ASTM E1876-09
(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
This test method may be used for material development, characterization, design data generation, and quality control purposes.
This test method is specifically appropriate for determining the modulus of materials that are elastic, homogeneous, and isotropic (1).
This test method addresses the room temperature determination of dynamic moduli of elasticity of slender bars (rectangular cross section) and rods (cylindrical). Flat plates and disks may also be measured similarly, but the required equations for determining the moduli are not addressed herein.
This dynamic test method has several advantages and differences from static loading techniques and from resonant techniques requiring continuous excitation.
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.
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.
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 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 tol...
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 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 ...
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Designation: E1876 − 09
StandardTest 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 and health practices and determine the applica-
1.1 This test method covers determination of the dynamic
bility of regulatory limitations prior to use.
elastic properties of elastic materials at ambient temperatures.
Specimens of these materials possess specific mechanical
2. Referenced Documents
resonant frequencies that are determined by the elastic
2
2.1 ASTM Standards:
modulus, mass, and geometry of the test specimen. The
C215 Test Method for Fundamental Transverse,
dynamic elastic properties of a material can therefore be
Longitudinal, and Torsional Resonant Frequencies of
computed if the geometry, mass, and mechanical resonant
Concrete Specimens
frequencies of a suitable (rectangular or cylindrical geometry)
C372 Test Method for Linear Thermal Expansion of Porce-
test specimen of that material can be measured. Dynamic
lainEnamelandGlazeFritsandFiredCeramicWhiteware
Young’s modulus is determined using the resonant frequency
Products by the Dilatometer Method
in either the flexural or longitudinal mode of vibration. The
C623 Test Method for Young’s Modulus, Shear Modulus,
dynamic shear modulus, or modulus of rigidity, is found using
and Poisson’s Ratio for Glass and Glass-Ceramics by
torsional resonant vibrations. Dynamic Young’s modulus and
Resonance
dynamic shear modulus are used to compute Poisson’s ratio.
C747 Test Method for Moduli of Elasticity and Fundamental
1.2 Although not specifically described herein, this test
Frequencies of Carbon and Graphite Materials by Sonic
method can also be performed at cryogenic and high tempera-
Resonance
tures with suitable equipment modifications and appropriate
C848 Test Method for Young’s Modulus, Shear Modulus,
modifications to the calculations to compensate for thermal
and Poisson’s Ratio For Ceramic Whitewares by Reso-
expansion.
nance
1.3 There are material specific ASTM standards that cover
C1161 Test Method for Flexural Strength of Advanced
the determination of resonance frequencies and elastic proper- Ceramics at Ambient Temperature
ties of specific materials by sonic resonance or by impulse
C1198 Test Method for Dynamic Young’s Modulus, Shear
excitationofvibration.TestMethodsC215,C623,C747,C848, Modulus, and Poisson’s Ratio for Advanced Ceramics by
C1198, and C1259 may differ from this test method in several
Sonic Resonance
areas (for example; sample size, dimensional tolerances, C1259 Test Method for Dynamic Young’s Modulus, Shear
sample preparation). The testing of these materials shall be
Modulus, and Poisson’s Ratio for Advanced Ceramics by
done in compliance with these material specific standards. Impulse Excitation of Vibration
Where possible, the procedures, sample specifications and
E6 Terminology Relating to Methods of Mechanical Testing
calculations are consistent with these test methods. E177 Practice for Use of the Terms Precision and Bias in
ASTM 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
3. Terminology
standard.
3.1 Definitions:
1.5 This standard does not purport to address all of the
3.1.1 The definitions of terms relating to mechanical testing
safety concerns, if any, associated with its use. It is the
appearing in Terminology E6C1198 should be considered as
applying to the terms used in this test method.
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 April 1, 2009. Published April 2009. Originally contact ASTM Customer Service at service@astm.org. For Annual Book of ASTM
approved in 1997. Last previous edition approved in 2007 as E1876 – 07. DOI: Standards volume information, refer to the standard’s Document Summary page on
10.1520/E1876-09. the ASTM website.
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States
1
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E1876 − 09
3.1.2 dynamic mechanical measurement, n—a technique in 3.2.6 isotropic, adj—the condition of a specimen such that
which either the modulus or damping, or both, of a s
...
This document is not anASTM standard and is intended only to provide the user of anASTM 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:E1876–07 Designation: E 1876 – 09
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 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 (´) 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 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 specificASTM 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, C747, C848C 747,
C1198C 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.
1.4The values stated in SI units are to be regarded as the standard.
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 and health practices and determine the applicability of regulatory
limitations prior to use.
2. Referenced Documents
2
2.1 ASTM Standards:
C 215 Test Method for Fundamental Transverse, Longitudinal, and Torsional Resonant Frequencies of Concrete Specimens
C 372 Test Method for LinearThermal Expansion of Porcelain Enamel and Glaze Frits and Fired CeramicWhiteware Products
by the Dilatometer Method
C 623 Test Method for Young’s Modulus, Shear Modulus, and Poisson’s Ratio for Glass and Glass-Ceramics by Resonance
C 747 Test Method for Moduli of Elasticity and Fundamental Frequencies of Carbon and Graphite Materials by Sonic
Resonance
C 848 Test Method for Young’s Modulus, Shear Modulus, and Poisson’s Ratio For Ceramic Whitewares by Resonance
C 1161 Test Method for Flexural Strength of Advanced Ceramics at Ambient Temperature
C 1198 Test Method for Dynamic Young’s Modulus, Shear Modulus, and Poisson’s Ratio for Advanced Ceramics by Sonic
Resonance
C 1259 Test Method for Dynamic Young’s Modulus, Shear Modulus, and Poisson’s Ratio forAdvanced Ceramics by Impulse
Excitation of Vibration
E6 Terminology Relating to Methods of Mechanical Testing
E 177 Practice for Use of the Terms Precision and Bias in ASTM Test Methods
1
This test method is under the jurisdiction ofASTM Committee E28 on Mechanical Testing and is the direct responsibility of Subcommittee E28.04 on Uniaxial Testing.
Current edition approved JuneApril 1, 2007.2009. Published June 2007.April 2009. Originally approved in 1997. Last previous edition approved in 20062007 as
E1876–01(2006).E 1876 – 07.
2
For referencedASTM standards, visit theASTM website, www.astm.org, or contactASTM Customer Service at service@astm.org. For Annual Book of ASTM Standards
volume information, refer to the standard’s Document Summary page on the ASTM website.
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959, United States.
1
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