidate modulus of elasticity measurements calculated from static loading.
5.2 This test method is suitable for detecting whether a material meets the specifications, if cognizance is given to one important fact in materials are often sensitive to thermal history. Therefore, the thermal history of a test specimen must be considered in comparing experimental values of moduli to reference or standard values. Specimen descriptions should include any specific thermal treatments that the specimens have received.
SCOPE
1.1 This test method covers the determination of the dynamic elastic properties of elastic materials. Specimens of these materials possess specific mechanical resonant frequencies that are determined by the modulus of elasticity, mass, and geometry of the test specimen. Therefore, the dynamic elastic properties of a material can be computed if the geometry, mass, and mechanical resonant frequencies of a suitable test specimen of that material can be measured. The dynamic Young's modulus is determined using the fundamental flexural resonant frequency. The dynamic shear modulus, or modulus of rigidity, is found using the fundamental torsional resonant frequency. Dynamic Young's modulus and dynamic shear modulus are used to compute Poisson's ratio.
1.2 This test method is specifically appropriate for materials that are elastic, homogeneous, and isotropic (1).2
1.3 Materials of a composite character (particulate, whisker, or fiber reinforced) may be tested by this test method with the understanding that the character (volume fraction, size, morphology, distribution, orientation, elastic properties, and interfacial bonding) of the reinforcement in the test specimen will have a direct effect on the elastic properties. These reinforcement effects shall be considered in interpreting the test results for composites.
1.4 This test method shall not be used for determination of Poisson’s ratio of anisotropic materials.
Note 1: For anisotropic materials, Poisson’s ratio can have different values in different directions. Due to the lack of symmetry in anisotropic materials, the elasticity tensor cannot be reduced to only two independent numbers, and the simplified relation between E, G, and µ is not valid.
1.5 This test method should not be used for specimens that have cracks or voids that are major discontinuities in the specimen.
1.6 The test method should not be used when materials cannot be fabricated in a uniform rectangular or circular cross section.
1.7 An elevated-temperature furnace and cryogenic chamber are described for measuring the dynamic elastic moduli as a function of temperature from –195 °C to 1200 °C.
1.8 This test method may be modified for use in quality control. A range of acceptable resonant frequencies is determined for a specimen with a particular geometry and mass. Any specimen with a frequency response falling outside this frequency range is rejected. The actual modulus of each specimen need not be determined as long as the limits of the selected frequency range are known to include the resonant frequency that the specimen must possess if its geometry and mass are within specified tolerances.
1.9 There are material-specific ASTM standards that cover the determination of resonant frequencies and elastic properties of specific materials by sonic resonance or by impulse excitation of vibration. Test Methods C215, C623, C74...
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This international standard was developed in accordance with internationally recognized principles on standardization established in the Decision on Principles for the
Development of International Standards, Guides and Recommendations issued by the World Trade Organization Technical Barriers to Trade (TBT) Committee.
Designation: E1875 − 20a
Standard Test Method for
Dynamic Young’s Modulus, Shear Modulus, and Poisson’s
1
Ratio by Sonic Resonance
This standard is issued under the fixed designation E1875; 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.
1. Scope* 1.6 The test method should not be used when materials
cannot be fabricated in a uniform rectangular or circular cross
1.1 This test method covers the determination of the dy-
section.
namic elastic properties of elastic materials. Specimens of
these materials possess specific mechanical resonant frequen-
1.7 An elevated-temperature furnace and cryogenic cham-
cies that are determined by the modulus of elasticity, mass, and
ber are described for measuring the dynamic elastic moduli as
geometry of the test specimen. Therefore, the dynamic elastic
a function of temperature from –195 °C to 1200 °C.
propertiesofamaterialcanbecomputedifthegeometry,mass,
1.8 This test method may be modified for use in quality
and mechanical resonant frequencies of a suitable test speci-
control. A range of acceptable resonant frequencies is deter-
men of that material can be measured. The dynamic Young’s
mined for a specimen with a particular geometry and mass.
modulus is determined using the fundamental flexural resonant
Any specimen with a frequency response falling outside this
frequency.The dynamic shear modulus, or modulus of rigidity,
frequency range is rejected. The actual modulus of each
is found using the fundamental torsional resonant frequency.
specimen need not be determined as long as the limits of the
Dynamic Young’s modulus and dynamic shear modulus are
selected frequency range are known to include the resonant
used to compute Poisson’s ratio.
frequency that the specimen must possess if its geometry and
1.2 This test method is specifically appropriate for materials
mass are within specified tolerances.
2
that are elastic, homogeneous, and isotropic (1).
1.9 There are material-specific ASTM standards that cover
1.3 Materials of a composite character (particulate, whisker,
thedeterminationofresonantfrequenciesandelasticproperties
or fiber reinforced) may be tested by this test method with the
of specific materials by sonic resonance or by impulse excita-
understanding that the character (volume fraction, size,
tion of vibration. Test Methods C215, C623, C747, C848,
morphology, distribution, orientation, elastic properties, and
C1198, C1259, and C1548 differ from this test method in
interfacial bonding) of the reinforcement in the test specimen
several areas (for example; specimen size, dimensional
will have a direct effect on the elastic properties. These
tolerances, specimen preparation). The testing of these mate-
reinforcementeffectsshallbeconsideredininterpretingthetest
rials shall be done in compliance with these material specific
results for composites.
standards. Where possible, the procedures, specimen
1.4 This test method shall not be used for determination of
specifications, and calculations are consistent with these test
Poisson’s ratio of anisotropic materials. methods.
NOTE 1—For anisotropic materials, Poisson’s ratio can have different
1.10 A separate standard, Test Method E1876, governs
values in different directions. Due to the lack of symmetry in anisotropic
determination of dynamic elastic moduli by impulse excitation
materials, the elasticity tensor cannot be reduced to only two independent
instead of sonic resonance.
numbers, and the simplified relation between E, G, and µ is not valid.
1.11 The values stated in SI units are to be regarded as
1.5 This test method should not be used for specimens that
standard. No other units of measurement are included in this
have cracks or voids that are major discontinuities in the
standard.
specimen.
1.12 This standard does not purport to address all of the
safety concerns, if any, associated with its use. It is the
1
This test method is under the jurisdiction of ASTM Committee E28 on
responsibility of the user of this standard to establish appro-
Mechanical Testing and is the direct responsibility of Subcommittee E28.04 on
priate safety, health, and environmental practices and deter-
Uniaxial Testing.
Current edition approved Dec. 1, 2020. Published March 2021. Originally mine the applicability of regulatory limitations prior to use.
approved in 1997. Last previous edition approved in 2020 as E1875-20. DOI:
1.13 This international standard was developed in accor-
1
...
This document is not an ASTM standard and is intended only to provide the user of an ASTM standard an indication of what changes have been made to the previous version. Because
it may not be technically possible to adequately depict all changes accurately, ASTM recommends that users consult prior editions as appropriate. In all cases only the current version
of the standard as published by ASTM is to be considered the official document.
Designation: E1875 − 20 E1875 − 20a
Standard Test Method for
Dynamic Young’s Modulus, Shear Modulus, and Poisson’s
1
Ratio by Sonic Resonance
This standard is issued under the fixed designation E1875; 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.
1. Scope*
1.1 This test method covers the determination of the dynamic elastic properties of elastic materials. Specimens of these materials
possess specific mechanical resonant frequencies that are determined by the modulus of elasticity, mass, and geometry of the test
specimen. Therefore, the dynamic elastic properties of a material can be computed if the geometry, mass, and mechanical resonant
frequencies of a suitable test specimen of that material can be measured. Dynamic The dynamic Young’s modulus is determined
using the resonant frequency in the flexural mode of vibration. fundamental flexural resonant frequency. The dynamic shear
modulus, or modulus of rigidity, is found using the fundamental torsional resonant vibrations.frequency. Dynamic Young’s
modulus and dynamic shear modulus are used to compute Poisson’s ratio.
2
1.2 This test method is specifically appropriate for materials that are elastic, homogeneous, and isotropic (1).
1.3 This test method is specifically appropriate for materials that are elastic, homogeneous, and isotropic (1).Materials of a
composite character (particulate, whisker, or fiber reinforced) may be tested by this test method with the understanding that the
character (volume fraction, size, morphology, distribution, orientation, elastic properties, and interfacial bonding) of the
reinforcement in the test specimen will have a direct effect on the elastic properties. These reinforcement effects mustshall be
considered in interpreting the test results for composites. This test method is not satisfactory for specimens that have cracks or
voids that are major discontinuities in the specimen. Neither is the test method satisfactory when these materials cannot be
fabricated in a uniform rectangular or circular cross section.
1.4 This test method shall not be used for determination of Poisson’s ratio of anisotropic materials.
NOTE 1—For anisotropic materials, Poisson’s ratio can have different values in different directions. Due to the lack of symmetry in anisotropic materials,
the elasticity tensor cannot be reduced to only two independent numbers, and the simplified relation between E,G, and μ is not valid.
1.5 This test method should not be used for specimens that have cracks or voids that are major discontinuities in the specimen.
1.6 The test method should not be used when materials cannot be fabricated in a uniform rectangular or circular cross section.
1.7 A high-temperatureAn elevated-temperature furnace and cryogenic cabinetchamber are described for measuring the dynamic
elastic moduli as a function of temperature from –195–195 °C to 1200 °C.
1
This test method is under the jurisdiction of ASTM Committee E28 on Mechanical Testing and is the direct responsibility of Subcommittee E28.04 on Uniaxial Testing.
Current edition approved April 15, 2020Dec. 1, 2020. Published May 2020March 2021. Originally approved in 1997. Last previous edition approved in 20132020 as
E1875-13.-20. DOI: 10.1520/E1875-20.10.1520/E1875-20A.
2
The boldface numbers in parentheses refer to a list of references at the end of this standard.
*A Summary of Changes section appears at the end of this standard
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States
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E1875 − 20a
1.8 Modification of this This test method may be modified for use in quality control is possible. control. A range of acceptable
resonant frequencies is determined for a specimen with a particular geometry and mass. Any specimen with a frequency response
falling outside this frequency range is rejected. The actual modulus of each specimen need not be determined as long as the limits
of the selected frequency range are known to include the resonant frequency that the specimen must possess if its geometry and
mass are within specified tolerances.
1.9 There are material-specific ASTM standards that cover the determination of resonanceresonant frequencies and elastic
properties of specific materials by son
...
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