ASTM E1876-21

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 (1).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 th...
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 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.  
1.4 The values stated in SI units are to be regarded as standard. No other units of measurement are included in this 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 st...

General Information

• Status: Historical
• Publication Date: 31-Oct-2021
• ICS: 81.060.20 - Ceramic products
• Technical Committee: E28 - Mechanical Testing
• Drafting Committee: E28.04 - Uniaxial Testing

Standards Content (Sample)

NOTICE: This standard has either been superseded and replaced by a new version or withdrawn.
Contact ASTM International (www.astm.org) for the latest information
Designation: E1876 − 21
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* responsibility of the user of this standard to establish appro-
priate safety, health, and environmental practices and deter-
1.1 This test method covers determination of the dynamic
mine the applicability of regulatory limitations prior to use.
elastic properties of elastic materials at ambient temperatures.
1.6 This international standard was developed in accor-
Specimens of these materials possess specific mechanical
dance with internationally recognized principles on standard-
resonant frequencies that are determined by the elastic
ization established in the Decision on Principles for the
modulus, mass, and geometry of the test specimen. The
Development of International Standards, Guides and Recom-
dynamic elastic properties of a material can therefore be
mendations issued by the World Trade Organization Technical
computed if the geometry, mass, and mechanical resonant
Barriers to Trade (TBT) Committee.
frequencies of a suitable (rectangular or cylindrical geometry)
test specimen of that material can be measured. Dynamic
2. Referenced Documents
Young’s modulus is determined using the resonant frequency
2
2.1 ASTM Standards:
in either the flexural or longitudinal mode of vibration. The
C215 Test Method for Fundamental Transverse,
dynamic shear modulus, or modulus of rigidity, is found using
Longitudinal, and Torsional Resonant Frequencies of
torsional resonant vibrations. Dynamic Young’s modulus and
Concrete Specimens
dynamic shear modulus are used to compute Poisson’s ratio.
C372 Test Method for Linear Thermal Expansion of Porce-
1.2 Although not specifically described herein, this test
lainEnamelandGlazeFritsandFiredCeramicWhiteware
method can also be performed at cryogenic and high tempera-
Products by Dilatometer Method
tures with suitable equipment modifications and appropriate
C623 Test Method for Young’s Modulus, Shear Modulus,
modifications to the calculations to compensate for thermal
and Poisson’s Ratio for Glass and Glass-Ceramics by
expansion.
Resonance
1.3 There are material specific ASTM standards that cover
C747 Test Method for Moduli of Elasticity and Fundamental
the determination of resonance frequencies and elastic proper- Frequencies of Carbon and Graphite Materials by Sonic
ties of specific materials by sonic resonance or by impulse
Resonance
excitationofvibration.TestMethodsC215,C623,C747,C848, C848 Test Method for Young’s Modulus, Shear Modulus,
C1198, and C1259 may differ from this test method in several
and Poisson’s Ratio For Ceramic Whitewares by Reso-
areas (for example; sample size, dimensional tolerances, nance
sample preparation). The testing of these materials shall be
C1161 Test Method for Flexural Strength of Advanced
done in compliance with these material specific standards. Ceramics at Ambient Temperature
Where possible, the procedures, sample specifications and
C1198 Test Method for Dynamic Young’s Modulus, Shear
calculations are consistent with these test methods. Modulus, and Poisson’s Ratio for Advanced Ceramics by
Sonic Resonance
1.4 The values stated in SI units are to be regarded as
C1259 Test Method for Dynamic Young’s Modulus, Shear
standard. No other units of measurement are included in this
Modulus, and Poisson’s Ratio for Advanced Ceramics by
standard.
Impulse Excitation of Vibration
1.5 This standard does not purport to address all of the
E6 Terminology Relating to Methods of Mechanical Testing
safety concerns, if any, associated with its use. It is the
E177 Practice for Use of the Terms Precision and Bias in
ASTM Test Methods
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
2
Uniaxial Testing. For referenced ASTM standards, visit the ASTM website, www.astm.org, or
Current edition approved Nov. 1, 2021. Published February 2022. Originally contact ASTM Customer Service at [e-mail]. For Annual Book of ASTM
approved in 1997. Last previous edition approved in 2015 as E1876 – 15. DOI: Standards volume information, refer to the standard’s Document Summary page on
10.1520/E1876-21. the ASTM website.
*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
1

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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 − 15 E1876 − 21
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 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 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.
1.4 The values stated in SI units are to be regarded as standard. No other units of measurement are included in this 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 safety, health, and healthenvironmental practices and determine the
applicability of regulatory limitations prior to use.
1.6 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.
2. Referenced Documents
2
2.1 ASTM Standards:
C215 Test Method for Fundamental Transverse, Longitudinal, and Torsional Resonant Frequencies of Concrete Specimens
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 Dec. 15, 2015Nov. 1, 2021. Published March 2016February 2022. Originally approved in 1997. Last previous edition approved in 20092015 as
E1876 – 09.E1876 – 15. DOI: 10.1520/E1876-15.10.1520/E1876-21.
2
For referenced ASTM standards, visit the ASTM website, www.astm.org, or contact ASTM Customer Service at [e-mail]. For Annual Book of ASTM Standards
volume information, refer to the standard’s Document Summary page on the ASTM website.
*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
1

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E1876 − 21
C372 Test Method for Linear Thermal Expansion of Porcelain Enamel and Glaze Frits and Fired Ceramic Whiteware Products
by Dilatometer Method
C623 Test Method for Young’s Modulus, Shear Modulus, and Poisson’s Ratio for Glass and Glass-Ceramics by Resonance
C747 Test Method for Moduli of Elasticity and Fundamental Frequencies of Carbon and Graphite Materials by Sonic Resonance
C848 Test Method for Young’s Modulus, Shear Modulus, and Poisson’s Ratio For Ceramic Whitewares by Resonance
C1161 Test Method for Flexural Strength of Advanced Ceramics at Ambi
...