ASTM E1876-22
(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
SIGNIFICANCE AND USE
5.1 This test method may be used for material development, characterization, design data generation, and quality control purposes.
5.2 This test method is specifically appropriate for determining the dynamic elastic modulus of materials that are elastic, homogeneous, and isotropic (3).
5.3 This test method addresses the room temperature determination of dynamic elastic moduli of elasticity of slender bars (rectangular cross section) rods (cylindrical), and flat disks. Flat plates may also be measured similarly, but the required equations for determining the moduli are not presented.
5.4 This dynamic test method has several advantages and differences from static loading techniques and from resonant techniques requiring continuous excitation.
5.4.1 The test method is nondestructive in nature and can be used for specimens prepared for other tests. The specimens are subjected to minute strains; hence, the moduli are measured at or near the origin of the stress-strain curve, with the minimum possibility of fracture.
5.4.2 The impulse excitation test uses an impact tool and simple supports for the test specimen. There is no requirement for complex support systems that require elaborate setup or alignment.
5.5 This technique can be used to measure resonant frequencies alone for the purposes of quality control and acceptance of test specimens of both regular and complex shapes. A range of acceptable resonant frequencies is determined for a specimen with a particular geometry and mass. The technique is particularly suitable for testing specimens with complex geometries (other than parallelepipeds, cylinders/rods, or disks) that would not be suitable for testing by other procedures. Any specimen with a frequency response falling outside the prescribed frequency range is rejected. The actual dynamic elastic 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...
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 Calculations are valid for materials that are elastic, homogeneous, and isotropic. Anisotropy can add additional calculation errors. See Appendix X1 for details.
1.3 The use of mixed numerical-experimental techniques (MNET) is outside the scope of this standard.
1.4 This test method may be used for determining dynamic Young’s modulus for materials of a composite character (particulate, whisker or fiber reinforced) or other anisotropic materials only after the effect of the reinforcement in the test specimen has been considered. Examples of the characteristics of the reinforcement that can affect the measured dynamic Young’s modulus are volume fraction, size, morphology, distribution, orientation, elastic properties, and interfacial bonding.
1.4.1 The effect of the character of the reinforcement shall be considered in interpreting the test results for these types of materials.
Note 1: The properties of the reinforcement will directly affect measured elastic properties. Data shown in (1)2 indicates the possibility of underestimating the dynamic Young’s modulus by as much as 20 % due to anisotropy...
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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: E1876 − 22
Standard Test Method for
Dynamic Young’s Modulus, Shear Modulus, and Poisson’s
1
Ratio by Impulse Excitation of Vibration
This standard is issued under the fixed designation E1876; 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.
2
measured elastic properties. Data shown in (1) indicates the possibility of
1. Scope*
underestimating the dynamicYoung’s modulus by as much as 20 % due to
1.1 This test method covers determination of the dynamic
anisotropy
elastic properties of elastic materials at ambient temperatures.
1.5 This test method should not be used for establishing
Specimens of these materials possess specific mechanical
accurate dynamic Young’s modulus, dynamic shear modulus,
resonant frequencies that are determined by the elastic
or Poisson’s ratio for specimens that have cracks, voids, or
modulus, mass, and geometry of the test specimen. The
other major structural discontinuities.
dynamic elastic properties of a material can therefore be
1.6 This test method may be used for determining whether
computed if the geometry, mass, and mechanical resonant
structural discontinuities exist in a specimen by comparing
frequencies of a suitable (rectangular or cylindrical geometry)
results with a specimen that is defect free.
test specimen of that material can be measured. Dynamic
Young’s modulus is determined using the resonant frequency
1.7 This test method shall not be used for establishing
in either the flexural or longitudinal mode of vibration. The
accuratedynamicYoung’smodulus,dynamicshearmodulusor
dynamic shear modulus, or modulus of rigidity, is found using
Poisson’s ratio for materials that cannot be fabricated in
torsional resonant vibrations. Dynamic Young’s modulus and
uniform rectangular or cylindrical cross section.
dynamic shear modulus are used to compute Poisson’s ratio.
1.8 The values stated in SI units are to be regarded as
1.2 Calculations are valid for materials that are elastic,
standard. No other units of measurement are included in this
homogeneous, and isotropic. Anisotropy can add additional
standard.
calculation errors. See Appendix X1 for details.
1.9 This standard does not purport to address all of the
1.3 The use of mixed numerical-experimental techniques
safety concerns, if any, associated with its use. It is the
(MNET) is outside the scope of this standard.
responsibility of the user of this standard to establish appro-
priate safety, health, and environmental practices and deter-
1.4 This test method may be used for determining dynamic
mine the applicability of regulatory limitations prior to use.
Young’s modulus for materials of a composite character
1.10 This international standard was developed in accor-
(particulate, whisker or fiber reinforced) or other anisotropic
dance with internationally recognized principles on standard-
materials only after the effect of the reinforcement in the test
ization established in the Decision on Principles for the
specimen has been considered. Examples of the characteristics
Development of International Standards, Guides and Recom-
of the reinforcement that can affect the measured dynamic
mendations issued by the World Trade Organization Technical
Young’s modulus are volume fraction, size, morphology,
Barriers to Trade (TBT) Committee.
distribution, orientation, elastic properties, and interfacial
bonding.
2. Referenced Documents
1.4.1 The effect of the character of the reinforcement shall
3
2.1 ASTM Standards:
be considered in interpreting the test results for these types of
C372 Test Method for Linear Thermal Expansion of Porce-
materials.
NOTE 1—The properties of the reinforcement will directly affect lainEnamelandGlazeFritsandFiredCeramicWhiteware
Products by Dilatometer Method
C1161 Test Method for Flexural Strength of Advanced
1 2
This test method is under the jurisdiction of ASTM Committee E28 on The boldface numbers in parentheses refer to a list of references at the end of
Mechanical Testing and is the direct responsibility of Subcommittee E28.04 on this standard.
3
Uniaxial Testing. For referenced ASTM standards, visit the ASTM website, www.astm.org, or
Current edition approved April 1, 2022. Published July 2022. Originally contact ASTM Customer Service at service@astm.org. For Annual Book of ASTM
approved in 1997. Last previous edition approved in 2021 as E1876 – 21. DOI: Standards volume information, refer to the standard’s Document Summary page
...
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: E1876 − 21 E1876 − 22
Standard Test Method for
Dynamic Young’s Modulus, Shear Modulus, and Poisson’s
1
Ratio by Impulse Excitation of Vibration
This standard is issued under the fixed designation E1876; 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 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 Calculations are valid for materials that are elastic, homogeneous, and isotropic. Anisotropy can add additional calculation
errors. See Appendix X1 for details.
1.3 The use of mixed numerical-experimental techniques (MNET) is outside the scope of this standard.
1.4 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. This test
method may be used for determining dynamic Young’s modulus for materials of a composite character (particulate, whisker or fiber
reinforced) or other anisotropic materials only after the effect of the reinforcement in the test specimen has been considered.
Examples of the characteristics of the reinforcement that can affect the measured dynamic Young’s modulus are volume fraction,
size, morphology, distribution, orientation, elastic properties, and interfacial bonding.
1.4.1 The effect of the character of the reinforcement shall be considered in interpreting the test results for these types of materials.
2
NOTE 1—The properties of the reinforcement will directly affect measured elastic properties. Data shown in (1) indicates the possibility of
underestimating the dynamic Young’s modulus by as much as 20 % due to anisotropy
1.5 This test method should not be used for establishing accurate dynamic Young’s modulus, dynamic shear modulus, or Poisson’s
ratio for specimens that have cracks, voids, or other major structural discontinuities.
1.6 This test method may be used for determining whether structural discontinuities exist in a specimen by comparing results with
a specimen that is defect free.
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 Nov. 1, 2021April 1, 2022. Published February 2022July 2022. Originally approved in 1997. Last previous edition approved in 20152021 as
E1876 – 15.E1876 – 21. DOI: 10.1520/E1876-21.10.1520/E1876-22.
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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E1876 − 22
1.7 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 This C215, C623, C747, C848, C1198,
and C1259 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.test method shall not be used for
establishing accurate dynamic Young’s modulus, dynamic shear modulus or Poisson’s ratio for materials that canno
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